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Solution Manual for Fundamentals of Corporate Finance, 5th Edition Robert Parrino, Kidwell Bates

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Fundamentals of Corporate Finance, 5th edition

Solutions Manual

Chapter 21

International Financial Management Before You Go On Questions and Answers Section 21.1 1.

What is globalization? Globalization refers to the removal of barriers to free trade and the closer integration of national economies. Consumers in many countries buy goods that are purchased from a number of countries, other than just their own. The production of goods and services has also become highly globalized. Like product markets, the financial system has also become highly integrated.

What are multinational corporations? Multinational corporations are business firms that have their operations in at least one other country than their home country where they are headquartered. These firms are headquartered all over the world and are owned by a mixture of domestic and foreign stockholders.

Explain the difference between American and European business executives’ views on wealth maximization. American business executives embrace shareholder wealth maximization as their number one goal, whereas in most parts of Europe, the main goal of business executives is to maximize corporate wealth. This means that shareholders are treated on par with other stakeholders, such as management, employees, creditors, or the government.

Section 21.2 1.

What is foreign exchange rate risk?

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Foreign exchange risk is the risk of a change in investment’s value due to changes in currency exchange rates. This risk usually affects firms that import/export goods as well as investors that make international investments.

How is the equilibrium exchange rate determined? The equilibrium exchange rate is the point of intersection between the currencies’ supply and demand curves. It is the point at which the quantity of the currency demanded equals the quantity of currency supplied.

What does it mean to hedge a financial transaction? To hedge a financial transaction with foreign exchange means to reduce the potential gains or losses caused by fluctuations in the price of foreign exchange. Many instruments can be used to hedge this risk, such as foreign currency options.

Section 21.3 1.

What difficulties do firms face in estimating cash flows from an overseas project? Estimating cash flows from an overseas project is difficult because of the various ways a firm is likely to get cash flows from a subsidiary – dividends, royalty or license payments, debt repayment, management, or consulting fees. It is also difficult to precisely time the cash flows or estimate the magnitude because of restrictions and controls a country is likely to put on the transfer of funds from the overseas project back to the home country.

Why is the repatriation of cash flows from an overseas project considered critical to the project’s value? From a parent firm’s point of view, the cash flows expected from the subsidiary are the basis for undertaking a project or rejecting it. Any delays in receiving the cash flows will affect the NPV of the project. Parent companies often rely on the cash flows from foreign operations to be repatriated and to fund projects in other countries.

When do companies have to consider country or political risk?

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Any company doing business in a foreign country has to consider political or country risks. Especially if the target country has a relatively unstable political environment, financial managers must incorporate the potential risk into the cost of the project.

Section 21.4 1.

Which currency is the preferred currency of exchange in global financial markets? Why? The U.S. dollar is the preferred currency of exchange on the global financial markets, as it is perceived to be the most stable currency. This is mainly due to the size and strength of the U.S. economy, the long history of political stability, and the strength of military forces.

What is the difference between foreign bonds and Eurobonds? Both foreign bonds and Eurobonds are types of international bonds. However, foreign bonds are long-term debt instruments sold by a foreign firm to investors in another country, and they are denominated in that country’s currency. On the other hand, Eurobonds are longterm debt instruments sold by a firm in one country but are denominated in the currency of another country.

Section 21.5 1.

Why is credit risk higher in international markets? In international markets, the credit risk of borrowers is higher, as it is more difficult to obtain credit information abroad. It is mainly the issue of familiarity with foreign economic conditions and business practices. Thus, the cost of gathering all this necessary information is higher, which is then being passed onto the customer in terms of higher premium.

List the inputs that are used in calculating a Eurocredit price. The loan pricing for Eurocredits is similar to the loan pricing that U.S. money center banks use for their largest domestic customers. The loan rate (k) is equal to a base rate, such as LIBOR, which represents the bank’s cost of funds, plus a markup, which is the bank’s lending margin:

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k = Base rate + X where X is the lending margin. The lending margin depends on the borrower’s credit risk; international risk factors, such as foreign exchange risk and country risk; and the bank’s gross profit margin. Equation 21.3 represents the Eurocredit pricing. k = BR + DRP + FXR + CR + GPMAR where k = individual firm’s loan rate BR = Eurocurrency base rate, such as LIBOR DRP = default risk premium FXR = foreign exchange or currency risk premium CR = country risk premium GPMAR = bank’s gross profit margin

Self-Study Problems 21.1

If a Volkswagen Passat costs $26,350 in Baltimore and €21,675 in Frankfurt, what is the exchange rate between the U.S. dollar and the euro?

Solution: Cost of the car in Baltimore = $26,350 Cost of the car in Frankfurt

= €21,675

Dollar to euro exchange rate = $26,350 / €21,675 = $1.2157/€ LO: 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: International/Global Perspective

21.2

Calculate the following exchange rates given the following information. Given

Compute

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¥101.3500/$

$/¥

$1.3578/£

£/$

$0.7843/C$

C$/$

Solution: a.

1 / ¥101.3500/$

$0.00987/¥

1 / $1.3578/£

£0.7365/$

1 / $0.7843/C$

C$1.2750/$

LO: 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: International/Global Perspective

21.3

Digital, Inc., an electronic games manufacturer, is planning to purchase flash memory from one of two sources. Kyoto, Inc., quotes a price of ¥6,800 per gigabyte. The current exchange rate is ¥102.30/$. Another Japanese manufacture offers to supply the same flash memory at a price of €58.46 per gigabyte. The spot rate available is ¥126.09/€. Which is the cheaper source of flash memory for Digital?

Solution: Cost from Vendor 1: Flash memory price quote

¥6,800 per gigabyte

Spot rate for U.S. dollar

¥102.30/$

Cost to Digital in dollars

¥6,800 / ¥102.30/$

$66.47 per gigabyte

Flash memory price quote

€58.46 per gigabyte

Spot rate for euro

¥126.09/€

Cost from Vendor 2:

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¥126.09/€ = $1.2326/ € ¥102.30 / $ Cost to Digital in dollars

Field Code Changed =

€58.46 × $1.2326/€

$72.05 per gigabyte

The first vendor has the cheaper quote for Digital. LO: 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: International/Global Perspective

21.4

Columbia Corp. has just made a sale to a British customer. The sale was for a total value of £135,000 and is to be paid 60 days from now. Columbia is concerned that the British pound will depreciate against the U.S. dollar, and management plans to hedge. The company’s bank informs management that the spot rate is $1.2461/£ and the 60-day forward rate is $1.2283/£. If Columbia sells its pounds receivable at the forward rate, what is the dollar value of its receivables? If it did not enter into a forward contract and the spot rate 60 days later was $1.2107/£, how much did the company lose by not hedging?

Solution: Amount received by Columbia by selling at the forward rate: = £135,000 × $1.2283/£ = $165,820.50 Amount received by Columbia by selling at the spot rate 60 days later: = £135,000 × $1.2107/£ = $163,444.50 Loss incurred by not hedging = $165,820.50- $163,444.50= $2,376.00. LO: 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: International/Global Perspective

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American Bancorp is planning to make a $3.5 million loan to a French firm. Currently, LIBOR is at 0.5 percent. American considers a default risk premium of 1.15 percent, a foreign exchange risk premium of 0.35 percent, and a country risk premium of 0.13 percent. What is the loan rate charged by American Bancorp?

Solution: The loan rate charged by American Bancorp is calculated as follows: k

= BR + DRP + FXR + CR = 0.5% + 1.15% + 0.35% + 0.13% = 2.13%

LO: 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: International/Global Perspective

Discussion Questions 21.1

Royal Dutch Shell, an oil company, has headquarters in both the Netherlands and the United Kingdom. What type of firm is it?

Solution: This company is both a multinational corporation and a transnational company. Since it produces, refines, and sells oil in a variety of different locations around the world, it is an MNC. Since it is owned by investors in more than one country and is managed from a global perspective, it is a transnational firm. LO: 1 Level: Basic Bloomcode: Knowledge AASCB: Analytic IMA: Corporate Finance AICPA: International/Global Perspective

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International economic integration and technological changes in the last couple of decades have dramatically increased globalization across many industries. Explain how a biotech firm or a medical firm (for example, a hospital) can take advantage of these changes.

Solution: Technological changes have come in a variety of forms—computers, telecommunication, data digitalization, and such. A biotech firm may be able to conduct research and development on new drugs in India, clinical trials in other countries before submitting it for FDA approval. A hospital in the United States may be able to cost efficiently digitalize medical records by transmitting the records overseas. Hospitals and doctors can use these digital records to consult physicians halfway across the world to get a more precise diagnosis. Additionally cost savings can be achieved by outsourcing and other instances of global economic integration resulting from the reduction or elimination of trade barriers. LO: 1 Level: Basic Bloomcode: Knowledge AASCB: Analytic IMA: Corporate Finance AICPA: International/Global Perspective

21.3

In the United States, managers are asked to focus on maximizing stockholder value. Is this consistent with the goals of managers in Germany and Japan?

Solution: In countries such as France and Germany, stockholders are treated no differently from other stakeholders of the firm. Thus, they are on a par with employees, suppliers, creditors, customers, and even the government. The firm’s management focus is on maximizing the wealth of the firm such that everyone benefits, not just the shareholders. In Japan, a group of businesses have ownerships in each other. This is known as keiretsu. Japanese managers focus on growing the market share of their firm such that the wealth of their keiretsu, and not the wealth of the shareholders, is maximized. Maximizing Copyright © 2022 John Wiley & Sons, Inc.

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shareholder wealth is consistent with these other goals. Management taking this approach will, in the long run, help all the stakeholders of the firms, including the community in which they operate, to benefit. LO: 1 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance AICPA: International/Global Perspective

21.4

A Canadian cooperative of wheat farmers sold wheat to a grain company in Russia. Under what circumstances will the Canadian farmers be exposed to foreign exchange risk? When will the Russian importer be facing foreign exchange risk?

Solution: If the payment to the Canadian exporter is in any currency other than the Canadian dollar, the Canadian exporter faces foreign exchange risk. If the Russian importer is forced to pay the Canadian exporter in Canadian dollars, then the entire foreign exchange risk is borne by the Russian importer. LO: 1 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance AICPA: International/Global Perspective

21.5

Stardust, Inc., is an exporter of plumbing fixtures. About 30 percent of its sales are made in Canada. The sales department just found out that the Canadian dollar is at a premium against the U.S. dollar based on the 90-day forward rate, while the 180-day forward rate indicates that the Canadian dollar is at a forward discount. What is the likely impact of these rates on the company’s sales to Canada?

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Solution: The fact that the Canadian dollar is at a forward premium indicates that the Canadian dollar will be able to buy more U.S. dollars. In the short run, this can lead to increased sales for Stardust since Canadians will be able to buy more plumbing fixtures with their money. Six months from now, the Canadian dollar is at a forward discount. This will make imports from the United States more expensive for Canadians, and this could lead to Stardust seeing a decrease in their exports to Canada at that time. LO: 2 Level: Basic Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: International/Global Perspective

21.6

Mello Wines, a California winery, grows its grapes locally, uses local labor, and sells its wines only in the United States. Can this firm be exposed to foreign exchange risk?

Solution: Even though Mello is merely a domestic company, it does have foreign exchange risk. Suppose the U.S. dollar appreciates against the euro. This will make imported wine from the euro zone more affordable to Americans and increase import competition to Mello. LO: 2 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance AICPA: International/Global Perspective

21.7

A U.S. firm owns a subsidiary in Belgium. What kind of foreign exchange risk does the U.S. firm face?

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Since it owns assets and has liabilities in Belgium denominated in euros, the firm faces foreign exchange risk. Converting the euro-denominated assets and liabilities to U.S. dollars for reporting purposes will make the dollar value of the Belgian subsidiary’s assets and liabilities fluctuate. Additionally, it can make the preparation of financial statements more complicated because of the foreign exchange exposure. LO: 5 Level: Basic Bloomcode: Knowledge AASCB: Analytic IMA: Corporate Finance AICPA: International/Global Perspective

21.8

Ray Corp is a U.S. electronics manufacturer with a production plant in Turkey. This morning, the Turkish government introduced a new law prohibiting the repatriation of any funds from the country for two years. What type of risk does Ray Corp. face?

Solution: Ray Corp. is facing a form of country or political risk. Country risk can be of many forms, including changes in tax or labor laws, currency or trade controls, remittance controls, or even expropriation of the firm’s assets. LO: 5 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance AICPA: International/Global Perspective

21.9

Suppose GE issues bearer bonds in France denominated in British pounds. What type of bonds are these?

Solution:

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This is an example of a Eurobond. GE, a foreign issuer in France is issuing a bearer bond in a currency (British pounds) to investors in a country whose currency is different from that of the bond issue. LO: 4 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance AICPA: International/Global Perspective

21.10 Give examples of U.S. banks facing different risks in international lending. Solution: The first risk that a bank will face in any market is credit risk—the risk that the interest and/or principal will not be paid. Suppose Citicorp made a loan to a firm in Honduras. Unlike lending in the domestic market, the bank is likely to be less familiar with the new market, economic conditions, and business practices. That makes it more difficult to judge the credit worthiness of a loan customer. The second risk to consider is currency risk. The loan is made in the Honduran currency, and repayment of principal and interest payments are also going to be in it. So, Citicorp needs to protect itself against currency risk. The third risk is potentially the worst. This is political or country risk, which affects the ability of Citicorp to make a profitable loan and be able to remit the funds back to the United States due to the political climate in Honduras. The more unstable a government is, the higher the country risk that Citicorp will face. LO: 5 Level: Basic Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: International/Global Perspective

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Questions and Problems BASIC 21.1

Spot rate: Ryan wants to buy a pair of leather shoes at Harrods in London that cost £113.60. If the exchange rate is $1.3686/£, what is Ryan’s cost in U.S. dollars?

Solution: Cost of shoes in London = £113.60 Spot rate = $1.3686/£ Dollar cost of shoes = £113.60 × $1.3686/£ = $155.47 LO: 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: International/Global Perspective

21.2

Spot rate: Crescent Corporation’s recent sale to a firm in Mexico produced revenues of 19,500,000 Mexican pesos (MPs). If the firm sold the pesos to its bank and was credited with $1,077,873.60, what was the spot rate at which the pesos were converted?

Solution: Revenue from sale to Mexican firm = MP 19,500,000 Dollar revenue received from sale = $1,077,873.60 Spot rate at which the foreign currency revenue was converted:

$1,077,873.60 = $0.05528/MP MP 19,500,000

Field Code Changed

This is the same as MP18.09/$ LO: 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: International/Global Perspective

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Spot rate: Given the following direct quotes, calculate the equivalent indirect quotes. a. $0.0507/Mexican pesos b. £0.8513/€ c. Indian rupee Rs 54.64/ C$

Solution: a.

1 = MP19.7239 /$ $0.0507/MP

1 / £0.8513/€ = €1.1747£

1 / Rs 54.64/ C$ = C$0.0183/Rs.

Field Code Changed

LO: 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: International/Global Perspective

21.4

Spot rate: Convert the following indirect quotes to the appropriate American quotes. a. £0.6917/$ b. ¥104.28/$ c. SF 1.0769/$

Solution: a.

1 / £0.6917/$ = $1.4457/£

1 / ¥104.28/$ = $0.0096 / ¥

1 / SF 1.0769/$ = $0.9286 / SF

LO: 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: International/Global Perspective

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Spot rate: Suppose a BMW 528i is priced at $68,750 in New York and € 50,267 in Berlin. In which city is the car more expensive if the spot rate is $1.2150/€?

Solution: Cost of car in New York = $68,750 Cost of car in Berlin = € 50,267 Spot rate = $1.2150/€? Dollar cost in Berlin = € 50,267 × $1.2150/€? = $61,074.41 The cost of the car is quite a bit cheaper in Berlin! LO: 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: International/Global Perspective

21.6

Forward rate: Explain the relation between each pair of currencies. Spot Rate

Forward Rate

$1.3455/ £

$1.2801/£

¥104.45/$

¥102.33/$

C$1.1940/$

C$1.2121/$

Solution: a.

Since the forward rate indicates that fewer dollars will be required to buy a pound in the future, we say that the dollar is at a forward premium against the British pound.

The yen is at a forward premium against the dollar as the forward quote indicates that the dollar can be purchased with fewer yen.

The U.S. dollar is at a forward premium against the Canadian dollar as a dollar is expected to purchase more Canadian dollars in the future.

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21.7

Forward rate: If the spot rate was $0.7885/C$ and the 90-day forward rate was $0.8003/C$, how much more (in U.S. dollars) would you receive by selling C$ 1,000,000 at the forward rate than at the spot rate?

Solution: If C$1,000,000 was sold at the spot rate, dollar revenue received: C$1,000,000 × $0.7885/C$

= $788,500

If C$1,000,000 was sold at the 90-day forward rate, dollar revenue received: C$1,000,000 × $0.8003/C$

= $800,300

Additional revenue received by selling forward = $800,300 - $788,500 = $11,800 LO: 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: International/Global Perspective

21.8

Forward rate: Crane, Inc., sold equipment to an Irish firm and will receive €1,319,405 in 30 days. If the company entered a forward contract to sell at the 30-day forward rate of $1.2183/€, what is the dollar revenue received?

Solution: Expected euro revenue = €1,319,405 30-day forward rate = $1.2183/€ Dollar revenue received = €1,319,405 × $1.2183/€ = $1,607,431 LO: 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: International/Global Perspective

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Forward rate: Brilliant Equipment purchased machinery from a Japanese firm and must make a payment of ¥313.25 million in 45 days. The bank quotes a forward rate of ¥103.01/$ to buy the required yen. What is the cost to Brilliant in U.S. dollars?

Solution: Cost of machinery = ¥313.25 million Forward rate = ¥103.01/$ Cost of equipment in dollars = ¥313,250,000 / ¥103.01/$ = $3,040,966.90 LO: 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: International/Global Perspective

21.10 Forward rate: Triumph Autos has contracted with an Indian software firm for design software. The payment of 22,779,750 rupees (Rs) is due in 30 days. What is the cost in dollars if the 30-day forward rate is Rs71.13/$? Solution: Cost of software = Rs22,779,750 Forward rate= Rs71.13/$ Cost of software in dollars = Rs22,779,750 / Rs71.13/$= $320,255.17 LO: 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: International/Global Perspective

21.11 Forward rate: The three-month forward rate on the Swiss Francs is $1.13310/SF and the spot rate $1.12630/SF. The three-month forward rate on the Japanese yen is $0.008754/¥ and the spot rate is $0.008720/¥.: a.

Is the Swiss franc selling for a premium or a discount against the U.S. dollar?

Is the Japanese yen selling for a premium or a discount against the U.S. dollar?

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Given the information above, what do you think will happen to the value of the U.S. dollar relative to the Swiss franc and the Japanese yen?

Solution: a.

The three-month forward rate on the Swiss Francs is $1.13310/SF relative to the spot rate of $1.12630/SF. The forward premium (discount) = ($1.13310 – $1.12630)/$1.12630 = 0.604%. So, there is a forward premium on the Swiss franc against the U.S. dollar.

The three-month forward rate on the Japanese yen is $0.008754/¥, while the spot rate is $0.00872/¥. The forward premium (discount) = (0.008754 – 0. 0.00872)/0.00872 = 0.39%. The yen is at a forward premium against the U. S. dollar.

Given the data on forward rates in a.) and b.) above, we can expect the Swiss franc and the Japanese yen to appreciate relative to the U.S. dollar over the next three months.

LO: 2 Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance AICPA: International/Global Perspective

21.12 Bid-ask spread: Nova Scotia Bank offers quotes on the Canadian dollar as shown below. What is the bid-ask spread based on these quotes? Bid C$ 1.3081/$

Ask C$ 1.3087/$

Solution: Bid-ask spread = (Ask rate – Bid rate) / Ask rate = (1.3087 – 1.3801) / 1.3087 = 0.0005 = 0.05% LO: 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: International/Global Perspective Copyright © 2022 John Wiley & Sons, Inc.

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21.13 Bid-ask spread: A local community bank has requested foreign exchange quotes for the Swiss Franc from Citibank. Citibank quotes a bid rate of $1.0934/SF and an ask rate of $1.0997/SF. What is the bid-ask spread? Solution:

Ask rate - Bid rate 1.0997 − 1.0934 = Ask rate 1.0997 = 0.00573 = 0.573%

Bid - ask spread =

LO: 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: International/Global Perspective

21.14 Bid-ask spread: A foreign exchange dealer is willing to buy the Danish krone (DKr) at $0.1556/DKr and will sell it at a rate of $0.1563/DKr. What is the bid-ask spread on the Danish krone? Solution:

Ask rate - Bid rate 0.1563 - 0.1556 = Ask rate 0.1563 = 0.00448 = 0.45%

Bid - ask spread =

LO: 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: International/Global Perspective 21.15 Cross rate: Given the following quotes, calculate the €/£ cross rate. Bank of America

$1.3862/£

JP Morgan Chase

$1.2148/€

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To find the €/£ cross rate, divide the Bank of America quote by the JP Morgan Chase quote. Cross rate = $1.663/£ ÷ $1.2148/€ = €1.3689/£ LO: 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: International/Global Perspective

21.16 Cross rate: Barclays Bank of London has offered the following exchange rate quotes: ¥134.64/£ and Korean won 13.8374/¥. What is the cross rate between the Korean won and the British pound? Solution: To find the won/£ cross rate, multiply the Korean won quote by the yen quote. Cross rate = Won 13.8374/¥ × ¥ 134.64/£ = Won 1,863.07 /£ LO: 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: International/Global Perspective

21.17 Cross rate: Bremer Corporation observes that the Swiss franc (SF) is being quoted at €0.9282/SF, while the Swedish krona (SK) is quoted at €0.0991/SK. What is the SK/SF cross rate? Solution: To find the SK/SF cross rate, divide the Swiss franc quote by the Swedish krona quote. Cross rate = €0.9282/SF ÷ €0.0991/SK = SK9.3663/SF LO: 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance Copyright © 2022 John Wiley & Sons, Inc.

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21.18 Country risk: Ford Motor Company maintains production facilities in many different countries including Brazil, Taiwan, and the United States. Given the data in Exhibit 21.6, which production plant is likely to face the greatest country risk? How does country risk affect a firm’s capital budgeting decisions? Solution: Exhibit 21.6 contains composite country risk ratings as per 2016 survey. Using these ratings, Brazil has the greatest country risk while Taiwan has the least. Country risk factors are associated with additional systematic risk for projects located in that country and therefore are associated with a relatively higher discount rate. LO: 3 Bloomcode: Synthesis AASCB: Analytic IMA: Corporate Finance AICPA: International/Global Perspective

21.19 Foreign exchange risk: How is transaction exposure different from operating exposure? Solution: Transaction exposure is a result of a contractual obligation that causes foreign exchange risk. This is because a firm may have a contract that specifies revenues or expenses denominated in a foreign currency, while operating exposure focuses on foreign currency cash flows generated from operation that might change because a change of exchange rates. As the exchange rate changes, the home currency value of these revenues or expenses changes, leading to transaction exposure. If exchange rate changes are more permanent in nature and modify the way a firm does its business, then we say that a firm is facing operating exposure. LO: 3 Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance Copyright © 2022 John Wiley & Sons, Inc.

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21.20 International debt: What are Yankee bonds? Solution: When corporate bonds are issued by a foreign firm in the United States and denominated in U.S. dollars, they are considered to be foreign bonds and referred to as “Yankee” bonds. LO: 4 Bloomcode: Knowledge AASCB: Analytic IMA: Corporate Finance AICPA: International/Global Perspective

INTERMEDIATE 21.21 Forward premium: The spot rate on the London market was £0.7531/$, while the 90day forward rate is £0.7602/$. What is the annualized forward premium or discount on the British pound? Solution:

Forward rate − Spot rate 360   100 Spot rate n 0.7602 − 0.7531 360 =   100 = 3.77% 0.7531 90

Field Code Changed

Forward premium (discount) =

Field Code Changed

There is a forward premium per U.S. dollar. This also means that the British pound is at a forward discount against the U.S. dollar since it takes more pounds to buy a dollar at the forward rate. LO: 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: International/Global Perspective Copyright © 2022 John Wiley & Sons, Inc.

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21.22 Forward premium: Bank of America quotes the 180-day forward rate on the Swiss franc at $1.0407/SF. The spot rate is quoted at $1.0268/SF. What is the annualized forward premium or discount on the Swiss franc? Solution:

Forward premium (discount) =

Forward rate − Spot rate 360   100 Spot rate n

Field Code Changed Field Code Changed

$1.0407 − $1.0268 360 =   100 = 2.71% $1.0268 180 The Swiss franc is at a 2.71 percent forward premium against the dollar. LO: 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: International/Global Perspective 21.23 Forward premium: The foreign exchange department at Tokyo’s Daiwa Bank quotes the spot rate on the euro at €0.007269/¥. The 90-day forward rate is quoted at a premium of 5.42 percent on the euro. What is the 90-day forward rate? Solution: Spot rate = €0.007269/¥ 90-day forward premium on the euro = 5.42% It means that 90-day forward discount on the Yen= –5.42%

Forward rate − 0.007269 360  0.007269 90 −0.0542  0.007269  90 Forward rate − 0.007269 = 360 Forward rate = €0.007367/¥

Field Code Changed

−0.0542 =

Field Code Changed Field Code Changed

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IMA: Corporate Finance AICPA: International/Global Perspective

21.24 Forward premium: The spot rate of the Australian dollar (A$) is A$1.1667/$. The Australian dollar is quoted at a 30-day forward premium of 4.90 percent against the U.S. dollar. What is the 30-day forward quote? Solution: Spot rate = A$1.1667/$ 30-day forward premium on the Australian dollar = 4.90%Its mean that 90-day forward discount on the dollar= –4.90%

Forward premium (discount) =

Forward rate − Spot rate 360   100 Spot rate n

Field Code Changed Field Code Changed

F − 1.1667 360 −0.049 = 0  1.1667 30 −0.049  1.1667  30 F0 − 1.1667 = 360 F0 = −0.004764 + 1.1667 = A$1.1619/$

Field Code Changed

The 30-day forward rate is A$1.1619/$. LO: 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: International/Global Perspective

21.25 Bid-ask spread: The foreign exchange department of Bank of America has a bid quote on Canadian dollars (C$) of C$1.2350/$. If the bank typically tries to make a bid-ask spread of 0.5 percent on these foreign exchange transactions, what will the ask rate have to be? Solution:

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Ask rate − Bid rate Ask rate Ask rate − 1.2350 0.005 = 1.1667 Ask rate − 0.005  Ask rate = 1.2350 1.235 Ask rate = = 1.2412 0.995

Field Code Changed

Bid-ask spread =

Field Code Changed Field Code Changed

The ask rate will have to be C$1.2412/$ to provide a 0.5 percent bid-ask spread. LO: 2 Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance AICPA: International/Global Perspective

21.26 Bid-ask spread: Banco Santiago wants to make a bid-ask spread of 0.65 percent on its foreign exchange transactions. If the ask rate on the Mexican peso (MP) is MP18.3092/$, what does the bid rate have to be? Solution:

Ask rate − Bid rate Ask rate MP18.3092 − Bid rate 0.0065 = MP18.3092 MP10.3092 − Bid rate = 0.0065  MP18.3092 = 0.119 Bid-ask spread =

Bid rate = MP18.3092 − 0.119 = MP18.1902 / $ The ask rate will have to be MP18.1902/$ to provide a 0.65 percent bid-ask spread. LO: 2 Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance AICPA: International/Global Perspective

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21.27 Cross rate: Alcor Pharma just received revenues of $3,165,300 in Australian dollars (A$). Management has the following exchange rates: A$1.7110/£ and $1.3675/£. What is the U.S. dollar value of the company’s revenues? Solution: Revenues received by Alcor Pharma = A$3,165,300 To determine the A$ /$ cross rate, you divide the A$ to £ quote by the $/£ quote. Cross rate = A$1.7110/£ ÷ $1.3675/£ = A$1.2512/$ U.S. dollar value of their revenue = A$3,165,300 ÷ A$1.2512/$ = $2,529,835 LO: 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: International/Global Perspective

21.28 Cross rate: Flint Corp. recently purchased auto parts worth 17.5 million Mexican pesos (MP) on credit. Management needs to find out the U.S. dollar cost of the purchase. It has access to two quotes for Canadian dollars (C$): C$1.2430/$ and C$0.0620/MP. What did it cost Flint to purchase the auto parts? Solution: Foreign currency payables = MP 17.5 million To find the MP/$ quote, divide the C$/MP quote by the C$/$ quote. Cross rate = C$0.0620/MP ÷ C$1.2430/$ = $0.0499/MP Dollar cost of payables = MP 17,500,000 × $0.0499/MP = $872,888 LO: 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: International/Global Perspective

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21.29 Hedging: Tricolor Industries has purchased equipment from a Brazilian firm for a total cost of 272,500 Brazilian reals. The firm has to pay in 30 days. Citibank has given the firm a 30-day forward quote of $0.1829/real. Assume that on the day the payment is due, the spot rate is expected to be $0.2103/real. How much would Tricolor have saved by hedging with a forward contract? Solution: Foreign currency payables = BR 272,500 Spot rate on payment date

= $0.2103/real

Dollar cost of payables

= BR 272,500 × $0.2103/real = $57,306.75

30-day forward rate

= $0.1829/real

Cost if hedged at forward rate = BR 272,500 × $0.1829/real = $49,840.25 Cost savings = $57,306.75− $49,840.25 = $7,466.50 LO: 2 Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance AICPA: International/Global Perspective

21.30 Eurocredit Loan: A Swiss sporting goods company borrows in yen in the Eurocredit market at a rate of 4.35 percent from Bank of America using a three-month rollover loan. Bank of America assigns a default risk premium of 2 percent on the loan, the country risk is an additional 0.75 percent, and the foreign exchange rate risk premium is 0.25 percent. The Bank can borrow funds in the Euromarket at the three-month LIBOR rate of 0.26 percent. What is Bank of America’s gross profit margin on this loan? Solution: GPMAR = k - BR – DRP – CR = 4.35% - 0.26% - 2.0% - 0.75% = 1.34% LO: 5 Bloomcode: Synthesis AASCB: Analytic IMA: Corporate Finance AICPA: International/Global Perspective Copyright © 2022 John Wiley & Sons, Inc.

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ADVANCED 21.31 Covington Industries just sold equipment to a Mexican firm. Payment of 11,315,000 pesos will be due to Covington in 30 days. Covington has the option of selling the pesos today at a 30-day forward rate of $0.06139/peso. If it waits 30 days to sell the pesos, the expected spot rate is $0.05881/peso. In dollars, how much better off is Covington by selling the pesos in the forward market? Solution: Foreign currency receivables

= MP 11,315,000

Spot rate on payment date

= $0.05881/peso

Dollar revenues from receivables = MP 11,315,000 × $0.05881/peso= $665,435.15 30-day forward rate

= $0.06139/peso

Revenues if hedged at forward rate = MP 11,315,000 × $0.06139/peso= $694,627.85 Additional revenues received = $694,627.85 − $665,435.15 = $29,192.70 LO: 2 Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance AICPA: International/Global Perspective

21.32 Barrington Fertilizers, Inc., exports its specialized lawn care products to Canada. It made a sale worth C$1,150,000, with the payment due in 90 days. Barrington’s banker gave it a forward quote of $0.7963/C$. By using the forward rate, the firm gained an additional $8,433.25 over what it would have received if it had sold the Canadian dollars in the spot market 90 days later. What was the spot rate at the time the payment was received? Solution: Foreign currency receivables = C$1,150,000 90-day forward rate = $0.7963/C$ Revenues if hedged at forward rate = C$1,150,000 × $0.7963/C$= $915,745 Additional dollar revenues received = $8,433.25 Copyright © 2022 John Wiley & Sons, Inc.

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Revenues at spot rate = $915,745 − $8,433.25 = $907,311.75 Spot rate on payment date = $907,311.75 / C$1,150,000 = $0.7890/C$ LO: 2 Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance AICPA: International/Global Perspective

21.33 Moon Rhee Auto Supply, a Korean supplier of parts to Kia Motors, is evaluating an opportunity to set up a plant in Alabama, where Kia Motors has an auto assembly plant for its SUVs. The cost of this plant will be $13.5 million. The current spot rate is 1,120.318 Korean won per U.S. dollar. The firm is expected to use this plant for the next five years and is expecting to generate the following cash flows.

Years 1

$2.3

$4.2

$3.6

$5.8

$7.6

1,105.231

1,115.632

1,146.155

1,120.221

1,110.670

Cash flows ($ millions) Expected exchange rate (Korean won/$)

The firm uses a discount rate of 9 percent for projects like this in the United States. What is the NPV of this project? Should Moon Rhee Auto Supply take on this project? Solution: Moon Rhee Auto Supply knows what the expected cash flows in U. S. dollars and the expected cash flows to the parent firm in Korean won can be calculated by dividing the dollar cash flows by the appropriate exchange rate.

Year

4___________5__

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4.2

3.6

5.8

7.6

Given in the following table are the cash flows that the Korean firm expects to receive from its American subsidiary in U.S. dollars.

Cash Flows (in

Exchange Rate

Cash Flows (in

Year

millions of U.S. $)

(won/$)

millions of won)

(13.5)

1,120.318

(15,124.293)

2.3

1,105.231

2,542.031

4.2

1,115.632

4,685.654

3.6

1,146.155

4,126.158

5.8

1,120.221

6,497.282

7.6

1,110.670

8,441.092

The firm has determined that the appropriate discount rate is 9 percent for capital budgeting projects in the United States. By discounting the cash flow at the risk-adjusted discount rate of 9 percent, we can compute the NPV for this project. NPV = −15,124.293 + 2,542.031/ (1.09)1 + 4,685.654/ (1.09)2 + 4,126.158/ (1.09)3 +6,497.282/ (1.09)4 + 8,441.092/ (1.09)5 million won = −15,124.293 + 2,332.13881+ 3,943.82156 + 3,186.15104 + 4,602.83823 + 5,486.13063 million won = 4,426.787million won Since NPV is positive, the project should be accepted. LO: 3 Bloomcode: Synthesis AASCB: Analytic IMA: Corporate Finance AICPA: International/Global Perspective

21.34 The Boeing Company has two different debt issues, both maturing four years from now. The domestic bond issue pays semiannual coupons and has a coupon rate of 4.80 percent.

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The current price on the bond is $962.75. The Eurobond issue is priced at $964.33 and pays an annual coupon of 4.95 percent. What is the yield to maturity for each bond? Solution: For the Euro bond with annual compounding, the coupon payment is $49.50 per year, and the yield calculation is: $964.33 =

$49.50 $49.50 $49.50 $1,049.50 + + + (1 + i)1 (1 + i)2 (1 + i)3 (1 + i)4

Field Code Changed

Using our financial calculator, the annual yield of the Eurodollar bond issue is 5.9789 percent.

For the domestic bond issue, the semiannual coupon payments are $24 ($48/2), and the semiannual bond yield calculation is: $962.75 =

$24 $24 + + (1 + i)1 (1 + i)2

$1,024 (1 + i)8

Field Code Changed

Making the calculation, the bond issue’s semiannual yield is 2.9291 percent. As discussed in Chapter 8, to compare interest rates with different compounding periods, we need to compute the effective annual yield (EAY). Applying the equation EAY: EAY = (1 + quoted rate/m)m – 1 = (1 + 0.029291)2 – 1 = 1.05944 – 1 = 5.94% An investor in Boeing’s Eurobond will earn 5.98 percent, while the domestic bond would provide a yield of 5.94 percent. Thus, by earning 4 basis points more, the Eurobond is the better investment. LO: 4 Bloomcode: Evaluation AASCB: Analytic IMA: Corporate Finance AICPA: International/Global Perspective

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21.35 Caterpillar, Inc. management is trying to decide between selling a new bond issue in the U.S. or the Eurodollar bond market. In either market the bonds will be denominated in dollars and will have a three-year maturity. The domestic bond will have a coupon rate of 4.1 percent, paid semiannually, and would sell at a market price of $1,034.25. The Eurobonds will have a coupon rate of 4 percent, paid annually, and will sell at $1,029.76. Which bond issue will have the lowest cost to the firm? Solution: For the domestic bond issue the semiannual coupon payments are $20.50 ($41/2), and the semiannual bond yield calculation is: $1,034.25 =

$20.50 $20.50 + + (1 + i)1 (1 + i)2

$1,020.50 (1 + i)6

Field Code Changed

Making the calculation, we see that the bond issue’s semiannual yield is 1.4499 percent. As discussed in Chapter 8, to compare interest rates with different compounding periods, we need to compute the effective annual yield (EAY). Applying the equation EAY: EAY = (1 + quoted rate/m)m – 1 = (1 + 0.014499)2 – 1 = 1.02921 – 1 = 2.92%

For the Eurodollar bond with annual compounding, the coupon payment is $40 per year, and the yield calculation is: $1,029.76 =

$40 $40 $1,040 + + (1 + i)1 (1 + i)2 (1 + i)3

Field Code Changed

Using our financial calculator, the annual yield of the Eurodollar bond issue yield is 2.9489 percent. From Caterpillar’s perspective, the domestic bond issue is the cheaper alternative. LO: 4 Bloomcode: Synthesis AASCB: Analytic IMA: Corporate Finance Copyright © 2022 John Wiley & Sons, Inc.

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AICPA: International/Global Perspective 21.36 IBM’s German unit is looking to borrow €7.5 million from Deutsche Bank. Deutsche Bank quotes a rate of three-month LIBOR plus 0.25 percent for the 90-day loan. Currently, the three-month LIBOR is 0.27 percent. What is IBM’s interest cost on the loan in Euros? If the exchange rate on the payoff date is €0.8164/$, what is the dollar cost of the loan? Solution: Amount IBM plans to borrow = €7.5 million Term of loan = 90 days Interest cost = LIBOR + 0.25% = 0.27% + 0.25% = 0.52% Interest cost in euros = €7,500,000 x 0.0052 × (90/360) = €9,750 Spot rate on payoff date = €0.8164/$ Dollar interest cost = €9,750 / €0.8164/$ = $11,942.68 LO: 5 Bloomcode: Synthesis AASCB: Analytic IMA: Corporate Finance AICPA: International/Global Perspective

21.37 Toyota is interested in borrowing $5 million for 90 days. Bank of America has quoted a rate that is 1.85 percent under the prime rate of 3.55 percent. Daiwa Bank is offering Toyota a rate that is 0.95 percent over the three-month LIBOR of 0.29 percent. Which is the better deal for Toyota, and what is the lower interest cost in dollars? Solution: Bank of America Loan Amount Toyota plans to borrow = $5 million Term of loan = 90 days Interest cost = Prime rate − 1.85% = 3.55% − 1.85% = 1.7% Interest cost = $5,000,000 × 0.017 × (90/360) = $21,250 Daiwa Bank Loan Copyright © 2022 John Wiley & Sons, Inc.

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Amount Toyota plans to borrow = $5 million Term of loan = 90 days Interest cost

= LIBOR + 0.95% = 0.29% + 0.95% = 1.24%

Interest cost = $5,000,000 × 0.0124 × (90/360) = $15,500 The Daiwa Bank offers Toyota the lower cost loan with a lower interest cost of $15,500 versus Bank of America’s cost of $21,250. LO: 5 Bloomcode: Synthesis AASCB: Analytic IMA: Corporate Finance AICPA: International/Global Perspective

Sample Test Problems 21.1

What are six factors that cause international transactions to differ from domestic transactions?

Solution: Six factors that cause international transactions to differ from domestic transactions are differences in: 1) Currencies 2) Legal systems and tax codes 3) Languages 4) Cultures 5) Economic systems 6) Country risks LO: 1 Bloomcode: Knowledge AASCB: Analytic IMA: Corporate Finance AICPA: International/Global Perspective

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If a Dell Studio laptop sells for $999 in Austin, Texas and £689 in London, what is the implied exchange rate between the U.S. dollar and the euro?

Solution: Cost of the computer in Austin

= $999

Cost of the computer in London = £689 Dollar to euro exchange rate

= $999 / £689 = $1.4499/£

LO: 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: International/Global Perspective

21.3

A bank in India has offered a spot rate quote on Indian rupees (Rs) of Rs72.2905/$. The Indian rupee is quoted at a 30-day forward premium of 5.22 percent against the dollar. What is the 30-day forward quote?

Solution: Spot rate = Rs72.2905/$ 30-day forward premium against the dollar = 5.22%

Forward rate − Spot rate 360   100 Spot rate n F − Rs72.2905/$ 360 0.0522 = 0  Rs72.2905/$ 30 Rs72.2905 30 = F0 − Rs72.2905/$ = 0.0522   $ 360 F0 = Rs72.2905/$ + (0.0522  Rs6.02421/$) = Rs72.605/$ The 30-day forward rate is Rs72.605/$. Forward premium (discount) =

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Technocorp has purchased industrial parts from a German company for a total cost of €1,225,000. The firm has 30 days to pay. A bank has given Technocorp a 30-day forward quote of $1.1278/€. Assume that on the day the payment is due, the spot rate is $1.1468/€. How much would Technocorp have saved by hedging with a forward contract?

Solution: Foreign currency payable = €1,225,000 Spot exchange rate on payment date = $1.1468/€. Dollar cost of payables = €1,225,000 × $1.1468/€ = $1,404,830 30-day forward rate = $1.1278/€ Cost if hedged at forward rate = €1,225,000 × $1.1278/€ = $1,381,555 Cost savings = $1,404,830 − $1,381,555 = $23,275 LO: 2 Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance AICPA: International/Global Perspective

21.5

Tass Co., Ltd, a Japanese electrical parts producer, is considering building a plant in the U.S. The cost of this plant will be $20 million and the current spot exchange rate between the yen and the U.S. dollar is ¥101.8/$. Tass management expects to use this plant for the next five years and expects it to generate the following cash flows during this period. Year

Cash flows ($ millions) Expected exchange rate (¥/$)

$2.0

$3.6

$5.0

$6.8

$8.0

¥101.5/$

¥100.4/$

¥98.6/$

¥95.9/$

¥92.5/$

If Tass uses a discount rate of 8 percent for projects in the United States, what is the NPV of this project? Should Tass Company take on this project? Solution:

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Expected cash flows to Tass in yen can be calculated by multiplying the dollar cash flows by the appropriate exchange rate.

Cash Flows (U.S. $

Exchange Rate (¥/$)

Cash Flows (in

Year

in millions)

millions of ¥)

($20)

¥101.8/$

(¥2,036.00)

$2.0

¥101.5/$

¥203.00

$3.6

¥100.4/$

¥361.44

$5.0

¥98.6/$

¥493.00

$6.8

¥95.9/$

¥652.12

$8.0

¥92.5/$

¥740.00

By discounting the cash flow at the risk-adjusted discount rate of 8 percent, we can compute the NPV for this project. NPV = −2,036 + 203 / 1.08 + 361.44 / (1.08)2 + 493 / (1.08)3 +652.12 / (1.08)4 + 740 / (1.08)5 = −2,036 + 187.96 + 309.88 + 391.36 + 479.33 + 503.63 = − ¥163.84 million The NPV is negative, so the project should be rejected. LO: 3 Bloomcode: Evaluation AASCB: Analytic IMA: Corporate Finance AICPA: International/Global Perspective

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Chapter 20

Options and Corporate Finance Before You Go On

Section 20.1 1.

What is a call option, and what do the payoff functions for the owner and seller of a call option look like? A call option gives the owner the right to buy or “call” the underlying asset at a prespecified price. The payoff for the owner of a call option is zero when the value of the underlying asset is below the exercise price and increases or decreases dollar for dollar with the price of the underlying asset once the asset price goes above the exercise price. The owner of the call option pays a call premium for the right to purchase the asset at the exercise price, and the seller receives that call premium.

What is a put option, and what do the payoff functions for the owner and seller of a put option look like? A put option gives the owner the right to sell the underlying asset at a pre-specified price. The payoff for the owner of a put option is zero when the value of the underlying asset is above the exercise price and increases (decreases) dollar for dollar with decrease (increase) of the price of the underlying asset when the asset price drops below the exercise price. Similar to a call option, the owner of a put option pays a premium for the right to sell the asset, and the seller of the put receives that put premium.

Why does the payoff function for an option have a kink in it?

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The payoff function for an option has a “kink” at the exercise price. This kink exists because the owner of the option has a right, not an obligation, to buy or sell the underlying asset. If it is not in the owner’s interest to exercise the option, he or she can simply let it expire.

Section 20.2 1.

What are the limits on the value of a call option prior to its expiration date? The value of a call option can never be less than zero since the owner of the option can always decide not to exercise it if doing so is not beneficial. A second limit on the value of a call option is that it can never be greater than the value of the underlying asset. It would not make sense to pay more for the right to buy an asset than you would pay for the asset itself. The third limit is that the value of a call option prior to expiration will never be less than the value of that option at expiration. Because of the time value of money, the final limit is that the value of a call option prior to expiration will never be less than the difference between the current value of the underlying asset and the present value of the exercise price.

What variables affect the value of a call option? The following five variables affect the value of a call option prior to expiration: (1) Current value of the underlying asset (2) Exercise price (3) Volatility of the value of the underlying asset (4) Time until the expiration of the option (5) Risk-free rate of interest

Why are the variables that affect the value of a put option the same as those that affect the value of a call option? Given the value of a call option, the value of a put option can be calculated using the putcall parity: P = C + Xe-rt – V

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where "P" is the value of the put option, "C" is the value of the call option, "X" is the exercise price, "r" is the risk-free rate, "t" is the amount of time before the option expires, and "V" is the current value of the underlying asset. The term "e–rt" is the exponential function that you can calculate using the “ex” key on your calculator; it is simply a discount factor that assumes continuous compounding. We can see that the formula does not include any variables other than the five factors in valuation of a call option.

Section 20.3 1.

What is a real option? Real options are options on real assets. In some cases, the value of real options can be incorporated into an investment analysis by valuing the option separately using valuation methods similar to those used to value financial options, and then adding this value to the value estimated by traditional NPV analysis.

What are four different types of real options commonly found in business? (1) Options to defer investment. (2) Options to make follow-on investments. (3) Options to change operations. (4) Options to abandon projects.

Is it always possible to estimate the value of a real option? Why or why not? In some instances, it is not possible to estimate the value of a real option because we do not have enough information or because the necessary analysis is too complex. Although it might not even be possible to directly estimate the value of the real options associated with a project, it is important to recognize that they exist when you perform a project analysis.

Section 20.4 1.

What do the payoff functions for stockholders and lenders look like?

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The payoff function for the stockholders looks exactly like that for the owner of a call option where the exercise price is the amount owed on the loan and the underlying asset is the firm itself. The payoff function for the lenders looks like that for the seller of a put option, where the exercise price is the amount of the loan and the underlying asset is the firm itself.

What does the payoff function for a typical manager look like? When a company defaults on its debt, the payoff function for the manager will look something like that for the lender—it will slope downward as the value of the firm decreases. On the positive side, a manager’s payoff will increase with the value of the firm when this value is above the amount that the company owes to its lenders.

Section 20.5 1.

What is hedging? Hedging is a method of reducing financial risks faced by a firm. Technically, a firm hedges when it purchases an asset whose payoffs are not perfectly positively correlated with the payoffs of its other assets. When the correlation is -1, the asset risk is said to be perfectly hedged. Options, along with other derivative instruments, such as forwards, futures, and swaps, are commonly used in hedging.

What types of risks can options be used to manage? Options can be used to manage risks associated with commodity prices, interest rates, foreign exchange rates, and equity prices. Insurance policies are a specialized type of put option and are among the most common forms of hedging used by managers.

Self-Study Problems 20.1

Of the two parties to an option contract, the buyer and the seller, who has a right and who has an obligation?

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The buyer (owner) of the option has the right to exercise the option but is not required to do so. The seller (or writer) of the option is obligated to take the other side of the transaction if the option owner decides to exercise it.

20.2

The stock of Augusta Light and Power is currently selling at $12 per share. Over the next year the company is undertaking a new electricity production project. If the project is successful, the company’s stock is expected to rise to $24 per share. If the project fails, the stock is expected to fall to $8 per share. The risk-free rate is 6 percent. Calculate the value today of a one year call option on one share of Augusta Light and Power with an exercise price of $20.

Solution: First determine the payoffs for the stock, a risk-free loan, and the call option under the two possible outcomes. In one year, the stock price is expected to be either $8 or $24. The loan will be worth $1.06 regardless of whether the project is successful. If the project fails, the stock price will be less than the exercise price of the call option. The option will not be exercised and will be worth $0. If the project is successful, the stock price will be higher than the exercise price of the call option. The option will be exercised and its value will be the difference between the stock price and the exercise price, $4. Stock (x) Today

$12

Expiration

Risk-Free Loan (y) $1

$24

$1.06

Call Option ?

$1.06

$0 $24 – $20 = $4

The stock and loan can be used to create a replicating portfolio which has the same payoff as the call option: ($8 × x) + (1.06 × y) = $0 ($24 × x) + (1.06 × y) = $4 Solving the two equations yields: x = 0.25, y = –1.887 The value of the call option is the same as the current value of this portfolio:

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($12 × 0.25) + ($1 × -1.887) = $1.11

20.3

ADCAP International is a U.S.-based company which sells its products primarily in overseas markets. The company’s stock is currently trading at $50 per share. Depending on the outcome of U.S. trade negotiations with the countries to which ADCAP exports its products, the company’s stock price is expected to be either $65 or $30 in six months. The risk-free rate is 8 percent per year. What is the value of a put option on ADCAP stock that has an exercise price of $40 per share?

Solution: Here we solve directly for the value of the put option. First we determine the payoffs for the stock, a risk free bond, and the put option under the two possible outcomes. To determine payoff of the bond six months from now, we must calculate the six-month risk free interest rate given the one year risk free rate in the problem statement. Six month risk free rate = (1 + 0.08)1/2 – 1 = 1.039, or 3.9% The payoffs are therefore:

Today

Expiration

Stock (x)

Risk-Free Loan (y)

$50

$30

$65

$1.039

Put Option ?

$1.039

$40 – $30 = $10

Now we can use the stock and bond to create a replicating portfolio, which will give the same payoff as the put option: ($30 × x) + (1.039 × y) = $10 ($65 × x) + (1.039 × y) = $0 Solving the two equations we determine x = –0.286, y = 17.87 The value of the put option is the same as the current value of this portfolio: ($50 × –0.286) + ($1 × 17.87) = $3.58 Alternatively, you could solve this problem by calculating the value of a call option with an exercise price of $40 per share and then using the put-call parity relation. The value of

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the call option is $15.09 and the value of the associated put option calculated using the put-call parity relation is $3.52. The difference ($3.58 vs. $3.52) is due to rounding and the compounding assumption for the discount rate.

20.4

Your company is considering opening a new factory in Europe to serve the growing demand for your product there. What real options might you want to consider in your capital budgeting analysis of the factory?

Solution: Several significant real options might be associated with the factory. First, by having a factory in Europe, and the employees and management associated with it, your company might be better positioned to introduce products to the European markets. In addition, you will have options to change operations, to sell the factory, or to simply abandon the project.

20.5 Your firm, which uses oil as an input to its production processes, hedges its exposure to changes in the price of oil by buying call options on oil at today’s price. If the price of oil goes down by the time the contract expires, what effect will that have on your company? Solution: The effect on your company of the decline in the price of oil will be to increase earnings. This is because the oil is an input to your production process, and a drop in prices will reduce your expenses. If the price of oil goes down, you would let the call option expire without exercising it. Of course, the benefit your company receives from the drop in oil prices would be reduced by the amount that you paid to purchase the option. .

Discussion Questions 20.1

Options can be combined to create more complicated payoff structures. Consider the combination of one put option and one call option with the same expiration date

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and the same strike price. Draw the payoff diagram and describe what the purchaser of such a combination thinks will happen before expiration. Solution: The payoff diagram will be in the shape of a V centered at the strike price:

Buy Put

Value

and Call

Stock Price

This combination is called a straddle. Its purchaser thinks that the value of the underlying asset will change significantly, but he is unsure in which direction it will move. If he is correct, one of his options will expire worthless, but the other will be exercised (and have value). If he is wrong, the payoff from the option that ends up being exercised will not be enough to cover the expense of buying the options in the first place. LO: 1 Level: Basic Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

20.2

A writer (seller) of a call option may or may not actually own the underlying asset. If he or she owns the asset, and therefore will have the asset available to deliver should the option be exercised, he or she is said to be writing a covered call.

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Otherwise, he or she is writing a naked call and will have to buy the underlying asset on the open market should the option be exercised. Draw the payoff diagram of a covered call (including the value of the owned underlying asset) and compare it with the payoff of other options. Solution:

Value

Covered Call

Stock Price

A covered call has the same payoff shape as a put option, but it is shifted upward by the value of the strike price. This is equivalent to the combination of a put option and a riskfree bond. LO: 1 Level: Basic Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

20.3

An American option will never be worth less than a European option. Evaluate this statement.

Solution:

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This statement is true. An American option has all the rights that a European option has. In addition, it can be exercised on any date prior to the exercise date. Since these additional rights can never have a negative value, an American option will always be worth at least as much as a corresponding European option. LO: 1 Level: Basic Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

20.4

Explain why, in the binomial pricing theory, the probabilities of an upward move versus a downward move are not important.

Solution: The replicating portfolio calculated to value the option in this model will have the same value as the option whether the stock goes up or down. The probability of an up move could be 99 percent or 1 percent, and that would not change. The replicating portfolio is not determined by the likelihood of the two possibilities—only the option value in those two cases. That said, the value of the replicating portfolio (and therefore the option) is affected by the current stock price, which, presumably, would change with the probabilities of up or down stock price moves. LO: 2 Level: Basic Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

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Like all other models, the binomial pricing model is a simplification of reality. In this model, how do we represent high volatility or low volatility of the value of the underlying asset?

Solution: The difference between the high and low possible future prices represents volatility. If these two numbers are relatively close together, that represents low volatility of the value of the underlying asset. The further apart they are, the higher the volatility the model represents. LO: 2 Level: Basic Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

20.6

What kinds of real options should be considered in the following situations? a. Wingnuts R Us is considering two sites for a new factory. One is just large enough for the planned facility, while the other is three times larger. b. Carousel Cruises is purchasing three new cruise ships to be built sequentially. The first ship will commence construction today and will take one year to build. The second will then be started. Carousel can cancel the order for a given cruise ship at any time before construction begins.

Solution: a. Wingnuts R Us should consider the option to expand operations. b. Carousel should consider the option to abandon their order and not take delivery of the additional ships. LO: 3 Level: Basic Bloomcode: Analysis AASCP: Analytic

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20.7

Future Enterprises is considering building a factory that will include an option to expand operations in three years. If things go well, the anticipated expansion will have a value of $10 million and will cost $2 million to undertake. Otherwise, the anticipated expansion will have a value of only $1 million and will not take place. What information would we need in order to analyze this capital budgeting problem using the traditional NPV approach that we would not need using option valuation techniques?

Solution: In order to use traditional NPV techniques, we need to know the probability of “things going well” so that we can estimate the expected cash flows. We will also need to know how the performance of the overall economy affects these probabilities so that we can estimate an appropriate discount rate for the expected expansion cash flows. LO: 3 Level: Basic Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

20.8

Corporations frequently include employee stock options as a part of the compensation for their managers and sometimes for all of their employees. These options allow the holder to buy the stock of the company for a preset price like any other option, but they are usually very long lived, with maturities of 10 years. The goal of stock option plans is to align the incentives of employees with those of stockholders. What are the implications of these compensation plans for current stockholders?

Solution:

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Such plans have the effect of diluting the value of any gains in stock price. When the value of the firm goes up, the options will be exercised and the result will be more people with a claim on the same underlying assets. The value of each claim will be reduced. At the same time, the objective of the plans is to mitigate the agency problems associated with managers’ and employees’ incentives. Managers and employees who have been granted stock options have more to gain when the company does well. They are less likely to be too conservative when deciding which projects the company will pursue. If the stock option plans achieve their objective, the firm will be worth more than it would have been without the plan, and so there will be more wealth to split up. Finding a good trade-off between these effects is a challenge. LO: 1 Level: Intermediate Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

20.9

You own ABC Corp. bonds. Using option pricing theory, explain what agency concerns you would have if ABC were in danger of bankruptcy.

Solution: The equity of a firm can be thought of as a call option on the assets of the firm. If the firm is close to bankruptcy, you as a bondholder should be concerned that the company will take actions to increase the volatility of the assets by investing in highly risky projects, turn down positive-NPV projects, and, possibly, try to increase the dividend payouts. All of these actions can increase the value of the equity at the expense of the value of the debt holders. LO: 4 Level: Basic Bloomcode: Comprehension AASCP: Analytic

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20.10 A bond covenant is a part of a bond contract that restricts the behavior of the firm, barring it from taking certain actions. Using the terminology of options, explain why a bond contract might include a covenant preventing the firm from making large dividend payments to its stockholders. Solution: Cash on hand reduces the total volatility of the value of the firm. If any cash on hand is paid out to stockholders in the form of a large dividend payment, the volatility of the firm will increase and the value of the debt will decrease. In order to prevent this, bonds often feature covenants restricting the firm to dividend payments no larger than some fraction of current earnings. LO: 4 Level: Basic Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

20.11 How can the insurance policy on a car be viewed as an option? Solution: The insurance policy on a car can be viewed as a put option. In the extreme case, where your car is totaled, you have the right to put the car to the insurance company for its market value prior to the accident. LO: 5 Level: Basic Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance

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Questions and Problems BASIC 20.1

Option characteristics: What is an option?

Solution: An option is the right to buy or sell an asset at a pre-specified price on or before a prespecified date. LO: 1 Bloomcode: Knowledge AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

20.2

Option characteristics: Explain how the payoff functions differ for the owner (buyer) and the seller: (1) of a call option; (2) of a put option.

Solution: (1) Call option: When the value of the underlying asset is below the exercise price, the payoffs for both the buyer and seller of a call option are 0. Once the asset price goes above the exercise price, the payoff for the buyer increases dollar for dollar with the price of the underlying asset, while the payoff for the seller decreases dollar for dollar with the price of the underlying asset. The sum of the payoffs of the buyer and seller of a call option is always 0. (2) Put option: When the value of the underlying asset is above the exercise price, the payoffs for both the buyer and seller of a put option are 0. Once the asset price drops below the exercise Copyright © 2022 John Wiley & Sons, Inc.

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price, the payoff for the buyer increases dollar for dollar with decrease of the price of the underlying asset, while the payoff for the seller decreases dollar for dollar with decrease of the price of the underlying asset. The sum of the payoffs of the buyer and seller of a put option is always 0. LO: 1 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

20.3

Option payoffs: What is the payoff for a call option with a strike price of $50 if the stock price at expiration is $40? What if the stock price is $65?

Solution: If the stock price is $40, then the option will not be exercised and the option is worthless. (Why buy for $50 what you can buy in the market for $40?) If the stock price is $65, then the option is worth the difference between the price and the strike price: $65 – $50 = $15. LO: 1 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

20.4

Option payoffs: What is the payoff for a put option with a strike price of $50 if the stock price at expiration is $40? What if the stock price is $65?

Solution: If the stock price is $40, then the option is worth the difference between the strike price and the stock price: $50 – $40 = $10. If the stock price is $65, then the option is worthless. LO: 1 Bloomcode: Application

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20.5

Option valuation: What are the five variables that affect the value of an option, and how do changes in each of these variables affect the value of a call option?

Solution: The value of a call option increases as: (1) Current value of the underlying asset increases; (2) Exercise price decreases; (3) Volatility of the value of the underlying asset increases; (4) Time until the expiration of the option increases; or (5) Risk-free rate of interest increases. LO: 2 Bloomcode: Knowledge AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

20.6

Option valuation: Assuming nothing else changes, what happens to the value of an option as time passes and the expiration date gets closer?

Solution: The value of an option declines as time passes. LO: 2 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

20.7

Option valuation: What does the seller of a put option hope will happen?

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Solution: The seller of an option hopes the option will not be exercised. In this case, the option will be exercised if the asset value at expiration is lower than the strike price, so the seller hopes the asset value will rise (or at least will remain above the strike price). LO: 2 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

20.8

Option valuation: What is the value of a call option if the stock price is zero? What if the stock price is extremely high (relative to the strike price)?

Solution: If the stock price is zero, then there is no possibility that the stock will have positive value. Thus the option to buy the stock in the future is worthless. If the stock price is extremely high compared to the strike price, then there is essentially zero probability that the stock price will be below the strike price at expiration. The option will always be exercised, and the value of the option is the difference between the current stock price and the present value of the strike price. LO: 2 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

20.9

Option valuation: Like owners of stock, owners of options can lose no more than the amount they invested. They are far more likely to lose that full amount, but they cannot lose more. Do sellers of options have the same limitation on their losses?

Solution:

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No. The seller of a call option can lose a theoretically unlimited amount of money because the value of the underlying asset can go arbitrarily high. The seller of a put option is limited to losing the amount of the strike price (since that is how much they would lose if the stock price went to zero). LO: 2 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

20.10 Option valuation: What is the value at expiration of a call option with a strike price of $65 if the stock price is $1? $50? $65? $100? $1,000? Solution: The value of the option for any stock price less than $65 (including $1 and $50) is zero because the option would not be exercised. When the stock price is equal to the strike price ($65 in this case), the option owner does not care whether or not he exercises the option. He gains (or loses) nothing. Again, the option is worth zero. If the stock price is higher than the strike price, the option is worth the difference. If the stock is worth $100, the option is worth $35. If the stock is worth $1,000, the option is worth $935. LO: 2 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

20.11 Option valuation: Suppose you have an option to buy a share of ABC Corp. stock for $100. The option expires tomorrow, and the current price of ABC Corp. is $95. How much is your option worth? Solution:

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Your option is worth very slightly more than zero. There is little chance that the stock price will move above $100 by tomorrow, but the chance is not zero, so the option still has some value. LO: 2 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

20.12 Option valuation: You hold an American option to sell one share of Zyther Co. stock. The option expires tomorrow. The strike price of the option is $50, and the current stock price is $49. What is the value of exercising the option today? If you wanted to sell the option instead, about how much would you expect to receive? Solution: The value of exercising today is the difference between the strike price and the stock price: $50 – $49 = $1. If you sold the option, you should expect to receive slightly more than that. LO: 2 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

20.13 Real options: What is the difference between a financial option and a real option? Solution: The underlying asset of a financial option is a financial asset, while the underlying asset of a real option is a real asset like investment projects. LO: 3 Bloomcode: Analysis AASCP: Analytic

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20.14 Real options: List and describe four different types of real options that are associated with investment projects. Solution: Four types of real options are associated with investment projects: (1)

Options to defer investment: the ability to defer an investment decision until information on its future cash flows is less uncertain.

(2)

Options to make follow-on investments: the possibility to exploit future business opportunities that will not otherwise be available if the investment is not taken.

(3)

Options to change operations: the flexibility in changing operations as business conditions change if the investment is taken.

(4)

Options to abandon projects: the ability to terminate the project at a smaller loss if things do not go as well as anticipated.

LO: 3 Bloomcode: Knowledge AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

20.15 Agency costs: How are options related to the agency costs of debt and equity? Solution: Agency costs arise since the incentives of shareholders are different from those of the debt holders. Equity and debt claims are like different types of options on the firm. The payoff function for the stockholders looks exactly like that for the owner of a call option where the exercise price is the amount owed on the loan and the underlying asset is the firm itself. The payoff function for the lenders looks like that for the seller of a put option, where the exercise price is the amount of the loan and the underlying asset is the firm itself. The different payoff functions create different incentives for shareholders and debt

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holders. For example, shareholders are likely to pursue more risky projects. The increased volatility of cash flows increases the expected payout for the holder of a call option, the shareholder, and decreases the expected payout for the seller of a put option, the debt holder. LO: 4 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

INTERMEDIATE 20.16 Option valuation: Suppose that you own a call option and a put option on the same stock and that these options have the same exercise price. Explain how the relative values of these two options will change as the stock price increases or decreases. Solution: When stock prices increase, the value of the call option increases and the value of the put option decreases; when stock prices decrease, the value of the call option decreases and the value of the put option increases. The further the stock price is from the exercise price, the more valuable the combination of these options becomes. LO: 2 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

20.17 Other options: A callable bond is a bond that can be bought back by the bond issuer before maturity for some pre-specified price (normally a small amount above face value) at the discretion of the bond issuer. How would you go about finding the value of such a bond? Would the bond be worth more or less than an equivalent noncallable bond? Copyright © 2022 John Wiley & Sons, Inc.

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Solution: The purchaser of a callable bond is simultaneously selling the issuer a call option on that bond. The value would be equal to the value of the straight bond minus the value of the option. This is clearly less than the value of the (noncallable) bond by itself. LO: 2 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

20.18 Other options: A convertible bond is a bond that can be exchanged for stock at the discretion of the bondholder. How would you go about finding the value of such a bond? Would the bond be worth more or less than an equivalent nonconvertible bond? Solution: A convertible bond is equivalent to a combination of a nonconvertible bond and a call option on the stock, where the strike price of the option is the value of the bond. Because the value of the bond may change along with the value of the stock, this is not a straightforward problem, but the value would be equal to the value of the straight bond plus the value of the option. This is clearly more than the value of the (nonconvertible) bond by itself. LO: 2 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

20.19 Option valuation: The seller of an option can never make any money from a change in the value of the underlying asset; he or she can only hope that the option will not be exercised and that he or she will not lose any money. Given that this is the case, why do people sell options?

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Solution: Option writers receive the value of the option up front. The money the seller receives by selling the option is referred to as the call or put premium. This payment compensates them for the obligation they are taking on. LO: 2 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

20.20 Option valuation: The stock of Socrates Motors is currently trading for $40 and will either rise to $50 or fall to $35 in one month. The risk-free rate for one month is 1.5 percent. What is the value of a one-month call option with a strike price of $40? Solution:

Today

Expiration

Stock (X)

Risk-Free (Y)

Option

$40

???

$35

$50

$1.015

$10

These two equations define our portfolio: $10 = ($50 × X) + ($1.015 × Y) $0 = ($35 × X) + ($1.015 × Y) and the solution is X = 2/3 and Y = -$22.99. That is, we borrow $22.99 and buy twothirds of a share of Socrates Motors at a cost of $40.00 per share. The total net cost of this portfolio is $40.00 × (2/3) – 22.99 = $3.68 and this is the value of the option. LO: 2 Bloomcode: Application

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AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

20.21 Option valuation: Again assume that the price of Socrates Motors stock will either rise to $50 or fall to $35 in one month and that the risk-free rate for one month is 1.5 percent. How much is a call option with a strike price of $40 worth if the current stock price is $45 instead of $40? Solution: The replicating portfolio of X = 2/3 and Y = -$22.99 does not depend on the current stock price and so would not change. The value of that portfolio would now be $45 × (2/3) – $22.99 = $7.01 and this is the value of the option. LO: 2 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

20.22 Option valuation: Assume that the stock of Socrates Motors is currently trading for $40 and will either rise to $50 or fall to $35 in one month. The risk-free rate for one month is 1.5 percent. What is the value of a one-month call option with a strike price of $25? Solution:

Today

Expiration

Stock (X)

Risk-Free (Y)

Option

$40

???

$35

$50

$1.015

$10

$25

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These two equations define our portfolio: $25 = ($50 × X) + ($1.015 × Y) $10 = ($35 × X) + ($1.015 × Y) and the solution is X = 1 and Y = -$24.63. That is, we borrow $24.63 and buy 1 share of Socrates Motors at a cost of $40. The total net cost of this portfolio is $40 – $24.63 = $15.37, and this is the value of the option. LO: 2 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

20.23 Option valuation: You are considering buying a three-month put option on Wing and a Prayer Construction stock. The company’s stock currently trades for $10 per share and its price will either rise to $15 or fall to $7 in three months. The risk-free rate for three months is 2 percent. What is the appropriate price for a put option with a strike price of $9? Solution: If the stock rises to $15, then the option will not be exercised and its payoff will be $0. If the stock falls to $7, the option will be exercised and its value will be the difference between the strike price and the stock price, $2.

Today

Expiration

Stock (X)

Risk-Free (Y)

Option

$10

???

$15

$1.02

The formulas that define the replicating portfolio are:

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$2 = ($7 × X) + ($1.02 × Y) $0 = ($15 × X) + ($1.02 × Y) and the solution is X = -$0.25 and Y = $3.68. That is, we will short sell one-fourth of a share of the stock, receiving $2.5, and we will lend $3.68 at the risk-free rate. (Short selling is the process of borrowing an asset that you do not own and selling, with the promise that at some time in the future you will buy it back and return it to its owner.) The net cost is $3.68 – $2.50 = $1.18. This is the value of the option. LO: 2 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

20.24 Option valuation: You hold a European put option on Tubes, Inc., stock, with a strike price of $100. Things haven’t been going too well for Tubes. The current stock price is $2, and you think that it will either rise to $3 or fall to $1.50 at the expiration of your option. The appropriate risk-free rate is 5 percent. What is the value of the option? If this were an American option, would it be worth more? Solution: Note that this option will be exercised regardless.

Stock (X)

Risk-Free (Y)

Option

$2.0

???

Today

Expiration

$1.5

$3.0

$1.05

$98.5

$97

The formulas that define the replicating portfolio are: $98.5 = ($1.5 × X) + ($1.05 × Y)

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$97 = ($3 × X) + ($1.05 × Y) and the solution is X = –1 and Y = $95.24. That is, we will short sell 1 of a share of the stock, receiving $2, and we will lend $95.24 at the risk-free rate. The net cost is $95.24 – $2.00 = $93.24. This is the value of the (European) option. If this were an American option, we could exercise today if we wanted. We would want to do so if the value of exercising today was greater than the value of the option. Exercising today would allow us to sell for $100 something worth $2, a gain of $98. This is more than $93.24. The American option is worth more. LO: 2 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective 20.25 Other options: A golden parachute is a part of a manager’s compensation package that makes a large lump-sum payment in the event that the manager is fired (or loses his or her job in a merger, for example). Providing such payouts to managers seems ill advised to most people first hearing about it. Explain how a golden parachute can help reduce agency costs between stockholders and managers. Solution: Managers have incentives to avoid bankruptcy or even underperformance because the personal cost to them is quite high. As a result they may choose to avoid high risk investments even if those investments are highly positive NPV. The costs to the manager if the project goes badly outweigh the benefits if it goes well. However, stockholders want the manager to take positive-NPV projects, even if they are risky. Golden parachutes help to solve this problem by reducing the costs to the manager associated with poor performance or bankruptcy. The manager faces a payoff structure like the seller of an option. Golden parachutes serve to reduce the volatility of that option and therefore to reduce the value of that option. LO: 4

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Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

ADVANCED 20.26 Consider the following payoff diagram.

Covered Call

Value

$10

$40 $50 Stock price

$60

Find a combination of calls, puts, risk-free bonds, and stock that has this payoff. (You need not use all of these instruments, and there are many possible solutions.) Solution: One possible solution would consist of four options: (a) Buy a call with a strike of $50. (b) Buy a put with a strike of $50. (c) Sell a put with a strike of $40. (d) Sell a call with a strike of $60.

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If the stock price at expiration is below $40, then neither call will be exercised, but both puts will be. We will be forced to buy the stock for $40 because of option c, but we will be able to sell it for $50, using option b. Our net gain will be $10. If the stock price is between $40 and $50, the only option to be exercised will be option b, and we will gain the difference between $50 and the stock price. If the stock price is between $50 and $60, the only option to be exercised will be a call option and we will gain the difference between the stock price and $50. If the stock price is above $60, then neither put will be exercised, but both calls will be. We will be able to buy the stock for $50 using option a, but we will be forced to sell it for $60 by the owner of option d. Our net gain will be $10. LO: 1 Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

20.27 Consider the payoff structures of the following two portfolios: a. Buying a one month call option on one share of stock at a strike price of $50 and saving the present value of $50 (so that at expiration it will have grown to $50 with interest). b. Buying a one month put option on one share of stock at a strike price of $50 and buying one share of stock. What conclusion can you draw about the relation between call prices and put prices from a comparison of these two portfolios? Solution: The payoff of these two portfolios is identical. In the first case, if the stock price is below $50 at expiration, you will not exercise and you will be left with $50. If it is above $50, you will exercise and you will have a share of stock (whatever it is worth). In the second case, if the price is below $50, you will exercise your put option and get $50 for your

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share of stock. If it is above $50, you will not exercise and you will retain your share of stock (whatever it is worth). From this, we can see that the value of the two portfolios today must be the same. That is: P = C + Xe-rt – V where P is the value of the put option, C is the value of the call option, X is the exercise price, r is the risk-free rate, t is the amount of time before the option expires, and V is the current value of the underlying asset. The e term e-rt is the exponential function that you can calculate using the “ex” key on your calculator; it is simply a discount factor that assumes continuous compounding. If we know the value of a call (and the current stock price and interest rate), we can calculate the value of a put. This relation is call put-call parity. Note that this relation is not dependent on any option pricing model. LO: 2 Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

20.28 One way to extend the binomial pricing model is by including multiple time periods. Suppose Splittime, Inc., is currently trading for $100 per share. In one month, the price will either increase by $10 (to $110) or decrease by $10 (to $90). The following month will be the same. The price will either increase by $10 or decrease by $10. Notice that in two months, the price could be $120, $100, or $80. The risk-free rate is 1 percent per month. Find the value today of an option to buy one share of Splittime in two months for a strike price of $105. (Hint: To do this, first find the value of the option at each of the two possible one-month prices. Then use those values as the payoffs at one month and find the value today.) Solution: If the price of Splittime goes from $100 to $90 during the first month, then this option will never be exercised because the highest price to which Splittime could rise by two

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months is $100, which is lower than the strike price of $105. Therefore, the value of the option in the “down case” is $0. If the price rises to $110 in the first month, then the payoff of the option will be either $15 (if the price continues to rise to $120) or $0 (if the price falls back to $100).

One month

Expiration

Stock (X)

Risk-Free (Y)

Option

$110

???

$100

$120

$1.01

$15

These two equations define our portfolio: $15 = $120 × X + $1.01 × Y $0 = $100 × X + $1.01 × Y The solution is X = 0.75 shares and Y = -$74.26. The value of this portfolio, and therefore the value of the option at this point, is $8.24. (0.75 × $110 – $74.26). Now we are ready to calculate the value of the option today using $0 and $8.24 as the one-month option “payoffs.”

Today

One month

Stock (X)

Risk-Free (Y)

Option

$100

???

$90

$110

$1.01

$8.24

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The solution is X = 0.412 and Y = -$36.72. The portfolio value is$4.49, and this is the value of the option. LO: 2 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

20.29 SpinTheWheel Co. has assets currently worth $10 million in the form of one-year riskfree bonds that will return 10 percent. The company has debt with a face value of $5.5 million due in one year. (No interest payments will be made.) The stockholders decided to sell $8 million of the risk-free bonds and to invest the money in a very risky venture. This venture consists of giving Mr. William Kid the money now and, in one year, flipping a coin. If it comes up heads, Mr. Kid will pay SpinTheWheel $17.6 million. If it is tails, SpinTheWheel gets nothing. This investment has an NPV of zero. a. What is the value of the debt and equity before the stockholders make this “investment”? b. Using the binomial pricing model, with the payoff to the equity holders representing the option and the assets of the company representing the underlying asset, estimate the value of the equity after the stockholders make the investment. c. What is the new value of the debt after the investment? Solution: a. The firm is certain to have the $5.5 million owed to the debt holders in one year, so the correct discount rate for the debt is the risk-free rate, 10 percent. Thus the value today of the debt is the present value of the debt at the risk-free rate: $5.5 million / 1.1 = $5 million. The value of the equity is therefore $10 million – $5 million = $5 million. b. The payoffs of the option (the equity), the underlying (the firm), and the risk-free bond are:

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Firm

Risk-Free (Y)

Equity

$10 million

???

$2.2 million $19.8 million $1.1

$1.1

$14.3

Note that the payoff of $14.3 for the option in the up case comes from the $19.8 million less the $5.5 million they will pay the bondholders. In the down case, there is not enough money to pay the bondholders what they are owed, so the bondholders will receive the entire $2.2 million value of the firm and the equity holders get nothing. The equations are:

$14.3 = $19.8 × X + $1.1 × Y $0 = $2.2 × X + $1.1 × Y and the solution is X = 0.8125 and Y = -$1.625. The value of this portfolio is $6.5 million. This is the new value of the equity. c. The current value of the firm did not change (this was a zero NPV project) and remains at $10 million. If the equity has increased in value to $6.5 million, the debt has decreased in value to $3.5 million. LO: 4 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

20.30 The price of a stock that does not pay dividends is currently $35, and the risk-free rate is 4 percent. A European call option on the stock, with a strike price of $35 and which

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expires in six months, sells for $3.04. A European put option on the same stock with the same strike price sells for $2.35. Is there an arbitrage opportunity here? If so, what is it? Solution: To check whether there is an arbitrage opportunity, substitute the values into the put-call parity relation and see if it holds. P = C + Xe–rt – V $2.35 = $3.04 + $35e-(0.04) (6/12) - $35 Since the put-call parity relation holds, there is no arbitrage opportunity. LO: 1 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

20.31 Two call options have been written on the same underlying stock. Call #1 has a strike price of $42, and call #2 has a strike price of $52. Call #1 is selling for $5.00, and call #2 is selling for $6.00. What arbitrage opportunity do these prices present investors? Show the potential payoffs from this opportunity.

Option Value at Expiration

Solution: The payoff diagrams for the buyers of the two call options are as follows:

$20 $18 $16 $14 $12 $10 $8 $6 $4 $2 $0

$42 Call $52 Call

$28

$32

$36

$40

$44

$48

$52

$56

$60

Stock Price

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Notice that call #1 has a lower strike price and costs less. In a situation like this you can earn an arbitrage opportunity by purchasing the less expensive option (#1) and selling the more expensive (#2). The payoffs for this strategy are:

Buy $42 Call $0 $0 $0 $0 $0 $0 $0 $0 $2 $4 $6 $8 $10 $12 $14 $16 $18

Sell $52 Total Call Proceeds $6 $6 $6 $6 $6 $6 $6 $6 $6 $6 $6 $6 $6 $6 $6 $6 $6 $8 $6 $10 $6 $12 $6 $14 $6 $16 $4 $16 $2 $16 $0 $16 -$2 $16

$20

Option Value at Expiration

Stock Price $28 $30 $32 $34 $36 $38 $40 $42 $44 $46 $48 $50 $52 $54 $56 $58 $60

$42 Call

$15

$52 Call Total Proceeds

$10

$28

$32

$36

$40

$44

$48

$52

$56

$60

-$5 Stock Price

LO: 4 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

20.32 Husky Motors has two debt issues outstanding, both of which mature in five years. The senior debt issue, which has a face value of $10 million, must be paid in full before any of the principal for the junior debt issue is paid. The junior debt issue also has a face value of $10 million. Draw the payoff diagrams for Husky’s equity and both debt issues as the value of the firm changes. Under what circumstances would you expect to see conflicts between the senior and junior debt holders? Solution: The payoff functions are as follows:

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VD Senior

VF VD Junior

VF VE VF $10

$20

From these payoff functions you can see that there are likely to be conflicts between the senior and junior debt holders when the value of the firm is near or below $20 million. Below $20 million, the payoff function for the junior debt holder looks like that for the stockholders. This means that the junior debt holders will prefer riskier investments and strategies than the senior debt holders. These types of conflicts between lenders are quite common when a firm gets into financial distress. LO: 4 Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

20.33 The payoff function for the holder of straight debt looks like that for the seller of a put option. Convertible debt is straight debt plus a call option on a firm’s stock. How does the addition of a call option to straight debt affect the concern that lenders have about the asset substitution problem, and why? Solution:

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It mitigates this concern because the lenders will benefit through the call option from increased volatility in the value of the firm. How much a conversion option mitigates this concern depends on the specific characteristics of the option. LO: 2 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

Sample Test Problems 20.1

You own a call option on Pepsico stock with a strike price of $60 per share that expires in 60 days. The current market price of Pepsico stock is $63.50 per share. What are the limits on the value of the call option you own?

Solution: The value of a call option must be equal to or greater than zero. The option also cannot be worth less than the value that you would receive if you exercised it immediately, where the exercise price is computed using the present value of the $60 exercise price, discounted for 60 days at the risk free rate. LO: 1 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

20.2

Assume that the current market price of Montrose Industrials stock is $28 per share and will either rise to $38 per share or fall to $21 per share in one month. The risk-free rate for one month is 1 percent. What is the value of a one-month call option with a strike price of $24 per share?

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If the stock rises to $38, the option will be exercised and the payoff will be the $38 – $24 = $14. If the stock falls to $21, then the option will not be exercised and its payoff will be $0.

Today

Expiration

Stock (x)

Risk-Free (y)

Option

$28

???

$21

$38

$1.01

$14

The two equations define the replicating portfolio are: $14 = ($38 × x) + ($1.01 × y) $0 = ($21 × x) + ($1.01 × y) Solving for x and y yields x = 0.8235 and y = –$17.12. That is, we borrow $17.12 and buy 0.8235 of a share of Montrose Industrial stock at a cost of $28 per share. The total cost of this portfolio is ($28.00 × 0.8235) – $17.12 = $5.94, which is the value of the call option. LO: 2 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

20.3

The market value of General Motors stock is currently $53.73 per share, and the annual risk-free rate is 3 percent. A three-month call option on the stock with a strike price of $55 sells for $2.15. What is the value of a put option on General Motors stock that has the same strike price and expiration date if there are no arbitrage opportunities?

Solution: P = C + Xe–rt – V

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= $2.15 + $55e–(0.03)(3/12) – $53.73 = $3.01 LO: 2 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

20.4

Why is it hard to account for real options in an NPV analysis

Solution: The riskiness of a project with real options varies with time and the appropriate discount rate varies with risk. To account for real options in an NPV analysis, you must not only project future cash flows, but also the probability that the options will be exercised and the impact of these exercise decisions on the rate used to discount the cash flows. LO: 3 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

20.5

Fuel costs are a significant fraction of total costs in the airline industry. How might airline managers use options to manage fuel costs? What is the downside of doing this?

Solution: Airline managers can use options to reduce volatility in operating expenses (fuel costs) and therefore profitability. By purchasing call options on fuel, they can lock in fuel prices for at least some of their fuel purchases. This can reduce the impact of increases in fuel prices on profits. The downside of doing this is that if fuel prices go down, the options will expire worthless and yet the airlines will still incur the costs (the call premiums) of buying the options. LO: 5

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Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

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Chapter 19

Financial Planning and Forecasting Before You Go On Questions and Answers Section 19.1 1.

What are the four planning documents on which the financial plan is based? The four important planning documents are: (1) the strategic plan, which describes where the firm is headed and articulates the strategies that will be used to get it there; (2) the investment plan, which identifies the capital assets needed to execute the strategies; (3) the financing plan, which explains how the firm will raise the money to buy the assets; and (4) the cash budget, which determines whether the firm will have sufficient cash to pay its bills. These four planning documents provide the foundation for the firm’s financial plan, which consolidates the documents into a single scheme.

What is the strategic plan? The strategic plan is developed to communicate the firm’s long-term goals from a very high conceptual level. It is extremely important as the strategy of the firm ultimately drives all other decisions at the firm.

How are the investment decision and financing decision related? When a firm makes a decision to invest in some asset, it must also identify a source of funding to pay for it. Thus, these two decisions are intertwined and must be made together.

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Why is the sales forecast the key component of a financial model? Sales forecast is the key component in a financial model as the majority of data used are calculated as a percentage of sales. Hence, it is important to get as accurate a sales forecast as possible in order to build a meaningful model.

What are pro forma financial statements, and why are they an important part of the financial planning process? Pro forma financial statements are hypothetical statements that are projected into the future. They are then evaluated to determine which investment and under what conditions will be the most beneficial for the firm.

What is the plug value in a financial model? The plug value in a financial model is the amount of external financing needed by the firm to bring the balance sheet into balance.

Section 19.3 1.

How are historical financial data used to determine the forecasted values of balance sheet accounts? To forecast balance sheet values, the financial manager prepares a table that shows several years of historical accounting data as a percentage of sales. The financial manager can then fit some simple trend lines to the data to see what type of relationship exists between the variable and sales. This allows the forecaster to decide which financial accounts can safely be estimated as a percent of sales and which must be forecasted using other information.

Why might you expect accounts receivable to vary with sales? Accounts receivable can be expected to vary with sales since higher sales mean more money coming in, and hence increased level of receivables.

Section 19.4

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Why is it that some working capital accounts may not vary proportionately with sales? Working capital takes into account current assets and current liabilities, and in many instances inventories and cash balances do not proportionately change with sales. The working capital ratio often increases at a decreasing rate as sales increase.

What are lumpy assets, and how do these assets vary with sales? In most instances, fixed assets do not vary directly with sales, but are rather periodically added in large increments or lumps, hence the name “lumpy assets”.

Section 19.5 1.

What two factors determine the amount of EFN? The amount of EFN is determined by the difference between the total amount of new assets the firm needs to finance less the amount of internal financing available.

What is IGR, and why is it of interest to management? IGR stands for internal growth rate and is defined as the maximum growth rate a firm can achieve without external financing. IGR is of management interest, as firms that can generate a high volume of retained earnings and/or use fewer assets can sustain a higher growth rate without raising more capital.

If a firm continually exceeds its SGR, what problems may it face in the future? If the firm’s actual growth rate consistently exceeds its sustainable growth, the firm will have a cash shortage problem if it is unwilling to change its targeted capital structure or sell equity. If the firm has a high credit rating and its use of leverage is not excessive, the firm may have no problem going to the market and securing additional funds.

Self-Study Problems

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The Starlight, Inc. financial statements for the fiscal year ended June 30, 2021, are presented below. The firm’s sales are projected to grow at a rate of 20 percent next year, and all financial statement accounts will vary directly with sales. Based on that projection, develop a pro forma balance sheet and income statement for the fiscal year ending June 30, 2022. Starlight, Inc., Balance Sheet as of June 30, 2021 Liabilities and Stockholders’ Equity:

Assets: Cash

$ 25,135

Accounts payables

Accounts receivables

43,758

Inventories

167,112

Total current assets

$236,005

Total current liabilities

$104,309

Net fixed assets

325,422

Long-term debt

223,125

Other assets

13,125

Common stock

150,000

Retained earnings

97,118

Total assets

$574,552

Notes payables

$ 67,855

Total liabilities and equity

36,454

$574,552

Starlight, Inc. Income Statement for the Fiscal Year Ended June 30, 2021 Net Sales Costs EBITDA Depreciation EBIT Interest EBT

$1,450,000 812,500 $ 637,500 175,000 $ 462,500 89,575 $ 372,925

Taxes (35%)

130,524

Net income

$ 242,401

Solution: The pro forma statements for Starlight are as follows:

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Starlight, Inc. Balance Sheet as of June 30, 2022 Liabilities and Stockholders’ Equity:

Assets: Cash

$ 30,162 Accounts payables

$ 81,426

Accounts receivables

52,510 Notes payables

43,745

Inventories

200,534

Total current assets

$283,206 Total current liabilities

$125,171

Net fixed assets

390,506 Long-term debt

267,750

Other assets

15,750 Common stock

180,000

Retained earnings Total assets

$689,462

Total liabilities and equity

116,542 $689,462

Starlight, Inc. Income Statement for the Fiscal Year Ended June 30, 2022

Net Sales Costs EBITDA Depreciation

19.2

$1,740,000 975,000 $ 765,000 210,000

EBIT

$ 555,000

Interest

107,490

EBT

$ 447,510

Taxes (35%)

156,629

Net income

$ 290,882

Use the financial information for Starlight from Problem 19.1. Assume now that equity accounts do not vary directly with sales but change when retained earning change or new equity is issued. The company pays 45 percent of its income as dividends every year. In addition, the company plans to expand production capacity by building a new facility that will cost $225,000. The firm has no plans to issue new equity this year. Any funds that need to be raised will be in the form of long-term debt. Prepare a pro forma balance sheet using this information.

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Solution: The pro forma income statement is the same as that shown in the solution to Problem 19.1. We now have to accommodate the payment of dividends. Since the company pays 45 percent of its net income as dividends, the amount of retained earnings is calculated as follows: Retained earnings from 2022 income statement = $290,882 × (1 - 0.45) = $159,985 ▪

This is the amount by which retained earnings will increase in 2022, from $97,118 to $257,103.

▪

No new equity is added.

▪

The increase in assets is financed externally through the sale of long-term debt.

The pro forma balance sheet is as follows: Starlight, Inc. Balance Sheet as of June 30, 2022 Liabilities and Stockholders’ Equity:

Assets: Cash

$ 30,162 Accounts payables

$ 81,426

Accounts receivables

52,510 Notes payables

43,745

Inventories

200,534

Total current assets

$283,206 Total current liabilities

$125,171

Net fixed assets

390,506 Long-term debt

382,188

Addition to fixed assets

225,000 Common stock

150,000

Other assets

15,750 Retained earnings

257,103

Total assets

19.3

$914,462

Total liabilities and equity

$914,462

Use the financial statements from Problem 19.1 and the information from Problem 19.2 to calculate the company’s retention(plowback) ratio, external funds needed (EFN), internal growth rate (IGR) and sustainable growth rate (SGR).

Solution: The retention (plowback) ratio, external funds needed, internal growth rate, and sustainable growth rate are calculated as follows:

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Addition to retained earnings Net income $159,985 = $290,882 = 0.55, or 55%

Retention (plowback) ratio =

= (Growth rate × Initial assets) – Addition to retained earnings

EFN

= (0.20 × $574,552) ─ $159,985 = ─ $45,075 Thus, without considering the investment of $225,000 for the new facility, the firm will not need any external financing. However, if you add that in, then, = New investments – Addition to retained earnings

EFN

= (0.20 × $574,552) + $225,000 ─ $159,985 = $179,925 Addition to retained earnings Initial total assets $159,985 = $574,552 = 0.278 or 27.8%

IGR =

SGR = Plowback ratio× ROE Addition to retained earnings Net income = × Net income Total equity = 0.55× 0.7145 = 0.393 or 39.3%

19.4

Northwood Corp. has a dividend payout ratio of 60 percent, return on equity of 14.5 percent, total assets of $11,500,450, and equity of $4,652,125. Calculate the firm’s internal rate of growth (IGR).

Solution: We calculate Northwood’s internal growth rate as follows: IGR = Plowback ratio × ROE × Measure of leverage $4,652,125 $11,500, 450 = 0.235 or 2.35%

= 0.40×0.145×

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Renewal Company has net income of $1.25 million and a dividend payout ratio of 35 percent. It currently has equity of $2,875,223. What is the firm’s sustainable growth rate?

Solution: Renewal’s sustainable growth rate is: SGR = Plowback ratio × ROE $1, 250,000 $2,875, 223 = 0.283 or 28.3%

= 0.65×

Discussion Questions 19.1

What is financial planning? What four types of plans/budgets are involved in financial planning? Financial planning is the process by which a company’s management identifies the best investment opportunities from a strategic perspective and determines how to finance these investments. The end result is referred to as a financial plan. The four plans in financial planning are the strategic plan, the investment plan or capital budget, the financing plan, and the cash budget.

LO: 1 Level: Basic Bloomcode: Knowledge AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

19.2

Why is the capital budget an important part of a firm’s financial planning? The investment plan, also known as the capital budget, lays out the firm’s proposed spending on capital assets for the year. The capital budget describes in detail all the firm’s planned spending on productive assets like plant and equipment, a new production line, etc.

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Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

19.3

Why do financing and investment decisions have to be made concurrently? Any investment decision has to be linked to a source of funds to pay for the investment or any capital expenditures, and hence the investment decision and the financing decision have to be made concurrently.

LO: 1 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

19.4

Explain how sales can be used to develop pro forma financial statements. For most financial planning models, the principal input variable is a forecast of the firm’s sales or sales growth rate. The forecasted sales can be the basis for a financial planning model because so many items on the income statement and balance sheet vary with changes in the level of sales. Sales forecasts are given for some time period, such as a quarter or a year, and are often expressed as percent change in sales: % ∆S = (St+1 –St)/ St

LO: 2 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Budget Preparation AICPA: Industry/Sector Perspective

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Why is sales not always a good measure to use in forecasting fixed assets? When a percent of sales method is used to prepare pro forma financial statements, the issue of whether or not a firm is operating at full capacity is ignored. Only if the firm is operating at full capacity does fixed assets vary directly with sales. If a firm has excess capacity, then sales can increase without a need to invest in additional fixed assets.

LO: 3 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Budget Preparation AICPA: Industry/Sector Perspective

19.6

List all the accounts that can be affected by the “plug” value. How does this value help managers? The plug value relates to the amount of external funds needed based on a given level of sales. Thus, all the various sources of funds for a firm like short-term and long-term debt, common equity, and retained earnings are affected by the plug value.

LO: 2 Level: Basic Bloomcode: Knowledge AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

19.7

Explain why the fixed asset account may or may not vary with sales. By definition, fixed assets are a fixed cost in the short run. Generally, companies invest in fixed assets in large discrete amounts rather than in small, continuous amounts. Thus, each investment in fixed assets can accommodate a further growth in sales without calling for additional investment in plant and equipment. Only after each level of sales is accomplished at full production capacity would management have to consider another increase in fixed assets.

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LO: 3 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

19.8

How does the dividend payout ratio affect the amount of funds needed to finance growth? Any change in the dividend payout ratio directly affects the amount of funds retained by the company. The higher the firm’s dividend payout ratio for a given level of net income, the lower the amount of retained earnings, and hence a larger amount of external debt financing would be needed by the firm.

LO: 5 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: FSA AICPA: Industry/Sector Perspective

19.9

Define internal growth rate (IGR). Identify the characteristics of a high-growth firm that has no external funds needed. Internal growth rate (IGR) is the maximum growth rate a firm can sustain without needing any external financing. Such firms have a high enough retention ratio to fund growth, generate a high level of net income for every dollar of equity than other firms, and use low amounts of leverage or debt financing.

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AICPA: Industry/Sector Perspective

19.10 What is the sustainable growth rate? Why is it important? Sustainable growth rate (SGR) is the maximum growth rate a firm can sustain without needing any external equity financing, holding leverage constant. Holding the firm to a sustainable growth rate allows the firm to avoid costly equity issues, thus reducing the dilution of earnings. Whenever firms grow faster than the SGR, the firm is going to need external financing and may have to resort to debt financing, which increases the company’s risk. LO: 5 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: FSA AICPA: Industry/Sector Perspective

Questions and Problems BASIC 19.1

Strategic plan: Explain the importance of the strategic plan.

Solution: The strategic plan is the blueprint for a company’s management that determines the firm’s long-term goals, identifies the strategies to achieve these goals, and determines the company’s ability to be competitive. It drives all decision making within the firm and covers all areas of a firm’s operations. LO: 1 Bloomcode: Comprehension AASCB: Analytic IMA: Strategic Planning Copyright © 2022 John Wiley & Sons, Inc.

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AICPA: Industry/Sector Perspective

19.2

Capital budget: What are the various steps in preparing a capital budget?

Solution: First, management identifies all strategically acceptable investment opportunities and ranks them based on their contribution to shareholder wealth. Next, the senior management reviews the capital budget plan and may revise it, if necessary, based on need and the amount they can finance. LO: 1 Bloomcode: Knowledge AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

19.3

Financing plan: What are the elements of a financing plan?

Solution: First, the financing plan identifies the amount of external financing needed and where the funds could be obtained from. Second, the plan identifies the firm’s target capital structure. Last, the plan identifies the firm’s dividend policy, which directly affects the amount of funds available for new investment projects, the more funds the firm payout as cash dividends, the more the external funding needed for its investment. LO: 1 Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

19.4

Financial planning: Identify the steps in the financial planning process.

Solution: o

Establish a set of strategic goals.

Identify the investment opportunities and financing alternatives.

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Solutions Manual

Employ a financial planning model.

Evaluate the investment and financing choices and decide on the ones that are the best fit for the firm.

Prepare contingency plans for future use.

LO: 1 Bloomcode: Knowledge AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

19.5

Financial modeling: List the various elements of financial modeling.

Solution: The important elements of financial modeling are the sales forecast, economic assumptions, pro forma statements, investment decisions, financing requirements, and the “plug factor” that determines the source of the external funds needed. LO: 2 Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

19.6

Payout ratio: Define the retention (plowback) ratio and the dividend payout ratio.

Solution: The dividend payout ratio tells us how much of a firm’s earnings are paid to the shareholders as dividends. The retention ratio is complementary to the payout ratio and tells us how much of the firm’s earnings are retained in the firm. Thus, the retention ratio equals: Retention ratio = (1 − Dividend payout ratio)

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IMA: FSA AICPA: Industry/Sector Perspective

19.7

Addition to retained earnings: Northwood, Inc., has revenue of $455,316, costs of $316,487, and a tax rate of 31 percent. If the firm pays out 45 percent of its earnings as dividends every year, how much earnings are retained and what is the firm’s retention ratio?

Solution: Revenue = $455,316

Costs = $316,487

Tax rate = 31%

Payout ratio = 45%

Net income = ($455,316 - $316,487) × (1 – 0.31) = $95,792 Retained earnings = $95,792  (1 − 0.45) = $52, 686 Retention ratio = (1 − Dividend payout ratio) Retention ratio = (1 − 0.45) = 55%

LO: 3 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Industry/Sector Perspective

19.8

Payout and retention ratio: Goodwin Corp. has revenues of $12,112,659, costs of $9,080,545, interest payments of $412,375, and a tax rate of 27 percent. It paid dividends of $1,025,000 to its stockholders. What are the firm’s dividend payout ratio and retention ratio? Solution: Goodwin Corp.

$12,112,659 9,080,545 $ 3,032,114 412,375 $ 2,619,739 SM 19-15

Fundamentals of Corporate Finance, 5th edition

Solutions Manual

Taxes (27%) Net income

707,330 $1,912,409

Dividends paid = $1,025,000 Dividends $1,025,000 = = 53.60% Net income $1,912, 409 Retention ratio = (1 − Dividend Payout ratio) = (1 − 0.5360) = 46.40%

Dividend payout ratio =

LO: 3 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Industry/Sector Perspective

19.9

Percent of sales: Cattail Corporation’s financial statements for the fiscal year just ended are shown below: Cattail Corporation Financial Statements for Fiscal Year Just Ended ($ thousands) Income Statement Net sales Costs Net income

Balance Sheet $1,500

Assets

$700

350

Debt

$600

Equity 100

$1,150

Total

$700

Total $700

Cattail management expects sales to increase by 14 percent next year. Assume that the financial statement accounts vary directly with changes in sales and that management has no financing plan at this time. Given this information, develop a pro forma income statement for Cattail for the next fiscal year. Solution: Projected sales = $1,500,000 × 1.14 = $1,710,000 Projected costs = $350,000 × 1.14 = $399,000

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Net sales

$1,710

Costs

399

Net income

$1,311

LO: 3 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Industry/Sector Perspective

19.10 Percent of sales: Given the data for Cattail Corporation in Problem 19.9, if you assume that all balance sheet items also vary with the change in sales, develop a pro forma balance sheet for Cattail for the next fiscal year. Assuming that the firm did not sell or repurchase stock, what is the cash dividend implied by the pro forma income statement and balance sheet? Solution: Projected assets = $700,000 × 1.14 = $798,000 Projected debt = $600,000 × 1.14 = $684,000 Projected equity = $100,000 × 1.14 = $114,000

Cattail Corporation Pro Forma Income Statement ($ thousands) Balance Sheet Assets

Total

$798

Debt

$684

Equity

$114

Total

$798

Pro forma net income is $1,311,000 and the change in the equity account is $14,000, therefore the difference ($1,311,000 - $14,000 = $1,297,000) is the amount of the cash dividends that must have been paid. LO: 3 Bloomcode: Application Copyright © 2022 John Wiley & Sons, Inc.

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AASCB: Analytic IMA: FSA AICPA: Industry/Sector Perspective

19.11 Capital intensity ratio: Define capital intensity ratio, and explain its significance. Solution: The capital intensity ratio measures the amount of assets needed to generate one dollar in sales. The higher the ratio, the more assets are needed to generate every dollar of sales, and hence, the more capital intense is the firm and vice versa. LO: 3 Bloomcode: Knowledge AASCB: Analytic IMA: FSA AICPA: Industry/Sector Perspective

19.12 Capital intensity ratio: Tantrix Confectioners has total assets of $3,257,845 and net sales of $5,123,951. What is the firm’s capital intensity ratio? Solution: Total assets = $3,257,845

Sales = $5,123,951

Total assets Net sales $3,257,845 = = 63.6% $5,123,951

Capital intensity ratio =

LO: 3 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Industry/Sector Perspective

19.13 Capital intensity ratio: McDonald Metal Works has been able to generate net sales of $13,445,196 on assets of $9,145,633. What is the firm’s capital intensity ratio? Solution: Copyright © 2022 John Wiley & Sons, Inc.

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Sales = $13,445,196 Total assets = $9,145,633

Total assets Net sales $9,145, 633 = = 0.6802 or 68.02% $13, 445,196

Capital intensity ratio =

LO: 3 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Industry/Sector Perspective

19.14 Capital intensity ratio: For McDonald Metal Works in Problem 19.13, how much must net sales grow if the capital intensity ratio has to drop to 60 percent? State your answer as both a percent of sales and a dollar sales increase. Solution: Target capital intensity ratio = 60%

Total assets Net sales $9,145,633 0.60 = Net sales $9,145,633 Net sales = = $15,242,721.67 0.60

Capital intensity ratio =

Growth in net sales needed

= New sales – Old sales

= $15,242,722 – $13,445,196 = $1,797,526 Percentage change in net sales needed = $1,797,526 / $13,445,196 = 13.37% LO: 3 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Industry/Sector Perspective

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Solutions Manual

19.15 Internal growth rate: Swan Supply Company has net income of $1,212,335, assets of $12,522,788 and retains 70 percent of its income every year. What is the company’s internal growth rate? Solution: Net income = $1,212,335 Total assets = $12,522,788 Plowback ratio = 70% Internal growth rate (IGR) = Plowback ratio  ROE  Measure of Leverage = Plowback ratio 

Net income Equity  Equity Total assets

= Plowback ratio 

Net income Total assets

= 0.70 

$1,212,335 $12,522,788

= 6.8%

IGR = Addition to retained earnings/Initial total assets Addition to retained earnings= 70% × $1,212,335=$ 848,634.5 So, IGR = $ 848,634.5/$12,522,788 = 6.8% LO: 5 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Industry/Sector Perspective

19.16 Sustainable growth rate: If Newell Corp. has a ROE of 13.7 percent and a dividend payout ratio of 32 percent, what is its sustainable growth rate? Solution: ROE = 13.7% Payout ratio = 32% Plowback ratio = (1 − Payout ratio) = (1 − 0.32) = 68%

SGR = Plowback ratio × ROE = 0.68 × 0.137

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Solutions Manual

= 9.3% LO: 5 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Industry/Sector Perspective

19.17 EFN and growth: Refer to Exhibits 19.10 and 19.11 in the text. The EFN for several growth rates for Empire Enterprises are as follows: Growth Rate (%)

EFN ($ millions)_

-$4.8

-2.3

9.6

0.0

0.2

2.7

5.2

Check the calculations and plot the line to replicate the graph in Exhibit 19.11. Solution: Exhibit 19.11 gives you the plot. LO: 5 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Industry/Sector Perspective

INTERMEDIATE 19.18 Retention ratio: Refer to Problem 19.7. Northwood expects to increase its sales by 15 percent next year. All costs vary directly with sales. If Northwood wants to retain

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Solutions Manual

$65,000 of earnings next year, will it have to change its dividend payout ratio? If so, what will be the new dividend payout and retention ratios for the firm? Solution: Expected increase in sales = 15% All costs vary directly with sales Revenues next year = $455,316  (1.15) = $523,613 Costs = $316, 487  (1.15) = $363,960 EBT = $159, 653 Net income = $159, 653  (1- 0.31) = $110,161

Targeted retained earnings = $65,000 Retention ratio = $65,000/$110,161 = 59.0% Dividend payout ratio = (1 – 0.59) = 41% So, the dividend payout ratio declines from 45 percent to 41 percent. LO: 3 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Industry/Sector Perspective

19.19 Capital intensity: Identify two industries (other than airlines) that are capital intensive. Using online or other data sources, compute the capital intensity ratio for the largest firm in each of the chosen industries. Solution: Two industries that may be considered to be capital intensive are the electric utilities industry and the aluminum processing industry. There may be others as well. LO: 3 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Industry/Sector Perspective

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19.20 Percent of sales: Tomey Supply Company’s financial statements for the most recent fiscal year are shown below. The company management projects that sales will increase by 20 percent next year. Assume that all costs and assets increase directly with sales. The company has a constant 33 percent dividend payout ratio and has no plans to issue new equity. Any financing needed will be raised through the sale of long-term debt. Prepare pro forma financial statements for the coming year based on this information, and calculate the EFN for Tomey. Tomey Supply Company Income Statement and Balance Sheet Income Statement Balance Sheet Net sales $1,768,121 Assets: Costs 1,116,487 Current assets $280,754 EBT $651,634 Net fixed assets 713,655 Taxes (28%) 182,458 Total assets $994,409 Net income $ 469,176 Liabilities and Equity: Current liabilities $167,326 Long-term debt 319,456 Common stock 200,000 Retained earnings 307,627 Total liabilities and equity $994,409 Solution: Tomey Supply Company Net sales Costs EBT Taxes (28%) Net income Dividends paid Addition to retained earnings

Multiplication Factor $1,768,121 1.2 1,116,487 1.2 $ 651,634 182,458 $ 469,176

Pro Forma $2,121,745 1,339,784 $ 781,961 218,949 $ 563,012 185,794 $377,218

Assets: Current assets Net fixed assets Total assets

$ 280,754 713,655 $ 994,409

1.2 1.2

$ 336,905 856,386 $1,193,291

Liabilities and Equity: Current liabilities

$ 167,326

1.2

$ 200,791

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Fundamentals of Corporate Finance, 5th edition

Long-term debt Common stock Retained earnings Total liabilities & equity

Solutions Manual

319,456 200,000 307,627 $ 994,409

107,655 200,000 684,845 $1,193,291

EFN = (Initial assets  Growth rate) − Addition to retained earnings = ($994, 409  0.20) − $377,218 = −$178,336 Addition to current liabilities = $33,465 So, actual EFN = –$178,336 – $33,465 = –$211,801

Since EFN is negative, our pro forma level of long-term debt will decline. LO: 3 Bloomcode: Application AASCB: Analytic IMA: Budget Preparation AICPA: Industry/Sector Perspective 19.21 Internal growth rate: Using the pro forma financial statements for Tomey Supply Company developed in Problem 19.20, find the internal growth rate for Tomey. Solution: IGR = Addition to retained earnings / Initial total assets = $377,218/$994, 409 = 0.3793 or 37.93% LO: 5 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Industry/Sector Perspective 19.22 Sustainable growth rate: Use the following pro forma information for Tomey Supply Company for next year: net income = $563,012; addition to retained earnings = $377,218; common equity = $884,845; net sales = $2,121,745. Assume that management does not want the ratio of long-term debt to equity to exceed the current long-term debtto-equity ratio of 63 percent and also does not want to issue new equity. What level of sales growth can Tomey Supply Company sustain? Calculate the new sales at this level of sustainable growth. Solution: Current debt to equity ratio = 63% Sustainable growth rate (SGR) = Plowback ratio × ROE Copyright © 2022 John Wiley & Sons, Inc.

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Fundamentals of Corporate Finance, 5th edition

SGR =

Solutions Manual

Addition to retained earnings Net income  Net income Total equity

$377,218 $563,012  $563,012 $884,845 = 42.63%

New sales level = Old sales  (1 + SGR) = $2,121,745  (1.4263) = $3,026,245

LO: 5 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Industry/Sector Perspective 19.23 Sustainable growth rate: Rowan Company has a net profit margin of 8.3 percent, debt ratio of 45 percent, total assets of $4,157,550, and sales of $6,852,654. If the company has a dividend payout ratio of 67 percent, what is its sustainable growth rate? Solution: Net profit margin = 8.3% Debt ratio = 45% Total assets = $4,157,550 Sales = $6,852,654 Dividend payout ratio = 67% Plowback ratio = (1 − 0.67) = 33% Net profit margin =

Net income Sales

Net income = Sales × Net profit margin = $6,852,654 × 0.083 = $568,770 Measure of Leverage = 1- Debt ratio = (1- 0.45) = 55% Total equity = 0.55  $4,157,550 = $2, 286, 653

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Fundamentals of Corporate Finance, 5th edition

SGR =

Solutions Manual

Net income × Plowback ratio Total equity

$568, 770 × 0.33 $2, 286, 653 = 8.2%

LO: 5 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Industry/Sector Perspective

19.24 Sustainable growth rate: Refer to the information for Rowan Company in Problem 19.23. The firm’s management desires a sustainable growth rate (SGR) of 10 percent but does not wish to change the company’s level of debt or its payout ratio. What will the firm’s new profit margin have to be in order to achieve the desired growth rate? Solution: Target SGR = 10% Plowback ratio = 33% Debt ratio = 45% Equity multiplier = EM =

1 1 = = 1.82 Equity (1 − 0.45)

Total assets turnover ratio = TATO = ROE =

Sales $6,852,654 = = 1.65 Times Total assets $4,157,550

SGR 0.10 = = 30.3% Plowback ratio 0.33

ROE = PM ×TATO× EM Net profit margin = PM =

ROE 0.303 = = 10.1% TATO× EM (1.65×1.82)

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AICPA: Industry/Sector Perspective

19.25 Sustainable growth rate: Rocky Sales, Inc., has current sales of $1,215,326 and net income of $211,253. It also has a debt ratio of 25 percent and a dividend payout ratio of 75 percent. The company’s total assets are $712,455. What is its sustainable growth rate? Solution: Sales = $1,215,326 Net income = $211,253 Debt ratio = 25% Dividend payout ratio = 75% Total assets = $712,455

Plowback ratio = (1- 0.75) = 25% Equity ratio or Measure of leverage = (1- 0.25) = 75% Total equity = 0.75  Total assets = 0.75  $712,455 = $534,341 ROE =

Net income $211,253 = = 39.5% Total equity $534,341

SGR = Plowback ratio  ROE = 0.25  0.395 = 9.9% LO: 5 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Industry/Sector Perspective

19.26 Sustainable growth rate: Ellicott Textile Mills management has reported the following financial information for the year ended September 30, 2021. The company generated a net income of $915, 366 on a net profit margin of 6.4 percent. It has a dividend payout ratio of 50 percent, a capital intensity ratio of 62 percent, and a debt ratio of 45 percent. What is the company’s sustainable growth rate?

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Fundamentals of Corporate Finance, 5th edition

Solutions Manual

Solution: Net income = $915,366 Net profit margin = 6.4% Dividend payout ratio = 50% Capital intensity ratio = 62% Debt ratio = 45%

Net income $915,366 = = $14, 302,594 Profit margin 0.064 Total assets Capital intensity ratio = Sales

Sales =

Total Assets = Capital intensity ratio ×sales = 0.62 ×$14,302,594 = $8,867,608

Equity = (1- Debt ratio) × Total assets (1- 0.45) ×$8,867,608 = $4, 877,184

ROE =

Net income $915,366 = = 18.8% Total equity $4,877,184

SGR = Plowback ratio  ROE = 0.50  0.188 = 9.4% LO: 3, 5 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Industry/Sector Perspective

19.27 Internal growth rate: Given the information in Problem 19.26, what is the internal growth rate of Ellicott Textile Mills? Solution:

IGR = Plowback ratio  ROA = 0.50 

$915,366 = 5.2% $8,867,608

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LO: 5 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Industry/Sector Perspective

19.28 Internal growth rate: Fantasy Travel Company has a return on equity of 17.5 percent, a total equity/total assets ratio of 65 percent, and a dividend payout ratio of 75 percent. What is the company’s internal growth rate? Solution: ROE = 17.5% Equity ratio = 65% Dividend payout ratio = 75% Plowback ratio = (1 - 0.75) = 25%

IGR = Plowback ratio  ROE  Measure of Leverage = 0.25  0.175  0.65 = 2.8% LO: 5 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Industry/Sector Perspective

19.29 EFN: Maryland Micro Brewers generated revenues of $12,125,800 with a 72 percent capital intensity ratio during the year ended September 30, 2021. Its net income was $873,058. With the introduction of a half dozen new specialty beers, management expects to grow sales by 15 percent next year. Assume that all costs vary directly with sales and that the firm maintains a dividend payout ratio of 70 percent. What will be the EFN needed by this firm? If the company wants to raise no more than $750,000 externally and is not averse to adjusting its payout policy, what will be the new dividend payout ratio?

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Solution: Total sales = $12,125,800 Capital intensity ratio = 72% Total assets = Capacity intensity ratio×Sales = 0.72×$12,125,800 = $8,730,576

Net income = $873,058 Projected net income =$873,058 x 1.15 =$1,004,017 Dividend payout ratio = 70% Addition to retained earnings = $1,004,017(1-0.7) = $301,205

EFN = (Growth rate×Total assets) - Addition to retained earnings = (0.15×$8, 730,576) − $301, 205 = $1, 008,381 Target EFN = $750,000

Addition to retained earnings = (Growthrate  Total assets)- EFN = (0.15  $8,730,576) − $750,000 = $559,586

Plowback ratio =

$559,586 = 55.73% $1, 004 , 017

Dividend payout ratio = (1- Plowback ratio) = (1- 0.5573) = 44.27%

LO: 5 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Industry/Sector Perspective

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19.30 EFN: Ritchie Marble Company has total assets of $12,899,450, sales of $18,174,652, and net income of $4,589,774. Management expects sales to grow by 25 percent next year. All assets and costs (including taxes) vary directly with sales, and management expects to maintain a payout ratio of 65 percent. Calculate Ritchie’s EFN. Solution: Total assets = $12,899,450 Sales = $18,174,652 Net income = $4,589,774 Expected growth rate = 25% Projected net income = $4,589,774 (1.25) = $5,737,217.50 Payout ratio = 65% Addition to retained earnings = Net income ×(1- Payout ratio) = $5,737,217.50 ×0.35 = $2,008, 026.13 EFN = (Growth rate × Total assets) - Addition to retained earnings = (0.25×$12,899,450) - $2,008,026 = $1, 216,836

LO: 5 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Industry/Sector Perspective

19.31 EFN: Norton Group, Inc., expects to add $1,213,777 to retained earnings and currently has total assets of $23,159,852. If the company has the ability to borrow up to $1 million, how much growth can the firm support if it is willing to borrow to its maximum capacity? Solution: Addition to retained earnings = $1,213,777 Total Assets = $23,159,852 EFN = $1,000,000

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Solutions Manual

EFN + Addition to retained earnings Total assets $1,000,000 + $1, 213,777 = = 9.6% $23,159,852

Growth rate =

LO: 5 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Industry/Sector Perspective

19.32 EFN: Capstone Marketing Group has total assets of $5,568,000, sales of $3,008,725, and net income of $822,000. The company expects its sales to grow by 12 percent next year. All assets and costs (including taxes) vary directly with sales, and the firm expects to maintain a payout ratio of 55 percent. Calculate Capstone’s EFN. Solution: With a growth rate in sales of 12 percent, if all costs increase at the same rate, then pro forma net income will be: $822,000 × 1.12 = $920,640. Addition to retained earnings = (1 ─ 0.55) × $920,640 = $414,288 EFN = (0.12 × $5,568,000) – $414,288 = $253,872 LO: 5 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Industry/Sector Perspective

19.33 Maximum sales growth: Given the data for Capstone Marketing Group in Problem 19.32, what would Capstone’s payout ratio have to be for the firm’s EFN to be zero? Solution: EFN will be equal to zero if the change in assets is equal to the change in retained earnings. Projected net income = $822,000 × 1.12 = $920,640 Copyright © 2022 John Wiley & Sons, Inc.

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Projected change in assets = 0.12 × $5,568,000 = $668,160 $668,160 = $920,640 × (1 – payout ratio) Payout ratio = 0.274, or 27.4% LO: 5 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Industry/Sector Perspective

19.34 Maximum sales growth: Rockville Consulting Group expects to add $271,898 to retained earnings this year. The company has total assets of $3,425,693 and wishes to add no new external funds for the coming year. If assets and costs vary directly with sales, how much sales growth can the company support while retaining an EFN of zero? What is the firm’s internal growth rate? Solution: Addition to retained earnings = $271,898 Total assets = $3,425,693 EFN = 0

(EFN + Addition to retained earnings) Total assets (0 + $271,898) = = 7.9% $3, 425,693)

Maximum growth rate =

IGR =

Addition to retained earnings $271,898 = = 7.9% Initial assets $3, 425,693

With no external financing, the maximum possible growth equals the internal growth rate. LO: 5 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Industry/Sector Perspective

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ADVANCED 19.35 The financial statements for the year ended June 30, 2021, are given below for Morgan Construction Company. The firm’s sales are projected to grow at a rate of 25 percent next year, and all financial statement accounts will vary directly with sales. Based on that projection, develop a pro forma balance sheet and an income statement for the 2022 fiscal year. Morgan Construction Company Balance Sheet as of June 30, 2021 Assets: Liabilities and Stockholders’ Equity: Cash $ 3,349,239 Accounts payable $ 9,041,679 Accounts receivable 5,830,754 Notes payable 4,857,496 Inventories 22,267,674 Total current assets $31,447,667 Total current liabilities $13,899,175 Net fixed assets Other assets

43,362,482 Long-term debt 1,748,906 Common stock Retained earnings $76,559,055 Total liabilities and equity

Total assets

29,731,406 19,987,500 12,940,974 $76,559,055

Morgan Construction Company Income Statement for the Fiscal Year Ended June 30, 2021 Net sales $193,212,500 Costs 145,265,625 EBITDA $ 47,946,875 Depreciation 23,318,750 EBIT $ 24,628,125 Interest 11,935,869 EBT $ 12,692,256 Taxes (28%) 3,553,832 Net income $ 9,138,424 Solution: Morgan Construction Company—Pro Forma Balance Sheet for Year Ended June 30 2021 Cash Accounts receivable

2022

$ 3,349,239

1.25

$ 4,186,549

5,830,754

1.25

7,288,443

2021 Accounts payable Notes payable

2022

$ 9,041,679

1.25

$11,302,099

4,857,496

1.25

6,071,870

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Inventories

22,267,674

Total current assets

$31,447,667

Net fixed assets Other assets

43,362,482 1,748,906

Total assets

1.25

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27,834,593 $39,309,584

Total current liabilities

$13,899,175

1.25

54,203,103

29,731,406

1.25

37,164,258

1.25

2,186,133

Long-term debt Common stock Retained earnings Total liabilities & equity

19,987,500

1.25

24,984,375

12,940,974

1.25

16,176,218

$76,559,055

$95,698,819

Pro Forma Income Statement for Year Ended June 30 2021 Revenues $193,212,500 Costs 145,265,625 EBITDA $ 47,946,875 Depreciation 23,318,750 EBIT $ 24,628,125 Interest 11,935,869 EBT $ 12,692,256 Taxes (28%) 3,553,832 Net income $ 9,138,424

$76,559,055

1.25 1.25 1.25 1.25 1.25

$17,373,969

$95,698,819

2022 $241,515,625 181,582,031 $ 59,933,594 29,148,438 $ 30,785,156 14,919,836 $ 15,865,320 4,442,290 $ 11,423,030

LO: 3 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Industry/Sector Perspective 19.36 Use the financial information for Morgan Construction Company from Problem 19.35. Assume now that equity accounts do not vary directly with sales but change when retained earnings change or new equity is issued. The company pays 75 percent of its income as dividends every year. In addition, the company plans to expand production capacity by expanding the current facility and acquiring additional equipment. This will cost the firm $10 million. The firm has no plans to issue new equity this year. Prepare a pro forma balance sheet using this information. Any funds that need to be raised (in addition to changes in current liabilities) will be in the form of long-term debt. What is the external funding needed in this case? Solution: Copyright © 2022 John Wiley & Sons, Inc.

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Retention ratio = 25% Net income in 2022 = $11,423,030 Addition to retained earnings = $2,855,758 Morgan Construction Company—Pro Forma Balance Sheet for Year Ended June 30 2021 $ 3,349,239

1.25

2022 $ 4,186,549

5,830,754

1.25

7,288,443

22,267,674 $31,447,667

1.25

27,834,593 $ 39,309,584

Net fixed assets Addition to fixed assets Other assets

43,362,482

1.25

Total assets

$76,559,055

Cash Accounts receivable Inventories Total current assets

54,203,102 10,000,000

1,748,906

1.25

2,186,133 $105,698,819

Accounts payable Notes payable

2021 $ 9,041,679

1.25

2022 $11,302,099

4,857,496

1.25

6,071,870

Total current liabilities

$13,899,175

$ 17,373,969

Long-term debt Common stock Retained earnings Total liabilities & equity

29,731,406

$52,540,618

19,987,500

12,940,974

15,796,732

$76,559,055

$105,698,819

EFN = (Growth rate  Total assets) − Addition to Retained earnings = (0.25  $76,559,055) − $2,855,758 = $16,284,006 Addition to current liabilities = $3,474,794 So, actual EFN = $16,284,006 - $3,474,794 = $12,809,212 However, if you add the investment, then, EFN= New investment – Addition to retained earnings (0.25 ×$76,559,055) + $10,000,000 – $2,855,758 = $26,284,006 Addition to current liabilities = $3,474,794 So, actual EFN = $26,284,006 - $3,474,794 = $22,809,212 in additional Long-term debt LO: 3, 5 Bloomcode: Application AASCB: Analytic IMA: FSA Copyright © 2022 John Wiley & Sons, Inc.

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AICPA: Industry/Sector Perspective

19.37 Using the information for Morgan Construction Company in the preceding problem, calculate the firm’s internal growth rate and sustainable growth rate. Solution:

Addition to retained earnings $2,855,758 = = 3.73% Initial assets $76,559,055 Net Income $11, 423,030 ROE = = = 27.75% Equity $41,160,593 IGR =

SGR = Plowback ratio  ROE = 0.25  0.2775 = 6.94% LO: 5 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Industry/Sector Perspective

19.38 Use the information for Morgan Construction Company from Problems 19.35 and 19.36. Assume that equity accounts do not vary directly with sales, but change when retained earnings change or new equity is issued. The company’s long-term debt-to-equity ratio is approximately 90 percent, and its equity-to-total assets ratio is about 43 percent. The company management wishes to increase its equity-to-total assets ratio to at least 50 percent. Management is willing to reduce the company’s payout ratio, but will retain no more than 40 percent of earnings. The company will raise any additional funds needed, including funds for expansion, by selling new equity. No new long-term debt will be issued. Prepare pro forma statements to reflect this new scenario. a. b. c. d. e.

What is the external funding needed to accommodate the expected growth? What is the firm’s internal growth rate? What is the firm’s sustainable growth rate? How much new equity will the firm have to issue? What is the firm’s new equity ratio and debt-to-equity ratio?

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EFN = (Growth rate  Total assets) − Addition to retained earnings = (0.25  $76,559,055) − (0.40  $11,423,030) = $14,570,552 EFN including expansion = $24,570,552 Addition to retained earnings $4,569,212 IGR = = = 5.97% Initial assets $76,559,055

SGR = Plowback ratio  ROE

= 0.40  0.2775 = 11.10% Retained earnings in 2022 = $12,940,974 + $4,569,212 = $17,510,186 Total liabilities and equity = $105,698,819 Current liabilities = $17,373,969 Common equity = $105,698,819 – ($17,373,969+$29,731,406+$17,510,186) = $41,083,258 Common equity in 2021 = $19,987,500 New common equity issued = $41,083,258 – $19,987,500 = $21,095,758 Equity ($41,083,258 + $17,510,186) New equity ratio = = Total assets $105,698,818 = 55.43% Debt $29,731,406 Debt-to-equity ratio = = = 50.74% Equity $58,593,717

Morgan Construction Company—Pro Forma Balance Sheet for Year Ended June 20 Cash Accounts receivable Inventories Total current assets Net fixed assets Addition to fixed assets Other assets Total assets

2021 $ 3,349,239

1.25

2022 $ 4,186,549

5,830,754

1.25

7,288,443

22,267,674 $31,447,667

1.25

27,834,593 $ 39,309,584

43,362,482

1.25

54,203,103

10,000,000

1,748,906

1.25

$76,559,055

2,186,133 $105,698,819

Accounts payable Notes payable

2021 $ 9,041,679

1.25

2022 $11,302,099

4,857,496

1.25

6,071,870

Total current liabilities

$13,899,175

$ 17,373,969

Longterm debt Common stock

29,731,406

19,987,500

41,083,258

Retained earnings Total liabilities & equity

12,940,974

17,510,186

$76,559,055

$105,698,819

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LO: 5 Bloomcode: Application AASCB: Analytic IMA: Budget Preparation AICPA: Industry/Sector Perspective 19.39 Munson Communications Company has just reported earnings for the year ended June 30, 2021. Below are the firm’s income statement and balance sheet. The company had a 55 percent dividend payout ratio for the last 10 years and management does not plan to change this policy. Based on internal forecasts, Management expects sales growth in 2022 to be 20 percent. Assume that equity accounts and long-term debt do not vary directly with sales, but change when retained earnings change or additional capital is issued.

Munson Communications Company Balance Sheet as of June 30, 2021 Liabilities and Stockholders’ Equity:

Assets: Cash

$ 1,728,639 Accounts payable

$ 4,666,673

Accounts receivable

3,009,421 Notes payable

2,507,094

Inventories

11,492,993

Total current assets

$16,231,053 Total current liabilities

$ 7,173,767

Net fixed assets

22,380,636 Long-term debt

13,345,242

Other assets

1,748,906 Common stock

10,165,235

Retained earnings Total assets

$40,360,595

Total liabilities and equity

9,676,351 $40,360,595

Munson Communications Company Income Statement for the Fiscal Year Ended June 30, 2021 Net sales

$79,722,581

Costs

59,358,499

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EBITDA

$20,364,082

Depreciation

7,318,750

EBIT

$13,045,332

Interest

3,658,477

EBT

$ 9,386,855

Taxes (35%)

3,285,399

Net income

$ 6,101,456

What is the firm’s internal growth rate (IGR)?

What is the firm’s sustainable growth rate (SGR)?

What is the external funding needed (EFN) to accommodate the expected growth?

Construct the firm’s 2022 pro forma financial statements under the assumption that long-term debt will provide all external funding.

Solution: a.

Retention ratio = 45.0% Net income in 2021= $ 6,101,456 Expected net income in 2022 = $6,101,456 (1.20) = $7,321,747 Addition to retained earnings = $ 3,294,786 ROE = 30.8% Growth rate = 20%

IGR =

Addition to retained earnings $3,294,786 = = 8.16% Initial assets $40,360,595

SGR = Plowback ratio× ROE

= 0.45× 0.308 = 13.84%

EFN = (Growth rate×Total assets) - Addition to retained earnings

= (0.20×$40,360,595) - (0.45×$7,321,747) = $4, 777, 333

d. Munson Communications Company—Pro Forma Balance Sheet as of June 20, 2022 2021 Cash Accounts

2022

$ 1,728,639

1.20

$ 2,074,367

3,009,421

1.20

3,611,305

2021

2022

Accounts payable

4,666,673

1.20

$ 5,600,008

Notes payable

2,507,094

1.20

3,008,513

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Inventories

11,492,993

Total current

1.20

$16,231,053

Solutions Manual

13,791,592 $19,477,264

assets

Total current

$ 7,173,767

$ 8,608,521

liabilities

Net fixed assets

22,380,636

1.20

26,856,763

Long-term debt

13,345,242

1.20

16,687,821

Other assets

1,748,906

1.20

2,098,687

Common stock

10,165,235

1.20

10,165,235

Retained earnings

9,676,351

12,971,137

Total liabilities

$40,360,595

$48,432,714

Total assets

$40,360,595

$48,432,714

& equity

Pro Forma Income Statement for the Fiscal Year Ended June 30, 2022 2021

2022

Revenues

$79,722,581

1.20

$95,667,097

Costs

59,358,499

1.20

71,230,199

EBITDA

$20,364,082

Depreciation

7,318,750

EBIT

$13,045,332

Interest

3,658,477

EBT

$ 9,386,855

Taxes (35%)

3,285,399

Net income

$ 6,101,456

$24,436,898 1.20

8,782,500 $15,654,398

1.20

4,390,172 $11,264,226

1.20

3,942,479 $ 7,321,747

LO: 5 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Industry/Sector Perspective

Sample Test Problems 19.1 Mars Company had net sales of $18 million in the year that just ended. Next year, the company’s management expects a 15 percent increase in sales. If cost of goods sold is 60

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percent of sales and inventory is 25 percent of sales, what would you estimate sales, inventory, and cost of goods sold to be next year? Solution: Net sales (St) = $18 million % change in net sales (%ΔS) = 15% Expected net sales (St +1) = (0.15 × $18 million) + $18 million = $20.7 million Expected inventory (I t+1) = $20.7 million × 0.25 = $5.175 million Expected cost of goods sold (COGS t+1) = $20.7 million × 0.60 = $12.42 million LO: 2 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Industry/Sector Perspective

19.2 Lavaca Inc. management expects net sales to be $855,000, total costs to be $647,000, and to pay taxes at an average rate of 24 percent this year. If the Lavaca pays out 38 percent of its earnings as dividends, what is its retention ratio? How much will Lavaca’s retained earnings increase? Solution: Lavaca Inc. Pro Forma Income Statement Net sales $855,000 Total costs 647,000 Taxable income $208,000 Taxes (24%) 49,920 Net income $158,080 Dividends (38%) $ 60,070 Addition to retained earnings $ 98,010

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Increase in Lavaca’s retained earnings = Net income – Dividends = ($158,080 – $60,070) = $98,010 LO: 3 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Industry/Sector Perspective

19.3 Spurlock Inc. had net income of $266,778 in its most recent fiscal year and total assets of $1,833,400 at the end of the year. The company’s total debt ratio (total debt to total assets) is 35 percent, and Spurlock retains 60 percent of its income every year. What is Spurlock’s internal growth rate? What is its sustainable growth rate? Solution:

Internal Growth Rate (IGR) =

Addition to retained earnings Initial total assets

As Spurlock retains 60 percent of its income every year, its retention ratio = 0.60, or 60%. Spurlock’s addition to retained earnings = Retention ratio × Net income = 0.60 × $266,778 = $160,066.80 Initial total assets = $1,833,400

Internal Growth Rate (IGR) =

$160,066.80 = 0.0873, or 8.73% $1,833, 400.00

Sustainable growth rate (SGR) = Retention ratio × ROE Total debt = Total debt ratio × Total assets = 0.35 × $1,833,400 = $641,690 Total equity = Total assets – Total debt = $1,833,400 – $641,690 = $1,191,710

ROE =

Net income Total equity

ROE =

$266,778 = 0.2239, or 22.39% $1,191,710

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Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Industry/Sector Perspective 19.4 Using the information in Sample Test Problem 19.3, what is Spurlock’s capital intensity ratio if the company has net sales of $3,557,100? What does this ratio tell us? Solution:

Total assets Net sales $1,833,400 = $3,557,100 = 0.5154, or 51.54%

Capital intensity ratio =

Capital intensity ratio tells us something about the amount of assets the firm needs to generate $1 in sales. The higher the ratio, the more capital the firm needs to generate sales— that is, the more capital intensive the firm. LO: 3 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Industry/Sector Perspective

19.5 Edgefield Excavation Company has total assets of $4,976,456, sales of $1,225,700, and net income of $587,000. The company’s management expects sales to grow by 9 percent next year. All costs (including taxes) and assets vary directly with sales, and the firm expects to maintain a payout ratio of 35 percent. Calculate the external funds needed (EFN) by Edgefield. What would Edgefield’s payout ratio have to be in order for the company’s EFN to equal zero? Solution: External funds needed (EFN) = New investments – Addition to retained earnings New investments = Growth rate × Initial total assets New investments = 0.09 × $4,976,456 = $447,881.04 Copyright © 2022 John Wiley & Sons, Inc.

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Addition to retained earnings = Retention ratio × Net income = (1 – Dividend payout ratio) × Net income = (1 – 0.35) × $587,000 = $381,550 External funds needed (EFN) = $447,881.04 – $381,550 = $66,331.04 So external funds needed (EFN) by Edgefield is $66,331.04. The company’s EFN will be zero if new investments is equal to the addition to retained earnings. Edgefield’s addition to retained earnings = New investments = $447,881.04 Dividend payout ratio = 1 – Retention ratio

Addition to retained earnings Net income $447,881.04 = = 0.763, or 76.3% $587,000

Retention ratio =

Dividend payout ratio = (1 – 0.763) = 0.237 or 23.7% Therefore, to be in order for Edgefield’s EFN to equal zero, the company’s payout ratio would be 0.237, or 23.7%. LO: 5 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Industry/Sector Perspective

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CHAPTER 18 Business Formation, Growth, and Valuation Before You Go On Section 18.1 1. What are three general reasons that new businesses fail? Businesses fail for a variety of reasons. In some cases, a firm’s product(s) may find no demand among consumers. For others, the founding management may lack a clearly thought-out strategy or lack the skills to move the firm forward. In addition, a lot of firms fail because they run out of money to operate the business and are unable to raise more.

2. How do financing considerations affect the choice of organizational form? Of all the different forms of organizations, the sole proprietor takes the least amount of money to set up and is dependent only on the founder’s money. Forming a partnership is more involved and costs more. Setting up as a corporation is the most expensive and calls for a more active role by attorneys to set up the organization.

How does a cash budget help an entrepreneur? The cash budget is a very useful planning tool for entrepreneurs. It summarizes the cash flows into and out of a firm over a period of time. Cash budgets often present the inflows and outflows on a monthly basis but can be prepared for any period, including daily or weekly. Preparing a cash budget helps an entrepreneur better understand where money is coming from, where it is going, and how much external financing is likely to be needed and when. Understanding where the money is coming from and where it is going helps an entrepreneur maintain control of the company’s finances. Knowing how much external financing is likely to be needed and when helps the entrepreneur plan fund-raising efforts before it is too late.

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Section 18.2 1. Why is a business plan important in raising capital for a young company? A well-prepared business plan makes it easier for an entrepreneur to communicate to potential investors precisely what he or she expects the business to look like in the future, how he or she expects to get it to that point, and what returns an investor might expect to receive. This allows potential investors to get a feel for the strategic plan of the firm and also allows them to gauge the management ability of the entrepreneur.

What else can a business plan be used for? A business plan is a tool that: ▪

can help raise capital

▪

can help an entrepreneur set the goals and objectives for the company ▪

serve as a benchmark for evaluating and controlling the company’s performance,

▪

communicate the entrepreneur’s ideas to managers, outside directors, customers, suppliers, and others.

Why is it important to discuss the qualifications of the management team in a business plan? The discussion of the qualification of the management team is especially important when it comes to raising capital. Investors in young businesses invest in the key people as much as in the business idea itself.

Section 18.3 1. Why is it important to specify a valuation date when you value a business? The value of a business changes over time. This can be caused by changes in general economic conditions, industry conditions, and decisions that are made by the managers. All of these affect the value of the cash flows that a business is expected to generate in the future. Actions by competitors and the investment, operating, and financing decisions made by managers also affect the value of a business. Given this, it is important to

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specify a valuation date while valuing a business. This is the date as of which the value estimate applies.

2. What is the difference between investment value and fair market value? A strategic investor is one who has an interest in acquiring the business. The investment value of the firm to a strategic investor will take into consideration the benefits that can accrue from the acquisition and hence is likely to carry a higher value. In contrast, the fair market value is the valuation arrived by an investor who is only interested in the financial performance of the firm and not in acquiring the business. The fair market value can differ considerably from the investment value of the business.

What are the two market approaches that can be used to value a business, and how do they differ? The two market approaches that are commonly used to value a business are multiples analysis and transactions analysis. Multiples analysis uses stock price or other value multiples that are observed for public companies to estimate the value of a company’s stock or an entire business. In transaction analysis, analysts use the information from transactions involving a merger or an acquisition of similar companies to estimate the value of a company or its stock.

What is a nonoperating asset, and how are such assets accounted for in business valuation? Nonoperating assets (NOA) are assets like cash, earned in the past and not distributed to stockholders or other assets that are left over from old projects, that are not essential to support the operations of a business. As Equation 18.2 shows, when valuing a business, the nonoperating assets are included in the cash flows that are used to arrive at the value of a firm.

What are three income approaches used to value a business? The three income approaches to valuing a business are free cash flow from the firm (FCFF), free cash flow to equity (FCFE), and dividend discount model (DDM). In the free cash

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flow from the firm (FCFF) approach, an analyst values the discounted value of all free cash flows that the assets of the firm are expected to produce in the future to estimate the value of the enterprise. The free cash flow to equity (FCFE) approach uses the discounted value of all cash flows that are available for distribution to stockholders to estimate the value of the enterprise. The dividend discount model (DDM) approach estimates the value of an enterprise using the discounted value of the dividends to be distributed to stockholders in the future.

What is the difference between FCFE and dividends? The FCFE is an estimate of all cash flows available for distribution to shareholders of the firm. Recognize that not all of this will be distributed to stockholders as dividends. Thus, FCFE includes both dividends and retained earnings, the portion not distributed to shareholders but reinvested in the firm.

Section 18.4 1. How might financial statements for private companies differ from those for public companies? •

Some private companies have complete, audited financial statements, while others have incomplete financial statements that are not prepared in accordance with the GAAP. All public companies are required to file audited financial statements with the Securities and Exchange Commission (SEC).

•

In contrast to the financial statements of publicly held company, private company financials often include personal expenses of the owner and excess compensation expenses.

2. Why is marketability an important issue in business valuation? The shareholders of a publicly held company have an easier time of liquidating their holdings if they so desire. Since a market and the value for their holdings are already established, a simple call to a broker will take care of it. In contrast, the shareholders of a privately held firm will have to spend a lot more time and money to liquidate their shares.

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This additional time and effort is a reflection of a lower level of marketability of such firms and will result in a discount in the value of the firm.

What is a key person? If the cash flows that a business is expected to generate depend heavily on the retention of a particular individual or group of individuals, then that individual or group can be referred to as key people. The cash flows of the firm may be dependent on the continued employment of this individual or group.

Self-Study Problems 18.1

Your sister wants to open a store that sells antique-style jewelry and accessories. She has $15,000 of savings to invest but opening the store will require an initial investment of $20,000. Net cash inflows are expected to be −$2,000, −$1,000, and $0 in the first three months. It is expected that, as the store becomes better known, net cash inflows will become +$500 in the fourth month and grow at a constant rate of 5 percent in the following months. You want to help your sister by providing the additional money that she needs. How much money will you have to invest each month to start the store and keep it operating with a minimum cash balance of $1,000?

Solution: You will have to invest in $5,000 to open the store (the difference between $20,000 and $15,000). You will then have to invest an additional $3,000 during the first month to cover the cash flow of -$2,000 and to establish a cash balance of $1,000. Another $1,000 will be required in the second month to cover the negative cash flow during that month. Since cash flows will be $0 or positive beginning in the third month, you will not have to invest any additional funds after the second month.

18.2

You have the following information for a company you are valuing and for a comparable company: Comparable company:

Company you are valuing: SM 18-5

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Stock price = $23.45

n/a

Number of shares outstanding = 6.23 million

n/a

Value of debt = $18.45 million

Value of debt = $3.68 million

Est. EBITDA next year = $17.0 million

Est. EBITDA next year = $4.4 million

Est. income next year = $5.3 million

Est. income next year = $1.5 million

Estimate the enterprise value of the company you are evaluating using the P/E and enterprise value/EBITDA multiples. Solution: The P/E and enterprise value/EBITDA multiples for the comparable company are:

  Stock price P =     E Comparable  Earnings per share Comparable =

$23.45 per share $5.3 million 6.23 million shares

= 27.6  V + VE   Enterprise value  = D    EBITDA  Comparable  EBITDA Comparable =

$18.45 million + ($23.45 per share  6.23 million shares) $17.0 million

= 9.68

Using the P/E multiple, we can calculate the value of the equity as: P VE =    Net income company being valued  E Comparable = 27.6  $1.5 million = $41.4 million

which suggests an enterprise value of: VF = VE + VD = $41.4 million + $3.68 million = $45.08 million

Using the enterprise/EBITDA multiple, we obtain:

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 Enterprise value  VF =   EBITDA Company being valued  EBITDA  Comparable = 9.68  $4.4 million = $42.59 million

18.3

How do the cash flows that are discounted when the WACC approach (FCFF approach) is used to value a business differ from those that are discounted when the free cash flow to equity (FCFE) approach is used to value the equity in a business?

Solution: The cash flows that are discounted when the WACC approach is used to value a business are calculated in the same way the cash flows are calculated for a project analysis. These cash flows represent the total after-tax free cash flows that the business is expected to generate from operations. The cash flows that are discounted when the FCFE approach is used are the total after-tax free cash flows from the business that are available for distribution to the stockholders. In other words, they equal the total cash flows that the business is expected to generate less the net cash flows to the debt holders. The net cash flows to the debt holders is equal to the interest and principal payments that the firm makes less any proceeds for the sale of new debt.

18.4

You are valuing a company using the WACC approach and have estimated that the free cash flows from the firm (FCFF) in the next five years will be $36.7, $42.6, $45.1, $46.3, and $46.6 million, respectively. Beginning in year 6, you expect the cash flows to decrease at a rate of 3 percent per year for the indefinite future. You estimate that the appropriate WACC to use in discounting these cash flows is 10 percent. What is the value of this company?

Solution: The present value of the cash flows expected over the next five years is: PV(FCFF5 ) =

$36.7 million $42.6 million $45.1 million $46.3 million $46.6 million + + + + 2 3 4 5 1+ 0.1 (1+0.1) (1+0.1) (1+0.1) (1+0.1)

= $163.01million.

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TV5 =

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FCFF5  (1 + g) $46.6 million  (1 + 0.03) = = $685.69 million WACC − g 0.1 − 0.03

and the present value of the terminal value is:

PV(TV5 ) =

TV5 $685.69 million = = $425.76 million 5 (1+WACC) (1 + 0.1)5

Therefore, if there are no nonoperating assets, the value of the firm is: VF = $163.01 million + $425.76 million = $588.77 million

18.5

You want to estimate the value of a local advertising firm. The earnings of the firm are expected to be $2 million next year. Based on expected earnings next year, the average price-to-earnings ratio of similar firms in the same industry is 48. Therefore, you estimate the value of the firm you are valuing to be $96 million. Further investigation shows that a large portion of the firm’s business is obtained through connections that John Smith, a senior partner of the firm, has with various advertising executives at customer firms. Smith only recently started working with his junior partners to establish similar relationships with these customers. Smith is approaching 65 years of age and might announce his retirement at the next board meeting. If he does retire, revenues will drop significantly, and earnings are estimated to shrink by 30 percent. You estimate that the probability that Smith will retire this year is 50 percent. If he does not retire this year, you expect that he will have sufficient time to work with his junior partners so that his departure will not affect earnings when he departs. How does this information affect your estimate of the value of the firm?

Solution: Smith is a key person in this firm. An adjustment should be made to the valuation to account for his potential departure this year. Taking the possibility that Smith will retire into account, the expected earnings next year will be: (2,000,000 × 0.5) + [$2,000,000 × (1 – 0.30) × 0.5] = $1,700,000 Therefore, the adjusted value for the firm is: $1.7 million × 48 = $81.6 million. We can see that this implies a 15 percent key person discount from the original estimate of $96 million [($81.6 million ─ $96.0 million)/$96.0 million = ─ 0.15, or ─15 percent]. Copyright © 2022 John Wiley & Sons, Inc.

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Discussion Questions 18.1

Given that many new businesses fail in the first few years after they are established, how should an entrepreneur think about the risk of failure associated with a new business? From what you have learned in this chapter, what can an entrepreneur do to increase the chance of success? First of all, it is important for an entrepreneur to understand why many new businesses fail. Common reasons include poor products, poor business strategy, poor management skills, and ineffective financing decisions. However, the risk of failure should not stop the start of a new business if the entrepreneur believes that he or she has a great business idea and is capable of implementing the idea. The entrepreneur should be careful and realistic in assessing the opportunities and taking risks into consideration. From what we have learned in this chapter, the entrepreneur should consult an attorney and choose the right organizational form according to the business’s operating and financing needs. In addition, he or she should carefully prepare a business plan that incorporates the main aspects of the business and facilitates the raising of external capital. The entrepreneur can use several tools to assess the financing needs of the new business: cash flow break-even analysis and cash budget. To value the new business, the entrepreneur can use one or more of the following methods: cost approach, market approach, or income approach.

LO: 1 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

18.2

Explain how the taxation of a C-corporation differs from the taxation of the other forms of business organization discussed in this chapter. With the exception of C-corporations, all profits flow through to the owners in proportion to their ownership interests. These owners pay taxes on the business profits only when

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they file their personal tax returns. In contrast, profits earned in C-corporations are taxed at the corporate tax rate, and the after-tax profits are taxed a second time when they are distributed to stockholders in the form of dividends. On the bright side, because profits are taxed in the corporation, certain benefits like health insurances that are paid to stockholders who work in a C-corporation are tax deductible. These benefits are not generally deductible with the other forms of organization. LO: 1 Level: Basic Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

18.3

What is a business plan? Explain how a business plan can help an entrepreneur succeed in building a business. A business plan is a document that describes the details of how a business will be developed over time. A well-prepared business plan helps an entrepreneur raise external capital. It makes it easier for an entrepreneur to communicate to potential investors precisely what he or she expects the business to look like in the future, how he or she expects to get it to that point, and what returns an investor might expect to receive. In addition, a business plan is a tool that can help an entrepreneur set the goals and objectives for the company, serve as a benchmark for evaluating and controlling the company's performance, and communicate the entrepreneur’s ideas to managers and stakeholders.

LO: 2 Level: Basic Bloomcode: Knowledge AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

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You are entering negotiations to purchase a business and are trying to formulate a negotiating strategy. You want to determine the minimum price you should offer and the maximum you should be willing to pay. Explain how the concepts of fair market value and investment value can help you do this. An estimate of the fair market value of a business would provide you with an idea of the price that the seller could probably get from someone else. Since this is an indication of the alternatives available to the seller, it is a useful benchmark for determining the minimum price you should offer. The investment value of the business to you represents the maximum price that you should pay. If you pay more than the investment value, the acquisition will be a negative NPV project.

LO: 3 Level: Intermediate Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

18.5

You have just received a business valuation report that is dated six months ago. Describe the factors that might have changed during the past six months and thereby caused the value of the business today to be different from the value six months ago. Which of these changes affect the expected cash flows, and which affect the discount rate that you would use in a discounted cash flow valuation of this company? A lot might have changed in the last six months. For example, there might have been changes in general economic conditions, capital market conditions, the competitive environment in the industries in which the company competes, and in company characteristics such as the products it sells, the geographic markets it competes in, and management quality. Changes in all of these areas can affect expected cash flows through their impact on demand for the company’s products, the prices of these products, production costs, and investment requirements. Changes in capital market conditions can affect the company’s cost of capital and therefore, the discount rate.

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Level: Basic Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

18.6

Is the replacement cost of a business generally related to the value of the cash flows that the business is expected to produce in the future? Why or why not? Illustrate your answer with an example. The replacement cost of a business is an estimate of what it would cost to replace the tangible and intangible assets of an ongoing business rather than a reflection of the value of the expected future cash flows of the business. Let us say that you are planning to start a new coffee shop. You have a choice of either buying an existing coffee shop or starting one entirely from scratch. The replacement cost of the coffee shop business should include the cost of all tangible assets, such as property, plant, and equipment, and all intangible assets, such as brand names, customer lists, and the cost of hiring the people necessary to run the business and the time that it would take to build the business. This provides you a fair value of what you would pay for an existing business. If you can start a business from inception at a lower cost than that estimated value, then you should not buy the existing business. It does not reflect the cash flows that the existing coffee shop will produce in the future, but only what it is worth now.

LO: 3 Level: Intermediate Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

18.7

You want to estimate the value of a company that has three very different lines of business. It manufactures aircraft, is in the data-processing business, and manufactures automobiles. How could you use an income approach to value a

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company such as this—one with three very distinct businesses that will have different revenue growth rates, profit margins, investment requirements, discount rates, and so forth? In using an income approach like the free cash flow from the firm (FCFF) to value an entire firm, one would first estimate the expected future cash flows from each of the three distinct lines of business. If all three lines of businesses are financed the same way, then one would add up the cash flows across all the different lines of businesses and discount them using the firm’s WACC to estimate the value of the firm. If, however, the three distinct businesses have been financed differently, then each of the business’s value should be estimated independently, and then finally, added up to determine the value of the firm. LO: 3 Level: Basic Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

18.8

Your boss has asked you to estimate the intrinsic value of the equity for Netflix, which does not currently pay any dividends. You are going to use an income approach and are trying to choose between the free cash flow to equity (FCFE) approach and the dividend discount model (DDM) approach. Which would be more appropriate in this instance? Why? What concerns would you have in applying either of these valuation approaches to a company such as this? Netflix is a fast growing, young firm that is unlikely to pay dividends in the near future. The dividend discount model (DDM) approach typically uses the constant-growth model to determine the intrinsic value of the firm’s equity. This model will not be applicable to firms like Netflix until it has settled down to a steady growth pattern at some point in the future. In contrast, the FCFE approach values cash flows that are available for distribution to stockholders. It allows for the firm to not distribute all available cash flows as dividends in any particular year. Hence, it would be more appropriate to use the FCFE approach to determine the intrinsic value of Netflix’s equity.

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LO: 3 Level: Intermediate Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

18.9

Explain how the financial statements of a private company might differ from those of a public company. What does this imply for valuing a private company? Financial statements of many private companies are not as complete and reliable as those of public companies. One needs to take caution in valuing a private business based on its financial statements. For example, private company financials often include personal expenses of the owner and extremely high compensation expenses. Excess compensations for the owners benefit them by voiding double taxation. To value a private firm more precisely, adjustments for excess expenses and compensations should be made.

LO: 4 Level: Basic Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

18.10 Explain why it is difficult to value a young, rapidly growing company. It is difficult to value a young, rapidly growing company for several reasons. First, such a company has less reliable historical information available; second, the future of such a company is often less certain than a matured company; third, such a company is usually not yet profitable, and therefore, it is difficult to apply earnings multiples; and finally, such a company usually invests any excess cash into the company. LO: 4 Level: Basic Bloomcode: Comprehension Copyright © 2022 John Wiley & Sons, Inc.

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Questions and Problems BASIC 18.1

Organizational form: List some common forms of business organization, and discuss how access to capital differs across these forms of organization.

Solution: The forms of organizations discussed in this chapter include sole proprietorship, partnership (general partnership and limited partnership), limited liability company (LLC), and corporations (S-corporation and C-corporation). The closer the type of organization is to the end of the list above, the better is its access to capital. Sole proprietorships must rely on equity contribution from the proprietor and debt or lease financing. In contrast, partnerships can turn to all of the partners for additional capital, and corporations can sell shares to both insiders and outsiders. Limited partnerships and limited liability companies (LLCs) are less constrained than general partnerships because they can raise money from limited partners or “members,” as outside investors in LLCs are called, who are not directly involved in running the business. C-corporations can have a virtually unlimited number of stockholders. LO: 1 Bloomcode: Knowledge AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

18.2

Starting a business: What are some of the things that the founder of a company must do to launch a new business?

Solution:

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The founder of a company needs to decide on its products, market, and business strategy. Then, he or she needs to estimate the company’s financing needs and raise the money to develop the products, acquire assets, and hire employees. As the business is being built, the founder must also manage the day-to-day operations. LO: 1 Bloomcode: Knowledge AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

18.3

Organizational form: Explain how financial liabilities differ among different forms of business organization.

Solution: Sole proprietorships, general partnerships, and limited partnerships all are at a disadvantage. Sole proprietors and general partnerships face the possibility that their personal assets can be taken from them to satisfy claims against their businesses. In contrast, the liabilities of investors in limited partnerships, LLCs, and corporations are limited to the money that they have invested in the business. LO: 1 Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

18.4

Cash requirements: List two useful tools to help an entrepreneur to understand the cash requirements of a business and to estimate the financing needs of that business.

Solution: An entrepreneur can use cash flow break-even analysis and cash budget to estimate the cash requirement and financing needs of the business. The cash flow break-even analysis is used to compute the level of unit sales that is necessary to break even on operations from a pretax operating cash flow perspective. The cash budget presents the cash inflows and Copyright © 2022 John Wiley & Sons, Inc.

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outflows as well as additional financing needs, usually on a monthly basis but can be prepared for any period, including daily or weekly. LO: 1 Bloomcode: Knowledge AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

18.5

Cash requirements: You believe you have a great business idea and want to start your own company. However, you do not have enough savings to finance it. Where can you get the additional funds you need?

Solution: You can try to raise additional equity financing from your friends and family, from venture capitalists, or from other potential investors that you know. Debt financing might be obtained through bank loans, cash advances on credit cards, or loans from other local individual investors or other businesses. Of course, if a company is large enough, equity and debt financing can be obtained in the public markets. LO: 1 Bloomcode: Knowledge AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

18.6

Raising capital: Why is it especially difficult for an entrepreneur with a new business to raise capital? What tool can help him or her to raise external capital?

Solution: To raise external capital, an entrepreneur must convince potential investors that purchasing debt or equity from the firm will yield attractive returns, given the risks they will bear. It is especially difficult for an entrepreneur with a new business to do this because the business does not have a well-established record and its future is typically

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very uncertain. A well-written business plan can be very helpful in convincing potential investors to put their money in the business. LO: 2 Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

18.7

Replacement cost: What is the replacement cost of a business?

Solution: The replacement cost is the cost of duplicating the assets of a business in their present form, consisting of tangible and intangible assets as of the valuation date. LO: 3 Bloomcode: Knowledge AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

18.8 Multiples analysis: It is April 7, 2021, and your company is considering the possibility of purchasing the Chrysler automobile manufacturing business. Managers of Fiat Chrysler Automobiles N.V, the automobile manufacturer that owns Chrysler, have hinted that they might be interested in selling Chrysler. Since Chrysler does not have publicly traded shares of its own, you have decided to use Ford Motor Company as a comparable company to help you determine the market value of Chrysler. This morning Ford’s common stock was trading at $11.75 per share, and the company had 3.9 billion shares outstanding. You estimated that the market value of all of the company’s other outstanding securities (excluding the common stock but including special shares owned by the Ford family) is $35 billion and that its revenues from auto sales were $155 billion last year. Chrysler’s revenue in 2020 was $50 billion. Based on the enterprise value/revenue ratio, what is the total value of Chrysler that is implied by the Ford market values? Copyright © 2022 John Wiley & Sons, Inc.

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Solution: The enterprise value of Ford is: VF = VE + VOther outstanding securities = ($11.75 per share × 3.9 billion shares) + $35.0 billion = $80.825 billion and the enterprise value/revenue ratio is: $80.825 billion/$155.0 billion = 0.521 This suggests that the value of the Chrysler business is 0.521 × $50.0 billion = $26.1 billion. (Note that in this example we used the enterprise value/revenue ratio because EDITDA was unclear for Chrysler.) LO: 3 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

18.9

Nonoperating assets: Why is excess cash a nonoperating asset (NOA)? Why does it make sense to add the value of excess cash to the value of the discounted cash flows when we use the WACC (FCFF) or FCFE approach to value a business?

Solution: Excess cash is a nonoperating asset because, by definition, this cash can be distributed to stockholders without affecting the operations of the business and therefore, the value of the expected future cash flows. It makes sense to add back the value of excess cash because it represents value over and above that which the business is expected to produce. LO: 3 Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

18.10 Dividend discount approach: You want to estimate the total intrinsic value of a large gas and electric utility company. This company has publicly traded stock and has been paying Copyright © 2022 John Wiley & Sons, Inc.

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a regular dividend for many years. You decide that, due to the predictability of the dividend that this company pays, you can use the dividend discount valuation approach. The company is expected to pay a dividend of $1.25 per share next year, and the dividend is expected to grow at a rate of 3 percent per year thereafter. You estimate that the appropriate rate for discounting future dividends is 12 percent. In addition, you know that the company has 46 million shares outstanding and that the market value of its debt is $350 million. What is the total enterprise value of the company? Solution: The value of a share of stock can be calculated using the constant-growth dividend model as:

P0 =

D1 $1.25 = = $13.89. kcs − g (0.12 − 0.03)

Multiplying the price per share by the number of shares outstanding gives us the value of the equity: VE = $13.89 × 46 million = $638.94 million Therefore, the total value of the firm is: VF = VE + VD = $638.94 million + $350 million = $988.94 million LO: 3 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

18.11 Public versus private company valuation: You are considering investing in a private company that is owned by a friend of yours. You have read through the company’s financial statements and believe that they are reliable. Multiples of similar publicly traded companies in the same industry suggest that the value of a share of stock in your friend’s company is $12. Should you be willing to pay $12 per share? Solution: Shareholders in a private company may have to spend considerable resources in money and time to sell their shares. This additional transaction cost will make value derived from Copyright © 2022 John Wiley & Sons, Inc.

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similar publicly traded company an overestimated figure. Therefore, you will most likely not be willing to pay for $12 a share. You can apply an appropriate marketability discount to this price as a fair price for this private equity. LO: 4 Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

18.12 Control: Does the expected rate of return that is calculated using CAPM, with a beta estimated from stock returns in the public market, reflect a minority or a controlling ownership position? How is it likely to differ between a minority and a controlling position? Solution: The estimates we obtain using public market data with CAPM are based on small stock transactions. To the extent that having control would enable an investor to better manage the systematic risk associated with a business, a discount rate for a controlling transaction is likely to be lower than that implied by CAPM (this generates a higher value and therefore, a premium price for control). LO: 4 Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

INTERMEDIATE 18.13 Organizational form: Compare the characteristics of an LLC with those of a partnership and a C-corporation. Solution:

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An LLC is a hybrid of a limited partnership and a corporation. Like a corporation, an LLC provides limited liability for the people who make the business decisions in the firm while enabling all investors to retain the tax advantages of a limited partnership. LO: 1 Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

18.14 Organizational form: Discuss the pros and cons of an S-corporation compared with a C-corporation. Solution: An S-corporation is a variation of the C-corporation. The advantage of an S-corporation compared to a C-corporation is that all of its profits are passed directly to the stockholders, and therefore, double taxation is avoided while it still offers the protection of limited liability for shareholders. The disadvantage of an S-corporation is the limitation on stock ownership. Currently, an S-corporation can have no more than 100 stockholders and have only one class of common stock, and all stockholders must be individuals who are U.S. citizens or residents. As a result, access to capital is more limited for an S-corporation, and cost to transfer ownership is much higher for an S-corporation than for a C-corporation. LO: 1 Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

18.15 Break-even: You have started a business that sells a home gardening system that allows people to grow vegetables on their kitchen countertop. You are considering two options for marketing your product. The first is to advertise on local TV. The second is to distribute flyers in the local community. The TV option, which costs $50,000 annually, will promote the product more effectively and create a demand for 1,200 units per year. Copyright © 2022 John Wiley & Sons, Inc.

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The flyer advertisement option costs only $6,000, annually, but will create a demand for only 250 units per year. The price per unit of the indoor gardening system is $100, and the variable cost is $60 per unit. Assume that the production capacity is not limited and that the marketing cost is the only fixed cost involved in your business. What are the break-even points for both marketing options? Which one should you choose? Solution: The break-even point for TV advertisement = $50,000/($100 - $60) = 1,250 units. However, the demand is only 1,200 units with TV advertisement. Therefore, you cannot break even. The break-even point for flyers = $6,000/($100 - $60) = 150 units. With a market demand of only 250 units, you will make a profit. Therefore, you should choose the flyer option. LO: 1 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

18.16 Going-concern value: Aggie Motors is a chain of used car dealerships that has publicly traded stock. Using the adjusted book value approach, you have estimated the value of Aggie Motors to be $45,646,000. The company has $40.5 million of debt outstanding. Its stock price is $5.50 per share, and there are 1,378,000 shares outstanding. What is the going concern value of Aggie Motors? Solution: The going-concern value equals the difference between the market value of the business (the present value of the expected cash flows) and its adjusted book value. The market value of the business can be calculated as: VF = VD + VE = $40,500,000 + ($5.50 × 1,378,000) = $48,079,000 Therefore, the going concern value is $48,079,000 – $45,646,000 = $2,433,000 LO: 3 Bloomcode: Application AASCB: Analytic Copyright © 2022 John Wiley & Sons, Inc.

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IMA: Corporate Finance AICPA: Industry/Sector Perspective

Use the following information concerning Johnson Machine Tool Company in Problems 18.17, 18.18, and 18.19. Johnson’s income statement from the fiscal year that ended this past December is: Revenue

$995

Cost of goods sold

652

Gross profit

$343

Selling, general, & administrative expenses

135

Operating profit (EBIT)

$208

Interest expense Earnings before taxes Taxes Net income

48 $160 64 $ 96

All dollar values are in millions. Depreciation and amortization expenses last year were $42 million, and the company has $533 million of debt outstanding.

18.17 Multiples analysis: You are an analyst at a private equity firm that buys private companies, improves their operating performance, and sells them for a profit. Your boss has asked you to estimate the fair market value of the Johnson Machine Tool Company. Billy’s Tools is a public company with business operations that are virtually identical to those at Johnson. The most recent income statement for Billy’s Tools is as follows:

Revenue

$1,764

Cost of goods sold

1,168

Gross profit

$ 596

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$ 373 147

Net income

$ 226

All dollar values are in millions. Billy’s had depreciation and amortization expenses of $71 million last year and had 200 million shares and $600 million of debt outstanding as of the end of the year. Its stock is currently trading at $12.25 per share. Using the P/E multiple, what is the per share value of Johnson’s stock? What is the total value of Johnson Machine Tool Company? Solution: The P/E multiple for Billy’s Tools is:

P/E =

$12.25  200 million shares = 10.84 $226 million

which implies a value of 10.84 × $96 = $1,040.64 million for the equity of Johnson Machine Tools Company. Therefore, the implied total value of Johnson is: VF = VE + VD = $1,040.64 + $533.00 = $1,573.64 million LO: 3 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

18.18 Multiples analysis: Using the enterprise value/EBITDA multiple, what is the total value of Johnson Machine Tool Company? What is the per share value of Johnson’s stock? Solution: The enterprise value/EBITDA multiple for Billy’s is: EV/EBITDA = (($12.25 × 200 million shares) + $600 million debt) / ($385 million EBIT+ $71 million D&A) = 6.69 Therefore, the implied total value of Johnson is: Copyright © 2022 John Wiley & Sons, Inc.

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VF = 6.69 × ($208 million EBIT + $42 million D&A) = $1,672.50 million And the value of its stock is: VE = VF – VD = $1,672.50 million - $533.00 million = $1,139.50 million LO: 3 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

18.19 Multiples analysis: Which of the above multiples analyses do you believe is more appropriate? Solution: While the value estimates in the previous questions are reasonably similar, the enterprise value/EBITDA multiple is more appropriate for this analysis. The reason is that the capital structures of Johnson and Billy’s differ considerably, and the enterprise value/EBITDA multiple is less sensitive to differences in leverage. The debt/total capital ratio for Billy’s is $600 million /[($12.25 × 200 million shares) + $600 million debt] = 0.197 The debt/total capital ratio for Johnson is: $533 million / $1,672.50 million = 0.319 LO: 3 Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

18.20 Income approaches: You are using the FCFF approach to value a business. You have estimated that the FCFF for next year will be $123.65 million and that it will increase at a rate of 8 percent for each of the following four years. After that point, the FCFF will increase at a rate of 3 percent forever. If the WACC for this firm is 10 percent and it has no NOA, what is it worth? Copyright © 2022 John Wiley & Sons, Inc.

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Solution: You can value the FCFF for the first five years using the growing annuity formula from Chapter 6 (Equation 6.5).

  1 + g n    1.08 5  CF1 $123.65 PVA n =  1 −  1 − =  (WACC − g)   1 + WACC   (0.10 − 0.08)   1.1   = $541.98 million

The present value of the terminal value is

 FCFF1  (1 + g1 )4  (1 + g 2 )   $123.65  (1 + 0.08)4  (1 + 0.03)      (WACC − g2 ) (0.1 − 0.03) =  PV(TV5 ) =  5 5 (1 + WACC) (1 + 0.1) = $1,536.97 million and the value of the firm is therefore: VF = $541.98 million + $1,536.97 million = $2,078.95 million LO: 3 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

18.21 Valuing a private business: You want to estimate the value of a privately owned restaurant that is financed entirely with equity. Its most recent income statement is as follows:

Revenue Cost of goods sold

$3,000,000 600,000

Gross profit

$2,400,000

Salaries and wages

1,400,000

Selling expenses

100,000

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$ 585,000

You note that the profitability of this restaurant is significantly lower than that of comparable restaurants, primarily due to high salary and wage expenses. Further investigation reveals that the annual salaries for the owner and his wife, the firm’s accountant, are $900,000 and $300,000, respectively. These salaries are much higher than the industry median salaries for these two positions of $100,000 and $50,000, respectively. Compensation for other employees ($200,000 in total) appears to be consistent with the market rates. The median P/E ratio of comparable restaurants with no debt is 10. What is the total value of this restaurant? Solution: The owner is paying himself and his wife salaries that are above normal for this industry, probably to avoid double taxation (assuming that the restaurant is organized as a C corporation). You should adjust the income statement to reflect the market rates of compensation for these positions. The adjusted income statement is as follows:

Revenue Cost of goods sold Gross profit

$3,000,000 600,000 $2,400,000

Salaries and wages ($200,000 + $100,000 + $50,000)

350,000

Selling expenses

100,000

Operating profit (EBIT) Taxes (at 35%) Net income

$1,950,000 682,500 $1,267,500

Therefore, you estimate the company’s value to be: $1,267,500 × 10 = $12,675,000. The value of the company will be underestimated if no adjustment for excess compensation is made. LO: 3 Bloomcode: Application AASCB: Analytic Copyright © 2022 John Wiley & Sons, Inc.

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18.22 Valuing a private business: A few years ago, a friend of yours started a small business that develops gaming software. The company is doing well and is valued at $1.5 million based on multiples for comparable public companies after adjustments for their lack of marketability. With 300,000 shares outstanding, each share is estimated to be worth $5. Your friend, who has been serving as CEO and CTO (chief technology officer), has decided that he lacks sufficient managerial skills to continue to build the company. He wants to sell his 160,000 shares and invest the money in an MBA education. You believe you have the appropriate managerial skills to run the company. Would you pay $5 each for these shares? What are some of the factors you should consider in making this decision? Solution: You should consider at least two additional factors in valuing these equity shares. First, note that since the company has a total 300,000 shares of equity outstanding, you will be purchasing a majority of the shares and will gain control of the company. Second, while you might be able to use your excellent managerial skills to create new value for the firm, if your friend is a key person, you must consider the impact of his departure on the development and sales of the company’s products. Your valuation of the equity could be higher or lower than $5 per share, based on adjustments for both potential control premium and key person discount. LO: 4 Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

ADVANCED

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18.23 You plan to start a business that sells waterproof sun block with a unique formula that reduces the damage of UVA radiation 30 percent more effectively than similar products on the market. You expect to invest $50,000 in plant and equipment to begin the business. The targeted price of the sun block is $15 per bottle. You forecast that unit sales will total 1,500 bottles in the first month and will increase by 20 percent in each of the following months during the first year. You expect the cost of raw materials to be $3 per bottle. In addition, monthly gross wages and payroll are expected to be $13,000, rent is expected to be $3,000, and other expenses are expected to total $1,000. Advertising costs are estimated to be $35,000 in the first month, but to remain constant at $5,000 per month during the following eleven months. You have decided to finance the entire business at one time using your own savings. Is an initial investment of $75,000 adequate to avoid a negative cash balance in any given month? If not, how much more do you need to invest up front? How much do you need to invest up front to keep a minimum cash balance of $5,000? What is the break-even point for the business? Solution: The monthly cash budget is as follows: Monthly Cash Budget Month

$ 75,000

$ (9,000)

$ (9,400)

$ (5,480)

22,500

27,000

32,400

38,880

$ 97,500

$ 18,000

$ 23,000

$ 33,400

Raw materials

4,500

5,400

6,480

7,776

Gross wages and payroll

13,000

Advertising

35,000

5,000

Rent

3,000

Other expenses

1,000

Beginning cash balance Cash receipts Cash sales Total cash available Operations

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$ 56,500

$ 27,400

$ 28,480

$ 29,776

Capital expenditures

50,000

---

Total cash payments

$106,500

$ 27,400

$ 28,480

$ 29,776

Ending cash balance

$ (9,000)

$ (9,400)

$ (5,480)

$ 3,624

Financing and investments

With $75,000 of capital invested in the initial period, the company will have negative cash balances during each of the first three months and positive cash balances in the following months. Additional capital investment totaling $9,400 will be needed to avoid negative cash balances in month 2. In other words, you will have to invest $84,400* of capital in total at the beginning of the business just to avoid negative cash balances. To maintain a minimum cash balance of $5,000, you will need to make an initial capital investment of $89,400 ($84,400* + $5,000). Break-even: Fixed costs in the initial month will equal: $13,000 + $35,000 + $3,000 + $1,000 = $52,000 Fixed monthly costs in the following months will be: $13,000 + $5,000 + $3,000 + $1,000 = $22,000. Since variable costs per bottle are $3, the monthly break-even points for the firm are: $52,000 / ($15 – $3) = 4,333.3 bottles in the initial month and $22,000 / ($15 – $3) =1,833.3 bottles in the following months. The sales of the company are 1,500, 1,800, 2,160, and 2,592 bottles in the first four months. Therefore, the firm will start to make a profit in the third month. This can be seen from the cash budget analysis above. Month 3 is the first month the firm’s cash balance is increasing (becoming less negative). LO: 1 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

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18.24 For the previous question, assume that you do not have sufficient savings to cover the entire amount required to start your sunblock business. You are going to have to get external financing. A local banker whom you know has offered you a six-month loan of $20,000 at an APR of 12 percent. You will pay interest each month and repay the entire principal at the end of six months. Assume that instead of making a single up-front investment, you are going to finance the business by making monthly investments as cash is needed in the business. If the proceeds from the loan go directly into the business on the first day and are therefore available to pay for some of the capital expenditures, how much money do you need to take from your savings account every month to run the business and keep the cash balances positive? Solution: The monthly payment of the loan is $20,000 ×1% = $200. The cash budget without your investment is as follows: Monthly Cash Budget Month Beginning cash balance

$ 20,000 $(64,200) $(64,800) $(61,080) $(52,176) $(37,051)

Cash receipts Investments by owner Cash sales Total cash available

22,500

27,000

32,400

38,880

46,656

55,987

$ 42,500 $(37,200) $(32,400) $(22,200)

$(5,520)

$ 18,936

Cash payments Operations Raw materials

4,500

5,400

6,480

7,776

9,331

11,197

Gross wages and payroll

13,000

Advertising

35,000

5,000

Rent

3,000

Other expenses

1,000

Operations total

$ 56,500

$ 27,400

$ 28,480

$ 29,776

$ 31,331

$ 33,197

Financing and

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investments Capital expenditures

50,000

---

Debt/interest payment

*200

20, 200

Total cash payments

$106,700

$ 27,600

$28,680

$ 29,976

$ 31,531

$ 53,397

Ending cash balance

$(64,200) $(64,800) $(61,080) $(52,176) $(37,051) $(34,461)

*($20,000 x 12% x 1/12) Therefore, you need to put in $64,200 initially, and $600 ($64,800–64,200) in the next month. You don’t need to invest in more money afterward because the cash balance is increasing. LO: 1 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

18.25 Your friend is starting a new company. He wants to write a business plan to clarify the company’s business outlook and raise venture capital. Knowing that you have taken this course, he has asked you, as a favor, to help him prepare a template for a business plan. Prepare a template that includes the key elements of a business plan. Solution: Business varies and so does a business plan. Here is a template for an intermediate-level business plan, which could be tailored to specific industry and company situations: 1. Executive Summary 1.1 Objectives 1.2 Mission 1.3 Keys to Success 2. Company Overview 3. Product Description 4.

Market Analysis 2.1 Market Segmentation 2.2 Target Market Segment Strategy

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2.3 Market Needs 2.4 Competitions and Buying Patterns 5. Marketing and Sales 5.1 Competitive Edge 5.2 Sales Strategy 6. Operations 6.1 Production 6.2 Distribution 6.3 Supply 7. Management and Ownership 7.1 Organizational Structure 7.2 Management Team 7.3 Ownership 8. Financial Plan 8.1 Break-even Analysis 8.2 Projected Profit and Loss 8.3 Projected Cash Flow 9. Appendices: Tables and charts LO: 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

18.26 A friend of yours is trying to value the equity of a company and, knowing that you have read this book, has asked for your help. So far she has tried to use the FCFE approach. She estimated the cash flows to equity to be as follows:

Sales

$800.0

− CGS

−450.0

− Depreciation

−80.0

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− Interest

−24.0

Earnings before taxes (EBT)

$246.0

− Taxes (0.35 × EBT)

−86.1

= Cash flow to equity

$159.9

She also computed the cost of equity using CAPM as follows: kE = kF + βE(Risk premium) = 0.06 + (1.25 × 0.084) = 0.165 or 16.5% where the beta is estimated for a comparable publicly traded company. Using this cost of equity, she estimates the discount rate as WACC = xDebtkDebt pretax(1 − t) + xcs kcs = [ 0.20 × 0.06 × (1 − 0.35)] + (0.80 × 0.165) = 0.1398 or .14; or 14% Based on this analysis, she concludes that the value of equity is $159.9 million/0.14 = $1,142 million. Assuming that the numbers used in this analysis are all correct, what advice would you give your friend regarding her analysis? Solution: There are a number of potential problems with your friend’s analysis. First, she has calculated FCFF incorrectly. She is assuming that net income equals FCFE. Once she obtains net income she should add back depreciation, subtract capital expenditures and additions to working capital, and subtract any net repayment of debt principal. Second, she is using the incorrect discount rate. She should be using the cost of equity to discount the FCFE. Finally, since your friend is using the perpetuity formula, she is assuming that the expected future FCFE will be constant forever. You should inquire whether this is really what she expects. LO: 3 Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

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18.27 Forever Youth Technology is a biochemical company that is two years old. Its main product, an antioxidant drink that is supposed to energize the consumer and delay aging, is still under development. The company’s equity consists of $5 million invested by its founders and $5 million from a venture capitalist. The company has spent $3 million in each of the past two years, mostly on lab equipment and R&D costs. The company has had no sales so far. What are the challenges associated with valuing such a young and uncertain company? Solution: As discussed in the chapter, it is very difficult to value such a young firm with many uncertainties. The company has a short history, high investments, no sales, and highly uncertain cash flows in the future. The cost approach is not valid for such a young biochemical company. It is hard to value the company using multiples analysis because of the lack of sales and negativity of earnings, and because of lack of comparable companies of the same business. The transaction analysis approach is also hard to apply. Despite the many uncertainties, we should try to estimate the future cash flows and risks associated with these cash flows. First of all, we need to estimate the probability and time length to achieve success in developing the product. In addition, we need to find out what happens in case the firm’s capital is used up before the product is developed. We need to decide whether, based on the company’s future prospects, it is possible to raise additional external capital at that point of time, and if not, we need to decide whether the business has any liquidation value. Then, we need to estimate the market demand and shares as well as target price of the product, in case it is developed successfully. We also need to estimate the short-term and long-term growth rate of the company based on market, industry, and firm-specific conditions. LO: 4 Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

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18.28 Mad Rock Inc. is a company that sells music online. It is expected to generate earnings of $1 per share this year after its Web site is upgraded and online marketing is stepped up. The stock price of Mad Rock has rocketed from $8 to $95 per share in the past 12 months. The cost of capital for the company is 18 percent. Of course, the future of a young Internet company such as Mad Rock is highly uncertain. Nevertheless, using the very limited information provided in this problem, do you think $95 per share could be a fair price for its stock? Support your argument with a simple analysis. Solution: Assume that the earnings of $1 will be realized. To simplify the problem, assume that all earnings will be paid out as dividends. Using the dividend growth model, $95 = $1/ (0.18 – g), which implies that g = 16.9474%. We know that it is not possible for a firm to grow at this rate forever because g is a growth rate that must be sustainable in perpetuity. No firm can grow indefinitely at such a high rate, which is many times the average growth rate of the world economy. Therefore, this analysis suggests that Mad Rock’s stock is overpriced. On the other hand, it is possible that Mad Rock could grow very rapidly for a few years and then grow at a sustainable rate that justifies the $95 price. For example, if we assume that a sustainable rate is 6 percent, we can solve for the earnings per share that would be required to justify a $95 stock price. This value is $95 = D/ (0.18 – 0.06) which implies D = $11.40. Therefore, if the earnings per share increased rapidly to a value above $11.40, it is possible that a price of $95 could be justified. How much above $11.40 it would have to be, would depend on how quickly it increased. One other consideration here is that, as the business matures, its cost of capital is likely to decrease because its risk will decline. This will tend to increase the value of the equity. LO: 4 Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective Copyright © 2022 John Wiley & Sons, Inc.

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18.29 At the end of 2020, the value of the S&P 500 Index divided by the estimated 2020 earnings for S&P 500 firms (the S&P 500 P/E multiple) was 36.80. Assume that the long-term Treasury bond yield was 1.88 percent, the market risk premium was 6 percent, and firms in the S&P 500 were expected to pay out an average of 40.2 percent of their earnings as dividends in the future. At what rate were dividends paid by S&P 500 firms expected to grow in the future? Solution: The equation 18.1 for the Price/earnings multiple based on constant-growth model can be used to answer this question.

P0 b = E1 kcs − g Recognizing that E1 = E0 × (1 + g) we can rewrite this equation as:

P0 (1+g)  b = E0 kcs − g Since we know that P0/E0 = 36.80, and b = 40.2%, all that we have to do is calculate kcs in order to use the above equation to solve for g. We can use CAPM to estimate kcs: kcs = Rrf + (βcs × Market risk premium) From the problem statement, we know that Rrf = 1.88 percent and that the market risk premium equals 6 percent. Therefore, we only need a value for βcs in order to calculate kcs. Since The S&P 500 represents more than 70 percent of the market capitalization of all stocks traded in the U.S. (see Chapter 9), we know that the beta for the S&P will be relatively close to 1. Using this value in CAPM we estimate that kcs equals: kcs = 0.0188 + (1 × 0.06) = 0.0788. We can now write the formula for the P/E as follows:

P0 (1+g)  0.402 = 36.80 = E0 (0.0788 − g) Solving for g yields g = 0.06714, or 6.71 percent. The S&P 500 index value at the end of 2020 implied that the market expected the dividends paid by firms in the S&P 500 to increase at an average annual rate of 6.71 percent forever. Copyright © 2022 John Wiley & Sons, Inc.

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LO: 3 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

18.30 The S&P 500 P/E multiple of 36.80 at the end of 2020 was higher than its historical average of approximately 16. Some financial commentators argued that this meant that the firms in the S&P 500 were, on average, overvalued at the end of 2020. Based on your analysis in problem 18.29 and the concepts covered in this book, do you think that these commentators are right or wrong? Solution: There is no way to know for sure whether the commentators are right or wrong. If the market is semi-strong form efficient, as this term is defined in Chapter 2, then all public information should be reflected in the prices of S&P 500 shares. This implies that there is no way for an outsider to know for sure whether the firms in the S&P 500 were, on average, over- or undervalued. However, we can make some observations. First, with regards to the analysis in problem 18.29, if the constant growth perpetuity model (which was used to derive Equation 18.1) is an appropriate model for the dividends paid by S&P 500 firms, then the implied growth rate of 6.71 percent suggests that the market might be over-valuing the shares of S&P 500 firms. Recall from Chapter 9 that g cannot be greater than the sum of the expected real growth rate in the economy and the expected rate of inflation. This sum has historically been less than 6.71 percent. If g turns out to be less that 6.71 percent in the future, then the value of the S&P 500 index will decline⎯meaning that the firms in the S&P 500 would have been overvalued on average at the end of 2020. On the other hand, if the mixed (supernormal) dividend growth model discussed in Chapter 9 is a more appropriate model for dividend growth at S&P 500 firms, then it is possible that the firms in the S&P 500 were not, on average, overvalued at the end of 2020. For example, with the election of a new President in 2020 investors might have expected

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relatively large increases in earnings during the following two or three years as new progrowth and tax policies were expected to be implemented. LO: 3 Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

18.31 You own a company that produces and distributes course packets for classes at local universities online. You have asked a friend to invest $35,000 in the business. Your friend wants to know what the business is worth so that he can determine how much of the equity (e.g., what percentage) he should expect to receive for his investment. You offer to help him value the business. The business is expected to generate revenue of $110,000 and incur cash operating expenses of $70,000 next year. Over the following three years, revenue and cash operating expenses are expected to increase 15 percent, 10 percent, and 7 percent. After year 4 they are expected to grow 2 percent per year forever. Depreciation and amortization, capital expenditures, and additions to working capital are expected to equal 5 percent, 6 percent, and 1 percent of revenue, respectively, in the future. You have determined that a target capital structure of 10 percent debt and 90 percent equity is reasonable for this business. With this capital structure, the pretax cost of debt will be 6 percent and the beta for the equity will be 1.30. The average tax rate for the business is 10 percent, and the marginal rate is 20 percent. The risk-free rate is 4.25 percent, and the market risk premium is 6.01 percent. What is a 100 percent equity interest in the business worth? What percentage of the equity should your friend get for his investment? Solution: We can value the equity of this business using the FCFF Income approach. We will first estimate the WACC using Equation 13.7. To do this we calculate kcs using Equation 13.4: kcs = Rrf + (βcs × Market risk premium) = 0.0425 + (1.30)(0.0601) = 0.1206, or 12.06% and substitute into Equation 13.7:

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WACC = xDebt kDebtpretax (1 − t ) + xps kps + xcs kcs = (0.10)(0.06)(1 − .10) + (0)(0) + (0.9)(0.1206) = 0.1140 or 11.40% Note that we use the average tax rate in this calculation because we are assuming that the company will continue to operate on a stand-alone basis and that its average tax rate will continue to be 10 percent. We next forecast the FCFF and discount them to the present using the WACC to obtain the enterprise value. There is no mention of NOA in the problem statement and so we assume that there are none. Since we are assuming that the firm will have 10 percent debt, the value of the equity equals 90 percent of the enterprise value. The spreadsheet below shows the forecasted FCFF for the next five years and the calculation of the equity value. The trickiest part of the calculations in the spreadsheet is in estimating the additions to working capital. Unlike depreciation and amortization and capital expenditures, we do not simply multiply the 1 percent value given in the problem statement by revenue in the same year to obtain additions to working capital. The 1percent value is for the total working capital that the business has. Since it already has working capital in the previous year, we multiply the change in revenue in the upcoming year by 1 percent. This tells us how much must be invested in working capital at the beginning of that year in order to have enough working capital to support the forecasted revenue. For example, the additions to working capital for Year 1 (remember that this is also the beginning of Year 2) equals: $110,000 Year 1 revenue × 15% Year 2 revenue growth × 1% = $165

YEARS 1

$110,000

$126,500

$139,150

$148,891

$151,868

Operating costs

70,000

$80,500

$88,550

$94,749

$96,643

Depreciation and amortization (5%)

5,500

6,325

6,958

7,445

7,593

Operating profit

34,500

39,675

43,643

46,697

47,631

Taxes (10%)

3,450

3,968

4,364

4,670

4,763

NOPAT

31,050

35,707

39,278

42,027

42,869

Revenues

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Depreciation and amortization

5,500

6,325

6,958

7,445

7,593

Capital expenditures (6%)

6,600

7,590

8,349

8,933

9,112

165

127

$29,785

$34,315

$37,790

$40,509

$41,319

Additions to working capital (1%) FCFF Terminal Value with 2% growth

$439,721

FCFF + TV

$29,785

$34,315

$37,790

$480,230

PV(FCFF) @ 11.40%

$26,738

$27,654

$27,337

$311,860

Enterprise Value

$393,589

Less: 10% debt

$39,359

Equity value

$354,230

The equity value that we have calculated does not take into account any adjustments for control, lack of marketability (remember that it is a private firm), or key people. Since there is no information in the problem statement, we do not consider them here. With this caveat, we can calculate the percentage of the equity that your friend should receive as: $35,000/$354,230 = 0.988, or 9.88% LO: 3 Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

Sample Test Problems 18.1

You plan to start a business to produce and sell custom kitchen cabinets. The targeted price for each order of cabinets is $10,000. You estimate that you will receive orders for cabinets for eight kitchens in each of the first two months, nine kitchens in the third month, and ten kitchens in the fourth month. The cost of the equipment necessary to produce the cabinets is $105,000. You expect the cost of raw materials to be $3,000 per order. In addition, you expect monthly gross wages and payroll to be $27,000, rent to be $8,000, and other expenses to total $4,000. You also expect advertising costs to be $10,000 in the first month,

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but to remain constant at $1,000 per month during the following three months. How much will you have to initially invest ensure that you have a cash balance of $10,000 at the beginning of the second month? If you invest this amount, what will be your cash balance at the end of the fourth month? Solution: Ending cash balance of Month 1 = Beginning cash balance of Month 2 = $10,000 Ending cash balance of Month 1 = Beginning cash balance of Month 1 + Cash receipt – Cash payment $10,000 = Beginning cash balance of Month 1 + $80,000* – $178,000** Beginning cash balance of Month 1 = $108,000 Cash Budget for 4 months: Month 1

Month 2

Month 3

Month 4

$108,000

$10,000

$26,000

$49,000

80,000

90,000

100,000

Total cash receipts

*$80,000

$80,000

$90,000

$100,000

Total cash available

$188,000

$90,000

$116,000

$149,000

$105,000

Raw material cost

24,000

27,000

30,000

Gross wages

27,000

Rent

8,000

Other expenses

4,000

Advertising cost

10,000

1,000

Total cash payments

**$178,000

$64,000

$ 67,000

$ 70,000

Ending cash balance

$10,000

$26,000

$ 49,000

$ 79,000

Beginning cash balance Cash receipts: Cash sales

Cash payments: Equipment

We have to initially invest $108,000 to ensure that we have a cash balance of $10,000 at the beginning of the second month. If we invest $108,000, our cash balance at the end of the fourth month will be $79,000. LO: 1 Bloomcode: Application Copyright © 2022 John Wiley & Sons, Inc.

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AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

18.2

Which of the following is/are usually included in an entrepreneur’s business plan? a. Detailed description of the company’s products and services. b. Discussion of the management team, including organizational structure. c. A listing of the types of securities that have been issued and who owns them. d. A market analysis. e. All of the above are typically included in a business plan.

Solution: Option “e” is the correct answer because all of the above items are usually included in a business plan. LO: 2 Bloomcode: Knowledge AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

18.3

Sessler Corporation is a private company that had EBIT of $186 million and depreciation and amortization of $22 million in the most recent fiscal year. At the end of that year, a similar public firm has an enterprise value/EBITDA multiple of 4.3. What is the implied enterprise value of Sessler?

Solution: We can estimate the enterprise value for the Sessler Corporation as:

 Enterprise value  VF =   EBITDACompany being valued  EBITDA  Comparable EBITDA = EBIT + DA = $186 million + $22 million = $208 million VF = 4.3 × $208 million VF = $894.40 million LO: 3 Copyright © 2022 John Wiley & Sons, Inc.

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Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

18.4

Winters Inc. management estimates that the company will generate after-tax free cash flows from the firm (FCFF) of $12.5 million, $16.8 million and $19.7 million, respectively, over the next three years. After that, FCFF are expected to grow at a constant five percent per year forever. The company has $5 million in nonoperating assets. If the appropriate WACC is 8 percent, what is the enterprise value of this business?

Solution: We can calculate the enterprise value of Winters Inc. using following equation: VF = PV(FCFT) + PV(TVT) + NOA The present value of the free cash flows is:

PV(FCFF3 ) =

$12.5 million $16.8 million $19.7 million + + = $41.62 million 1 + 0.08 (1 + 0.08)2 (1 + 0.08)3

We can then estimate the cash flows for the remainder of the business’s life (the terminal value) using two simple steps: (1) calculating the present value of all cash flows after the final (third) year of the detailed forecast using the formula for a growing perpetuity (2) discounting this value to the present

TV3 =

FCFF3  (1 + g) $19.7 million  (1+0.05) + = $689.50 million WACC − g 0.08 − 0.05

PV(TV3 ) =

TV3 $689.50 million + = $547.35 million 3 (1+WACC) (1 + 0.08)3

The total value of Winters Inc.: VF = PV(FCFT) + PV(TVT) + NOA VF = $41.62 million + $547.35 + $5 million VF = $593.97 million Enterprise value of Winters Inc. is $593.97 million. LO: 3 Copyright © 2022 John Wiley & Sons, Inc.

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Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

18.5

Do private companies have audited financial statements prepared in accordance with GAAP?

Solution: There is no requirement that the financial statements of private companies be audited. Some private companies have complete, audited financial statements, whereas others have incomplete financial statements that are not prepared in accordance with the generally accepted accounting principles (GAAP). LO: 4 Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

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Chapter 17

Dividends, Stock Repurchases, and Payout Policy Before You Go On Questions and Answers Section 17.1 1.

How does a dividend affect the size of a stockholder’s investment in a firm? A dividend reduces the size of the stockholder’s investment in a firm. After a dividend is issued, the shareholder owns the same percentage of the firm, but its value falls by an equivalent amount. It reduces the stockholders’ investment in a firm by distributing some of that investment to them. The value that stockholders receive through a dividend was already theirs. A dividend simply takes this value out of the firm and returns it to them. The shareholder can use the dividend as he or she sees fit (after paying taxes).

List and define four types of dividends. 1. Regular Cash Dividend — Paid out regularly, usually quarterly. This dividend is usually set at a level that the board expects to be sustainable in the long run. 2. Extra Dividend — Usually paid at the same time as a regular dividend. Often used to pay out extra earnings that will not be maintainable over the long run and/or to ensure that a certain percentage of earnings are returned to shareholders as dividends. 3. Special Dividend — One-time dividend usually resulting from a special event such as the sale of an asset or a large cash balance. For example, Microsoft’s special dividend of $32.4 billion as described in the chapter.

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4. Liquidating Dividend — Dividend resulting from the sale of assets of a company being liquidated (dissolved). This is the value left over for shareholders after the claims of other investors, such as bondholders, have been paid.

What are the key events and dates in the dividend payment process? •

Board Vote — The firm’s board votes to issue a dividend, specifying the amount and key dates of the issue.

•

Public Announcement Date — The firm releases the information regarding the dividend payment. Often the stock price will move on the dividend announcement date because investors use this dividend information as a signal regarding the future prospects of the firm.

•

Ex-Dividend Date — This is the first date on which purchasing the stock will not result in receiving a dividend.

•

Record Date — This is the date on which one must be a stockholder of record to receive a dividend. This date is set by the board and is used by the exchange to set the ex-dividend day. The difference between the ex-dividend date and the record date reflects the time needed to compile and update the records of stock ownership.

•

Payable Date — This is the date the dividend will actually be paid.

Section 17.2 1.

What is a stock repurchase? A stock repurchase takes place when a company purchases some of its own stock from shareholders. Shareholders who choose to participate receive payment in exchange for their shares.

How do stock repurchases differ from dividends? There are four major ways in which stock repurchases differ from dividends. First, the payments are not made on a pro-rata basis. Some stockholders choose to take the repurchase offer, whereas others choose to hold on to their shares. Second, stock repurchases reduce the number of outstanding shares. This can change the liquidity of the

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shares and ownership control of the firm. Third, stock repurchases are taxed differently, often resulting in a smaller tax burden for investors. Finally, accounting for stock repurchases and dividends is different. When a dividend is issued, the retained earnings account decreases on the liability and stockholder’s equity side of the balance sheet. For a stock repurchase, the treasury stock account on the right side of the balance sheet becomes more negative. Both stock repurchases and dividends reduce the cash account on the asset side of the balance sheet.

In what ways can a company repurchase its stock? Open-Market Repurchase — The company purchases shares at the exchange in the same manner as normal trades. This is convenient for small ongoing repurchases. Regulations meant to prevent price manipulation limit the amount that a company can purchase at the exchange in a day. These regulations make an open-market repurchase cumbersome for large share repurchases. Tender Offer Repurchases — The company makes an open offer to buy shares. There are two types of tender offers. In a fixed-price offer, the company offers a fixed price to investors who agree to sell their shares. In a Dutch auction offer, the company seeks bids for the number of shares investors would sell at a series of prices. The company may then choose the price in the series that will result in the desired number of shares being repurchased. Targeted Stock Repurchase — A company repurchases shares directly from one or more large stockholders. This is sometimes used to negotiate with a large stockholder who is attempting to gain control of the company.

Section 17.3 1.

What are the benefits and costs associated with dividends? The benefits associated with dividends are as follows: a.

Dividends may attract investors who prefer to receive income directly from their investments. However, the tax costs of dividends may drive away other investors.

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Dividends can function as a signal to investors that the company is performing well and has higher than expected cash flows.

Dividends can help align manager and stockholder incentives. By issuing dividends and raising capital through equity issues (rather than internal funds), managers are subject to more scrutiny. This increases the incentives for managers to perform well.

Dividends reduce equity claims on the company; this can help managers achieve the target capital structure suggested by the trade-off theory.

Some costs associated with dividends include: a.

Taxes. Dividends have historically been taxed at a higher rate than other forms of income.

Reinvestment costs. Investors who don’t intend to spend the cash must pay the transactions costs associated with reinvesting (brokerage fees, etc.).

Increased cost of debt. By reducing the amount of equity through a dividend issue, the firm becomes more leveraged. If the increase is significant, this could increase the risk associated with the company and increase the cost of debt should the company desire to borrow.

How do stock prices react to dividend announcements? Stock prices generally react favorably to announcements of higher-than-expected dividends and negatively to announcements of lower-than-expected dividends. This is consistent with the theory that dividends act as signals that convey to investors positive or negative changes to the firm’s fundamentals.

Why might stock repurchases be preferred to dividends? Stock repurchases might be preferred to dividends because they result in lower taxes for investors and allow management more flexibility in distributing value. If the company has excess cash flow that is uncertain to continue in the future, it may be beneficial for

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management to initiate a stock repurchase, which can be quietly halted without sending a negative signal to investors.

Section 17.4 1.

What is a stock dividend? A stock dividend is a distribution of shares of stock to existing stockholders in proportion to the fraction of shares they own.

How does a stock dividend differ from a stock split? A stock dividend usually occurs on a regular basis, and the number of new shares is usually small compared to the number of existing shares. Stock splits are infrequent and involve a large number of new shares. For example, in a 2-for-1 split the number of newly created shares is equal to the number of existing shares, and the total number of shares is doubled.

How does a stock dividend differ from other types of dividends? Unlike other dividends, a stock dividend does not distribute anything of value, as the stockholders’ claim on the assets of the firm is unchanged. A stockholder may own more shares, but each share is worth less. The effects must exactly offset each other.

Section 17.5 1.

How are dividend payouts affected by expected earnings? Managers tend to set dividend policies that are achievable with expected long-run sustainable earnings. Because of the negative effect of a dividend reduction, managers are hesitant to increase dividends if they are concerned that the increase may have to be undone in the future.

What did the 2005 study conclude about how managers view stock repurchases? The study concluded that managers tend to view repurchases as the preferred option for returning extra cash left over after investment spending. The study also found that

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managers prefer the flexibility of stock repurchase plans, repurchasing shares when they believe the companies’ stock is undervalued. Finally, managers believe that the decision between stock repurchases, and dividend payments has little effect on what type of investor is likely to own the company’s stock.

List three practical considerations that managers should take into account when setting a dividend policy? •

The level of earnings (cash flows from operations) in excess of a company’s investment requirements over the long run and how certain this level is.

•

Whether the firm has sufficient financial reserves to maintain the dividend payout during periods when earnings are down, or investment opportunities are up.

•

Whether the firm has sufficient financial flexibility to maintain dividends if unforeseen circumstances wipe out its financial reserves when earnings are down.

•

Whether the firm is able to quickly raise enough capital if necessary.

•

The control (voting) implications if a firm chooses to finance dividends by selling equity.

Self-Study Problems 17.1

You would like to own a common stock that has a record date of Friday, September 4, 2020. What is the last date that you can purchase the stock and still receive the dividend?

Solution: The ex-dividend date is the first day that the stock will be trading without the rights to the dividend, and that occurs two days before the record date, or on Wednesday, September 2, 2020. Therefore, the last day that you can purchase the stock and still receive the dividend will be the day before the ex-dividend date, or Tuesday, September 1, 2020.

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You believe that the average investor is subject to a 20 percent tax rate on dividend payments. If a firm is going to pay a $0.30 dividend, by what amount would you expect the stock price to drop on the ex-dividend date?

Solution: If the tax rate of the average investor is reflected in the stock price change, we would expect investors to receive 80 percent (1.0 − 0.20 = 0.80 or 80 percent) of the dividend after paying taxes. This would necessitate a $0.24 (0.80 × $0.30 = $.24) drop in the stock price of the firm on the ex-dividend date.

17.3

Management of the Veil Acts Company just announced that instead of a regular dividend this quarter, it will be repurchasing shares using the same amount of cash that would have been paid in the suspended dividend. Should this be a positive or negative signal from the firm?

Solution: Veiled Acts has replaced a committed cash flow with one that is stated but does not have to be acted on. Therefore, the firm’s actions should be greeted with suspicion, and the signal is not a positive one.

17.4

Management of the Bernie Rubbel Company has just declared a three-for-one stock split. If you own 12,000 shares before the split, how many shares do you own after the split? What if it were a one-for-three reverse stock split?

Solution: You will own three shares of Bernie Rubbel for every one share that you currently own. Therefore, you will own 3 × 12,000 = 36,000 shares of the company. In the case of the reverse split, you will own 1/3 × 12,000 = 4,000 shares of the company.

17.5

Two publicly traded companies in the same industry are similar in all respects except one. Whereas Publicks has issued debt in the public markets, Privicks has never borrowed from any public source. In fact, it always uses private bank debt for

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its borrowing. Which firm might be marginally more inclined to have a more aggressive regular dividend payout than the other? Explain. Solution: If all other things are the same about the two companies, then Publicks could be expected to have a more aggressive dividend payout. Since Publicks has issued debt in the past, while Privicks has not, Publicks is likely to have greater access to the capital markets than Privicks. Firms with greater access to capital markets can be more aggressive in their dividend payouts to the extent that they can raise capital more easily (cheaply) if necessary.

Discussion Questions 17.1

Suppose that you live in a country where it takes 10 days to settle a stock purchase. By how many days will the ex-dividend date precede the record date? The ex-dividend date is the first day that a stock will trade without the right to a dividend. In the United States, where it takes three days for a stock purchase to settle, the exdividend date is two days before the record date. Therefore, if it takes ten days for a stock purchase to settle, then the ex-dividend date will be nine days before the record date.

LO: 1 Level: Basic Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

17.2

The price of a share of stock is $15.00 on Tuesday, November 17, 2020. The record date for a $0.50 dividend is Friday, November 20, 2020 If there are no taxes on dividends, what would you expect the price of a share to be on each day from

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November 17 through 20 if no other information relevant to the price of the shares becomes public? Since we are excluding all non- dividend related information, the price of the shares will remain constant until the ex-dividend date, when the price will drop by $0.50 per share. November 17—$15.00 November 18—$15.00 November 19—$14.50 November 20—$14.50 LO: 1 Level: Basic Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

17.3

You find that you are the only investor in a particular stock who is subject to a 15 percent tax rate on dividends (all other investors are subject to a 5 percent tax rate on dividends). Is there greater value to you in holding the stock beyond the exdividend date or selling the stock and then repurchasing it on or after the exdividend date? Assume that the stock is currently selling for $10.00 per share and the dividend will be $0.25 per share. All other investors (who we can assume will be dictating the market equilibrium price) expect to pay 5 percent tax rate on their dividend receipt. Therefore, they expect to keep $0.25 × (1 – 0.05) = $0.2375 of the dividend after taxes are paid. Then, you would expect the price of the shares to be $9.7625 ($10.00 – $0.2375) on the ex-dividend date. However, you believe the correct price (based on your tax situation) to be $10.00 – (0.25 × (1 – 0.15)) = $9.7875. Therefore, by holding on to the stock, you would find that the share price dropped by $0.025 more than what you expected. Therefore, if we ignore transactions costs, it would be beneficial for you to sell your shares before the ex-

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dividend date and then repurchase them on the ex-dividend date. This argument, of course, ignores any taxes that might have to be paid by selling the shares at $10.00. LO: 1 Level: Intermediate Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

17.4

Discuss why the dividend payment process is so much simpler for private companies than for public companies. Since private companies have greater access to their shareholders than their public counterparts, the process of paying a dividend is not complicated by having to constantly monitor who owns the companies’ shares at any given time. In fact, the shares are bought and sold less frequently in private companies. This makes the dividend process much easier for private companies than for the public ones.

LO: 1 Level: Basic Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

17.5

You are the CEO of a firm that appears to be the target of a hostile takeover attempt. Thibeaux Piques has been accumulating the shares of your stock and now holds a substantial percentage of the outstanding shares. You would like to purchase the shares that he owns. What method of stock repurchase will you choose? Since Mr. Piques is hostile to your firm, it will probably not help you to use an openmarket purchase. You could announce a tender offer, but unless he is willing to sell his shares for purely economic gain (and ignore the benefits of control of your firm), then a

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tender offer would probably not work very well either. You could negotiate directly with Mr. Piques for his shares and therefore isolate the shares that you need to purchase using a targeted share repurchase. However, this direct negotiation might not be advantageous to your remaining shareholders, and it may require a premium price to convince Mr. Piques to sell his shares. LO: 2 Level: Basic Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

17.6

You have accumulated stock in a firm that does not pay cash dividends. You have read that, according to Modigliani and Miller, you can create a “homemade” dividend should you require cash. Discuss why this choice may not be very good for the value of your position. You could sell a portion of your shares to generate a cash dividend for yourself. However, if no other investors take that course of action, then you would be the only investor liquidating a portion of your holdings. If 20 percent of the voting interest in this firm helps you maintain a certain level of control of the firm, then dropping below that threshold might be enough for your diluted voting interest to lose whatever control of the firm you had maintained. Additionally, because of the real life existence of information or transaction costs and taxes, as well as the firm’s real investment policy, the value of your investment may be affected.

LO: 3 Level: Basic Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

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You have just read a press release in which a firm claims that it will be able to generate a higher level of cash flows for its investors going forward. Justify the choice of a dividend payout that could credibly convey that information to the market. Either an extra or a special dividend is signaling a higher level of cash flow but without sustainability. The best way to convey to the market that this new level of cash flow is permanent is to increase (or commence) a regular cash dividend since a regular dividend comes with the expectation that it will not be reduced without unforeseen events occurring in the future.

LO: 5 Level: Basic Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

17.8

Some people argue that a high tax rate on dividends creates incentives for managers to go about their business without credibly convincing investors that the firm is doing well, even when it is. Discuss why this may be true. A credible signal is usually interpreted as a signal that is costly. Paying a regular dividend is costly, and we know that it credibly signals that the firm expects to maintain the current level of cash flow. If dividends are taxed at a rate high enough to discourage firms from paying them (discouraged because a very small portion of the cash sent to investors reaches them after the effects of taxes), the government is discouraging a credible signal that the firm’s prospects are still good. Without that costly signal, managers may continue about their normal routine without finding other ways to convey a firm’s prospects to investors.

LO: 3 Level: Basic

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Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

17.9

Fled Flightstone Mining’s management does not like to pay cash dividends due to the volatility of the company’s cash flows. Fled management has found, however, that when it does not pay dividends, its stock price becomes too high for individual investors to afford round lots. What course of action could Fled take to get its stock price down without dissipating firm value for stockholders? Fled Flightstone Mining can double, triple, quadruple, etc., the number of shares outstanding without taking any meaningful economic steps. That is, it can take a 2-for-1, 3-for-1, or 4-for-1, etc., stock split. This would increase the number of shares outstanding and decrease the value of each share outstanding proportionately. Since each shareholder would continue owning his or her prior pro-rata share of the firm, shareholders would not see any of their value dissipated by the firm’s actions.

LO: 5 Level: Basic Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

17.10 Lintner found that firms are reluctant to make dividend changes that might have to be reversed. Discuss the rationale for that behavior. The simplest reason is that the markets look to dividends for the information that the dividends convey as well as for their economic benefit. That is, an increase in the dividend rate tells the market that the cash flow that the firm produces, above and beyond that needed for projects, is anticipated to remain high. If the firm were to quickly reverse the increased dividend rate, then that might convey to the market that the firm’s fortunes

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either were not that good to begin with or have changed drastically. Such a reversal could convey that the firm is riskier than what investors anticipated before the series of events described above. Therefore, firm management would naturally want to keep from having to quickly reverse its dividend decisions. LO: 5 Level: Basic Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

Questions and Problems BASIC 17.1

Dividends: The Poseidon Shipping Company has paid a $0.25 dividend per quarter for the past three years. Poseidon just lowered its declared dividend to $0.20 for the next dividend payment. Discuss what this new information might convey concerning Poseidon management’s belief about the future of the company.

Solution: Since dividends convey information concerning the future prospects of the firm, any change in dividend levels is also believed to convey a change in management’s forecast of the firm’s prospects. That is, lowering the dividend from $0.25 to $0.20 suggests that the firm’s future cash flow may be reduced. This reduction could be because of a general reduced level of profitability, because the firm’s projects are winding down, or even because of an increased need to invest in new positive NPV projects for the future. LO: 1 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance Copyright © 2022 John Wiley & Sons, Inc.

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AICPA: Industry/Sector Perspective

17.2

Dividends: Marx Political Consultants has decided to discontinue all of its business operations. The firm has total debt of $7 million, and the liquidation value of its assets is $10 million. If the book value of the firm’s equity is $5 million, then what will be the amount of the liquidating dividend when the firm liquidates all of its assets?

Solution: The liquidating value of the firm’s assets is $10 million while the firm owes $7 million. Therefore, $3 million will remain after complete liquidation for the shareholders. The firm will be able to pay a $3 million dividend to its shareholders. LO: 1 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

17.3

Dividends: Place the following in the proper chronological order, and describe the purpose of each: ex-dividend date, record date, payment date, and declaration date.

Solution: 1. Declaration date: the day the dividend payment was announced. 2. Ex-dividend date: the first day you can buy shares and not receive the dividend. 3. Record date: the day shareholders of record receive the dividend when it is paid. 4. Payment date: the date when the dividend is actually paid. LO: 1 Bloomcode: Knowledge AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

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Dividends and firm value: Explain how the issuance of new securities by a firm can produce useful information about the issuing firm. How can this information make the shares of the firm more valuable, even if it only confirms existing information about the firm?

Solution: When issuing new securities, the issuing firm must submit to a process that amounts to a special audit by outsiders such as investment bankers and other experts. This additional production of information increases the level of monitoring concerning the firm’s actual financial status. In a sense, it reduces the variability in the information that the firm may already have released. If the production of this information reduces the level of risk borne by investors, then the issue of new securities could actually increase the value of the securities issued by the firm and, in turn, the total value of the firm. LO: 1 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

17.5

Dividends: Explain why holders of a firm’s debt should insist on a covenant that restricts the amount of cash dividends the firm pays.

Solution: We have to remember that any cash paid to shareholders reduces the amount that is available to bondholders in the event of bankruptcy. Because bondholders are aware of this potential problem, they should then restrict the amount of cash that can be paid to shareholders to at least a level where bondholders will still be able to generate their expected rate of return. LO: 1 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance

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AICPA: Industry/Sector Perspective

17.6

Stock splits and stock dividends: Explain why managers of firms might prefer that their firms’ shares trade in a moderate per-share price range rather than in a high per-share price range. How do managers of firms keep their shares trading in a moderate price range?

Solution: Historically, the transactions and liquidity costs to trade 100 shares were lower than the cost to trade a smaller number of shares. Therefore, if small investors could not afford to trade 100 shares, then they might refrain from purchasing the shares. In that event, the high per-share price of the shares might eliminate potential investors for those shares. Consequently, firms preferred that their shares trade in an affordable range rather than at an expensive price per share. Note that no conclusive empirical evidence supports that notion. LO: 4 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

17.7

Dividends: Scintilla, Inc., stock is trading for $10.00 per share on the day before the exdividend date. If the dividend is $0.25 and there are no taxes, what should the price of the shares be on the ex-dividend date?

Solution: Since there are no taxes, the value of the shares should drop by the amount of the dividend. Therefore, the shares should trade for $9.75 on the ex-dividend date. LO: 1 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance

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AICPA: Industry/Sector Perspective

17.8

Dividends: A company’s management announces a $1.00 per share dividend payment. Assuming all investors are subject to a 15 percent tax rate on dividends, how much should the company’s share price drop on the ex-dividend date?

Solution: Investors will be able to capture 85 percent of the amount of any dividend paid. Therefore, the price on the ex-dividend date should go down by $0.85 [$1.00 x (1 – 15%)] per share. LO: 1 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

INTERMEDIATE 17.9

Dividends and firm value: Explain how a stock repurchase is different from a dividend payment.

Solution: A share repurchase, if followed through by management, will place the same amount of cash in the hands of its shareholders. However, since shareholders have the option of selling their shares or holding on to their shares, the repurchase leaves it up to the individual shareholders whether or not they would like to receive the cash. The dividend payment method will effectively force the shareholders to receive the cash. LO: 2 Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective Copyright © 2022 John Wiley & Sons, Inc.

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17.10 Dividends and firm value: You have just encountered two identical firms with identical investment opportunities, as well as the ability to fund these opportunities. One of the firms has just announced that it will pay a dividend, while the other has continued to pay no dividend. Which of the two firms is worth more under the M&M assumptions? Explain. Solution: Neither, the two firms are worth the same. If we begin with a world described by the Modigliani and Miller paper in 1961, which assumes that (1) investors incur no taxes, (2) there are no information or transactions costs, and (3) the dividend payout rates have no effect on the firm’s real investment policy, then both firms will be worth exactly the same. That is because investors who want dividends but own a no-dividend stock can liquidate their appreciated value shares to create a homemade dividend, and shareholders who do not want dividends but own a dividend-paying stock can use their “unwanted” dividends to purchase additional shares of that stock. However, since M&M assumptions do not apply in the real world, dividend decisions made by the firm and investor preferences can influence its value. LO: 3 Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

17.11 Dividends and firm value: Explain what the introduction of transaction costs does to the Modigliani and Miller assumption that dividends are irrelevant. Start with a firm that pays dividends to investors that do not want to receive dividend payments. Do not consider taxes. Solution: The no-transaction costs assumption is required for investors to create their own homemade dividends or for investors to “undo” their unwanted dividend payments by

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purchasing additional shares of the company stock. Therefore, by relaxing the no transaction cost assumption, we would increase the cost of producing the homemade dividend or the cost of undoing the unwanted dividends, which would then make dividend policy a relevant factor when valuing shares. For instance, receiving an unwanted dividend would now make it more costly to convert that dividend into new shares, in as much as part of that dividend would be dissipated to transaction costs. In that situation, the investor would value a non-dividend paying share at a higher value than a dividend-paying share. LO: 3 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

17.12 Dividends and firm value: CashCo increased its cash dividend each quarter for the past eight quarters. While this may signal that the firm is financially very healthy, what else could we conclude from these actions? Solution: If we rule out the possibility that the firm is just producing a high level of cash, then we must conclude that the firm has more cash than it has investment opportunities to utilize that cash. In short, we might conclude that the firm’s growth rate will be slowing down in the future. LO: 3 Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

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17.13 Dividends and firm value: In 2013, the maximum tax rate on dividends increased from 15 percent to 23.8 percent. How would you expect this increase to affect the prices of dividend-paying stocks versus those of non-dividend-paying stocks? Solution: The value of a dividend received, after taxes are included, will be less than before. Therefore, we would expect the value of dividend-paying stocks to decrease relative to non-dividend-paying stocks. LO: 2 Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

17.14 Dividends: Undecided Corp. has excess cash on hand right now, although management is not sure about the level of cash flows going forward. If management would like to put ash in stockholders’ hands, what kind of dividend should the firm pay, and why? Solution: Since this is a one-time increase in cash flow, the firm would not want to commit to an ongoing higher dividend rate. If the firm went that route but then later had to reduce the dividend back to current dividend levels, then the market could interpret that action as indecision on the part of management, or worse. Therefore, an increase in the regular dividend would not be appropriate. A more appropriate choice would be to declare an extra dividend. Note that it would be called a special dividend if the extra cash flow came from something other than the firm’s regular operations or if the cash were an unusually large amount. LO: 3 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

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17.15 Dividends and firm value: A firm can deliver a negative signal to stockholders by increasing the level of dividends or by reducing the level of dividends. Explain why this is true. Solution: When a firm reduces its dividend, the firm is telling the market that it does not have sufficient cash, which is of course a bad or negative signal. However, by increasing the dividend, the firm is telling its investors that it has greater cash than it has investment uses for that cash. If the firm is currently viewed as a growth firm, then the market could interpret an increase in the dividend as a slowdown in the growth rate of the firm precipitated by the firm’s lower investment rate. LO: 3 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective 17.16 Dividends and firm value: A commentator on a financial talk show on TV says that “On average, firms pay out too little to stockholders. This is why stock prices go up with dividend increases and down with dividend decreases.” Is the commentator right? Solution: No. It is true that stock prices do tend to increase with dividend increases and to decrease with dividend decreases. However, this does not necessarily mean that firms are paying out too little to stockholders on average. The price of a company’s stock might increase when a firm increases its dividend because the increase signals to investors that the company’s management is optimistic about future cash flows or is willing to distribute excess cash rather than keep it and invest in negative NPV projects. The stock price might decrease when a firm reduces its dividend because investors might be concerned that a firm’s cash flows will decrease in the future or that management will invest excess cash that is not being distributed in negative NPV projects. These arguments do not

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require that the firm be paying out too little at that time that the dividend is increased or decreased. The stock price reaction to the announcement of a dividend change reflects a change in investor expectations about what the announcement tells them about the cash flows they can expect to receive in the future. As the cash flow identity suggests, there are a number of reasons besides those above that might cause stock prices to increase with dividend increases and to decrease with dividend decreases. LO: 3 Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

17.17 Dividends and firm value: You own shares in a firm that has extra cash on hand to distribute to stockholders. You do not want the cash. What course of action would you prefer the firm take? Solution: You would prefer that the firm initiate a share repurchase. You can opt not so sell your shares to the firm but still participate in the increased value of the firm’s shares since your pro-rata share of the expected future cash flows generated by the firm will increase. You would not like a dividend payment since you would then be required to receive the cash if you owned the shares at the time of the record date. LO: 4 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

17.18 Dividends and firm value: Stock repurchases, once announced, do not actually have to occur in total or in part. From a signaling perspective, why would a special dividend be better than a stock repurchase?

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Solution: If we ignore the preferences of individual shareholders, then a special dividend is preferred to a share repurchase. Although dividends are binding, once declared by the firm’s board of directors, a share repurchase is not binding. Therefore, a special dividend is considered a stronger signal than a share repurchase. LO: 4 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

17.19 Dividends and firm value: Consider a firm that repurchases shares from its stockholders in the open market, and explain why this action might be detrimental to the stockholders from whom the firm buys shares. Solution: To understand this argument, we have to consider two points. First, the firm should be managed for the benefit of its shareholders. Second, the firm is the ultimate insider concerning the value of its shares.

Given the above points, we must realize that any time the firm is purchasing its shares; it must be doing so because the firm’s management believes that the firm’s shares are undervalued. Therefore, by purchasing its shares, the firm is utilizing its inside information to purchase shares and ultimately to take advantage of the current owner of those shares in order to benefit the remaining shareholders of the firm. It is then not doing something in the interest of all of its shareholders since those who sell will be selling at a price lower than what they could have realized had they held their shares until the repurchase was complete. LO: 3 Bloomcode: Comprehension AASCP: Analytic

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17.20 Dividends and firm value: You read that a number of public companies have been financing their dividend payments in recent years entirely through equity issues. A colleague of yours argues that this only increase taxes paid by individual stockholders and boosts underwriting and other transactions costs for the company. He says that such a policy cannot make sense. What do you say? Solution: Such a policy can make sense. While there are costs associated with doing this, financing dividends with equity issues can help control agency conflicts by forcing managers to periodically submit to the scrutiny associated with the equity issuance process. It can ultimately lead to better company performance and the willingness of investors to pay a higher price for the company’s stock. LO: 3 Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

17.21 Stock repurchases: Briefly discuss the methods available for a firm to repurchase its shares and explain why you might expect the stock price reaction to the announcement of each of these methods to differ. Solution: 1. Open-market purchase — the firm simply purchases the shares in the market. 2. Tender offer — the firm makes an offer through a general announcement, offering to buy up to a certain number of shares from anyone who wishes to sell. Note that either the fixed-price or Dutch auction method can be used for a tender offer. 3. Targeted share repurchases — the firm directly negotiates with an individual shareholder to buy shares from that individual.

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LO: 2 Bloomcode: Knowledge AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

17.22 Stock repurchases: What is the advantage of a Dutch auction over a fixed-price tender offer? Solution: If the firm that is trying to purchase its own shares believes that there may be some variability in the supply curve for those shares, then a Dutch auction would essentially provide the firm with the necessary information to make the tender offer successful. In those same circumstances, a fixed-price tender offer might leave the firm paying too much for the shares or unable to purchase the desired number of shares given the fixedprice offer. LO: 2 Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

ADVANCED 17.23 In the early 1990s, the amount of time that elapsed between purchasing a stock and actually obtaining that stock was five business days. This period was known as the settlement period. The settlement period for stock purchases is now two business days. Describe what should have happened to the number of days between the ex-dividend date and the record date at the time of this change. Solution:

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The purpose of setting the number of days between the ex-dividend date and the record date is to allow for a sale of securities to clear in order to determine which “owner” is entitled to the dividend. Since the settlement period was reduced from five days to two days, we should have seen the number of days between the ex-dividend date and the record date to be reduced from four days to one. LO: 1 Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

17.24 Dividend reinvestment programs (DRIPs) sometimes sell shares at a discount to stockholders who reinvest their dividends through such plans. Your boss tells you that such plans are just a scheme to transfer wealth from nonparticipating to participating stockholders and that they should be stopped. Do you agree? Why or why not? Solution: Disagree. It is true that the cost of a DRIPs (including any discount) is borne by all stockholders. However, it is not necessarily true that DRIPs are bad for non-participating stockholders. DRIPs help firms attract investors who might not otherwise invest in a dividend-paying stock. Being able to attract these investors can help improve the liquidity of the shares and benefit all stockholders. Even without this benefit, it can make sense to sell shares at a discount. If DRIPs reduces the amount of capital that the firm has to raise in the future, it also reduces the issuance costs that the firm incurs in raising that capital. These cost savings can more than offset the cost of a discount offered to participating stockholders. LO: 3 Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

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17.25 WeAreProfits, Inc., has not issued any new debt securities in 10 years. It will begin paying cash dividends to its stockholders for the first time next year. Explain how a dividend might help the firm get closer to its optimal capital structure of 50 percent debt and 50 percent equity. Solution: If the firm has been successful over the last 10 years, then the value of its equity has increased but the total value of its debt has not increased accordingly. Therefore, the debtto-equity ratio of the firm has been dropping. By paying a dividend, the value of the equity, after the dividend is paid, will drop relative to that of the debt. This will help the firm to balance out its debt-equity ratio and get closer to a 50 percent-50 percent mix (assume that the debt was below the 50 percent level to begin with). LO: 3 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

17.26 Shadows, Inc., had shares outstanding that were valued at $120 per share before a twofor-one stock split. After the stock split, the shares were valued at $62 per share. If we accept that the firm’s financial maneuver did not create any new value, then why might the market be increasing the total value of the firm’s equity? Solution: We know that the stock split did not create value for investors by itself. Therefore, there must be information in the split that accounts for the $4 increase in value to shareholders. Generally speaking, firms have a tendency to increase their dividend rate after a stock split. Therefore, since a stock split is generally followed by dividend rate increases, the notification of an intended stock split tends to generate information for investors that there is a potential increase in cash flow to investors of the firm’s equity. LO: 4

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17.27 Saguaro Company currently has 30,000 shares outstanding. Each share has a market value of $20. If the firm pays $5 per share in dividends, what will each share be worth after the dividend payment? Ignore taxes. Solution: The current value of all of the shares is 30,000 × $20 = $600,000. If the firm pays $5 per share, then the total cash paid out will be 30,000 × $5 = $150,000. Therefore, the value of all of the shares will be worth $150,000 less or $450,000, and the price of each share will be $450,000 / 30,000 = $15 per share. However, it seems logical that if shares were worth $20 before the dividend payout, then they should be worth $5 less after the dividend payout or $15 just as we have calculated. LO: 1 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

17.28 Cholla Company currently has 30,000 shares outstanding. Each share has a market value of $20. If the firm repurchases $150,000 worth of shares, then what will be the value of each share outstanding after the repurchase? Ignore taxes. Solution: The current value of all of the shares is 30,000 × $20 = $600,000. If the firm repurchases $150,000 worth of shares, then it will repurchase $150,000 / $20 = 7,500 shares. Therefore, the value of all of the shares not purchased will be worth $150,000 less, or $450,000, and the price of each share will be $450,000 / (30,000 – 7,500) = $20 per share.

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It seems logical, however, that if shares were worth $20 before the repurchase, then they should be worth $20 after the repurchase since investors should be indifferent between selling their shares to the firm and retaining shares. LO: 3 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

17.29 You purchased 1,000 shares of Koogal stock five years ago for $30 per share. Today Koogal is repurchasing your shares through a fixed-price tender offer for $80 per share. What are the after-tax proceeds to you if your capital gain is taxed at a 15 percent rate? Solution: The tax on the stock would be 1,000 × ($80 – $30) × 0.15 = $7,500. Therefore, the aftertax proceeds would equal (1,000 × $80) – $7,500 = $72,500. LO: 1 Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

17.30 You purchased 1,000 shares of Zebulon Copper Co. five years ago for $50 per share. Today Zebulon management is trying to decide whether to repurchase shares for $70 per share through a fixed-price tender offer or pay a $70 cash dividend per share. If capital gains are taxed at a 15 percent rate, then at what rate must dividends be taxed for you to be indifferent between receiving the dividend and selling your shares back to Zebulon? Solution: The tax on the stock would be 1,000 × ($70 – $50) × 0.15 = $3,000. Therefore, the tax on the dividend must be equal to $3,000 for you to be indifferent between the two choices. Therefore,

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$3,000 = 1,000 × $70 × Dividend Tax rate  Dividend Tax rate = 4.29% If dividends are taxed at any rate higher than 4.29 percent, then you would prefer the share repurchase. Note that the point of indifference is partially a function of the ratio of capital gains to the cash dividend. LO: 2 Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

17.31 Llama Wool Company management is doing some financial planning for the coming year. Llama plans to raise $10,000 in new equity this year and wants to pay a dividend to stockholders of $30,000. The firm must pay $20,000 of interest during the year and will also pay down principal on its debt obligations by $10,000. Its capital budgeting plan calls for $100,000 of capital expenditures during the year. Given the above information, how much cash must be provided from operations for the firm to meet its plan? Solution: Using the equation given in the text: CFOAt + Equityt + Debtt = Divt + Repurchasest + Interestt + Principalt + Invt CFOAt + $10,000 = $30,000 + $20,000 + $10,000 + $100,000 CFOAt = $150,000 LO: 3 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

17.32 You are the Chief Financial Officer (CFO) of a large publicly traded company. You would like to convey positive information about the firm to the market. If you agree with

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the conclusions from the Lintner study, will you keep paying your currently high dividend or raise that dividend by a small amount? Explain. Solution: Although the current high level of dividends certainly suggests that the firm has the ability to sustain a high payout to investors, that high payout does not convey any positive information to the market. However, by increasing the dividend, the CFO would be telling the market that the firm will be able to support an even higher level of cash payout in the future. Therefore, it would be better to increase the dividend by a small amount. LO: 3 Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

17.33 You are the CFO of a public company that advises distressed companies about how to manage their businesses. Your company has been performing extremely well. In fact, it has earned so much money that the increase in its retained earnings has resulted in a decline in the firm’s debt to total capital ratio from 30 percent to 15 percent. Much of the retained earnings is sitting in a cash account because your firm does not need the money to fund investments. You would like to increase the debt-to-total capital ratio to 30 percent, which you view as optimal for your firm. How would you recommend doing this if you want to complete the adjustment as soon as possible? Solution: You can do this by paying out some of the cash that the firm has accumulated using either a special dividend or a stock repurchase. A special dividend can be completed quickly, but would subject your stockholders to taxes if they are not tax-exempt organizations, and would negatively affect stockholders who wanted to retain the same dollar investment in your firm. LO: 3 Bloomcode: Analysis

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Sample Test Problems 17.1

Shares of Convoy West, Inc. are trading for $55.45 on the day before the ex-dividend date. If the quarterly dividend is $0.16 per share and there are no taxes, how will the share price change on the ex-dividend date?

Solution: Since there are no taxes, the value of the shares drop by the $0.16, the amount of the dividend. Therefore, the shares should trade for $55.29 ($55.45 – $0.16 = $55.29) on the ex-dividend date if no other information relevant to the price of the stock becomes public. LO: 1 Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

17.2

Three years ago, you purchased 4,000 shares of Metwa Inc. for $17 per share. Today Metwa is repurchasing its shares through a fixed-price tender offer at a price of $45 per share. What are the after-tax proceeds that you will receive if capital gains are taxed at a rate of 20 percent?

Solution: The tax on the stock would be 4,000 × ($45 – $17) × 0.20 = $22,400. Your after-tax proceeds would equal (4,000 × $45) – $22,400 = $157,600. LO: 2 Bloomcode: Application AASCP: Analytic

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17.3

Why does an ongoing stock repurchase program offer management greater flexibility in distributing value to stockholders than a regular cash dividend?

Solution: An ongoing stock repurchase program, such as that announced by Hilton in the chapter opener, is perceived in the stock market as being less of a commitment than a regular cash dividend. The actual amount of cash being distributed through such a program is also less visible than the amount of money being distributed through dividends. If management decides to decrease the amount of cash being distributed to stockholders through a repurchase program, it can cut back or even terminate the program without causing the negative stock price reaction that typically accompanies reductions in regular cash dividends. LO: 3 Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

17.4

Why would management of a company undertake a reverse stock split?

Solution: Often, a reverse stock split is undertaken to satisfy exchange requirements. A reverse stock split can be used to increase the share price to a level above the required threshold at an exchange such as the NYSE or NASDAQ. LO: 4 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

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Tesla, Inc. completed a 10-for-1 stock split on August 28, 2020. Immediately before the stock split there were 186.32 million shares outstanding at a price of $2,213.00 per share. After the split how many shares were outstanding, and at what price would you expect them trade? Did the stock split cause any substantial change for Tesla or its investors? Why would Tesla management choose to split the company’s stock?

Solution: After the stock split, there would be 186.32 million × 10 = 1,863.2 million shares outstanding at a price of $2,213 / 10 = $221.30 per share. Nothing substantially changed for Tesla or its investors. There were ten times as many shares outstanding after the split, but each was worth only one tenth as much as a share was worth before the split. Tesla management might have split the stock to lower their share price, hoping to make the stock more accessible to investors. Tesla management might also split the stock to send a positive signal to investors about management’s outlook for the company’s future. LO: 4 Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

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Chapter 16

Capital Structure Policy Before You Go On Questions and Answers Section 16.1 1.

What is the optimal capital structure for a firm? The optimal capital structure for a firm is the combination of debt and equity financing, which minimizes the overall cost of financing the firm’s real activities (projects). Minimizing the overall cost of financing a firm’s real activities maximizes the value of its cash flows.

What is M&M Proposition 1? M&M Proposition 2? Modigliani-Miller Proposition 1: The capital structure of a firm does not affect the firm’s value if the following three assumptions hold: a. There are no taxes. b. There are no information or transaction costs. c. A firm’s capital structure does not affect the firm’s real investment policy. Modigliani-Miller Proposition 2: The required rate of return on a firm’s equity (cost of equity) increases as the firm’s debt-to-equity ratio increases.

What is the difference between business risk and financial risk? Business risk reflects the uncertainty associated with the underlying assets of the firm. The level of business risk is reflected in the required rate of return associated with these assets. Financial risk represents the uncertainty that fixed debt payments introduce to the cash flows to the stockholders. The total risk faced by stockholders is affected by both the business risk of the firm and its financial risk.

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How can the three conditions specified by M&M help us understand how the capital structure of a firm affects its value? M&M identify the three conditions under which the capital structure of a firm would not affect its value. By examining the three conditions specified by M&M, and how they are violated in the real world, we can better understand why capital structure does affect firm value.

Section 16.2 1.

What are some benefits of using debt financing? The benefits of using debt financing are: •

The interest tax shield (interest is tax deductible, dividends are not).

•

The cost of issuing debt (underwriting spreads and out-of-pocket costs) are lower than the cost of issuing equity.

•

With more debt, managers have greater incentives to work hard to produce larger cash flows and thus avoid bankruptcy.

•

Increased debt limits the manager’s flexibility to spend money on wasteful, negative NPV projects.

What are bankruptcy costs, and what are the two types of bankruptcy costs? Bankruptcy costs are costs that firms face when they are in financial distress. Direct bankruptcy costs are out-of-pocket costs, such as the payments that are made to lawyers, accountants, and consultants, as well as court costs, when a firm gets into financial distress. Indirect bankruptcy costs result from changes in the behavior of the people that contract with the firm when they learn that it is in distress. For example, there may be less demand for a distressed firm’s product because of the concern that the firm will not exist to provide customer support in the future or suppliers might demand cash on delivery out of concern that the firm will not be able to pay for supplies.

What are agency costs, and how are they related to the use of debt financing? Agency costs are costs that are incurred when someone delegates decision-making authority to someone who has different objectives. Agency costs might arise in

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relationships between stockholders and the managers they hire because managers do not have the same incentives as stockholders. For example, when a firm has debt, managers can have incentives to invest in low-risk projects that do not maximize stockholder value. Agency costs also arise between stockholders and debt holders. Stockholders, through the managers they hire, can have incentives to engage in asset substitution, turn down positive-NPV projects (underinvestment), or pay out excess cash in the form of dividends.

Section 16.3 1.

What is the trade-off theory of capital structure? The trade-off theory of capital structure postulates that managers set a specific target for the capital structure of a firm in which they try to achieve the mix of debt and equity that will minimize the cost of financing the firm’s projects and thereby maximize its value.

What is the pecking order theory of capital structure? The pecking order theory says that, instead of trying to achieve a specified target capital structure, firms use the cheapest form of capital available at any given time, until it is used up. According to this theory, the cost of capital from least expensive to most expensive is: 1. Internally generated funds 2. Debt issue 3. Equity issue

What does the empirical evidence tell us about the two theories? The empirical evidence provides some support for both theories. Studies find that industries with significant tangible assets tend to have more debt. This is consistent with the trade-off theory. These companies can generally borrow at a lower rate using their tangible assets as collateral.

There is also evidence that more profitable firms hold less debt. This is consistent with the pecking order theory. These companies are capable of financing more projects with Copyright © 2022 John Wiley & Sons, Inc.

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internal funds before taking on debt. The trade-off theory would suggest that more profitable companies should carry more debt, because they have more to benefit from the tax shelter of interest payments.

Section 16.4 1.

Why is financial flexibility important in the choice of a capital structure? The choice of capital structure may limit the ability of managers to take advantage of unexpected opportunities or to deal appropriately with unexpected problems. For example, suppose the firm learns of a positive-NPV project that is available for only a short period of time. If the firm already holds significant amounts of debt, lenders may be unwilling to loan more money to the firm. Raising funds though issuing equity is often a slow process, and the window of opportunity to accept the project may have passed. A firm that holds cash or can quickly issue debt (e.g., through a line of credit) has more flexibility in financing new projects.

How can capital structure decisions affect the risk associated with net income? The more debt a firm carries, the more risk will be associated with the firm’s net income. This occurs because given a certain level of fluctuating operating income, a larger fixed debt payments will magnify the effects of the fluctuations on net income.

How can capital structure decisions affect the control of a firm? Issuing new equity reduces the control of the firm’s existing stockholders (assuming the existing stockholders do not purchase the new issues). In some cases, firms may issue debt rather than equity to prevent the control of existing stockholders from being diluted. For example, if a firm is 51 percent owned by the founders, the founders may require the company to issue debt rather than equity to finance a new project. This will prevent the founder’s ownership from falling to less than 50 percent.

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Relaxing which of the three assumptions in Modigliani and Miller Proposition 1 will have the most predictably quantifiable impact on the value of the firm?

Solution: The assumption with the most measurable impact is that involving taxes. We can calculate the present value of the tax shield generated by the interest costs of borrowing. The impacts of the other two assumptions, though real, are more difficult to predict. LO: 1 Level: Basic

16.2

If we assume that the cash flows for a firm with financial leverage are equal to the cash flows for the same firm without financial leverage, what can we say about the value of this firm if its cost of capital also does not vary with the degree of leverage utilized?

Solution: If the cash flows produced by the firm and the cost of capital for the firm are the same, regardless of the amount of leverage utilized, then we can say that the value of the firm is also unchanged by the amount of financial leverage. LO: 2 Level: Basic

16.3

Are taxes necessary for the cost of debt financing to be less than the cost of equity financing?

Solution: The deduction for interest expense does make debt borrowing more attractive than it would otherwise be. However, even without the interest deduction benefit, the cost of debt is less than the cost of equity, because equity is a riskier investment than debt. This means that the pretax cost to the firm for debt is still lower than the cost of equity. LO: 1 Level: Basic

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You are offered jobs with identical responsibilities by two different firms in the same industry. One has no debt in its capital structure, and the other has 99 percent debt in its capital structure. Will you require a higher level of compensation from one firm than from the other? If so, which firm will have to pay you more?

Solution: The firm with the large amount of debt financing (the 99 percent debt firm) has a higher probability of becoming financially distressed. Therefore, you should require greater compensation from that firm because your income is less certain and working at that firm poses a greater risk to your career. LO: 2 Level: Basic

16.5

You are valuing two otherwise identical firms in the same industry. One firm has a corporate jet for every executive at the vice president level and above, while the other does not have a single corporate jet. More than likely, which firm has the greatest stockholder-manager agency costs?

Solution: While corporate jets can make economic sense because they enable managers to use their time more efficiently, one jet per vice president is certainly not cost effective. The multi-jet firm has higher stockholder-manager agency costs than the no-jet firm. It is spending too much on jets. The cash that is being spent on excess jets could be invested in positive NPV projects or returned to the firm’s stockholders. LO: 2 Level: Basic

Discussion Questions 16.1

List and briefly describe the three key assumptions in Modigliani and Miller’s Proposition 1 that are required for total firm value to be independent of capital structure.

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1. There are no taxes. This assumption is necessary in order to avoid creating a tax benefit when using debt instead of equity to finance firm assets. 2. There are no information or transactions costs for the firm. a. There are no bankruptcy costs (financial distress) to the firm associated with increased supplier, employee, and customer expenses, due to the firm having a higher likelihood of not being able to meet its debt obligations. Note that one interpretation of this assumption is that, the firm has a zero probability of not being able to meet its debt obligations. b. There are no agency costs. There are no costs associated with the conflict of interest between managers and stockholders, and there are no costs associated with the conflict between the interest between stockholders and debt holders of the firm. c. There are no market frictions. This means that individuals may borrow and lend at the same rate that the firm can borrow and lend. 3. The real investment policy of the firm is not affected by its capital structure decisions. Without this, the assumption that an individual investor could replicate the actions of the firm, does not hold because the actual investment policy of the firm would be affected by the capital structure decision. Investors cannot replicate real investments. LO: 1 Level: Basic Bloomcode: Knowledge AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

16.2

Evaluate the statement that the weighted average cost of capital (WACC) for a firm (assuming that all three assumptions of Modigliani and Miller’s propositions hold) is always less than or equal to the cost of equity for the firm. If we look at the following WACC formula for a firm (without taxes): WACC = [Vcs/(VDebt+Vcs)] × kcs + [VDebt/(VDebt+Vcs )] × kDebt

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We see that with 100 percent equity financing, the WACC = kcs. A firm cannot be 100 percent debt-financed, even so as D/V approaches 1, then the WACC approaches kDebt. Since we know that debt is less risky than equity, we know that the WACC in that instance, must be greater than kDebt but less than kcs. Therefore, the WACC must be greater than kDebt but less than or equal to kcs . LO: 1 Level: Basic Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

16.3

If the value of the firm remains constant as a function of its capital structure and the three Modigliani and Miller assumptions apply, why might the overall cost of capital change or not change as capital structure changes? If the cash flow produced by a firm is unchanged, and the value of the firm producing that cash flow is unchanged by a firm’s capital structure changes, we can use a perpetual cash flow valuation model as follows: VFirm = CF/i If we know that VFirm and CF are unchanged due to capital structure changes; then kAssets must also remain unchanged.

LO: 1 Level: Basic Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

16.4

Consider the WACC for a firm that pays taxes. Explain what the best course of action would be to minimize the firm’s WACC and thereby maximize its value. Use the WACC formula for your explanation.

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WACC = (1 – t) × kDebt × [VDebt/(VDebt+Vcs)] + kcs × [Vcs/(VDebt+Vcs)] If kcs > kDebt, then it would make sense to increase debt relative to equity, in order to raise as much financing as possible with borrowing, rather than the more expensive equity. Therefore, by blindly following the WACC formula, we are led to believe that more debt will increase the value of the firm from its current valuation. This highlights the effect of taxes without taking into account the other M&M assumptions. LO: 1 Level: Basic Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

16.5

The Modigliani and Miller propositions, when the no-tax assumption is relaxed, suggest that the firm should finance itself with as much debt as possible. Taking this suggestion to the extreme, is it even possible to finance a firm with 100 percent debt and no equity? Why or why not? Even with the list of assumptions required to get this result, a 100 percent debt firm is not practical. While we might think that there is no residual claimant for the firm’s cash flows, even this is not true. In fact, a 100 percent debt-financed firm is really a 100 percent equity-financed firm since the debt holders themselves must then be the residual claimants.

LO: 1 Level: Basic Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

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16.6

Solutions Manual

Crossler Automobiles sells autos in a market where the standard auto comes with a 10-year/100,000-mile warranty on all parts and labor. Describe how an increased probability of bankruptcy could affect sales of autos by Crossler. In a market, where a warranty is a significant portion of the cost of an automobile, purchasing a car where the seller might not be able to completely perform on that warranty, due to increased probability of bankruptcy of Crossler, would have negative impact on the firm’s future automobile sales. This would decrease the amount of cash flow available to the investors of the firm, which would lower the value of the firm.

LO; 2 Level: Basic Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

16.7

Agency problems occur because the nonowner managers and stockholders of a firm have different interests. Propose a capital structure change that might help better align these different interests. The managers of a firm would rather work as little as possible, given a set level of compensation, whereas stockholders would rather compensate the manager for a high level of effort, with a low effort receiving very little compensation. Increasing the proportion of debt in the capital structure would increase the probability of the firm falling into bankruptcy. This increased probability of bankruptcy, and therefore the increased chance that the manager will lose his job, would then help to align the interests of the manager and stockholders by giving the manager an additional incentive to work harder for the stockholders.

LO: 2 Level: Basic Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance

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AICPA: Industry/Sector Perspective

16.8

If a firm increases its debt to a very high level, then the positive effect of debt in aligning the interests of management with those of stockholders tends to become negative. Explain why this occurs. Increasing the debt level for a firm tends to catch management’s attention and force the managers to work harder; therefore, a very high level of debt can be detrimental. That is, at very high levels of debt, risk-averse managers begin to minimize the risks that a firm takes on, given the managers’ own job preservation needs. This risk minimization can deter managers from taking risky, but positive-NPV projects, which are needed to help the firm meet the very debt obligations that are causing the problem. In addition, the financially risky firm may also bear costs not previously borne in relationships with employees, suppliers, and customers.

LO: 2 Level: Basic Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

16.9

Using the Modigliani and Miller framework, but excluding the assumptions that there are no taxes and no information or transaction costs, describe the value of the firm as a function of the proportion of debt in its capital structure. With taxes included, we would predict that the firm would take on greater proportions of debt. Agency costs (part of the information and transactions cost) are actually reduced when adding moderate portions of debt. This would also predict that the firm value increases as we add moderate levels of debt to the firm. However, agency costs once again become positive (in total) as very high levels of debt are incurred. This suggests that at very high levels of debt the value of the firm could be dropping. Bankruptcy costs (which are also part of the information and transactions cost) are probably immaterial at low debt levels, but can become very high at higher levels of debt. Therefore, we should

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predict that by dropping the three assumptions in the question, the value of the firm should increase with additional debt for moderate debt levels, but should decrease for high levels of debt. LO: 1 Level: Basic Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

16.10 When we observe the capital structure of many firms, we find that they tend to utilize lower levels of debt than that predicted by the trade-off theory. Offer an explanation for this. This empirical result is consistent with a firm maintaining a reserve level of debt or high cash levels in order to have ample internally generated funds for new projects. One explanation would be that, firms like to have this “reserve” financing available for new projects when they are identified. Another explanation is that, firms do not have to offer an explanation to the new investors for the use of these funds and that makes it less expensive on an information basis to keep this reserve, compared to having to issue new securities for the financing of the new projects. Both of these explanations are in line with the pecking order theory. LO: 2 Level: Basic Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

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BASIC 16.1

M&M Proposition 1: The Modigliani and Miller theory suggests that the value of the firm’s assets is equal to the value of the claims on those assets and is not dependent on how the asset claims are divided. The common analogy to the theorem is that the total amount of pie available to be eaten (the firm) does not depend on the size of each slice of pie. If we continue with that analogy, then what if we cut up the pie with a very dull knife such that the total amount of pie available to be eaten is less after it is cut than before it was cut. Which of the three Modigliani and Miller assumptions, if relaxed, is analogous to the dull knife? Hint: Think about the process by which investors could undo the effects of a firm’s capital structure decisions.

Solution: The inability of individual investors to borrow and lend and at the same rate as firms, is analogous to the dull knife. This friction is part of the no information or transactions costs assumption. Since the process of rearranging the claims on the firm’s assets is similar to carving up the firm into different pieces, it is easy to see that such a market friction is similar to the dull knife in our pie example. LO: 1 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

16.2

M&M Proposition 1: Describe what exactly is meant when someone is describing the value of the firm versus the value of the equity of the firm.

Solution: The value of the firm can be described as either the total market value of all the assets owned by the firm, or the total market value of all the claims of all the investors in the firm. In that case, it means that we are valuing all of the equity claims (shares) in the firm in addition to all of the debt claims (bonds, bank borrowing, etc.) of the firm. LO: 1 Bloomcode: Comprehension Copyright © 2022 John Wiley & Sons, Inc.

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AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

16.3

M&M Proposition 1: Under Modigliani and Miller’s Proposition 1, when all three of the assumptions remain in effect, explain how the value of the firm changes due to changes in the proportion of debt and equity utilized by the firm.

Solution: Under Modigliani and Miller’s Proposition 1, the value of the firm is independent of the proportion of debt and equity utilized by the firm. LO: 1 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

16.4

M&M Proposition 1: Cerberus Security Company produces a cash flow of $200 per year and is expected to continue doing so in the infinite future. The cost of equity capital for Cerberus is 20 percent, and the firm is financed entirely with equity. Management would like to repurchase $100 in shares by borrowing $100 at a 10 percent rate (assume that the debt will also be outstanding into the infinite future). Using Modigliani and Miller’s Proposition 1, what is the value of the firm today, and what will be the value of the claims on the firm’s assets after the stock repurchase? What will be the rate of return on common stock required by investors after the share repurchase?

Solution: Using the 20 percent cost of equity capital, the value of the firm today is $200/0.2 = $1,000, keeping in mind that the cash flow is expected to be produced into the infinite future. Note that, using M&M Proposition 1, this must be the value of the firm after the repurchase. The value of the debt claim must be $100 at the time of the borrowing, so we know that the value of the outstanding equity after the repurchase must be $1,000 – $100 = $900. Since $10 in cash flow must be paid to the debt holders each year, $190 will be

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available to the stockholders on an annual basis. This implies that the new cost of equity capital for the firm must be such that $900 = $190 / kcs, or kcs = 21.11%. LO: 1 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

16.5

M&M Proposition 1: A firm that is financed completely with equity currently has a cost of capital equal to 15 percent. Assume that the assumptions in Modigliani and Miller’s Proposition 1 hold and that the firm’s management plans to change its capital structure to 50 percent debt and 50 percent equity. What will be the cost of equity after the change if the cost of debt is 10 percent?

Solution: It is easy to see that the current cost of capital (also the cost of equity in this case) is 15 percent. Given the proposition, we know that the cost of capital (or WACC) for the firm must be constant at 15 percent. If we know that the firm can borrow at a 10 percent cost of capital, with a 50–50 percent debt-equity mix, then we can use the WACC formula to solve for the new cost of equity capital as follows:

WACC = xDebt kDebt + xcs kcs 0.15 = 0.5 × (0.10) + 0.5 × (kcs) kcs = 0.20, or 20% LO: 1 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

16.6

M&M Proposition 1: Swan Specialty Cycles is currently financed with 50 percent debt and 50 percent equity. The firm pays $125 each year to its debt investors (at a 10 percent cost of debt), and the debt has no maturity date. What will be the value of the equity if the

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firm repurchases all of its debt and raises the funds to do this by issuing equity? Assume that all of the assumptions in Modigliani and Miller’s Proposition 1 hold. Solution: Since the debt has no maturity date, we can find the value of the current debt claims: Value = $125 / 0.10 = $1,250. Since debt is 50 percent of the capital structure, then the value of the entire firm must be 2 × Value of debt = $2,500, which must be the value of the equity in an all-equity firm. LO: 1 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

16.7

M&M Proposition 1: The weighted average cost of capital for a firm, assuming all three Modigliani and Miller assumptions hold, is 10 percent. What is the current cost of equity capital for the firm if the cost of debt for the firm is 8 percent and the firm is 80 percent financed with debt?

Solution: Using the formula given in the text: kcs = kAssets + (VDebt /Vcs) × (kAssets – kDebt) kcs = 0.10 + (0.8 / 0.2) × (0.10 – 0.08) = 0.18, or 18% LO: 1 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

16.8

Interest tax shield benefit: Legitron Corporation has $350 million of debt outstanding at an interest rate of 9 percent. What is the dollar value of the tax shield on that debt, just for this year, if Legitron is subject to a 27 percent marginal tax rate?

Solution:

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Legitron will pay $31,500,000 ($350,000,000 × 0.09) in interest this year, which will shield Legitron from paying a tax amount equal to: VTax-savings debt = D × t = $31,500,000 × 0.27= $8,505,000 Therefore, the amount of this year’s tax shield, due to debt issuance, for Legitron is $8,505,000. LO: 2 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

16.9

Interest tax shield benefit: FAJ, Inc. has $500 million of debt outstanding at an interest rate of 9 percent. What is the present value of the tax shield on that debt if it has no maturity and if FAJ is subject to a 30 percent marginal tax rate?

Solution: The present value of FAJ’s tax shield is: t × D = 0.30 × $500,000,000 = $150,000,000 An alternative calculation would be: (t × D × kDebt ) / kDebt = (0.30 × $500,000,000 × 0.09) / 0.09 = $150,000,000 LO: 2 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

16.10 Interest tax shield benefit: Springer Corp. has $250 million of debt outstanding at an interest rate of 11 percent. What is the present value of the interest tax shield if the debt has no maturity and if Springer is subject to a 26 percent marginal tax rate? Solution: The present value of Springer’s tax shield is: t × D = 0.26 × $250,000,000 = $65,000,000

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LO: 2 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

16.11 Interest tax shield benefit: Structural Corp. currently has a cost of equity capital equal to 15 percent. Assume that the Modigliani and Miller Proposition 1 assumptions hold, with the exception of the assumption that there are no taxes, and that the firm’s capital structure consists of 50 percent debt and 50 percent equity. What is the weighted average cost of capital for the firm if the cost of debt is 10 percent and the firm is subject to a 28 percent marginal tax rate? Solution:

WACC = xDebt kDebt + xcs kcs = [0.5 × 0.10 × (1 - 0.28)] + (0.5 × 0.15) = 0.111, or 11.1% LO: 2 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

16.12 Practical considerations in capital structure choice: List and describe three practical considerations that concern managers when they make capital structure decisions. Solution: 1.

Financial flexibility: Managers must minimize the firm’s cost of capital while also ensuring that the firm has the flexibility to raise new capital quickly to deal with unexpected problems or to take advantage of unexpected opportunities.

Net income risk: Increasing the leverage of a firm increases the risk associated with firm’s net income, and the risk of default.

Earnings impact: When a project is financed with debt, the interest payments reduce the accounting dollar value of net income. However, when debt is used, no

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new shares of equity are issued, so the company’s earnings per share would be expected to increase (given a positive NPV project). Although financial theory suggests that neither of these effects should matter, managers often take them into account when making financing decisions. LO: 4 Bloomcode: Knowledge AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

INTERMEDIATE 16.13 M&M Proposition 1: Keyboard Chiropractic Clinics produces $300,000 of cash flow each year. The firm has no debt outstanding, and its cost of equity capital is 25 percent. The firm’s management would like to repurchase $600,000 of its equity by borrowing $600,000 at a rate of 8 percent per year. If we assume that the debt will be perpetual, find the cost of equity capital for Keyboard after it changes its capital structure. Assume that the Modigliani and Miller Proposition 1 assumptions hold. Solution: Using the 25 percent cost of equity capital, the value of the firm today is $300,000/0.25 = $1,200,000 This must be the value of the firm after the repurchase. The value of the debt claim must be $600,000 at the time of the borrowing, so the value of the outstanding equity after the repurchase must be $1,200,000 – $600,000 = $600,000 Since $48,000 ($600,000 × 0.08) in cash flow must be paid to the debt holders each year, $252,000 ($300,000 – $48,000) will be available to the stockholders on an annual basis. This implies that the new cost of equity capital for the firm must be such that $600,000 = $252,000 / kcs, or kcs = 0.42, or 42.00% LO: 1 Bloomcode: Application Copyright © 2022 John Wiley & Sons, Inc.

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AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

16.14 M&M Proposition 1: Marx and Spender Corp. currently has a WACC of 21 percent. If the cost of debt capital for the firm is 12 percent and the firm is currently financed with 25 percent debt, then what is the current cost of equity capital for the firm? Assume that the assumptions in Modigliani and Miller’s Proposition 1 hold. Solution: Using the WACC formula we can solve for the cost of equity capital for the firm:

WACC = xDebt kDebt + xcs kcs 0.21 = 0.25 × (0.12) + 0.75(kcs) kcs = 0.24, or 24% LO: 1 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective 16.15 M&M Proposition 1: What is the effect on Modigliani and Miller’s Proposition 1 of relaxing the assumption that there are no information or transaction costs? Solution: No information or transaction costs means, for example, that individuals may borrow and lend at the same rate that the firm can borrow and lend. If an investor were unable to sell (or buy) shares by investing (or borrowing) without transaction costs, then some of the value conserved in the Modigliani and Miller arguments through personal trading would be dissipated by transaction costs. This dissipation would then negate the conservation of value proposed by M&M. LO: 1 Bloomcode: Comprehension AASCP: Analytic Copyright © 2022 John Wiley & Sons, Inc.

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IMA: Corporate Finance AICPA: Industry/Sector Perspective

16.16 M&M Proposition 1: The weighted average cost of capital for a firm (assuming all three Modigliani and Miller Proposition 1 assumptions apply) is 15 percent. What is the current cost of equity capital for the firm if its cost of debt is 10 percent and the proportion of debt to total firm value for the firm is 0.5? Solution: Since VDebt /VFirm = 0.5, VDebt /Vcs = 0.5 / 0.5 = 1 Using the formula given in the text, kcs = kAssets + (VDebt /Vcs) × (kAssets – kDebt) = 0.15 + (1) × (0.15 – 0.10) = 0.2, or 20% LO: 1 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

16.17 M&M Proposition 2: Mikos Processed Foods is currently valued at $500 million. Mikos will be repurchasing $100 million of its equity by issuing perpetual debt at an annual interest rate of 10 percent. Mikos is subject to a 30 percent marginal tax rate. If the Modigliani and Miller assumptions apply, except the assumption that there are no taxes, what will be the value of Mikos after the recapitalization? Solution: Mikos will be worth $500,000,000 plus the present value of the tax shield. The present value of the tax shield is $100,000,000 × 0.3 = $30,000,000. Therefore, Mikos will be worth $530,000,000 after the recapitalization. LO: 1 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance

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16.18 M&M Proposition 2: Backwards Resources Company has a WACC of 12.6 percent, and it is subject to a 40 percent marginal tax rate. Backwards has $250 million of debt outstanding at an interest rate of 9 percent and $750 million of equity (at market value) outstanding. What is the expected return on the equity with this capital structure? Solution: Using the WACC formula when taxes are included: WACC = (1-t) × kDebt × (VDebt/VFirm) + kcs × (Vcs/VFirm) We can solve for the missing variable: 0.126 = (1-0.4) × 0.09 × [250 million / (250 million + 750 million)] + kcs × (750 million / [250 million + 750 million]) kcs = 0.15, or 15% LO: 1 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

16.19 The costs of debt: Briefly discuss costs of financial distress to a firm that may arise when employees believe it is highly likely that the firm will declare bankruptcy. Solution: If the employees of a firm understand that the firm has a significant chance of filing for bankruptcy, then costs to the firm could be manifested in a number of ways, including: 1. Lower productivity due to lower morale and job hunting. This could be as simple as employees spending time gossiping about what is going to happen to them as well as employees actively pursuing other jobs while on the payroll of the troubled firm. 2. Higher recruiting costs. Understanding that working for the firm is a risky venture, new employees will seek compensation for this additional risk. Therefore, recruiting employees will become more expensive due to greater recruiting efforts as well as greater compensation expense when a new employee is finally located and hired.

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LO: 2 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective 16.20 The costs of debt: Santa’s Shoes is a retailer that has just begun having financial difficulty. Santa’s suppliers are aware of the increased possibility of bankruptcy. What might Santa’s suppliers do based on this information? Solution: Santa’s Shoes is not certain to go into bankruptcy, so its suppliers would still like to do business with Santa’s Shoes as long as it is profitable to do so. Therefore, the suppliers would still make sales to Santa’s Shoes as long as payment for the sales was made at the time of purchase rather than on credit. This would require Santa’s Shoes to maintain a higher cash balance. This requirement to hold additional cash could be viewed as a cost of financial distress to Santa’s Shoes. LO: 2 Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

16.21 Stockholder-manager agency costs: Deficit Corp. management has determined that the firm be $50 million short of being able to pay its debt obligations at the end of this year. Management has identified a positive NPV project that will require a great deal of effort on their part. However, this project is expected to generate only $40 million at the end of the year. Assume that all the members of Deficit’s management team will lose their jobs if the firm goes into bankruptcy at the end of the year. How likely is management to take the positive NPV project? If management declines the project, what kind of cost will Deficit’s stockholders incur? Solution:

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Managers expect to lose their jobs in one year whether they work hard or not and take the project or not. Although, there may be a slim chance that the firm will not declare bankruptcy, management has no incentive to take on the difficult project. This makes the shortage to the debt holders, as well as the stockholders, greater than it would be if the firm followed the rule of always accepting positive NPV projects. This is another example of agency costs that can arise from financial distress. LO: 2 Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

16.22 Two theories of capital structure: Use the information in the following table to make a suggestion concerning the proportion of debt that the firm should utilize in its capital structure.

Benefit or (Cost)

No Debt

25% Debt

50% Debt

75% Debt

Tax shield

$10

$20

$30

Agency cost

−$10

−$5

−$20

Financial distress cost

−$1

−$3

−$10

Solution: By totaling the costs and offsetting by the benefit for each proportion of debt we find: Benefit or (Cost)

No Debt

Total cost/benefit

-$11

25% Debt $2

50% Debt

75% Debt

Therefore, this firm can maximize the firm’s value by choosing a 50 percent debt capital structure. LO: 3 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

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16.23 Two theories of capital structure: Problem 16.22 introduces taxes and information and transaction costs to the simplified Modigliani and Miller model. If the marginal tax rate for the firm were to suddenly increase by a material amount, would the capital structure that maximizes the firm’s value include less or more debt? Solution: If we hold all other things equal, then the value of the tax shield would become more valuable in the scenarios with positive debt amounts. While we cannot say for certain, given the information in the question, an increase in the tax rate will increase the value of the tax shield and should increase the amount of debt in the optimal capital structure. Therefore, it would appear that an increase in the tax rate should motivate firms to increase their debt levels. LO: 3 Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

16.24 Two theories of capital structure: Describe how managers who subscribe to the pecking order theory of financing would rank the alternative sources of financing. Evaluate that ranking in terms of the costs of each source relative to the costs of other sources. Solution: According to the pecking order theory, the costs, from lowest to highest, are: 1. Internally generated funds (this is essentially retained earnings)—This will actually be the cheapest source in this list. 2. New issue debt—This will be more expensive than internally generated funds, but still relatively inexpensive and the second most inexpensive source in this list. 3. New issue equity—This will be the most expensive source in this list. Managers who subscribe to the pecking order theory choose the cheapest sources of financing before moving on to more expensive sources.

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LO: 3 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

16.25 Two theories of capital structure: The pecking order theory suggests that managers prefer to first use internally generated equity to finance new projects. Does this preference mean that these funds represent an even cheaper source of funds than debt? Justify your answer. Solution: The internally generated equity is utilized first as a source of financing, but it does not mean that the internally generated funds are cheaper than debt. Internally generated funds belong to stockholders and, therefore, are really equity financing, which is riskier and more expensive than debt. However, using internally generated funds enables the firm to avoid the costs associated with borrowing or selling stock (including the costs associated with the signals that financing announcements send investors), which, in turn, can make internal funds most attractive. LO: 3 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

16.26 The costs of debt: Discuss how the legal costs of financial distress may increase with the probability that a firm will formally declare bankruptcy, even if the firm has not reached that point yet. Solution: If a firm is anticipating bankruptcy to a greater extent, then it will increase its legal efforts to protect the firm from creditors or if the firm reaches that point. Therefore, the legal costs of bankruptcy will increase with financial distress even if the firm has not yet declared bankruptcy.

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LO: 2 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

ADVANCED 16.27 Operating a firm without debt is generally considered to be a conservative practice. Discuss how such a conservative approach to a firm’s capital structure is good or bad for the value of the firm in the absence of information or transaction costs and any effect of debt on the real investment policy of the firm. Solution: In the absence of information or transaction costs and any effect of debt on the real investment policy of the firm, value of the firm is increasing in proportion to debt in the firm’s capital structure, due to the present value of the tax shield on the debt. Therefore, although operating without debt may be a safer play for investors, it does not maximize stockholder value, which should be the goal of managers. LO: 2 Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

16.28 Finite Corp. has $250 million of debt outstanding at an interest rate of 11 percent. What is the present value of the debt tax shield if the debt will mature in five years (and no new debt will replace the old debt), assuming that Finite is subject to a 40 percent marginal tax rate? Solution: Finite will pay $27,500,000 ($250,000,000 × 0.11) in interest each year, which will shield Finite from paying a tax amount equal to $11,000,000 ($27,500,000 × 0.4). The tax Copyright © 2022 John Wiley & Sons, Inc.

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shield will last for five years, so the present value of receiving this amount for the next five years is: $11,000,000 × PVIFA (11%, 5) = $11,000,000 × 3.695897 = $40,654,867.19 LO: 2 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

16.29 The Boring Corporation is currently valued at $900 million, but management wants to completely pay off its perpetual debt of $300 million. Boring is subject to a 30 percent marginal tax rate. If Boring pays off its debt, what will be the total value of its equity? Solution: Boring will be worth $900 million less the present value of the tax shield on its current debt. The present value of the tax shield is $300,000,000 × 0.3 = $90,000,000 Therefore, Boring will be worth $810 million after the recapitalization, and since it will be an all-equity firm, that will be the value of the equity. LO: 2 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

16.30 If we drop the assumption that there are no information or transaction costs, in addition to dropping the no-tax assumption, then will the Modigliani and Miller model still suggest that the firm should take on greater proportions of debt in its capital structure? Explain. Solution: If we only drop the no-tax assumption, then it is evident that the firm should always increase its use of debt within a firm’s capital structure. However, if we drop the no

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information or transaction costs assumption, then we are effectively introducing the possibility that the firm will default on its debt obligations. The higher the level of debt, the greater the possibility of defaulting and then the greater the interest costs on the debt. Given this increasing cost of debt, relative to the increased use of debt within a firm’s capital structure, then we are introducing the possibility that the firm’s overall cost of capital will increase at some high-debt level capital structure, thereby reducing the value of the firm. Therefore, by dropping the no information or transaction costs assumption, the firm will not always increase its use of debt. LO: 1 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective 16.31 PolyAna Corporation has such high cash flows that the company’s managers take Fridays off for a weekly luncheon in Cancun using the corporate jet. Describe how altering the capital structure of the firm might make the management of this firm stay in the office on Fridays in order to work on new positive NPV projects. Solution: The root of the problem is that the firm’s management is too comfortable, because their weekly trip to Cancun is not costly enough to the managers of the firm. PolyAna could drastically increase the proportion of debt in the firm’s capital structure. This would decrease the amount of “free” cash that PolyAna’s management could spend on their weekly outings. If enough debt is placed on this firm, then a cash shortage, or lack of a large cash surplus, would necessitate that the managers of the firm work on new positive NPV projects rather than spend their Fridays in Cancun. LO: 2 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

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16.32 M&M Proposition 2 with taxes: Forwards Resources Company is currently an allequity firm with a WACC of 14% and a 40 percent marginal tax rate. Forwards wants to move to a capital structure with $250 million of debt outstanding at an interest rate of 9 percent and a market value of equity equal to $750 million outstanding. Using M&M Proposition 2 with taxes, equation 16.5, what is the expected return on equity at the new capital structure? Solution: If Forwards is all equity then kcs = kAssets = 14%. At the new capital structure: kcs = kAssets + (VDebt /Vcs) × (kAssets – kDebt) × (1 – t) kcs = 0.14 + ($250 million /$750 million) × (0.14 – 0.09) × (1 – 0.40) kcs = 0.15 or 15% LO: 1,2 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

16.33 M&M Proposition 2 with taxes: You own all of the equity in a debt-free app development business that generates cash flows of $400,000 each year in perpetuity. The cost of assets, kAssets is 10 percent and the tax rate is 25 percent. What is the value of your all-equity firm? If you decide to replace $1 million of equity by borrowing $1 million at an interest rate of 6 percent, how much would the value of the firm increase? What would the kcs and WACC for your business be before and after the proposed financial restructuring? Use M&M Proposition 2 with taxes, Equation 16.5, to determine the expected return on the equity for input to the WACC calculation. Assume that all cash flows are perpetuities and that the second and third M&M conditions hold. Solution:

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With $400,000 of pre-tax earnings, we would pay tax of 25% leaving $400,000 × (1-0.25) = $300,000 as a dividend. At a cost of equity of 10% the value of the allequity firm in perpetuity is: VFirm = [$400,000 × (1 – 0.25)] /0.10 = $300,000/0.10 = $3,000,000 The value of the tax shield is: D × t = $1,000,000 × 0.25 = $250,000. Therefore, after the restructuring, the value of the firm would be $3.25 million VFirm_After = $3,000,000 + $250,000 = $3,250,000. Of this $1,000,000 is debt, and the value of equity is $2,250,000 ($3,250,000 $1,000,000). The WACC before the financial restructuring just equals the kAssets, which is the same as the kcs of 10 percent, as we have zero debt. To calculate the WACC after the restructuring we first need to use Equation 16.5 to determine the kcs after the change: kcs = kAssets + (VDebt /Vcs) × (kAssets – kDebt) (1 – t) kcs = 10% + ($1,000,000 /$2,250,000) × (10% – 6%) (1 – 0.25) kcs = 10% + 1.33% kcs = 11.33% Now using the WACC formula where taxes are included: WACC = xDebt × kDebt pretax × (1-t) + xps × kps + xcs × kcs As we have only debt and common stock WACC = xDebt × kDebt pretax × (1-t) + xcs × kcs or

WACC = (VDebt/VFirm) × kDebt pretax × (1-t) + (Vcs/VFirm) × kcs

WACC = ($1,000,000/$3,250,000) × 6% × (1-.25) + 11.33% × ($2,250,000/$3,250,000) WACC = 1.38%+ 7.84% WACC = 9.23% Note that the WACC is lower due to the tax deductibility of interest on debt. LO: 1, 2 Bloomcode: Comprehension

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AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

CFA PROBLEMS 16.34 Consider two companies that operate in the same line of business and have the same degree of operating leverage: the Basic Company and the Grundlegend Company. The Basic Company has no debt in its capital structure, but the Grundlegend Company has a capital structure that consists of 50 percent debt. Which of the following statements is true? a.

The Grundlegend Company has a degree of total leverage that exceeds that of the Basic Company by 50 percent.

The Grundlegend Company has the same sensitivity of net earnings to changes in earnings before interest and taxes as the Basic Company.

The Grundlegend Company has the same sensitivity of earnings before interest and taxes to changes in sales as the Basic Company.

The Grundlegend Company has the same sensitivity of net earnings to changes in sales as the Basic Company.

Solution: c is correct. The degree of total leverage of the Grundlegend Company exceeds that of the Basic Company, but the extent of the difference depends on the amount of interest expense, not the amount of debt. In the case of financial leverage, it is the interest that acts as a fulcrum. LO: 2 Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

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New debt is preferable to new equity.

New equity is preferable to internally generated funds.

New debt is preferable to internally generated funds.

New equity is always preferable to other sources of capital.

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Solution:

a is correct. According to pecking order theory, internally generated funds are preferable to both new equity and new debt. But new debt is preferable to new equity as it has lower cost. LO: 3 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

16.36 According to the trade-off theory: a.

The amount of debt a company has is irrelevant.

Debt should be used only as a last resort.

Debt will not be used if a company’s tax rate is high.

Companies have an optimal level of debt.

Solution: d is correct. The static trade-off theory indicates that there is a trade-off between the tax shield from interest on debt and the costs of financial distress, leading to an optimal range of debt for a company. LO: 3 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

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Sample Test Problems 16.1

Central Grocers Inc. produces annual cash flows of $175,000, which are expected to continue indefinitely. The company is financed entirely with equity capital at an annual cost of 12 percent. Management is considering borrowing $400,000 at an annual interest rate of 6 percent to repurchase $400,000 of the company’s outstanding stock (You can assume that the debt will be outstanding into the indefinite future.). What is the total value of Central Grocers’ stock before the stock repurchase? Under Modigliani and Miller’s Proposition 1, what would be the value of the total claims on the company’s assets after the stock repurchase? What will be the rate of return on common stock required by investors after the repurchase?

Solution: Using the perpetuity formula, we can compute the value of Central Grocers’ stock before the repurchase to be $175,000/0.12 = $1,458,333 if the cash flow is expected to be produced into the infinite future. Under M&M Proposition 1, the value of the firm will be the same before and after the repurchase. Therefore, since the value of the debt claim will be $400,000 at the time of the transaction, the value of the outstanding equity after the repurchase must be $1,458,333 – $400,000 = $1,058,333. Since interest of $400,000 × 0.06 = $24,000 must be paid to the debt holders each year, the amount that will be available for the stockholders each year will equal $175,000 $24,000 = $151,000. This implies that the new cost of equity capital for the firm will be $1,058,333 = $151,000/kcs, or kcs = 0.1427, or 14.27%. LO: 1 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

16.2

The required rate of return on the assets of a firm is 12 percent, the firm has a debtto-common-stock ratio of 40 percent, and the cost of debt is 6 percent. If the firm

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has no preferred stock and the three conditions specified by M&M hold, what is the expected rate of return on the firm's common stock? Solution: Using the equation for M&M Proposition 2, Equation 16.3, we get: kcs = kAssets + (VDebt /Vcs) × (kAssets – kDebt) = 0.12 + [(0.4) × (0.12 – 0.06)] = 0.144, or 14.4% LO: 1 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

16.3

Your boss at Box and Freight Company asks you how much additional debt the company would have to add through a capital restructuring in order to create $9 million in present value from the resulting interest tax shields. What will you tell your boss if the debt will have no maturity and if Box and Freight is subject to a 32 percent marginal tax rate?

Solution: The present value of Box & Freight’s additional tax shield will be: tc × D = 0.32 × D = $9,000,000 Therefore: D = $28,125,000 LO: 2 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

16.4

Southwest Airlines has substantial cash reserves and an investment-grade bond rating. How would the trade-off theory predict that managers of Southwest would

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raise capital and choose the company’s capital structure if they were planning an expansion into Mexico? What would the pecking order theory suggest? Solution: The trade-off theory would predict that Southwest would raise additional funds by first issuing more debt. The additional debt would provide tax savings, and as long as the incremental tax savings exceeded any added financial distress or agency costs, Southwest’s managers would increase the debt in the company’s capital structure. The pecking order theory would suggest that internally generated funds, specifically, cash on hand, would be the cheapest source of capital, and therefore used first to fund the expansion. Only after exhausting the internal funds would Southwest managers seek to add more debt to the company’s capital structure. LO: 3 Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

16.5

What control implications do a firm’s capital structure decisions have?

Solution: Issuing debt does not change the ownership and therefore control of the firm, unless it is so much debt as to cause financial distress and the stockholders lose control to creditors. Issuing more common stock could dilute existing shareholders’ ownership if they do not purchase a proportionate amount of the new shares, thereby reducing their control. LO: 4 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

Appendix A16

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Before You Go On 1.

What is a lease? What are the two types of leases? A lease is an alternative way of financing the acquisition of an asset. In a lease agreement the lessee pays for the right to use the asset during the term of the lease while the lessor, who owns the asset, receives the lease payments in return for giving up the right to use the asset during the term of the lease. The lessor retains the right to use the asset after the term of the lease. The two types of leases that the IRS recognizes are: (1) leases which are truly rentals called operating leases, and (2) leases that have the key elements of an outright sale, known as capital leases.

What is the most common motivation for leasing? The primary motivation for leasing an asset is that leasing can be a less expensive way of obtaining the use of an asset for a period of time than purchasing the asset.

What types of conflicts arise with leases, and why? The two conflicts that arise with leases are the (1) intensity of use and (2) maintenance conflicts. These conflicts arise because a lease separates the right to use an asset during the term of a lease from the right to use the asset afterwards. Since two different parties own these rights (the lessee and the lessor) conflicts of interest are bound to arise.

Self-Study Problem A16.1 You own a real estate investment firm and have been asked by the owner of Big Box Shipping Company if you would be willing to construct an office building and lease it to Big Box. The owner of Big Box has some very unusual requirements for the interior layout of the building and is only willing to commit to leasing the building for 10 years, even though the life of the building is likely to be many times that long. What should concern you about this proposal? Solution:

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Assuming that there is likely to be sufficient demand for office space in the same area by other businesses at the end of the 10 years, the biggest concern would be the interior layout requirements. If the owner of Big Box wants permanent interior walls for this layout and future potential tenants are likely to demand costly changes, this building would be a firm-specific asset and might not be a good investment for you. You should consider making the investment only if the lease payments include the cost of reconfiguring the space when Big Box moves out. Avoiding this sort of problem is a major reason that modern office buildings are often built without permanent interior walls and tenants use movable cubicles instead.

Discussion Questions A16.1 Your boss just read an article about the tax benefits of leasing. He states that your firm should lease all of its assets, since it faces a low tax rate. How would you respond? Solution: A company in a high tax bracket has a substantial benefit resulting from the depreciation tax shield and interest deduction when an asset is purchased. The tax benefit of leasing results from the ability to take a deduction for the lease expense which is usually much lower than the accelerated depreciation expenses that result from ownership. Since your firm is in a low tax bracket it will only be beneficial if it is able to negotiate a low lease arrangement with a leasing company that is eligible to enjoy significant tax savings because it has a higher marginal tax rate.

A16.2 You have decided to open a Segway Personal Transporter (PT) rental shop on your campus. If you plan to rent Segway PTs by the day, what sort of asset abuse problems are you likely to be concerned about and how might you control them? Solution: Asset abuse problems include the intensity of use and how well it is maintained by the lessee. The lessee may have an incentive to use the leased asset more intensely than the lessor would prefer and not look after it well. These types of problems may be controlled Copyright © 2022 John Wiley & Sons, Inc.

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by pricing the lease to compensate Segway Personal Transporter for the greater susceptibility to asset abuse. Other options include requiring a damage deposit, bundling the lease contract with a service contract, placing explicit restrictions on how the Segway PT may be used or providing the lessee with the right to buy the asset when the lease expires reducing the incentive to abuse the asset during the rental period.

Questions and Problems Basic A16.1 Leasing: What characteristic of a lease leads to conflicts between the lessee and the lessor? Solution: The characteristic of separation of the right to use an asset during the term of a lease from the right to use the asset afterward creates two natural conflicts of interest between lessees and lessors. These conflicts concern how intensely the asset is used and how well it is maintained during the term of the lease. The intensity of use and maintenance conflicts lead to the asset abuse problem in leasing.

Intermediate A16.2 Leasing: Fresno Machine Shop management has decided to acquire a new machine that costs $3,000. The machine will be worthless after three years. Only straight-line depreciation is allowed by the IRS for this type of machine. ABC Leasing, Inc., offers to lease the same machine to Fresno under an operating lease. Annual lease payments are $1,200 per year and are due at the end of each of the three years. The market-wide borrowing rate is 8 percent for loans on assets such as this. Fresno’s marginal tax rate is 35 percent. Should Fresno lease the machine or buy it? Assume that Fresno would not borrow to purchase the machine. Solution:

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Assuming that the asset abuse problem is not an important concern with this lease, the analysis of the lease versus purchase options involves calculating the present value of the after-tax cash flows that are unique to each of them. After tax cash flows of purchasing the machine: After-tax cost of debt = 0.08 × (1 – 0.25) = 0.06 or 6% Year 0: 0 (assuming the machine is financed at an after-tax cost of 6%) Year 1: Depreciation Tax Shield - Interest charges = ($1,000 × 0.35) - (0.06 × $3,000) = $170 Year 2: Depreciation Tax Shield - Interest charges = $170 Year 3: Depreciation Tax Shield - Interest charges - Principal Repayment = $170 - $3,000 = -$2,830 NPV of purchasing the machine: $170/(1.06) + $170/(1.06)2 - $2,830/(1.06)3 = -$2,064.45 After tax annual cost of lease: $1,200 × (1 – 0.35) = $780 3 payments which occur at the end of the year NPV of leasing the machine: $780/(1.06) + $780/(1.06)2 + $780/(1.06)3 = -$2,084.95 The NPV analysis suggests that Fresno Machine shop should purchase the machine because it is less expensive to purchase than to lease it.

Advanced A16.3 Your firm is considering leasing a chromebook laptop computer. The lease would last for three years and require four payments of $100 per year, with the first payment due immediately. The computer would cost $360 to buy and would be depreciated using straight-line depreciation over three years to a salvage value of zero. The actual salvage value is expected to be $100 after three years. The borrowing rate is 10 percent for loans on assets such as this, and your firm’s marginal tax rate is 25 percent. Should your firm lease or buy the computer? Solution: Copyright © 2022 John Wiley & Sons, Inc.

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Assuming that the asset abuse problem is not an important concern with this lease, the analysis of the lease versus purchase options involves calculating the present value of the after-tax cash flows that are unique to each of them. After tax cash flows of purchasing the computer: After-tax cost of debt = 0.10 × (1 – 0.25) = 0.075 or 7.5% Year 0: 0 (assuming the machine is financed at an after-tax cost of 7.5%) Year 1: Depreciation Tax Shield - Interest charges = ($120 × 0.25) - (0.075 × $360) = $3 Year 2: Depreciation Tax Shield - Interest charges = $3 Year 3: Depreciation Tax Shield - Interest charges - Principal Repayment + Salvage value = $3 - $360 + $100 = -$257 NPV of purchasing the machine: $3/(1.075) + $3/(1.075)2 - $257/(1.075)3 = -$201.49 After tax annual cost of lease: $100 × (1 – 0.25) = $75 3 Payments, each made at the beginning of the year NPV of leasing the machine: [$75/(1.075) + $75/(1.075)2 + $75/(1.075)3] × 1.075 = -$209.67 The NPV analysis suggests that the firm should purchase the laptop because it is less expensive to than to lease it.

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CHAPTER 15

How Firms Raise Capital Before You Go On Questions and Answers Section 15.1 1.

Explain bootstrapping, and list the most common sources of seed money. Bootstrapping refers to the securing of initial funding by entrepreneurs to start a new business. It alludes to the idea of an individual or small group of entrepreneurs who keep their business idea barely alive by securing money to keep it going. The initial “seed” money usually comes from the entrepreneur or other founders. Other cash may come from personal savings, the sale of assets such as cars and boats, loans from family members and friends, and loans secured from credit cards.

Section 15.2 1.

Who are venture capitalists, and what do they do? Venture capitalists are individuals or groups of people that help new businesses to get started and provide much of their early financing. They pool money from various sources, such as wealthy individuals, insurance companies, pension funds, or large corporations and invest in start-up ventures. The primary types of businesses seeking the services of venture capitalists are high-tech firms.

How is venture capital financing different from traditional sources of financing? Venture capital financing is different from traditional sources of financing because entrepreneurs without long track records do not have access to traditional sources of funding. Venture capital investors tend to invest in companies that have a higher degree of risk and are expected to deliver higher returns. Additionally, new firms generally have

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less tangible assets and more intangibles such as patents or trade secrets which make it difficult to secure financing. Another importance difference occurs because many times there are asymmetric information problems. This occurs because the entrepreneur is operating in a highly specialized environment, one that most traditional investors do not have the expertise to evaluate.

How do venture capitalists reduce the risk of their investments? Venture capitalists reduce the risk of their investments in two ways: (1) stage funding, which gives the investors a chance to periodically reassess the project, the management team, and the firm’s financial performance, and to make necessary corrections throughout the duration of the project, and (2) personal investment by the entrepreneurs. Requiring the entrepreneurs to make a substantial personal investment in the business is to make sure that they are highly motivated to succeed.

Explain the venture capital funding cycle. The venture capital funding cycle starts with the development of a detailed business plan by the start-up company. Once a venture capitalist (VC) that will fund the project is selected, they state their terms of funding—how much money will they supply in what stages, criteria of success, and so on. Finally, an exit strategy is developed. Since VCs are not long-term investors, it is important that a clear understanding of how the VC can exit the deal is part of the initial agreement. This can involve taking the firm public or sometimes selling the new firm to another business.

Section 15.3 1.

What is a seasoned offering, and why are seasoned securities valued more highly than securities sold in an IPO? A seasoned offering is a sale of securities by a firm that already has publicly traded securities outstanding. These are usually more expensive as they are viewed to be less risky than IPO securities; since they are sold by firms that already established a reputation for quality with the investing public, many investors prefer them to new issues.

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Explain the two ways a security issue can be underwritten. A security can be underwritten in two ways: (1) firm-commitment basis—in this case the banker guarantees the issuer a fixed amount of money from the security sale, and (2) best-effort basis—whereby the banker makes no guarantee to sell the securities at a particular price, but instead promises to sell as much of the issue as possible above a certain price. The main difference between these two types of underwriting is who bears the risk. With the firm-commitment basis, it is the banking firm that buys the securities first before selling them to public. On the other hand, in a best-effort type of deal, the issuer is the risk bearer.

List the steps in the IPO process. The IPO process involves the following steps: (1) selection of the investment bank, (2) preparation of the registration paperwork and SEC process, (3) determination of the structural features of the offering, (4) valuation, (5) marketing of the IPO, and (6) sale of the securities.

Section 15.4 1.

What is underpricing, and why is it a cost to the stockholders? Underpricing is defined as the offering of new securities for sale at an offer price below the intrinsic value of the security. It is considered to be a cost to a firm, because if the stock sells at a low price, the issuer is essentially losing money, which goes into the pockets of investors that bought the issues for less than they are worth.

What are the components of the cost associated with an IPO? The cost of issuing an IPO includes the following: (1) underwriting spread, (2) out-ofpocket expenses, and (3) underpricing.

Section 15.5 1.

Explain why firms generally sell their equity and complicated debt issues through negotiated sales.

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Negotiated sales allow the investment bankers to form a closer relationship with the issuer and develop a better understanding of the firm. This enables them to form more effective selling teams. As a result, a negotiated sale should allow the bankers to reduce uncertainty surrounding the issue, resulting in a lower issue cost.

Explain the importance of shelf registration. Shelf registration allows firms to register the inventory of securities for a two-year period. During this time the firm can take the securities and sell them as needed. This process simplifies the sale, as there are no flotation costs involved after the initial registration statement. The firm can also sell as many or as few securities at a time as it needs to, taking advantage of favorable market conditions. There is no penalty if authorized securities are not issued.

Section 15.6 1.

What are the disadvantages of a private placement sale compared with a public sale? Private placement has three main disadvantages compared to public sale. First, because of the lack of liquidity, nominal yields are higher, increasing costs to the issuer. Second, since private placement securities are not registered, the covenants are stricter. And finally, compared to public securities, private placement securities are more difficult to sell in the secondary market.

Why do companies engage in PIPE transactions? Small and midsize companies can find it difficult or costly to raise money in the public markets. In these circumstances, it can be more efficient or cost effective to sell stock privately, even if the company’s stock is already publicly traded.

PIPE transactions bring several advantages to the issuing firm. They give the firm faster access to capital and a lower funding cost than a registered public offering. A PIPE transaction can be completed in as short a time as two weeks, whereas a typical public offering underwritten by an investment bank takes several months. PIPE transactions

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involving a healthy firm can also be executed without the use of an investment bank, resulting in a cost saving of 7 to 8 percent of the proceeds. A PIPE transaction can be the only way for a small financially distressed company to raise equity capital.

Self-Study Problems 15.1

Management of Oakley, Inc., is planning to raise $1 million in new equity through a private placement. If the sale price is $18 per share, how many shares does the company have to issue?

Solution: To raise $1million, Oakley has to issue 55,556 shares: ($1,000,000 / $18 per share = 55,556 shares).

15.2

Suppose a firm is doing an IPO and the investment bank offers to buy the securities for $39 per share with an offering price of $42. What is the underwriter’s spread? Assume that the underwriter’s cost of bringing the security to the market is $1 per share. What is the net profit?

Solution: Underwriter’s spread: $42 – $39 = $3, or 7.1% ($3 / $42 = 0.071, or 7.1%) Net profit per share: $3 – $1 = $2

15.3

Management of Stride Rite Corporation, designer and marketer of athletic apparel, is planning an expansion into foreign markets and needs to raise $10 million to finance this move. Management anticipates raising the money through a general cash offering for $13 a share. If the underwriters charge a 5 percent spread, how many shares will the company have to sell to achieve its goal?

Solution: Underwriter’s spread = 5% Price per share for the firm = [$13 × (1-0.05)] = $12.35

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To raise $10 million, the company needs to issue: ($10,000,000 / $12.35) = 809,717 new shares

15.4

Dean Foods Co. needs to borrow $23 million for a factory equipment upgrade. Management decides to sell 10-year bonds. Managers determine that a 3-month Treasury bill yields 4.32 percent, the firm’s credit rating is AA, and the yield on 10year Treasury bonds is 1.06 percent higher than for 3-month bills. Right now, AA bond rates are 1.35 percent above the 10-year Treasury bond rate. What is the borrowing cost for this transaction?

Solution: The borrowing cost for Dean Foods can be calculated as follows: kl = 4.32% + 1.35% + 1.06% = 6.73% The approach used here is similar to that used in the bank loan pricing model.

15.5

You are considering starting a new online dating service, but you lack the initial capital. What are your options for obtaining the necessary financing?

Solution: Possible sources of capital include your own savings, family and friends, wealthy individuals, venture capital firms, and financial institutions such as banks.

Discussion Questions 15.1

Assume you work for a venture capital firm and have been approached by a couple of recent college graduates with a request to fund their new business. If you are interested in the idea, what process will you follow? After setting up the initial meeting, we should carefully review their business plan and make sure that it contains all the important information a business plan should, such as industry and market analysis, vision and mission statements, management team description, and cost analysis along with the proposed budget. If we like the plan and decide to fund the project, we will try to minimize our risk of investing and only fund the

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project in stages. In addition, we will require some personal investment from the candidates to ensure their serious interest in the project. Finally, we will draft an exit strategy, outlining the timing and calculation of the exit price. LO: 2 Level: Basic Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

15.2

Identify the three basic services investment bankers provide to help firms bring new security issues to the market. During which stage of the typical IPO does the investment banker take on the risk of the offering? Is there an alternative in which the risk remains with the company going public? The three services provided by an investment banker in an initial public offering are origination, underwriting, and distribution. The underwriter takes on the risk during the second stage of the IPO process that is underwriting, providing a firm-commitment underwriting deal is in place. Under this scenario, the banker actually buys the securities from the firm at a fixed price and resells them to the public. Hence, the underwriter bears the risk that the securities may be sold for less than the underwriter paid for them. An alternative arrangement is the best-effort underwriting, where the investment banking firm makes no guarantee to sell the securities at a particular price, but instead promises only to make its “best effort” to sell as much of the issue as possible at a certain price. In this scenario, the risk stays with the offering firm. LO: 3 Level: Basic Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

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Define underpricing, and explain why the majority of IPOs are underpriced. What role do investment banks play in the price-setting process? Underpricing is defined as offering new securities for sale at a price below their true value. It is the loss that the issuer incurs from selling below its intrinsic value. Asymmetric information plays a big role in an IPO underpricing, since both the bankers and the public know less about private companies going public than they do about already publicly traded firms. The lower offering price is to compensate the investors for taking on the risk of buying into a company for which not a lot of information is available. One way for companies to reduce underpricing is to choose a well-known investment bank to take them public. This will send a signal to the potential investors that the bank has done its due diligence and considers the firm to be creditworthy. LO: 4 Level: Intermediate Bloomcode: Knowledge AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

15.4

Explain why the owners of a company might choose to keep it private. By remaining private, a company effectively avoids being subjected to SEC regulations. Many of the large private companies are family owned with a long history and prefer not to be subjected to public scrutiny. In addition, the management of the company is not pressured by Wall Street to report short-term earnings but can concentrate their efforts on long-term growth and strategy realization. LO: 6 Level: Basic Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

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Identify the three cost components that make up the total cost of issuing securities for a company. Briefly describe each. The total cost for a firm to issue securities is equal to the sum of the underwriting spread, out-of-pocket expenses, and underpricing. The underwriting spread is the difference between the proceeds the issuer receives, and the total amount raised in the offering. Outof-pocket expenses usually include administrative costs such as investment banking fees, legal fees, accounting expenses, SEC filing fees, and so on. Finally, the total amount of underpricing is determined as the difference between the offering price and the closing price on the first day of trading in the public market. LO: 3 Level: Basic Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

15.6

What are the characteristics of a public bond? (Think in terms of comparing it to private placement and bank term loans.) A public bond is usually the most suitable security for a large firm looking for a large loan. It tends to have the lowest interest costs as well as the lowest default risk, but usually has a long maturity. While it has very few restrictive covenants, it is also very difficult to renegotiate. LO: 3 Level: Basic Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

15.7

Discuss the advantages of shelf registration. What kinds of securities are most likely to be registered this way?

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Shelf registration allows the company to register an inventory of securities for a two-year period, allowing the company to sell the securities when market conditions are most favorable. The company can take the securities “off the shelf” and sell them within minutes. They can also sell securities on a periodic basis, whenever cash is needed. Plain vanilla bonds are most likely to be sold by shelf registration through competitive bidding. LO: 5 Level: Basic Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

15.8

Identify whether each of the following factors implies a lower or higher price for a bond. a.

Low marketability of the security.

Short term to maturity.

Low credit rating of the issuer.

No call provision. Bond prices and yields move inversely with each other. The prices are observed in the market but investors care about the rate of return or the bond yields, so the factors are identified below.

Factor

Bond yield

Bond Price

a. Low marketability of the security

Increase

Decrease

b. Short term to maturity

Decrease

Increase

c. Low credit rating of the issuer

Increase

Decrease

c. No call provision

Decrease

Increase

LO: 6 Level: Intermediate Bloomcode: Comprehension AASCP: Analytic

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IMA: Corporate Finance AICPA: Industry/Sector Perspective

15.9

Explain why time might play a significant role during low-interest periods in a decision of whether to choose a private placement or public sale. Private placement deals tend to be completed much more quickly than public sales. Since there is uncertainty about the future behavior of interest rates in the market, a firm might decide to go with private deal in order to lock in the favorable interest rates. LO: 6 Level: Basic Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

15.10 Managers at a large firm are looking for a medium-size loan with a long term to maturity and low liquidity. Which of the following types of debt would be the most appropriate? a.

Public bond.

Private placement.

Bank term loan.

A large firm can have its pick of the three alternatives. A public offering of debt would be helpful to raise large amounts, but the terms of the bond contract may not be easily negotiated. Private placements have a number of advantages, relative to public offerings, for certain issuers. These include lower cost of funds, ability to negotiate changes to a bond contract, speed of private placement deals, and flexibility in issue size. Bank term loans are preferable when the loan term is short to medium term. A large firm may choose a bank loan only if it cannot raise funds publicly or through private placement. Bank loans offer some similar advantages as private placements. LO: 7 Level: Intermediate

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Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

Questions and Problems BASIC 15.1

Venture capital: What items in a business plan does a venture capitalist look for in deciding whether to provide initial financing?

Solution: Every business plan should contain the following information: •

A description of the business and industry trends.

•

Vision and key strategies for the business.

•

Principal products or services and any innovative features or patents.

•

The management team and their experience.

•

Market analysis and sales forecast.

•

How the products will be marketed and sold.

•

Production costs such as materials and labor.

•

Facilities needed and estimated costs.

•

Capital required and the use of the proceeds.

•

Detailed budget with six years of projected financial statements.

LO: 2 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

15.2

Venture capital: You finally decide to act on your brilliant idea and start an online textbook rental company. You develop a detailed business plan and calculate that you

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will need about $350,000 of initial funding to get the business going. Luckily for you, you have lined up two venture capital firms offering to supply the funding. What criteria should guide your decision to select one firm over the other? Solution: Criteria include in-depth knowledge of the business, industry and technology, references, chemistry, access to additional capital, networking, exit strategy, and proximity. LO: 2 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

15.3

Venture capital: What are some viable exit strategies for investors in a start-up company?

Solution: A firm can choose to either sell the business at some period, take it public, or in some instances remain a private company with few shareholders. LO: 2 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

13.4

IPO: Briefly describe the IPO process.

Solution: The IPO process has three phases: origination, which is financial advising and getting the issue ready to sell; underwriting, which involves the investment banker buying the securities from the firm; and distribution, which is when the investment banker resells the securities to the public. LO: 3 Bloomcode: Comprehension

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15.5

IPO: Based on your knowledge from this and previous chapters, what are some methods an investment banker uses to determine an IPO price? What factors will play a significant role in the calculation?

Solution: In order to determine the price of a new security, the investment banker can look at comparable companies and see what they are trading for. Another approach is to do a discounted cash flow analysis, which is just like determining the price of a stock. You forecast future cash flows of the company, usually for a time horizon of 5 to 10 years, and discount them back to the present in order to get the firm value. The discount rate will be a factor of both the cost of debt and cost of equity (WACC). LO: 3 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

15.6

IPO: A majority of firms choose a firm-commitment underwriting arrangement rather than a best-effort arrangement for their IPO. Explain why.

Solution: With a firm-commitment arrangement, the issuing firm is guaranteed to receive a specific amount of money from proceeds of the IPO. The underwriter bears the price risk of the issue. Price risk is the risk that the resale price to the market might be lower than that of agreed price to the issuing firm. LO: 3 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance

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AICPA: Industry/Sector Perspective

15.7

Competitive versus negotiated sale: Why might a negotiated sale be the lowest cost means of issuing a complex debt security?

Solution: Debt issues that are complex in nature and/or issued at times of uncertainty often tend to be brought to the market by negotiated sales. This approach allows the underwriter to better control the uncertain situation and better explains the firm to potential investors, thereby leading to lower issue costs. LO: 5 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

15.8

IPO pricing: Trajax, Inc., a high-technology firm in Portland, raised a total of $90 million in an IPO. The company received $27 of the $30 per share offering price. The firm’s legal fees, SEC registration fees, and other out-of-pocket costs were $450,000. The firm’s stock price increased 17 percent on the first day of trading. What was the total cost to the firm of issuing the securities?

Solution: The total costs to issue the securities are as follows: 1.

Underwriting Spread:

Underwriter’s spread ($30 per share - $27 per share) =$3 per share. Number of shares outstanding = ($90 million/$30 per share) = 3,000,000 shares. Underwriting cost = ($3 per share × 3,000,000 shares) = $9,000,000. 2.

Out-of-Pocket Expenses:

Out-of-pocket expenses are $450,000. 3.

Underpricing:

Stock price at end of first day = $30 per share (1.17) = $35.10 per share.

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First-day underpricing = ($35.10 per share - $30.00 per share) = $5.10 per share. Total underpricing = ($5.10 per share × 3,000,000 shares) = $15,300,000. Total cost to the firm of selling the IPO = $9,000,000 + $450,000 + $15,300,000 = $24,750,000 LO: 4 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

15.9

IPO pricing: Myriad Biotech management plans a $114 million IPO in which the offering price to the public will be $51 per share. The company will receive $47.50 per share. The firm’s legal fees, SEC registration fees, and other out-of-pocket costs will total $525,000. If the stock price increases 14 percent on the first day of trading, what will be the total cost of issuing the securities?

Solution: The total costs to issue the securities are as follows: 1.

Underwriting Spread:

Underwriter’s gross spread ($51per share - $47.50 per share) =$3.50 per share. Number of shares outstanding = ($114 million/$51 per share) = 2,235,294 shares. Underwriting cost = ($3.50 per share × 2,235,294 shares) = $7,823,529. 2.

Out-of-Pocket Expenses:

Out-of-pocket expenses are $525,000. 3.

Underpricing:

Stock price at end of first day = ($51per share × 1.14) = $58.14 First-day underpricing = ($58.14 per share - $51per share) = $7.14 per share. Total underpricing = ($7.14 per share × 2,235,294 shares) = $15,959,999. Total cost to the firm of selling the IPO = $7,823,529 + $525,000 + $15,959,999 = $24,308,528 LO: 4 Bloomcode: Comprehension

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AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

15.10 Shelf registration: Are the following statements true or false? a.

Shelf registration allows firms to register an inventory of securities for an unlimited time.

The securities can be taken off the shelf at any time within 2 years of such registration and sold to the public.

Shelf registration reduces flotation and other expenses associated with registration.

There is a large penalty if the authorized securities are not issued.

A shelf registration can cover multiple securities.

Solution: a. False b. True c. True d. False e. True LO: 5 Bloomcode: Knowledge AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

15.11 General cash offer: What are the steps in a general cash offering? Explain each of them. Solution: (1) Type of security and amount to be raised. (2) Approvals. (3) Registration statement. (4) Offer price and (5) Closing. LO: 5 Bloomcode: Knowledge AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

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15.12 General Cash Offer: Explain the difference between a competitive and negotiated cash sale. Which method of sale is likely to yield the lowest funding cost for firms selling plain vanilla bonds in stable markets? Solution: In a competitive offer, an investment bank does the origination work for the securities to be issued and then invites underwriters to competitively bid for the issue. The investment banking firm that pays the highest price for the securities wins the bid. The winning underwriter then pays for the securities and makes them available to individual investors at the offer price. In a negotiated offer, an underwriter works with the issuing firm to both originate and sell the firm’s securities to individual investors.

It is generally assumed that competitive offers yield the lowest cost of funding for firms issuing plain vanilla bonds. This is because the terms of the loans are standardized and well-known to the market participants. LO: 5 Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

15.13 Issuing securities: Explain what is meant by economies of scale in issuing securities. Solution: The economies of scale in issuing securities means that as the size of the issue increases, the total issue cost, as a percentage of the amount raised, declines. High fixed costs get spread out over a larger sum. LO: 5 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

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15.14 Bank term lending: Explain how term to maturity affects the price of a bank loan. Solution: Term to maturity (MAT) will usually increase the borrowing rate. It is defined as the difference between the yield on a Treasury security with the same maturity as the term loan and the yield on 3-month Treasury bill rate. Thus, the longer the loan, the higher the borrowing rate will be. The term to maturity reflects inflation risks and may also reflect interest rate risk and increased default risk. LO: 7 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

15.15 Private placement versus public debt offering: Nalco Holding is an international company that operates in 130 countries, has a market capitalization (market value of equity) of $2.3 billion, and reported net income of $45 million on $3.3 billion in revenues last year. The company needs to raise $200 million in debt, and management is deciding between private placement and public offering. What are the advantages and disadvantages of the two alternatives, and which is likely to be the best choice? Solution: Public market allows for higher security since SEC is involved, it offers more liquidity, which might be important for a large issue, and most of the times to earn higher yield. Private placement, on the other hand, offers faster speed to market, lower issuance cost, and ease of restructuring. Given the size of the Nalco Holdings, the company would be better off choosing to raise debt in public market. LO: 6 Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

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15.16 Prime-rate lending: Suppose two firms want to borrow money from a bank for a period of one year. Firm A has excellent credit, whereas Firm B’s credit standing is such that it would pay prime + 2 percent. The current prime rate is 6.75 percent, the 30-year Treasury bond yield is 4.35 percent, the three-month Treasury bill yield is 3.54 percent, and the 10year Treasury note yield is 4.22 percent. What are the appropriate loan rates for each firm? Solution: Firm A = Prime rate = 6.75% Firm B = Prime rate + 2% = 8.75% LO: 7 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

15.17 Prime-rate lending: Now suppose that Firm B from Problem 15.16 decides to get a term loan for 10 years. How does this affect the company’s borrowing cost? Solution: Maturity risk premium = k10-year – kT-bill = 4.22% - 3.54% = 0.68% Borrowing rate for firm B = k = PR + DRP + MAT = 6.75% + 2% + 0.68% = 9.43% LO: 7 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

15.18 Prime-rate lending: Cartco needs to borrow $5 million for an upgrade to its headquarters and manufacturing facility. Management has decided to borrow using a five-year term loan from its existing commercial bank. The prime rate is 3.25 percent, and Cartco’s current rating is prime + 2.48 percent. The yield on a five-year U.S.

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Treasury note is 2.01 percent, and the three-month U.S. Treasury bill rate is 0.09 percent. What is the estimated loan rate for the five-year bank loan? Solution: kl = PR + DRP + MAT MAT = y5-year - y3-mo = 2.01% – 0.09% = 1.92%

PR = 3.25% DRP = 2.48% k = 3.25% + 2.48% + 1.92% = 7.65% LO: 7 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

INTERMEDIATE 15.19 Venture capital: You work for a venture capital firm and are approached to finance a new high-tech start-up. While you believe in the business idea, you also believe it is very risky. What strategies can help to mitigate the risk of the investment to your firm? Explain how these measures would work. Solution: You can fund the project in stages. This will allow you to review the project’s profitability before you commit to further financing. You may also require the entrepreneurs to invest some of their own capital in the new start-up, which will tie them to the project and make it harder for them to simply abandon the idea. LO: 2 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

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15.20 IPO: On December 9, 2020, DoorDash completed its IPO of 33 million shares to the initial investors at $102.00 per share. The closing price of the stock that same day was $189.51. What was the dollar value of the underpricing associated with the Google IPO? Solution: With a closing price of $189.51 per share, the market value of DoorDash shares was $6.254 billion after the issue. The shares issued at $102.00 yielded proceeds of $3.366 billion for DoorDash, therefore total underpricing was $2.888 billion. LO: 4 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

15.21 IPO: Deere and Bros. is a broker that brings new issues of small firms to the public market. Its most recent deal for Dextra, Inc., had the following characteristics: Number of shares: 1,000,000

Price to public: $15 per share

Proceeds to Dextra: $13,500,000 The legal fees were $150,000, printing costs were $56,000, and all the other expenses were $72,000. What is the profit or loss for Deere and Bros.? Solution: Total proceeds from offer = $15 × 1,000,000 shares = $15 million Proceeds to Dextra = $13.5 million Gross underwriting spread to Deere = $15 million - $13.5 million = $1.5 million Underwriting costs = $150,000 + 56,000 + $72,000 = $278,000 Net profit to underwriter = $1,500,000 - $278,000 = $1,222,000 LO: 3 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

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15.22 IPO: When Global Partners went public in September 2016, the offer price was $22.00 per share and the closing price at the end of the first day was $23.90. The firm issued 4.9 million shares. What was the loss to the company due to underpricing? Solution: Change in price on first day = $23.90 - $22.00 = $1.90 Number of shares outstanding = 4.9 million Loss due to underpricing = $1.90 × 4,900,000 = $9,310,000 LO: 4 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

15.23 IPO: Bellex Technologies agreed to complete its IPO on a best-effort basis. The company’s investment bank demanded a spread of 17 percent of the offer price, which was set at $30 per share. Three million shares were issued; however, the bank’s management was overly optimistic and eventually was able to sell all of the stock for only $28 per share. What were the proceeds for the issuer and the underwriter? Solution: Gross proceeds from offer = $30.00 × 3,000,000 = $90,000,000 Underwriting spread = $90,000,000 × 0.17 = $15,300,000 Proceeds to issuer = ($28 × 3,000,000) − $15,300,000 = $68,700,000 LO: 3 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

15.24 IPO: Suppose a biotech company in Boston, Massachusetts, completes an $85 million IPO priced to the public at $75 per share. The firm receives $72 per share, and the out-of-

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pocket expenses are $340,000. The stock’s closing price at the end of the first day is $84. What is the total cost to the firm of issuing the securities? Solution: The total cost to issue the securities is calculated as follows: Underwriter’s spread = $75 per share – $72 per share = $3 per share No. of shares outstanding = $85,000,000 / $75 = 1,133,333 shares Underwriting cost = $3 per share × 1,133,333 = $3,399,999 First-day underpricing per share = $84 – $75 = $9.00 Total underpricing on day 1 = $9.00 × 1,133,333 shares = $10,199,997 Total cost to the firm = $10,199,997 + $3,399,999 + $340,000 = $13,939,996 LO: 4 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

15.25 IPO: An online medical advice company just completed an IPO with an investment bank on a firm-commitment basis. The firm issued five million shares of common stock, and the underwriting fees were $1.90 per share. The offering price was $26.00 per share. a.

What were the total proceeds from the common-stock sale?

How much money did the company receive?

How much money did the investment bank receive in fees?

Solution: a.

Total proceeds from issue = $26.00 per share × 5,000,000 = $130,000,000

Net proceeds to firm = ($26.00 per share - $1.90 per share) x 5,000,000 =

$120,500,000 c.

Underwriting spread = $1.90 per share x 5,000,000 = $9,500,000

LO: 3 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance

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AICPA: Industry/Sector Perspective

15.26 IPO underpricing: Suppose that a biotech firm in Pittsburgh raised $120 million in an IPO. The firm received $23 per share, and the stock sold to the public for $25 per share. The firm’s legal fees, SEC registration fees, and other out-of-pocket costs were $270,000. The firm’s stock price increased 17.5 percent on the first day. What was the total cost to the firm of issuing the securities? Solution: The total cost to issue the securities is calculated as follows: a.

Underwriting Cost: Underwriter’s spread = $25per share - $23 per share = $2 per share No. of shares outstanding = $120,000,000 / $25 = 4,800,000 shares Underwriting cost = $2 × 4,800,000 = $9,600,000

Underpricing: Price of stock at end of first day = $25 per share × (1.175) = $29.375 Underpricing per share = $29.375 - $25 = $4.375 Total underpricing on day 1= $4.375 × 4,800,000 = $21,000,000 Total cost to the firm= $21,000,000 + $9,600,000 + $270,000 = $30,870,000

LO: 4 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective 15.27 Long-term corporate debt: The 20-year Treasury rate is 4.67 percent, and a firm’s credit rating is BB. Suppose management of the firm decides to raise $20 million by selling 20-year bonds. Management determines that since it has plenty of experience, it will not need to hire an investment banker. At present, 20-year BB bonds are selling for 185 basis points above the 20-year Treasury rate, and it is forecast that interest rates will not stay this low for long. What is the cost of borrowing? What role does timing play in this situation?

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Solution: Cost of borrowing = 4.67% + 1.85% = 6.52% Cost of borrowing is 6.52 percent. Since the economy is supposed to improve, the interest rates are expected to go up in the near future, which could make the cost of borrowing more expensive. Time is of essence in this case. LO: 5 Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

Sample Test Problems 15.1

Why are traditional sources of funding not usually available for new or emerging businesses? Solution: There are three reasons such businesses often have little or no access to traditional funding: 1) The high degree of risk associated with them. 2) Their primary assets are often intangible assets that are not as well understood by lenders or other potential investors as tangible assets 3) Potential investors often have limited knowledge of highly specialized technologies or new business areas and therefore find it difficult to assess the quality of their management teams or their prospects.

LO: 2 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

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A firm is making an initial public offering. The investment bankers agree to a firmcommitment underwriting for 500,000 shares that would be priced to the public at $36 a share. The underwriter’s spread is 7 percent. What will be the proceeds for the issuer and the underwriter? Solution: Gross proceeds from offer = $36 × 500,000 = $18,000,000 Underwriting spread = Proceeds to Underwriter = $18,000,000 × 0.07 = $1,260,000 Proceeds to issuer = ($36 × 500,000) − $1,260,000 = $16,740,000

LO: 3 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

15.3

Hilton Worldwide Holdings Inc. completed an initial public offering on December 12, 2013. The offer price was $20.00 per share and the closing price at the end of the first day was $21.50. The firm issued 117.6 million shares. What was the loss to Hilton due to underpricing? Who received this value? Solution: Change in price on first day of trading = $21.50 - $20.00 = $1.50 Number of shares outstanding = 117.6 million Loss due to underpricing = $1.50 × 117.6 million = $176.4 million The initial investor, who purchased the shares allocated by the underwriters of the IPO received this value.

LO: 4 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

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SMA Inc. is considering issuing the following securities. For which security would a competitive sale be less costly than a negotiated sale under stable market conditions? Why? a) Plain vanilla bonds. b) IPO of common stock. c) Secondary offering of common stock. d) Convertible bonds. Solution: a) Plain vanilla bonds. A competitive sale will be the least costly for bonds with standardized features in a stable market. In a stable market investors better understand the risks associated with these securities and are more comfortable purchasing them. The other three securities are more complex and these complexities are better handled through negotiated sales in which the underwriter can address investor uncertainty concerning the securities and better explain the firm’s situation. This will result in a lower funding cost for complex securities.

LO: 5 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

15.5

Management of Southern Parts Company has decided to sell 10-year bonds to finance expansion into the Pacific Northwest. The loan rate on these bonds is 8 percent and the 3-month Treasury bill rate is 2.1 percent. The firm’s credit rating is B, and the yield on 10-year Treasury bonds is 2.5 percent higher than that on 3month Treasury bills. How much of a premium over the 10-year Treasury bond are these Southern Parts bonds selling for?

Solution: kl = PR + DRP + MAT 8.0% = 2.1% + DRP + 2.5% DRP = 3.4%

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LO: 7 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

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CHAPTER 14

Working Capital Management Before You Go On Questions and Answers Section 14.1 1.

How do you calculate net working capital, and why is it important? Net working capital is calculated as the difference between the current assets and current liabilities. It is important for a firm to keep a positive net working capital balance, as these funds are used to cover the day-to-day expenses and short-term liabilities as they come due.

What are some of the trade-offs required in the management of working capital accounts? When managing working capital accounts, a financial manager attempts to balance tradeoffs including delaying paying accounts payable as long as possible without suffering any penalties, maintaining minimal finished goods inventories without losing sales, and collecting cash payments on accounts receivable as fast as possible to close the loop.

Section 14.2 1.

What is the operating cycle, and how is it related to the cash conversion cycle? The operating cycle starts with the receipt of raw materials and ends with the collection of cash from customers for the sale of finished goods. The operating cycle can be described in terms of two components: days’ sales in inventory and days’ sales outstanding. The cash conversion cycle is the length of time between the actual cash outflow for materials and the actual cash inflow from sales. To calculate it, we need all of the information used to calculate the operating cycle plus one additional measure: days’ payables outstanding.

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Section 14.3 1.

What are the two general current asset management strategies discussed in this section, and how do they differ? Typically, the two main current asset investment strategies are flexible and restrictive strategies. The flexible strategy prompts management to keep large balances of cash, marketable securities, and inventory. This strategy is perceived to be a relatively low-risk and low-return course of action for management to follow. The restrictive strategy, on the other hand, prompts management to keep the usage of current assets to a minimum and is perceived to be high risk and high return.

What are the types of costs associated with each of these strategies? The flexible strategy is associated with a high level of carrying costs because of a firm’s high levels of inventory and providing liberal credit for customers. The restrictive strategy is associated with shortage costs, which can be either financial or operating in nature.

Section 14.4 1.

What does “4/15, net 30” mean? If a company declares a “4/15, net 30” means of sale, it signifies that it will grant the customer a 4 percent discount if the customer pays the full amount within 15 days of the invoice date. Otherwise, the customer has 30 days from the date of the delivery to pay the full amount.

What is an aging schedule, and what is its purpose? The aging schedule for a firm lists the accounts receivable broken down by the number of days until they are due or past due. Firms use aging schedules to keep track of their accounts receivables and to assess how effective they are collecting on these accounts.

Section 14.5 1.

What is the economic order quantity model?

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The economic order quantity model is an inventory management tool that mathematically determines the minimum total inventory cost, taking into account inventory reorder costs and inventory carrying costs. The main objective of the model is to find the trade-off between the two costs.

Why can cash investments in inventory be costly? Investments in inventory is considered costly, because inventory must be stored, which results in rental and maintenance costs. Furthermore, inventory on hand is subject to loss and theft, and faces the possibility of becoming obsolete. Finally, investment in inventory provides no return unlike an investment in financial or real assets would.

Section 14.6 1.

What is float? The collection time, which is the time between when a customer makes a payment and the time the cash becomes available is to the firm, is also referred to as float.

Explain how lockboxes are used. Lockboxes are post office boxes set up by the firm for its customers to deliver their payments to these boxes instead of the firm’s business address. The post office then collects these payments and delivers them to the bank. The main purpose of lockboxes is to minimize collection time for firms through cutting down on postal time and through processing the payments directly at the bank.

Section 14.7 1.

List and briefly describe the three main strategies a firm may use to finance its working capital and fixed assets. The three main strategies for financing working capital and fixed assets are (1) maturity matching strategy, in which the maturity of the liabilities is matched with that of assets; (2) long-term funding strategy, which relies more heavily on long-term financing to finance fixed assets, permanent working capital, and seasonal working capital; and (3) short-term financing strategy, which relies primarily on short-term financing including

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accounts payable, short-term bank loans, lines of credit, and commercial paper to finance all seasonal working capital and a portion of the permanent working capital and fixed assets.

What are the advantages and disadvantages of short-term financing? Short-term financing offers companies greater flexibility and usually a lower cost of capital. On the other hand, short-term financing often comes with some illiquidity problems as well as uncertainty due to increased exposure to interest rate fluctuations.

Give some examples of sources of short-term financing. Examples of short-term financing include accounts payable, short-term bank loans, informal lines of credit, formal lines of credit, or commercial paper. The two main current asset investment strategies are (1) flexible strategy, which encourages management to keep large balances of current assets, and (2) restrictive strategy, which keeps the usage of current assets to a minimum.

Self-Study Problems 14.1

You are provided the following working capital information for the Blue Ridge Company for the most recent fiscal year: Account

Beginning Balance

Ending Balance

Inventory

$2,600

$2,890

Accounts receivable

$3,222

$2,800

Accounts payable

$2,500

$2,670

Net sales

$24,589

Cost of goods sold

$19,630

What are the firm’s operating and cash conversion cycles? Solution:

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We calculate the operating and cash conversion cycles for Blue Ridge as follows: Inventory = $2,890 Accounts receivable = $2,800 Accounts payable = $2,670 Net sales = $24,589 Cost of goods sold = $19,630

DSI =

365 days 365 days = = 53.7 days COGS $19,630 Inventory $2,890

DSO =

365 days 365 days = = 41.6 days Credit sales $24,589 Accounts receivable $2,890

DPO =

365 days 365 days = = 49.6 days COGS $19,630 Accounts payable $2,670

Field Code Changed Field Code Changed Field Code Changed Field Code Changed

Operating cycle = DSI + DSO

Field Code Changed Field Code Changed

= 53.7 days + 41.6 days

Field Code Changed

= 95.3 days

Field Code Changed

Cash conversion cycle = DSI + DSO – DPO

Field Code Changed

= 53.7 days + 41.6 days – 49.6 days = 45.7 days

14.2

Merrifield Cosmetics management calculates that the firm’s operating cycle for last year was 76 days. The company had $230,000 in its accounts receivable account and had sales of $1.92 million. Approximately how many days does it take from the time the raw materials are received at Merrifield until the finished products they are used to produce are sold?

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DSO =

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Field Code Changed

365 days 365 days = = 43.7 days Credit sales $1,920,000 Accounts receivables $230,000

Field Code Changed Field Code Changed

Operating cycle = DSI + DS 76 days = DSI + 43.7 days DSI = 32.3 days Merrifield Cosmetics takes 32.3 days to turn its inventory into sales.

14.3

Below is a partial aging of accounts receivable for Bitar Roofing Services. Fill in the rest of the information and determine Bitar’s days’ sales outstanding. How does it compare to the industry average of 40 days? Age of Accounts (in days)

Value of Account ($)

0-10

$211,000

11-30

120,360

31-45

103,220

46-60

72,800

Over 60

23,740

Total

$531,120

% of Total Account

Solution: The missing information for Bitar Roofing and its days’ sales outstanding are as follows: Bitar Roofing Age of Accounts (in days)

Value of Account ($)

% of Total Account

0-10

$211,000

39.7%

11-30

120,360

22.7

31-45

103,220

19.4

46-60

72,800

13.7

Over 60

23,740

4.5

Total

$531,120

100%

Effective DSO = (0.397 × 10 days) + (0.227 × 30 days) + (0.194 × 45 days) + (0.137 × 60 days) + (0.045 × 365 days)

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= 3.97 days + 6.81 days + 8.73 days + 8.22 days + 16.43 days = 44.2 days

Bitar takes about 4 days longer than the industry average of 40 to collect on its receivables. The firm should focus collection efforts on all credit sales that take 60 days or more to collect.

14.4

By obtaining a lockbox, Nizam’s Manufacturing was able to reduce its total cash collection time by two days. The firm has annual sales of $570,000 and can earn 4.75 percent annual interest. Assuming that the lockbox costs $50 per year, calculate the savings that can be attributed to the lockbox.

Solution: The savings that can be attributed to Nizam’s lockbox are: Annual sales = $570,000 Annual interest rate = 4.75% Annual cost of lockbox = $50 Collection time saved = 2 days

$570,000 = $1,561.64 365 Savings = ( $1,561.64  0.0475  2 ) − $50 = $98.36 Average daily sales =

Field Code Changed

The firm can save $98.36 each year by using the lockbox.

14.5

Rockville Corporation is going to borrow $250,000 from its bank at an APR of 8.5 percent. The bank requires its customers to maintain a 10 percent compensating balance. What is the effective interest rate on this bank loan?

Solution: The effective rate on Rockville Corporation’s loan is calculated as follows: Amount to be borrowed = $250,000 Stated annual interest rate = 8.5% Compensating balance = 10% Amount deposited as compensating balance = $250,000 × 0.10 = $25,000

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Effective borrowing amount equal to $250,000 − $25,000 = $225,000 Interest expense = $250,000 × 0.085 = $21,250 Effective interest rate =

Interest expense $21,250 = = 9.44% Effective borrowing amount $225,000

A compensating balance of 10 percent, or $25,000 on the loan, increases the effective interest rate to 9.44 percent.

Discussion Questions 14.1

What factors must a financial manager consider when making decisions about accounts receivable? When dealing with accounts receivable, important decisions for the financial manager include the amount of credit offered to various customers and the term of the credit. Financial managers should keep close track of both the aging schedule and the effective DSO. If either or both show consistent deterioration, it may be time to reconsider the firm’s credit policy or the characteristics of its customers. In addition, in some industries, sales vary by season. Managers must be aware of seasonal patterns and make the necessary adjustments before drawing any conclusions about firm’s receivables.

LO: 4 Level: Basic Bloomcode: Comprehension AASCP: Analytic IMA: Decision Analysis AICPA: Industry/Sector Perspective

14.2

List some of the working capital management practices you would expect to see in a manufacturing company following just-in-time inventory practices. Manufacturing companies like Dell are likely to do an exceptional job of managing their inventory and collecting on their receivables. Dell employs a strategy similar to just-intime management where they maintain just sufficient inventory to meet the needs for a

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very short time. This saves the firm a huge investment in inventory. Thus their days’ sales in inventory (DSI) will be very low compared to other industries. Similar to Dell, firms will have a short collection period, and their operating cycle will be much lower than firms in other industries. If other computer manufacturing firms follow the Dell operating philosophy, they will extend their days’ payable outstanding (DPO) to the point that their cash conversion cycle is negative. In other words, instead of having to invest in its working capital, these firms will end up taking more time to pay their suppliers than the time taken to produce, sell, and collect on the receivables. In addition, firms like Dell have inventories that become obsolete very quickly, which is another reason for carrying minimum inventory. LO: 5 Level: Basic Bloomcode: Knowledge AASCP: Analytic IMA: Strategic Planning AICPA: Industry/Sector Perspective

14.3

What costs would a firm following a flexible current asset management strategy consider, and why? The strategy’s downsides can include the high carrying costs associated with owning a high level of inventory and providing liberal credit terms to customers. By investing in current assets, management foregoes the higher rate of return it could have earned by investing in long-term assets. Therefore, there is an opportunity cost involved when investing in current assets. Furthermore, large investments in some types of inventory can require significant storage, tax, and insurance costs, which can be expensive and cause obsolescence.

LO: 3 Level: Intermediate Bloomcode: Comprehension AASCP: Analytic IMA: Strategic Planning

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14.4

How are customers and suppliers affected by a firm’s working capital management decisions? Customers want firms to maintain large, finished goods inventories because when they go to make a purchase, the item they want will likely be in stock. In general, large inventory helps stimulate sales and increase customer satisfaction, but that can be a costly item on a firm’s balance sheet. Management’s decisions on the firm’s receivables policy is driven by the industry type. Companies selling perishable products, such as food companies, might ask for payment in full in less than 10 days. On the other hand, if the firm is selling durable goods, the terms of credit are likely to be more generous. The terms of sale are also affected by the creditworthiness of the customer. If the firm is confident that it will be paid, it is far more likely to extend credit than if there was some doubt about payment. If the customer is a particularly large firm or if there is a likelihood of repeat business, then extending credit may be part of the marketing effect to secure the order. Thus, when the financial manager makes a decision to increase working capital, good things are likely to happen to the firm—sales should increase, relationships with vendors and suppliers should improve, and work or manufacturing stoppages should be less likely.

LO: 4 Level: Intermediate Bloomcode: Comprehension AASCP: Analytic IMA: Strategic Planning AICPA: Industry/Sector Perspective

14.5

A beverage bottling company in Vermont has days’ sales outstanding of 23.7 days. Is this good? Explain. In general, a lower DSO reflects the fact that the firm is managing its receivables very well. However, it is not possible to decide whether a DSO of 23.7 days is good or bad unless you have a basis for comparison. That basis of comparison could be a peer group, historical data for the firm itself, or targets set by the management.

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LO: 2 Level: Basic Bloomcode: Analysis AASCP: Analytic IMA: Strategic Planning AICPA: Industry/Sector Perspective

14.6

How do the following circumstances affect the cash conversion cycle: (a) favorable credit terms allow the firm to pay its accounts payable slower, (b) inventory turnover increases, and (c) accounts receivable turnover decreases? (a)

Favorable credit terms from suppliers allow the firm to use the suppliers’ funds to finance their working capital. It also reduces the firm’s cash conversion cycle.

(b)

An increase in the inventory turnover results into decrease in DSI, which reduces both the firm’s operating cycle and the cash conversion cycle.

(c)

As the accounts receivable turnover or Day Sales Outstanding (DSO) decreases, the firm improves its receivables management and reduces its operating cycle and hence, its cash conversion cycle.

LO: 2 Level: Basic Bloomcode: Comprehension AASCP: Analytic IMA: Strategic Planning AICPA: Industry/Sector Perspective

14.7

What are some industries in which the use of lockboxes would especially benefit companies? Explain. Lockboxes are a useful tool to speed up collection of receivables when the customer base is dispersed across a large geographical area. Normally, this would mean customer payments would have to be mailed in, consolidated, and then deposited at the firm’s bank. The alternative of setting up a lockbox system allows the firm to redirect customer payments to regional locations for quicker consolidation and cashing of payments. This is

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typical in the retail industry where each store of a chain is located in a different city or state. LO: 6 Level: Basic Bloomcode: Comprehension AASCP: Analytic IMA: Strategic Planning AICPA: Industry/Sector Perspective

14.8

Suppose you are a financial manager at a big firm and you expect interest rates to decline in the near future. What current asset investment strategy would you recommend that the company pursue? At a big firm, management would have access to the commercial paper market, which can provide cheaper funding than short-term bank financing. To borrow in the commercial paper market, a firm has to be financially strong. Thus, all or a portion of the working capital needs can be funded through short-term funds that can be rolled over as long as interest rates are declining.

LO: 7 Level: Basic Bloomcode: Analysis AASCP: Analytic IMA: Decision Analysis AICPA: Industry/Sector Perspective

14.9

Why is the commercial paper market available only to the most creditworthy companies? Commercial paper is available only to the companies that are financially strong for two reasons. First, there is no secondary market for investors to liquidate prior to maturity. Consequently, investors must hold it to maturity and have the confidence that the issuer would pay them back at that time. Second, this type of debt is not secured by any real

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assets of the issuing firm. Thus, the companies that are the most creditworthy are able to raise funds in this market at costs that are lower than bank loans. LO: 7 Level: Basic Bloomcode: Comprehension AASCP: Analytic IMA: Decision Analysis AICPA: Industry/Sector Perspective

14.10 Explain what a negative cash conversion cycle means. Recognizing the cash conversion cycle is a function of a firm’s receivables turnover, inventory turnover, and payables turnover. Firms that are highly efficient in managing their inventory and receivables will have a short operating cycle and do not need a large investment in working capital. A large payables turnover implies that the firm is making use of their suppliers’ funds to fund their working capital needs. The difference between the operating cycle and the payables turnover is the cash conversion cycle. A negative cash conversion cycle means that the time taken by the firm to meet its payables exceeds its operating cycle. In other words, the amount of time to manage their inventory and the time taken to collect its receivables is less than the time taken to pay its suppliers. LO: 2 Level: Basic Bloomcode: Comprehension AASCP: Analytic IMA: Strategic Planning AICPA: Industry/Sector Perspective

Questions and Problems BASIC 14.1 Cash conversion cycle: Wolfgang’s Masonry management estimates that it takes the company 27 days on average to pay its suppliers. Management also knows that the company has days’ sales in inventory of 64 days and days’ sales outstanding of 32 days. How does Copyright © 2022 John Wiley & Sons, Inc.

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Wolfgang’s cash conversion cycle compare with the industry average of 75 days? Solution: DPO = 27 days DSI = 64 days DSO = 32 days Industry average for cash conversion cycle = 75 days. Wolfgang’s cash conversion cycle:

Cash conversion cycle = DSO + DSI − DPO = 32 days + 64 days − 27 days = 69 days Since the firm’s Cash conversion cycle is less than the industry average of 75 days, the firm is more efficient than other firms in the industry in managing its working capital. LO: 2 Bloomcode: Analysis AASCP: Analytic IMA: Strategic Planning AICPA: Industry/Sector Perspective

14.2 Cash conversion cycle: Northern Manufacturing Company management found that during the last year it took an average of 47 days to pay its suppliers, whereas it took 63 days to collect its receivables. The company’s days’ sales in inventory was 49 days. What was Northern’s cash conversion cycle? Solution: DPO = 47 days DSI = 49 days DSO = 63 days

Northern's Cash conversion cycle = DSO + DSI − DPO = 63 days + 49 days − 47 days = 65 days LO: 2

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14.3

Cash conversion cycle: Devon Automotive management estimates that it takes the company 62 days to collect cash from customers on finished goods from the day it receives raw materials, and it takes 65 days to pay its suppliers. What is the company’s cash conversion cycle? Interpret your answer.

Solution: DPO = 65 days Operating cycle = 62 days Devon’s cash conversion cycle = Operating cycle – DPO = 62 days – 65 days = –3 days This firm has a negative cash conversion cycle. The amount of time to manage its inventory and the time taken to collect its receivables is less than the time taken to pay its suppliers. LO: 2 Bloomcode: Application AASCP: Analytic IMA: Strategic Planning AICPA: Industry/Sector Perspective

14.4

Operating cycle: Lilly’s Bakery distributes its products to more than 75 restaurants and delis. The company’s average collection period is 27 days, and it keeps its inventory for an average of four days. What is Lilly’s operating cycle?

Solution: DSI = 4 days DSO = 27 days

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Lilly's Operating cycle = DSO + DSI = 27 days + 4 days = 31 days LO: 2 Bloomcode: Application AASCP: Analytic IMA: Strategic Planning AICPA: Industry/Sector Perspective

14.5

Operating cycle: NetSpeed Technologies is a telecom component manufacturer. The firm typically has a collection period of 44 days and days’ sales in inventory of 29 days. What is the operating cycle for NetSpeed?

Solution: DSI = 29 days DSO = 44 days NetSpeed’s operating cycle = DSO + DSI = 44 days + 29 days = 73 days LO: 2 Bloomcode: Application AASCP: Analytic IMA: Strategic Planning AICPA: Industry/Sector Perspective

14.6

Operating Cycle: Devlin Construction Inc., reported the following balance sheet information for the last fiscal year. Devlin also reported net sales of $980,770 and days sales in inventory of 48.90 days. Devlin Construction Inc. Assets Cash and marketable securities

$15,032

Accounts receivable

$140,500

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Inventories

$289,809

Other current assets

$12,647

Total current assets

$457,988

Calculate the firm’s operating cycle. Solution: Operating cycle = DSI + DSO DSO = 365 days / ($980,770/$140,500) = 52.28 days. Operating cycle = 48.90 + 52.28 = 101.18 days. LO: 2 Bloomcode: Application AASCP: Analytic IMA: Strategic Planning AICPA: Industry/Sector Perspective

14.7

Current asset management strategy: Describe the risks that are associated with a restrictive current asset management strategy.

Solution: The risk of a restrictive current asset management strategy comes from an exposure to shortage costs, which can be either financial or operating costs. Financial costs are associated with a sudden and unforeseen loss of liquidity that makes it difficult for a firm to repay its current liabilities. In this condition, firms may be forced to rely on costly external emergency borrowing, or if such funds can’t be secured, firms may have to default on their loan obligations. Operating shortage costs result from lost production or sales that occur if a firm does not have sufficient raw material or finished goods. Operating shortage costs may also occur if a firm’s credit policies are too restrictive and deter a significant number of sales to potential customers. LO: 3 Bloomcode: Comprehension AASCP: Analytic IMA: Strategic Planning

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AICPA: Industry/Sector Perspective

14.8

Cost of trade credit: Sybex Corp. sells its goods with terms of 2/10 EOM, net 30. What is the implicit cost of the trade credit?

Solution: Credit terms = 2/10 EOM, net 30   Discount Effective annual rate of accounts receivable =  1 +  Discounted price  

365/days credit

−1

Field Code Changed

= (1 + 2/98)365/20 – 1 = (1.0204)18.25 – 1 = 1.4456 – 1 = 0.4456, or 44.56 percent LO: 4 Bloomcode: Application AASCP: Analytic IMA: Strategic Planning AICPA: Industry/Sector Perspective

14.9

Cost of trade credit: Mill Street Corporation sells its goods with terms of 4/10 EOM, net 60. What is the implicit cost of the trade credit?

Solution:   Discount Effective annual rate of accounts receivable =  1 +   Discounted price 

365/days credit

−1

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14.10 Lockbox: Rosenthal Design has daily sales of $59,000. The financial management team has determined that a lockbox would reduce the collection time by 1.6 days. Assuming the company can earn 5.2 percent interest per year, what are the savings from the lockbox? Solution: All sales are assumed to be credit sales. Annual interest rate = 5.2% Collection time saved = 1.6 days

Average daily sales = $59,000 Savings = $59,000  0.052 1.6 = $4,908.80 The firm can save $4,908.80 with the use of lockbox. LO: 6 Bloomcode: Application AASCP: Analytic IMA: Strategic Planning AICPA: Industry/Sector Perspective 14.11 Lockbox: Pacific Traders has annual sales of $1,895,000. The firm’s financial manager has determined that using a lockbox will reduce collection time by 2.3 days. If the firm’s opportunity cost on savings is 5.25 percent, what are the savings from using the lockbox? Solution: Annual sales = $1,895,000 Annual interest rate = 5.25% Collection time saved = 2.3 days Field Code Changed

$1,895,000 = $5,191.78 365 Savings = $5,191.78  0.0525  2.3 days = $626.91 Average daily sales =

The firm can save $626.91 with the use of lockbox. LO: 6

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Bloomcode: Application AASCP: Analytic IMA: Strategic Planning AICPA: Industry/Sector Perspective

14.12 Effective interest rate: The Kellogg Bank requires borrowers to keep an 8 percent compensating balance. Gorman Jewels borrows $340,000 at a 7 percent stated APR. What is the effective interest rate on the loan? Solution: Amount borrowed = $340,000 Stated annual interest rate = 7% Compensating balance = 8% Amount deposited as compensating balance = $340,000 × 0.08 = $27,200 Effective borrowing amount = $340,000 − $27,200 = $312,800 Interest expense = $340,000 × 0.07 = $23,800 Effective interest rate =

Field Code Changed

Interest expense $23,800 = = 7.61% Effective borrowing amount $312,800

By setting aside a compensating balance of 8 percent or $27,200 on the loan, the firm increases its interest rate effectively to 7.61 percent. LO: 7 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

14.13 Effective interest rate: Morgan Contractors borrowed $1.75 million at an APR of 10.2 percent. The loan called for a compensating balance of 12 percent. What is the effective interest rate on the loan?

Solution: Amount to be borrowed = $1,750,000

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Stated annual interest rate = 10.2% Compensating balance = 12% Amount deposited as compensating balance = $1,750,000 × 0.12 = $210,000 Effective borrowing amount equal to $1,750,000 − $210,000 = $1,540,000 Interest expense = $1,750,000 × 0.102 = $178,500 Effective interest rate =

Field Code Changed

Interest expense $178,500 = = 11.6% Effective borrowing amount $1,540,000

By setting aside a compensating balance of 12 percent or $210,000 on the loan, the firm increases its interest rate effectively to 11.6 percent. LO: 7 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

14.14 Factoring: Maltz Landscaping has an average collection period of 38 days for its accounts receivable. Currently, Maltz factors all of its receivables at a 2 percent discount. What is the effective annual interest rate on the financing from the factor? Solution: The terms of this factor indicate that for every dollar of receivables sold to the factor today, the firm receives 98-cents today and 38-days later the factor receives the dollar in receivables. The cost to Maltz in percentage terms is 2.04 percent over a 38 day period. There are 9.61 periods (m) during a 365 day year. 365

  days credit Discount EAR on financing from the factor =  1 + −1   Discounted price  Effective annual rate (EAR) on financing from the factor = (1 + 2/98)365/38 – 1 = (1 + 0.0204)9.605 – 1 = 0.2142 or 21.42 percent. LO: 7 Bloomcode: Application AASCP: Analytic Copyright © 2022 John Wiley & Sons, Inc.

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IMA: Corporate Finance AICPA: Industry/Sector Perspective

14.15 Formal line of credit: Winegartner Cosmetics management is setting up a line of credit at the company’s bank for $5 million for up to two years. The interest rate is 5.875 percent, and the loan agreement calls for an annual fee of 40 basis points on any unused balance for the year. If the firm borrows $2 million on the day the loan agreement is signed, what is the effective rate for the line of credit? Solution: Line of credit limit = $5,000,000 Loan rate = 5.875% Annual fee on used balance = 0.4% Amount borrowed = $2,000,000 Unused balance = $3,000,000 Annual fee = $3,000,000 × 0.004 = $12,000 Interest expense = $2,000,000 × 0.05875 = $117,500  Interest expense + Annual fee  Effective interest rate =   Borrowed amount   $117,500 + $12,000 = = 0.0648 = 6.48% $2,000,000

Field Code Changed Field Code Changed

The effective borrowing rate for the firm is 6.48% with the annual fee of 40 basis points. LO: 7 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

INTERMEDIATE 14.16 Cash conversion cycle: Your boss asks you to compute your company’s cash conversion cycle. Looking at the financial statements, you see that the average inventory for the year

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was $26,300, accounts receivable averaged $17,900, and accounts payable averaged $15,100. You also see that the company had sales of $154,000 and that cost of goods sold was $122,000. Calculate and interpret your firm’s cash conversion cycle. Solution: All sales are assumed to be credit sales. Accounts receivable = $17,900 Accounts payable = $15,100 Sales = $154,000 Average inventory = $26,300 Cost of goods sold = $122,000

Accounts receivable $17,900 = = 42.4 days Credit sales $154,000 365 365

Field Code Changed

Inventory $26,300 = = 78.7 days COGS $122,000 365 365

Field Code Changed

DSO =

DSI =

DPO =

Accounts payable $15,100 = = 45.2 days COGS $122,000 365 365

Cash Conversion Cycle = DSI + DSO − DPO

Field Code Changed

= 42.4 days + 78.7 days − 45.2 days = 75.9 days The firm takes nearly 76 days from the time it pays for its raw materials to the time it realizes cash from its credit sales. By taking a couple of more days to pay it suppliers relative to the time it takes to collect on its receivables, it reduces the cash conversion cycle. LO: 2 Bloomcode: Application AASCP: Analytic IMA: Strategic Planning AICPA: Industry/Sector Perspective

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14.17 Cash conversion cycle: Blackwell Automotive, Inc., reported the following financial information for the last fiscal year. Blackwell Automotive, Inc. Assets

Liabilities and Equity

Cash and marketable securities

$23,015

Accounts payable and

$163,257

accruals Accounts receivable

$141,258

Notes payable

$21,115

Inventories

$212,444

Total current liabilities

$184,372

Other current assets

$11,223

Sales and Costs

Total current assets

$387,940

Net sales

$912,332

Cost of goods sold

$547,400

Calculate the firm’s cash conversion cycle and operating cycle.

Solution: All sales are assumed to be credit sales. Accounts receivable = $141,258 Accounts payable = $163,257 Net sales = $912,332 Inventory = $212,444 Cost of goods sold = $547,400

Accounts receivable $141,258 = = 56.5 days Credit sales $912,332 365 365

Field Code Changed

Inventory $212, 444 = = 141.7 days COGS $547,400 365 365

Field Code Changed

Accounts payable $163,257 = = 108.9 days COGS $547,400 365 365

Field Code Changed

DSO =

DSI =

DPO =

Operating cycle = DSO + DSI = 56.5 days + 141.7 days = 198.2 days

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Cash conversion cycle = DSO + DSI – DPO = 56.5 days + 141.7 days – 108.9 days = 89.3 days LO: 2 Bloomcode: Application AASCP: Analytic IMA: Strategic Planning AICPA: Industry/Sector Perspective

14.18 Cash conversion cycle: Elsee, Inc., has net sales of $13 million, and 75 percent of these are credit sales. Its cost of goods sold is 65 percent of annual net sales. The firm’s cash conversion cycle is 41.3 days. The inventory balance at the firm is $1,817,344, while its accounts payable balance is $2,171,690. What is the firm’s accounts receivable balance? Solution: Net sales = $13,000,000 Credit sales = (0.75 × Sales) = (0.75 × $13,000,000) = $9,750,000 Accounts payable balance = $2,171,690 Inventory balance = $1,817,344 Cost of goods sold = (0.65 × Sales) = (0.65 × $13,000,000) = $8,450,000 Cash conversion cycle = 41.3 days

Accounts payable $2,171,690 = = 93.8 days COGS $8,450,000 365 365

Field Code Changed

Inventory $1,817,344 = = 78.5 days COGS $8,450,000 365 365

Field Code Changed

DPO =

DSI =

Cash conversion cycle = DSO + DSI – DPO 41.3 days = DSO + 78.5 days – 93.8 days DSO = 56.6 days Using the DSO equation, we can solve for the accounts receivable.

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Solutions Manual

Field Code Changed

Accounts receivable Acct. Rec. = = 56.6 days Credit sales $9,750,000 365 365 Accounts receivable = 56.6  $26,712.33 = $1,511,917.81

DSO =

Field Code Changed Field Code Changed

The firm has accounts receivable of $1,511,918. LO: 2 Bloomcode: Application AASCP: Analytic IMA: Strategic Planning AICPA: Industry/Sector Perspective

14.19 Cash conversion cycle: Joanna Handicrafts, Inc., has net sales of $4.23 million with 50 percent being credit sales. Its cost of goods sold is $2.54 million. The firm’s cash conversion cycle is 47.9 days and its operating cycle is 86.3 days. What is the firm’s accounts payable balance? Solution: Net sales = $4,230,000 Credit sales = (0.5 × $4,230,000) = $2,115,000 Cash conversion cycle = 47.9 days Operating cycle = 86.3 days Cost of goods sold = $2,540,000 Cash conversion cycle = (DSO + DSI) – DPO 47.9 days = 86.3 days – DPO DPO = 38.4 days Field Code Changed

Accounts payable Accounts payable = = 38.4 days COGS $2,540,000 365 365 Accounts payable = 38.4  $6,958.90 = $267,221.92

DPO =

The firm has accounts payable of $267,222. LO: 2 Bloomcode: Application AASCP: Analytic

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IMA: Strategic Planning AICPA: Industry/Sector Perspective 14.20 Operating cycle: Aviva Technology’s operating cycle is 81 days. Its inventory was $134,000 at the end of last year, and the company had cost of goods sold of $1.1 million. How long does it take Aviva to collect its receivables on average? Solution: Operating cycle = 81 days Inventory = $134,000 Cost of goods sold = $1,100,000

DSI =

Field Code Changed

Inventory $134,000 = = 44.5 days COGS $1,100,000 365 365

Operating cycle = DSO + DSI 81 days = DSO + 44.5 days DSO = 36.5 days It takes Aviva 36.5 days to collect its receivables. LO: 2 Bloomcode: Application AASCP: Analytic IMA: Strategic Planning AICPA: Industry/Sector Perspective

14.21 Operating cycle: Premier Corp. has net sales of $812,344, and cost of goods sold equal to 70 percent of net sales. Assume all sales are credit sales. If the firm’s accounts receivable total $113,902 and its operating cycle is 81.6 days, how much inventory does the firm have? Solution: All sales are assumed to be credit sales. Credit sales = $812,344 Operating cycle = 81.6 days

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Solutions Manual

Cost of goods sold = (0.7 × $812,344) = $568,641 Accounts receivable = $113,902

DSO =

Field Code Changed

Accounts receivable $113,902 = = 51.2 days Credit sales $812,344 365 365

Operating cycle = DSO + DSI 81.6 days = 51.2 days + DSI DSI = 30.4 days

DSI =

Field Code Changed

Inventory Inventory = = 30.4 days COGS $568,641 365 365 Inventory = $47,360.78

The firm has inventory of $47,361. LO: 2 Bloomcode: Application AASCP: Analytic IMA: Strategic Planning AICPA: Industry/Sector Perspective

14.22 Operating cycle: Telecraft Enterprises carries 45 days of inventory in its stores. Last year Telecraft reported net sales of $1,400,000, and the company had receivables of $325,000 at the end of the year. What is the operating cycle at Telecraft? Solution: All sales are assumed to be credit sales

DSO =

Field Code Changed

Accounts receivable $325,000 = = 84.7 days Credit sales $1,400,000 365 365

DSI = 45 days Operating cycle = DSO + DSI = 84.7 days + 45 days = 129.7 days LO: 2

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Bloomcode: Application AASCP: Analytic IMA: Strategic Planning AICPA: Industry/Sector Perspective

14.23 Operating Cycle: Given the data for Telecraft Enterprises in problem 14.22, re-estimate the firm’s operating cycle if days’ sales outstanding decreased to 75 days. For the same level of net sales, what is the implied dollar value of receivables with 75 days’ sales outstanding? Solution: Operating cycle = DSO + DSI = 75 days + 45 days = 120 days If the DSO is 75 days: DSO = 365 days / (credit sales / accounts receivable) 75 days = 365 days / ($1,400,000/accounts receivable) 75 days × $1,400,000 = 365 days × accounts receivable Accounts receivables = $1,400,000 × 75 days / 365 days Accounts receivables = $287,671.23 The value of receivables with 75 days’ sales outstanding is $287,671. LO: 2 Bloomcode: Application AASCP: Analytic IMA: Strategic Planning AICPA: Industry/Sector Perspective

14.24

Sliver Computing Inc., reported the following balance sheet information for the last fiscal year. Sliver Computing also reported cost of goods sold of $291,240 for the same period. Internal auditors state that the firm’s cash conversion cycle is 21.53 days. Sliver Computing Inc.

Assets

Liabilities

Cash and marketable securities

$94,032

Accounts payable

$68,561

Accounts receivable

$160,684

Notes Payable

$136,320

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Inventories

$19,809

Other current assets

Solutions Manual

Total current liabilities

$204,881

$ 647

Total current assets

$275,172

Calculate the firm’s day’s sales outstanding. Solution:

DSI =

Field Code Changed

Inventory $19,809 = = 24.83 days COGS $291,240 365 365

DPO =

Field Code Changed

Accounts payable $68,561 = = 85.92 days COGS $291,240 365 365

Cash conversion cycle = DSI + DSO – DPO. DSO = Cash conversion cycle – DSI + DP0 DSO = 21.53 – 24.83 + 85.92 = 82.62 days.

14.25 Economic order quantity: Longhorn Traders is one of the largest RV dealers in Austin, Texas, and sells about 2,800 recreational vehicles a year. The cost of placing an order with Longhorn’s supplier is $800, and the inventory carrying costs are $150 for each RV. Management likes to maintain safety stock of 12 RVs. Most of its sales are made in either the spring or the fall. How many orders should the firm place this year? Solution: Annual sales = 2,800 units Cost of placing an order = $800 Inventory carrying cost per RV = $150 Safety stock = 12 RVs EOQ =

2  Reorder costs  Sales per period Carrying costs

EOQ =

2  $800  $2,800 = 172.8 $150

Economic order quantity = 173 RVs

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Solutions Manual

Number of orders the firm needs to place = 2,800 / 173 = 16 LO: 5 Bloomcode: Application AASCP: Analytic IMA: Strategic Planning AICPA: Industry/Sector Perspective

14.26 Effective interest rate: The Clarkson Designer Company management wants to borrow $750,000.The bank will provide the loan at an APR of 6.875. Since the loan calls for a compensating balance, the effective interest rate is actually 9.25 percent. What is the compensating balance on this loan? Solution: Amount to be borrowed = $750,000 Stated annual interest rate = 6.875% Compensating balance = ? Effective interest rate = 9.25% Interest expense = $750,000 × 0.06875 = $51,562.50 Field Code Changed

Interest expense Effective borrowing amount $51,562.50 9.25% = Effective borrowing amount

Effective interest rate =

Effective borrowing amount =

Field Code Changed

$51,562.50 = $557, 432.43 0.0925

Effective borrowing amount = $750,000 − compensating balance deposit = $557,432.43 Compensating balance deposit = $750,000 - $557,432.43 = $192,567.57 Compensating balance rate = $192,567.57 / $750,000 = 25.7% By setting aside a compensating balance of 25.7% on the loan, the firm increases its interest rate effectively from 6.875 to 9.25 percent. LO: 7 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance Copyright © 2022 John Wiley & Sons, Inc.

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AICPA: Industry/Sector Perspective

14.27 Effective interest rate: The Colonial Window Treatments Company is borrowing $1.5 million. The loan requires a 10 percent compensating balance, and the effective interest rate on the loan is 9.75 percent. What is the stated APR on this loan? Solution: Amount to be borrowed = $1,500,000 Stated annual interest rate = ? Compensating balance = 10% Effective interest rate = 9.75% Compensating balance = (0.10 × $1,500,000) = $150,000 Effective borrowing amount = $1,500,000 − $150,000 = $1,350,000 Field Code Changed

Interest expense Effective borrowing amount Interest expense 9.75% = $1,350,000

Effective interest rate =

Interest expense = 0.0975 × $1,350,000 = $131,625 Stated interest rate = $131,625/ $1,500,000 = 8.775% LO: 7 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

14.28 Formal line of credit: Gruppa, Inc., has just set up a formal line of credit of $10 million with First Community Commercial Bank. The line of credit is good for up to five years. The bank will charge Gruppa an interest rate of 6.25 percent on any amount borrowed, and the firm will pay an annual fee of 60 basis points on the unused balance. The firm borrowed $7.5 million on the first day the credit line became available. What is the effective interest rate on this line of credit? Solution:

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Line of credit limit = $10,000,000 Interest rate = 6.25% Annual fee on used balance = 0.6% Amount borrowed = $7,500,000 Unused balance = $10,000,000 – $7,500,000 = $2,500,000 Annual fee = $2,500,000 × 0.006 = $15,000 Interest expense = $7,500,000 × 0.0625 = $468,750 Interest expense + Annual fee Effective borrowing amount ($468,750 + $15,000) = = 0.0645 = 6.45% $7,500,000

Effective interest rate =

Field Code Changed

The effective interest rate on the line of credit is 6.45% LO: 7 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

14.29 Formal line of credit: Lansdowne Electronics has a formal line of credit of $1 million for up to three years with HND Bank. The interest rate on the loan is 5.3 percent, and under the agreement, Lansdowne has to pay an annual fee of 50 basis points on the unused amount. Suppose the firm borrows $675,000 the first day of the agreement. What is the fee the company must pay on the unused balance? What is the effective interest rate? Solution: Line of credit limit = $1,000,000 Interest rate = 5.3% Annual fee on used balance = 0.5% Amount borrowed = $675,000 Unused balance = $1,000,000 - $675,000 = $325,000 Annual fee = $325,000 × 0.005 = $1,625

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Solutions Manual

Interest expense = $675,000 × 0.053 = $35,775 Interest expense + Annual fee Effective borrowing amount ($35,775 + $1,625) = = 0.0554 = 5.54% $675,000

Effective interest rate =

Field Code Changed

The effective interest rate is 5.54% LO: 7 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

14.30 Lockbox: Jennifer Electrical is evaluating whether a lockbox it is currently using is worth keeping. Management estimates that the lockbox reduces the mail float by 1.8 days and the processing by half a day. The remittances average $50,000 a day for Jennifer Electrical, with the average check being for $500. The bank charges $0.34 per processed check. Assume that there are 270 business days in a year and that the firm’s opportunity cost for these funds is 6 percent. What will the firm’s savings be from using the lockbox? Solution: Average daily sales = $50,000 No. of business days = 270 Opportunity cost of funds = 6% Average check amount = $500 No. of checks processed per day = $50,000 / $500 = 100 Collection time saved = 1.8 days Processing time saved = 0.5 days Per check processing fee = $0.34 The annual cost of a lockbox = 100 checks  $0.34 per check  270 days = $9,180 Savings from mail float = 1.8 days  $50,000 = $90,000 Savings from processing float = 0.5 days  $50,000 = $25,000

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Solutions Manual

Total savings = (Savings from mail float + Savings from processing float) = $90,000 + $25,000 = $115,000 Savings from lockbox = $115,000 × 0.06= $6,900 Since the savings from the lockbox of $6,900 is less than the cost of the lockbox of $9,180, it is not worth keeping the lockbox for Jennifer Electricals. LO: 6 Bloomcode: Application AASCP: Analytic IMA: Strategic Planning AICPA: Industry/Sector Perspective

14.31 Lockbox: Hazel Corp. has just signed up for a lockbox. Management expects the lockbox to reduce the mail float by 2.1 days. Hazel Corp.’s remittances average $37,000 a day, and the average check is $125. The bank charges $0.37 per processed check. Assume that there are 270 business days in a year. What will the firm’s savings be from using the lockbox if the opportunity cost for these funds is 12 percent? Solution: Average daily sales = $37,000 No. of business days = 270 Average check amount = $125 No. of checks processed per day = $37,000 / $125 = 296 Collection time saved = 2.1 days Per check processing fee = $0.37 The annual cost of a lockbox = 296 checks  $0.37 per check  270 days = $29,570.40 Savings from mail float = 2.1 days  $37,000 = $77,700 Opportunity cost of funds = 12% Savings from lockbox = $77,700 × 0.12= $9,324 Since the savings from the lockbox of $9,324 is less than the cost of the lockbox of $29,570.40, it is not worth keeping the lockbox for Hazel Corp. LO: 6 Bloomcode: Application Copyright © 2022 John Wiley & Sons, Inc.

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AASCP: Analytic IMA: Strategic Planning AICPA: Industry/Sector Perspective

14.32 Aging schedule: Ginseng Company collects 50 percent of its receivables in 10 days or fewer, 31 percent in 11 to 30 days, 7 percent in 31 to 45 days, 7 percent in 46 to 60 days, and 5 percent in more than 60 days. The company has $1,213,000 in accounts receivable. Prepare an aging schedule for Ginseng Company.

Solution: Accounts receivables = $1,213,000 Age of Account (days)

Value of Account

% of Total Value

0-10

$ 606,500

50%

11-30

376,030

31-45

84,910

46-60

84,910

Over 60

60,650

Total

$1,213,000

100%

LO: 4 Bloomcode: Application AASCP: Analytic IMA: Strategic Planning AICPA: Industry/Sector Perspective

14.33 Aging schedule: A partial aging of accounts receivable for Lincoln Cleaning Services is given in the accompanying table. What percent of receivables are in the 45-day range? Determine the firm’s effective days’ sales outstanding. How does it compare with the industry average of 35 days? Age of Account (days)

Value of Account

$271,000

% of Total Value

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Solutions Manual

$145,220

45 60

$53,980

$31,245

Total

$589,218

100.0%

Solution: Accounts receivable = $589,218 Age of Account (days)

Value of Account

% of Total Value

$271,000

46.0%

145,220

24.6

87,773

14.9

53,980

9.2

31,245

5.3

Total

$589,218

100.0%

Effective DSO = Age of the account category  Percent of AR for the account category = [(10 × 0.46) + (30 × 0.246) + (45 × 0.149) + (60 × 0.092) + (75 × 0.053)] = 4.6 + 7.4 + 6.7 + 5.5 + 4 = 28.2 days The firm is more efficient than other firms in the industry as its effective DSO is lower. LO: 4 Bloomcode: Application AASCP: Analytic IMA: Strategic Planning AICPA: Industry/Sector Perspective

14.34 Aging schedule: Keswick Fencing Company collects 45 percent of its receivables in 10 days or fewer, 34 percent in 11 to 30 days, 12 percent in 31 to 45 days, 5 percent in 46 to 60 days, and 4 percent in more than 60 days. The company has $937,000 in accounts

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Solutions Manual

receivable. Prepare an aging schedule for Keswick Fencing. Solution: Accounts receivable = $937,000 Age of Account (days)

Value of Account

% of Total Value

0-10

$421,650

45%

11-30

318,580

31-45

112,440

46-60

46,850

Over 60

37,480

Total

$937,000

100%

LO: 4 Bloomcode: Application AASCP: Analytic IMA: Strategic Planning AICPA: Industry/Sector Perspective

14.35 Factoring: Zenex, Inc., sells $250,000 of its accounts receivable to factors at a 3 percent discount. The firm’s average collection period is 90 days. What is the dollar cost of the factoring service? What is the simple annual interest cost of the factoring service? Solution: Accounts receivable sold = $250,000 Factor discount = 3% Average collection period = 90 days Dollar cost of factoring per month = $250,000 × 0.03 = $7,500 Dollar cost over 90 days = $7,500 × 90/30 = $22,500 Simple monthly interest cost of factoring = 3/97 or 0.03 / (1 - 0.03) = 0.03093 Simple annual interest cost of factoring = 0.03093 × 12 months = 37.1% LO: 4 Bloomcode: Application AASCP: Analytic

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IMA: Strategic Planning AICPA: Industry/Sector Perspective

14.36 Factoring: A firm sells $100,000 of its accounts receivable to factors at a 2 percent discount. The firm’s average collection period is one month. What is the dollar cost of the factoring service? Solution: Accounts receivable sold = $100,000 Factor discount = 2% Average collection period = 30 days Dollar cost of factoring service per month = $100,000 × 0.02 = $2,000 LO: 7 Bloomcode: Application AASCP: Analytic IMA: Strategic Planning AICPA: Industry/Sector Perspective

ADVANCED 14.37 What impact would the following actions have on the operating and cash conversion cycles? Would the cycles increase, decrease, or remain unchanged? a. More raw material than usual is purchased. b. The company enters into an off season, and finished goods inventory builds up. c. Better terms of payment are negotiated with suppliers. d. The cash discounts offered to customers are decreased. e. All else remaining the same, an improvement in manufacturing technique decreases the cost of goods sold. Solution: Situation

Operating cycle

Cash conversion cycle

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a. More raw material than usual is purchased.

Increase

b. The company enters into an off season, and finished goods inventory builds up. c. Better terms of payment are negotiated with suppliers. d. The cash discounts offered to customers are decreased. e. All else remaining the same, an improvement in manufacturing technique decreases the cost of goods sold. LO: 2

Increase

No change

Decrease

Increase

Unchanged

Bloomcode: Comprehension AASCP: Analytic IMA: Strategic Planning AICPA: Industry/Sector Perspective

14.38 What impact would the following actions have on the operating and cash conversion cycles? Would the cycles increase, decrease, or remain unchanged? a. Less raw material than usual is purchased. b. The company encounters unseasonable demand, and inventory declines rapidly. c. Tighter terms of payment are demanded by suppliers. d. The cash discounts offered to customers are increased. e. All else remaining the same, due to labor turnover and poor efficiency, the cost of goods sold increases. Solution: Cash conversion

Situation

Operating cycle

a. Less raw material than usual is purchased.

Decrease

b. The company encounters unseasonable demand, and inventory declines rapidly. c. Tighter terms of payment are demanded by suppliers. d. The cash discounts offered to customers are increased.

Decrease

No change

Increase

Decrease

cycle

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e. All else remaining the same, due to labor turnover and poor efficiency, the cost of goods sold increases.

Solutions Manual

Decrease

Unchanged

LO: 2 Bloomcode: Comprehension AASCP: Analytic IMA: Strategic Planning AICPA: Industry/Sector Perspective

14.39 Morgan Sports Equipment Company just reported the following financial information. Morgan Sports Equipment Company Assets

Liabilities and Equity

Cash

$ 677,423 Accounts payable

$1,721,669

Accounts receivable

1,845,113 Notes payable

2,113,345

Inventories

1,312,478

$3,835,014

Total current assets

Total current liabilities

$3,835,014 Sales and Costs Net sales

$9,912,332

Cost of goods sold

$5,947,399

Calculate the firm’s days’ sales outstanding.

What is the firm’s days’ sales in inventory?

What is the firm’s days’ payables outstanding?

What is the firm’s operating cycle? How does it compare with the industry average of 72 days?

What is the firm’s cash conversion cycle? How does it compare with the industry average of 42 days?

Solution: All sales are assumed to be credit sales.

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Accounts receivable $1,845,113 = = 67.9 days Credit sales $9,912,332 365 365

Field Code Changed

Inventory $1,312, 478 = = 80.6 days COGS $5,947,399 365 365

Field Code Changed

Accounts Payable $1,721,669 = = 105.7 days COGS $5,947,399 365 365

Field Code Changed

DSO =

DSI =

DPO =

Operating cycle = DSI + DSO = 67.9 days + 80.6 days = 148.5 days The firm is very inefficient in managing its receivable and inventory as its operating cycle exceeds the industry average of 72 days by about 77 days.

Cash conversion cycle = DSO + DSI – DPO = (67.9 days + 80.6 days) – 105.7 days = 42.8 days The firm’s cash conversion cycle is on a par with the industry average of 42 days thanks to its suppliers’ very generous credit policy.

LO: 2 Bloomcode: Application AASCP: Analytic IMA: Strategic Planning AICPA: Industry/Sector Perspective

14.40 Jackson Electrical, one of the largest generator dealers in Phoenix, sells about 2,000 generators a year. The cost of placing an order with its supplier is $750, and the inventory

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carrying costs are $170 for each generator. Jackson likes to maintain safety stock of 15 generators at all times. a.

What is the firm’s EOQ?

How many orders will the firm need to place this year?

What is the average inventory for the season?

Solution: Annual sales = 2,000 generators Cost of placing an order = $750 Inventory carrying cost per generator = $170 Safety stock = 15 generators a.

EOQ = =

2  Reorder costs  Sales per period Carrying costs

Field Code Changed

2  $750  2,000 = 132.8 $170

Field Code Changed

Economic order quantity = 133 generators b.

No. of orders the firm needs to place = 2,000 / 133 = 15 orders

Average inventory = ((133 – 0)/2) + 15 = 82 generators

LO: 5 Bloomcode: Application AASCP: Analytic IMA: Strategic Planning AICPA: Industry/Sector Perspective

14.41 Tanzaniqe, Inc., sells $200,000 of its accounts receivable to factors at a 5 percent discount. The firm’s average collection period is 90 days. a.

What is the dollar cost of the factoring service?

What is the simple annual interest cost of the loan?

What is the effective annual interest cost of the loan?

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Solutions Manual

Average collection period = 90 days a.

Dollar cost of factoring per month = $200,000 × 0.05 = $10,000 Dollar cost over 90 days = $10,000 × 3 or $10,000 × 90 / 30 = $30,000

Simple monthly interest cost of factoring = 5/95 or 0.05 / (1 - 0.05) = 0.0526 Simple annual interest cost of factoring = 0.0526 × 12 = 63.2% m

Quoted rate   Effective annual rate (EAR) =  1 +  −1 m   12 = (1 + 0.0526) − 1 = 1 − 1.850 = 0.850 = 85.0%

LO: 7 Bloomcode: Application AASCP: Analytic IMA: Strategic Planning AICPA: Industry/Sector Perspective

CFA PROBLEMS 14.42 A company increasing its credit terms for customers from 1/10, net 30 to 1/10, net 60 will likely experience: a.

An increase in cash on hand.

An increase in the average collection period.

Higher net income.

A higher level of uncollectible accounts.

LO: 6 Bloomcode: Application AASCP: Analytic IMA: Decision Analysis AICPA: Industry/Sector Perspective Solution: b is correct.

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14.43 Suppose a company uses trade credit with the terms of 2/10, net 50. If the company pays its account on the 50th day, the effective borrowing cost of skipping the discount on Day 10 is closest to a.

14.6 percent.

14.9 percent.

15.0 percent.

20.2 percent.

LO: 4 Bloomcode: Application AASCP: Analytic IMA: Decision Analysis AICPA: Industry/Sector Perspective Solution: d is correct. Field Code Changed

365

0.02  40  Cost =  1 + − 1 = (1 + .0204)9.125 − 1 = .2024 = 20.24 percent 0.98  

The following information relates to Problems 14.44 through 14.46. Mary Gonzales is evaluating companies in the office supply industry and has compiled the following information: 2019

2020 Average

Average

Receivables

Company

Credit Sales

Balance

Credit Sales

Balance

$5.0 million

$1.0 million

$6.0 million

$1.2 million

$3.0 million

$1.2 million

$4.0 million

$1.5 million

$2.5 million

$0.8 million

$3.0 million

$1.0 million

$0.5 million

$0.1 million

$0.6 million

$0.2 million

Industry

$25.0 million

$5.0 million

$28.0 million

$5.4 million

14.44 Which of the companies has the lowest accounts receivable turnover in 2020? a.

Company A.

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Fundamentals of Corporate Finance, 5th edition

Company B.

Company C.

Company D.

Solutions Manual

LO: 4 Bloomcode: Analysis AASCP: Analytic IMA: Strategic Planning AICPA: Industry/Sector Perspective

Solution: b is correct. Company A: $6.0 million/$1.2 million = 5.00 Company B: $4.0 million/$1.5 million = 2.67 Company C: $3.0 million/$1.0 million = 3.00 Company D: $0.6 million/$0.2 million = 3.00

14.45 The industry average receivables collection period: a.

Increased from 2019 to 2020.

Decreased from 2019 to 2020.

Did not change from 2019 to 2020.

Increased along with the increase in the industry accounts receivable turnover.

LO: 4 Bloomcode: Analysis AASCP: Analytic IMA: Strategic Planning AICPA: Industry/Sector Perspective Solution: b is correct. 2019: 73 days 2020: 70.393 days Note: If the number of days decreased from 2019 to 2020, the receivable turnover has increased.

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14.46 Which of the companies reduced the average time it took to collect on accounts receivable from 2019 to 2020? a.

Company A.

Company B.

Company C.

Company D.

LO: 4 Bloomcode: Analysis AASCP: Analytic IMA: Strategic Planning AICPA: Industry/Sector Perspective Solution: b is correct. Company B increased its accounts receivable (A/R) turnover (rom 2.500 million to 2.667) and reduced its number of days of receivables between 2019 and 2020 (from 146.000 days to 136.875 days).

2019 Company

2020

Acct. Rec.

Number

Acct. Rec.

Number

turnover

of days of

turnover

of days of

receivable

5.000

73.000

5.000

73.000

2.500

146.000

2.667

136.857

3.125

116.800

3.000

121.667

5.000

73.000

3.000

121.667

Sample Test Problems 14.1

The Great Foods Market, Inc. balance sheet for the latest fiscal year included the following: total current assets of $1,975 million, total assets of $6,341 million, total

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current liabilities of $1,341 million, and total liabilities of $3,117 million. What was the company’s net working capital at the end of the fiscal year? What does this tell us? Solution: Net Working Capital = Total Current assets – Total Current Liabilities = $1,975,000 - $1,341,000 = $634,000 This tells us that Great Foods Market could pay off all its current liabilities (those that will come due in the next year) with the cash and other assets that could reasonably be expected to be converted to cash within the next year and still have $634 million left over. LO:1 Bloomcode: Analysis AASCP: Analytic IMA: Strategic Planning AICPA: Industry/Sector Perspective

14.2

Last year, Perpetual Plastics Company took an average of 46 days to pay suppliers and 38 days to collect its receivables. The company’s average days’ sales in inventory was 52 days. What were Perpetual’s operating cycle and cash conversion cycles last year?

Solution: DPO = 46 days DSO = 38 days DSI = 52 days Perpetual’s operating cycle = DSO + DSI = 38 days + 52 days = 90 days Perpetual’s cash conversion cycle = DSO + DSI – DPO = 38 days + 52 days – 46 days = 44 days LO: 2

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Bloomcode: Application AASCP: Analytic IMA: Strategic Planning AICPA: Industry/Sector Perspective

14.3

Montrose, Inc. sells its products with terms of 3/15 EOM, net 30. What is the cost of the trade credit it provides its customers?

Solution: Credit terms = 3/15 EOM, net 30   Discount Effective annual rate (EAR) =  1 +   Discounted price  = (1 + 3 / 97)365/15 − 1

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365/days credit

−1

= (1.030928)24.333333 − 1 = 2.0984 − 1 = 1.0984, or 109.84%

LO: 4 Bloomcode: Application AASCP: Analytic IMA: Strategic Planning AICPA: Industry/Sector Perspective

14.4

FRA Manufacturing Company purchases 9,000 units of Part 3BX each year. The cost of placing an order is $5, and the cost of carrying one part in inventory for a year is $1. What is the economic order quantity (EOQ) for part 3BX if the company carries a safety stock of 200 units? How many orders will the company need to place this year?

Solution: Annual purchases = 9,000 units Cost of placing an order = $5 Inventory carrying cost per part = $1 Safety stock = 200 parts

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EOQ = =

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2  Reorder costs  Sales(or purchases) per period Carrying costs

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2  $5  9,000 = 300 parts $1

The number of orders that the firm should place each year is 9,000/300 = 30 orders LO: 5 Bloomcode: Analysis AASCP: Analytic IMA: Strategic Planning AICPA: Industry/Sector Perspective

14.5

Rosemary Corporation has daily sales of $139,000. The financial manager at the firm has determined that a lockbox would reduce collection time by 2.2 days. Assuming the company can earn 5.5 percent interest per year, what are the potential annual savings from the lockbox?

Solution: Average daily sales = $139,000 Collection time saved = 2.2 days Savings from mail float = 2.2 days × $139,000 = $305,800 Annual savings if invested = $305,800 × 0.055 = $16,819 LO: 6 Bloomcode: Application AASCP: Analytic IMA: Strategic Planning AICPA: Industry/Sector Perspective 14.6

Sunny Way Landscaping has a formal line of credit of $500,000 with First Commerce Bank. The interest rate on the loan is 6 percent, and under the agreement, Sunny Way must pay an annual fee of 75 basis points on the unused amount. The amount currently outstanding on the loan is $325,000. What is the annual fee the company must pay on the current unused balance? What is the effective interest rate?

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Solution: Line of credit limit = $500,000 Interest rate = 6% Annual fee on unused balance = 0.75% Amount borrowed = $325,000 Unused balance = $175,000 Annual fee = $175,000 × 0.0075 = $1,312.50 Interest expense for amount borrowed = $325,000 × 0.06 = $19,500.00

Interest expense + Annual fee Borrowed amount ($19,500.00 + $1,312.50) = = 0.0640 = 6.40% $325,000.00

Field Code Changed

Effective interest rate =

Field Code Changed

LO: 7 Bloomcode: Application AASCP: Analytic IMA: Strategic Planning AICPA: Industry/Sector Perspective

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Chapter 13

The Cost of Capital Before You Go On Questions and Answers Section 13.1 1. Why does the market value of the claims on the assets of a firm equal the market value of the assets? The investors who own the debt and equity claims on the assets of a firm have the right to receive all of the after-tax cash flows that the assets of the firm produce. Since the market value of the assets equals the present value of the cash flows the assets produce, the market value of the assets must equal the value of the claims on those assets.

2. How is the WACC for a firm calculated? The WACC is calculated as the weighted average of the different types of claims on the firm’s assets. The weights in this calculation are the fractions of the total value of the financing that is represented by each individual type of financing. Equation 13.2 is the general form of the WACC calculation. n

kfirm =  xi ki = x1k1 + x2k2 + x3k3 + ... + xnkn i =1

3. What does the WACC for a firm tell us? The WACC tells us the overall cost of the capital that has been used to finance the firm. It is the weighted average of the costs of the different types of financing used by the firm.

Section 13.2 1. Why do analysts care about the current cost of long-term debt when estimating a firm’s cost of capital?

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Managers care about the current cost of long-term debt because the opportunity cost of capital that is relevant when discounting future cash flows is the opportunity cost of capital as of today. Managers focus on long-term debt because firms generally use it to finance their long-term assets, and it is the long-term assets that they are concerned about when they think about the value of a firm’s assets.

2. How do you estimate the cost of debt for a firm with more than one type of debt? When a firm has more than one type of debt, its overall cost of debt is estimated as a weighted average of the costs of each type of debt. The weights in this calculation are the fractions of the total value of the debt represented by each individual type of debt.

3. How do taxes affect the cost of debt? In the United States, the ability of firms to deduct interest payments when they compute their taxes actually reduces the cost of using debt. The after-tax cost of debt equals the pretax cost of debt times one minus the firm’s marginal tax rate.

Section 13.3 1. What information is needed to use the CAPM to estimate kcs or kps? In order to use the CAPM to estimate kcs or kps, you need to know the risk-free rate, the market risk premium, and the beta for the stock.

2. Under what circumstances can you use the constant-growth dividend formula to estimate kcs? The constant-growth dividend formula can be used to estimate kcs if you can observe the current market price of the common stock and you can estimate the dividend that stockholders will receive next period, D1, and the rate at which the market expects dividends to grow over the long run, g. Of course, it only makes sense to use this model if dividends are expected to grow at a constant rate for the foreseeable future and this growth rate is not greater than the long-term growth rate of the economy.

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3. What is the advantage of using a multistage-growth dividend model, rather than the constant-growth dividend model, to estimate kcs? The advantage of using the multistage-growth dividend model is that it is much more flexible than the constant-growth dividend model because we do not have to assume that dividends grow at the same rate forever.

Section 13.4 1. Do analysts use book values or market values to calculate the weights when they use Equation13.7? Why? Analysts use market values because this is what the theory underlying the calculation says they should use. Book values are relevant only if they just happen to equal the market values.

2. What kinds of errors can be made when the WACC for a firm is used as the discount rate for evaluating all projects in the firm? Using the WACC to discount cash flows for projects that are less risky than the firm can result in managers rejecting positive-NPV projects. When one uses the WACC to discount cash flows for projects that are more risky than the firm, it can result in managers erroneously accepting negative-NPV projects.

3. Under what conditions is the WACC the appropriate discount rate for a project? The WACC is the appropriate discount rate for a project when the project has the same level of systematic risk as the firm and when the project will be financed with the same proportion of debt, preferred shares, and common shares that have been used to finance the assets of the firm.

Self-Study Problems 13.1 The market value of a firm’s assets is $3 billion. If the market value of the firm’s liabilities is $2 billion, what is the market value of the stockholders’ investment, and why?

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Solution: Since the identity that Value of assets = Value of liabilities + Value of equity holds for market values as well as book values, we know that the market value of the firm’s equity is $3 billion - $2 billion = $1 billion.

13.2 Berron Comics, Inc., has borrowed $100 million and is required to pay its lenders $8 million in interest this year. If Berron has a 28 percent marginal tax bracket, then what is the after-tax cost of debt (in dollars as well as in annual interest) to Berron. Solution: Because Berron enjoys a tax deduction for its interest charges, the after-tax interest expense for Berron is $8 million × (1 – 0.28) = $5.76 million, which translates into an annual aftertax interest percentage of $5.76/$100 = 0.0576, or 5.76 percent.

13.3 Explain why the after-tax cost of equity (common or preferred) does not have to be adjusted by the marginal income tax rate for the firm. Solution: The U.S. tax code allows a deduction for interest expense incurred on borrowing. Preferred and common shares are not considered debt and, thus, do not benefit from an interest deduction. As a result, there is no distinction between the before-tax and after-tax cost of equity capital. 13.4 Mike’s T-Shirts, Inc., has debt claims of $400 (market value) and equity claims of $600 (market value). If the after-tax cost of debt financing is 11 percent and the cost of equity is 17 percent, then what is Mike’s weighted average cost of capital? Solution: Mike’s T-Shirts’ total firm value = $400 + $600 = $1,000. Therefore, Debt = 40 percent of financing Equity = 60 percent of financing WACC = xDebtkDebt(1-t) + xpskps + xcskcs WACC = (0.4 × 0.11) + (0.6 × 0.17) = 0.146, or 14.6%

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13.5 You are analyzing a firm that is financed with 60 percent debt and 40 percent equity. The current cost of debt financing is 10 percent, but due to a recent downgrade by the rating agencies, the firm’s cost of debt is expected to increase to 12 percent immediately. How will this change the firm’s weighted average cost of capital if you ignore taxes and the firm is subject to a 25 percent marginal tax rate? Solution: The pretax debt contribution to the cost of capital is xDebt × kDebt, and since the firm’s pretax cost of debt is expected to increase by 2 percent, we know that the effect on WACC (pretax) will be 0.6 × 0.02 = 0.012, or 1.2 percent. If we assume that the firm is subject to the 25 percent marginal tax rate, then the after-tax contribution to the cost of capital for the firm would be 0.012 × (1 – 0.25) = 0.009, or 0.90 percent.

Discussion Questions 13.1

Explain why the required rate of return on a firm’s assets must be equal to the weighted average cost of capital associated with its liabilities and equity.

Solution: In order to conceptualize the answer to this question, it helps to think of the case in which the firm has raised all of its capital needs from a single source that owns all of the liability and all of the equity claims on the firm. Assume that this source has no other investments. If we were to measure the rate of return on the combined portfolio of investments for this source, we would find that it is exactly equal to the return on the total assets of the firm since that is the ultimate source of the returns. The weighted return of that portfolio, which is the weighted average cost of capital for the firm (if for the time being we abstract away tax effects), is the return on the assets of the firm. LO: 1 Level: Basic Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance

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AICPA: Industry/Sector Perspective

13.2

Which is easier to calculate directly, the expected rate of return on the assets of a firm or the expected rate of return on the firm’s debt and equity? Assume that you are an outsider to the firm.

Solution: As an outsider to the firm, you will not be privy to the complete information about the projected cash flows of each of the firm’s assets, and so that is a somewhat difficult proposition. However, the collective market has made an inference concerning the expected cash flows of each of the financing claims of the firm, and by pricing those cash flows has given us an expected return for each of those claims. Therefore, finding the expected return on the debt and equity claims of the firm is much easier than finding the expected return on the assets of the firm, although that return can then be calculated from the expected return on the financing claims of the firm. LO: 1 Level: Basic Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

13.3

With respect to the level of risk and the required return for a firm’s portfolio of projects, discuss how the market and a firm’s management can have inconsistent information and expectations.

Solution: Firm management will be fully informed concerning the firm’s project risks, but their ability to accurately predict the required return for the firm’s projects depends on the market’s assessment of those project risks. Alternatively, the collective market is not fully informed (as outsiders) concerning the firm’s project risks and yet uses its incomplete information set to dictate a required return for the firm’s projects. This suggests that if the firm were able to better inform the market, and thereby reduce the market’s perceived risk

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on the firm’s projects, then the firm might be able to reduce the required rate of return on the firm’s projects. LO: 1 Level: Basic Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

13.4

Your friend has recently told you that the federal government effectively subsidizes the use of debt financing (vs. equity financing) for corporations. Do you agree with that statement? Explain.

Solution: Your friend is correct. Because interest expense on debt is tax deductible, whereas dividend payments on equity are not, the firm effectively gets a rebate on interest paid through a lowered tax bill. Two firms with identical EBIT amounts with different interest expenses will have different cash flow available to its collective set of investors. The firm with greater interest expense (assuming it is less than the EBIT amount) will have greater cash flow available to all of its investors. LO: 2 Level: Basic Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

13.5

Your firm will have a fixed interest expense for the next 10 years. You recently found out that the marginal income tax rate for the firm will change from 30 percent to 40 percent next year. Describe how the change will affect the cash flow available to investors.

Solution:

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Let’s compare our firm to the firm with no interest expense. In order to make a concrete example, assume that our firm has interest expense of $100 per year. Since the after-tax cost of debt for the firm is equal to kDebt pretax × (1 – t), then we can calculate the tax benefit to using debt to be kDebt pretax × t. In order to calculate that benefit in dollar terms, we would just multiply (interest expense) × t. Therefore, the current dollar benefit to the interest expense is $100 × 0.3 = $30. Next year, the dollar benefit is $100 × 0.4 = $40. The net benefit of interest expense from the increased marginal corporate tax rate is $10 ($40 - $30), and that is a positive benefit. Note that the analysis isolates the effect on debt and does not consider the lower operating earnings figure caused by the increased tax rate. Overall, the increase in tax rate will result in less cash flows available to investors, but for the leveraged (debt holding) firm, the reduction in cash flow is mitigated by the benefit from being able to deduct interest expenses. LO: 2 Level: Intermediate Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

13.6

Describe why it is not usually appropriate to use the coupon rate on a firm’s bonds to estimate the pretax cost of debt for the firm.

Solution: The pretax cost of debt for the firm is the current annual economic cost of borrowing for the firm (before any tax effects). That cost is better measured by the current yield to maturity on the firm’s debt than by the coupon rate that is currently paid on that debt. Since most firms try to issue new bonds very close to par, the coupon rate on a bond is an indication of the yield to maturity on the bond issue at the time of issue. Unless the market-determined borrowing rate for the firm is the same as when the bond was issued, then the current yield to maturity of a bond will not be equal to the current coupon rate on the bond. LO: 2

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Level: Basic Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

13.7

Maltese Falcone, Inc., has not checked its weighted average cost of capital for four years. The firm’s top managers claim that since Maltese has not had to raise capital for new projects in four years, they should not have to worry about their current weighted average cost of capital. They argue that they have essentially locked in their cost of capital. Critique management’s statements.

Solution: That is a false statement. Maltese is assuming that since it does not have to raise capital for new projects, then it has essentially locked in its cost of capital. However, in a liquid capital market, every firm competes for capital every day since the firm’s investors have the opportunity to sell their investments to other investors. If a firm does not provide investors with an ample return, then the investors will sell their investments in the firm, which, in aggregate, will have the effect of actually raising the cost of capital for the firm (since the current price of the securities will move down). Therefore, a firm that ignores its current cost of capital by thinking that it has locked in a cost of capital might even be raising its cost of capital by making that incorrect assumption. LO: 1 Level: Intermediate Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

13.8

Ten years ago, the Edson Water Company issued preferred stock at a price equal to the par value of $100. If the dividend yield on that issue was 12 percent, explain why the firm’s current cost of preferred capital is not likely to equal 12 percent.

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Solution: Since the price of the preferred shares at issue was $100 and the dividend yield was 12 percent, then we know that the annual dividend on the shares is $12. We also then know that the required rate of return at the time of issue was 12 percent. If during the last 10 years, the required rate of return on Edson’s preferred shares has changed at all, the current required rate of return will not be 12 percent. This will, in turn, change the price of the shares to some amount other than $100. LO: 3 Level: Intermediate Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

13.9

Discuss under what circumstances you might be able to use a model that assumes constant growth in dividends to calculate the current cost of equity capital for a firm.

Solution: A constant growth model can be used when it is reasonable to assume that the dividends will grow at a constant rate, and when the analyst has a good idea what that growth rate will be. If one expects the growth in dividends to change in the future, then using a constant-growth dividend assumption is incorrect and only an estimation. LO: 3 Level: Basic Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

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13.10 Your boss just finished computing your firm’s weighted average cost of capital. He is relieved because he says that he can now use that cost of capital to evaluate all projects that the firm is considering for the next four years. Evaluate that statement. Solution: Your boss is incorrect. A firm is always subject to revisions to its cost of capital due to current market and firm conditions. In addition, the firm could also be making an error by using the same cost of capital for all of its future projects. For that particular error to not be made, two conditions must be met. That is, future projects must be financed with the same mix of capital (debt, preferred shares, and common shares) with which the entire firm is currently financed. In addition, the future projects must contain the same level of systematic risk as that of the average project that the firm is currently operating. LO: 4 Level: Basic Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

Questions and Problems BASIC 13.1

Finance balance sheet: KneeMan Markup Company has total debt obligations with book and market values equal to $30 million and $28 million, respectively. It also has total equity with book and market values equal to $20 million and $70 million, respectively. If you were going to buy all of the assets of KneeMan Markup today, how much should you be willing to pay?

Solution: The price you should be willing to pay for all of the assets of the firm is the market value of those assets. Using the market price version of the balance sheet identity, we can add

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the market price of the debt obligations and the equity to find the market price of the assets. That is, $28 million + $70 million = $98 million. LO: 1 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

13.2

WACC: What is the weighted average cost of capital for a firm?

Solution: The weighted average cost of capital (WACC) is the weighted average of the costs to the different sources of capital used to fund a firm; that is, the cost of each type of capital is weighted by the proportion of the total capital that it represents. The WACC is often used as an estimate of the cost of financing a new project given the firm’s current mix of debt and equity. LO: 1 Bloomcode: Knowledge AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

13.3

Taxes and the cost of debt: How are taxes accounted for when we calculate the cost of debt?

Solution: When we calculate the cost of debt for a U.S. firm, we must take into account the tax subsidy given in the United States for interest payments on debt. For every dollar the firm pays in interest, the firm’s tax bill will decline by ($1 × t), where t is the firm’s marginal tax rate. We adjust for this tax benefit by multiplying the pretax cost of debt by (1 - t). This calculation gives us the after-tax cost of debt. We use the after-tax cost of debt for cost of capital calculations such as when we calculate the WACC. LO: 2

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13.4

Cost of common stock: List and describe each of the three methods used to calculate the cost of common stock.

Solution: 1) The Capital Asset Pricing Model (CAPM) formula for the cost of common stock, given in Equation 13.4 (kcs = Rrf + (βcs × Market risk premium), can be used to calculate the return investors will demand on investment in the company’s common stock. Read Chapter 7 for further discussion of the CAPM. 2) The constant-growth dividend model can be used to calculate the cost of equity implied by the firm’s current stock price. In an efficient market, the current price of the company’s stock should reflect the cash flows (dividends) that investors will receive in the future from holding equity in the firm, discounted by an appropriate rate (the cost of equity). By knowing the current dividend paid by the firm and the expected growth rate of dividends, we can use Equation 13.5 [(kcs = D1/ P0) + g] to compute the cost of capital that is implied in the firm’s current stock price. The constant-growth dividend model is only appropriate when there is a reasonable expectation that the firm’s dividend will continue growing at approximately the same rate forever. For example, it might be used to calculate the cost of equity for a mature company whose growth rate is similar to that of the economy. 3) The multistage-growth dividend model is very similar to the constant-growth dividend model, but the multistage-growth dividend model can be applied in situations when the growth rate is expected to change in the near term followed by a constant long term growth rate—for example, a small, fast growing company whose growth will certainly slow as the company becomes larger. See Section 13.3 for discussion of the calculation of cost of equity using the multistage-growth dividend model. LO: 3

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13.5

Cost of common stock: Whitewall Tire Co. just paid an annual dividend of $1.60 on its common shares. If Whitewall is expected to increase its annual dividend by 2 percent per year into the foreseeable future and the current price of Whitewall’s common shares is $11.66, what is the cost of common stock for Whitewall?

Solution: The cost of common equity for Whitewall can be found using the constant-growth assumption equation:

Pcs =

D  (1 + g ) $1.60  (1 + 0.02 )  D1 = 0 = = $11.66 kcs − g kcs − g kcs − 0.02

Solving for kcs, we find it is equal to 0.16 or 16 percent. LO: 3 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

13.6

Cost of common stock: Seerex Wok Co. is expected to pay a dividend of $1.10 one year from today on its common shares. That dividend is expected to increase by 5 percent every year thereafter. If the price of Seerex common stock is $13.75, what is the cost of its common equity capital?

Solution: We can use the formula to find the cost of common equity assuming constant growth.

kcs =

D1 $1.10 +g= + 0.05 = 0.13, or 13% Pcs $13.75

LO: 3 Bloomcode: Application

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AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

13.7

Cost of common stock: Two-Stage Rocket paid an annual dividend of $1.25 yesterday, and it is commonly known that the firm’s management expects to increase its dividend by 8 percent for the next two years and by 2 percent thereafter. If the current price of TwoStage’s common stock is $17.80, what is the cost of common equity capital for the firm?

Solution: Pcs =

D0 (1 + g1 ) 1 + kcs

$17.80 =

D0 (1 + g1 )2

(1 + kcs )

D0 (1 + g1 )2 (1 + g2 )

( kcs − g2 )(1 + kcs )

[$1.25  (1 + 0.08)] [$1.25  (1 + 0.08)2 ] [$1.25  (1 + 0.08)2  (1 + 0.02)] + + 1 + kcs (1 + kcs )2 [(kcs − 0.02)(1 + kcs )2 ]

Using a spreadsheet to solve for the value of kcs, we find that the cost of common equity capital is 10 percent. LO: 3 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

13.8

Cost of preferred stock: Fjord Luxury Liners has preferred shares outstanding that pay an annual dividend equal to $15 per year. If the current price of Fjord preferred shares is $107.14, what is the after-tax cost of preferred stock for Fjord?

Solution: Using the equation for finding the cost of preferred equity, we have

kps =

Dps Pps

$15 = 0.14, 4 or 14. $107.14

LO: 3 Bloomcode: Application AASCP: Analytic

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13.9

Cost of preferred stock: Kresler Autos has preferred shares outstanding that pay annual dividends of $12, and the current price of the shares is $80. What is the after-tax cost of new preferred shares for Kresler if the flotation (issuance) costs for preferred shares are 5 percent?

Solution: Kresler will only receive 95 percent of the proceeds, so we know that we can use the equation to solve for the cost of preferred equity by adjusting the denominator for the reduced proceeds from the sale of new equity. We then have:

kps =

Dps

Pps (1 − F )

$12 $12 = = 0.158, or 15.8% $80 (1 − 0.05 ) $76

LO: 3 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective 13.10 WACC: Describe the alternatives to using a firm’s WACC as a discount rate when evaluating a project. Solution: There are no perfect alternatives to using the WAAC of a firm to evaluate its projects. In absence of publicly traded common stock for most individual projects, there are two main considerations that managers must keep in mind: 1. It is not appropriate to use a firm’s WACC to discount a project’s free cash flows if the systematic risk of the project is very different from the systematic risk of the firm. To account for this potential problem, some firms estimate discount rates that directly reflect the risk involved in the project’s cash flows. For example, a risky project might be assigned a discount rate that is significantly higher than the firm’s WACC.

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2. It is not appropriate to use a firm’s WACC when a project that has the same systematic risk as the firm is not being financed using the same mix of debt and equity as the firm— for example, if a project will be financed entirely with equity. The project’s cash flows should be discounted using the cost of equity rather than the firm’s WACC. These two rates will be the same only if the firm has no debt. LO: 4 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

13.11 WACC: Capital Co. has a capital structure, based on current market values, that consists of 50 percent debt, 10 percent preferred stock, and 40 percent common stock. If the returns required by investors are 8 percent, 10 percent, and 15 percent for the debt, preferred equity, and common stock, respectively, what is Capital’s after-tax WACC? Assume that the firm’s marginal tax rate is 28 percent. Solution:

WACC = xdebt kdebt (1 − t ) + xpskps + xcskcs WACC = [0.5  0.08  (1 − 0.28)] + [0.1  0.10] + [0.4  0.15] = 0.0988, or 9.9%

Field Code Changed Field Code Changed

LO: 4

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Bloomcode: Application

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AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

13.12 WACC: What are direct out-of-pocket costs? Solution: Direct out-of-pocket costs are the actual out-of-pocket costs that a firm incurs when it raises capital. They include such things as fees paid to investment bankers and legal and accounting expenses. LO: 4 Copyright © 2022 John Wiley & Sons, Inc.

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Bloomcode: Knowledge AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

INTERMEDIATE 13.13 Finance balance sheet: Explain why the total value of all of the securities used to finance a firm must be equal to the value of the firm. Solution: The value of the firm’s assets is equal to the present value of the future cash flows expected to be generated by those assets. The cash flow claim on those assets is prioritized by the financing of those assets. Therefore, the financing claims on the assets of the firm fully account for the entire value of the assets, and the value of the financing claims must equal the value of the assets that are carved up by those claims. LO: 1 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

13.14 Finance balance sheet: Explain why the cost of capital for a firm is equal to the expected rate of return to the investors in the firm. Solution: If we view the firm as a conduit for the cash flows provided by the assets of the firm, then it is easy to see that the cash flows provided by the assets of the firm must equal the cash flows provided to the aggregate investor group of the firm. We also know that the capital invested in the firm must equal the capital invested by the firm. Therefore, we then know that the rate of return for the investors of the firm must equal the cost of capital provided to the firm. The expected return to investors will also equal the expected cost of capital for the firm.

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LO: 1 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

13.15 Current cost of a bond: You know that the after-tax cost of debt capital for Bubbles Champagne Company is 7 percent. If the firm has only one issue of five-year bonds outstanding, what is the current price of the bonds if the coupon rate on those bonds is 10 percent? Assume the bonds make semiannual coupon payments and the marginal tax rate is 30 percent. Solution: We know the after-tax cost of debt, and from that we can find the pretax cost of debt by dividing by 1 minus the tax rate. This becomes 0.07/ (1 – 0.3) = 0.10 or 10%. Since the YTM on the bonds is equal to the coupon rate, then we know the bonds are priced at par, or $1,000. LO: 2 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective Excel Template available in Wiley Course Resources Excel Template Solution available in Wiley Instructor Resources 13.16 Current cost of a bond: Perpetual Ltd. has issued bonds that never require the principal amount to be repaid to investors. Correspondingly, Perpetual must make interest payments into the infinite future. If the bondholders receive annual payments of $75 and the current price of the bonds is $882.35, what is the after-tax cost of this debt for Perpetual if the firm is subject to a 40 percent marginal tax rate? Solution: Since the bonds represent a perpetuity, we know that the pretax cost of debt can be solved using the following: Copyright © 2022 John Wiley & Sons, Inc.

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kDebt =

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Field Code Changed

Coupon Payment $75 = = 0.085 Bond Price $882.35

And the after-tax cost is 0.085 × (1 - 0.4) = 0.051, or 5.1% LO: 2 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

13.17 Current cost of a bond: You are analyzing the cost of debt for a firm. You know that the firm’s 14-year maturity, 8.5 percent coupon bonds are selling at a price of $823.48. The bonds pay interest semiannually. If these bonds are the only debt outstanding, what is the after-tax cost of debt for this firm if it is subject to a 30 percent marginal and average tax rates? Solution: The current YTM for the bonds can be calculated as follows. Semiannual interest payment = $1,000 x .085 x 6/12 = $42.50* $823.48 = $42.50* × PVIFA(28, YTM/2) + $1,000 × PVIF(28, YTM/2) Solving, we find that YTM = 0.11, and therefore, the after-tax cost of debt is equal to: 0.11 × (1 – 0.3) = 0.077, or 7.7% LO: 2 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

13.18 Taxes and the cost of debt: Holding all other things constant, does a decrease in the marginal tax rate for a firm provide incentive for the managers of a firm to increase or decrease its use of debt? Solution:

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The after-tax cost of debt for the firm is equal kDebt pretax x (1 – t). We can then calculate the tax benefit of using debt to be kDebt pretax x t. Therefore, the value of the tax benefit to debt increases with the marginal tax rate. If the marginal tax rate decreases, then the tax benefit to debt decreases as well. Therefore, the incentive to borrow actually decreases with a decrease in the marginal tax rate. LO: 2 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

13.19 Cost of debt for a firm: You are analyzing the after-tax cost of debt for a firm. You know that the firm’s 12-year maturity, 9.5 percent semiannual coupon bonds are selling at a price of $1,200. Assuming that these bonds are the only debt outstanding for the firm, what is the after-tax cost of debt for this firm if it has a marginal tax rate of 34 percent? What if the bonds are selling at par? Solution: The current YTM for the bonds can be calculated as follows.

1    1 − (1 + i)n  Fn PB = C ( + n i   (1 + i)  

1    1 − (1 + i)24  $1,000 $1200 = $47.50  ( + 24 i   (1 + i)  

Field Code Changed Field Code Changed

Semiannual interest payment = $1,000 x .095 x 6/12 = $47.50

Solving, we find that YTM = 0.07008 or 7.008% and therefore, the after-tax cost of debt is equal to 0.07008 × (1 – 0.34) = 0.046253, or 4.63% If the bonds are priced at par, then the YTM on the bonds is 9.5 percent and then the after-tax cost of debt would be 6.27%.

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LO: 2 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective 13.20 Cost of common stock: Underestimated Inc.’s common shares currently sell for $36 each. The firm’s management believes that its shares should really sell for $54 each. If the firm just paid an annual dividend of $2 per share and management expects those dividends to increase by 8 percent per year forever (and this is common knowledge to the market), what is the current cost of common equity for the firm, and what does management believe is the correct cost of common equity for the firm? Solution: The current cost of equity for the firm is kcs =

( $2.00  1.08 ) + 0.08 = 0.14, or 14% D1 +g= Pcs $36.00

Field Code Changed

But the firm believes that its cost of capital is more appropriately kcs =

( $2.00  1.08 ) + 0.08 = 0.12, or 12% D1 +g= Pcs $54.00

Field Code Changed

LO: 3 Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

13.21 Cost of common stock: Write out the general equation for the price of the stock for a firm that will grow dividends very rapidly at a constant rate for the four years after the next dividend is paid and will grow dividends thereafter at a constant, but lower rate. Discuss the problems in estimating the cost of equity capital for such a stock. Solution:

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Pcs =

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D (1 + g1 ) D1 (1 + g1 ) 2 D1 (1 + g1 )3 D1 (1 + g1 ) 4 D1 (1 + g1 ) 4 (1 + g 2 ) D1 + 1 + + + + 3 4 5 1 + kcs (1 + kcs )2 (1 + kcs )5 (1 + kcs ) (1 + kcs ) ( kcs − g 2 )(1 + kcs )

It is easy to see that in order to solve for a cost of capital, kcs, you must have a good idea of what g1 and g2 are. If those growth rates are poor estimates, then the calculation for kcs, will also be a poor estimate. LO: 3 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

13.22 Cost of common stock: You have calculated the cost of common stock using all three methods described in this chapter. Unfortunately, all three methods have yielded different answers. Describe which answer (if any) is most appropriate. Solution: Two of the methods involve an estimate of the growth rate in dividends for the firm. If you are confident in your estimate of the growth rate, then those methods might be most appropriate. Otherwise, utilizing the CAPM, which does not involve any dividend growth rate estimates, would probably be the best. You may choose to average the results of all three methods. LO: 3 Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

13.23 WACC: The managers of a firm financed entirely with common stock are evaluating two distinct projects. The first project has a large amount of unsystematic risk and a small amount of systematic risk. The second project has a small amount of unsystematic risk and a large amount of systematic risk. Which project, if taken, is more likely to increase the firm’s cost of capital? Copyright © 2022 John Wiley & Sons, Inc.

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Solution: Markets adjust the cost of capital according to the level of systematic risk in a project. Therefore, the project with the greatest level of systematic risk will have the greatest positive impact on the cost of capital for the firm, even if it has the lowest level of unsystematic risk. LO: 4 Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

13.24 WACC: The Imaginary Products Co. currently has debt with a market value of $300 million outstanding. The debt consists of 9 percent coupon bonds (semiannual coupon payments) which have a maturity of 15 years and are currently priced at $1,440.03 per bond. The firm also has an issue of 2 million preferred shares outstanding with a market price of $12.00 per share. The preferred shares pay an annual dividend of $1.20. Imaginary also has 14 million shares of common stock outstanding with a price of $20.00 per share. The firm is expected to pay a $2.20 common dividend one year from today, and that dividend is expected to increase by 5 percent per year forever. If Imaginary is subject to a 28 percent marginal tax rate, then what is the firm’s weighted average cost of capital? Solution: Step 1: Total amount of debt, common equity, and preferred equity: Debt = $300,000,000 (given) Preferred equity = $12 × 2,000,000 = $24,000,000 Common equity = $20 × 14,000,000 = $280,000,000 Total capital = $604,000,000 xDebt = 300 million/604 million = 0.4967 xps = 24 million/604 million = 0.0397 xcs = 280 million/604 million= 0.4636 Step 2: Cost of capital components:

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Cost of debt: Semiannual interest payment = $1,000 x .09 x 6/12 = $45* $1,440.03 = $45 × PVIFA (30, YTM / 2) + $1,000 × PVIF (30, YTM / 2) Solving, we find that YTM = 0.0484 (this is a pretax number). Cost of preferred equity:

kps =

Field Code Changed

D $1.20 = = 0.10 Pps $12.00

Cost of common equity:

kcs =

Field Code Changed

D1 $2.20 +g= + 0.05 = 0.16 Pcs $20.00

Step 3: Combine using the WACC formula. WACC = xDebt kDebt (1 − t ) + xps kps + xcs kcs

Field Code Changed

WACC = ( 0.4967  0.0484  (1 − 0.28) ) + (0.0397  0.10) + (0.4636  0.16)

Field Code Changed Field Code Changed

= 0.0955, or 9.55%

Field Code Changed Field Code Changed

LO: 4

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Bloomcode: Application

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AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective Excel Template available in Wiley Course Resources Excel Template Solution available in Wiley Instructor Resources 13.25 Choosing a discount rate: For the Imaginary Products firm in Problem 13.24, calculate the appropriate cost of capital for a new project that is financed with the same proportion of debt, preferred shares, and common shares as the firm’s current capital structure. Assume that the project has the same degree of systematic risk as the average project that the firm is currently undertaking. Also assume the project is in the same general industry as the firm’s current line of business. Solution: Since Imaginary will be financing the project with the same mix of capital that the firm is currently utilizing for its projects, we will have met the first restriction concerning

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financing mix. In addition, the new project will have the same degree of systematic risk (in addition to being in the same general line of business). Therefore, Imaginary can use the 9.26 percent cost of capital to evaluate its project. LO: 1 Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective 13.26 Choosing a discount rate: If a firm’s management anticipates financing a project with a capital mix that is different from its current capital structure, describe how the firm is subjecting itself to a calculation error if its historical WACC is used to evaluate the project. Solution: Since the firm is financing the project with a different capital mix than it has historically used, we know that the weights and rates for debt, preferred, and common shares in the WACC formula will be different. We know that the cost of capital for each component is a function of the individual weights and rates, and that the WACC will be different for the overall firm versus that of the individual project. Therefore, using its historical WACC can result in an error in the NPV estimate for the project. LO: 1 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

ADVANCED 13.27 You are analyzing the cost of capital for MacroSwift Corporation, which develops software operating systems for computers. The firm’s dividend growth rate has been a constant 3 percent per year for the past 15 years. Competition for the firm’s current Copyright © 2022 John Wiley & Sons, Inc.

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products is expected to develop in the next year, and MacroSwift is currently expanding its revenue stream into the multimedia industry. Evaluate the appropriateness of continuing to use a 3 percent growth rate in dividends for MacroSwift in your cost of capital model. Solution: While the growth in dividends has been extremely constant for Macroswift over the last 15 years, it is appropriate to assume a constant-growth rate only if that same rate will continue in the future. Two factors will act to alter that growth in the future. MacroSwift will have competition for its current product list in the near future, and that could alter the firm’s growth rate. In addition, the firm is expanding its product line into an area that will probably not yield the same level of growth. It is therefore, unlikely that MacroSwift’s dividend growth rate will continue at a 3 percent annual rate. This suggests that we should consider something other than constant growth in our modeling. LO: 3 Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

13.28 You are an external financial analyst evaluating the merits of a stock. Since you are using a dividend discount model approach to evaluate a cost of equity capital, you need to estimate the dividend growth rate for the firm in the future. Describe how you might go about doing this. Solution: One source for this data would be to measure the firm’s dividend growth rate in recent history. If we could assume that such a growth in dividends will continue into the future, then our measure would be reasonable. One additional source would be to read a financial analyst’s report in which the author of the report may have a better estimate of the firm’s future prospects. LO: 3 Bloomcode: Application

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AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

13.29 You know that the return of Momentum Cyclicals’ common shares is 1.6 times as sensitive to macroeconomic information as the return of the market. If the risk-free rate of return is 3.50 percent and the market risk premium is 6.00 percent, what is Momentum Cyclicals’ cost of common equity capital? Solution: We know that the beta for Momentum Cyclicals is 1.6, and we can use the remaining information in the CAPM as follows: E ( R CS ) = R rf +  ( E ( R m ) − R rf )

Field Code Changed Field Code Changed

= 0.0350 + 1.6(0.0600) = 0.131 = 13.1%

LO: 3 Bloomcode: Application AASCP: Analytic IMA: Quantitative Methods AICPA: Industry/Sector Perspective

13.30 In your analysis of the cost of capital for a common stock, you calculate a cost of capital using a dividend discount model that is much lower than the calculation for the cost of capital using the CAPM model. Explain a possible source for the discrepancy. Solution: Comparing the two formulas for the two methods, we have: E ( R cs ) = R rf +  ( E ( R m ) − R rf ) and kcs =

Field Code Changed

D1 +g Pcs

Field Code Changed

Given these two sources of information, we see that the only variable that we are not able to get directly from the market is the growth rate in dividends (note that future dividends are also a function of this growth rate), which is an estimate. Since our dividend discount method provided a lower cost of capital than the CAPM, it seems likely that we estimated the growth rate lower than what the aggregate market has assumed. Of course, this Copyright © 2022 John Wiley & Sons, Inc.

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assumes that the market is efficiently pricing the stock. If the market price of the stock is mispriced, then this might lead to a difference. LO: 3 Bloomcode: Analysis AASCP: Analytic IMA: Quantitative Methods AICPA: Industry/Sector Perspective

13.31 RetRyder Hand Trucks has a preferred share issue outstanding that pays a dividend of $1.30 per year. The current cost of preferred equity for RetRyder is 9 percent. If RetRyder issues additional preferred shares that pay exactly the same dividend and the investment banker retains 8 percent of the sale price, what is the cost of new preferred shares for RetRyder? Solution: The current cost of preferred shares for RetRyder is

Pps =

Field Code Changed

D $1.30 = = $14.44 kps 0.09

and then RetRyder would receive 92 percent of the proceeds. We could then adapt the cost of preferred equity to the following:

kps =

Field Code Changed

D $1.30 $1.30 = = =0.0978, or 9.78% Pps (1 − F ) $14.44 (1 − 0.08 ) $13.29

LO: 3 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective 13.32 Enigma Corporation’s management believes that the firm’s cost of capital (WACC) is too high because the firm has been too secretive with the market concerning its operations. Evaluate that statement. Solution: Copyright © 2022 John Wiley & Sons, Inc.

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The WACC is a function of the perceived risk involved in the cash flows of the projects that the firm is currently operating. If the market perceives that risk to be higher than the actual risk due to a lack of information concerning those projects, then the firm might be able to lower that perceived risk by sharing more information with the market. That could have the effect of lowering the firm’s WACC. LO: 4 Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

13.33 Discuss what valuable information would be lost if you decided to use book values in order to calculate the cost of each of the capital components within a firm’s capital structure. Solution: Market returns are impounded in market prices. If those prices are ignored, then the benefits from the efficiency of the market’s information process are essentially thrown away. Since the market adjusts securities prices according to the expected return for investing in a security, then ignoring that information is the same as ignoring what the market deems to be an appropriate cost of capital for the firm. The theory underlying the discounting process requires that the cost of the different types of financing be weighted by their relative market values. LO: 4 Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

13.34 Hurricane Corporation is financed with debt, preferred equity, and common equity with market values of $20 million, $10 million, and $30 million, respectively. The betas for the debt, preferred stock, and common stock are 0.2, 0.5, and 1.1, respectively. If the risk-

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free rate is 3 percent, the market risk premium is 6 percent, and Hurricane’s average and marginal tax rates are both 30 percent, what is the company’s weighted average cost of capital? Solution: The fractions of the total financing represented by debt, common equity, and preferred equity are: Debt = $20 million Preferred equity = $10 million Common equity = $30 million Total capital = $60 million xdebt = $20/$60 = 0.3333 xps = $10/$60 = 0.1667 xcs = $30/$60 = 0.5000

The costs of debt, common equity, and preferred equity are: E(RDebt) = Rrf + βDebt (E(RM) – Rrf) = 0.03 + (0.2 × 0.06) = 0.042, or 4.2% E(Rps)

= Rrf + βps (E(RM) – Rrf) = 0.03 + (0.5 × 0.06) = 0.06, or 6.0%

E(Rcs)

= Rrf + βcs (E(RM) – Rrf) = 0.03 + (1.1 × 0.06) = 0.096 or 9.6%

WACC = (0.3333 × 0.042 × (1 - 0.3)) + (0.1667 × 0.060) + (0.5 × 0.096) = 0.0677999, or 6.78% LO: 4 Bloomcode: Application AASCP: Analytic IMA: Quantitative Methods AICPA: Industry/Sector Perspective Excel Template available in Wiley Course Resources Excel Template Solution available in Wiley Instructor Resources

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13.35 You are working as an intern at Coral Gables Products, a privately owned manufacturing company. Shortly after you read Chapter 13 in this book, you got into a discussion with the Chief Financial Officer (CFO) at Coral Gables about weighted average cost of capital calculations. She pointed out that, just as the beta of the assets of a firm equals a weighted average of the betas for the individual assets, as shown in Equation7.13: Field Code Changed

n Asset portfolio = xi i = x1 1 + x2 2 + x3 3 + . . . + xn n i =1

the beta of the assets of a firm also equals a weighted average of the betas for the debt, preferred stock, and common stock of a firm: Field Code Changed

n Asset firm = xi i = xDebt Debt + xps ps + xcs cs i =1

Why must this be true? Solution: Since, collectively, the debt and equity holders are entitled to receive all of the cash flows that the assets of the firm are expected to produce, the systematic risk of the cash flows that they are entitled to receive must be the same as the systematic risk of the cash flows the assets are expected to produce. LO: 1 Bloomcode: Analysis AASCP: Analytic IMA: Quantitative Methods AICPA: Industry/Sector Perspective

13.36 The CFO described in Problem 13.35 asks you to estimate the beta for Coral Gables’s common stock. Since the common stock is not publicly traded, you do not have the data necessary to estimate the beta using regression analysis. However, you have found a company with publicly traded stock that has operations exactly like those at Coral Gables. Using stock returns for this pure-play comparable firm, you estimate the beta for the comparable company’s stock to be 1.06. The market value of that company’s common equity is $45 million, and it has one debt issue

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outstanding with a market value of $15 million and an annual pretax cost of 4.85 percent. The comparable company has no preferred stock. a. If the risk-free rate is 4.25 percent and the market risk premium is 6 percent, what is the beta of the assets of the comparable company? b. If the total market value of Coral Gables’s financing consists of 35 percent debt and 65 percent equity (this is what the CFO estimates the market values to be) and the pretax cost of its debt is 5.45 percent, what is the beta for Coral Gables’s common stock? Solution: You can solve this problem using the equation: Field Code Changed

n Asset portfolio =  xi i = xDebt Debt + xps  ps + xcs  cs i =1

Since neither company has preferred stock, the equation in this case has only two terms:

n Asset portfolio = xDebt Debt + xcs cs

Field Code Changed

a. To calculate the beta of the assets of the comparable company, you must first estimate the beta of the comparable firm’s debt and the fractions of the total market value of the comparable firm’s financing which is represented by the debt and equity. The beta of the comparable firm’s debt can be estimated using the CAPM formula (Equation 7.12): E(Ri) = Rrf + βi[E(Rm) – Rrf] Since this formula can be used to calculate the expected return on debt, it can be written as: E(RDebt) = Rrf + βDebt[E(Rm) – Rrf] If we assume that the market is pricing the debt correctly, the pretax cost of debt equals the expected return on debt in this equation. Therefore, substituting the information from the problem statement into this equation yields: 4.85% = 4.25% + βDebt [6%] and the beta of the debt equals: Copyright © 2022 John Wiley & Sons, Inc.

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βDebt = (4.85% - 4.25%)/ 6% = 0.10 The fractions of the total financing represented by debt and common equity are: Debt = $15 million Common equity = $45 million Total capital = $60 million xDebt = $15/$60 = 0.25 xcs = $45/$60 = 0.75

Finally, the beta of the assets of the comparable company is: βn Asset portfolio = xDebtβDebt + xcsβcs = (0.25 × 0.10) + (0.75 × 1.06) = 0.82

b. Since the comparable company is exactly like Coral Gables, this is a good estimate of the asset beta for Coral Gables. To calculate the beta for Coral Gables’s common equity, you use the following equation with the beta of the assets for the comparable company and the beta of debt and financing fractions for Coral Gables.

n Asset portfolio = xDebt Debt + xcs cs

Field Code Changed

The beta of the Coral Gables debt is: E(RDebt) = Rrf + βDebt[E(Rm) – Rrf] 5.45% = 4.25% + (βDebt× 6%) βDebt = (5.45% - 4.25%)/ 6% = 0.2 and the beta of the firm’s equity is: βn Asset portfolio = xDebtβDebt + xcsβcs 0.82 = (0.35 × 0.2) + (0.65 × βCS)

0.82 − ( 0.35  0.2)

cs = 

0.65

Field Code Changed

0.75 = 1.1538 0.65

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13.37 Estimate the weighted average cost of capital for Coral Gables using your estimated beta and the information in the problem statement in Problem 13.36? Assume that the average and marginal tax rates for Coral Gables are both 25 percent. Solution: The cost of equity is: E(Rcs) = Rrf + βcs[E(Rm) – Rrf] E(Rcs) = 4.25% + (1.1538 × 6%) = 11.17% The weighted average cost of capital is: WACC = [(0.35 × 5.45% × (1 - 0.25)] + (0.65 × 11.17%) = 8.693% LO: 3, 4 Bloomcode: Application AASCP: Analytic IMA: Quantitative Methods AICPA: Industry/Sector Perspective

CFA Problems 13.38 The cost of equity is equal to the: a.

Expected market return.

Rate of return required by stockholders.

Cost of retained earnings plus dividends.

Risk the company incurs when financing.

Solution: b is correct. The cost of equity is defined as the rate of return required by stockholders. LO: 1 Bloomcode: Knowledge AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

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13.39 Dot.Com has determined that it could issue $1,000 face value bonds with an 8 percent coupon paid semiannually and a five-year maturity at $900 per bond. If Dot.Com’s marginal tax rate is 30 percent, its after-tax cost of debt is closest to: a.

7.2 percent.

7.4 percent.

7.6 percent.

7.8 percent.

Solution: b is correct. FV = $1,000; PMT = $40 ($1,000 x .08 x 6/12); N = 10; PV = -$900 Solve for i. The six-month yield, i, is 5.3149% YTM = 5.3149%  2 = 10.6298% kDebt pretax (1 – t) = 10.6298% × ( 1 – 0.3) = 7.441% LO: 2 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

13.40 Morgan Insurance Ltd. issued a fixed-rate perpetual preferred stock three years ago and placed it privately with institutional investors. The stock was issued at $25.00 per share with a $1.75 dividend. If the company were to issue preferred stock today, the yield would be 6.5 percent. The stock’s current value is: a.

$25.00.

$26.92.

$37.31.

$40.18.

Solution: b is correct. The company can issue preferred stock at 6.5%. Pps= $1.75/0.065 = $26.92 Note: Dividends are not tax deductible so there is no adjustment for taxes. Copyright © 2022 John Wiley & Sons, Inc.

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LO: 3 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

13.41 The Gearing Company has an after-tax cost of debt capital of 4 percent, a cost of preferred stock of 8 percent, a cost of equity capital of 10 percent, and a weighted average cost of capital of 7 percent. Gearing intends to maintain its current capital structure as it raises additional capital. In making its capital-budgeting decisions for the average-risk project, the relevant cost of capital is: a.

4 percent.

7 percent.

8 percent.

10 percent.

Solution: b is correct. The weighted average cost of capital, using weights derived from the current capital structure, is the best estimate of the cost of capital for the average-risk project of a company. LO: 4 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

13.42 Suppose the cost of capital of the Gadget Company is 10 percent. If Gadget has a capital structure that is 50 percent debt and 50 percent equity, its before-tax cost of debt is 5 percent, and its marginal tax rate is 20 percent, then its cost of equity capital is closest to: a.

10 percent.

12 percent.

14 percent.

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16 percent.

LO: 1 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective Solution: c is correct. re = ra + (ra – rd) (D/E) × (1-t) Note: If D/(D + E) = 0.50, then D/E = 1.0 re = 0.10 + [(0.10 – 0.05) × (1.0) × (1 – 0.2)] re = 0.10 + [0.05(0.80)] = 0.10 + 0.04 = 0.14, or 14%

Sample Test Problems 13.1

Howard Power and Telecommunications Corporation has three divisions. The names of these divisions, along with the after-tax cost of capital for each division and the market value of the assets in each division are as follows:

Division Name

Cost of Capital

MV of Assets

Infrastructure development

8.75

$250,000,000

Power

7.50

$325,000,000

Telecommunications

8.25

$675,000,000

What is the overall after-tax cost of capital for Howard Power and Telecommunications? Solution: The overall after-tax cost of capital for a firm is a value-weighted average of the after-tax cost of capital for the projects (assets) in that firm. We can calculate the overall after-tax cost of capital using Equation 13.2 as follows:

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kFirm =  xi ki = x1k1 + x2 k2 + x3k3 + ... + xn kn . i =1

$250,000,000 + $325,000,000 + $675,000,000 = $1,250,000 x1 = $250,000 / $1,250,000 = 0.20 x2 = $325,000 / $1,250,000 = 0.26 x1 = $675,000 / $1,250,000 = 0.54 (0.20 × 0.0875) + (0.26 × 0.0750) + (0.54 × 0.0825) = 0.0816, or 8.16% LO: 1 Bloomcode: Application AASCP: Analytic IMA: Quantitative Methods AICPA: Industry/Sector Perspective

13.2

Quarri Industries has 8 percent coupon bonds outstanding. These bonds have a market price of $954.41, pay interest semiannually, and will mature in 6 years. If the tax rate is 35 percent, what are the pre-tax cost and after-tax cost of this debt?

Solution:

   1 $1,000  + $954.41 = $40   1 − 12 12   1+k  (1 + k  ( Debt pretax ) Debt pretax )      kDebt pretax = 0.045, or 4.5%

Field Code Changed

The annualized pretax cost is:

Field Code Changed

kDebt pretax = (1 + 0.045)2 − 1 = 0.0920, or 9.20% And the after-tax cost is:

kDebt after-tax = 0.0920  (1 − 0.35) = 0.0598, or 5.98% Field Code Changed

Bloomcode: Application AASCP: Analytic IMA: Quantitative Methods AICPA: Industry/Sector Perspective

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Quarri Industries’ common stock has a beta of 1.6. If the current risk-free rate is 4 percent and the market risk premium is 5 percent, what is Quarri’s cost of common stock?

Solution: kcs = Rrf + βcs (E(RM) – Rrf) kcs = 0.04 + [1.6 × (0.05)] = 0.12, or 12% LO: 3 Bloomcode: Application AASCP: Analytic IMA: Quantitative Methods AICPA: Industry/Sector Perspective

13.4

Miron’s Copper Corp. management expects its common stock dividends to grow 1.5 percent per year for the indefinite future. The firm’s shares are currently selling for $18.45, and the firm just paid a dividend of $3.00 yesterday. What is the cost of common stock for Miron? P0 =

D (1 + g ) D1 D  kcs = 1 + g = 0 +g kcs − g P0 P0

 kcs =

[$3.00  (1 + 0.015)] + 0.015 = 0.18, or 18% $18.45 Field Code Changed

LO: 3 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

13.5

Use the information in questions 13.2 and 13.3 as well as the following information to compute the WACC for Quarri Industries. In addition to common stock, Quarri has 500,000 preferred shares outstanding that pay a quarterly dividend of $0.50 per share and are currently trading for $20.00 a share. The company’s outstanding bonds have a face

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value of $209,553,546. There are 2 million shares of common stock outstanding with a current market price of $98.00 per share. Solution: The total value of the outstanding debt, preferred stock and common stock are as follows: Debt = $209,553,546 × 0.95441 = $200,000,000 Preferred stock = $20 × 500,000 = $10,000,000 Common stock = $98 × 2,000,000 = $196,000,000 Total capital = $406,000,000 xDebt = $200/$406 = 0.4926 xps = $10/$406 = 0.0246 xcs = $196/$406 = 0.4828

The costs for the individual types of capital are: After-tax cost of debt (from problem 13.2): kDebt after-tax = 5.98% Cost of preferred stock:

kps =

D 4  $0.50 = = 0.10, or 10% Pps $20

Cost of common equity (from problem 13.3): kcs = 12%

WACC calculation:

WACC= xDebt kDebtafter-tax + xpskps + xcskcs WACC = (0.4926  0.0598) + ( 0.0246  0.10) + ( 0.4828  0.12) WACC = 0.0899, or 8.99%

LO: 3, 4 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

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Staunton Energy Corporation managers are considering a capital budgeting project to replace some machinery used in one of the company’s oil refineries. Is the company’s WACC the appropriate discount rate to use in the NPV analysis of this project? Explain.

Solution: If the systematic risk of the individual project is the same as the systematic risk of the portfolio of projects that comprise the company as a whole, and the project is likely to be financed with the same financing mix as the company, then company’s WACC is the appropriate discount rate to use. However, since a project involving replacement of machinery is probably less risky than the overall company, the company’s WACC might be too high of a discount rate. If so, using the WACC as the discount rate could cause the company managers to underestimate the NPV of this project. They should probably use a lower discount rate to more accurately reflect the systematic risk of the project. LO: 4 Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

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Chapter 12

Evaluating Project Economics

Before You Go On Questions and Answers Section 12.1 1.

Why do analysts care about how sensitive EBITDA and EBIT are to changes in revenue? Comparing the sensitivity of EBITDA to changes in revenue can help you better understand risks and returns associated with alternative options. For example, if we assume that the sensitivity of EBITDA to changes in revenue is higher for one alternative than for the other. This means that EBITDA for the more sensitive alternative will decline more when revenue is lower than expected. A larger decline in EBITDA reduces the value of the project more and has a greater impact on the amount of cash the firm has available to fund other positive NPV projects. Conversely, EBITDA will increase more when revenue is greater than expected if the level of sensitivity is higher.

How is the proportion of fixed costs in a project’s cost structure related to the sensitivity of EBITDA and EBIT to changes in revenue? The greater the proportion of fixed costs, the more sensitive EBITDA and EBIT will be to changes in revenue.

Section 12.2 1.

How does operating leverage change when there is an increase in the proportion of a project’s costs that are fixed? An increase in the proportion of a project’s costs that are fixed increases the operating leverage of the project.

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What do the degree of pretax cash flow operating leverage (Cash Flow DOL) and the degree of accounting operating leverage (Accounting DOL) tell us? Cash Flow DOL provides us with a measure of how sensitive pretax operating cash flows are to changes in revenue. Cash Flow DOL changes with the level of revenue. Accounting DOL is a measure of how sensitive accounting operating profits (EBIT) are to changes in revenue. Accounting DOL focuses on EBIT, whereas Cash Flow DOL focuses on EBITDA.

Section 12.3 1.

How is the per-unit contribution related to the pretax operating cash flow breakeven point? The per unit contribution the dollar amount that is left over from the sale of a single unit after all the variable costs associated with that unit have been paid; this is the amount that is available to help cover FC for the project. When we calculate the pretax operating cash flow break-even point, we divide the FC by the per unit contribution. A higher per-unit contribution level would mean that more from each sale could be used to cover fixed costs. Therefore, the pretax operating cash flow break-even point is the amount of units that must be sold to help cover FC for the project.

How is the per-unit contribution related to the accounting operating profit breakeven point? The per unit contribution is how much is left from the sale of a single unit after paying the variable costs associated with that unit. This is the amount that is available to help cover FC and D&A for the project. When we calculate the accounting operating profit break-even point, we divide the sum of FC and D&A by the per unit contribution to determine how many units must be sold to cover FC and D&A.

What is the difference between the pretax operating cash flow break-even point and the accounting operating profit break-even point?

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The pretax operating cash flow break-even point is the number of units that must be sold in a particular year for cash inflows to exactly equal cash outflows. The accounting operating profit break-even point is the number of units that must be sold in a particular year for the project to have operating profits of $0—in other words, to break even on an accounting operating profit basis.

Section 12.4 1.

How is the economic break-even point a more comprehensive measure of the impact of a project on a firm’s financial performance than the pretax operating cash flow break-even point or the accounting operating profit break-even point? The economic break-even point is a more comprehensive measure as it considers both the life of the project as well as the after-tax free cash flows. Unlike the other measures, the economic break-even point accounts for both the taxes and the investments associated with a project.

Section 12.5 1.

How is a sensitivity analysis used in project analysis? Sensitivity analysis is used to examine the sensitivity of a project’s NPV to changes in an individual assumption.

How does a scenario analysis differ from a sensitivity analysis? Scenario analysis recognizes that variables typically do not change one at a time. A change in economic or market conditions will usually cause several assumptions to change. Scenario analysis recognizes this by examining a project under alternative scenarios in which each assumption can change under each scenario.

What is a simulation analysis, and what can it tell us? Simulation analysis involves creating a large number of scenarios, often using random numbers and probability distributions, to evaluate the effects of different scenarios. Simulation analysis uses a computer to generate a large number of scenarios quickly, and

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calculate the range of outcomes (standard deviation, inter-quartile range, etc) and the probabilities of particular outcomes.

Self-Study Problems 12.1

The Yellow Shelf Company sells all of its shelves for $100 per shelf and incurs $50 in variable costs to produce each. If the fixed costs for the firm are $2,000,000 per year, what will the EBIT for the firm be if it produces and sells 45,000 shelves next year? Assume that depreciation and amortization are included in the fixed costs.

Solution:

12.2

Revenue

$100 per unit × 45,000 units =

$4,500,000

$50 per unit × 45,000 units =

2,250,000

FC + D&A

2,000,000

EBIT

$ 250,000

Hydrogen Batteries sells its specialty automobile batteries for $85 each, while its current variable cost per unit is $65. Total fixed costs (include ing depreciation and amortization expense) are $150,000 per year. Management expects to sell 10,000 batteries next year but is concerned that variable cost will increase next year due to material cost increases. What is the maximum variable cost per unit increase that will keep the EBIT from becoming negative?

Solution: The forecasted EBIT for Hydrogen Batteries is: Revenue

$85 per unit × 10,000 units = $850,000

$65 per unit × 10,000 units = 650,000

FC + D&A

150,000

EBIT

$ 50,000

Therefore, total variable cost may increase by $50,000, which means that if the firm produces and sells 10,000 batteries, then the variable cost per unit may increase by $5 ($50,000/10,000 units = $5 per unit). Copyright © 2022 John Wiley & Sons, Inc.

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The Vinyl CD Co. is going to take on a project that is expected to increase its EBIT by $90,000, its fixed cost cash expenditures by $100,000, and its depreciation and amortization by $80,000 next year. If the project yields an additional 10 percent in revenue, what percentage increase in the project’s EBIT will result from the additional revenue?

Solution:

FC + D&A EBIT $100,000 + $80,000 =1+ =3 $90,000

Accounting DOL = 1 +

Therefore, a 10 percent additional increase in revenue should result in approximately a 30 percent increase in EBIT.

12.4

You are considering investing in a business that has monthly fixed costs of $5,500 and sells a single product that costs $35 per unit to make. This product sells for $90 per unit. What is the annual pretax operating cash flow break-even point for this business?

Solution: You can solve for the monthly pretax operating cash flow break-even point using Equation 12.4:

EBITDA Break-Even =

FC $5,500 = = 100 units per month Price − Unit VC $90 − $35

Therefore, the annual EBITDA break-even point is 100 units per month  12 months per year = 1,200 units.

12.5

Belt Bottoms, Inc. is considering a five-year project with an initial investment of $20,000. What annual free cash flow (FCF) would be required for this project to have an NPV of $0 if the opportunity cost capital is 11 percent?

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If the FCF is equal in each of the five years, then we can solve for FCF using the present value of an ordinary annuity formula: $20,000 =

FCFt  1   → FCF = $5, 411.41  1 − 0.11  (1.11)5   

We can also use a financial calculator to solve this problem: N=5; I/Y=11; PV=-20,000; FV=0 → CPT → PMT=5,411.11 If using a spreadsheet to solve this problem:

RATE

0.11

RATE

0.11

NPER

-20,000

PMT

=PMT(B1,B2, B3, B4)

PMT

$5,411.41

Discussion Questions 12.1

You are involved in the planning process for a firm that is expected to have a large increase in sales next year. Which type of firm would benefit the most from that sales increase: a firm with low fixed costs and high variable costs or a firm with high fixed costs and low variable costs?

Solution: Under the circumstances described the firm with the high fixed costs would incur lower total future costs associated with the increased sales than the firm with the low fixed costs due to the higher variable cost per unit of sales. Therefore, the firm with the high fixed costs structure would benefit the most. LO: 1 Level: Basic Bloomcode: Comprehension Copyright © 2022 John Wiley & Sons, Inc.

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AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

12.2

You own a firm with a single new product that is about to be introduced to the public for the first time. Your marketing analysis suggests that the annual demand for this product could be anywhere between 500,000 units and 5,000,000 units. Given such a wide range, discuss the safest cost structure alternative for your firm.

Solution: Since there is a great deal of variability concerning the demand for the product, then the safest alternative would be to create a cost structure that limits the variability of the firm’s EBIT. This means that you would create a cost structure that is composed of high unit variable costs with low fixed costs. Although this would not enable the firm to maximize earnings if the 5,000,000-unit forecast occurs, it limits the downside profitability for the firm in the event that the 500,000-unit forecast occurs. LO: 1 Level: Intermediate Bloomcode: Application AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

12.3

Discuss the interpretation of the degree of accounting operating leverage and degree of pretax cash flow operating leverage.

Solution: While the degree of accounting operating leverage is defined as:

Accounting DOL = 1 +

FC + D&A EBIT

it is used to interpret the percentage change in EBIT that will be driven by a given percentage change in net revenue. Similarly, the degree of pretax cash flow operating leverage is defined as: Copyright © 2022 John Wiley & Sons, Inc.

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Cash Flow DOL = 1 +

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FC EBIT + D&A

but it is used to interpret the percentage change in EBITDA (or pretax operating cash flow) that will be driven by a given percentage change in net revenue. LO: 2 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

12.4

Explain how EBITDA differs from incremental after-tax free cash flows (FCF) and discuss the types of businesses for which this difference would be especially small or large.

Solution: Depreciation and amortization, taxes, capital expenditures, and working capital are not reflected in EBITDA. If any of these is not equal to zero, then EBITDA is likely to differ from FCF, which is equal to EBIT(1-T) + depreciation—increases in working capital— capital expenditures. The type of businesses that require large capital expenditures (and therefore have large depreciation expenses per year) such as heavy manufacturing, are likely to have substantial differences between EBITDA and FCF. Conversely, smaller firms that have smaller capital expenditures, such as firms in retail sales, will likely have small differences between FCF and EBITDA for. Setting aside depreciation and special tax subsidies, taxes will always create a difference between EBITDA and FCF for a profitable firm. LO: 2 Level: Intermediate Bloomcode: Analysis AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective Copyright © 2022 John Wiley & Sons, Inc.

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Describe how the pretax operating cash flow break-even point is related to the economic break-even point.

Solution: The pretax operating cash flow break-even point establishes the number of units that must be sold in a given year to break even for a particular year. The economic break-even calculation looks at cash flows over the course of an entire project and tells us how many units must be sold to achieve an NPV of $0. The NPV calculation is useful when deciding whether to undertake a project in an economic sense. The cash flow break-even calculation is useful when considering whether to abandon a project or to make changes to a project’s cost structure. LO: 4 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

12.6

Is it possible to have a crossover point where the accounting break-even point is the same for two alternatives - that is, above the break-even point for a low-fixed-cost alternative but below the break-even point for a high-fixed-cost alternative? Explain.

Solution: No. Above the low fixed cost break-even sales level implies that income is positive. Below the high fixed cost break-even sales level implies that income is negative. However, the cross-over point is defined as the sales level at which the income level for both alternatives is the same. Therefore, it cannot occur. LO: 3 Level: Basic Bloomcode: Comprehension AASCB: Analytic Copyright © 2022 John Wiley & Sons, Inc.

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12.7

What is the fundamental difference between a sensitivity analysis and a scenario analysis?

Solution: A sensitivity analysis is a form of “what if” analysis that is very useful for identifying key individual assumptions in models used for financial analysis such as an NPV calculation. Scenario analysis identifies relationships across several key individual assumptions and is therefore a good way of estimating how project values might vary under different economic scenarios. LO: 5 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

12.8

The economics break-even calculation assumes that the number of units sold is the same each year during the life of the project. It is possible for the NPV of a project to be negative if unit sakes are not the same each year and the average unit sales are higher than those estimated using the economic break-even calculation? Explain.

Solution: Yes. This is possible, if, for example, actual unit sales are lower than the average in the early years of a project’s life and higher than the average in the latter years of a project’s life. This is due to the time value of money. Unit sales in early years have a greater present value than unit sales in later years. LO: 5 Bloomcode: Comprehension AASCB: Analytic IMA: Business Economics Copyright © 2022 John Wiley & Sons, Inc.

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12.9

How does the pretax operating cash flow for a project differ from the economic profit for that project?

Solution: The pretax operating cash flow is a measure of the extent to which revenues exceed cash operating expenses. It does not account for taxes or the opportunity cost of the capital that is invested in the project. Economic profit is a measure of the extent to which revenues exceed cash operating expenses, taxes, and the opportunity cost of the capital invested in a project. Economic profit accounts for all of the costs associated with producing a project’s revenue. LO: 4 Bloomcode: Analysis AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

12.10 What is the advantage of using a simulation analysis instead of a scenario analysis to assess the risk of a project? Solution: Simulation analysis is like a scenario analysis except that in simulation analysis an analyst uses a computer to examine a large number of scenarios in a short period of time. This description from the text suggests that simulation analysis allows for more efficient use of the analyst’s time. In addition, since an analyst can examine a very large number of scenarios (typically in the thousands) in a simulation analysis, this analytical tool can enable the analyst to get a more complete picture of the risks associated with a project. LO: 5 Bloomcode: Comprehension AASCB: Analytic IMA: Business Economics Copyright © 2022 John Wiley & Sons, Inc.

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Questions and Problems BASIC 12.1

Fixed and variable costs: Define variable costs and fixed costs, and give an example of each.

Solution: Fixed costs are costs that in the short term cannot be changed regardless of how much output the project produces. One example is the in-home technical computer support business (discussed in Learning by Doing Application 12.1). Regardless of the number of house calls the technical support firm makes, it will incur the full cost of advertising. Variable costs are costs that depend on the number of units of output produced by the project. An example is the gas that the technical support firm uses to make house calls. The cost to keep the vehicles gassed up is directly related to the number of service calls the firm makes. LO: 1 Bloomcode: Knowledge AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

12.2

EBIT: Describe the role that the mix of variable versus fixed costs has in the variation of earnings before interest and taxes (EBIT) for the firm.

Solution: By definition, variable costs do not occur unless matching sales or matching revenues also occur, whereas fixed costs are not a function of the level of sales. Therefore, a large mix of fixed costs within a firm’s cost structure will make the firm’s EBIT very reactive to a change in the level of sales for the firm. The greater the proportion of fixed costs, (compared to variable costs), the greater the variability in EBIT for the firm. Copyright © 2022 John Wiley & Sons, Inc.

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LO: 1 Bloomcode: Comprehension AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

12.3

EBIT: The Generic Publications Textbook Company sells all of its books for $100 per book, and it currently costs $50 in variable costs to produce each text. The fixed costs, which include depreciation and amortization for the firm, are currently $2 million per year. Management is considering changing its production technology, which will increase the fixed costs for the firm by 50 percent but decrease the variable costs per unit by 50 percent. If management expects to sell 45,000 books next year, should they switch technologies?

Solution: The current EBIT for the firm is: Revenue

$100 per book × 45,000 books

$4,500,000

$50 per book × 45,000 books

2,250,000

FC + D&A

2,000,000

EBIT

$250,000

If the fixed costs increase by 50 percent, then they will be $2,000,000 × 1.5 = $3,000,000, while the unit variable costs would be 0.5 × $50 = $25. The new EBIT for the firm would then be: Revenue

$100 per book × 45,000 books

$4,500,000

$25 per book × 45,000 books

1,125,000

FC + D&A

3,000,000

EBIT

$375,000

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12.4

EBIT: WalkAbout Kangaroo Shoe Stores forecasts that it will sell 9,500 pairs of shoes next year. The firm buys its shoes for $50 per pair from the wholesaler and sells them for $75 per pair. If the firm will incur fixed costs plus depreciation and amortization of $100,000, then what is the percent increase in EBIT if the actual sales next year equal 11,500 pairs of shoes instead of 9,500?

Solution: The forecasted EBIT for the firm is: Revenue

$75 per pair × 9,500 pairs

$712,500

$50 per pair × 9,500 pairs

475,000

FC + D&A

100,000

EBIT

$137,500

The actual EBIT for the firm is: Revenue

$75 per pair × 11,500 pairs

$862,500

$50 per pair × 11,500 pairs

575,000

FC + D&A

100,000

EBIT

$187,500

Therefore, the percent increase in EBIT would be ($187,500 – $137,500) / $137,500 = 0.3636 = 36.36%. LO: 1 Bloomcode: Application AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

12.5

Cash Flow DOL: The law firm of Dewey, Cheatem, and Howe has monthly fixed costs of $100,000, EBIT of $250,000, and depreciation charges on its office furniture and computers of $5,000. Calculate the Cash Flow DOL for this firm.

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FC $100,000 =1+ = 1.392 EBITDA $250,000 + $5,000

LO: 2 Bloomcode: Application AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

12.6. Cash Flow DOL: The degree of pretax cash flow operating leverage at Rackit Corporation is 2.7 when it sells 100,000 units of its new tennis racket and its EBITDA is $95,000. Ignoring the effects of taxes, what are the fixed costs for Rackit Corporation? Solution: Cash Flow DOL = 1 +

FC = 2.7 EBITDA

FC $95,000 FC = $161,500 2.7 = 1 +

LO: 2 Bloomcode: Application AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector

12.7

Accounting DOL: Explain how the value of the degree of accounting operating leverage can be used.

Solution: The degree of accounting operating leverage gives us the ratio by which the firm can convert revenues into EBIT. That is, if the firm’s operating leverage is 3, then a 15 percent increase will convert to a 45 percent (15% x 3) increase in EBIT for the firm. LO: 2 Bloomcode: Comprehension Copyright © 2022 John Wiley & Sons, Inc.

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12.8

Accounting DOL: Caterpillar, Inc., is a manufacturer of large earth-moving and mining equipment. This firm and other heavy equipment manufacturers have degrees of accounting leverage that are relatively high. Explain why.

Solution: Caterpillar and other heavy equipment manufacturers are heavily dependent on assets in place, like manufacturing equipment and facilities, for production. These investments result in relatively high fixed costs and depreciation and amortization expenses compared to variable costs of production, leading to a high degree of accounting leverage. LO: 2 Bloomcode: Comprehension AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

12.9

Break-even analysis: Why is the per-unit contribution important in a break-even analysis?

Solution: Per-unit contribution is critical to break-even analysis in order for a firm to determine how many units are required to be sold to cover the firm’s fixed costs. The underlying known variable is the dollar amount of the contribution margin the firm will generate from each unit sold in order to make the above calculation. EBITDA Break-even = FC / (Price – Unit VC) and EBIT break-even = (FC + D&A) / (Price – Unit VC) demonstrate the calculation for EBITDA and EBIT break-even points respectively. The term in the denominator (Price-Unit VC) represents the per-unit cash flow contribution. LO: 3 Bloomcode: Comprehension Copyright © 2022 John Wiley & Sons, Inc.

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12.10 Break Even: Calculate the accounting operating profit break-even point and pretax operating cash flow break-even point for each of the three production choices outlined below. Choice

Price

Unit VC

D&A

$250

$160

$15,000

$3,000

$55

$10

$1,100

$200

$10

$1.50

$100

Solution:

Pretax Choice

Unit

Fixed

price

costs

D&A

EBIT

operating

breakeven*

cash flow breakeven**

$250

$160

$15,000

$3,000

200

167

$55

$10

$1,100

$200

$10

$1.50

$100

* EBIT breakeven = (Fixed Costs + D&A) / (Price – Unit VC) ** Pretax operating cash flow breakeven = Fixed Costs / (Price – Unit VC) LO: 3 Bloomcode: Application AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

12.11 Break-even point: The accounting operating profit break-even point tells us

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the number of units that must be sold for a firm to break-even in a given year from an accounting operating profit perspective. What measure tells us the number of units that must be sold each year during the life of a project in order for the project to break even with regards to its opportunity cost of capital? Solution: The accounting operating break-even point tells us the number of units that must be sold each year during the life of a project in order for the project to break even with regards to its opportunity cost of capital. Because the accounting operating break-even point calculation accounts for all cash flows over the life of a project, it enables us to compute the annual level of unit sales that will result in an NPV of $0. This is, by definition, the break-even point with regards to a project’s opportunity cost of capital. LO: 4 Bloomcode: Comprehension AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

12.12 Simulation analysis: What is simulation analysis, and how is it used? Solution: Simulation analysis is like scenario analysis except that in simulation analysis an analyst typically uses a computer to examine a large number of scenarios in a short period of time. Rather than selecting individual values for each of the assumptions—such as unit sales, unit price, and unit variable costs—the analyst assumes that those assumptions can be represented by statistical distributions. The computer then draws upon the distribution of each variable in order to generate an observation for a single scenario. After repeating the number of computer-generated scenarios, a distribution of cash flow outcomes will be generated, thereby offering the analyst the ability to perform a probability-based analysis on the cash flow distribution. LO: 4 Bloomcode: Knowledge Copyright © 2022 John Wiley & Sons, Inc.

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INTERMEDIATE 12.13 EBIT: If a manufacturing firm and a service firm have identical cash fixed costs, but the manufacturing firm has much higher depreciation and amortization, then which firm is more likely to have a large discrepancy between its FCF and its EBIT? Solution: Since depreciation and amortization are noncash items, the manufacturing firm would have the greatest discrepancy between FCF and EBIT. LO: 1 Bloomcode: Analysis AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

12.14 EBIT: Duplicate Footballs, Inc., expects to sell 15,000 balls this year. The balls sell for $110 each and have a variable cost per unit of $80. Fixed costs, including depreciation and amortization, are currently $220,000 per year. How much can either the fixed costs or the variable cost per unit increase before the company has a negative EBIT? Solution: The forecasted EBIT for the firm is: Revenue

$110 per ball × 15,000 balls

$1,650,000

$80 per ball × 15,000 balls

1,200,000

FC + D&A EBIT

220,000 $230,000

Therefore, the fixed costs could increase by $230,000 and still keep the EBIT from being negative. If we focus on the variable costs, we know that total variable costs could increase by $230,000. If that cost is spread over 15,000 units, then the variable cost per Copyright © 2022 John Wiley & Sons, Inc.

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unit could increase by ($230,000/ 15,000) = $15.33 and still keep the EBIT from being negative. Note that the analysis assumes that increases in either the fixed cost or the variable cost per unit will not change the other. This is probably not a realistic assumption. Excel Template available in Wiley Course Resources Excel Template Solution available in Wiley Instructor Resources LO: 1 Bloomcode: Analysis AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

12.15 EBIT: Specialty Light Bulbs anticipates selling 3,000 light bulbs this year at a price of $15 per bulb. It costs Specialty $10 in variable costs to produce each light bulb, and the fixed costs for the firm are $10,000. Specialty has an opportunity to sell an additional 1,000 bulbs next year at the same price and variable cost, but by doing so the firm will incur an additional fixed cost of $4,000. Should Specialty produce and sell the additional bulbs? Solution: The forecasted EBIT (Additional production) for the firm is: Revenue

$15 per bulb × 1,000 bulbs

$15,000

$10 per bulb × 1,000 bulbs

10,000

4,000

EBIT

$1,000

Since the EBIT is positive, then Specialty should produce and sell the additional bulbs. LO: 1 Bloomcode: Analysis AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

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12.16. Cash Flow DOL: The pretax operating cash flow of Memphis Motors declined so much during the recession of 2008 and 2009 that the company almost defaulted on its debt. The owner of the company wants to change the cost structure of his business so that this does not happen again. He has been able to reduce fixed costs from $500,000 to $300,000 and, in doing so, reduce the Cash Flow DOL for Memphis Motors from 3.0 to 2.2 with sales of $1,000,000 and pretax operating cash flow of $250,000. If sales declined by 20 percent from this level, how much more pretax operating cash flow would Memphis Motors have with the new cost structure than under the old? Solution: With the old cost structure, pretax operating cash flow would decline by 3.0 × 20% = 60% to $100,000 ($250,000 × (1 – 0.6)). With the new cost structure, pretax operating cash flow would decline by 2.2 × 20% = 44% to $140,000 ($250,000 × (1 – 0.44)).

Memphis Motors would have $40,000 more pretax operating cash flow under the cost new structure. LO: 2 Bloomcode: Application AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

12.17 Cash Flow DOL: For the Vinyl CD Co. in Self-Study Problem 12.3, what percentage increase in pretax operating cash flow will be driven by the additional revenue? Solution: Cash flow DOL

= 1 + (FC) / (EBIT + D&A) =1 + ($100,000) / ($90,000 + $80,000) = 1.59

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Use the following information for Problems 12.18, 12.19, and 12.20: Dandle’s Candles will be producing a new line of dripless candles in the coming years and has the choice of producing the candles in a large factory with a small number of workers or a small factory with a large number of workers. Each candle will be sold for $10. If the large factory is chosen, the cost per unit to produce each candle will be $2.50. The cost per unit will be $7.50 in the small factory. The large factory would have fixed cash costs of $2 million and a depreciation expense of $300,000 per year, while those expenses would be $500,000 and $100,000, respectively, in the small factory.

12.18 Accounting operating profit break-even: Calculate the accounting operating profit break-even point for both factory choices for Dandle’s Candles. Solution: The formula for the accounting operating profit break-even is: EBIT break-even = (FC + D&A) / (Price – Unit VC) For the large factory: EBIT break-even = ($2,000,000 + $300,000) / ($10 – $2.50) = 306,667 units For the small factory: EBIT break-even = ($500,000 + $100,000) / ($10 – $7.50) = 240,000 units LO: 3 Bloomcode: Application AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

12.19. Crossover level of unit sales: Calculate the number of candles for which the accounting operating profit at Dandle's Candles is the same regardless of the factory choice. Solution: Copyright © 2022 John Wiley & Sons, Inc.

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The formula for the crossover level of unit sales for EBIT (COEBIT) is: COEBIT =

COEBIT =

( FC + D&A )Alternative 1 − ( FC + D&A )Alternative 2 Unit Contribution Alternative 1 − Unit Contribution Alternative 2

$2,300,000 − $600,000 = 340, 000 units ( $10 − $2.5) − ($10 − $7.5 )

LO: 3 Bloomcode: Application AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

12.20 Pretax operating cash flow break-even: Calculate the pretax operating cash flow break-even point for both factory choices for Dandle’s Candles. Solution: The formula for the pretax operating cash flow break-even is: EBITDA Break-even = FC / (Price – Unit VC) and so the EBITDA break-even for the large factory is: EBITDA Break-even = $2,000,000/ ($10 – $2.5) = 266,667 units and the EBITDA break-even for the small factory is: EBITDA Break-even = $500,000/ ($10 – $7.5) = 200,000 units LO: 3 Bloomcode: Application AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

12.21 Accounting and cash flow break-even: Your analysis tells you that at a projected level of sales, a project your firm is considering will be below accounting break-even but above cash flow break-even. Explain why this might still be a viable project for your firm. Solution: Copyright © 2022 John Wiley & Sons, Inc.

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While the business may show an accounting loss, our focus should be on the cash flow gain or loss. The reason that the project will produce an accounting loss, but cash flow income is that the depreciation and amortization charges do not apply to the cash flow calculations as they are noncash expenses that help to reduce the tax liability. Therefore, the project is viable if it does not show a cash flow loss. LO: 3 Bloomcode: Analysis AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

12.22 Economic break-even point: Management of March and Dine Inc. has estimated that the firm’s new TV dinner project must generate $10,200 in FCF during each of the next six years to have an NPV of $0. Management anticipates that depreciation and amortization charges will equal $3,000, capital expenditures will equal $2,000, and additions to working capital will equal $500 during each of those years. What level of EBIT corresponds to an annual FCF of $10,200 if the firm is subject to a 30 percent marginal tax rate? Solution: From step 2 of the economic break-even point calculations described in the text, we can calculate the EBIT as follows: EBITt = (FCFt – D&At + Cap Expt + Add WCt)/ (1 – t) EBIT = ($10,200 - $3,000 + $2,000 + $500)/ (1 – 0.3) = $13,857.14 LO: 4 Bloomcode: Application AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

12.23 Economic break-even point: Rose Weiser Company Management is considering a project that will require an initial investment of $50,000 and will last for 10 years. No Copyright © 2022 John Wiley & Sons, Inc.

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other capital expenditures or increases in working capital are anticipated during the life of the project. What is the annual EBIT that will make project economically viable if the cost of capital for the project is 9 percent and the firm will depreciate the investment using straight-line depreciation and a salvage value of $0? Assume that the marginal tax rate is 24 percent. Solution: If the FCF are expected to be equal in each of the ten years, we can solve for FCF using the present value of an ordinary annuity formula: $50,000 = FCF

 1  1  → FCF = $7,791.00  1 − 0.09  (1.09 )10   

EBITt = (FCFt – D&At + Cap Exp t+ Add WCt)/ (1 – t) EBIT = ($7,791 - $5,000 + $0 + $0)/ (1 – 0.24) = $3,672 We can also use a financial calculator to solve this problem: N=10; I/Y=9; PV=-50,000; FV=0 → CPT → PMT=7,791.00 You may use a spreadsheet to solve this problem Excel Template available in Wiley Course Resources Excel Template Solution available in Wiley Instructor Resources LO: 4 Bloomcode: Application AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

12.24 Economic break-even point: The BowGus Archery Company management estimates that its new Galactically Flexible Bow project will have to generate EBIT of $20,000 each year to be viable. The project’s fixed cash expenses are expected to equal $8,000 and its depreciation and amortization expenses are expected to be $5,000 each year. If the new bows are expected to sell for $150 each and the variable cost to produce each bow is expected to be $100, then how many of these bows must the firm produce and sell each year to generate annual EBIT of $20,000? Solution Copyright © 2022 John Wiley & Sons, Inc.

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Using step 3 of the economic break-even point calculations described in the text, we can compute what the total contribution for the project must be: Revenue – VC = EBIT + D&A + FC = $20,000 + $5,000 + $8,000 = $33,000. From step 4, we know that we can divide this value by the contribution margin per unit to obtain the required number of units: $33,000/($150 - $100) = 660 units. LO: 4 Bloomcode: Application AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

12.25 Sensitivity and scenario analyses: Sensitivity analysis and scenario analysis are somewhat similar. Describe which is a more realistic method of analyzing the impact of different scenarios on a project. Solution: Sensitivity analysis captures the effect of a change in a single item such as unit selling price or a change in the number of units sold on a specific item such as EBIT. However, it is unlikely that a change in the selling price of an item will not affect the demand, and consequently the number of units sold, for the product in question. Scenario analysis analyzes the multiple effects of a scenario on an item such as EBIT by changing several interrelated variables at the same time to measure the effect of an entire scenario change. Therefore, scenario analysis is a much more practical tool for stress-testing a project. LO: 5 Bloomcode: Comprehension AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

12.26 Sensitivity analysis: Describe the circumstances under which sensitivity analysis might be a reasonable basis for determining changes to a firm’s EBIT or FCF. Copyright © 2022 John Wiley & Sons, Inc.

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Solution: Since sensitivity analysis assumes independence among variables (otherwise the analysis is too superficial), then that is the time when the analysis can yield the most meaningful results. One time when that might occur is if the sales level and product price are completely unaffected by movements in the other as with an industry monopoly. In a competitive market, such an assumption could yield disastrous results if they are followed without caution. LO: 5 Bloomcode: Comprehension AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective 12.27 Scenario analysis: Chip’s Home Brew Whiskey management forecasts that if the firm sells each bottle of Snake-Bite for $20, then the demand for the product will be 15,000 bottles per year, whereas sales will be 90 percent as high if the price is raised 10 percent. Chip’s variable cost per bottle is $10, and the total fixed cash cost for the year is $100,000. Depreciation and amortization charges are $20,000, and the firm has a 30 percent marginal tax rate. Management anticipates an increased working capital need of $3,000 for the year. What will be the effect of the price increase on the firm’s FCF for the year? Solution: If the firm increases its price to $22 per bottle, then it will sell 0.9 × 15,000 = 13,500 units next year. We can now find the effect of the change in price. Normal

Price Hike

Revenue

$300,000

$297,000 ($22 per bottle × 13,500)

Less: VC

150,000

135,000 ($10 per bottle × 13,500)

Less: FC

100,000

EBITDA

$ 50,000

$ 62,000

Less: D&A

20,000

$ 30,000

$ 42,000

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9,000

12,600

NOPAT

$ 21,000

$ 29,400

Add: D&A

20,000

CF Operations

$ 41,000

$ 49,400

Less: Add WC

3,000

$ 38,000

$ 46,400

FCF

By increasing the price of a bottle by 10 percent, the FCF increases by $8,400 from $38,000 to $46,400. Excel Template available in Wiley Course Resources Excel Template Solution available in Wiley Instructor Resources LO: 5 Bloomcode: Application AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

12.28 Sensitivity, scenario, and simulation analysis: If you were interested in calculating the probability that your project will have a positive FCF, what type of risk analysis tool will you most likely use? Solution: Sensitivity analysis can only manage a single movement in a modeled variable and can therefore only show the net impact of that movement. Scenario analysis is much more flexible and can quantify the impact of moving many interdependent variables at once, but it cannot produce confidence intervals for a given level of FCF. Simulation analysis begins with a distribution for the range of possible values for each variable. All of these modeled variables are then “freed up” to randomly move, all at the same time, within the modeled range in order to produce an individual observation. If this process is repeated a large number of times, then a distribution of observations is generated for the FCF value (or EBIT or a whole host of other calculations) in order to be able to make statistical inferences about the probability of achieving a given level of FCF. LO: 5 Copyright © 2022 John Wiley & Sons, Inc.

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ADVANCED 12.29 Mick’s Soft Lemonade is starting to develop a new product for which the cash fixed costs are expected to be $80,000. The projected EBIT is $100,000, and the Accounting DOL is expected to be 2.0. What is the Cash Flow DOL for the firm? Solution: Accounting DOL = 1 + (FC + D&A) / (EBIT) = 1 + ($80,000 + D&A) / $100,000 = 2 => D&A = $20,000 Cash flow DOL = 1 + (FC) / (EBIT + D&A) = 1 + ($80,000) / ($100,000 + $20,000) = 1.67 LO: 2 Bloomcode: Application AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

12.30 If a firm has a fixed asset base, meaning that its depreciation and amortization for any year is positive, discuss the relation between its Accounting DOL and its Cash flow DOL. Solution: By comparing the equations for the Accounting DOL and Cash Flow DOL: Accounting DOL = 1 + (FC + D&A) / (EBIT) Cash flow DOL = 1 + (FC) / (EBIT + D&A) We find that the denominator of the Cash Flow DOL will always be greater than the denominator of the Accounting DOL if depreciation and amortization is greater than zero. In addition, the numerator of the Cash Flow DOL will always be less than the Copyright © 2022 John Wiley & Sons, Inc.

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denominator of the Accounting DOL if depreciation and amortization is greater than zero. Therefore, if depreciation and amortization is positive, then Cash Flow DOL must be less than Accounting DOL. LO: 2 Bloomcode: Comprehension AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

12.31 Silver Polygon, Inc., has determined that if its revenues were to increase by 10 percent, then EBIT would increase by 25 percent to $100,000. The fixed costs (cash only) for the firm are $100,000. Given the same 10 percent increase in revenues, what would be the corresponding change in EBITDA? Solution: Since a 10 percent increase in revenue will drive a 25 percent corresponding increase in EBIT, then we know that Accounting DOL = 2.5. The new EBIT would be $100,000, after the 25 percent increase, so the original EBIT was$ 100,000 / (1 + 0.25) = $80,000. Therefore, Accounting DOL = 1 + (FC + D&A)/ (EBIT) = 2.5 = 1 + ($100,000 + D&A)/ ($80,000) = 2.5 ==> D&A = $20,000 Cash Flow DOL = 1 + (FC)/ (EBIT + D&A) = = 1 + ($100,000) / ($80,000 + $20,000) = 2.0 A 10 percent increase in revenue will drive a 20 percent increase in EBITDA. LO: 2 Bloomcode: Application AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

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12.32 If a firm’s costs (both variable and fixed) are known with certainty, then what are the only two sources of volatility for the firm’s operating profits or its operating cash flows? Solution: If the cost structure is known, then costs will only vary according to the firm’s unit sales. Therefore, one source of volatility would be net revenue uncertainty. The second source of volatility is based on the mix of variable and fixed costs within the firm’s cost structure. A higher mix of fixed costs would increase the operating leverage for a firm (both accounting and cash flow) and therefore increase the accounting profit and cash flow volatility for the firm. LO: 1 Bloomcode: Comprehension AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

12.33 In most circumstances, given the choice between a higher fixed-cost structure and a lower fixed-cost structure, which of the two would generate a larger contribution margin? Solution: The firm with the higher fixed cost should have a lower variable cost per unit, assuming that there is a trade-off. A lower variable cost per unit would then create a higher contribution margin for that firm. LO: 1 Bloomcode: Comprehension AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

12.34 Using the same logic as with the accounting break-even calculation in Problem 12.19, adapt the formula for the crossover level of unit sales to find the number of Copyright © 2022 John Wiley & Sons, Inc.

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units sold where the pretax operating cash flow is the same whether the firm chooses the large or small factory. Solution: The formula for the cross-over level of unit sales, based on accounting EBIT, is as follows: COEBIT =

( FC + D&A )Alternative 1 − ( FC + D&A )Alternative 2 Unit Contribution Alternative 1 − Unit Contribution Alternative 2

Eliminating D&A, since D&A are non-cash charges, gives us

COEBITDA =

FCAlternative 1 − FCAlternative 2 Unit Contribution Alternative 1 − Unit Contribution Alternative 2

COEBITDA =

$2,000,000 − $500,000 $1,500,000 = = 300, 000 units ($10 − $2.5) − ($10 − $7.5) $7.5 − $2.5

LO: 3 Bloomcode: Application AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

12.35 You are the project manager for Eagle Golf Corporation. You are considering manufacturing a new golf wedge with a unique groove design. You have put together the estimates in the following table about the potential demand for the new club, and the associated selling and manufacturing prices. You expect to sell the club for five years. The equipment required for the manufacturing process can be depreciated using straight- line depreciation over five years and will have a zero salvage value at the end of the project’s life. No additional capital expenditures are required. No new working capital is needed for the project. The required return for projects of this type is 12 percent, and the company has a 23 percent marginal tax rate. You estimate that there is a 50 percent chance the project will achieve the expected sales and a 25 percent chance of achieving either the weak or strong sales outcomes. Should you recommend the project? (Assume that the company is Copyright © 2022 John Wiley & Sons, Inc.

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profitable, so any losses associated with this project will reduce the total taxes for the firm.) Strong Sales

Expected Sales

Weak Sales

Units sold

15,000

10,000

7,000

Selling price per unit

$130

$120

$110

Variable costs per unit

$70

$65

$60

Fixed Costs per year

$258,000

Initial Investment

$1,000,000

Solution Expected unit sales = (0.25 × 15,000) + (0.50 × 10,000) + (0.25 × 7,000) = 10,500 units Expected unit price = (0.25 × $130) + (0.50 × $120) + (0.25 × $110) = $120 Expected unit variable cost = (0.25 × $70) + (0.50 × $65) + (0.25 × $60) = $65 Based on the expected values outlined below, the NPV of the project is $52,649 so it should be accepted. Opportunity cost of capital

12%

Tax rate

23%

Expected unit sales

10,500

Expected unit price

$120

Expected unit variable cost

$65

Fixed costs Initial investment D&A

$258,000 $1,000,000 $200,000

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1,260,000

−VC

682,500

−FC

258,000

EBITDA

319,500

−D&A

200,000

EBIT

119,500

-taxes

27,485

NOPAT

92,015

+D&A

200,000

CF Opns

292,015

Revenue

−Cap Exp

-1,000,000

−Add WC FCF

-1,000,000

NPV

52,649

Financial Calculator Solution: CF0 = -1,000,000 CF1 = 292,015; F1 = 5 NPV using the required return of 12% = 52,649 LO: 5 Bloomcode: Analysis AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

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12.36 You are working for Eagle Golf Corporation as described in Problem 12.35. A different equipment manufacturer is recommending its “Wedge 2100” club-making machine. The initial cost of the Wedge 2100 is $1,070,000, and the fixed costs of production will be $260,000 per year. However, because the Wedge 2100 is much more efficient than the original machine, its variable cost per unit will be $63. Assume that you will choose one of the two machines. (a) If the other financial information in Problem 12.35 applies, do you recommend the original machine or the Wedge 2100? (b) After seeing a news report that the demand for golf equipment is surging, your CFO believes that the most likely sales outcome is 15,000 units per year. Does the updated sales forecast change your recommendation? Solution: a) The NPV of the Wedge 2100 is $46,994 which is less than the original machine’s NPV of $52,649 (from Problem 12.35). Therefore, you would recommend the original machine. Opportunity cost of

12%

capital Tax rate

23%

Expected unit sales

10,500

Expected unit price

$120

Expected unit variable

$63

cost Fixed costs

$260,000 $1,070,00

Initial investment

D&A

$214,000

1,260,00

1,260,000

661,500

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-FC

260,000

EBITDA

338,500

−D&A

214,000

EBIT

124,500

-taxes

28,635

NOPAT

95,865

+D&A

214,000

CF Opns

309,865

−Cap Exp

-1,070,000

−Add WC

FCF

-1,070,000

309,865

NPV

46,994

b) At unit sales of 15,000 the NPV of the original machine is $947,805 while the NPV of the Wedge 2100 is $1,175,307. You would recommend the Wedge 2100 as it has the higher NPV.

Original machine: Opportunity cost of capital

12%

Tax rate

23%

Expected unit sales

15,000

Expected unit price

$130

Expected unit variable cost

$70

Fixed costs

$258,000

Initial investment

$1,000,000

D&A

$200,000

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Revenue

1,950,000

1,950,000 1,950,000 1,950,000 1,950,000

−VC

1,050,000

1,050,000 1,050,000 1,050,000 1,050,000

−FC

258,000

EBITDA

642,000

−D&A

200,000

EBIT

442,000

-taxes

101,660

NOPAT

340,340

+D&A

200,000

CF Opns

540,340

−Cap Exp

-1,000,000

−Add WC FCF

-1,000,000

NPV

947,805

Wedge 2100 Opportunity cost of capital

12%

Tax rate

23%

Expected unit sales

15,000

Expected unit price

$130

Expected unit variable cost

$70

Fixed costs

$260,000

Initital investment

$1,070,000

D&A

$214,000

0 Revenue

1,950,000 1,950,000 1,950,000 1,950,000 1,950,000

−VC

945,000

−FC

260,000

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EBITDA

745,000

−D&A

214,000

EBIT

531,000

-taxes

122,130

NOPAT

408,870

+D&A

214,000

CF Opns

622,870

FCF

-1,070,000 622,870

622,870

NPV

1,175,307

−Cap Exp

-1,070,000

−Add WC

LO: 5 Bloomcode: Analysis AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

12.37 Commodore Motors management is considering a project to produce toy cars. The project would require an initial outlay of $100,000 and have an expected life of 10 years. Management estimates that each year during the life of the project depreciation and amortization would be $8,000, capital expenditures would be $4,000, additions to working capital would be $2,000, and fixed costs would be $3,000. Also, each toy car would sell for $15 and cost $7 to produce. Finally, the cost of capital for the project would be 12 percent, cash flows from the project would be taxed at a 25 percent rate, and the assets would be depreciated to a salvage value of $0. How many units must be sold each year in order for this project to break-even from an economic standpoint? Solution: Step one: The required annual FCF is: Copyright © 2022 John Wiley & Sons, Inc.

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$100,000 = FCF

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 1  1  → FCF = $17,698.42  1 − 0.12  (1.12)10   

We can also use a financial calculator to solve this problem: N=10; I/Y=12; PV=-100,000; FV=0 → CPT → PMT=17,698.42 If using a spreadsheet to solve this problem: A

RATE

0.12

RATE

0.12

NPER

-100,000

PMT

=PMT(B1,B2, B3, B4)

PMT

$17,698,42

Step two: The required EBIT is: EBIT = (FCF – D&A + Cap Exp + Add WC)/ (1 – t) EBIT = ($17,698.42 - $8,000 + $4,000 + $2,000)/ (1 – 0.25) = $20,931.23 Step three: The required contribution is: Revenue – VC = EBIT + D&A + FC = $20,931.22 + $8,000 + $3,000 = $31,931.23 Step four: Economic break-even level of unit sales is: = $31,931.22/ ($15 – 7) = 3,991.4, or 3,992 cars LO: 4 Bloomcode: Analysis AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

CFA PROBLEMS 12.38. Operating leverage is a measure of the: a.

Sensitivity of net earnings to changes in operating earnings.

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Sensitivity of net earnings to changes in sales.

Sensitivity of fixed operating costs to changes in variable costs.

Sensitivity of earnings before interest and taxes to changes in the number of units produced and sold.

Solution: d is correct. Operating leverage is the sensitivity of earnings before interest and taxes to changes in the number of units produced and sold. The degree of operating leverage is the elasticity of operating earnings with respect to the number of units produced and sold. LO: 2 Bloomcode: Knowledge AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

12.39. The Fulcrum Company produces decorative swivel platforms for home televisions. If Fulcrum produces 40 million units, it estimates that it can sell them for $100 each. The variable production costs are $65 per unit, whereas the fixed production costs are $1.05 billion. Which of the following statements is true? a.

The Fulcrum Company produces a positive operating income if it produces and sells more than 25 million swivel platforms.

The Fulcrum Company’s degree of operating leverage is 1.333.

If the Fulcrum Company increases production and sales by 5 percent, its operating earnings are expected to increase by 20 percent.

Increasing the fixed production costs by 10 percent will result in a lower sensitivity of operating earnings to changes in units produced and sold.

Solution:

c is correct. Degree of operating leverage (DOL) =

40 million ($100 − $65) [40 million ($100 − $65)] − $1.05 billion

= $1.4 billion/$0.35 billion = 4

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Operating Break-even =

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$1.05 billion = 30 million units $35

Fulcrum produces positive operating income if it produces more than 30 million units. If it produces and sells fewer than 30 million, it will generate a loss. The DOL is 4. If unit sales increase by 5 percent, Fulcrum’s operating earnings are expected to increase by 4 × 5% = 20%. Increasing fixed production costs will increase the sensitivity of Fulcrum’s operating earnings to changes in sales. LO: 1 Bloomcode: Application AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

Sample Test Problems 12.1. Retro Inc. sells vintage football jerseys for $72 each. Variable costs are $58 per unit, and total fixed costs (including depreciation and amortization expense) are $84,000 per year. If sales for next year are expected to equal 8,000 jerseys, how much can variable costs per unit increase without EBIT becoming negative? Solution: The values in the problem statement indicate that the expected EBIT for Retro Inc. next year is: Revenue

$72 × 8,000 =

$576,000

$58 × 8,000 =

464,000

FC + D&A

84,000

EBIT

$28,000

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If the firm sells 8,000 jerseys, then the variable cost per unit could increase by as much as $3.50 ($28,000/8,000 units = $3.50 per unit). LO: 1 Bloomcode: Application AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

12.2

How would a capital-intensive company fare during good and poor economic times as compared with other companies? Explain. Solution: A capital-intensive company has a higher proportion of fixed costs and therefore higher operating leverage than less capital-intensive companies. High operating leverage causes the pretax operating cash flows and accounting profits to be more sensitive to changes in revenues. As a result, during good economic times these cash flows and profits will increase more and during poor economic times periods they will fall more than the corresponding measures at companies that have less operating leverage.

LO: 1 Bloomcode: Comprehension AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

12.3

The manager of Roy’s Restaurant has determined that if revenues were to increase by 20 percent, then EBIT would increase by 45 percent to $87,000. What would be the corresponding change in EBITDA if revenues increased 20 percent and cash fixed costs are $35,000? Solution: If a 20 percent increase in revenue causes a 45 percent increase in EBIT, Accounting DOL must equal 2.25. Also, since EBIT would be $87,000 after the 45 percent increase, the original EBIT was $87,000/(1 + 0.45) = $60,000. Therefore:

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Accounting DOL = 2.25 = 1 + (FC + D&A)/EBIT = 2.25 = 1 + ($35,000 + D&A)/$60,000 => D&A = $40,000 Cash Flow DOL = 1 + FC/(EBIT + D&A) = 1 + $35,000/($60,000 + $40,000) = 1.35 Which tells us that a 20 percent increase in revenues will result in a 27 percent (20 percent × 1.35 = 27 percent) increase in EBITDA. LO: 2 Bloomcode: Application AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

12.4

Luminosity Inc. produces modern light fixtures that sell for $150 per unit. The firm’s management is considering purchasing a high-capacity manufacturing machine. If the high-capacity machine is purchased, then the firm’s annual cash fixed costs will be $60,000 per year, variable costs will be $55 per unit, and annual depreciation and amortization expenses will equal $30,000. If the machine is not purchased, annual cash fixed costs will be $25,000, variable costs will be $105 per unit, and annual depreciation and amortization expenses will equal $10,000. What is the minimum level of unit sales necessary in order for EBIT with the high-capacity machine will be higher than EBIT without that machine? Solution: This question is asking for the crossover level of unit sales for EBIT, COEBIT. Using Equation 12.7 we find that:

COEBIT =

( FC + D&A )High capacity − ( FC + D&A )No high capacity Unit contribution High capacity − Unit contribution No high capacity

and so

COEBIT =

$90,000 − $35,000 = 1,100 units ($150 − $55) − ($150 − $105)

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Bloomcode: Application AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

12.5

Paper Christmas Trees Inc. is considering introducing a new line of inexpensive Christmas trees. The initial outlay for the project is $175,000, and the company will have to invest $5,000 in working capital and $10,000 in fixed assets each year during the six-year life of the project. The initial outlay will be depreciated assuming a salvage value of $0. Annual depreciation and amortization charges for the project will be $15,000 and cash-related fixed costs will be $6,000 per year. The firm will sell each tree for $75, and the variable cost to produce each tree will be $40. Calculate the number of trees that the firm must produce and sell in order to break even economically. Assume that the appropriate cost of capital for the project is 15 percent and that the marginal tax rate for the firm is 23 percent. Solution: Step one: The required annual FCF is: $175,000 = FCF 

1  1    FCF = $46,241.46  1 − 0.15  (1.15 )6   

Step two: The corresponding EBIT is: EBIT = (FCF – D&A + Cap Exp + Add WC)/ (1 - t) EBIT = ($46,241.46 – $15,000 + $10,000 + $5,000)/ (1 - 0.23) = $60,053.84 Step three: Therefore, the total contribution is: Revenue - VC = EBIT + D&A + FC = $60,053.84+ $5,000 + $6,000 = $71,053.84 Step four: Finally, the economic break-even level of sales is: $71,053.84/ ($75 – $40) = 2,030.11 or 2,031 trees. LO: 4 Bloomcode: Application AASCB: Analytic IMA: Business Economics Copyright © 2022 John Wiley & Sons, Inc.

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Chapter 11 Cash Flows and Capital Budgeting

Before You Go On Questions and Answers Section 11.1 1. Why do we care about incremental cash flows at the firm level when we evaluate a project? We care about incremental cash flows at the firm level because they reflect the impact of the project on a firm’s future investment outlays and cash flows from operations. This is what the stockholders care about. The NPV of a project is the difference between the present value of the expected cash flows from the firm with the project and the present value of the expected cash flows from the firm without the project. Our NPV estimate will be incorrect if we do not account for all of the incremental cash flows at the firm level.

2. Why is D&A first subtracted and then added back in FCF calculations? By subtracting D&A, calculating the tax obligation, and then adding back D&A, we are accounting for the fact that D&A is a noncash charge that reduces the firm’s tax obligation by the product of D&A and the tax rate (D&A x t). If we did not do this, we would overstate the tax obligation and understate FCF.

3. What types of investments should be included in FCF calculations? All investments directly associated with the project should be included in FCF calculations. These can include both investments in tangible and intangible assets. They can also include investments in additions to working capital, such as for the credit a firm extends to its customers and inventories.

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(1) Include cash flows and only cash flows in your calculations. (2) Include the impact of the project on cash flows from other product lines. (3) Include all opportunity costs. (4) Forget sunk costs. (5) Include only after-tax cash flows in the cash flow calculations.

2. What is the difference between nominal and real dollars? Why is it important not to mix them in an NPV analysis? When most people talk about dollar amounts, they are referring to nominal dollars. Nominal dollars do not take into account changes in purchasing power. Real dollars are dollar amounts that are adjusted for changes in purchasing power (or inflation). For example, 100 real dollars have the same purchasing power whether they are received today or at some future date. It is important not to mix nominal and real dollars in an NPV analysis because the discount rate is either a nominal rate, which is used to discount nominal dollars, or a real rate, which is used to discount real dollars. Since the discount rate must be either a nominal rate or a real rate, if real and nominal dollars are mixed in an NPV analysis, the NPV will be calculated incorrectly. 3. What is a progressive tax system? What is the difference between a firm’s marginal and average tax rates? A progressive tax system is one in which the marginal tax rate at low levels of income is lower than the marginal tax rate at high levels of income. A firm’s marginal tax rate is the rate that it pays on the last dollar earned while the average tax rate is the average rate paid on the firm’s total earnings (tax paid divided by taxable income). 4. How can FCF in the terminal year of a project’s life differ from FCF in the other years? FCF in the terminal year can differ from FCF in other years in several ways. The terminal year cash flows can include cash flows from the asset sales, including the actual proceeds from the sales themselves and taxes due or received if there is a gain or loss on the sale. Terminal year cash flows can also include cash flows associated with recovery of working capital.

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5. Why is it important to understand that cash flow forecasts in an NPV analysis are expected values? It is important to recognize that we are forecasting expected cash flows in an NPV analysis because uncertainties regarding future cash flows that are unique to the project should be reflected in the cash flow forecasts.

Section 11.3 1. What is the difference between variable and fixed costs, and what are examples of each? Variable costs vary directly with unit sales. Fixed costs do not vary with unit sales. For an example of each, see the video game player scenario on page 379. Variable costs are those associated with purchasing the components for the player, the labor required, and sales and marketing. These costs will vary according to the number of units produced. Fixed costs are those associated with assembly space, and administrative expenses.

2. How are working capital items forecast? Why are accounts receivable typically forecast as a percentage of revenue and accounts payable and inventories as percentages of the cost of goods sold? Working capital items are forecast using 1) cash and cash equivalents, 2) accounts receivable, 3) inventories, and 4) accounts payable. Accounts receivable are forecast as a percentage of revenue as this represents the amount of money that must be set aside to finance purchases by customers. Inventories are forecast as a percentage of the cost of goods sold because the COGS represent a measure of the amount of money invested in inventories. Accounts payable are also forecast this way because the COGS is a measure of the amount of money owed to suppliers.

Section 11.4 1. When can we not simply compare the NPVs of two mutually exclusive projects? If we expect to replace at least one of the projects at the end of its life, we cannot simply compare the NPVs. Doing so would ignore the subsequent investment(s). You can only directly compare the NPVs of mutually exclusive projects under one condition—that is, if you expect to Copyright © 2022 John Wiley & Sons, Inc.

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terminate the project that is chosen (e.g., sell the lawn mower) on or before the end of the life of the shorter-lived project.

2. When choosing between mutually exclusive projects of unequal lives, how can we ensure that the best decision is made? We can effectively make the lives of mutually exclusive projects equal by repeating one or both investments and comparing the Net Present Values of both projects, or by creating the Equivalent Annual Cost (EAC) of both projects and choosing the less expensive one.

3. How do we decide when to harvest an asset? We choose the harvest date that maximizes the NPV of the asset. To identify this date, we compare the NPVs expected from harvesting the asset for each of the feasible harvest dates. The best date to harvest the asset is the date that produces the largest NPV, once the NPVs for all of the alternative harvest dates have been discounted to the same point in time.

4. Under what circumstance would you replace an old machine that is still operating with a new one? You should replace the old machine when the EAC of the new machine is lower than the EAC of the old machine (if revenues are the same for both machines) or when the annualized cash inflow from the replacement is greater.

Self-Study Problems 11.1

Explain why the announcement of a new investment is usually accompanied by a change in the firm’s stock price.

Solution: A firm’s investments cause changes in its future after-tax cash flows and stockholders are the residual claimants (owners) of those cash flows. Therefore, the stock price should increase when stockholders expect an investment to have a positive NPV and decrease when it is expected to have a negative NPV. Copyright © 2022 John Wiley & Sons, Inc.

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In calculating the NPV of a project, should we use all of the after-tax cash flows associated with the project, or incremental after-tax cash flows from the project? Why?

Solution: We should use incremental cash flows of the project. Incremental cash flows reflect the amount by which the firm’s total cash flows will change if the project is adopted. In other words, incremental cash flows represent the net difference in cash revenues, costs, and investment outlays (in net working capital and capital expenditures) at the firm level with and without the project, which is precisely what the stockholders care about.

11.3

You are considering opening a new restaurant in the Texas Burgers chain. The new restaurant will have annual revenue of $300,000 and operating expenses of $150,000. The annual depreciation and amortization for the assets used in the restaurant will equal $50,000. An annual capital expenditure of $10,000 will be required to offset wearand-tear on the assets used in the restaurant, but no additions to working capital will be required. The marginal tax rate will be 40 percent. Calculate the incremental annual free cash flow for the project.

Solution: The incremental annual free cash flow is calculated as:

11.4

Sunglass Heaven, Inc., is launching a new store in a shopping mall in Houston. The annual revenue of the store depends on the weather conditions in the summer in Houston. The annual revenue will be $240,000 in a sizzling summer, with probability of 0.3; $80,000 in a cool summer, with probability of 0.2; and $150,000 in a normal summer, with probability of 0.5. What is the expected annual revenue of the store?

Solution: The expected annual revenue is: E(Revenue) = (0.3 × $240,000) + (0.2 × $80,000) + (0.5 × $150,000) = $163,000

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Sprigg Lane Manufacturing, Inc., needs to purchase a new central air-conditioning system for a plant. There are two choices. The first system costs $50,000 and is expected to last 10 years, and the second system costs $72,000 and is expected to last 15 years. Assume that the opportunity cost of capital is 10 percent. Which air-conditioning system should Sprigg Lane purchase?

Solution: The equivalent annual cost for each system is:

(1.1)10 EAC1 = ( 0.1 )( $50, 000 ) = $8,137.27 (1.1)10 − 1 EAC2 = ( 0.1 )( $72, 000 )

(1.1)15 = $9, 466.11 (1.1)15 − 1

Therefore, Sprigg Lane should purchase the first one.

Discussion Questions 11.1

Do you agree or disagree with the following statement, given the discussion in this chapter? We can calculate future cash flows precisely and obtain an exact value for the NPV of an investment. The statement is not true. The nature of the real business world includes those risks which cannot be forecasted or foreseen such as changes in a nation’s economic policy, fluctuation in inflation and interest rates and the like. Given this, it is almost certain that the cash flows generated by a project will differ from the forecasts used to decide whether to proceed with the project. However, techniques discussed in this chapter provide an important and useful framework that helps minimize errors and ensures that forecasts are internally consistent.

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AICPA: Industry/Sector Perspective

11.2

What are the differences between cash flows used in capital budgeting calculations and past accounting earnings? Cash flows used in capital budgeting calculations are forward looking; they are incremental after-tax cash flows based on forecasts. Accounting earnings are backward looking; they represent a record of past performance and may not accurately reflect cash flows.

LO: 1 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.3

Suppose that FRA Corporation already has divisions in both Dallas and Houston. FRA is now considering setting up a third division in Austin. This expansion will require that one senior manager from Dallas and one from Houston relocate to Austin. Ignore relocation expenses. Is their annual compensation relevant to the decision to expand? The annual compensations of existing senior managers are not incremental to the new investment and therefore are not relevant for capital budgeting analysis. This is consistent with our Rule 1 for incremental cash flow calculations: Include cash flows and only cash flows; do not include allocated costs unless they reflect cash flows.

LO: 1, 2 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.4

MusicHeaven, Inc., is a producer of media players which currently have either 20 gigabytes or 30 gigabytes of storage. Now the company is considering launching a new

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production line making mini media players with 5 gigabytes of storage. Analysts forecast that MusicHeaven will be able to sell 1 million such mini media players if the investment is made. In making the investment decision, discuss what the company should consider other than the sales of the mini media players. The company’s launch of the new mini media players may reduce its current sales of media players of bigger storage. This impact has to be considered. This is consistent with our Rule 2 for incremental cash flow calculations: Include the impact of the project on cash flows from other product lines. LO: 1, 2 Level: Basic Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.5

Quality Living Trust is a real estate investment company that builds and remodels apartment buildings in northern California. It is currently considering remodeling a few idle buildings that it owns in San Jose into luxury apartment buildings. The company bought those buildings eight months ago. How should the market value of the buildings be treated in evaluating this project? Although the buildings are not currently in use, the company can sell them at their market value rather than remodel them into apartments. Therefore, the market value of the buildings is the opportunity cost of the project and should be considered as a cash outflow in the investment decision. This is consistent with our Rule 3 for incremental cash flow calculations: Include all opportunity costs.

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High-End Fashions, Inc., bought a production line of ankle-length skirts last year at a cost of $500,000. This year, however, miniskirts are in and ankle-length skirts are completely out of fashion. High-End has the option to rebuild the production line and use it to produce miniskirts with an annual operating cost of $300,000 and expected revenue of $700,000. How should the company treat the $500,000 cost of the old production line in evaluating the rebuilding plan? The cost of the old production line occurred in the past. It cannot be changed whether or not the company rebuilds it into the miniskirt production line. Therefore, High-End should not consider the cost of $500,000. This is consistent with our Rule 4 for incremental cash flow calculations: Forget sunk costs.

LO: 1, 2 Level: Basic Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.7

How is the MACRS depreciation method under IRS rules different from the straightline depreciation allowed under GAAP rules? What is the implication for incremental after-tax free cash flows from firms’ investments? GAAP allows the straight-line depreciation method. In contrast, an “accelerated” method of depreciation, Modified Accelerated Cost Recovery System (MACRS), has been used for U.S. federal tax calculations. The advantage of MACRS, relative to straight-line depreciation, is that it enables a firm to deduct depreciation changes sooner, thereby realizing the tax saving sooner and increasing the present value of the tax savings.

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11.8

Explain the difference between marginal and average tax rates, and identify which of these rates is used in capital budgeting and why? The marginal tax rate is the rate paid on the next dollar earned. The average tax rate is the dollar value of total taxes paid divided by total income. The marginal tax rate is the appropriate rate to use in capital budgeting analysis because this is the tax rate that will be paid on the incremental income earned by the project.

LO: 2 Level: Basic Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.9

Under what circumstances will the sale of an asset result in a taxable gain? How do you estimate the taxes or tax benefits associated with the sale of an asset? The sale of an asset results in a taxable gain when the selling price of the asset exceeds its book value. Tax on the sale of an asset = (Selling price of asset – Book value of asset) × Tax rate (t)

LO: 2 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.10 When two mutually exclusive projects have different lives, how can an analyst determine which is better? What is the underlying assumption in this method? When we choose from mutually exclusive projects with different lives, instead of electing the project with higher NPV or lower net present value of costs, we should choose the Copyright © 2022 John Wiley & Sons, Inc.

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project with higher Equivalent Annual Revenue or lower Equivalent Annual Cost. The underlying assumption is that we will continue to operate with the same equivalent annual revenue or equivalent annual cost in the future. LO: 4 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.11 What is the opportunity cost of using an existing asset? Give an example of the opportunity cost of using the excess capacity of a machine. The opportunity cost of using an existing asset in a project is the present value of the change in the firm’s cash flows that is attributed to the fact that this asset is being used in the project. For example, by using the excess capacity of a machine, you may accelerate the wear-andtear of the machine and hence will need to replace it sooner. The present value of the added annualized costs is the opportunity cost of using the excess capacity. LO: 4 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.12 You are providing financial advice to a shrimp farmer who will be harvesting his last crop of farm-raised shrimp. His crop is very young and will, therefore, grow, and become more valuable as the shrimps’ weight increases. Describe how you would determine the appropriate time to harvest the shrimp. Assuming that the price of shrimp is directly (and linearly) related to the weight of the shrimp, then the optimal point in time to harvest the shrimp would be where the rate of weight increase is no longer greater than the opportunity cost of capital for the shrimp Copyright © 2022 John Wiley & Sons, Inc.

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farmer. Alternatively, the appropriate time is when the value increase of the shrimp is no longer greater than the opportunity cost of capital. LO: 5 Level: Basic Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

Questions and Problems BASIC 11.1 Calculating project cash flows: Why do we use forecasted incremental after-tax free cash flows instead of forecasted accounting earnings in estimating the NPV of a project? Solution: Accounting earnings can differ from cash flows for a number of reasons, making accounting earnings an unreliable measure of the costs and benefits of a project. For example, ease of manipulating earnings components such as accounts receivable and depreciation may result in distorted estimation of capital budgeting; using forecasted cash flows eliminates such possibilities. In addition, because there is time value of money, cash flows better reflect the actual available funds to be distributed to shareholders at each point in time. LO: 1 Bloomcode: Comprehension AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.2 The FCF calculation: How do we calculate incremental after-tax free cash flows from forecasted earnings of a project? What are the common adjustment items? Solution: Copyright © 2022 John Wiley & Sons, Inc.

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We need to adjust for the depreciation and amortization tax shield, capital expenditures, and changes in working capital (including receivables and payables). LO: 2 Bloomcode: Comprehension AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.3 The FCF calculation: How do we adjust for depreciation when we calculate incremental after-tax free cash flow from EBITDA? What is the intuition for the adjustment? Solution: There are two ways to adjust for depreciation: (1) subtract depreciation from EBITDA, multiply it by (1 – tax rate), and then add depreciation back; (2) add the tax shield from depreciation (depreciation multiplied by tax rate) to revenue. These two methods yield the same results. The intuition is that although depreciation itself is not a cash inflow or outflow, an increase in depreciation will result in a decrease in taxable income. This saving on tax is treated as a cash inflow in calculating incremental after-tax free cash flows. LO: 2 Bloomcode: Comprehension AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.4

Nominal versus real cash flows: What is the difference between nominal and real cash flows? Which rate of return should we use to discount each type of cash flow?

Solution: Nominal cash flows are cash flows stated as we usually think of them. They represent the actual cash flow that we expect a project to generate in the future, without any adjustment, for changes in purchasing power over time. Real cash flows are cash flows stated so that their purchasing power remains constant. We should use nominal rate of return to discount future

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nominal cash flows and real rate of return to discount future real cash flows. By doing this, we will get meaningful present values of cash flows and purchasing power. LO: 2 Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.5

Taxes and depreciation: What is the difference between average tax rate and the marginal tax rate? Which one should we use in calculating incremental after-tax cash flows?

Solution: The average tax rate is the total amount of tax divided by total amount of money earned, while the marginal tax rate is the rate paid on the last dollar earned. In a progressive tax system, the marginal tax rate will differ from the average tax rate. Since a firm already pays taxes, the appropriate tax rate used for the firm’s new project is the tax rate that the firm will pay on any additional profits that are earned because the project is adopted. Therefore, we use the marginal tax rate in calculating incremental after-tax cash flows. LO: 2 Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.6

Computing terminal-year FCF: Healthy Potions, Inc., a pharmaceutical company, bought a machine at a cost of $2 million five years ago that produces pain-reliever medicine. The machine has been depreciated over the past five years, and the current book value is $800,000. The company decides to sell the machine now at its market price of $1 million. The marginal tax rate is 30 percent. What are the relevant cash flows? How do they change if the market price of the machine is $600,000 instead?

Solution:

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The relevant cash flows include the sale price of the machine, as well as the tax on the capital gain: $1,000,000 – 0.3 × ($1,000,000 – $800,000) = $940,000 When the market price of the machine is changed to $600,000, the relevant cash flows include the sale price and tax saving on capital loss: $600,000 + 0.3 × ($800,000 – $600,000) = $660,000 LO: 2 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.7

Cash flows from operations: What are variable costs and fixed costs? What are some examples of each? How are these costs estimated in forecasting operating expenses?

Solution: Variable costs vary directly with unit sales, while fixed costs do not. Variable costs are those associated with purchasing the components for the product, the labor required, and sales and marketing. These costs will vary according to the number of units produced. Fixed costs are those associated with assembly space, and administrative expenses. LO: 3 Bloomcode: Analysis AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

11.8

Cash flows from operations: When forecasting operating expenses, explain the difference between a fixed cost and a variable cost.

Solution: While forecasting operating expenses, fixed costs are based on the cost of manufacturing space, administrative expenses required for administration of the project, and so forth. While variable costs vary directly with the number of units sold, they can be forecasted by Copyright © 2022 John Wiley & Sons, Inc.

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multiplying the variable cost per unit (that has been estimated to be produced) by the number of units expected to be sold each year. LO: 3 Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.9

Investment cash flows: Zippy Corporation just purchased computing equipment for $20,000. The equipment will be depreciated using a five-year MACRS depreciation schedule. If the equipment is sold at the end of its fourth year for $12,000, what are the aftertax proceeds from the sale, assuming the marginal tax rate is 30 percent??

Solution: The 5-year depreciation schedule allows us to depreciate 20 percent of the value of the equipment in year 1, 32 percent in year two, 19.20 percent in year 3, and 11.52 percent in year four after the purchase. The associated depreciation charges in years 1 through 4 in order are $4,000, $6,400, $ 3,840, and $2,304, respectively. Total depreciation at the end of year 4 is $16,544, so the book value of the equipment when sold is $3,456. Since the equipment is sold for $12,000 the tax on the sale of the asset is equal to ($12,000-$3,456) × 0.30 = $2,563.20. The total after tax proceeds are $12,000 - $2,563.20 = $9,436.80 LO: 2 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.10 Investment cash flows: Six Twelve, Inc., is considering opening up a new convenience store in downtown New York City. The expected annual revenue at the new store is $800,000. To estimate the increase in working capital, analysts estimate that for firms in the same industry the ratio of cash and cash-equivalents to revenue is 0.03 and the ratios of receivables, inventories, and payables to revenue are 0.05, 0.10, and 0.04, respectively. Applying these Copyright © 2022 John Wiley & Sons, Inc.

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industry estimates to Six Twelve, Inc., what is the expected incremental cash flow related to working capital when the store is opened? Solution: Cash flow related to working capital in year0 = $800,000 × (0.03 + 0.05 + 0.10 - 0.04) = $112,000 LO: 2 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.11 Investment cash flows: Keswick Supply Company wants to set up a division that provides copy and fax services to businesses. Customers will be given 20 days to pay for such services. The annual revenue of the division is estimated to be $25,000. Assuming that the customers take the full 20 days to pay, what is the incremental cash flow associated with accounts receivable? Solution: The average accounts receivable balance will be (20days/365days/year) ×100% ×25,000 = 5.48% × 25,000 = $1,370.

Alternatively, the average daily credit sale = $25,000 / 365 = $68.49, and it takes 20 days, on average, to collect the sale.

Therefore, the incremental cash flow related to working capital when the store is opened: 20 × $68.49 = $1,369.86, or about $1,370. LO: 2 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

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11.12 Expected cash flows: Define expected cash flows, and explain why this concept is important in evaluating projects. Solution: Expected cash flows are probability-weighted averages of the future cash flows generated by a project under alternative scenarios. In the real business world, there are a lot of uncertainties. Future cash flows may vary across different states of the world. It is not possible to estimate a unique number of cash flow for all states. We can estimate the expected cash flows across different states and use that as an estimation of future cash flows. The cash flows that are discounted in an NPV analysis are the expected incremental cash flows the project will produce. LO: 2 Bloomcode: Knowledge AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.13 Projects with different lives: Explain the concept of equivalent annual cost and how it is used to compare projects with different lives. Solution: The equivalent annual cost (EAC) is the annualized cost of an investment stated in nominal dollars. In other words, it is the annual payment from an annuity with a life equal to that of a project that has the same NPV as the project. Since it is a measure of the annual cost or cash inflow from a project, the EAC for one project can be compared directly with the EAC from another project, regardless of the lives of those two projects. LO: 4 Bloomcode: Comprehension AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

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11.14. Replace an existing asset: Explain how we determine the optimal time to replace an existing asset with a new one. Solution: The optimal time to replace an existing asset with a new one is if the benefits of replacing the machine exceed the costs. LO: 4 Bloomcode: Comprehension AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.15. Projects with different lives: If you had to choose between one project with an expected life of five years and a second project with an expected life of six years, how could you do this without using the equivalent annual cost concept? Solution: You can effectively make the lives of the projects the same by assuming repeated investments over some identical period and compare the NPVs. LO: 4 Bloomcode: Comprehension AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

INTERMEDIATE 11.16 Nominal versus real cash flows: You are buying a sofa. You will pay $200 today and make three consecutive annual payments of $300 in the future. The real rate of return is 10 percent, and the expected inflation rate is 4 percent. What is the actual price of the sofa? Solution: We can calculate it in two different ways: (1)

Use nominal dollars and nominal rate of return:

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Nominal rate of return = (1 + 10%) × (1 + 4%) - 1 = 14.4% Price = 200 + 300/ (1 + 14.4%) + 300/ (1 + 14.4%)2 + 300/ (1 + 14.4%)3 = $891.84

Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: Cash Flow (C)

Frequency (F)

200

300

Then solve by pressing NPV, enter the rate of 14.4% and compute NPV= 891.84

(2)

Use real dollars and a real rate of return: Real annual payments are: 300/ (1 + 4%) = 288.46, 300/ (1 + 4%)2 = 277.37, and 300/ (1 + 4%)3 = 266.70 Price = 200 + 288.46/ (1 + 10%) + 277.37/ (1 + 10%)2+266.7/ (1+10%)3 =891.84

Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: Cash Flow (C)

Frequency (F)

200

288.46

277.37

266.7

Then solve by pressing NPV, enter the rate of 10% and compute NPV= 891.84 Note that we get identical results as long as we are consistent in using nominal or real cash flows and corresponding discount rates. LO: 2 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions Copyright © 2022 John Wiley & Sons, Inc.

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AICPA: Industry/Sector Perspective

11.17 Nominal versus real cash flows: You are graduating in two years. You want to invest your current savings of $5,000 in bonds and use the proceeds to purchase a new car when you graduate. You can invest the money in either Bond A, a two-year bond with a 3 percent annual interest rate, or Bond B, an inflation-indexed two-year bond paying 1 percent real interest above the inflation rate (assume this bond makes annual interest payments). The inflation rate over the next two years is expected to be 1.5 percent. Assume that both bonds are default free and have the same market price. Which bond should you invest in? Solution: The nominal interest rate is 3 percent for bond A, and (1 + 1%) × (1 +1.5%) – 1 = 2.52% for the inflation-indexed bond B. You should invest in bond A. LO: 2 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.18 Marginal and average tax rates. MoCo, Inc., operates in a state where companies face a tax rate of 9 percent on taxable income up to $1,000,000 and 10.5 percent on taxable income above $1,000,000. Assume the federal tax rate is a flat 21 percent and MoCo, Inc., will have taxable income of $1,500,000 for the year. What is the firm’s average blended federal and state tax rate? What is the firm’s marginal blended federal and state tax rate? If MoCo, Inc., is evaluating a new investment, what tax rate should it use for NPV calculations? Solution: MoCo, Inc., will owe federal taxes of (0.21 × $1,500,000) = $315,000

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= $90,000

10.5 percent on taxable income over $1,000,000: = (0.105 × ($1,500,000-$1,000,000)) = (0.105 × $500,000) = $52,500

For a total state tax of $90,000 + $52,500 = $142,500

Total federal and state taxes are: $315,000 + $142,500 = $457,500

The average blended state and federal tax rate is the total taxes payable divided by total taxable income: = $457,500 / $1,500,000 = 0.305 or 30.5 percent

The blended marginal federal and state tax rate is the federal 21 percent plus the 10.5 percent state tax rate (as the firm already has taxable income over $1,000,000 it faces the higher 10.5 percent state tax rate) for a blended marginal rate of 31.5 percent.

When evaluating a new investment MoCo, Inc., should use the blended marginal rate of 31.5 percent as that is the tax rate they will face on the next dollar of taxable income. LO: 2 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.19 Investment cash flows: Healthy Potions, Inc., is considering investing in a new production line for eye drops. Other than investing in the equipment, the company needs to increase its cash and cash equivalents by $10,000, increase the level of inventory by $30,000, increase Copyright © 2022 John Wiley & Sons, Inc.

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accounts receivable by $25,000, and increase accounts payable by $5,000 at the beginning of the project. Healthy Potions will recover these changes in working capital at the end of the project 10 years later. Assume the appropriate discount rate is 12 percent. What are the present values of the relevant investment cash flows? Solution: The relevant cash flow related to working capital at the beginning of the project is: $10,000 +$30,000+$25,000 - $5,000 = $60,000 The present value of relevant cash flow related to working capital at the end of the project is: $60,000 / (1 + 0.12)10 = $19,318.39 LO: 1 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.20 Cash flows from operations: Given the desire to cut carbon emissions, Ford is considering introducing a new production line of electric sedans. The expected annual unit sales of the electric cars is 30,000, and the selling price is $22,000 per car. Variable costs of production are $10,000 per car. The fixed overhead, including salary of top executives, is $80 million per year. However, the introduction of the electric sedans will decrease Ford’s sales of regular sedans by 10,000 cars per year; the regular sedans have a unit price of $20,000, a unit variable cost of $12,000, and fixed costs of $250,000 per year. Depreciation costs of the new production line are $50,000 per year. The marginal tax rate is 29 percent. What is the incremental annual cash flow from operations? Solution: Step One: Revenue: $22,000 × 30,000 cars =$660,000,000 Step Two: Op Exp: $10,000 × 30,000 cars = $300,000,000, plus lost net revenue from regular sedans = ($20,000 – $12,000) × 10,000 cars = $80,000,000; total Op Exp = $380,000,000 Step Three: D&A: $50,000 Step Four: Plug information into the textbook template as below. Change in: Copyright © 2022 John Wiley & Sons, Inc.

$ SM 11-23

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Revenue

660,000,000

−Op Ex

380,000,000

EBITDA

280,000,000

−D&A

50,000

EBIT

279,950,000

×(1 − t)

0.71

NOPAT

198,764,500

+D&A

50,000

CF Opns

198,814,500

−Cap Exp

−Add WC

FCF

198,814,500

Alternatively, the incremental annual cash flow from operations is: (($22,000-$10,000) ×30,000-($20,000-$12,000) ×10,000) × (1-0.29) + $50,000 ×0.29 = $168,020,000 Note that the fixed costs are not included in the incremental cash flow calculations, since they exist regardless of the investment in the new production line. LO: 3 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.21 FCF and NPV for a project: Archer Daniels Midland Company is considering buying a new farm that it plans to operate for 10 years. The farm will require an initial investment of $12 million. This investment will consist of $2 million for land and $10 million for trucks and other equipment. The land, all trucks, and all other equipment are expected to be sold at the end of 10 years for a price of $5 million, which is $2 million above book value. The farm is expected to produce revenue of $2 million each year, and annual cash flow from operations

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equals $1.8 million. The marginal tax rate is 25 percent, and the appropriate discount rate is 10 percent. Calculate the NPV of this investment. Solution: Cash flow of investment in year 0 is: $(12,000,000) Annual cash flows from operations = $1,800,000 Present value of free cash flows: PV (FCF1-10 ) = Annual CF PV Annuity factor  1  10    1 − (1.10 )   = –$1, 800, 000     0.10       = $11, 060, 220.79

Financial Calculator Solution:

-1,800,000

PMT

11,060,220.79

Book value of asset = $3,000,000 Sale price of asset = $5,000,000 Tax on sale of an asset = (Selling price of asset - Book value of asset) × t = $2,000,000 × 0.25 = $500,000 PV of after-tax salvage value in year 10 is:

( $5, 000, 000 − $500, 000 )  10

(1.10 )

= $1,734, 944.80

-4,500,000

PMT

1,734,944.80

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NPV = −$12, 000, 000 + $11, 060,220.79 + $1,734, 944.80 = $795,165.59 Since NPV > 0, project should be accepted. LO: 1 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.22 Projects with different lives: You are trying to choose between purchasing one of two machines for a factory. Machine A costs $15,000 to purchase and has a three-year life. Machine B costs $17,700 to purchase but has a four-year life. Regardless of which machine you purchase, it will have to be replaced at the end of its operating life. Which machine should you choose? Assume a marginal tax rate of 21 percent and a discount rate of 15 percent. Solution: Since the machines have difference purchase costs and different operating lives, you should choose the machine that has the lowest equivalent annual cost (EAC).

 ( 1 + k )t  EACA = k NPVA   t  (1 + k ) − 1 

(1.15 ) = −$6,569.65 = ( 0.15 )( −$15,000 )  3 (1.15 ) − 1 3

(1.15)4 EACB = ( 0.15 )( −$17,700 ) = −$6,199.70 (1.15)4 − 1 You should choose machine B because it has the lower equivalent annual cost. LO: 4 Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions Copyright © 2022 John Wiley & Sons, Inc.

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AICPA: Industry/Sector Perspective

11.23 Projects with different lives: You are starting a family pizza parlor and need to buy a motorcycle for delivery orders. You have two models in mind. Model A costs $9,000 and is expected to run for 6 years; Model B is more expensive, with a price of $14,000, and has an expected life of 10 years. The annual maintenance costs are $800 for Model A and $700 for Model B. Assume that the opportunity cost of capital is 10 percent. Which one should you buy? Solution: You need to first calculate the NPV of costs for each of the motorcycles:

1   1−  (1.10)6  NPVA = −$9, 000 + ( −$800 )   = −$12, 484.21 0.10     Financial Calculator Solution:

Using a financial calculator, enter the cash flows as follows: Motorcycle A

Cash Flow (C)

Frequency (F)

-9,000

-800

Then solve by pressing NPV, enter the rate of 10% and compute NPV=-12,484.21.

1   1−  (1.10)10  NPVB = −$14, 000 + ( −$700 )   = −$18, 301.20 0.10    

Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: Motorcycle A

Cash Flow (C)

Frequency (F)

-14,000

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-700

Then solve by pressing NPV, enter the rate of 10% and compute NPV=-18,301.20 Then you need to calculate the EAC of each model:

 (1 + k )t  EACA = k NPVA   t  (1 + k ) − 1 

(1.10 ) = −$2,866.47 = ( 0.10 )( −$12, 484.21 )  6 (1.10 ) − 1 6

Financial Calculator Solution: 6

-12,484.21

0 PMT

2,866.47

(1.10)10 EACB = ( 0.10 )( −$18,301.20 )  = −$2,978.44 (1.10)10 − 1 Financial Calculator Solution: 10

-18,301.20

0 PMT

2,978.44

Since EAC is lower for Model A, you should buy Model A. LO: 4 Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.24 When to harvest an asset: Predator LLC, a leveraged-buyout specialist, recently bought a company and wants to determine the optimal time to sell it. The partner in charge of this investment has estimated the after-tax cash flows from a sale at different times to be as Copyright © 2022 John Wiley & Sons, Inc.

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follows: $700,000 if sold one year later; $1,000,000 if sold two years later; $1,200,000 if sold three years later; and $1,300,000 if sold four years later. The opportunity cost of capital is 12 percent. When should Predator sell the company? Why? Solution: The NPV of each choice is: NPV1 = $700,000/ (1.12)1 = $625,000 NPV2 = $1,000,000/ (1.12)2 = $797,194 NPV3 = $1,200,000/ (1.12)3 = $854,136 NPV4 = $1,300,000/ (1.12)4 = $826,174 Selling the company in 3 years provides the highest NPV. If we calculate the difference in the original NPV values we can see that they increase by 43 percent from year 1 to 2, 20 percent from year 2 to 3, and 8 percent from year 3 to 4. So the optimal time to harvest is the year prior to the year during which the rate of increase drops below the 12 percent cost of capital, again this is year 3. LO: 5 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.25 Replace an existing asset: Bell Mountain Vineyards is considering updating its current manual accounting system with a high-end electronic system. While the new accounting system would save the company money, the cost of the system continues to decline. The Bell Mountain’s opportunity cost of capital is 10 percent, and the costs and values of investments made at different times in the future are as follows: Year

Cost

Value of Future Savings (at time of purchase)

$5,000

$7,000

4,500

7,000

4,000

7,000

3,600

7,000

3,300

7,000

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3,100

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7,000

When should Bell Mountain buy the new accounting system? Solution: The NPV of each choice is: NPV0 = Future savings – Cost = $7,000 - $5,000 = $2,000 NPV1 = $2,500/ (1.1)1 = $2,273 NPV2 = $3,000/ (1.1)2 =$ 2,479 NPV3 = $3,400/ (1.1)3 =$2,554 NPV4 = $3,700/ (1.1)4 = $2,527 NPV5 = $3,900/ (1.1)5 = $2,422 Therefore, the company should purchase the system in year 3. Excel Template available in Wiley Course Resources Excel Template Solution available in Wiley Instructor Resources LO: 4 Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.26 Replace an existing asset: You have a 2000 Nissan that is expected to run for another three years, but you are considering buying a new Hyundai before the Nissan wears out. You will donate the Nissan to Goodwill when you buy the new car. The annual maintenance cost is $1,500 per year for the Nissan and $200 for the Hyundai. The price of your favorite Hyundai model is $18,000, and it is expected to run for 15 years. Your opportunity cost of capital is 3 percent. Ignore taxes. When should you buy the new Hyundai? Solution: NPV of cost of the new car is:

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Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: Hyundai

Cash Flow (C)

Frequency (F)

-18,000

-200

Then solve by pressing NPV, enter the rate of 3% and compute NPV=-20,387.59 Then you need to calculate the EAC of each car: EAC of the new car is:

 (1 + k )t  EACHyundai = k NPVA   t  (1 + k ) − 1 

(1.03 ) = −$1,707.80 = ( 0.03 )( −$20,387.59 )  15 (1.03 ) − 1 15

Financial Calculator Solution: 15

-20,387.59

0 PMT

1,707.80

Since the EAC of the new car is $1,707.80 and exceeds that of the Nissan ($1,500), you should drive the 2000 Nissan for three more years and then buy a new Hyundai. LO: 4 Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.27 Replace an existing asset: Assume that you are considering replacing your old Nissan with a new Hyundai, as in the previous problem. However, the annual maintenance cost of the old Copyright © 2022 John Wiley & Sons, Inc.

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Nissan increases as time goes by. It is $1,200 in the first year, $1,500 in the second year, and $1,800 in the third year. When should you replace it with the new Hyundai in this case?

Solution:

 ( 1 + k )t  EACHyundai = k NPVA   t  (1 + k ) − 1 

(1.03 ) = −$1,707.80 = ( 0.03 )( −$20, 387.59 )  15 (1.03 ) − 1 15

The EAC of the Hyundai remains at $1,707.80, as calculated above. Comparing this amount with the annual maintenance costs of the Nissan and you will see that in year 2 it is cheaper to drive the Nissan, but in year 3 it is cheaper to drive the Hyundai. Therefore, the optimal time to replace the old car is at the end of year 2. LO: 4 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.28 When to harvest an existing asset: Anaconda Manufacturing Company currently own a mine that is known to contain a certain amount of gold. Since Anaconda does not have any gold-mining expertise, the company plans to sell the entire mine and base the selling price on a fixed multiple of the spot price for gold at the time of the sale. Analysts at Anaconda have forecast the spot price for gold and have determined that the price will increase by 14 percent, 12 percent, 9 percent, and 6 percent during the next one, two, three, and four years, respectively. If Anaconda’s opportunity cost of capital is 10 percent, what is the optimal time for Anaconda to sell the mine? Solution:

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The rate of gold price appreciation is greater than the opportunity cost of capital for the next two years and then it drops below the opportunity cost of capital. Therefore, Anaconda should sell the gold at the beginning of the third year (or at the end of the second year). LO: 5 Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.29 Replace an existing asset: You are thinking about delivering pizzas in your spare time. Since you must use your own car to deliver the pizzas, you will wear out your current car one year earlier, which is one year from today, than if you did not take on the delivery job. You estimate that when you purchase a new car, regardless of when that occurs, you will pay $20,000 for the car and it will last you five years. If your opportunity cost of capital is 7 percent, what is the opportunity cost of using your car to deliver pizzas? Solution:

 (1 + 0.07)5  EACNew Car = 0.07  −$20, 000    = −$4, 877.81 5  (1 + 0.07) − 1  Financial Calculator Solution: 5

-20,000.00

0 PMT

4,877.81 Therefore, the opportunity cost of wearing out your car a year earlier is

NPVUsing your car = −$4, 877.81/(1.07)1 = −$4,558,70 Financial Calculator Solution: 1

4,877.81

PMT

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Fundamentals of Corporate Finance, 5th edition

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AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

ADVANCED 11.30 You are the CFO of SlimBody, Inc., a retailer of the exercise machine Slimbody6 and related accessories. Your firm is considering opening a new store in Los Angeles. The store will have a life of 20 years. It will generate annual sales of 5,000 exercise machines, and the price of each machine is $2,500. The annual sales of accessories will be $600,000, and the operating expenses of running the store, including labor and rent, will amount to 50 percent of the revenues from the exercise machines. The initial investment in the store will equal $30 million and will be fully depreciated on a straight-line basis over the 20-year life of the store. Your firm will need to invest $2 million in additional working capital immediately and recover it at the end of the investment. Your firm’s marginal tax rate is 30 percent. The opportunity cost of opening up the store is 10 percent. What are the incremental free cash flows from this project at the beginning of the project as well as in years 1-19 and 20? Should you approve it? Solution: Step One: Initial outlay = $30,000,000 + $2,000,000 (WC requirement) = $32,000,000 Step Two: ΔNR for years 1- 20: $2,500 × 5,000 machines = $12,500,000 plus $600,000 = $13,100,000 Step Three: ΔOpExp for years 1- 20: $1,250 × 5,000 machines = $6,250,000 Step Four: ΔD&A for years 1- 20: $30,000,000 / 20 years = $1,500,000 / year Step Five: Plug information into the textbook template as below. Step Six: Yr 20 recapture of WC requirements that were funded in year 0. Yrs 1-19

Yr 20

∆NR

$13,100,000

∆OpEx

-6,250,000

6,250,000

∆EBITDA

6,850,000

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Fundamentals of Corporate Finance, 5th edition

∆D&A

Solutions Manual

-1,500,000

1,500,000

5,350,000 (0.7)

∆NOPAT

3,745,000

∆D&A

1,500,000

∆CFO

5,245,000

∆EBIT (1-t)

∆CapEx

-30,000,000

∆AWC

-2,000,000

2,000,000

∆FCF

-$32,000,000

$5,245,000

$7,245,000

Therefore, the NPV of the project is:  1  19    1 − (1.10 )  +  $7, 245, 000  1  NPV = –$32, 000, 000 + $5, 245, 000   20    0.10 1.10 )  (        = $12, 950, 928.97

Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: Cash Flow (C)

Frequency (F)

-32,000,000

5,245,000

7,245,000

Then solve by pressing NPV, enter the rate of 10% and compute NPV=12,950,928.97. You should approve the project since it has a positive NPV.

Alternative Solution: Incremental cash flows in year 0 is: FCF0 = -$30,000,000-$2,000,000= -$32,000,000 Annual incremental cash flows through the life of the investment are: FCFt = (($2,500 × 2,500) + $600,000) × (1-0.3) + (0.3 × $1,500,000) = $5,245,000 Additional incremental cash flows at the end of the project are: $2,000,000 Copyright © 2022 John Wiley & Sons, Inc.

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Fundamentals of Corporate Finance, 5th edition

Solutions Manual

Therefore, the NPV of the project is:  1  19    1 − (1.10 )  +  $7, 245, 000  1  NPV = –$32, 000, 000 + $5, 245, 000   20    0.10 (1.10 )         = $12, 950, 928.97

You should approve the project since it has a positive NPV. LO: 1, 3, 4 Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.31 Merton Shovel Corporation has decided to bid for a contract to supply shovels to the Honduran Army. The Honduran Army intends to buy 1,000 shovels per year for the next three years. To supply these shovels, Merton will have to acquire manufacturing equipment at a cost of $150,000. This equipment will be depreciated on a straight-line basis over its five-year lifetime. At the end of the third year, Merton can sell the equipment for exactly its book value ($60,000). Additional fixed costs will be $36,000 per year, and variable costs will be $3.00 per shovel. An additional investment of $25,000 in net working capital will be required when the project is initiated. This investment will be recovered at the end of the third year. Merton Shovel has a 27 percent marginal tax rate and a 17 percent required rate of return on the project. What is the lowest possible per shovel price that Merton can offer for the contract and still create value for its stockholders? Solution: Year 0 cash flow = Cap Exp + Add WC = -$150,000 – $25,000 = -$175,000 Year 3: Cap Exp + Add WC = $60,000 + $25,000 = $85,000 We can’t directly solve for CF Opns since revenue depends on what we are going to charge per shovel. Since CF Opns must be the same in years 1, 2, and 3 of the project this is a threeyear annuity and we can solve for the total value of CF Opns as: Copyright © 2022 John Wiley & Sons, Inc.

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Fundamentals of Corporate Finance, 5th edition

Solutions Manual

Present value of CF Opns = CF Opns × [(1-1/(1.17)3)/0.17] NPV of the shovel contract = -$175,000 + $85,000/(1.17)3 + OCF [(1-1/(1.17)3)/0.17] Set NPV = 0 and solve for CF Opns: CF Opns = $55,178 Now solve CF Opns formula for the price of each shovel (P): CF Opns = [Revenue – OpEx – D&A) × (1 – t)] + D&A $55,178 = [(P × 1,000) – ($3.00 × 1,000) – $36,000 - $30,000] × (1-0.27) + $30,000 P × 730 = $55,178 + [($3,000 + $36,000 + $30,000) × 0.73] - $30,000 P = $75,548 / 730 P = $103.49 round up to $103.50 This is the minimum bid price for a shovel. If Merton Shovel charges less than this price per shovel, the NPV of the contract will be less than zero. LO: 1, 3 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.32 Rocky Mountain Lumber, Inc., is considering purchasing a new wood saw that costs $50,000. The saw will generate revenues of $100,000 per year for five years. The cost of materials and labor needed to generate these revenues will total $60,000 per year, and other cash expenses will be $10,000 per year. The machine is expected to sell for $1,000 at the end of its five-year life and will be depreciated on a straight-line basis over five years to zero. Rocky Mountain’s tax rate is 26 percent, and its opportunity cost of capital is 10 percent. Should the company purchase the saw? Explain why or why not? Solution: Step One: Initial outlay = $50,000 Step Two: ΔNR for years 1- 5: $100,000 Step Three: ΔOpExp for years 1- 5: $60,000 + $10,000 = $70,000 Step Four: ΔD&A for years 1- 5: $50,000 / 5 years = $10,000 / year Step Five: Plug into the textbook template as below. Copyright © 2022 John Wiley & Sons, Inc.

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Fundamentals of Corporate Finance, 5th edition

Solutions Manual

Step Six: Yr 5: Capital recovery = $1,000 – (0.26 × $1,000 gain on sale) = $740.

Year 0

Years 1-4

Year 5

Revenue

100,000

−Op Exp

70,000

EBITDA

30,000

−D&A

10,000

EBIT

20,000

× (1 − t)

0.74

NOPAT

14,800

+ D&A

10,000

CF Opns

24,800

Change in

− Cap Exp

-50,000

740

− Add WC

-50,000

24,800

25,540

FCF

Therefore, NPV of investment is: NPV = −$50,000 +

$24,800 $24,800 $24,800 $24,800 $25,540 + + + + (1.10 ) (1.10 )2 (1.10 )3 (1.10 )4 (1.10 )5 = $44, 471

Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: Cash Flow (C)

Frequency (F)

-50,000

24,800

25,540

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Fundamentals of Corporate Finance, 5th edition

Solutions Manual

Alternatively: The annual operating cash flows from year 1 to 5 are: ($100,000-$60,000-$10,000) × (1-0.26) + 0.26 ×10,000=$24,800 The after-tax terminal value in year 5 is: $1,000 - (0.26) × ($1,000-$0) = $740 Therefore, NPV of investment is:

NPV = −$50,000 +

$24,800 $24,800 $24,800 $24,800 $25,540 + + + + (1.10 ) (1.10 )2 (1.10 )3 (1.10 )4 (1.10 )5 = $44, 471

Excel Template available in Wiley Course Resources Excel Template Solution available in Wiley Instructor Resources LO: 1,3,4 Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.33 A beauty product company is developing a new fragrance named Happy Forever. There is a probability of 0.5 that consumers will love Happy Forever, and in this case, annual sales will be 1 million bottles; a probability of 0.4 that consumers will find the smell acceptable and annual sales will be 200,000 bottles; and a probability of 0.1 that consumers will find the smell unpleasant and annual sales will be only 50,000 bottles. The selling price is $38, and the variable cost is $8 per bottle. Fixed production costs will be $1 million per year, and depreciation will be $1.2 million. Assume that the marginal tax rate is 27 percent. What are the expected annual incremental after-tax free cash flows from the new fragrance? Solution: Step One: Expected sales units: (0.5) ×1,000,000 + (0.4) ×200,000 + (0.1) ×50,000 = 585,000 units Step Two: ΔNR: 585,000 units × $38 = $22,230,000 Copyright © 2022 John Wiley & Sons, Inc.

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Fundamentals of Corporate Finance, 5th edition

Solutions Manual

Step Three: ΔOpExp: 585,000 units x $8 + $1,000,000 = $5,680,000 Step Four: ΔD&A: $1,200,000 Step Five: Plug into the textbook template as below.

Change in

Revenue

22,230,000

−Op Ex

5,680,000

EBITDA

16,550,000

−D&A

1,200,000

EBIT

15,350,000

× (1 − t)

0.73

NOPAT

11,205,500

+D&A

1,200,000

CF Opns

12,405,500

−Cap Exp −Add WC FCF

0 12,405,500

Alternatively, the expected annual incremental cash flows are: {[((0.5 × 1,000,000) + (0.4 × 200,000) + (0.1 × 50,000)) × ($38-$8)) - 1,000,000] × (1 0.27)} + (1,200,000 × 0.27) = $12,405,500 LO: 1,3,4 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.34 Great Fit, Inc., is a company that manufactures clothing. The company has a production line that produces women’s tops of regular sizes. The same machine could be used to produce petite sizes as well. However, the remaining life of the machines will be reduced from four years to two years if the petite size production is added. The cost of identical machines with Copyright © 2022 John Wiley & Sons, Inc.

SM 11-40

Fundamentals of Corporate Finance, 5th edition

Solutions Manual

a life of eight years is $2 million. Assume the opportunity cost of capital is 8 percent. What is the opportunity cost of adding petite sizes? Solution: The opportunity cost is the incremental costs of the machine in year 3 and year 4 if petite sizes are in production. The EAC of the machine is:

 (1 + k )t  EACA = k NPVA   t  (1 + k ) − 1 

(1.08 ) = −$348,029.52 = ( 0.08 )( −$2,000,000 )  8 (1.03 ) − 1 8

The present value of such cost in year 3 and year 4 is: NPV = –

$348, 029.52

(1.10 )

$348, 029.52

(1.10 )

= $532, 089.14

LO: 4 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.35 Biotech Partners LLC has been farming a new strain of radioactive-material-eating bacteria that the electrical utility industry can use to help dispose of its nuclear waste. Two opposing factors affect Biotech’s decision of when to harvest the bacteria: the growth rate of the bacteria and its market price. The bacteria are currently growing at a 22 percent annual rate. Due to competition from other top firms, Biotech analysts estimate that the price for the bacteria will decline according to the schedule below. If the opportunity cost of capital is 10 percent, and free cash flows change in the same way as the change in market price, Biotech should harvest the entire bacteria colony at the end of which year? Year

Change in Price Due to Competition

-2

SM 11-41

Fundamentals of Corporate Finance, 5th edition

Solutions Manual

-8

-10

-15

-25

Solution: Change in free cash flows: Yr 1

(1.05) × (1.22) = 1.2810 or 28.1%

Yr 2

(0.98) × (1.22) = 1.1956 or 19.56%

Yr 3

(0.92) × (1.22) = 1.1224 or 12.24%

Yr 4

(0.90) × (1.22) = 1.0980 or 9.80%

Yr 5

(0.85) × (1.22) = 1.037 or 3.70%

Yr 6

(0.75) × (1.22) = 0.9150 or -8.50%

Since the change in free cash flow drops below the 10% opportunity cost of capital in year four, Biotech should sell its bacteria colony the year prior to this point – so at the end of the third year. LO: 5 Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.36 ACME Manufacturing is considering replacing an existing production line with a new line that has a greater output capacity and operates with less labor than the existing line. The new line would cost $1 million, have a five-year life, and be depreciated using the MACRS three-year schedule. At the end of five years, the new line could be sold as scrap for $200,000 (in Year 5 dollars). Because the new line is more automated, it would require fewer operators, resulting in a savings of $40,000 per year before tax and unadjusted for inflation (in today’s dollars). Additional sales with the new machine are expected to result in additional net cash inflows, before tax, of $60,000 per year (in today’s dollars). If ACME invests in the new line, a one-time investment of $10,000 in additional working capital will Copyright © 2022 John Wiley & Sons, Inc.

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Solutions Manual

be required. The working capital investment will be recovered at the end of the project's life. The tax rate is 28 percent, the opportunity cost of capital is 10 percent, and the annual rate of inflation is 3 percent. What is the NPV of the new production line? Solution:

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Fundamentals of Corporate Finance, 5th d edition

Time, years

Solutions Manual

Revenue

61,800

63,654

65,564

67,531

69,556

Savings

41,200

42,436

43,709

45,020

46,371

Depreciation

333,300

444,500

148,100

74,100

Earnings before taxes

(230,300)

(338,410)

(38,827)

38,451

115,927

Taxes

(64,484)

(94,755)

(10,872)

10,766

32,460

Net income

(165,816)

(243,655)

(27,956)

27,685

83,468

Net operating cash flow

167,484

200,845

120,144

101,785

83,468

Incremental

Cost of new machine Investment in working capital

(1,000,000) (10,000)

10,000

Terminal value Market value

200,000

Book value

Taxes

56,000

Terminal after tax cash flow

144,000

Free cash flow

(1,010,000)

Project NPV

(384,519)

167,484

200,845

SM 11-44

120,144

101,785

237,468

Fundamentals of Corporate Finance, 5th d edition

NPV = −$1,010,000 +

Solutions Manual

$167, 484 $200,845 $120,144 $101,785 $237, 468 + + + + 2 3 4 5 (1.10 ) (1.10 ) (1.10 ) (1.10 ) (1.10 ) = −$384,519

Excel Template available in Wiley Course Resources Excel Template Solution available in Wiley Instructor Resources LO: 4 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.37 The alternative to investing in the new production line in Problem 11.36 is to overhaul the existing line, which currently has both a book value and a salvage value of $0. It would cost $300,000 to overhaul the existing line, but this expenditure would extend its useful life to five years. The line would have a $0 salvage value at the end of five years. The overhaul outlay would be capitalized and depreciated using the MACRS three-year schedule. Should ACME replace or renovate the existing line?

Solution:

SM 11-45

Fundamentals of Corporate Finance, 5th d edition

Time, years

Solutions Manual

Revenue

Savings

Depreciation

99,990

133,350

44,430

22,230

Earnings before taxes

(99,990)

(133,350)

(44,430)

(22,230)

Taxes

(27,997)

(37,338)

(12,440)

(6,224)

Net income

(71,993)

(96,012)

(31,990)

(16,006)

Net operating cash flow

27,997

37,338

12,440

6,224

27,997

37,338

12,440

6,224

Incremental

Cost of renovating old machine

(300,000)

Free cash flow

(300,000)

Project NPV

(230,092)

SM 11-46

Fundamentals of Corporate Finance, 5th d edition

NPV = −$300,000 +

Solutions Manual

$27,997 $37,338 $137,338 $12, 440 $6,224 + + + + (1.10 ) (1.10 )2 (1.10 )3 (1.10 )4 (1.10 )5 = −$230,092

The NPV of renovating the old line is -$230,092 while the NPV of the new machine (from question 11.36) is -$384,519 so renovating the old production line is less costly. LO: 4 Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective 11.38 Paye’s Panes manufactures insulated windowpanes. The company’s CFO has asked you to assess a new manufacturing plant she is considering. The initial cost will be $475,000. While for tax purposes the plant can be depreciated straight-line to zero book value over 10 years, the CFO expects that the firm will sell the plant at the end of Year 5. At that time, the CFO estimates that there is a 20 percent chance that the plant can be sold for $80,000, a 30 percent chance it can be sold for $70,000, and a 50 percent chance that it can be sold for $25,000. The initial investment in working capital of $30,000 will be recovered when the machine is sold. Additional revenues from the plant are expected to be $205,000 per year, and additional operating costs will be $73,000 per year. The firm has a marginal tax rate of 23 percent and a 9 percent cost of capital. (a) What is the NPV of the new plant? (b) You complete your analysis and read in the Wall Street Journal that a new process for making insulated window will be available five years from today. You believe that this will lower the Year 5 sales price of the plant dramatically. To the nearest dollar, what is the lowest amount that you can sell the plant for and still recommend to your CFO that she undertake the investment? Solution: a)

In order to get the value of the after-tax proceeds on sale of the plant or the incremental capital expenditures (Cap Exp) in Year 5 first calculate the selling price expected in Year 5:

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Fundamentals of Corporate Finance, 5th d edition

Solutions Manual

Expected

Probability*expected

Probability

sales price

0.2

$80,000

$16,000

0.3

70,000

$21,000

0.5

25,000

$12,500

Sum (p*expected)

$49,500

Next calculate the after-tax proceeds from the sale based on the expected selling price. We first need the book value of the plant when we sell it. As we depreciate straight line over 10 years the Annual Depreciation = $475,000/10 = $47,500. By Year 5 we have accumulated depreciation of 5 × $47,500 = $237,500. Therefore, the book value is: $475,000 - $237,500 = $237,500.

Next, calculate the Gain/Loss on sale: Sell machine at end (S)

$49,500

Book value at end (BV)

237,500

Gain (- is a Loss) on Sale = (S – BV)

-$188,000

Finally, deduct the taxes that result from the Gain/Loss from the sales price: Sales price of machine at year 5 (S)

$49,500

- Tax on Gain/Loss = 0.23 × -$188,000

-$43,240

After-tax proceeds from Sale (S – Tax)

$92,740

Note that the loss on sale results in a negative tax, which is a tax benefit. We can then create a table showing the cash flows over the five-year period.

SM 11-48

Fundamentals of Corporate Finance, 5th d edition

Solutions Manual

Revenue

$205,000

−Op Ex

73,000

EBITDA

132,000

−D&A

47,500

EBIT

84,500

× (1 − t)

× 0.77

NOPAT

65,065

+D&A

47,500

CF Opns

112,565

−Cap Exp

$475,000

−Add WC

30,000

FCF

-$505,000

-92,740 0 $112,565

$112,565

SM 11-49

30,000 $112,565

$235,305

Fundamentals of Corporate Finance, 5th d edition

NPV = −$505,000 +

Solutions Manual

$112,565 $112,565 $112,565 $112,565 $235,305 + + + + 2 3 4 5 (1.09 ) (1.09 ) (1.09 ) (1.09 ) (1.09 ) = $12, 611.17

The NPV is positive, so accept the project.

Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: Cash Flow (C)

Frequency (F)

-505,000

112,565

235,305

Then solve by pressing NPV, enter the rate of 9% and compute NPV=12,611.17

To determine the lowest amount that we can sell the plant for and still recommend to the CFO that she should undertake the investment we need to find the selling price of the machine at Year 5 such that the NPV of the machine is zero. Currently the NPV of the incremental cash flows of undertaking the investment is $12,611.17 which includes the benefit from the sale of the plant and the tax shields expected in Year 5. Let’s first calculate the NPV of the project if there are zero after-tax proceeds from the sale when the machine is sold. This will tell us what the present value of the after-tax proceeds from the sale must be in order to have a zero NPV. From that we can back out the value of the after-tax proceeds from the sale that we would need at year 5, and thus the sales price.

If the after-tax proceeds from the sale in Year 5 are zero, the NPV would be $12,611 less the present value of $92,740 or $12,611.17 - $60,274.64 = -$47,663.47. Therefore, to breakeven, the after-tax proceeds from the sale of the plant in Year 5 must be: = $47,663.47 × (1.09)5 = $73,336.15 Copyright © 2022 John Wiley & Sons, Inc.

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Fundamentals of Corporate Finance, 5th d edition

Solutions Manual

The after-tax proceeds from the sale are: (S-BV) × t. By setting this value equal to $73,336.15 we can back out the sales price as follows: S – (S - BV) × t = $73,336.15 S – St + (BV × t) = $73,336.15 S (1- t) + (BV× t) = $73,336.15 S (1- t) = $73,336.15 – (BV × t) S = ($73,336.15 – (BV × t)) / (1-t) S = ($73,336.15 – ($237,500 × 0.23)) / (0.77) S = $18,711.15/0.77 = $24,300.20 or to the nearest dollar $24,300 So long as you can sell the machine at the end of the project’s life for at least $24,300 it will be a positive NPV investment. LO: 4 Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

CFA PROBLEMS 11.39 FITCO is considering the purchase of new equipment. The equipment costs $350,000, and an additional $110,000 is needed to install it. The equipment will be depreciated straight-line to zero over a five-year life. The equipment will generate additional annual revenues of $265,000, and it will have annual cash operating expenses of $83,000. The equipment will be sold for $85,000 after five years. An inventory investment of $73,000 is required during the life of the investment. FITCO has a marginal tax rate of 28 percent , and its cost of capital is 10 percent. What is the project’s NPV? a.

$97,449

$144,723

$162,767

$231,371

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Fundamentals of Corporate Finance, 5th d edition

Solutions Manual

Solution:

d is correct. The installed cost of the equipment is $350,000 + $110,000 = $460,000. The initial increase in Net working capital is $73,000. Annual depreciation is $460,000/5 = $92,000 The annual after-tax operating cash flow for Years 1–5 is CF = (Sales – Costs – Deprec) x (1 – T) + Deprec = (265,000 – 83,000 – 92,000) x (1 – 0.28) + 92,000 CF = $156,800

After tax cash flow from selling equipment: Sales price

85,000

Book value at project end

Gain on Sale

85,000

Tax on Gain

23,800

Net ATCF on Sale

61,200

The return of working capital is $73,000

Revenue

$265,000

−Op Ex

83,000

EBITDA

182,000

−D&A

92,000

EBIT

90,000

×(1 − t)

0.72

NOPAT

64800

64,800

+D&A

92,000

CF Opns

156,800

−Cap Exp

-460,000

−Add WC

-73,000

61,200 0

73,000 SM 11-52

Fundamentals of Corporate Finance, 5th d edition

FCF

-533,000

NPV@10%

144,723

Solutions Manual

156,800

291,000

Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: Cash Flow (C)

Frequency (F)

-533,000

156,800

291,000

Then solve by pressing NPV, enter the rate of 10% and compute NPV=144,723 Alternatively, the NPV is: 4

NPV = −$533,000 + 

$156,800

t =1

(1.10 )

$291,000

(1.10 )

= $144,723

LO: 4 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions

AICPA: Industry/Sector Perspective 11.40 After estimating a project’s NPV, the analyst is advised that the fixed capital outlay will be revised upward by $100,000. The fixed capital outlay is depreciated straight-line over an eight-year life. The tax rate is 25 percent, and the required rate of return is 10 percent. No changes in cash operating revenues, cash operating expenses, or salvage value are expected. What is the effect on the project NPV? a.

$81,328 decrease

$73,325 decrease

$59,988 decrease

No change

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a is correct. The additional annual depreciation is $100,000/8 = $12,500. The depreciation tax savings is 0.25($12,500) = $53,125. The change in project NPV is

−100,000 +  t =1

3,125

(1.10 )

= −100,000 + 18,672 = −$81,328

Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: Cash Flow (C)

Frequency (F)

-100,000

3,125

Then solve by pressing NPV, enter the rate of 10% and compute NPV=-81,328 LO: 4 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions

AICPA: Industry/Sector Perspective 11.41. When assembling the cash flows to calculate an NPV or IRR, the project’s after-tax interest expenses should be subtracted from the cash flows for: a.

The NPV calculation, but not the IRR calculation.

The IRR calculation, but not the NPV calculation.

Both the NPV calculation and the IRR calculation.

Neither the NPV calculation nor the IRR calculation.

Solution: d is correct. Financing costs are not subtracted from the cash flows for either the NPV or the IRR. The effects of financing costs are captured in the discount rate used. LO: 1 Bloomcode: Application AASCB: Analytic Copyright © 2022 John Wiley & Sons, Inc.

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IMA: Investment Decisions AICPA: Industry/Sector Perspective

Sample Test Problems 11.1

You purchased 100 shares of stocks of an oil company, Texas Energy, Inc., at $50 per share. The company has 1 million shares outstanding. Ten days later, Texas Energy announced an investment in an oil field in east Texas. The probability that the investment will be successful and generate an NPV of $10 million is 0.2; the probability that the investment will be a failure and generate an NPV of negative $1 million is 0.8. How would you expect the stock price to change upon the company’s announcement of the investment?

Solution: The expected change in the stock price should be equal to the expected NPV of the project divided by the number of shares outstanding. The expected NPV of the project is (0.2 × $10,000,000) + (0.8 × –$1,000,000) = $1,200,000 Therefore, the change in Texas Energy’s stock price should equal $1,200,000 / 1,000,000 shares = $1.2 per share when the investment is announced. The total value of your shares should increase by 100 shares × $1.20 per share = $120. LO: 4 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.2

A division of Virginia City Highlands Manufacturing is considering purchasing a machine for $1,500,000 that automates the process of inserting electronic components onto computer motherboards. The annual cost of operating the machine will be $50,000, but it will save the company $370,000 in labor costs each year. The machine will have a useful life of 10 years, and its salvage value in 10 years is estimated to be $300,000.

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However, for tax purposes the initial purchase price of the machine will be depreciated straight-line to zero. If the marginal corporate tax rate is 21 percent and the appropriate discount rate is 12 percent, what is the NPV of this project? Solution: The incremental after-tax free cash flow (FCF) in year 0 is: FCF0 = –$1,500,000 The FCF in years 1 through 9 is: Annual Depreciation = ($1,500,000) / 10 = $150,000 per year FCFt = [($370,000 – $50,000) × (1 – 0.21)] + [ 0.21 × $150,000] = $284,300 The FCF in year 10 is: FCF10 = $284,300 + $300,000 – [(Salvage Value – Book Value) × 0.21] FCF10 = $284,300 + $300,000 – [(300,000 – 0) × 0.21] = $521,300 Therefore, the NPV of the project is:

 1   9   1– 1.12 )    ( 1    NPV = –$1, 500, 000 + $284, 300  + $521, 300   10   0.12    1.12  ( )          = –$1, 500, 000 + $1, 514 , 821 + $167, 845 = $182, 666

Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: Cash Flow (C)

Frequency (F)

-1,500,000

284,300

521,300

Then solve by pressing NPV, enter the rate of 12% and compute NPV=182,666 Virginia City Highlands Manufacturing should approve the project since it has a positive NPV. Copyright © 2022 John Wiley & Sons, Inc.

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11.3

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After examining the NPV analysis for a potential project that would increase the firm’s output by 5 percent, an analyst’s manager tells the analyst to increase the initial fixed capital outlay in the analysis by $480,000. The initial fixed capital outlay would be fully depreciated on a straight-line basis over a 12-year life, regardless of whether it was increased. If the firm’s average tax rate is 28 percent, its marginal tax rate is 30 percent, and the required rate of return is 10 percent, what is the effect of the adjustment on the project NPV?

Solution: The additional annual depreciation is $480,000 / 12 = $40,000. For a project such as this we would use the marginal tax rate. Therefore, the annual depreciation tax savings is 0.30 × $40,000 = $12,000. The change in the overall NPV of the project is:

 1   12    1− (1.10 )  Change in NPV = –$480, 000 + $12, 000      0.10         = −$480, 000 + $81,764 = −$398, 236

Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: Cash Flow (C)

Frequency (F)

-480,000

12,000

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IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.4

Which of the following are relevant cash flows in the evaluation of a proposal to produce a new product? a. Decrease in the cash flows of a substitute product. b. Alternative of leasing an existing building that would be used for manufacturing this product. c. The cost of a new machine required to produce this product. d. Salvage value of the new machine at the end of its useful life. e. Increase in net working capital at the beginning of the project’s life. f. Cost to develop a product prototype last year.

Solution: a, b, c, d, and e are all relevant cash flows. f is a sunk cost and is therefore not relevant. LO: 2 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.5

Managers of Central Embroidery have decided to purchase a new monogram machine and are considering two alternatives. The first machine costs $100,000 and is expected to last five years. The second machine costs $160,000 and is expected to last eight years. Assume that the opportunity cost of capital is 8 percent. Which machine should Central Embroidery purchase?

Solution: The equivalent annual cost for each system is:

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-100,000

0 PMT

25,045.65

 (1.08)8  EACMachine 2 = 0.08 × $160,000 ×   = $27, 842.37 8  (1.08) – 1  Financial Calculator Solution: 8

-160,000

0 PMT

27,842.37

Central Embroidery should purchase the first machine because it has a lower EAC. LO: 4 Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.6

You have inherited an apple orchard and want to sell it in the next four years. An expert in apple orchard valuation has estimated the after-tax cash flow you would receive if you sold at the end of each of the next four years as follows: $1,000,000 if you sell in one year; $1,300,000 if you sell in two years; $1,500,000 if you sell in three years; and $1,600,000 if you sell in four years. Your opportunity cost of capital is 10 percent. When should you sell the orchard?

Solution: The NPV in today’s dollars for each alternative is: NPV1 = $1,000,000 / (1.10)1 = $909,091 NPV2 = $1,300,000 / (1.10)2 = $1,074,380 NPV3 = $1,500,000 / (1.10)3 = $1,126,972 NPV4 = $1,600,000 / (1.10)4 = $1,092,822 Copyright © 2022 John Wiley & Sons, Inc.

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You should sell the orchard in 3 years because the present value of the NPV is highest in year three. After year three, the value of the orchard is expected to increase at a rate that is less than your opportunity cost of capital. Therefore, it is better for you to sell the orchard after three years and invest the proceeds elsewhere. LO: 5 Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

Ethics Case Discussion Questions 1.

Should Unilever stockholders endorse a sustainability plan? Why or why not? The purpose of this question is to get students to seriously consider whether a strategy of sustainability will contribute to Unilever’s bottom line. Students should be challenged to discuss whether associating Unilever products like Dove soap or Lipton tea with sustainable business is effective. They might compare and contrast Unilever’s financials with Procter and Gamble’s in doing the analysis.

Are there business advantages to using sustainable or green suppliers? If so, what are they? If not, do you think a traditional return on investment analysis captures all possible benefits of going green? Whichever choice the student makes, he or she must consider what the ROI might be. Students who think sustainable sourcing will give a good return on investment should be challenged about whether a positive return is enough. Perhaps Unilever should adopt some strategies that give an even higher return. Green investments usually have a long payoff time. Students who are skeptical need to consider whether traditional ROI analysis is sufficient. Does the traditional analysis give appropriate weight to reputation effects of going green, for

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example? This is also an opportunity to introduce the notion of “triple bottom line accounting” and to consider its strengths and weaknesses.

Are there any ethical criticisms of Unilever’s sustainable living strategy? If so, what are they? This question confronts the unease that many students have about whether business decisions like going green are ethical if they are also profitable. Be sure to point out that, based on utilitarian theories, there is no problem. The problem arises only for ethicists who emphasize the profit motive and believe that making money is an unethical motive. This gives you the opportunity to point out that making money for stockholders in a public company is a moral requirement for managers and that sound financial and ethical decisions should not be separated. It is a question not of choosing either-or, but rather of achieving both.

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CHAPTER 10

The Fundamentals of Capital Budgeting Before You Go On Questions and Answers Section 10.1 1.

Why are capital investments the most important decisions made by a firm’s management? Capital investments are the most important decisions made by a firm’s management, because they usually involve large cash inflows and outflows. These cash flows, representing significant long-term projects that define the firm’s future line of business, are generally expected to significantly contribute to future revenues and once made, are not easily reversed.

What are the differences between capital projects that are independent, mutually exclusive, and contingent? A project is independent if accepting or rejecting the project does not affect the decision about implementing other projects. On the other hand, projects are mutually exclusive if the acceptance of one implies rejection of the other. Contingent projects are those in which the acceptance of one project is dependent on another project.

3. What is the cost of capital? The cost of capital can be thought of as a “hurdle rate” or the minimum rate that a company expects to earn when investing in a project. It is the “opportunity cost”, or the rate of return that is possible from the next best alternative investment opportunity with similar risk.

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Firms often have a limited amount of money for investment and qualified projects whose total cost exceeds this amount. In this situation, managers of those firms must allocate the available money to the set of projects that add the most value to its shareholders. This allocation process is known as capital rationing.

Section 10.2 1.

What is the NPV of a project? A project’s NPV is the difference between the present value of its expected future cash inflows and its outflows, including the present value of its cost. It is the recommended technique used to value capital investments, as it takes into account both the timing of the cash flows and their risk.

If a firm accepts a project with a $10,000 NPV, what is the effect on the value of the firm? If a firm accepts a project with a $10,000 NPV, it will increase its value by $10,000.

What are the five steps used in NPV analysis? The five-step process used in the NPV analysis is as follows: (1) Determine the initial cost of the project. (2) Estimate the project’s future cash flows over its expected life. (3) Determine the riskiness of the project and the appropriate cost of capital. (4) Compute the project’s NPV. (5) Make a decision. A project with a positive NPV adds value to the firm and should be accepted.

Section 10.3 1.

What is the payback period? The payback period is defined as the number of years it takes to recover the project’s initial investment. All other things being equal, the project with the shortest payback period is usually the optimal investment.

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Why does the payback period provide a measure of a project’s liquidity risk? The payback period determines how quickly you recover your investment in a project. Thus, it serves as a good measure of the project’s liquidity.

What are the main shortcomings of the payback method? The payback method does not account for time value of money, nor does it distinguish between high- and low-risk projects. It also ignore any cash flows received after the payback period. Two projects can have the same payback period with one having cash flow stopping at the end of the payback period and another that continues on for a period of time. In addition, there is no rationale behind choosing the cutoff criteria. For all these reasons, the payback method is not the ideal capital decision rule.

Section 10.4 1.

What are the major shortcomings of using the accounting rate of return (ARR) method as a capital budgeting method? The biggest shortcoming of using ARR as a capital budgeting tool is that it uses historical, or book value data rather than cash flows and thus, disregards the time value of money principle. In addition, as with the payback method, it fails to establish a rationale behind picking the appropriate hurdle rate.

Section 10.5 1.

What is the internal rate of return (IRR) method? The IRR, or the internal rate of return, is the discount rate that equates the present value of a project’s cost to the present value of its expected cash inflows. The IRR determines whether the project’s return rate is higher or lower than the required rate of return, which is the firm’s cost of capital. Normally, a project should be accepted if the IRR exceeds the firm’s cost of capital; otherwise the project should be rejected.

Under what circumstances do the NPV and IRR decision rules always yield the same decision?

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When a project has normal or conventional cash flows and when the project is completely independent of other projects, both of these decision rules will yield the same accept/reject decision.

In capital budgeting, what is a conventional cash flow pattern? A conventional project cash flow in capital budgeting is one in which an initial cash outflow is followed by one or more future cash inflows.

Why should the NPV method be the primary decision tool used in making capital investment decisions? Given all the different methods to evaluate capital investment decisions, the NPV method is the preferred valuation tool since it accounts for both the time value of money and the project’s risk. Furthermore, the NPV is not sensitive to nonconventional projects, and therefore, it is superior to the IRR technique. Finally, investment decisions made using NPV are always consistent with the goal of maximizing the value of the firm, even when discriminating between mutually exclusive projects.

Section 10.6 1.

What might cause a firm to face capital constraints? A firm might face capital constraints because it can be difficult for outside investors (new creditors, bondholders, or stockholders) to accurately assess the risks and returns associated with the firm’s projects. This might cause the investors to require returns for their capital that are so high that they make positive-NPV projects unattractive, because those projects cannot produce the high returns required by investors.

What decision criteria should managers use in selecting projects when a firm faces capital constraints? When a firm faces capital constraints, the basic principle to follow when choosing a set of projects that create the greatest value in a given period, is to select the bundle of projects that yield the largest value per dollar invested.

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How can the profitability index (PI) help in choosing projects when a firm faces capital constraints? What are its limitations? The basic concept underlying the profitability index (PI) is that managers should select the bundle of projects that creates the greatest value per dollar invested. The PI tells us the NPV per dollar invested for an individual project. In a single period, the PI can be used to identify the bundle of projects that yields the largest NPV per dollar invested. However, the PI will not necessarily help identify the most valuable bundle of projects if investments are being compared across more than one year and the timing of cash flows from early investments affects the firm’s ability to make subsequent investments.

Section 10.7 1.

What changes have taken place in the capital budgeting techniques used by U.S. companies? Over the years, there has been a shift from using payback and accounting rate of return (ARR) as the primary capital budgeting tools to using net present value (NPV) and internal rate of return (IRR) instead. Managers today understand the importance of the time value of money and discounting and thus, regard ARR as an inaccurate and obsolete decision tool.

Self-Study Problems 10.1

The management of Premium Manufacturing Company is evaluating two forklift systems to use in its plant that produces the towers for a windmill power farm. The costs and the cash flows from these systems are shown below. If the company uses a 12 percent discount rate for all projects, determine which forklift system should be purchased using the net present value (NPV) approach.

Otis

Year 0

Year 1

Year 2

Year 3

−$3,123,450

$979,225

$1,358,886

$2,111,497

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Craigmore

−$4,137,410

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$875,236

$1,765,225

$2,865,110

Forklifts Solution: NPV for Otis Forklifts: n

CFt (1 + k )t t =0

NPV = 

$979,225 $1,358,886 $2,111, 497 + + (1 + 0.12)1 (1.12)2 (1.12)3 = −$3,123, 450 + $874,308 + $1,083,295 + $1,502,922 = $337,075

= −$3,123, 450 +

Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: Otis

Cash Flow (C)

Frequency (F)

-3,123,450

979,225

1,358,886

2,111,497

Then solve by pressing NPV, enter the rate of 12% and compute NPV= 337,075.

NPV for Craigmore Forklifts:

CFt t t = 0 (1 + k )

NPV = 

$875,236 $1,765,225 $2,865,110 + + (1 + 0.12)1 (1.12)2 (1.12)3 = −$4,137, 410 + $781, 461 + $1, 407,226 + $2,039,329 = $90,606

= −$4,137, 410 +

Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows:

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Craigmore

Cash Flow (C)

Frequency (F)

-4,137,410

875,236

1,765,225

2,865,110

Then solve by pressing NPV, enter the rate of 12% and compute NPV= 90,606. Premium should purchase the Otis forklift since it has a larger NPV.

10.2

Perryman Crafts Corp. management is evaluating two independent capital projects that will each cost the company $250,000. The two projects are expected to provide the following cash flows:

Year

Project A

Project B

$80,750

$32,450

$93,450

$76,125

$40,325

$153,250

$145,655

$96,110

Which project will be chosen if the company’s payback criterion is three years? What if the company accepts all projects as long as the payback period is less than five years? Solution: Payback periods for Perryman projects A and B: Project A Cumulative Year

Cash Flow

Cash Flows

-$250,000

80,750

1-69,250

93,450

-75,800

40,235

-35,565

145,655

110,090

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Project B Cumulative Year

Cash Flow

Cash Flows

-$250,000

32,450

217,550

76,125

141,425

153,250

11,825

96,110

107,935

Payback period for Project A:

Payback period = Years before cost recovery +

Remaining cost to recover Cash flow during the year

$35,565 $145,655 per year = 3.24 years

= 3+

Payback period for Project B:

Payback period = Years before cost recovery +

Remaining cost to recover Cash flow during the year

$141, 425 $153, 250 per year = 2.92 years

=2+

If the payback period is three years, only project B will be chosen. If the payback criterion is five years, both A and B will be chosen.

10.3

Terrell Corp. management is considering purchasing a machine that will cost $117,250 and will be depreciated on a straight-line basis over a five-year period. The sales and expenses (excluding depreciation) for the next five years are shown in the following table. The company’s tax rate is 34 percent.

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Year 1

Year 2

Year 3

Year 4

Year 5

Sales

$123,450

$176,875

$242,455

$255,440

$267,125

Expenses

$137,410

$126,488

$141,289

$143,112

$133,556

Terrell will accept all projects that provide an accounting rate of return (ARR) of at least 45 percent. Should the company accept the project? Solution: Year 1

Year 2

Year 3

Year 4

Year 5

Sales

$123,450 $176,875

$242,455

$255,440

$267,125

Expenses

137,410

126,488

141,289

143,112

133,556

Depreciation*

23,450

$ (37,410) $ 26,937

$ 77,716

$ 88,878

$110,119

9,159

26,423

30,219

37,440

$ (24,691) $ 17,778

$ 51,293

$ 58,659

$ 72,679

EBIT Taxes (34%)

12,719

Net income Beginning book value

117,250

93,800

70,350

46,900

23,450

Less: Depreciation*

(23,450)

Ending book value

$ 93,800 $ 70,350

$ 46,900

$ 23,450

*$117,250/5 years Average net income

= (–$24,691 + $17,778 + $51,293 + $58,659 + $72,679) / 5 = $35,143.60

Average book value

= ($117,250 + $93,800 + $70,350 + $46,900 + $23,450 + $0)/6 = $58,625

Accounting rate of return

= $35,143.60 / $58,625 = 0.599 or 59.9%

The company should accept the project.

10.4

Refer to Problem 10.1. Compute the IRR for each of the two systems. Is the investment decision different from the one determined by NPV?

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Solution: IRR for two forklift systems: Otis Forklifts: First compute the IRR by the trial-and-error approach: NPV (Otis) = $337,075 > 0 We should use a higher discount rate to get NPV = 0 At k = 15%, $979,225 $1,358,886 $2,111, 497 + + (1 + 0.15)1 (1.15)2 (1.15)3 = −$3,123, 450 + $851,500 + $1,027,513 + $1,388,343

NPVOtis = −$3,123, 450 + = $143,906

Try a higher rate. At k = 17%,

NPVOtis = −$3,123,450 + $836,944 + $992,685 + $1,318,356 = $24,535 Try a higher rate. At k = 17.5%,

NPVOtis = −$3,123,450 + $833,383 + $984,254 + $1,301,598 = −$4,215 Thus the IRR for Otis is less than 17.5 percent. Using a financial calculator, you can find that the exact rate to be 17.43 percent.

Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: Otis

Cash Flow (C)

Frequency (F)

-3,123,450

979,225

1,358,886

2,111,497

Then solve by pressing IRR to get 17.43%

Craigmore Forklifts:

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First compute the IRR by the trial-and-error approach: NPV (Craigmore) = $90,606 > 0 Use a higher discount rate to get NPV = 0 At k = 15%, $875, 236 $1,765, 225 $2,865,110 + + (1.15)1 (1.12) 2 (1.12)3 = −$4,137, 410 + $761,075 + $1,334,764 + $1,883,856 = −$157,715

NPVCraigmore = −$4,137, 410 +

Try a lower rate. At k = 13%,

NPVCraigmore = −$4,137,410 + $774,545 + $1,382,430 + $1,985,665 = $5,230 Try a higher rate. At k = 13.1%,

NPVCraigmore = −$4,137,410 + $773,860 + $1,379,987 + $1,980,403 = −$3,161 Thus the IRR for Craigmore is less than 13.1 percent. The exact rate is 13.06 percent.

Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: Craigmore

Cash Flow (C)

Frequency (F)

-4,137,410

875,236

1,765,225

2,865,110

Then solve by pressing IRR to get 13.06% Based on the IRR, we would still pick Otis over Craigmore forklift systems. The decision is the same as that indicated by NPV since both projects are conventional.

10.5

You are considering a project that has an initial outlay of $1 million. The profitability index of the project is 2.24. What is the NPV of the project?

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NPV + Initial investment Initial investment NPV + $1,000,000 2.24 = $1,000,000 PI

Therefore: NPV = $1,240,000

Discussion Questions 10.1

Explain why the cost of capital is referred to as the “hurdle” rate in capital budgeting.

Solution The cost of capital is the minimum required return on any new investment that allows a firm to break even. Since we are using the cost of capital as a benchmark or “hurdle” to compare the return earned by any project, it is sometimes referred to as the hurdle rate. LO: 1 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.2

a. Sykes, Inc. management is considering two projects: a plant expansion and a new computer system for the firm’s production department. Classify these projects as independent, mutually exclusive, or contingent projects and explain your reasoning.

b. A company is building a new plant on the outskirts of Smallesville. The town has offered to donate the land, and as part of the agreement, the company will have to build an access road from the main highway to the plant. How will the project of building the road be classified in the capital budgeting analysis? Copyright © 2022 John Wiley & Sons, Inc.

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c. Management of your firm is currently considering upgrading the operating systems of all the firm’s computers. One alternative is to choose the Linux operating system that a local computer services firm has offered to install and maintain. Microsoft has also put in a bid to install the new Windows operating system for businesses. How would these projects be classified? Solution a. These two projects are independent projects. Accepting or rejecting one will not influence the decision on the other project. The cash flows of the two projects are unrelated.

b. This is a contingent project. Acceptance of the road-building project is contingent on the new plant being a financially viable project. If the new plant will not have a positive value, then the firm will not even consider this project. However, the cost of building the road will have to be considered along with the cost of building the new plant in the capital budgeting analysis. c. These are two mutually exclusive projects. The company’s computers need only one operating system. Either the Linux or the Windows operating system needs to be installed, not both. Hence, the selection of one will eliminate the other from consideration. LO: 1 Level: Intermediate Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.3

In the context of capital budgeting, what is “capital rationing”?

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the available projects. In other words, funding needs exceed funding resources. Thus, the available capital will be allocated to the projects that will benefit the firm and its shareholders the most. Projects that create the largest increase in shareholder wealth will be accepted until all the available resources have been allocated. LO: 1 Level: Basic Bloomcode: Knowledge AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.4

Provide two conditions under which a set of projects might be characterized as mutually exclusive.

Solution When projects are mutually exclusive, acceptance of one project precludes the acceptance of others. Typically, mutually exclusive projects perform the same function and so only one of them needs to be accepted. A funding or resource constraint can also cause projects to be mutually exclusive. LO: 1 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.5

a. A firm invests in a project that is expected to earn a return of 12 percent. If the appropriate cost of capital is also 12 percent, did the firm make the right decision. Explain.

b. What is the impact on the firm if it accepts a project with a negative NPV?

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Solution a. We would normally argue that a firm should only accept projects in which the project’s return exceeds the cost of capital. In other words, only if the net present value exceeds zero should a project be accepted. But in reality, projects with a zero NPV should also be accepted because the project earns a return that equals the cost of capital. For some firms like the one above, this could be the situation because they may not have projects that provide a return greater than the cost of capital for the firm. b. When a firm takes on positive NPV projects, the value of the firm increases. By the same token, when a project undertaken has a negative NPV, the value of the firm will decrease by the amount of the net present value. LO: 2 Level: Basic Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.6

Identify the weaknesses of the payback period method.

Solution There are several critical weaknesses in the payback period approach of evaluating capital projects. ▪

The payback period ignores the time value of money by not discounting future cash flows.

▪

When comparing projects, it ignores risk differences between the projects.

▪

A firm may establish payback criteria with no economic basis for that decision and thereby, run the risk of losing out on good projects.

▪

The method ignores cash flows beyond the payback period, thus leading to nonselection of projects that may produce cash flows well beyond the payback period or more cash flows than accepted projects. This leads to a bias against longer-term projects.

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LO: 3 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.7

What are the strengths and weaknesses of the accounting rate of return approach?

Solution The biggest advantage of accounting rate of return (ARR) approach is that it is easy to compute since accounting data is readily available, whereas estimating cash flows is more difficult. However, the disadvantages outweigh this specific advantage. Similar to the payback, it does not discount cash flows, but merely averages net income over time. No economic rationale is used in establishing an ARR cutoff rate. Finally, the ARR uses net income to evaluate the project and not cash flows or market data. This is a serious flaw in this approach. LO: 4 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.8

Under what circumstances might the IRR and NPV approaches produce conflicting

results? Solution IRR and the NPV methods of evaluating capital investment projects might produce dissimilar results under two circumstances. First, if the project’s cash flows are not conventional—that is, if the sign of the cash flow changes more than once during the life of a project—then multiple IRRs can be obtained as solutions. Therefore, we would be unable to identify the correct IRR for decision making. (See Learning by Doing Copyright © 2022 John Wiley & Sons, Inc.

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Application 10.3.) The second situation occurs when two or more projects are mutually exclusive. The project with the highest IRR may not necessarily be the one with the highest NPV and thereby, be the right choice. There is an important reason for this. IRR assumes that all cash flows received during the life of a project are reinvested at the IRR, whereas, the NPV method assumes that they are reinvested at the cost of capital. Since the cost of capital is the better proxy for opportunity cost, NPV uses the better proxy, while the IRR may use an unrealistically higher rate as proxy. LO: 5 Level: Intermediate Bloomcode: Comprehension AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.9

The modified IRR (MIRR) alleviates two concerns with using the IRR method for evaluating capital investments. What are they?

Solution IRR assumes that the cash flows from a project are reinvested at the project’s IRR, while the NPV assumes that they are invested at the firm’s cost of capital. The NPV assumption is correct more often than not. The MIRR assumes that each operating cash flow is reinvested at the firm’s cost of capital.

The second appeal of MIRR is that under this method all of the compounded operating cash flow values are summed up to get the project’s terminal value. Since most projects generate positive total net operating cash flows, MIRR does not suffer from issues associated with unconventional cash flows. LO: 5 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Investment Decisions Copyright © 2022 John Wiley & Sons, Inc.

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AICPA: Industry/Sector Perspective

10.10 Elkridge Construction Company has an average cost of capital of 12 percent. This cost of capital reflects the cost of capital for an Elkridge Construction project with average risk. However, the firm takes on projects of various risk levels. The company’s experience suggests that low-risk projects have a cost of capital of 10 percent and highrisk projects have a cost of capital of 15 percent. Which of the following projects should the company reject?

Project

Expected Return

Risk

1. Single-family homes

13%

Low

2. Multifamily residential

Average

3. Commercial

High

4. Single-family homes

Low

5. Commercial

High

Solution Required

Expected

Return

Low

10%

13%

2. Multifamily residential

Average

Accept / Indifferent

3. Commercial

High

4. Single-family homes

Low

Reject

5. Commercial

High

Reject

Project

Risk

1. Single-family homes

Decision

LO: 2 Level: Basic Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

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10.11 High Tech Monopoly Co. has plenty of cash to fund any conceivable positive NPV project. Can you describe a situation in which capital rationing could still occur?

Solution: Financial capital is not the only constrainable item within the firm. This might occur, for example, when human capital is in short supply, as is the case with most high-technology firms. Even if every positive NPV project could be funded, the firm might not have enough employees to manage the projects. Therefore, even with ample financial capital, firms will more than likely still be rationing projects. LO: 6 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective 10.12 The profitability index is a tool for measuring a project’s benefits relative to its costs. How might this help to eliminate bias in project selection? Solution: Since the profitability index is a modified pure-return-type measure, it offers a method to maximize the use of capital that is employed by the firm. This could help eliminate some types of bias if the measure were to be employed universally. However, it does not necessarily maximize the use of capital that is not employed, which could in some circumstances be problematic. LO: 6 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

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Questions and Problems BASIC 10.1

Net present value: Riggs Corp. management is planning to spend $650,000 on a newmarketing campaign. It believes that this action will result in additional cash flows of $325,000 over the next three years. If the discount rate is 17.5 percent, what is the NPV on this project?

Solution: Initial investment = $650,000 Annual cash flows = $325,000 Length of project = n = 3 years Required rate of return = k = 17.5% Net present value = NPV n

NCFt $325,000 $325,000 $325,000 = −$650,000 + + + t (1.175)1 (1.175)2 (1.175)3 t = 0 (1 + k ) = −$650,000 + 276,596 + $235, 401 + $200,341

NPV = 

= $62, 338

Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: Cash Flow (C)

Frequency (F)

-650,000

325,000

Then solve by pressing NPV, enter the rate of 17.5% and compute NPV=62,337.34. LO: 2 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

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Net present value: Kingston, Inc. management is considering purchasing a new machine at a cost of $4,133,250. It expects this equipment to produce cash flows of $814,322, $863,275, $937,250, $1,017,112, $1,212,960, and $1,225,000 over the next six years. If the appropriate discount rate is 15 percent, what is the NPV of this investment?

Solution: Cost of new machine = $4,133,250 Length of project = n = 6 years Required rate of return = k = 15% n

NPV =  t =0

NCFt (1 + k )t

$814,322 $863,275 $937,250 $1,017,112 $1,212,960 $1,225,000 + + + + + (1.15)1 (1.15)2 (1.15)3 (1.15)4 (1.15)5 (1.15)6 = −$4,133,250 + $708,106 + $652,760 + $616,257 + $581,537 + $603,055 + $529,601 = −$441, 934

= −$4,133,250 +

Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: Cash Flow (C)

Frequency (F)

-4,133,250

814,322

863,275

937,250

1,017,112

1,212,960

1,225,000

Then solve by pressing NPV, enter the rate of 15% and compute NPV= -441,933 LO: 2 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

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Net present value: Crescent Industries management is planning to replace some existing machinery in its plant. The cost of the new equipment and the resulting cash flows are shown in the accompanying table. If the firm uses an 18 percent discount rate for projects like this, should management go ahead with the project? Year

Cash Flow

−$3,300,000

875,123

966,222

1,145,000

1,250,399

1,504,445

Solution: Initial investment = $3,300,000 Length of project = n = 5 years Required rate of return = k = 18% n

NCFt (1 + k )t t =0

NPV = 

$875,123 $966,222 $1,145,000 $1,250,399 $1,504, 455 + + + + (1.18)1 (1.18)2 (1.18)3 (1.18)4 (1.18)5 = −$3,300,000 + $741,630 + $693,926 + $696,882 + $644,942 + $657,611 = $134, 991

= −$3,300,000 +

Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: Cash Flow (C)

Frequency (F)

-3,300,000

875,123

966,222

1,145,000

1,250,399

1,504,455

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Then solve by pressing NPV, enter the rate of 18% and compute NPV= 134,986 Since the NPV is positive, the firm should accept the project. LO: 2 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.4

Net present value: Management of Franklin Mints, a confectioner, is considering purchasing a new jelly bean-making machine at a cost of $312,500. It projects that the cash flows from this investment will be $121,450 for the next seven years. If the appropriate discount rate is 14 percent, what is the NPV for the project?

Solution: Initial investment = $312,500 Annual cash flows = $121,450 Length of project = n = 7 years Required rate of return = k = 14% n

NCFt t t = 0 (1 + k )

NPV = 

$121, 450 $121, 450 $121, 450 $121, 450 $121, 450 + + + + (1.14)1 (1.14)2 (1.14)3 (1.14)4 (1.14)5 $121, 450 $121, 450 + + (1.14)6 (1.14)7 = −$312,500 + $106,535 + $93, 452 + $81,975 + $71,908 + $63,077 + $55,331 + $48,536 = $208, 314

= −$312,500 +

Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows:

Cash Flow (C)

Frequency (F)

-312,500

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121,450

Then solve by pressing NPV, enter the rate of 14% and compute NPV= 208,315 LO: 2 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.5

Net present value: Blanda Incorporated management is considering investing in two alternative production systems. The systems are mutually exclusive, and the cost of the new equipment and the resulting cash flows are shown in the accompanying table. If the firm uses a 9 percent discount rate for production system projects, in which system should the firm invest?

Year

System 1

System 2

-15,000

-45,000

15,000

32,000

15,000

32,000

15,000

32,000

Solution NPV = NCF0 + =

NCF1 NCF2 NCFn + + ..... + 2 1 + k (1 + k ) (1 + k )n n

NCFt

 (1 + k ) t =0

The NPV is needed first for System 1: NPVSystem 1 = −$15,000 +

$15,000 $15,000 $15,000 + + = $2,650.78 (1.09)1 (1.09)2 (1.09)3

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Using a financial calculator, enter the cash flows as follows: System 1

Cash Flow (C)

Frequency (F)

-15,000

15,000

Solve by pressing NPV, enter the rate of 9% and compute NPV= 22,969.42

For System 2: NPVSystem 2 = −$45,000 +

$32,000 $32,000 $32,000 + + = $36,001.43 (1.09)1 (1.09)2 (1.09)3

NPVSystem 2 = −$45,000 + $29,357.80 + $26,933.76 + $24,709.87 = $36,001.43

Using a financial calculator, enter the cash flows as follows: System 2

Cash Flow (C)

Frequency (F)

-45,000

32,000

Then solve by pressing NPV, enter the rate of 9% and compute NPV= 36,001.43 The NPV of System 1 is $22,969.42 and the NPV of System 2 is $36,001.43. Since the NPV of the System 2 is larger than the NPV for System 1, and the investments are mutually exclusive, the firm should undertake System 2. LO: 2 Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.6

Payback: Refer to problem 10.5. What are the payback periods for Production Systems 1 and 2? If the systems are mutually exclusive and the firm always chooses projects with the lowest payback period, in which system should the firm invest?

Solution

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System 1 has a payback of exactly one year ($15,000/$15,000). System 2 has a payback of 1.41 years ($45,000/$32,000). Given the shorter payback period for System 1, the investment should be made in System 1 based on the payback criteria. LO: 3 Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.7

Payback: Quebec, Inc., is purchasing machinery at a cost of $3,768,966. The company’s management expects the machinery to produce cash flows of $979,225, $1,158,886, and $1,881,497 over the next three years, respectively. What is the payback period?

Solution: Cumulative Year

Cash Flow

-$3,768,966

979,225

-2,789,741

1,158,886

-1,630,855

1,881,497

250,642

PB = Years before cost recovery + (Remaining cost to recover/ Cash flow during the year) = 2 + ($1,630,855 / $1,881,497) = 2.87 years LO: 3 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.8

Payback: Northern Specialties just purchased inventory-management computer software at a cost of $1,645,276. Cost savings from the investment over the next six years will produce the following cash flow stream: $212,455, $292,333, $387,479, $516,345,

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$645,766, and $618,325. What is the payback period on this investment? Solution: Cumulative Year

Cash Flow

-$1,645,276

212,455

-1,432,821

292,333

-1,140,488

387,479

-753,009

516,345

-236,664

645,766

409,102

618,325

1,027,427

PB = Years before cost recovery + (Remaining cost to recover/ Cash flow during the year) = 4 + ($236,664 / $645,766) = 4.37 years LO: 3 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.9

Payback: Nakamichi Bancorp has made an investment in banking software at a cost of $1,875,000. If management expects productivity gains and cost savings over the next several years. If, as a result of this investment, the firm is expected to generate additional cash flows of $586,212, $713,277, $431,199, and $318,697 over the next four years, what is the investment’s payback period?

Solution: Cumulative Year 0

CF -$1,875,000

Cash Flow $-1,875,000

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586,212

-1,288,788

713,277

-575,511

431,199

-144,312

318,697

174,385

PB = Years before cost recovery + (Remaining cost to recover/ Cash flow during the year) = 3 + ($144,312 / $318,697) = 3.45 years LO: 3 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective 10.10 Average accounting rate of return (ARR): Capitol Corp. management is expecting a project to generate after-tax income of $63,435 in each of the next three years. The average book value of the project’s equipment over that period will be $212,500. If the firm’s investment decision on any project is based on an ARR of 37.5 percent, should this project be accepted? Solution: Annual after-tax income = $63,435 Average after-tax income = ($63,435 +$63,435 + $63,435) / 3 = $63,435 Average book value of equipment = $212,500 Average after - tax income Average book value $63,435 = = 29.9% $212,500

Accounting rate of return =

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IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.11 Internal rate of return: Refer to Problem 10.4. What is the IRR that Franklin Mints management can expect on this project? Solution: Initial investment = $312,500 Annual cash flows = $121,450 Length of project = n = 7 years Required rate of return = k = 14% To determine the IRR, a trial-and-error approach can be used. Set NPV = 0. Since the project had a positive NPV of $208,315, try IRR > k. Try IRR = 25%. n

NCFt t t = 0 (1 + IRR)

NPV = 0 = 

1    1 − (1.25)7  0  −$312,500 + $121, 450     0.25     −$312,500 + $383,920  $71, 420 Try a higher rate, IRR = 34%. n

NCFt t t = 0 (1 + IRR)

NPV = 0 = 

1    1 − (1.34)7  0  −$312,500 + $121, 450     0.34     −$312,500 + $311,161  −$1,339

Try a lower rate, IRR = 33.8%.

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NCFt t t = 0 (1 + IRR)

NPV = 0 = 

1    1 − (1.338)7  0 = −$312,500 + $121, 450     0.338    = −$312,500 + $312,515 = $15  0 The IRR of the project is approximately 33.8 percent. Using a financial calculator, we find that the IRR is 33.802 percent.

Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: Cash Flow (C)

Frequency (F)

-312,500

121,750

Then solve by pressing IRR to get 33.802%. LO: 5 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.12 Internal rate of return: Hathaway, Inc., a resort management company, is refurbishing one of its hotels at a cost of $7.8 million. Management expects that this will lead to additional cash flows of $1.8 million for each of the next six years. What is the IRR of this project? If the appropriate cost of capital is 12 percent, should Hathaway go ahead with this project? Solution: Initial investment = $7,800,000 Annual cash flows = $1,800,000 Length of project = n = 6 years Copyright © 2022 John Wiley & Sons, Inc.

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Required rate of return = k = 12% To determine the IRR, a trial-and-error approach can be used. Set NPV = 0. Try IRR = 12%. n

NCFt (1 + IRR)t t =0

NPV = 0 = 

1   1 − (1.12)6  0  −$7,800, 000 + $1,800, 000     0.12     −$7,800, 000 + $7, 400,533  −$399, 467

Since NPV < 0, try a lower rate, IRR = 10%. n

NCFt (1 + IRR)t t =0

NPV = 0 = 

1   1 − (1.10)6  0  −$7,800, 000 + $1,800, 000     0.10     −$7,800, 000 + $7,839, 469  $39, 469 Try IRR = 10.2%. n

NCFt t t = 0 (1 + IRR)

NPV = 0 = 

1   1 − (1.102)6  0  −$7,800, 000 + $1,800, 000     0.102     −$7,800, 000 + $7, 793, 735  −$6, 265 Try IRR = 10.15%.

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NCFt t t = 0 (1 + IRR)

NPV = 0 = 

1   1 − (1.1015) 6  0  −$7,800, 000 + $1,800, 000     0.1015     −$7,800, 000 + $7,805,129  $5,129 The IRR of the project is between 10.15 percent and 10.2 percent. Using a financial calculator, we find that the IRR is 10.1725 percent. Since IRR < k, reject the project.

Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: Cash Flow (C)

Frequency (F)

-7,800,000

1,800,000

Then solve by pressing IRR to get 10.1725% LO: 5 Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.13 Profitability index: What is the profitability index, and why is it helpful in the capital rationing process? Solution: The profitability index is a measure of the value a project generates for each dollar invested in that project. It is computed as the ratio of NPV plus initial investment divided by initial investment. In the capital rationing process, we can calculate the profitability index for each potential investment and choose the projects with the largest indexes until we run out of capital. This follows the basic principle that we need to choose the set of projects that creates the greatest value given the limited capital available. Copyright © 2022 John Wiley & Sons, Inc.

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LO: 6 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

INTERMEDIATE 10.14 Net present value: Champlain Corp. management is investigating two computer systems. The Alpha 8300 costs $3,122,300 and will generate cost savings of $1,345,500 in each of the next five years. The Beta 2100 system costs $3,750,000 and will produce cost savings of $1,125,000 in the first three years and then $2 million for the next two years. If the company’s discount rate for similar projects is 14 percent, what is the NPV for each system? Which one should be chosen based on the NPV? Solution: Cost of Alpha 8300 = $3,122,300 Annual cost savings = $1,345,500 Length of project = n = 5 years Required rate of return = k = 14% 1   1 − (1.14)5  NCFt NPV =  = −$3,122,300 + $1,345,500    t t = 0 (1 + k)  0.14    = −$3,122,300 + $4, 619, 210 n

= $1, 496, 910

Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: Alpha

Cash Flow (C)

Frequency (F)

-3,122,300

1,345,500

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Then solve by pressing NPV, enter the rate of 14% and compute NPV=1,496,910 Cost of Beta 2100 = $3,750,000 Length of project = n = 5 years Required rate of return = k = 14% 1    1 − (1.14)3  $2,000,000 $2,000,000 NCFt NPV =  = −$3,750,000 + $1,125,000   + + t (1.14)4 (1.14)5 t = 0 (1 + k )  0.14    = −$3,750,000 + $2,611,836 + $1,184,161 + 1,038,737 = $1, 084,734 n

Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: Beta

Cash Flow (C)

Frequency (F)

-375,000,000

1,125,500

Then solve by pressing NPV, enter the rate of 14% and compute NPV=1,084,734 Based on the NPV, the Alpha 8300 system should be chosen. LO: 2 Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.15 Net present value: Briarcrest Condiments is a spice-making firm. Recently, it developed a new process for producing spices. The process requires new machinery that would cost $1,968,450, have a life of five years, and would produce the cash flows shown in the following table. What is the NPV if the discount rate is 15.9 percent? Year

Cash Flow

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$512,496

-242,637

814,558

887,225

712,642

Solution: Cost of equipment = $1,968,450 Length of project = n = 5 years Required rate of return = k = 15.9% n

NCFt (1 + k)t t =0

NPV = 

$512, 496 $242, 637 $814,558 $887, 225 $712, 642 − + + + (1.159)1 (1.159)2 (1.159)3 (1.159)4 (1.159)5 = −$1,968, 450 + $442,188 − $180, 630 + $523, 205 + 491, 700 + 340, 764 = −$351, 223

= −$1,968, 450 +

Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: Cash Flow (C)

Frequency (F)

-1,968,450

$512,496

(242,637)

814,558

887,225

712,642

Then solve by pressing NPV, enter the rate of 15.9% and compute NPV=-351,223 LO: 2 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

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10.16 Net present value: Cranjet Industries is expanding its product line and its production capacity. The costs and expected cash flows of the two independent projects are given in the following table. The firm uses a discount rate of 16.4 percent for such projects. a.

What are the NPVs of the two projects?

Should both projects be accepted? Or either? Or neither? Explain your reasoning.

Product Line

Production Capacity

Year

Expansion

-$2,575,000

-$8,137,250

600,000

2,500,000

875,000

2,500,000

875,000

2,500,000

875,000

3,250,000

875,000

3,250,000

Solution: a.

Required rate of return = k =16.4% Product Line Expansion: Cost of product line expansion = $2,575,000 n

NPV =  t =0

NCFt (1 + k )t

$600, 000 $875, 000 $875, 000 $875, 000 $875, 000 + + + + (1.164)1 (1.164)2 (1.164)3 (1.164)4 (1.164)5 = −$2,575, 000 + $515, 464 + $645,806 + $554,816 + 476, 646 + 409, 490 = $27, 222 = −$2,575, 000 +

Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: Product Line

Cash Flow (C)

Frequency (F)

-2,575,000

600,000

875,000

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Solutions Manual

Then solve by pressing NPV, enter the rate of 16.4% and compute NPV=27,222

Production Capacity Expansion: Cost of production capacity expansion = $8,137,250 n

NCFt (1 + k)t t =0

NPV = 

1   1 − (1.164)3  $3, 250, 000 $3, 250, 000 = −$8,137, 250 + $2,500, 000   + + (1.164) 4 (1.164)5  0.164    = −$8,137, 250 + $5,578,116 + $1, 770, 400 + $1,520,962 = $732, 228

Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: Production Capacity

Cash Flow (C)

Frequency (F)

-8,137,250

2,500,000

3,250,000

Then solve by pressing NPV, enter the rate of 16.4% and compute NPV=732,227.95 b.

Since they are independent, and both have NPV > 0, both projects should be accepted.

LO: 2 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective 10.17 Net present value: Emporia Mills management is evaluating two alternative heating systems. Costs and projected energy savings are given in the following table. The firm uses 11.5 percent to discount such project cash flows. Which system should be chosen? Copyright © 2022 John Wiley & Sons, Inc.

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Year

System 100

System 200

-$1,750,000

-$1,735,000

275,223

750,000

512,445

612,500

648,997

550,112

875,000

384,226

Solution: Required rate of return = k = 11.5% System 100: Cost of System 100 = $1,750,000 n

NCFt $275, 223 $512, 445 $648,997 $875, 000 = −$1, 750, 000 + + + + t (1 + k) (1.115)1 (1.115) 2 (1.115)3 (1.115) 4 t =0 = −$1, 750, 000 + $246,837 + $412,190 + $468,186 + 566,120 = −$56, 667

NPV = 

Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: System 100

Cash Flow (C)

Frequency (F)

-1,750,000

275,223

512,445

648,997

875,000

Then solve by pressing NPV, enter the rate of 11.5% and compute NPV= -56,667.41

System 200: Cost of System 200 = $1,735,000

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NCFt $750, 000 $612,500 $550,112 $384, 226 = −$1, 735, 000 + + + + t (1 + k) (1.115)1 (1.115) 2 (1.115)3 (1.115) 4 t =0 = −$1, 735, 000 + $672, 646 + $492, 670 + $396,850 + 248,592 = $75, 758

NPV = 

Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: System 200

Cash Flow (C)

Frequency (F)

-1,735,000

750,000

612,500

550,112

384,226

Then solve by pressing NPV, enter the rate of 11.5% and compute NPV= 75,758 Since System 200 has a positive NPV, select that system. Reject System 100 as it has negative NPV. LO: 2 Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.18 Payback: Creative Solutions, Inc., has just invested $4,615,300 in new equipment. The firm uses a payback period criterion of rejecting any project that takes more than four years to recover its costs. Management anticipates cash flows of $644,386, $812,178, $943,279, $1,364,997, $2,616,300, and $2,225,375 over the next six years. Does this investment meet the firm’s payback criterion? Solution: Cumulative Year Copyright © 2022 John Wiley & Sons, Inc.

Cash Flow SM 10-39

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-$4,615,300

644,386

-3,970,914

812,178

-3,158,736

943,279

-2,215,457

1,364,997

-850,460

2,616,300

1,765,840

2,225,375

3,991,215

Payback period = Years before cost recovery +

Remaining cost to recover Cash flow during the year

$850, 460 $2,616,300 = 4.33 years

=4+

Since the project payback period exceeds the firm’s target of four years, it should not have been accepted. LO: 3 Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.19 Discounted payback: Timeline Manufacturing Co. management is evaluating two projects. The company uses payback criterion of three years or less. Project A has a cost of $912,855, and project B’s cost is $1,175,000. Cash flows from both projects are given in the following table. What are their discounted payback periods, and which will be accepted with a discount rate of 8 percent?

Year

Project A

Project B

$ 86,212

$586,212

313,562

413,277

427,594

231,199

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285,552

Solution: Project A Cumulative

Cumulative

Year

PVCF

-$912,855

86,212

-826,643

79,826

-833,029

313,562

-513,081

268,829

-564,200

427,594

-85,487

339,438

-224,762

285,552

200,065

209,889

-14,873

The payback period of Project A exceeds three years. Project B Cumulative

Cumulative

Year

PVCF

-$1,175,000

586,212

-588,788

542,789

-632,211

413,277

-175,511

354,318

-277,893

231,199

55,688

183,533

-94,360

The payback period of Project B exceeds three years. Since the firm’s acceptance criteria is three years, neither project will be accepted. LO: 3 Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.20 Payback: Regent Corp. management is evaluating three competing types of equipment. Costs and cash flow projections for all three are given in the following table. Which would be the best choice based on payback period? Copyright © 2022 John Wiley & Sons, Inc.

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Year

Solutions Manual

Type 1

Type 2

Type 3

$(1,311,450)

$(1,415,888)

$(1,612,856)

212,566

586,212

786,212

269,825

413,277

175,000

455,112

331,199

175,000

285,552

141,442

175,000

121,396

175,000

Solution: Type 1

Type 2

Cumulative

Type 3

Cumulative

Year

$(1,311,450)

$(1,415,888)

$(1,612,856)

($1,612,856)

212,566

(1,098,884)

586,212

(829,676)

786,212

(826,644)

269,825

(829,059)

413,277

(416,399)

175,000

(651,644)

455,112

(373,947)

331,199

(85,200)

175,000

(476,644)

285,552

(88,395)

141,442

56,242

175,000

(301,644)

121,396

33,001

175,000

(126,644)

175,000

48,356

Type 1: Payback period = Years before cost recovery +

Remaining cost to recover Cash flow during the year

$88,395 $121,396 = 4.73 years

=4+

Type 2: Payback period = Years before cost recovery +

Remaining cost to recover Cash flow during the year

$85, 200 $141, 442 = 3.6 years

= 3+

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Solutions Manual

Type 3: Payback period = Years before cost recovery +

Remaining cost to recover Cash flow during the year

$126,644 $175,000 = 5.72 years

= 5+

Select Type 2 because it has the lowest payback period. LO: 3 Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.21 Discounted payback: Nugent Communication Corp. is considering an investment in new technologies. The company’s management expects significant benefits in the first three years after installation, and smaller constant benefits in each of the next four years. Using the cash flows in the following table, calculate the discounted payback period for the project assuming a discount rate of 10 percent? Year

Cash Flow

-$9,365,000

$2,265,433

$4,558,721

$3,378,911

4-7

$1,250,000

Solution: Discount rate = k = 10% Cumulative

Cumulative

Year

PVCF

-$9,365,000

-$9,365,000)

-$9,365,000

2,265,433

-7,099,567

2,059,485

-7,305,515

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Solutions Manual

4,558,721

-2,540,846

3,767,538

-3,537,977

3,378,911

838,065

2,538,626

-999,351

1,250,000

2,088,065

853,767

-145,584

1,250,000

3,338,065

776,152

630,568

1,250,000

4,588,065

705,592

1,336,160

1,250,000

5,838,065

641,448

1,977,608

Discounted PB = Years before cost recovery + (Remaining cost to recover/ Cash flow during the year) = 4 + ($145,584 / $776,152) = 4.19 years LO: 3 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.22 Modified internal rate of return (MIRR): Morningside Bakeries recently purchased equipment at a cost of $650,000. Management expects the equipment to generate cash flows of $275,000 in each of the next four years. The cost of capital is 14 percent. What is the MIRR for this project? Solution: PV of costs = $650,000 Length of project = n = 4 years Cost of capital = k = 14% Annual cash flows = CFt = $275,000

TV = CF1 (1 + k ) n −1 + CF2 (1 + k ) n − 2 +  + CFn (1 + k ) n − n = $275,000(1.14)3 + $275,000(1.14) 2 + $275,000(1.14)1 + $275,000(1.14)0 = $407,425 + $357,390 + $313,500 + $275,000 = $1,353,315

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Find the Terminal Value of the annual cash inflows by using a financial calculator as follows: 4

275,000

PMT

FV -1,353,315

Now we can solve for the MIRR using Equation 10.5. TV (1 + MIRR)t $1,353,315 $650, 000 = (1 + MIRR) 4 $1,353,315 (1 + MIRR) 4 = = 2.0820 $650, 000 PVCos ts =

(1 + MIRR) = (2.0820) 4 = 1.2012 1

MIRR = 0.2012 = 20.1%

Financial Calculator Solution: 4 N

-650,000

1,353,315

PMT

i 20.12

LO: 5 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.23 Modified internal rate of return (MIRR): Management of Sycamore Home Furnishings is considering acquiring a new machine that can create customized window treatments. The equipment will cost $263,400 and will generate cash flows of $85,000 over each of the next six years. If the cost of capital is 12 percent, what is the MIRR on this project?

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Solutions Manual

PV of costs = $263,400 Length of project = n = 6 years Cost of capital = k = 12% Annual cash flows = CFt = $85,000

TV = CF1 (1 + k ) n −1 + CF2 (1 + k ) n − 2 +  + CFn (1 + k ) n − n = $85,000(1.12)5 + $85,000(1.12) 4 + $85,000(1.12)3 + $85,000(1.12) 2 + $85,000(1.12)1 + $85,000(1.12)0 = $149,799 + $133,749 + $119,419 + $106,624 + $95,200 + $85,000 = $689,791

Financial Calculator Solution: Find the Terminal Value of the annual cash inflows by using a financial calculator as follows: 6

85,000

PMT

FV -689,791.07

Now we can solve for the MIRR using Equation 10.5.

TV (1 + MIRR) t $689,791 $263, 400 = (1 + MIRR)6 $689,791 (1 + MIRR)6 = = 2.6188 $263, 400 PVCosts =

(1 + MIRR) = (2.6188) 6 = 1.1740 MIRR = 0.1740 = 17.4% 1

Financial Calculator Solution: 6 N

-263,400

689,791

PMT

17.40

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LO: 5 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.24 Internal rate of return: Management of Great Flights, Inc., an aviation firm, is considering purchasing three aircraft for a total cost of $161 million. The company would lease the aircraft to an airline. Cash flows from the proposed leases are shown in the following table. What is the IRR of this project? Years

Cash Flow

1–4

$23,500,000

5–7

$72,000,000

8–10

$80,000,000

Years

Cash Flow

1–4

$23,500,000

5–7

$72,000,000

8–10

$80,000,000

Solution:

Initial investment = $161,000,000 Length of project = n = 10 years Required rate of return = k =

To determine the IRR, the trial-and-error approach can be used. Set NPV=0. Try a higher rate than k = 15%; try IRR = 22%.

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NCFt t t = 0 (1 + IRR)

NPV = 0 = 

1  1     1 − (1.22)4   1 − (1.22)3  1 0  −$161,000,000 + $23,500,000    + $72,000,000    4  0.22   0.22  (1.22)     1    1 − (1.22)3  1 +$80,000,000    7 0.22 (1.22)      −$161,000,000 + $58,600,549 + $66,374,346 + $40,614,233  $4,589,128

Try IRR = 23%. n

NCFt t t = 0 (1 + IRR)

NPV = 0 = 

1  1     1 − (1.23)4   1 − (1.23)3  1 0  −$161,000,000 + $23,500,000    + $72,000,000    4 0.23 0.23 (1.23)         1    1 − (1.23)3  1 +$80,000,000    7 0.23 (1.23)      −$161,000,000 + $57,534,386 + $63,271,035 + $37,778,708  −$2, 415,871

Try IRR = 22.7%. n

NCFt (1 + IRR)t t =0

NPV = 0 = 

1 1      1 − (1.227)4   1 − (1.227)3  1 0  −$161,000,000 + $23,500,000    + $72,000,000    4 0.227 0.227 (1.227)         1    1 − (1.227)3  1 +$80,000,000    7 0.227 (1.227)      −$161,000,000 + $57, 850,786 + $64,183,552 + $38,605,355  −$360,307

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The IRR of the project is between 22 and 23 percent. Using a financial calculator, we find that the IRR is 22.65 percent.

Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: Cash Flow (C)

Frequency (F)

-161,000,000

23,500,000

72,000,000

80,000,000

Then solve by pressing IRR to get 22.65% LO: 5 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.25 Internal rate of return: Refer to problem 10.5. Compute the IRR for both Production System 1 and Production System 2. Which has the higher IRR? Which production system has the higher NVP? Explain why the IRR and NPV rankings of Systems 1 and 2 are different? Solution The IRR of System 1 is 83.93 percent, and the IRR of System 2 is 50.07 percent. The NPV of System 1 is $22,969.42 and the NPV of System 2 is $36,001.43. System 1 delivers a higher IRR because it requires a lower initial investment, and the cost is recovered the first year. Thus, even with lower cash inflows in the years after startup, System 1 is able to deliver a higher return on the initial investment. System 2 has a higher initial investment but delivers a higher net cash flow for the firm.

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Using a financial calculator, enter the cash flows as follows: System 1

Cash Flow (C)

Frequency (F)

-15,000

15,000

Then solve by pressing IRR to get 83.93%. Then solve by pressing NPV, enter the rate of 9% and compute NPV= 22,969.42

Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: System 2

Cash Flow (C)

Frequency (F)

-45,000

32,000

Then solve by pressing IRR to get 50.07%. Then solve by pressing NPV, enter the rate of 9% and compute NPV= 36,001.43 LO: 5 Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.26 Internal rate of return: Ancala Corporation management is considering investments in two new golf apparel lines for next season: golf hats and belts. Due to a funding constraint, these lines are mutually exclusive. A summary of each project’s estimated cash flows over its three -year life, as well as the IRR and NPV of each are outlined below. The CFO of the firm has decided to manufacture the belts; however, the CEO is questioning this decision given that the IRR is higher for manufacturing hats. Explain to the CEO why the IRRs and NPVs of the belt and hat projects disagree? Is the CFO’s decision correct?

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Year

Golf Belts

Golf Hats

-$1,000

-$500

1,000

500

300

500

300

NPV

$697.97

$427.87

IRR

54%

61%

Solution The IRRs and NPVs of the belt and hat lines disagree because of the differences in the scale of the project. Golf hats deliver a higher IRR because they require a lower initial investment. Thus, even with lower cash inflows in the years after startup, the golf hat project is able to deliver a higher return on the initial investment. While the golf belts project does cost more, it delivers a higher net cash flow for Ancala’s investors. This NPV factors in the initial cost of the project and reflects the total net cash flow for the firm’s shareholders. The CFO’s decision to choose the golf belts project is the right choice because it yields the higher net cash flows for Ancala’s investors. LO: 5 Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.27 Internal rate of return: Compute the IRR on the following cash flow streams: a.

An initial investment of $25,000 followed by a single cash flow of $37,450 in year 6.

An initial investment of $1 million followed by a single cash flow of $1,650,000 in year 4.

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An initial investment of $2 million followed by cash flows of $1,650,000 and $1,250,000 in years 2 and 4, respectively.

LO: 5 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective Solution: a.

Try IRR = 7%. n

NCFt (1 + IRR)t $37, 450 0  −$25, 000 + (1.07)6  −$25, 000 + $24,955  −$45

NPV = 0 =  t =0

Try IRR = 6.97%. n

NCFt t t = 0 (1 + IRR) $37, 450 0  −$25, 000 + (1.0697)6  −$25, 000 + $24,997  −$3

NPV = 0 = 

The IRR of the project is approximately 6.97 percent. Using a financial calculator, we find that the IRR is 6.968 percent.

Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: Cash Flow (C)

Frequency (F)

-25,000

37,450

Then solve by pressing IRR which gives the result 6.968%

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Try IRR = 12%. n

NCFt t t = 0 (1 + IRR) $1, 650, 000 0  −$1, 000, 000 + (1.12)4  −$1, 000, 000 + $1, 048, 605  $48, 605

NPV = 0 = 

Try IRR = 13%. n

NCFt (1 + IRR)t t =0 $1, 650, 000 0  −$1, 000, 000 + (1.13) 4  −$1, 000, 000 + $1, 011,976  $11,976

NPV = 0 = 

Try IRR = 13.3%. n

NCFt (1 + IRR)t $1, 650, 000 0  −$1, 000, 000 + (1.133)4  −$1, 000, 000 + $1, 001,300  $1,300

NPV = 0 =  t =0

The IRR of the project is approximately 13.3 percent. Using a financial calculator, we find that the IRR is 13.337 percent.

Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: Cash Flow (C)

Frequency (F)

-1,000,000

1,650,000

Then solve by pressing IRR which gives an answer of 13.337%

Alternatively:

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4 N

Solutions Manual

-1,000,000

1,650,000

PMT

i 13.337

Try IRR = 15%. n

NCFt (1 + IRR)t t =0 $1, 650, 000 $1, 250, 000 0  −$2, 000, 000 + + (1.15)2 (1.15)4  −$2, 000, 000 + $1, 247, 637 + $714, 692  −$37, 671

NPV = 0 = 

Try IRR = 14%. n

NCFt (1 + IRR)t $1, 650, 000 $1, 250, 000 0  −$2, 000, 000 + + (1.14)2 (1.14)4  −$2, 000, 000 + $1, 269, 621 + $740,100  $9, 721

NPV = 0 =  t =0

The IRR of the project is between 14 and 15 percent. Using a financial calculator, we find that the IRR is 14.202 percent.

Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: Cash Flow (C)

Frequency (F)

-2,000,000

1,650,000

1,250,000

Then solve by pressing IRR which gives an answer of 14.202%

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An initial outlay of $3,125,000 followed by annual cash flows of $565,325 for the next eight years.

An initial investment of $33,750 followed by annual cash flows of $9,430 for the next five years.

An initial outlay of $10,000 followed by annual cash flows of $2,500 for the next seven years.

Solution: a.

Initial investment = $3,125,000 Annual cash flows = $565,325 Length of investment = n = 8 years

Try IRR = 8%. 1   1 − (1.08)8  NCFt NPV =  = −$3,125, 000 + $565,325    t t = 0 (1 + k)  0.08    = −$3,125, 000 + $3, 248, 719 n

= $123, 719

Try a higher rate, IRR = 9%. 1   1 − (1.09)8  NCFt NPV =  = −$3,125, 000 + $565,325    t t = 0 (1 + k)  0.09    = −$3,125, 000 + $3,128,972 n

= $3, 972

The IRR of the project is approximately 9 percent. Using a financial calculator, we find that the IRR is 9.034 percent.

Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: Cash Flow (C)

Frequency (F)

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-3,125,000

565,325

Then solve by pressing IRR where we find it is 9.034%

Initial investment = $33,750 Annual cash flows = $9,430 Length of investment = n = 5 years Try IRR = 12%. 1   1 − (1.12)5  NCFt NPV =  = −$33, 750 + $9, 430    t t = 0 (1 + k)  0.12    = −$33, 750 + $33,993 = $243 n

Try IRR = 12.3%. 1   1 − (1.123)5  NCFt NPV =  = −$33, 750 + $9, 430    t t = 0 (1 + k)  0.123    = −$33, 750 + $33742 = −$8  0 n

The IRR of the project is approximately 12.3 percent. Using a financial calculator, we find that the IRR is 12.29 percent.

Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: Cash Flow (C)

Frequency (F)

-33,750

9,430

Then solve by pressing IRR where we find it is 12.29%

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Initial investment = $10,000 Annual cash flows = $2,500 Length of investment = n = 7 years Try IRR = 16%. 1   1 − (1.16)7  NCFt NPV =  = −$10, 000 + $2,500    t t = 0 (1 + k)  0.16    = −$10, 000 + $10, 096 = $96 n

Try IRR = 16.3%. 1   1 − (1.163)7  NCFt NPV =  = −$10, 000 + $2,500    t t = 0 (1 + k)  0.163    = −$10, 000 + $10, 008 = $8  0 n

The IRR of the project is approximately 16.3 percent. Using a financial calculator, we find that the IRR is 16.327 percent.

Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: Cash Flow (C)

Frequency (F)

-10,000

2,500

Then solve by pressing IRR where we find it is 16.327% LO: 5 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

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10.29 Profitability index: Suppose that you could invest in the following projects but have only $30,000 to invest. How would you make your decision and in which projects would you invest?

Project

Cost

NPV

$8,000

$4,000

11,000

7,000

9,000

5,000

7,000

4,000

Solution: One would compute the profitability index for each of the projects as follows:

PI =

NPV+Initial investment Initial investment

The profitability indexes of the projects are: PI A =

$4, 000 + $8, 000 = 1.50 $8, 000

PI B =

$7, 000 + $11, 000 = 1.64 11, 000

PI C =

$5, 000 + $9, 000 = 1.56 $9, 000

PI D =

$4, 000 + $7, 000 = 1.57 $7, 000

With $30,000, you should invest in B, D, and C ($11,000 + $7,000 + $9,000). The total cost is $27,000, and the total NPV is $16,000 ($7,000 + $4,000 + $5,000). LO: 6 Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

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10.30 Profitability index: Suppose that you could invest in the same projects as in the previous problem but have only $25,000 to invest. Which projects would you chose? Solution: The profitability indexes of the projects are: A: 1.50; B: 1.64; C: 1.56; D: 1.57 With $25,000, you cannot invest in all of B, D, and C, since the total cost is $27,000. You may think that you should then invest in only B and D, since they have the highest profitability indexes. This will yield a total NPV of $11,000, and you are left with $7,000 of idle capital. If you give up project B, however, which has the highest profitability index and highest cost, and invest instead in A, C, and D, which require less capital, you will get a total NPV of $13,000, and you are left with less idle capital, $1,000. From this example you can see that capital rationing with indivisible projects are sometimes complicated and require a careful thought of all possibilities (or linear/integer programming). LO: 6 Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

ADVANCED 10.31 Management of Draconian Measures, Inc., is evaluating two independent projects. The company uses a 13.8 percent discount rate for such projects. The costs and cash flows for the projects are shown in the following table. What are their NPVs? Year

Project 1

Project 2

-$8,425,375

-$11,368,000

3,225,997

2,112,589

1,775,882

3,787,552

1,375,112

3,125,650

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1,176,558

4,115,899

1,212,645

4,556,424

1,582,156

1,365,882

Solution: Project 1: Cost of Project 1 = $8,425,375 Length of project = n = 7 years Required rate of return = k = 13.8% n

NCFt (1 + k )t t =0

NPV = 

$3, 225,997 $1, 775,882 $1,375,112 $1,176,558 $1, 212, 645 + + + + (1.138)1 (1.138) 2 (1.138)3 (1.138) 4 (1.138)5 $1,582,156 $1,365,882 + + (1.138)6 (1.138)7 = −$8, 425,375 + $2,834, 795 + $1,371, 291 + $933, 064 + 701,527 + $635,364 + $728, 443 +$552, 608

= −$8, 425,375 +

= −$668, 283

Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: Project 1

Cash Flow (C)

Frequency (F)

-8,425,375

3,225,997

1,775,882

1,375,112

1,176,558

1,212,645

1,582,156

1,365,882

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Since Project 1 NPV is negative, we reject this project.

Project 2: Cost of Project 2 = $11,368,000 Length of project = n = 5 years Required rate of return = k = 13.8% n

NPV =  t =0

NCFt (1 + k)t

$2,112,589 $3, 787,552 $3,125, 650 $4,115,899 $4,556, 424 + + + + (1.138)1 (1.138) 2 (1.138)3 (1.138)4 (1.138)5 = −$11,368, 000 + $1,856, 405 + $2,924, 651 + $2,120,868 + $2, 454,119 + $2,387,332 = $375, 375

= −$11,368, 000 +

Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: Project 2

Cash Flow (C)

Frequency (F)

-11,368,000

2,112,589

3,787,552

3,125,650

4,115,899

4,556,424

Then solve by pressing NPV, enter the rate of 13.8% and compute NPV= 375,375 Since Project 2 NPV is positive, we accept this project. LO: 2 Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

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What are the IRRs for the projects?

Does the IRR criterion suggest a different decision than the NPV criterion?

Explain how you would expect the management of Draconian Measures to decide which project(s) to invest in.

Solution: a.

Project 1: At the required rate of return of 13.8 percent, Project 1 has a NPV of $(668,283). To find the IRR, try lower rates. Try IRR = 11%. n

NPV =  t =0

NCFt (1 + k )t

$3,225,997 $1,775,882 $1,375,112 $1,176,558 $1,212,645 + + + + (1.11)1 (1.11)2 (1.11)3 (1.11)4 (1.11)5 $1,582,156 $1,365,882 + + (1.11)6 (1.11)7 = −$8, 425,375 + $2,906,304 + $1,441,346 + $1,005,470 + $775,035 + $719,646

= −$8, 425,375 +

+$845,885 + $657,889 = −$73, 800

Try a lower rate, IRR=10.7%. n

NPV =  t =0

NCFt (1 + k )t

$3,225,997 $1,775,882 $1,375,112 $1,176,558 $1,212,645 + + + + (1.107)1 (1.107)2 (1.107)3 (1.107)4 (1.107)5 $1,582,156 $1,365,882 + + (1.107)6 (1.107)7 = −$8, 425,375 + $2,914,180 + $1,449,168 + $1,013,667 + $783,471 + $729,450

= −$8, 425,375 +

+$859,733 + $670,471 = −$5, 235

The IRR of the project is approximately 10.7 percent. Using a financial calculator, we find that the IRR is 10.677 percent.

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Project 1

Cash Flow (C)

Frequency (F)

-8,425,375

3,225,997

1,775,882

1,375,112

1,176,558

1,212,645

1,582,156

1,365,882

Then solve by pressing IRR to get 10.677% Project 2: At the required rate of return of 13.8 percent, Project 2 has a NPV of $ 375,375. To find the IRR, try higher rates. Try IRR = 15%. n

NCFt (1 + IRR)t t =0

NPV = 0 = 

$2,112,589 $3,787,552 $3,125,650 $4,115,899 $4,556, 424 + + + + (1.15)1 (1.15)2 (1.15)3 (1.15)4 (1.15)5 = −$11,368,000 + $1, 837, 034 + $2, 863, 933 + $2, 055,166 + $2, 353, 278 + $2, 265, 348 = $6,759

0 = −$11,368,000 +

Try IRR = 15.1%. n

NPV = 0 =  t =0

NCFt (1 + IRR)t

$2,112,589 $3,787,552 $3,125,650 $4,115,899 $4,556, 424 + + + + (1.151)1 (1.151)2 (1.151)3 (1.151)4 (1.151)5 = −$11,368,000 + $1, 835, 438 + $2, 858, 959 + $2, 049, 814 + $2, 345,111 + $2, 255, 524 = −$23,155

0 = −$11,368,000 +

The IRR of the project is between 15 and 15.1 percent. Using a financial calculator, we find that the IRR is 15.023 percent.

Financial Calculator Solution:

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Using a financial calculator, enter the cash flows as follows: Project 2

Cash Flow (C)

Frequency (F)

-11,368,000

2,112,589

3,787,552

3,125,650

4,115,899

4,556,424

Then solve by pressing IRR to get 15.023%.

Based on the IRR, Project 1 will be rejected and Project 2 will be accepted. These decisions are identical to those based on NPV. (Given that Project 1 had a negative NPV, the IRR will always be less than the required rate of return 13.8%.)

Management would use the decision spelled out by NPV, although in this case the IRR has come up with the same decision.

LO: 5 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.33 Management of Dravid, Inc., is currently evaluating three projects that are independent. The cost of funds can be either 13.6 percent or 14.8 percent depending on their financing plan. All three projects cost the same at $500,000. Expected cash flow streams are shown in the following table. Which projects would be accepted at a discount rate of 14.8 percent? What if the discount rate was 13.6 percent? Year

Project 1

Project 2

Project 3

$245,125

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125,000

212,336

150,000

500,000

112,500

375,000

500,000

74,000

Solution: Cost of projects = $500,000 Length of project = n = 4 years Required rate of return = k = 14.8%

Project 1: n

NCFt $0 $125,000 $150,000 $375,000 = −$500,000 + + + + (1 + k )t (1.148)1 (1.148)2 (1.148)3 (1.148) 4 = −$500,000 + $0 + $94,848 + $99,144 + $215,906

NPV =  t =0

= −$90,103

Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: Project 1

Cash Flow (C)

Frequency (F)

-500,000

125,000

150,000

375,000

Then solve by pressing NPV, enter the rate of 14.8% and compute NPV= -90,103 Also solve by pressing NPV, enter the rate of 13.6% and compute NPV= -75,645.18

Project 2: n

NCFt $0 $0 $500, 000 $500, 000 = −$500, 000 + + + + (1 + k )t (1.148)1 (1.148)2 (1.148)3 (1.148)4 = −$500, 000 + $0 + $0 + $330, 479 + $287,874 = $118, 353

NPV =  t =0

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Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: Project 2

Cash Flow (C)

Frequency (F)

-500,000

500,000

Then solve by pressing NPV, enter the rate of 14.8% and compute NPV=118,353 Also solve by pressing NPV, enter the rate of 13.6% and compute NPV= 141,295

Project 3: n

NCFt $245,125 $212,336 $112,500 $74, 000 = −$500, 000 + + + + t (1 + k ) (1.148)1 (1.148)2 (1.148)3 (1.148)4 t =0 = −$500, 000 + $213,524 + $161,116 + $74,358 + $42, 605 = −$8, 397

NPV = 

Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: Project 3

Cash Flow (C)

Frequency (F)

-500,000

213,524

161,116

74,358

42,605

Then solve by pressing NPV, enter the rate of 14.8% and compute NPV=-8,397 Also solve by pressing NPV, enter the rate of 13.6% and compute NPV= -1,491 At a discount rate of 14.8 percent, only project 2 will be accepted. At a discount rate of 13.6 percent, the NPVs of the three projects are -$75,645, $141,295, and $1,491 respectively. Both projects 2 and 3 have positive NPVs and will be accepted.

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Year

Project 1

PVCF

Project 2

PVCF

Project 3

PVCF

-$500,000

−

245,125

215,779

125,000

96,862

−

212,336

164,538

150,000

102,319

500,000

341,063

112,500

76,739

375,000

225,174

500,000

300,232

74,000

44,434

NPV

-75,645

141,295

1,490

LO: 2 Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.34 Management of Intrepid, Inc., is considering investing in three independent projects. The costs and the cash flows are given in the following table. The appropriate cost of capital is 14.5 percent. Compute the project IRRs and identify the projects that should be accepted. Year

Project 1

Project 2

Project 3

-$275,000

-$312,500

-$500,000

63,000

153,250

212,000

85,000

167,500

212,000

85,000

112,000

212,000

100,000

212,000

Solution: Project 1: Cost of Project 1 = $275,000 Length of project = n = 4 years Required rate of return = k = 14.5%

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NCFt (1 + k )t t =0

NPV = 

$63, 000 $85, 000 $85, 000 $100, 000 + + + (1.145)1 (1.145) 2 (1.145)3 (1.145) 4 = −$275, 000 + 55,022 + $64,835 + $56, 624 + $58,181 = −$40, 338

= −$275, 000 +

At the required rate of return of 14.5 percent, Project 1 has a NPV of $(40,338). To find the IRR, try lower rates. Try IRR = 7.6%. n

NCFt t t = 0 (1 + IRR) $63, 000 $85, 000 $85, 000 $100, 000 0 = −$275, 000 + + + + (1.076)1 (1.076) 2 (1.076)3 (1.076) 4 = −$275, 000 + 58,550 + $73, 417 + $68, 231 + $74, 602 = −$200  0

NPV = 0 = 

The IRR of the project is approximately 7.6 percent. Using a financial calculator, we find that the IRR is 7.57 percent. Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: Project 1

Cash Flow (C)

Frequency (F)

-275,000

63,000

85,000

100,000

Then compute IRR to get 7.57%

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NCFt $153, 250 $167,500 $112, 000 = −$312,500 + + + t (1 + k) (1.145)1 (1.145) 2 (1.145)3 t =0 = −$312,500 + $ 133,843 + $127, 763 + $74, 611 = $23, 717

NPV = 

At the required rate of return of 14.5 percent, Project 2 has a NPV of $23,717. To find the IRR, try higher rates. Try IRR =19%. n

NCFt (1 + IRR)t $153,250 $167,500 $112,000 0 = −$312,500 + + + (1.19)1 (1.19)2 (1.19)3 = −$312,500 + $128,782 + $118,283 + $66, 463 = $1, 028

NPV = 0 =  t =0

Try IRR=19.2%. n

NCFt (1 + IRR)t t =0 $153,250 $167,500 $112,000 0 = −$312,500 + + + (1.192)1 (1.192)2 (1.192)3 = −$312,500 + $128,565 + $117,886 + $66,129 = $80  0

NPV = 0 = 

The IRR of the project is approximately 19.2 percent. Using a financial calculator, we find that the IRR is 19.22 percent.

Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: Project 2

Cash Flow (C)

Frequency (F)

-312,500

153,250

167,500

112,000

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Cost of Project 3 = $500,000 Length of project = n = 4 years Required rate of return = k = 14.5% 1    1 − (1.145)4  NCFt NPV =  = −$500,000 + $212,000    t t = 0 (1 + k )  0.145    = −$500,000 + $611, 429 = $111, 429 n

At the required rate of return of 14.5 percent, Project 3 has a NPV of $111,429. To find the IRR, try higher rates. Try IRR =25%. n

NCFt t t = 0 (1 + IRR)

NPV = 0 = 

1    1 − (1.25)4  0 = −$500,000 + $212,000     0.25    = −$500,000 + $500,659  $659

Try IRR=25.1%. n

NCFt t t = 0 (1 + IRR)

NPV = 0 = 

1    1 − (1.251)4  0 = −$500,000 + $212,000     0.251    = −$500,000 + $499,769 = −$231  0

The IRR of the project is approximately 25.1 percent. Using a financial calculator, we find that the IRR is 25.07 percent.

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Project 2

Cash Flow (C)

Frequency (F)

-500,000

212,000

Then compute IRR to get 25.07%. Only Projects 2 and 3 will be accepted as the IRRs exceed the required rate of return of 14.5 percent. LO: 2 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.35 Jekyll & Hyde Corp. management is evaluating two mutually exclusive projects. The cost of capital is 15 percent. Costs and cash flows for each project are given in the following table. Which project should be accepted?

Year

Project 1

Project 2

-$1,250,000

250,000

350,000

450,000

350,000

500,000

350,000

750,000

350,000

Solution: Project 1: Cost of project = $1,250,000 Length of project = n = 5 years Required rate of return = k = 15%

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NCFt (1 + k )t t =0

NPV = 

$250, 000 $350, 000 $450, 000 $500, 000 $750, 000 + + + + (1.15)1 (1.15)2 (1.15)3 (1.15)4 (1.15)5 = −$1, 250, 000 + $217,391 + $264, 650 + $295,882 + $285,877 + $372,883 = $186, 683

= −$1, 250, 000 +

At the required rate of return of 15 percent, Project 1 has an NPV of $186,683.Based on the positive NPV, Project 1 should be accepted.

To find the IRR, try higher rates.

Try IRR = 20%. n

NCFt t t = 0 (1 + k )

NPV = 0 = 

$250,000 $350,000 $450,000 $500,000 $750,000 + + + + (1.20)1 (1.20)2 (1.20)3 (1.20)4 (1.20)5 = −$1,250,000 + $208,333 + $243,056 + $260, 417 + $241,127 + $301, 408  $4, 341

0 = −$1,250,000 +

Try IRR = 20.1%. n

NCFt (1 + IRR)t $250,000 $350,000 $450,000 $500,000 $750,000 0 = −$1,250,000 + + + + + (1.201)1 (1.201)2 (1.201)3 (1.201)4 (1.201)5 = −$1,250,000 + $208,160 + $242,651 + $259,767 + $240,324 + $300,155 = $1, 057  0

NPV = 0 =  t =0

The IRR of the project is approximately 20.1 percent. Using a financial calculator, we find that the IRR is 20.132 percent.

Financial Calculator Solution:

Using a financial calculator, enter the cash flows as follows: Project 1

Cash Flow (C)

Frequency (F)

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-1,250,000

250,000

350,000

450,000

500,000

750,000

Then solve by pressing IRR to get 20.132%.

Project 2: Cost of project = $1,250,000 Length of project = n = 5 years Required rate of return = k = 15% 1   1 − (1.15)5  NCFt NPV =  = −$1, 250, 000 + $350, 000    t t = 0 (1 + k )  0.15    = −$1, 250, 000 + $1,173, 254 n

= −$76, 746

At the required rate of return of 15 percent, Project 2 has an NPV of $(76,746). Based on the negative NPV, Project 2 should be rejected. To find the IRR, try lower rates. Try IRR = 12%. n

NCFt (1 + IRR)t t =0

NPV = 0 = 

1   1 − (1.12)5  0 = −$1, 250, 000 + $350, 000     0.12    = −$1, 250, 000 + $1, 261, 672 = $11, 672

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NCFt t t = 0 (1 + IRR)

NPV = 0 = 

1   1 − (1.124)5  0 = −$1, 250, 000 + $350, 000     0.124    = −$1, 250, 000 + $1, 249, 269 = −$731  0

The IRR of the project is approximately 12.4 percent. Using a financial calculator, we find that the IRR is 12.376 percent.

Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: Project 2

Cash Flow (C)

Frequency (F)

-1,250,000

350,000

Then solve by pressing IRR to get 12.376%.

Given a required rate of return of 15 percent, Project 1 will be accepted as the IRR of 20.1 percent exceeds the required rate of return. Project 2 will be rejected. LO: 5 Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.36 Management of Larsen Automotive, a manufacturer of auto parts, is considering investing in two projects. The company typically compares project returns to a cost of funds of 17 percent. Compute the IRRs based on the cash flows in the following table. Which project(s) will be accepted? Copyright © 2022 John Wiley & Sons, Inc.

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Year

Project 1

Project 2

$(475,000)

$(500,000)

300,000

117,500

110,000

181,300

125,000

244,112

140,000

278,955

Solution: Project 1: Cost of project = $475,000 Length of project = n = 4 years Required rate of return = k = 17% n

NCFt (1 + k )t t =0

NPV = 

$300,000 $110,000 $125,000 $140,000 + + + (1.17)1 (1.17)2 (1.17)3 (1.17)4 = −$475,000 + $256,410 + $80,356 + $78,046 + $74,711 = $14, 523

= −$475,000 +

At the required rate of return of 17 percent, Project 1 has an NPV of $14,524. To find the IRR, try higher rates.

Try IRR = 19%. n

NCFt t t = 0 (1 + k )

NPV = 

$300,000 $110,000 $125,000 $140,000 + + + (1.19)1 (1.19)2 (1.19)3 (1.19)4 = −$475,000 + $252,101 + $77,678 + $74,177 + $69,814  −$1, 230 = −$475,000 +

Try IRR = 18.8%.

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NCFt t t = 0 (1 + k )

NPV = 

$300,000 $110,000 $125,000 $140,000 + + + (1.188)1 (1.188)2 (1.188)3 (1.188)4 = −$475,000 + $252,525 + $77,940 + $74,552 + $70,285 = $302  0

= −$475,000 +

The IRR of the project is approximately 18.8 percent. Using a financial calculator, we find that the IRR is 18.839 percent.

Financial Calculator Solution:

Using a financial calculator, enter the cash flows as follows: Project 1

Cash Flow (C)

Frequency (F)

-475,000

300,000

110,000

125,000

140,000

Then solve by pressing IRR to get 18.839%.

Project 2: Cost of project = $500,000 Length of project = n = 4 years Required rate of return = k = 17% n

NCFt (1 + k )t t =0

NPV = 

$117,500 $181,300 $244,112 $278,955 + + + (1.17)1 (1.17)2 (1.17)3 (1.17)4 = −$500,000 + $100,427 + $132, 442 + $152, 416 + $148,864 = $34,149

= −$500,000 +

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Solutions Manual

At the required rate of return of 17 percent, Project 2 has an NPV of $34,150. To find the IRR, try higher rates.

Try IRR = 20%. n

NCFt (1 + IRR)t t =0 $117,500 $181,300 $244,112 $278,955 0 = −$500, 000 + + + + (1.20)1 (1.20) 2 (1.20)3 (1.20) 4 = −$500, 000 + $97,917 + $125,903 + $141, 269 + $134,527 = −$385  0

NPV = 0 = 

The IRR of the project is approximately 20 percent. Using a financial calculator, we find that the IRR is 19.965 percent.

Financial Calculator Solution:

Using a financial calculator, enter the cash flows as follows: Project 2

Cash Flow (C)

Frequency (F)

-500,000

117,500

181,300

244,112

278,955

Then solve by pressing IRR to get 19.965%.

Both projects can be accepted since their IRRs exceed the cost of capital of 17 percent. LO: 5 Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective 10.37 Compute the IRR for each of the following projects: Copyright © 2022 John Wiley & Sons, Inc.

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Year

Project 1

Project 2

Project 3

-$10,000

4,750

1,650

800

3,300

3,890

1,200

3,600

5,100

2,875

2,100

2,750

3,400

800

6,600

Solution: Project 1: Cost of project = $10,000 Length of project = n = 4 years n

NCFt (1 + IRR)t t =0 $4, 750 $3,300 $3, 600 $2,100 0 = −$10, 000 + + + + (1.16)1 (1.16) 2 (1.16)3 (1.16) 4 = −$10, 000 + $4,095 + $2, 452 + $2,306 + $1,160 = $13  0

NPV = 0 = 

The IRR of the project is approximately 16 percent. Using a financial calculator, we find that the IRR is 16.076 percent.

Financial Calculator Solution:

Using a financial calculator, enter the cash flows as follows: Project 1

Cash Flow (C)

Frequency (F)

-10,000

4,750

3,300

3,600

2,100

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Then solve by computing IRR to get 16.076% Project 2: Cost of project = $10,000 Length of project = n = 5 years n

NCFt (1 + IRR)t t =0 $1, 650 $3,890 $5,100 $2, 750 $800 0 = −$10, 000 + + + + + (1.137)1 (1.137) 2 (1.137)3 (1.137) 4 (1.137)5 = −$10, 000 + $1,451 + $3, 009 + $3, 470 + $1, 645 + $421 = −$4  0

NPV = 0 = 

The IRR of the project is approximately 13.7 percent. Using a financial calculator, we find that the IRR is 13.685 percent.

Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: Project 2

Cash Flow (C)

Frequency (F)

-10,000

1,650

3,890

5,100

2,750

800

Then solve by computing IRR to get 13.685%.

Project 3: Cost of project = $10,000 Length of project = n = 5 years

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NCFt t t = 0 (1 + IRR) $800 $1, 200 $2,875 $3, 400 $6, 600 0 = −$10, 000 + + + + + (1.109)1 (1.109)2 (1.109)3 (1.109)4 (1.109)5 = −$10, 000 + $721 + $976 + $2,108 + $2, 248 + $3,934 = −$13  0

NPV = 0 = 

The IRR of the project is approximately 10.9 percent. Using a financial calculator, we find that the IRR is 10.862 percent.

Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: Project 3

Cash Flow (C)

Frequency (F)

-10,000

800

1,200

2,875

3,400

6,600

Then solve by computing IRR to get 10.862%. LO: 5 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.38 Primus Corp. management is planning to convert an existing warehouse into a new plant that will increase its production capacity by 45 percent. The cost of this project will be $7,125,000. It will result in additional cash flows of $1,875,000 for each of the next eight years. The discount rate is 12 percent. a.

What is the payback period?

What is the NPV for this project?

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What is the IRR?

Solution: a. Year

Project 1

Cumulative CF

-$7,125,000

1,875,000

-5,250,000

1,875,000

-3,375,000

1,875,000

-1,500,000

1,875,000

375,000

1,875,000

2,250,000

1,875,000

4,125,000

1,875,000

6,000,000

1,875,000

7,875,000

PB = Years before cost recovery + (Remaining cost to recover/ Cash flow during the year) = 3 + ($1,500,000 / $1,875,000) = 3.80 years

Cost of this project = $7,125,000 Required rate of return = 12% Length of project = n = 8 years n

NPV =  t =0

NCFt (1 + k )t

1   1 − (1.12)8  = −$7,125, 000 + $1,875, 000     0.12    = −$7,125, 000 + $9,314,325 = $2,189, 325

To compute the IRR, try rates higher than 12 percent. Try IRR = 20%.

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NCFt t t = 0 (1 + k )

NPV = 0 = 

1   1 − (1.20)8  0 = −$7,125, 000 + $1,875, 000     0.20    = −$7,125, 000 + $7,194, 675 = $69, 675

Try IRR = 20.3%. n

NPV = 0 =  t =0

NCFt (1 + k )t

1   1 − (1.203)8  0 = −$7,125, 000 + $1,875, 000     0.203    = −$7,125, 000 + $7,130,832 = $5, 832

The IRR of the project is approximately 20.3 percent. Using a financial calculator, we find that the IRR is 20.328 percent. Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: Cash Flow (C)

Frequency (F)

-7,125,000

1,875,000

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10.39 Quasar Tech Co. management is investing $6 million in new machinery that will produce the next-generation routers. Sales to its customers will amount to $1,750,000 for the next three years and then increase to $2.4 million for three more years. The project is expected to last six years, and operating costs, excluding depreciation, will be $898,620 annually. The machinery will be depreciated to a salvage value of $0 over 6 years using the straight-line method. The company’s tax rate is 30 percent, and the cost of capital is 16 percent. a.

What is the payback period?

What is the average accounting return (ARR)?

Calculate the project NPV.

What is the IRR for the project?

Solution: a.

Year

Net Income

Depreciation

Project 1

Cumulative

Cash Flows

-$6,000,000

-$104,034

$1,000,000

895,966

-5,104,034

-$104,034

$1,000,000

895,966

-4,208,068

$104,034

$1,000,000

895,966

-3,312,102

350,966

$1,000,000

1,350,966

-1,961,136

350,966

$1,000,000

1,350,966

-610,170

350,966

$1,000,000

1,350,966

740,796

PB = Years before cost recovery + (Remaining cost to recover/ Cash flow during the year) = 5 + ($610,170 / $1,350,966) = 5.45 years b. Year 1 Sales

Year 2

Year 3

Year 4

Year 5

Year 6

$ 1,750,000 $ 1,750,000 $ 1,750,000 $ 2,400,000 $ 2,400,000 $ 2,400,000

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Expenses

Solutions Manual

898,620

1,000,000

-$148,620

$ 501,380

Taxes (30%)

44,586

-150,414

Net income

$ (104,034)

$ 350,966

Beginning BV

6,000,000

5,000,000

4,000,000

3,000,000

2,000,000

1,000,000

Less:

1,000,000

Depreciation* ($6,000,000/6) EBIT

Depreciation* Ending BV

$ 5,000,000 $ 4,000,000 $ 3,000,000 $ 2,000,000 $ 1,000,000

Average after-tax income = $123,466 Average book value of equipment = $3,000,000 Average after - tax income Average book value $123,466 = = 4.1% $3,000,000

Accounting rate of return =

Cost of this project = $6,000,000 Required rate of return = k =16% Length of project = n = 6 years n

NCFt (1 + k )t t =0

NPV = 

1  1    1 − (1.16)3  1 − (1.16)3  1 = −$6, 000, 000 + $895,966    + $1,350,966    3 0.16 0.16 (1.16)         = −$6, 000, 000 + $2, 012, 241 + $1,943,833 = −$2, 043, 927

Frequency (F) SM 10-84

Fundamentals of Corporate Finance, 5th edition

Solutions Manual

-6,000,000

895,966

1,350,966

Then solve by pressing NPV, enter the rate of 16% and compute NPV= -2,043,927. Also compute IRR to get 3.145%

To compute the IRR, try rates lower than 16 percent. Try IRR = 3%. n

NCFt (1 + IRR)t t =0

NPV = 0 = 

1  1    1 − (1.03)3  1 − (1.03)3  1 0 = −$6, 000, 000 + $895,966    + $1,350,966    3 0.03 0.03 (1.03)         = −$6, 000, 000 + $2,534,340 + $3, 497, 084 = $31, 424 Try IRR = 3.1%. n

NPV = 0 −  t =0

NCFt (1 + IRR)t

1 1     1 − (1.031)3  1 − (1.031)3  1 0 = −$6, 000, 000 + $895,966    + $1,350,966    3  0.031   0.031  (1.031)     = −$6, 000, 000 + $2,529, 475 + $3, 480, 225 = $9, 700 The IRR of the project is approximately 3.1 percent. Using a financial calculator, we find that the IRR is 3.145 percent. LO: 2, 3, 5 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions

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AICPA: Industry/Sector Perspective

10.40 Management of Skywards, Inc., an airline caterer, is purchasing refrigerated trucks at a total cost of $3.25 million. After-tax net income from this investment is expected to be $750,000 for each of the next five years. Annual depreciation expense will be $650,000. The cost of capital is 17 percent. a.

What is the discounted payback period?

Compute the ARR.

What is the NPV on this investment?

Calculate the IRR.

Solution: a.

Cumulative

Year

PVCF

-$3,250,000

1,400,000*

-1,850,000

1,196,581

-2,053,419

1,400,000

-450,000

1,022,719

-1,030,700

1,400,000

950,000

874,119

-156,581

1,400,000

2,350,000

747,110

590,529

1,400,000

3,750,000

638,556

1,229,085

*Net Income + Depreciation = Annual Cash Flow = ($750,000 + $650,000) Discount payback period = Years before recovery + (Remaining cost / Next year’s CF) = 3 + ($156,581 / $747,110) = 3.21 years

b. Year 1

Year 2

Year 3

Year 4

Year 5

Net income

$ 750,000

Beginning BV

3,250,000

2,600,000

1,950,000

1,300,000

650,000

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Less:

Solutions Manual

650,000

$2,600,000

$1,950,000

$1,300,000

$ 650,000

650,000

Depreciation Ending BV

Average after-tax income = $750,000 Average book value of equipment = $1,625,000

Average after - tax income Average book value $750,000 = = 46.2% $1,625,000

Accounting rate of return =

Cost of this project = $3,250,000 Required rate of return = k =17% Length of project = n = 5 years 1   1 − (1.17)5  NCFt NPV =  = −$3, 250, 000 + $1, 400, 000    t t = 0 (1 + k )  0.17    = −$3, 250, 000 + $4, 479, 085 n

= $1, 229, 085

Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: Cash Flow (C)

Frequency (F)

-3,250,000

1,400,000

Then solve by pressing NPV, enter the rate of 17% and compute NPV= 1,229,085.

To compute the IRR, try rates much higher than 17 percent. Try IRR = 30%.

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NCFt t t = 0 (1 + IRR)

NPV = 0 = 

1   1 − (1.30)5  0 = −$3, 250, 000 + $1, 400, 000     0.30    = −$3, 250, 000 + $3, 409, 798 = $159, 798

Try IRR = 32.5%.

NPV = 0 =  t =0

NCFt (1 + IRR)t

1   1 − (1.325)5  0 = −$3, 250, 000 + $1, 400, 000     0.325    = −$3, 250, 000 + $3, 252,904 = $2, 904  0 The IRR of the project is approximately 32.5 percent.

Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: Cash Flow (C)

Frequency (F)

-3,250,000

1,400,000

Then compute IRR to get 32.548%. LO: 2, 3, 4, 5 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

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10.41 Trident Corp. management is evaluating two independent projects. The costs and expected cash flows are given in the following table. The cost of capital is 10 percent. Year

-$312,500

-$395,000

121,450

153,552

121,450

158,711

121,450

166,220

121,450

132,000

121,450

122,000

Calculate the projects’ NPV.

Calculate the projects’ IRR.

Which project should be chosen based on NPV? Based on IRR? Is there a conflict?

If you are the decision maker for the firm, which project or projects will be accepted? Explain your reasoning.

Solution: a.

Project A: Cost of this project = $312,500 Annual cash flows = $121,450 Required rate of return = k = 10% Length of project = n = 5 years 1   1 − (1.10)5  NCFt NPV =  = −312,500 + $121, 450    t t = 0 (1 + k )  0.10    = −$312,500 + 460,391 n

= $147, 891

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Project A

Cash Flow (C)

Frequency (F)

-312,500

121,450

Then solve by pressing NPV, enter the rate of 10% and compute NPV=147,891. Project B: Cost of this project = $395,000 Required rate of return = k = 10% Length of project = n = 5 years n

NPV =  t =0

NCFt (1 + k )t

$153,552 $158, 711 $166, 220 $132, 000 $122, 000 + + + + (1.10)1 (1.10) 2 (1.10)3 (1.10) 4 (1.10) 5 = −395, 000 + $139,593 + $131,166 + $124,884 + 90,158 + 75, 752 = $166, 553 = −$395, 000 +

Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: Project B

Cash Flow (C)

Frequency (F)

-395,000

153,552

158,711

166,220

132,000

122,000

Then solve by pressing NPV, enter the rate of 10% and compute NPV= 166,553 b.

Project A: Since NPV > 0, to compute the IRR, try rates higher than 10 percent. Try IRR = 27%.

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NCFt t t = 0 (1 + IRR)

NPV = 0 = 

1   1 − (1.27)5  0 = −312,500 + $121, 450     0.27    = −$312,500 + 313, 666  $1,166

Try IRR = 27.2%, n

NPV = 0 =  t =0

NCFt (1 + IRR)t

1   1 − (1.272)5  0 = −312,500 + $121, 450     0.272    = −$312,500 + 312, 418 = −$82  0

The IRR of Project A is approximately 27.2 percent. Using a financial calculator, we find that the IRR is 27.187 percent.

Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: Project A

Cash Flow (C)

Frequency (F)

-312,500

121,450

Then solve by pressing IRR to get 27.187%

Project B: Since NPV > 0, to compute the IRR, try rates higher than 10 percent. Try IRR = 26%.

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NCFt t t = 0 (1 + IRR) $153,552 $158, 711 $166, 220 $132, 000 $122, 000 0 = −$395, 000 + + + + + (1.26)1 (1.26) 2 (1.26)3 (1.26) 4 (1.26) 5 = −$395, 000 + $121,867 + $99,969 + $83, 094 + $52,371 + $38, 416  $717

NPV = 0 = 

Try IRR = 26.1%. n

NCFt (1 + IRR)t $153,552 $158, 711 $166, 220 $132, 000 $122, 000 0 = −$395, 000 + + + + + (1.261)1 (1.261) 2 (1.261)3 (1.261) 4 (1.261)5 = −$395, 000 + $121, 770 + $99,811 + $82,897 + $52, 205 + $38, 263 = −$54  0

NPV = 0 =  t =0

The IRR of Project B is approximately 26.1 percent. Financial Calculator Solution: Using a financial calculator we can achieve more accuracy, enter the cash flows as follows: Project B

Cash Flow (C)

Frequency (F)

-395,000

153,552

158,711

166,220

132,000

122,000

Then solve by pressing IRR to get 26.093%.

Since both projects have positive NPVs and they are independent projects, both should be accepted under the NPV decision criteria. Under the IRR decision criteria, since both projects have IRRs greater than the cost of capital, both will be accepted. Thus, there is no conflict between the NPV and IRR decisions.

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Based on NPV, both projects will be accepted.

LO: 2, 5 Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective 10.42 Management of Tyler, Inc., is considering switching to a new production technology. The cost of the required equipment will be $4 million. The discount rate is 12 percent. The cash flows that management expects the new technology to generate are as follows. Years

1-2

3–5

$845,000

6–9

$1,450,000

Compute the payback and discounted payback periods for the project.

What is the NPV for the project? Should the firm go ahead with the project?

What is the IRR, and what would be the decision based on the IRR?

Solution: a. Cumulative

Cumulative

Year

Cash Flows

PVCF

-$4,000,000

-4,000,000

845,000

601,454

-3,155,000

-3,398,546

845,000

537,013

-2,310,000

-2,861,533

845,000

479,476

-1,465,000

-2,382,057

1,450,000

734,615

-15,000

-1,647,442

1,450,000

655,906

1,435,000

-991,536

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1,450,000

585,631

2,885,000

-405,905

1,450,000

522,885

4,335,000

116,980

Payback period = Years before cost recovery +

Remaining cost to recover Cash flow during the year

$15,000 $1, 450,000 = 6.01 years

= 6+

Discounted Payback period = Years before cost recovery +

Remaining cost to recover Cash flow during the year

$405,905 $522,885 = 8.8 years

=8+

Cost of this project = $4,000,000 Required rate of return = k = 12% Length of project = n = 9 years 1   1 − (1.12)3  NCFt 1 NPV =  = −$4, 000, 000 + 0 + 0 + $845, 000    t 2 (1 + k ) 0.12 (1.12) t =0     1   1 − (1.12) 4  1 +$1, 450, 000    5  0.12  (1.12)   n

= −$4, 000, 000 + 0 + 0 + $1, 617,943 + $2, 499, 037 = $116, 980

Since NPV > 0, the project should be accepted.

Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows:

Cash Flow (C)

Frequency (F)

-4,000,000

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845,000

1,450,000

Compute the NPV using a discount rate of 12% to get $116,980. Then solve by pressing IRR to get 12.539%

Given a positive NPV, to compute the IRR, one should try rates higher than 12 percent.

Try IRR = 12.5%. 1   1 − (1.125)3  NCFt 1 NPV =  = −$4, 000, 000 + 0 + 0 + $845, 000    t 2 (1 + k ) 0.125 (1.125) t =0     1   1 − (1.125)4  1 +$1, 450, 000    5 0.125 (1.125)     = −$4, 000, 000 + 0 + 0 + $1,589,915 + $2, 418, 479 n

= $8, 394

The IRR is approximately 12.5 percent. Using a financial calculator, we find that the IRR is 12.539 percent. Based on the IRR exceeding the cost of capital of 12 percent, the project should be accepted. LO: 2, 3, 5 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective 10.43 You are analyzing two proposed capital investments with the following cash flows: Year

Project X

Project Y

-$20,000

13,000

7,000

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6,000

7,000

6,000

7,000

2,000

7,000

The cost of capital for both projects is 10 percent. Calculate the profitability index (PI) for each project. Which project, or projects, should be accepted if you have unlimited funds to invest? Which project should be accepted if they are mutually exclusive? Solution: The PI calculations are as follows: The NPV is needed first: NPVx = −$20,000 +

$13,000 $6,000 $6,000 $2,000 + + + = $2,650.78 (1.10)1 (1.10)2 (1.10)3 (1.10)4

NPVx = −$20,000 + $11,818.18 + $4,958.68 + $4,507.88 + $1,366.03 = $2,650.78 $7,000 $7,000 $7,000 $7,000 + + + = $2,189.06 (1.10)1 (1.10)2 (1.10)3 (1.10)4 NPVy = −$20,000 + $6,363.64 + $5,785.12 + $5,259.20 + $4,781.09 = $2, 189.06

NPVy = −$20,000 +

Financial Calculator Solution:

Using a financial calculator, enter the cash flows as follows: Project X

Cash Flow (C)

Frequency (F)

-20,000

13,000

6,000

2,000

Then solve by pressing NPV, enter the rate 10% and compute NPV=2,650.78.

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Frequency (F) SM 10-96

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-20,000

7,000

Then solve by pressing NPV, enter the rate of 10% and compute NPV=2,189.06

PI x =

NPV + Initial Investment $22,650.78 = = 1.1325 Initial Investment $20,000

PI y =

NPV + Initial Investment $22,189.06 = = 1.1095 Initial Investment $20,000

Both methods rank Project X over Project Y. Therefore, both should be accepted if they are independent and sufficient resources are available. If the projects are mutually exclusive, we should choose the project with the higher PI at r = 10%, which in this case is Project X. LO: 6 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.44 You and a coworker are analyzing two proposed capital investments with the following cash flows:

Year

Project A

Project B

-$17,000

-$40,000

12,000

10,000

5,000

10,000

5,000

10,000

2,000

28,000

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b. Your coworker looks at your analysis and says, “Let’s recommend the project with the highest PI. If you have unlimited funds to invest, do you agree or disagree with your coworker? Explain why you agree or disagree? Assume that you have no other resource constraints and that you do not have to consider future investments. c. If the projects are mutually exclusive, which of the two projects do you recommend? Explain your reasoning. Solution: a. First it is necessary to calculate the NPV for both projects.

NPVA = −$17,000 +

$12,000 $5,000 $5,000 $2,000 + + + = $3,163.92 (1.10)1 (1.10)2 (1.10)3 (1.10)4

NPVA = −$17,000 + $10,909.09 + $4,132.23 + $3,756.57 + $1,366.03 = $3,163.92

Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: Year

Cash Flow (C)

Frequency (F)

-$17,000

$12,000

2, 3

$5,000

$2,000

Then solve by pressing NPV, enter the rate of 10% and compute NPV=3,163.92

NPVB = −$40,000 +

$10,000 $10,000 $10,000 $28,000 + + + = $3,992.89 (1.10)1 (1.10)2 (1.10)3 (1.10)4

NPVB = −$40,000 + $9,090.90 + $8,264.46 + $7,513.15 + $19,124.38 = $3,992.89

Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: Year

Cash Flow (C)

Frequency (F)

-$40,000

1, 2, 3

$10,000

$28,000

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Then solve by pressing NPV, enter the rate of 10% and compute NPV=3,992.90

PI A =

NPV + Initial Investment $20,164 = = 1.1861 Initial Investment $17,000

PIB =

NPV + Initial Investment $43,993 = = 1.0998 Initial Investment $40,000

b. As long as the projects are not mutually exclusive, in other words the cash flows are

independent of each other, I do not agree with my coworker. Both projects have a PI in excess of 1 which means with unlimited funds, both will add value to the company. c. If the projects are mutually exclusive, you and your coworker should choose the one with a higher PI or project A. LO: 6 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.45 The CFO of Edgeworth Inc., a cardboard box maker, is deciding between one of two new cardboard cutting machines: the Super Cutter and the Duper Cutter. The cash flows for the two cutters are as follows: Super Cutter

Duper Cutter

Year

Cash Flow

Year

Cash Flow

-$21,000

-80,000

6,000

21,000

6,000

21,000

6,000

21,000

6,000

21,000

6,000

21,000

6,000

21,000

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The cost of capital for both machines is 10 percent. Assume that you have no other resource constraints and that you do not have to consider future investments. a. Based on the IRR, which cutter do you recommend? Explain your reasoning. b. Based on the PI, which cutter do you recommend? Explain your reasoning. c. Overall, what is your recommendation to the CFO? Explain your recommendation given your answers to (a) and (b). Solution: a. IRR is the rate of return earned when the NPV = 0. To find IRR one must use trial and error

to solve the following for both cutters: NPVSuper Cutter = −$21,000 +

$6,000 $6,000 + + (1 + IRR)1 (1 + IRR)2

$6,000 =0 (1 + IRR)6

Since using trial and error is inefficient, one should either use a financial calculator or Excel.

Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: Year

Cash Flow (C)

Frequency (F)

-$21,000

1, 2, 3, 4, 5, 6

$6,000

Then solve by pressing IRR and compute IRR for Super Cutter = 17.97%

Perform the same sequence for Duper Cutter NPVDuper Cutter = −$80,000 +

$21,000 $21,000 + + (1 + IRR)1 (1 + IRR)2

$21,000 =0 (1 + IRR)6

Again, one should either use a financial calculator or Excel to solve for IRR.

Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: Year

Cash Flow (C)

Frequency (F)

-$80,000

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$21,000

Then solve by pressing IRR and compute IRR for Duper Cutter = 14.76% Since the cutters are mutually exclusive and the question advises to use the IRR we should choose the Super Cutter since it has a higher rate of return (17.97%) as measured by IRR.

b. To calculate the profitability index (PI) one must first calculate the net present value (NPV) for both cutters using the cost pf capital rate of 10%. NPVSuper Dutter = −$21,000 +

$6,000 $6,000 + + (1.10)1 (1.10)2

$6,000 = $5,131.56 (1.10)6

Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: Year

Cash Flow (C)

Frequency (F)

-$21,000

1, 2, 3, 4, 5, 6

$6,000

Then solve by pressing NPV and compute NPV = $5,131.56 Calculate the profitability index PI PISuper Cutter =

NPV + Initial Investment $26,132 = 1.244 Initial Investment $21,000

Perform the same sequence for the Duper Cutter NPVDuper Dutter = −$80,000 +

$21,000 $21,000 + + (1.10)1 (1.10)2

$21,000 = $11, 460.47 (1.10)6

Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: Year

Cash Flow (C)

Frequency (F)

-$80,000

1, 2, 3, 4, 5, 6

$21,000

Then solve by pressing NPV and compute NPV = $11,460.47 Calculate the profitability index (PI)

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PIDuper Cutter =

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NPV + Initial Investment $91, 460 = 1.143 Initial Investment $80,000

The cutters are mutually exclusive, and the question advises to use the PI, so we should choose the Super Cutter since it has a higher profitability index of 1.244 versus 1.143. c. In this case the Profitability Index method and the IRR do not give conflicting

recommendations, so using both methods the company would choose the Super Cutter. However, by computing the NPV we see that the Duper Cutter will add $6,328.90 more value to the company than the Super Cutter. This has happened because the scale of the Duper Cutter is much larger and as a result the value added as measured by NPV is higher. If there was a case

of limited resources, we would choose by investing in the cutter that creates more value per dollar of investment which is achieved by choosing the cutter with the higher profitability index, the Super Cutter. However according to the instructions in the question there are no resource

constraints, so I would advise the CFO to not use either IRR or PI for making his/her decision but instead choose the Duper Cutter. Based on the NPV analysis, it would add more value to the company. LO: 5, 6 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

CFA Problems 10.46 Given the following cash flows for a capital project, calculate the NPV and IRR. The required rate of return is 8 percent. Year

CASH FLOW

–50,000

15,000

20,000

10,000

5,000

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NPV

IRR

$1,905

10.9%

$1,905

26.0%

$3,379

10.9%

$3,379

26.0%

Solutions Manual

Solution c is correct. NPV = −$50,000 +

$15,000 $15,000 $20,000 $10,000 $5,000 + + + + (1.08)1 (1.08)2 (1.08)3 (1.08)4 (1.08)5

NPV = –$50,000 + $13,888.89 + $12,860.08 + $15,876.64 + $7,350.30 + $3,402.92 NPV = –$50,000 + $53,378.83 = $3,378.83 Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: Cash Flow (C)

Frequency (F)

-50,000

15,000

20,000

10,000

5,000

Then solve by pressing NPV, enter the rate of 8% and compute NPV=3,378.83. To solve for IRR one may either use trial and error or solve with the calculator to get 10.879%. LO: 6 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.47 Given the following cash flows for a capital project, calculate its payback period and discounted payback period. The required rate of return is 8 percent.

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Year

CASH FLOW

–50,000

15,000

20,000

10,000

5,000

The discounted payback period is a.

0.16 year longer than the payback period.

0.80 year longer than the payback period.

1.01 years longer than the payback period.

1.85 years longer than the payback period.

Solution c is correct. YEAR

CASH FLOW

–$50,000

$15,000

$20,000

$10,000

$5,000

–50,000

–35,000

–20,000

10,000

15,000

FLOW

–50,000

13,888.89

12,860.08

15,876.64

7,350.30

3,402.92

CUMULATIVE DCF

–$50,000

–$36,111.11

–$23,251.03

–$7,374.39

–$24.09

$3,378.83

CUMULATIVE CASH FLOW

DISCOUNTED CASH

As the table shows, the cumulative cash flow offsets the initial investment in exactly three years. The payback period is 3.00 years. The discounted payback period is between four and five years. The discounted payback period is 4 years plus 24.09/3,402.92 = 0.007 of the fifth-year cash flow, or 4.007 = 4.01 years. The discounted payback period is 4.01 – 3.00 = 1.01 years longer than the payback period. LO: 3 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

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10.46 An investment of $100 generates after-tax cash flows of $40 in Year 1, $80 in Year 2, and $120 in Year 3. The required rate of return is 20 percent. The net present value is closest to a.

$42.22

$58.33

$68.52

$98.95

Solution b is correct.

NPV =  t =0 n

NCFt 40 80 120 = −$100 + + + = $58.33 (1 + k )t 1.20 1.202 1.203

Financial Calculator Solution:

Using a financial calculator, enter the cash flows as follows: Cash Flow (C)

Frequency (F)

-100

120

Then solve by pressing NPV, enter the rate of 20% and compute NPV= 58.33 LO: 2 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

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10.49 An investment of $150,000 is expected to generate an after-tax cash flow of $100,000 in one year and another $120,000 in two years. The cost of capital is 10 percent. What is the internal rate of return? a.

28.19 percent

28.39 percent

28.59 percent

28.79 percent

Solution d is correct. The IRR can be found using a financial calculator or with trial and error. Using trial and error, the total PV is equal to zero if the discount rate is 28.79 percent. CASH

PRESENT VALUE

FLOW

28.19%

28.39%

28.59%

28.79%

–150,000

100,000

78,009

77,888

77,767

77,646

120,000

73,025

72,798

72,572

72,346

1,034

686

339

–8

YEAR

Total

Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: Cash Flow (C)

Frequency (F)

-150,000

100,000

120,000

Then solve for a more precise IRR which is 28.7855 percent that has a total PV closer to zero. LO: 5 Bloomcode: Application AASCB: AnalyticIMA: Investment Decisions AICPA: Industry/Sector Perspective Copyright © 2022 John Wiley & Sons, Inc.

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10.50 An investment requires an outlay of $100 and produces after-tax cash flows of $40 annually for four years. A project enhancement increases the required outlay by $15 and the annual after-tax cash flows by $5. How will the enhancement affect the project’s NPV profile? The vertical intercept of the NPV profile of the project shifts: a.

up and the horizontal intercept shifts left.

up and the horizontal intercept shifts right.

down and the horizontal intercept shifts left.

down and the horizontal intercept shifts right.

Solution a is correct. The vertical intercept changes from $60 to $65, and the horizontal intercept changes from 21.86 percent to 20.68 percent. LO: 2 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

Sample Test Problems 10.1

Testco Corporation is considering adding a new product line. The cost of the factory and equipment to produce this product is $1,780,000. Company management expects net cash flows from the sale of this product to be $450,000 in each of the next eight years. If Testco uses a discount rate of 12 percent for projects like this, what is the net present value of this project? What is the internal rate of return?

Solution: Investment = $1,780,000 Annual net cash flow = NCF = $450,000 Discount rate = k = 12% Length of project = n = 8 years

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1    1 − (1.12)8  NCFt NPV= = −$1,780,000 + $450,000    t t = 0 (1 + k )  0.12    = −$1,780,000 + $2,235, 438 NPV = $455, 438 n

Determine the IRR using trial and error: Since NPV > 0, try IRR > k. Try IRR = 20%

1    1 − (1.20)8  NCFt NPV = 0 =  = −$1,500,000 + $450,000    t t = 0 (1 + IRR)  0.20    = −$1,780,000 + $1,726,722  −$53, 278 n

Try IRR = 19% n

NCFt NPV = 0 =  = −$1,780,000 + $450,000  (1 + IRR)t t =0 = −$1,780,000 + $1,779, 465 = −$535  0

1−

1 (1.19)8 0.19

The IRR is approximately 19 percent.

Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: Cash Flow (C)

Frequency (F)

-1,780,000

450,000

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10.2

Flowers Unlimited is considering purchasing an additional delivery truck that will have a seven-year useful life. The new truck will cost $42,000. Cost savings with this truck are expected to be $12,800 for the first two years, $8,900 for the following two years, and $5,000 for the last 3 years of the truck’s useful life. What is the payback period for this project? What is the discounted payback period for this project with a discount rate of 10 percent?

Solution: Discount rate = k = 10% Cumulative Year

Cumulative

NCF

PV(NCF)

-$42,000

12,800

-29,200

11,636

-30,364

12,800

-16,400

10,579

-19,785

8,900

-7,500

6,687

-13,098

8,900

1,400

6,079

-7,019

5,000

6,400

3,105

-3,914

5,000

11,400

2,822

-1,092

5,000

16,400

2,566

1,474

PB = Years before cost recovery + (Remaining cost to recover/ Cash flow during the year) = 3 + ($7,500 / $8,900) = 3.84 years Discounted PB = Years before cost recovery + (Remaining cost to recover/ PV Cash flow during the year) = 6 + ($1,092 / $2,566) = 6.43 years LO: 3 Bloomcode: Application AASCB: Analytic Copyright © 2022 John Wiley & Sons, Inc.

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IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.3

What is the average accounting rate of return (ARR) on a piece of equipment that will cost $1.2 million and that will result in pretax cost savings of $380,000 for the first three years and then $280,000 for the following three years? Assume that the machinery will be depreciated to a salvage value of 0 over 6 years using the straight-line method and the company’s tax rate is 32 percent. If the acceptance decision is based on the project exceeding an ARR of 20 percent, should this machinery be purchased?

Solution: Cost savings Depreciation

Year 1

Year 2

Year 3

Year 4

Year 5

Year 6

$ 380,000

$ 280,000

200,000

$ 180,000

$ 80,000

57,600

25,600

Net income

$ 122,400

$ 54,400

Beg. book value

1,200,000

1,000,000

800,000

600,000

400,000

200,000

Less:

200,000

$ 1,000,000

$ 800,000

$ 600,000

$ 400,000

$ 200,000

EBIT Taxes (32%)

Depreciation End. book value

Average after-tax income (years 1 through 9) = $88,400 Average book value of equipment (years 0 through 6) = $600,000 Average after-tax income Average book value $88, 400 = = 14.7% $600, 000

Accounting rate of return =

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10.4

What do we know about that project’s IRR if we know that it has a positive NPV?

Solution: If a project has a positive NPV, the IRR of that project is greater than the required rate of return. Since the IRR is the discount rate that makes the NPV equal zero, a positive NPV results from the project’s IRR being greater than the required rate of return.

LO: 2, 5 Bloomcode: Comprehension AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.5

West Street Automotive is considering adding state safety inspections to its service offerings. The equipment necessary to perform these inspections will cost $557,000 and will generate cash flows of $195,000 over each of the next five years. If the cost of capital is 14 percent, what is the MIRR on this project? (LO: 5)

Solution: Investment (cost) = $557,000 Annual net cash flow = NCFt = $195,000 Length of project = n = 5 years Cost of capital = k = 14% TV = NCF1 (1 + k ) n −1 + NCF2 (1 + k ) n −2 +

+ NCFn (1 + k ) n −n

= $195, 000  (1.14) + $195, 000  (1.14) + $195, 000  (1.14) 2 + $195, 000 1.14 + $195, 000 4

= $329,347 + $288,901 + $253, 422 + $222,300 + $195, 000 = $1, 288,970

Financial Calculator Solution:

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195,000

PMT

FV 1,288,970

Solve for the MIRR: TV (1 + MIRR) n $1, 288,970 $557, 000 = (1 + MIRR)5 $1, 288,970 (1 + MIRR)5 = = 2.3141 $557, 000 PVCost =

(1 + MIRR) = (2.3141)1/5 = 1.1827 MIRR = 0.1827 = 18.3%

Financial Calculator Solution:

5 N

-557,000

1,288,970

PMT

18.27 LO: 5 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.6

You are chairperson of the investment committee at your firm. Five projects have been submitted to your committee for approval this month. The investment required and the project profitability index for each of these projects are presented in the following table:

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Project

Investment

A B C D E

$20,000 50,000 70,000 10,000 80,000

2.500 2.000 1.750 1.000 0.800

If you have $500,000 available for investments, which of these projects would you approve? Assume that you do not have to worry about having enough resources for future investments when making this decision. Solution: Definitely accept projects A, B, and C. They all have a positive NPV as can be seen by PI greater than 1. Project D just returns the opportunity cost of capital, so you would be indifferent with regards to accepting this project. Do not accept project E; it has a negative NPV. LO: 2, 6 Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

Ethics Case Discussion Questions 1. Identify 3 sets of stakeholders at GM and explain how each might i) benefit and ii) be harmed in some way from the firm’s plan to focus on the production of EVs in place of fossil-fuel powered vehicles. Solution: i.Shareholders a. If the demand for EVs increases and GM can sell more while lowering production costs then shareholder value should increase.

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b. GM is basing its strategy on its new Battery Electric Vehicle 3 platform and new Ultium battery. If it cannot compete with other automakers, e.g., Tesla, then shareholder value will decline. ii.Employees in the auto and related industries a. There will be new jobs for people with skills that are needed to produce and support EVs. b. Fewer employees will be needed to produce and support vehicles that rely on internal combustion engines, and many may be unable to use their skillset to work on EVs. iii.Cobalt mine workers in the DRC a. Increased demand for materials required in EV batteries would mean more work for more people. b. If mine safety and protections for employees are not in place, then the health of employees and their families may be at risk.

2. As noted in the case, light duty vehicles currently contribute about 17 percent to the total U.S. emissions. Identify 2 factors that would limit reductions in emissions when drivers switch to EVs. Solution: i.

Many vehicles that the drivers switch from would be sold to in the used car market and thus would continue to be driven and emit GHGs.

ii.

If the electricity used to recharge EV batteries were generated by coal-powered plants, then the increased demand for electricity to charge EV batteries could result in additional emissions.

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Chapter 9

Stock Valuation Before You Go On Questions and Answers Section 9.1 1. What is the NASDAQ? The NASDAQ system is one of the largest electronic stock markets in the world, listing over three thousand companies. It was created in 1971 by the National Association of Securities Dealers.

2. How do dealers differ from brokers? A dealer differs from a broker in that a dealer takes ownership of assets and is exposed to inventory risk, while a broker only facilitates a transaction on behalf of a client. Unlike brokers, dealers are subject to capital risk, because they must finance their inventories of securities.

3. List the major stock market indexes, and explain what they tell us. The major U.S. Stock market indexes are the Dow Jones Industrial Average, New York Stock Exchange, Standard & Poor’s 500 Index, and NASDAQ Composite Index. A stock market index is essentially a listing of stocks that bear some commonality, such as being traded on the same market exchange. They are used to measure the stock market performance and many are used to benchmark the performance of portfolios, such as mutual funds.

4. What does the price-earnings ratio tell us? The price-earnings ratio is the firm’s current price divided by the current earnings. When valuing a company’s stock, it is useful to look at a company’s P/E ratio and compare it to that Copyright © 2022 John Wiley & Sons, Inc.

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of similar firms. In general, a high P/E ratio means high projected earnings in the future. In addition, it also tells us how much investors are willing to pay per dollar of earnings.

Section 9.2 1. Describe the basic rights of owners of common stock and their position with respect to dividends. Common stockholders represent the basic ownership claim in a corporation, entitling the owners to vote on all important matters that affect the company, such as the election of the board of directors or a proposed merger or acquisition. Common stock owners are not guaranteed any dividend payments and have the lowest-priority claim on the firm’s assets in the event of bankruptcy. Legally, common stockholders enjoy limited liability; their losses are limited to the original amount of their investment in the firm. Common stocks are also considered perpetuities in the sense that they have no maturity; they can only be retired if management buys the stock back in the open market from investors or if the firm is liquidated.

2. Why do some people view preferred stock as a special type of a bond rather than a stock? Just like debt in the form of bonds, preferred stock is often callable and may be convertible into common stock. Also, like debt, it has “credit” ratings that are similar to those issued to bonds. But most important, preferred stock has no voting rights and just like bonds pays fixed dividends. For these reasons, many analysts treat preferred stock as a special kind of debt rather than as an equity.

Section 9.3 Note to instructor: There are no questions for this section.

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The general formula developed to value a share of stock is as follows:

P0 =

D3 D5 D1 D2 D4 + + + + + 2 3 4 (1 + R ) (1 + R) (1 + R) (1 + R) (1 + R)5

It says that the price of a share of stock is the present value of all expected future dividends, or: Stock price = PV (all future cash dividends).

2. What are growth stocks, and why do they typically pay little or no dividends? Growth stocks are defined as equity in any company whose earnings are growing faster than the average firm and the higher growth rate is expected to continue for some time. Instead of paying dividends, these firms reinvest the earnings back into the firm to pursue other highreturn investment opportunities.

Section 9.5 Note to instructor: There are no questions for this section.

Section 9.6 1. What three different models are used to value stocks based on different dividend patterns? Based on dividend patterns, we can use the following three models to value stock: (1) zerogrowth dividend model, (2) constant-growth dividend model, or (3) supernormal growth dividend growth model.

2. Explain why the growth rate g must always be less than the rate of return R for the constant-growth rate model? The constant-growth rate model assumes that the firm will grow at a constant rate forever. Any growth rate that is greater than this sum would imply that the firm will eventually take over the entire economy. This is of course not possible. Mathematically, according to the model, if g becomes greater than R, then the value of the stock would be negative.

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1. Why can skipping payment of a preferred dividend be a bad signal? A preferred dividend is treated like an interest payment on debt by financial markets and investors. Although the firm will not be in default, any delay or failure to declare and/or pay the dividends by the firm will be treated seriously by the financial markets and make them think that the firm is in financial difficulty.

2. How is a preferred stock with a fixed maturity valued? Any preferred stock with a defined maturity date is similar to a bond with a fixed maturity date. This similarity allows for the preferred stock to be valued in a similar fashion after adjusting for differences in the preferred stock relative to a bond. Using Equation 8.2, developed to value bonds, the coupons are replaced by the preferred dividends and the number of payments is adjusted to four per year to accommodate the fact that firms normally pay the dividends every quarter and not semi-annually or annually. This results in the model represented by Equation 9.7.

Self- Study Problems 9.1

Ted McKay has just bought the common stock of Ryland Corp. Management of Ryland expects the company to grow at the following rates for the next three years: 30 percent, 25 percent, and 15 percent. Last year the company paid a dividend of $2.50. Assume a required rate of return of 10 percent. Compute the expected dividends for the next three years and also the present value of these dividends if dividends grow at the same rate as the company.

Solution: Expected dividends for Ryland Corp and their present value: 0 10% 1 2 3 ├─────────┼─────────┼─────────┼───── ────┼─────────› D0 = $2.50 D1 D2 D3 g1 = 30% g2 = 25% g3 = 15% D1 =

D0 × (1 + g1) = $2.50(1 + 0.30) = $3.25

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D2 =

D1 × (1 + g2) = $3.25(1 + 0.25) = $4.06

D3 =

D2 × (1 + g3) = $4.06(1 + 0.15) = $4.67

Present value of the dividends = PV(D1) + PV(D2) + PV(D3) = $2.96 + $3.36 + $3.51 = $9.83 Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: Cash Flow (C)

Frequency (F)

3.25

4.06

4.67

Then solve by pressing NPV, enter the rate of 10% and compute NPV=9.82 (rounding error above).

9.2

Merriweather Manufacturing Company has been growing at a rate of 6 percent for the past two years, and the company’s CEO expects it to continue to grow at this rate for the next several years. The company paid a dividend of $1.20 last year. If your required rate of return is 14 percent, what is the maximum price that you would be willing to pay for this company’s stock?

Solution: Present value of Merriweather stock: 0

14%

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D1 $1.27 = (R − g ) (0.14 − 0.06) = $15.88

P0 =

The maximum price you should be willing to pay for this stock is $15.88.

9.3

Clarion Corp. has been selling electrical supplies for the past 20 years. The company’s product line has changed very little in the past five years, and the company’s management does not expect to add any new items for the foreseeable future. Last year, the company paid a dividend of $4.45 to its common stockholders. The company is not expected to increase its dividends in the future. If your required rate of return for such firms is 13 percent, what is the current value of this company’s stock?

Solution: Present value of Clarion Corp. stock: 0

13%

Year

├─────────┼─────────┼─────────┼───── ────┼─────› D0 = $4.45 D1 D2 D3 D4 g = 0% R = 13% Since the company’s dividends are not expected to grow, D0 = D1 =D2=……..D∞ = $4.45 = D Current value of the stock

9.4

D/R

$4.45/0.13

$34.23

Barrymore Infotech is a fast-growing communications company. The company did not pay a dividend last year and is not expected to do so for the next two years. Last year the company’s growth accelerated, and management expects to grow the business at a rate of 35 percent for the next five years before growth slows to a more

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stable rate of 7 percent. In the third year, management has forecasted a dividend payment of $1.10. Dividends will grow with the company thereafter. Calculate the value of the company’s stock at the end of its rapid growth period (i.e., at the end of five years). The required rate of return for such stocks is 17 percent. What is the current value of this stock? Solution: Present value of Barrymore Infotech stock: 0 17%

├────┼────┼────┼────┼────┼────┼───── ─> D0

g1 – g5 = 35%

g6 and beyond = 7%

R = 17% D0 = D1 = D2 = 0 D3 = $1.10 D4 = D3 × (1 + g4) = $1.10(1 + 0.35) =$1.485 D5 = D4 × (1 + g5) = $1.485(1 + 0.35) = $2.005 D6 = D5 × (1 + g6) = $2.005(1 + 0.07) = $2.145 Value of stock at

P5:

D6 $2.145 = (R − g ) (0.17 − 0.07) = $21.45

P5 =

Present value of the dividends in years 1 to 5 = PV(D1) + PV(D2) + PV(D3) + PV(D4) + PV(D5) $1.10 $1.485 $2.005 + + (1.17)3 (1.17) 4 (1.17)5 = $0 + $0 + $0.69 + $0.79 + $0.91

= $0 + $0 +

= $2.39

Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows:

Cash Flow (C)

Frequency (F)

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1.10

1.485

2.005

Then solve by pressing NPV, enter the rate of 17% and compute NPV=2.39. Current value of stock = PV(Dividends) + PV(P5) = $2.39 + [$21.45/(1.17)5] = $2.39 + $9.78 = $ 12.17

9.5

You are interested in buying the preferred stock of a bank that pays a dividend of $1.80 every quarter. If you discount such cash flows at 8 percent, what is the value of this stock?

Solution: Present value of preferred bank stock: Quarterly dividend on preferred stock = D = $1.80 Required rate of return = 8% Current value of stock = P0 = =

D R $1.80  4 0.08

= $90.00

Discussion Questions 9.1

Why can the market price of a stock differ from its true (intrinsic) value? Let us start by first defining the market price of a stock as the price that equates the demand for a stock with the supply of the stock. The role of the stock market is to bring

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buyers and sellers together in the most efficient way such that stocks are bought and sold at the market price. In reality, however, barriers of various kinds including the geographic separation of the two parties, strong demand that leads to overvaluation and vice versa, make the market price of a security slightly different than its true (intrinsic) value. The more efficient the marketplace, the smaller the deviation between the two. LO: 1 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.2

Why are investors and managers concerned about stock market efficiency? The role of secondary markets is to bring buyers and sellers together. Ideally, we would like stock markets to be as efficient as possible. Markets are efficient when current market prices of securities traded reflect all available information relevant to the security. If this is the case, security prices will be near or at their true value. The more efficient the market, the more likely this is to happen. This makes it easier for managers to price the stocks close to their intrinsic value. What investors are most concerned about is having complete information regarding a stock’s current price and where that price information can be obtained. Efficient markets allow them to trade at prices that are closer to the true value than otherwise possible. Thus, both investors who provide funds and managers (firms) who raise money are concerned when high transaction costs lead to inefficient markets.

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9.3

Solutions Manual

Why are common stockholders considered to be more at risk than the holders of other types of securities? In the hierarchy of lenders of funds to a firm, common stockholders have the most to lose. In the event of a firm becoming bankrupt, the law requires that creditors of different types, including bondholders, be paid off first. Next, preferred stockholders are paid off. Finally, common stockholders receive their investment if any funds are still available. Thus, common stockholders receive their money back last and are placed at most risk. This feature of common equity is referred to as residual claim.

LO: 1 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.4

Under what conditions does it make sense to use the constant-growth dividend model to value a stock? It only makes sense to use the constant-growth dividend model to value the stock of a company that is already paying a dividend and when that dividend can reasonably be expected to grow at a constant rate forever⎯in other words, the stock of a mature company. As discussed in the chapter, the growth rate of such a company will be less than the sum of the long-term rate of inflation and the real growth rate of the economy. It must also be less than the required rate of return on the stock.

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Solutions Manual

What does it mean when a company has a very high P/E ratio? Give examples of industries in which you believe high P/E ratios are justified. A high P/E ratio implies that investors believe that the firm has good prospects for earnings growth in the future. In fact, they believe that the firm will have higher growth potential than firms with lower P/E ratios. Companies in industries that are fast growing like biotech or any hi-tech industry have high P/E ratios. In the past, firms like Cisco and Intel had very high P/E ratios. As these firms matured and settled to annual growth rates of 15 percent or less, their P/E ratios have declined.

LO: 1 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.6

Explain why preferred stock is considered to be a hybrid of equity and debt securities. The law considers preferred stock as equity. Thus, holders are treated as the firm’s owners. Also, like common stockholders, preferred stockholders have to pay taxes on their dividend income. However, preferred stockholders do not have any voting rights. In addition, they receive only a fixed dividend just like bondholders. If a firm is liquidated, then they receive a stated value (par value) similar to bondholders. Preferred stock is rated by credit rating agencies just like bonds. Some preferred issues are convertible to the firm’s common stock just as convertible bonds. Some preferred issues are not perpetual and have a fixed maturity just like bonds. Thus, preferred stock is a hybrid security—like equity in some ways and like debt security in others.

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IMA: Corporate Finance AICPA: Measurement

9.7

Why is stock valuation more difficult than bond valuation? Despite the availability of mathematical models to value stocks, it is more difficult to apply valuation techniques to stocks than to bonds. First, unlike bonds, firms are not in default if dividends are not declared. This makes it difficult to determine the size and timing of the cash flows. Second, common stock, unlike bonds, does not have a fixed maturity, and hence, it is difficult to determine a terminal value unlike bonds, which have a maturity value. Next, it is easier to calculate the present value of a bond because the required rate of return is observable. In the case of stocks, it is rather difficult to estimate a required rate of return for many stocks and classify them into different risk groups.

LO: 2 Level: Intermediate Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.8

You are currently thinking about investing in a stock valued at $25.00 per share. The stock recently paid a dividend of $2.25 and its dividend is expected to grow at a rate of 5 percent for the foreseeable future. You normally require a return of 14 percent on stocks of similar risk. Is the stock overpriced, underpriced, or correctly priced? D0 = $2.25 Required rate of return (R) = 14% Growth rate (g) = 5% Using the Constant-growth model, the price of stock is:

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P0 =

D (1 + g ) D1 = 0 R−g R−g

$2.25(1.05) = $26.25 0.14 − 0.05

Solutions Manual

This stock is underpriced at $25. Using the constant-growth model, we arrived at a price of $26.25 for this stock. This makes the stock underpriced, and it should be considered a good buy. LO: 4 Level: Basic Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.9

Stock A and Stock B are both priced at $50 per share. Stock A has a P/E ratio of 17, while Stock B has a P/E ratio of 24. Which is the more attractive investment, considering everything else to be the same, and why? Stock A is the more attractive investment because it has a lower P/E ratio. The lower the P/E ratio, the larger the amount of earnings supporting the stock price. This makes Stock A more attractive of an investment than Stock B because the EPS for Stock A is $2.94 ($50/$17) whereas the EPS for Stock B is only $2.08 ($50/24).

LO: 1 Level: Basic Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.10

Facebook does not pay dividends. How can it have a positive stock price? Investors expect that Facebook will eventually start paying dividends and the value of its shares reflects the present value of these expected dividends. The fact that a company is

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not currently paying dividends does not mean that its stock is worthless. It is not uncommon for high growth firms not to pay dividends, since they often have to reinvest all of their earnings to maintain their high growth rate. However, if they are successful, as their growth rate slows over time they will begin to pay dividends. LO: 3, 4 Level: Intermediate Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

Questions and Problems BASIC 9.1

Stock Market Index: What is a stock market index?

Solution: A stock market index is used to measure the performance of the stock market. These indexes reflect the value of the stocks in a particular market, such as the NYSE or the NASDAQ, or across markets, and increase and decrease as the values of the stocks go up and down. Examples of stock market indexes include the Dow Jones Industrial Average, the New York Stock Exchange Index, the Standard & Poor’s 500 Index, and the NASDAQ Composite Index. LO: 1 Bloomcode: Knowledge AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.2

Stock Market Index: What is the Dow Jones Industrial Average?

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Solution: The Dow is the most widely published stock index and reflects the value of the stocks of 30 large companies. The value of the shares of these companies represents about 20 percent of the market value of all U.S. stocks. LO: 1 Bloomcode: Knowledge AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

9.3

Stock Market Index: What does NASDAQ stand for? What is NASDAQ?

Solution: NASDAQ stands for National Association of Securities Dealers Automated Quotation system. NASDAQ is one of the largest electronic stock markets in the world, listing over three thousand companies. It is an OTC market and does not have any physical location. Companies listed on NASDAQ had market capitalization of $21.77 trillion as of the end of 2020. LO: 1 Bloomcode: Knowledge AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

9.4

Dividend yield: What is a dividend yield? What does it tell us?

Solution: A dividend yield is the ratio of the annual dividend payout to the current market price of a stock. It tells us what percentage return we would earn from dividends alone if we purchased the stock at its current price. Alternatively, it tells us what percentage of the firm’s stock value is being distributed to stockholders each year. LO: 1 Bloomcode: Knowledge Copyright © 2022 John Wiley & Sons, Inc.

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AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.5

Present value of dividends: Fresno Corp. is a fast-growing company whose management expects it to grow at a rate of 30 percent over the next two years and then to slow to a growth rate of 18 percent for the following three years. If the last dividend paid by the company was $2.15, estimate the dividends for the next five years. Compute the present value of these dividends if the required rate of return is 14 percent.

Solution: 0

├───────┼────────┼───────┼────────┼─ ──────┤ D0 = $2.15

g1-2 = 30%;

g3-5 = 18%;

R = 14%

D1 = D0 × (1 + g1) = $2.15(1.30) = $2.795 D2 = D1 × (1 + g2) = $2.795(1.30) = $3.634 D3 = D2 × (1 + g3) = $3.634(1.18) = $4.288 D4 = D3 × (1 + g4) = $4.288(1.18) = $5.06 D5 = D4 × (1 + g5) = $5.06(1.18) = $5.97 $2.795 $3.634 $4.288 $5.06 $5.97 + + + + 1 2 3 4 (1.14) (1.14) (1.14) (1.14) (1.14)5 = $2.45 + $2.80 + $2.89 + $3.00 + $3.10

PV (Dividends) =

= $14.24

Financial Calculator Solution:

Using a financial calculator, enter the cash flows as follows: Cash Flow (C)

Frequency (F)

2.795

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3.634

4.288

5.06

5.97

Then solve by pressing NPV, enter the rate of 14% and compute NPV=14.24. LO: 4 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.6

Zero growth: Nynet, Inc., paid a dividend of $4.18 last year. The company’s management does not expect to increase its dividend in the foreseeable future. If the required rate of return is 18.5 percent, what is the current value of the stock?

Solution: D0 = $4.18; g = 0; P0 =

R = 18.5%

D $4.18 = = $22.60 R 0.185

LO: 4 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.7

Zero growth: Knight Supply Corp. has not grown for the past several years and management expects this lack of growth to continue. The firm last paid a dividend of $3.56. If you require a rate of return of 13 percent, what is the current value of this stock to you?

Solution: D0 = $3.56; g = 0;

R = 13%

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P0 =

Solutions Manual

D $3.56 = = $27.38 R 0.13

LO: 4 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.8

Zero growth: Ron Santana is interested in buying the stock of First National Bank. While the bank’s management expects no growth in the near future, Ron is attracted by the dividend income. Last year the bank paid a dividend of $5.65. If Ron requires a return of 14 percent on such stocks, what is the maximum price he should be willing to pay for a share of the bank’s stock?

Solution: D0 = $5.65; g = 0; P0 =

R = 14%

D $5.65 = = $40.36 R 0.14

LO: 4 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.9

Zero growth: The current stock price of Largent, Inc., is $44.72. If the required rate of return is 19 percent, what is the dividend paid by this firm if the dividend is not expected to grow in the future?

Solution: P0 = $44.72; P0 =

R = 19%;

D=?

D R

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$44.72 =

Solutions Manual

D 0.19

D = $44.72  0.19 = $8.50 LO: 4 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.10

Constant growth: Moriband Corp. paid a dividend of $2.15 yesterday. The company’s

dividend is expected to grow at a steady rate of 5 percent for the foreseeable future. If investors in stocks of companies like Moriband require a rate of return of 15 percent, what should be the market price of Moriband stock? Solution: D0 = $2.15;

g = 5%;

P0 =

D (1 + g ) D1 = 0 R−g R−g

$2.15(1.05) = $22.58 0.15 − 0.05

R = 15%

LO: 4 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.11

Constant growth: Nyeil, Inc., is a consumer products firm that is growing at a constant rate of 6.5 percent. The firm’s last dividend was $3.36. If the required rate of return is 18 percent, what is the market value of this stock if dividends grow at the same rate as the firm?

Solution: D0 = $3.36;

g = 6.5%;

R = 18% SM 9-19

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P0 =

Solutions Manual

D1 $3.36(1.065) = R − g 0.18 − 0.065

= $31.12

LO: 4 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.12

Constant growth: Reco Corp. is expected to pay a dividend of $2.25 next year. The forecast for the stock price a year from now is $37.50. If the required rate of return is 14 percent, what is the current stock price? Assume constant growth.

Solution: D1 = $2.25;

P1 = $37.50; P1 =

$37.50 =

R = 14%

D2 D (1 + g ) = 1 R−g R−g $2.25(1 + g ) 0.14 − g

$37.50(0.14 − g ) = $2.25 + 2.25 g $5.25 − 37.5 g = 2.25 + 2.25 g $5.25 − $2.25 = 37.5 g + 2.25 g g=

$3.00 = 7.55% $39.75

P0 =

D1 R−g

$2.25 = $34.87 0.14 − 0.0755

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AICPA: Measurement

9.13

Constant growth: Proxicam, Inc., is expected to grow at a constant rate of 7 percent. If the company’s next dividend, which will be paid in a year, is $1.15 and its current stock price is $22.35, what is the required rate of return on this stock?

Solution: D1 = $1.15;

P0 =

D1 R−g

D1 +g P0

P0 = $22.35;

g = 7%

$1.15 + 0.07 $22.35

= 0.0515 + 0.07 = 12.15%

LO: 4 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.14

Preferred stock valuation: X-Centric Energy Company has issued perpetual preferred stock with a stated (par) value of $100 and a dividend of 4.5 percent. If the required rate of return is 8.25 percent, what is the stock’s current market price?

Solution: D = 4.5% ($100) = $4.50; P0 =

R = 8.25%

D $4.50 = = $54.55 R 0.0825

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IMA: Corporate Finance AICPA: Measurement

9.15

Preferred stock valuation: The First Bank of Flagstaff has issued perpetual preferred stock with a $100 par value. The bank pays a quarterly dividend of $1.65 on this stock. What is the current price of this preferred stock given a required rate of return of 11.6 percent?

Solution: Quarterly dividend = $1.65 Required rate of return = R = 11.6%

P0 =

(1.65  4 ) = $56.90 0.116

LO: 6 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.16

Preferred stock valuation: The preferred stock of Axim Corp. is currently selling at $47.13. If the required rate of return is 12.2 percent, what is the dividend paid by this stock?

Solution: P0 = $47.13;

R = 12.2%

D 0.122 D = $47.13  0.122

P0 = $47.13 = = $5.75 LO: 6

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AICPA: Measurement

9.17

Preferred stock valuation: Each quarter, Sirkota, Inc., pays a dividend on its perpetual preferred stock. Today the stock is selling at $63.37. If the required rate of return for such stocks is 15.5 percent, what is the quarterly dividend paid by Sirkota?

Solution: P0 = $63.37;

R = 15.5%

D 0.155 D = $63.37  0.155

P0 = $63.37 = = $9.82

Annual dividend = $9.82 Quarterly dividend = $9.82 /4 = $2.46 LO: 6 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

INTERMEDIATE 9.18

Constant growth: Kay Williams is interested in purchasing the common stock of Reckers, Inc., which is currently priced at $37.45. The company is expected to pay a dividend of $2.58 next year and to increase its dividend at a constant rate of 7 percent. a. What should the market value of the stock be if the required rate of return is 14 percent? b. Is this a good buy? Why or why not?

Solution:

D1 $2.58 = = $36.86 R − g 0.148 − 0.07

P0 =

The stock is overpriced and not a good buy.

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LO: 4 Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.19

Constant growth: The required rate of return is 23 percent. Ninex Corp. has just paid a dividend of $3.12 and is expected to increase its dividend at a constant rate of 5 percent. What is the expected price of the stock three years from now?

Solution: R = 23%;

P3 =

D0 = $3.12;

g = 5%

D (1 + g ) 4 D4 = 0 R−g R−g

3.12(1.05) 4 = = $21.07 0.23 − 0.05 LO: 4 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.20

Constant growth: Jenny Banks is interested in buying the stock of Fervan, Inc., which is increasing its dividends at a constant rate of 6 percent. The firm recently paid a dividend of $2.65. The required rate of return is 16 percent. What is the current value of this stock? What should be the price of the stock in year 5?

Solution: g = 6%,

P0 =

D0 = $2.65,

R = 16%

$2.65 (1.06 ) D1 = = $28.09 R − g 0.16 − 0.06

P5 =

D6 $2.65(1.06)6 = = $37.59 R−g 0.16 − 0.06

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LO: 4 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.21

Constant growth: You own shares of Old World DVD Company and are interested in selling them. With so many people downloading music these days, sales, profits, and dividends at Old World have been declining 6 percent per year. The firm just paid a dividend of $1.15 per share. The required rate of return for a stock this risky is 15 percent. If dividends are expected to decline at 6 percent per year, what is a share of the stock worth today?

Solution: R = 15%;

P0 = =

D0 = $1.15;

g = -6%

D (1 + g ) D1 = 0 R−g R−g $1.15  (1 − 0.06) = $5.15 0.15 − (−0.06)

LO: 4 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.22

Nonconstant growth: You own a company that competes with Old World DVD Company (in the previous problem). Instead of selling DVDs, however, your company sells music downloads online. Things are going well now, but you know that it is only a matter of time before someone comes up with a better way to distribute music. Your company just paid a $1.50 per share dividend, and you expect to increase the dividend 10 percent next year. However, you then expect your dividend growth rate to begin going down - to 5 percent the following year, 2 percent the next year, and – 3 percent per year

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thereafter. Based upon these estimates, what is the value of a share of your company’s stock? Assume that the required rate of return is 12 percent. Solution: g1 = 10%, g2 = 5%, g3 =2%,

g = -3%,

D0 = $1.50

D1 = $1.50 × 1.1 = $1.65,

D2 = $1.65 × 1.05 = $1.7325,

D3 = $1.7325 ×1.02 = $1.7672,

D4 = $1.7672 × 0.97 = $1.7141.

P3 =

D4 $1.7141 = = $11.43 R − g 0.12 − ( −0.03 )

P0 =

D3 P3 D1 D2 + + + 2 3 1 + R (1 + R) (1 + R) (1 + R)3

P0 =

$1.65 $1.7325 $1.7672 $11.43 + + + 1.12 (1.12)2 (1.12)3 (1.12)3

R = 12%

P0 = $1.47 + $1.38 + $1.26 + $8.14 = $12.25

Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: Cash Flow (C)

Frequency (F)

1.65

1.7325

1.7672 + 11.43 =13.1972

Then solve by pressing NPV, enter the rate of 12% and compute NPV=12.25. LO: 5 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

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9.23

Solutions Manual

Nonconstant growth: Tre-Bien, Inc., is a fast-growing technology company. Management projects rapid growth of 30 percent for the next two years, then a growth rate of 17 percent for the following two years. After that, a constant growth rate of 8 percent is expected. The firm expects to pay its first dividend of $2.45 a year from now. If dividends will grow at the same rate as the firm and the required rate of return on stocks with similar risk is 22 percent, what is the current price of the stock?

Solution: g1 = g2 = 30%,

g3 = g4 = 17%,

D1 = $2.45,

D2 = $2.45 × 1.30 = $3.19,

D4 = $3.73 × 1.17 = $4.36,

g = 8%,

D1 = $2.45,

R = 22%

D3 = $3.19 × 1.17 = $3.73

D5 = 4.36 × 1.08 = $4.71

P4 =

D5 $4.71 = = $33.63 R − g 0.22 − 0.08

P0 =

D3 D1 D2 D4 P4 + + + + 2 3 4 1 + R (1 + R) (1 + R) (1 + R) (1 + R) 4

P0 =

$2.45 $3.19 $3.73 ( $4.36 + 33.63) + + + 2 1.22 (1.22) (1.22)3 (1.22)4

P0 = $2.01 + $2.14 + $2.05 + 17.15 P0 = $23.35

Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: Cash Flow (C)

Frequency (F)

2.45

3.19

3.73

4.36 + 33.63 = 37.99

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AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.24

Nonconstant growth: Management of ProCor, a biotech firm, forecasted the following growth rates for the next three years: 35 percent, 28 percent, and 22 percent. Management then expects the company to grow at a constant rate of 9 percent forever. The company paid a dividend of $1.75 last week. If the required rate of return is 20 percent, what is the value of this stock?

Solution: g1 = 35%; g2 = 28%; g3 = 22%; g4 = 9%; D0 = $1.75; R = 20%

D1 = D0 (1 + g 1 ) = $1.75 1.35 = $2.36 D 2 = D1 (1 + g 2 ) = $2.36 1.28 = $3.02 D3 = D 2 (1 + g3 ) = $3.02 1.22 = $3.68 D 4 = D3 (1 + g ) = $3.68 1.09 = $4.01

P3 =

D4 $4.01 = = $36.45 R − g 0.20 − 0.09

P0 =

D3 P3 D1 D2 + + + 2 3 1 + R (1 + R) (1 + R) (1 + R) 3

P0 =

$2.36 $3.02 $3.68 $36.45 + + + 2 1.20 (1.20) (1.20)3 (1.20)3

P0 = $1.97 + $2.10 + $2.13 + $21.16 P0 = $27.36

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2.36

3.02

3.69 + 36.57=40.26

Then solve by pressing NPV, enter the rate of 20% and compute NPV=27.36. LO: 5 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.25

Nonconstant growth: Revarop, Inc., is a fast-growth company that is expected to grow at a rate of 23 percent for the next four years. It is then expected to grow at a constant rate of 6 percent. Revarop’s first dividend, of $4.25, will be paid in year 3. If the required rate of return is 17 percent, what is the current value of the stock if dividends are expected to grow at the same rate as the company?

Solution: g1-4 = 23%; g = 6%;

D3 = $4.25;

R = 17%

D4 = D3 × 1.23 = $4.25 × 1.23 = $5.23

P4 =

D5 $5.23  (1.06) = = $50.40 R−g 0.17 − 0.06

D3 D1 D2 D +P + + + 4 44 2 3 1 + R (1 + R) (1 + R) (1 + R) $4.25 ($5.23 + $50.40) P0 = 0 + 0 + + (1.17)3 (1.17)4 P0 = $2.65 + $29.69 = $32.34

P0 =

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Cash Flow (C)

Frequency (F)

4.25

5.23 + 50.37 =55.60

Then solve by pressing NPV, enter the rate of 17% and compute NPV=32.34. LO: 5 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.26

Nonconstant growth: Quansi, Inc., management expects to pay no dividends for the next six years. It has projected a growth rate of 25 percent for the next seven years. After seven years, the firm will grow at a constant rate of 5 percent. Its first dividend, to be paid in year 7, will be $3.25. If the required rate of return is 24 percent, what is the stock worth today?

Solution: g = 5%; R = 24%; D7 = $3.25; D1 – D6 = 0 P7 =

D8 $3.25  (1.05) = = $17.96 R−g 0.24 − 0.05

P0 =

D 7 + P7 $3.25 + $17.96 = = $4.71 (1 + R)7 (1.24) 7

Frequency (F) SM 9-30

Fundamentals of Corporate Finance,5th edition

Solutions Manual

3.25 + 17.96 = 21.21

Then solve by pressing NPV, enter the rate of 24% and compute NPV=4.71. LO: 5 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.27

Nonconstant growth: Staggert Corp. will pay dividends of $5.00, $6.25, $4.75, and $3.00 in the next four years. Thereafter, management expects the dividend growth rate to be constant at 6 percent. If the required rate of return is 18.5 percent, what is the current value of the stock?

Solution: D1 = $5;

D2 = $6.25;

D3 = 4.75;

D4 = $3;

g = 6%;

P0 =

D3 D1 D2 D4 P4 + + + + 2 3 4 1 + R (1 + R) (1 + R) (1 + R) (1 + R) 4

P4 =

D5 $3  (1.06) = = $25.44 R − g 0.185 − 0.06

P0 =

$5 $6.25 $4.75 ($3 + $25.44) + + + 2 3 1.185 (1.185) (1.185) (1.185)4

R = 18.5%;

P0 = $4.22 + $4.45 + $2.86 + $14.42 = $25.95

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Solutions Manual

6.25

4.75

3 + 25.44 =28.44

Then solve by pressing NPV, enter the rate of 18.5% and compute NPV=25.95. LO: 5 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.28

Nonconstant growth: Diaz Corp. is expected to grow rapidly/ at a rate of 35 percent for the next seven years. The company’s first dividend, to be paid three years from now, will be $5. After seven years, the company (and the dividends it pays) will grow at a rate of 8.5 percent. What is the value of Diaz stock with a required rate of return of 14 percent?

Solution: g1-7 = 35%; D3 = $5.00; g = 8.5%; R = 14% D1 = D2 = 0;

D3 = $5

D4 = $5 × 1.35 = $6.75 D5 = $6.75 × 1.35 = $9.11 D6 =$9.11 × 1.35 = $12.30 D7 = $12.30 × 1.35 = $16.61 D8 = $16.61 × 1.085 = $18.02

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P7 =

D8 $18.02 = = $327.64 R − g 0.14 − 0.085

P0 =

D3 D5 D6 D +P D1 D2 D4 + + + + + + 7 77 2 3 4 5 6 1 + R (1 + R) (1 + R) (1 + R) (1 + R) (1 + R) (1 + R)

= 0+0+

$5 $6.75 $9.11 $12.30 ($16.61 + $327.64) + + + + 3 4 (1.14) (1.14) (1.14)5 (1.14) 6 (1.14) 7

= $3.38 + $4.00 + $4.73 + $5.60 + $137.58 = $155.29

Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: Cash Flow (C)

Frequency (F)

6.75

9.11

12.30

16.61 + 327.64 =344.25

Then solve by pressing NPV, enter the rate of 14% and compute NPV=155.28. LO: 5 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.29

Nonconstant growth: Tin-Tin Waste Management, Inc., is growing rapidly. Dividends are expected to grow at rates of 30 percent, 35 percent, 25 percent, and 18 percent over

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the next four years. Thereafter, management expects dividends to grow at a constant rate of 7 percent. The stock is currently selling at $47.85, and the required rate of return is 16 percent. Compute the dividend for the current year (D0). Solution: g1 = 30%; g2 = 35%; g3 = 25%; g4 = 18%; g = 7%; R = 16%; P0 = $47.85

P0 = $47.85 =

D3 D1 D2 D4 P4 + + + + 2 3 4 (1 + R 1 ) (1 + R 2 ) (1 + R 3 ) (1 + R 4 ) (1 + R 4 ) 4 D0  (1.30) D 0  (1.30)  (1.35) D 0  (1.30)  (1.35)  (1.25) + + 1.16 (1.16) 2 (1.16)3

D0  (2.5886)  (1.07) D  (1.30)  (1.35)  (1.25)  (1.18) 0.16 − 0.07 + 0 + (1.16) 4 (1.16) 4 $47.85 = D0  [1.12 + 1.30 + 1.41 + 1.43 + 17.00] D0 =

$47.85 = $2.15 $22.26

LO: 5 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

ADVANCED 9.30

Equation 9.4 shows the relation between a stock’s value and the dividend that is expected next year if dividends grow at a constant rate forever. If a firm pays all of its earnings as dividends, show how Equation 9.4 can be rearranged to calculate that firm’s P/E ratio. What does this tell us about the factors that determine a firm’s P/E ratio?

Solution: P0 =

D1 E1 = , where E1 is the earnings per share next year. R−g R−g

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Rearranging the formula:

P0 1 = . E1 R − g This formula tells us that the P/E ratio is determined by both the risk of the dividend cash flows and the rate at which they are expected to grow. LO: 4 Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.31

Riker Departmental Stores management has forecasted a growth rate of 40 percent for the next two years, followed by growth rates of 25 percent and 20 percent for the following two years. It then expects growth to stabilize at a constant rate of 7.5 percent forever. The firm paid a dividend of $3.50 recently. If the required rate of return is 18 percent, what is the current value of Riker’s stock?

Solution: g1-2 = 40%; g3 = 25%; g4 = 20%; g = 7.5%; D0 = $3.50; R = 18%

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D1 = D0  (1 + g 1 ) = $3.50  1.40 = $4.90 D2 = D1  (1 + g2 ) = $4.90  1.40 = $6.86 D3 = D2  (1 + g3 ) = $6.86  1.25 = $8.575 D4 = D3  (1 + g4 ) = $8.575  1.20 = $10.29 D5 = D4  (1 + g) = $10.29  1.075 = $11.06 P4 =

D5 $11.06 = = $105.33 R − g 0.18 − 0.075

P0 =

D3 D1 D2 D4 P4 + + + + 2 3 4 1 + R (1 + R) (1 + R) (1 + R) (1 + R) 4

P0 =

$4.90 $6.86 $8.575 $10.29 $105.33 + + + + 1.18 (1.18)2 (1.18)3 (1.18)4 (1.18)4

P0 = $4.15 + $4.93 + $5.22 + $5.31 + $54.33 P0 = $73.94

Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: Cash Flow (C)

Frequency (F)

4.90

6.86

8.575

10.29 + 105.35 =115.64

Then solve by pressing NPV, enter the rate of 18% and compute NPV=73.94. LO: 5 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

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Fundamentals of Corporate Finance,5th edition

9.32

Solutions Manual

Courtesy Bancorp issued perpetual preferred stock a few years ago. The bank pays an annual dividend of $4.27, and your required rate of return is 12.2 percent. a.

What is the value of the stock given your required rate of return?

Should you buy this stock if its current market price is $34.41? Explain.

Solution: a.

D = $4.27;

D $4.27 = = $35.00 R 0.122

P0 =

R = 12.2%

Since the stock is worth $35.00 but can be purchased for $34.41, you should buy this stock.

LO: 4 Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.33

Rhea Kirby owns shares in Ryoko Corp. Currently, the market price of the stock is $36.34. Management expects dividends to grow at a constant rate of 6 percent for the foreseeable future. Its last dividend was $3.25. Rhea’s required rate of return for such stocks is 16 percent. She wants to find out whether she should sell her shares or add to her holdings. a.

What is the value of this stock?

Based on your answer to part a, should Rhea buy additional shares in Ryoko Corp? Why or why not?

Solution:

$3.25  (1.06 ) D1 = = $34.45. R−g 0.16 − 0.06

P0 =

No, she should not buy more shares. This stock is overpriced with the stock selling at a higher price of $36.34, than what it is worth at $34.45. She should sell her shares.

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Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.34

Perry, Inc., paid a dividend of $2.50 yesterday. You are interested in investing in this company, which has forecasted a constant growth rate of 7 percent for its dividends, forever. The required rate of return is 18 percent. a.

Compute the expected dividends D1, D2, D3, and D4.

Compute the present value of these four dividends.

What is the expected value of the stock four years from now (P4)?

What is the value of the stock today based on the answers to parts b and c?

Use the equation for constant growth (Equation 9.4) to compute the value of the stock today.

Solution: a.

D0 = $2.50 g = 7% R = 18%

D1 = $2.50  (1.07 ) = $2.675 D2 = $2.50  (1.07)2 = $2.86 D3 = $2.50  (1.07)3 = $3.06 D4 = $2.50  (1.07)4 = $3.28

PV (Dividends) =

$2.675 $2.86 $3.06 $3.28 + + + 1 2 3 (1.18) (1.18) (1.18) (1.18)4

= $2.27 + 2.05 + $1.86 + $1.69 = $7.87

Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: Cash Flow (C)

Frequency (F)

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Solutions Manual

2.675

2.86

3.06

3.28

Then solve by pressing NPV, enter the rate of 18% and compute NPV=7.87. D5 = D4 (1 + g ) = $3.28  (1.07) = $3.51

P4 =

D5 $3.51 = = $31.91 R − g 0.18 − 0.07

PV(P4 ) =

$31.91 = $16.46 (1.18)4

P0 = PV (Dividends) + PV(P4 )

= $7.87 + $16.46 = $24.33

For a constant-growth stock: P0 =

D1 $2.675 = = $24.32 R − g 0.18 − 0.07

LO: 4 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.35

Zweite Pharma is a fast-growing drug company. Management forecasts that in the next three years, the company’s dividend growth rates will be 30 percent, 28 percent, and 24 percent, respectively. Last week it paid a dividend of $1.67. After three years,

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management expects dividend growth to stabilize at a rate of 8 percent. The required rate of return is 14 percent. a.

Compute the dividends for each of the next three years, and calculate their present value.

Calculate the price of the stock at the end of year 3, when the firm settles to a constant growth rate.

What is the current price of the stock?

Solution: g1 = 30%; g 2 = 28%; g3 = 24%; g = 8%; D0 = $1.67; R = 14%

D1 = D0 (1 + g 1 ) = $1.67  (1.30) = $2.17 D2 = D1 (1 + g2 ) = $2.171  (1.28) = $2.78 D3 = D2 (1 + g3 ) = $2.779  (1.24) = $3.45

a. PV (Dividends) =

D3 D1 D2 + + 2 1 + R (1 + R) (1 + R)3

$2.17 $2.78 $3.45 + + 2 1.14 (1.14) (1.14)3

= $1.90 + $2.14 + $2.33 = $6.37

Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: Cash Flow (C)

Frequency (F)

2.17

2.78

3.45

Then solve by pressing NPV, enter the rate of 14% and compute NPV=6.37.

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Solutions Manual

D4 = D3 (1 + g ) = $3.45  (1.08) = $3.73

P3 =

D4 $3.73 = = $62.17 R − g 0.14 − 0.08

PV(P3 ) =

$62.17 = $41.96 (1.14)3

P0 = PV(Dividends) + PV(P3 )

= $6.37 + $41.96 = $48.33

LO: 5 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.36

Triton Inc., is expected to grow at a rate of 22 percent for the next five years and then settle to a constant growth rate of 6 percent. The company recently paid a dividend of $2.35. The required rate of return is 15 percent. a.

Find the present value of the dividends during the rapid-growth period if dividends grow at the same rate as the company.

What is the value of the stock at the end of year 5?

What is the value of the stock today?

Solution: g1−5 = 22%; g = 6%; D0 = $2.35; R = 15%

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Solutions Manual

D1 = D0 (1 + g 1 ) = $2.35  (1.22) = $2.87 D2 = D1 (1 + g2 ) = $2.87  (1.22) = $3.50 D3 = D2 (1 + g3 ) = $3.50  (1.22) = $4.27 D4 = D3 (1 + g 4 ) = $4.27  (1.22) = $5.21 D5 = D4 (1 + g ) = $5.21  (1.22) = $6.35 PV (Dividends) = =

D3 D5 D1 D2 D4 + + + + 2 3 4 1 + R (1 + R) (1 + R) (1 + R) (1 + R)5 $2.87 $3.50 $4.27 $5.21 $6.35 + + + + 2 3 4 1.15 (1.15) (1.15) (1.15) (1.15)5

= $2.49 + $2.65 + $2.81 + $2.98 + $3.16 = $14.10

Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: Cash Flow (C)

Frequency (F)

2.87

3.50

4.27

5.21

6.35

Then solve by pressing NPV, enter the rate of 15% and compute NPV=14.10. D6 = D5 (1 + g ) = $6.35  (1.06) = $6.74

P5 =

D6 $6.74 = = $74.89 R − g 0.15 − 0.06

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PV(P5 ) =

Solutions Manual

$74.89 = $37.19 (1.15)5

P0 = PV (Dividends) + PV(P5 ) = $14.09 + $37.19 = $51.29

LO: 5 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.37

Ceebros Builders is expanding very fast and is expected to grow at a rate of 25 percent for the next four years. The company recently paid a dividend of $3.60 but is not expected to pay any dividends for the next three years. In year 4, management expects to pay a $5 dividend and thereafter to increase the dividend at a constant rate of 6 percent. The required rate of return on such stocks is 20 percent. a.

Calculate the present value of the dividends during the fast-growth period.

What is the value of the stock at the end of the fast-growth period (P4)?

What is the value of the stock today?

Would today’s stock value be affected by the length of time you intend to hold the stock?

Solution: a.

g1− 4 = 25% g = 6% D0 = $3.60 D 4 = $5.00 R = 20%

PV ( Dividends ) = 0 + 0 + 0 +

$5 = $2.41 (1.20) 4

$5.00  (1.06 ) D5 = = $37.86 R−g 0.20 − 0.06

P4 =

P0 = $2.41 +

No, the length of the holding period has no bearing on today’s stock price.

$37.86 = $20.67 (1.20) 4

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Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

Sample Test Problems 9.1

Which type of secondary market provides the most efficient market for financial securities?

Solution: An auction market is the most efficient type of secondary market because the buyers and sellers in an auction market interact directly with each other and bargain over price. LO: 1 Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

9.2

Is preferred stock a debt or an equity security?

Solution: Preferred stock represents an ownership interest in a corporation and is legally a form of equity. However, it does have characteristics that are similar to those of debt, such as no voting rights, fixed payments (dividends), and credit ratings similar to those issued to bonds. LO: 2 Bloomcode: Knowledge AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

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9.3

Solutions Manual

Burnes, Inc. is a mature firm that is growing at a constant rate of 5.5 percent per year. The last dividend that the firm paid was $1.50 per share. If dividends are expected to grow at the same rate as the firm and the required rate of return on Burnes’s stock is 12 percent, what is the market value of the company’s stock?

Solution: D0 = $1.50;

P0 =

g = 5.5%;

R = 12%

D1 $1.50 1.055 = = $24.35 R − g 0.12 − 0.055

LO: 4 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.4

Abacus Corporation will pay dividends of $2.25, $2.95, and $3.15 in the next three years. After three years, the dividends are expected to grow at a constant rate of 4 percent per year. If the required rate of return is 14.5 percent, what is the current value of the Abacus common stock? Solution: g constant = 4%; D1 = $2.25 D2 = $2.95 D3 = $3.15; R = 14.5%

P3 =

D4 $3.15 1.04 = = $31.20 R − g 0.145 − .04

$2.25 $2.95 $3.15 $31.20 + + + 2 3 (1.145) (1.145) (1.145) (1.145)3 = $1.97 + $2.25 + $2.10 + $20.78

P0 =

= $27.10

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Solutions Manual

Using a financial calculator, enter the cash flows as follows: Cash Flow (C)

Frequency (F)

2.25

2.95

3.15 + 31.20 = 34.65

Then solve by pressing NPV, enter the rate of 14.5% and compute NPV=27.10. LO: 4 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.5

The preferred stock of Wellcare Inc. is currently trading at $137.50 per share. If the required rate of return is 8 percent and this stock has no maturity date, what is the quarterly dividend paid by this stock? What is the quarterly dividend if the stock will mature in one year and it has a par value of $140?

Solution: With no maturity date: PS0 = $137.5; R = 8.0%

D 0.08 D = $137.50  0.08

PS0 = $137.50 = = $11.00

Annual dividend = $11.00 Quarterly dividend = $11.00 /4 = $2.75 We can use Equation 9.7 to solve for the dividend with a one-year maturity date:

SM 9-46

Fundamentals of Corporate Finance,5th edition

PS0 =

Solutions Manual

D/m + Pmn D/m D/m D/m + + + 2 3 (1 + i / m) (1 + i / m) (1 + i / m) (1 + i / m) 4

= $137.50 =

D/m D/m D/m D/m + $140 + + + 2 3 (1 + 0.08 / 4) (1 + 0.08 / 4) (1 + 0.08 / 4) (1 + 0.08 / 4) 4

= $137.50 =

D/m D/m D/m D/m + $140 + + + 2 1.02 (1.02) (1.02)3 (1.02) 4

Using a financial calculator to solve for PMT, we find that the quarterly dividend, D/m = $2.14.

Financial Calculator Solution: 4

-137.50

140 PMT

2.14

LO: 6 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

Ethics Case Discussion Questions 1. Discuss whether it would be unethical to buy a stock based on some information you found in the trash that had been thrown away by mistake. The point of questions 1 and 2 is to get students to see the difference between the legitimate use of information asymmetry as one trades in the market and ethical abuses of information asymmetry which if caught would likely be illegal as well as unethical. With respect to the information in the rubbish, it depends on how we view the ethics of a windfall. It also depends upon how one came upon the garbage. If a person was snooping in the garbage Copyright © 2022 John Wiley & Sons, Inc.

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Solutions Manual

looking for information, it clearly would be wrong because the person had no right to be snooping. However, if the wind blew the information onto the sidewalk and you just found it is that another matter? Suppose you found a $20 bill with no indication of who owned it. Would it be wrong to keep it? Probably not. So too with the discovery of the information that had blown out of the garbage. However, expect students to have a wide range of responses here.

2. Suppose you are the printer who has been given the job of preparing the official announcement of the FDA report. Can you use that information for personal gain? Why or why not? The question about the printer should be answered by saying that the printer’s actions would be unethical and illegal. The printer is an agent of the company and has privileged access to the information. The printer thus becomes an insider and trading on the information would be wrong because it violates the fairness criterion. Even if some students think this is morally acceptable, it is important that in class discussion they come to realize the ethical and legal hazards of acting on this information.

3. Some argue that insider trading brings information to the market more quickly and thus is morally acceptable on the grounds of efficiency. Do you agree with that argument? Why or why not? Those who think that efficiency is more important than fairness defend this position. In that case one would need to debate the merits of the alternative moral theories that provide the basis of efficiency and fairness. Note however, that when people discover that they are competing against those with inside information, they may tend to abandon the market, and this would decrease efficiency. Most scholars and business ethicists think that the efficiency argument can cut both ways and that the fairness argument is legitimate. Thus, the fairness argument and one form of the utilitarian argument establish the fact that insider trading is wrong.

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CHAPTER 8

Bond Valuation and the Structure of Interest Rates Before You Go On Questions and Answers Section 8.1 1.

What are the main differences between the corporate bond markets and stock markets?

The market for corporate bonds is very large, but smaller than the corporate equity market in the U.S. Most secondary market transactions involving corporate bonds take place in the over-thecounter market, making the corporate bond market thin relative to the more organized equity markets. Prices in the corporate bond market also tend to be more volatile than prices of securities sold in markets with greater trading volumes. This is because a few large trades can have a larger impact on a security’s price than numerous trades of various sizes. The biggest investors in corporate bonds are mutual funds, life insurance companies, and pension funds, and given the size of these investors, the trades are conducted in much larger blocks than in the stock market.

A bond has a 7 percent coupon rate, a face value of $1,000, and a maturity of four years. On a time line, lay out the cash flows for the bond.

The annual payments for the bond will be $70 ($1,000 x 7%); thus the time line for cash inflows would be as follows: 0

_______3

$70

_____4 $1,070 ($1,000 + $70)

Explain what a convertible bond is.

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Convertible bonds are bonds that can be converted into shares of common stock at some predetermined ratio at the discretion of the bondholder. The convertible feature allows the bondholder to take advantage of the firm’s prosperity if the share price rises above a certain value.

Section 8.2 1.

Explain conceptually how bonds are priced.

The current price of a bond is equal to the present value of all the cash flows that will be received from the investment. There are two sets of cash flows from a bond investment. First, there are the coupon payments to be received either annually or semiannually throughout the life of the bond. Second, there is the principal or face value of $1,000 that will be received when the bond matures. In order to find the price of the bond, we must find the present value of the coupon payments and the present value of the face value. We do this by discounting the entire cash flow stream at the current market rate and adding them up. This gives us the current price of the bond. Recognize that the coupon payments represent an annuity and that we can use the equation for the present value of an annuity from Chapter 6 to calculate the present value of this cash flow stream.

What is the compounding period for most bonds sold in the United States?

Most bonds sold in the United States pay interest semiannually, whereas European bonds typically only pay interest once a year.

What are zero coupon bonds, and how are they priced?

Zero coupon bonds are debt instruments that do not pay coupon interest payments but promise a single payment (interest earned plus principal) paid at maturity. The price of a zero coupon bond can be calculated using the same equation as used for coupon bonds, but setting the coupon payments to zero. The resulting formula is as follows: PB = Fmn/(1 + i/m)mn Because zero coupon bonds offer the entire payment at maturity, for a given change in interest rates, their price fluctuates more than coupon bonds with a similar maturity.

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Section 8.3 1.

Explain how bond yields are calculated.

A bond’s yield is calculated by finding the interest rate that equates the bond’s price to the present value of its interest payments and principal amount. The calculation of a bond’s yield, or its yield to maturity, considers the bond’s time to maturity, the coupon rate, and face value.

Section 8.4 1.

What is interest rate risk?

Bond prices are negatively related to interest rate movements. As interest rates rise, bond prices fall, and vice versa. Interest rate risk simply recognizes the fact that bond prices fluctuate as interest rates change, and, if you sell a bond before maturity, you may sell the bond for a price other than what you paid for it. The greater the fluctuation in bond prices due to changes in interest rates, the greater the interest rate risk.

Explain why long-term bonds with zero coupons are riskier than short-term bonds that pay coupon interest.

According to bond theorems number two and three, for a given change in interest rates, longerterm bonds with low coupon rates have greater price changes than shorter-term bonds with higher coupon rates. The likelihood of interest rates changing during the long run is higher than the short term. Thus, long-term zero coupon bonds have greater interest rate risk—greater price swings—than short-term bonds that pay coupon payments.

Section 8.5 (no questions) Note to instructor: There are no questions for this section.

Section 8.6 1.

What are default risk premiums, and what do they measure?

Default risk premiums are the amount of return that investors must be paid to purchase a security that possesses default risk compared to a similar risk-free investment. Default risk premiums, at

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any point in time, represent compensation for the expected financial injury for owning a bond plus some additional premium for bearing risk.

Describe the three most prominent bond rating systems.

Default risk premiums tend to increase during periods of economic decline and to narrow during periods of economic expansion. This phenomenon is due to changes in investors’ willingness to own bonds with different credit ratings over the business cycle, the so-called flight to quality argument. Specifically, during periods of expansion when few defaults take place, investors are willing to invest in bonds with low credit quality (these bonds typically pay higher interest rates) to gain higher yields. In contrast, during tough economic times when many businesses fail, investors are concerned with safety. Accordingly, they adjust their portfolios to include more high-quality credits and sell off bonds with low credit ratings. The three most prominent credit rating agencies are Moody’s Investors Service (Moody’s), Standard & Poor’s (S&P) and Fitch. Exhibit 8.4 describes the corporate bond rating systems used by the three rating agencies.

What are the key factors that most affect the level and shape of the yield curve?

The key factors that most affect the shape of the yield curve are the real rate of interest, the expected rate of inflation, and interest rate risk. If the future real rate of interest is expected to rise, it will result in an upward slope of the real rate of interest and consequently in an upward bias to the market yield curve. Similarly, increasing the expected rate of inflation will result in an upward-sloping yield curve, because long-term interest rates will contain a larger inflation premium than short-term interest rates. If these two variables are expected to decline in the future, the result will be a downward bias to the yield curve. In contrast, the longer a bond’s maturity, the greater the bond’s interest rate risk. Thus, interest rate risk premium always adds an upward bias to the slope of the yield curve, since the longer the maturity of a security, the greater its interest rate risk.

Self-Study Problems

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8.1

Solutions Manual

Calculate the price of a five-year bond that has a coupon of 6.5 percent paid annually. The current market rate is 5.75 percent.

Solution: 0

5.75%

5 Year

├───────┼────────┼───────┼────────┼───────┤ $65

$65

$1,065

C3 C +F C1 C2 C4 + + + + 5 55 2 3 4 1 + i (1 + i) (1 + i) (1 + i) (1 + i) $65 $65 $65 $65 ($65 + $1,000) = + + + + 1 2 3 4 (1 + 0.0575) (1.0575) (1.0575) (1.0575) (1.0575)5 = $61.47 + $58.12 + $54.96 + $51.97 + $805.28 = $1, 031.80

PB =

Financial Calculator Solution: Enter

5.75 N

Answer

8.2

PMT

1,000

-1,031.81

Bigbie Corp. issued a five-year bond one year ago with a coupon of 8 percent. The bond pays interest semiannually. If the yield to maturity on this bond is 9 percent, what is the price of the bond?

Solution: 0 9% 1

8 Semiannual Period

├───┼───┼───┼────┼───┼───┼───┼────┤ PB =? $40

$40

$1,040

C3 /m C +F C1 /m C2 /m + + + .......... + 8 8 8 1 2 3 (1 + i /m) (1 + i /m) (1 + i /m) (1 + i /m) $80 / 2 $40 $40 ($40 + $1,000) = + + + ........ + 1 2 3 (1 + 0.09/2) (1.045) (1.045) (1.045)8 = $38.28 + $36.63 + $35.05 + $33.54 + $32.10 + $30.72 + $29.39 + $731.31 = $967.02

PB =

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Fundamentals of Corporate Finance, 5th edition

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Alternatively, we can use the present value annuity factor (in Equation 5.5) and the present value equation (Equation 5.4) from Chapter 5 to solve for the price of the bond: 1   1   mn  1 − 1− 8  i  1+  Fn m +  (1 + 0.045 )  + $1,000 PB = C   = $40   mn m   (1.045 )8 i m 0.045   (1 + i m )         = $263.84 + $703.19

(

)

= $967.03

Financial Calculator Solution:

Enter

8 N

4.5

PMT

Answer

8.3

1,000 PV

-967.03

Rockwell Industries has a three-year bond outstanding that pays a 7.25 percent coupon rate and is currently priced at $913.88. What is the yield to maturity of this bond? Assume annual coupon payments.

Solution: 0

├───────┼────────┼───────┤ PB = -$913.88

$72.50

$1,072.50

Use the trial-and error approach to solve for YTM. Since the bond is selling at a discount, we know that the yield to maturity is higher than the coupon rate. Try YTM = 10%.

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PB = =

Solutions Manual

C +F C1 C2 + + 3 33 2 1 + i (1 + i ) (1 + i ) $72.50 $72.50 $72.50 + $1,000 + + 1.10 (1.10)2 (1.10)3

= $65.91 + $59.92 + $805.79  $931.62

Try a higher rate, say YTM = 11%.

PB = =

C +F C1 C2 + + 3 33 2 1 + i (1 + i ) (1 + i ) $72.50 $72.50 $72.50 + $1,000 + + 1.11 (1.11)2 (1.11)3

= $65.32 + $58.84 + $784.20  $908.36

Since this is less than the price of the bond, we know that the YTM is between 10 and 11 percent and closer to 11 percent. Try YTM = 10.75%. PB = =

C +F C1 C2 + + 3 33 2 1 + i (1 + i ) (1 + i ) $72.50 $72.50 $72.50 + $1,000 + + 2 1.1075 (1.1075) (1.1075)3

= $65.46 + $59.11 + $789.53  $914.10

Alternatively, we can use Equation 6.1 and Equation 5.4 to solve for the price of the bond:

1    1 − (1 + i )n  Fn PB = C   + n i   (1 + i )   1    1 − (1.1075)3  $1,000 $913.88 = $72.50   + 3  0.1075  (1.1075)   = $177.94 + $736.15  $914.09

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Solutions Manual

Thus, the YTM is approximately 10.75 percent. Using a financial calculator provided an exact YTM of 10.7594 percent. Financial Calculator Solution:

Enter

3 N

-913.88

1,000

PMT

Answer

8.4

72.50

10.7594

Hindenberg, Inc., has a 10-year bond that is priced at $1,100.00. It has a coupon of 8 percent paid semiannually. What is the yield to maturity on this bond?

Solution: The time line for Hindenberg’s 10-year bond looks like this: 0 i=? 1

├───┼───┼───┼───┼───┼────┼─── -$1,100

$40

─┼────┤

$40

$40 $1,000

The easiest way to calculate the yield to maturity is with a financial calculator. The inputs are as follows: Enter

20 N

Answer

−1,100

1,000

PMT

3.31

The answer we get is 3.31 percent, which is the semiannual interest rate. To obtain an annualized yield to maturity, we multiply this by two: YTM = 3.31%  2 YTM = 6.62%

8.5

Highland Corp., a U.S. company, has a five-year bond whose yield to maturity is 6.5 percent. The bond has no coupon payments. What is the price of this zero coupon bond? Solution:

You have the following information:

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Solutions Manual

YTM = 6.5% No coupon payments Most U.S. bonds pay interest semiannually. Thus m x n = 2 × 5 = 10 and i/2 = 0.065/2 = 0.0325. Using Equation 8.3, we obtain the following: PB =

Fmn

(1 + i m )

$1,000 (1.0325)10 = $726.27

Financial Calculator Solution: Enter

3.25

PMT

Answer

1,000 PV

-726.27

Discussion Questions 8.1

Because the conversion feature in a convertible bond is valuable to bondholders, convertible bond issues have lower coupon payments than otherwise similar bonds that are not convertible. Does this mean that a company can lower its cost of borrowing by selling convertible debt? Explain.

No. The interest (coupon) payments can be reduced by the company but the company cannot reduce the overall cost of borrowing by selling convertible debt. The reduction in the value of the interest payments is offset by the value of the conversion feature. If the company’s stock price goes above the price implied by the conversion ratio, the existing stockholders must share some of their gains with the bondholders. Investors are going to look for a required rate of return that compensates them for the risk that they are bearing. The only difference with a convertible bond is that some of that compensation comes in the form of the ability to benefit from appreciation in the company’s stock price. LO: 1 Level: Basic Bloomcode: Comprehension

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AASCB: Analytic IMA: Corporate Finance AICPA: Measurement What economic conditions would prompt investors to take advantage of a bond’s

8.2

convertibility feature? A bond’s convertibility feature becomes attractive when the company’s stock price rises above the bond’s price. This usually happens in times of economic expansion when the stock market is booming and interest rates are increasing, hence lowering the bond’s price. LO: 1 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

8.3

We know that a vanilla bond with a coupon rate below the market rate of interest will sell for a discount and that a vanilla bond with a coupon rate above the market rate of interest will sell for a premium. What kind of bond or loan will sell at its par value regardless of what happens to the market rate of interest?

A bond (or a loan) that pays a variable coupon (interest) rate that moves up and down with the market rate of interest will sell at its par value regardless of what happens in the market. While corporate bonds in the U.S. do not have variable coupon payments, bank loans often have variable rates which adjust frequently enough so that the value of the loans remains relatively constant as interest rates move up and down over time. LO: 1 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

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Solutions Manual

Define yield to maturity. Why is it important?

Yield to maturity (YTM) is the rate of return earned by investors if they buy a bond today at its market price and hold it to maturity. It is important because it represents the opportunity cost to the investor or the discount rate that makes the present value of the bond’s cash flows (i.e., its coupons and its principal payments) equal to the market price. So, YTM is also referred to as the going market rate or the appropriate discount rate for a bond’s cash flows.

It is important to understand that any investor who buys a bond and holds it to maturity will have a realized gain equal to the yield to maturity. If the investor sells before the maturity date, then realized gain will not be equal to the YTM but will only be based on cash flows earned to that point. Similarly, for callable bonds, investors are guaranteed a gain to the point in time when the bond is first called, but they cannot be assured of the yield to maturity because the issuer could call the bond before maturity. LO: 3 Level: Basic Bloomcode: Knowledge AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

8.5

Define interest rate risk. How can the CFOs manage this risk?

The change in a bond's prices caused by changes in interest rates is called interest rate risk. In other words, we can measure the interest rate risk to a bond’s investor by measuring the percentage change in the bond’s price caused by a 1 percent change in the market interest rates.

The key to managing interest rate risk is to understand the relationships between interest rates, bond prices, the coupon rate, and the bond’s term to maturity. Portfolio managers need to understand that as interest rates rise bond prices decline, and it declines more for low-coupon bonds and longer-term bonds than for the others. In such a scenario, bond portfolio managers can reduce the size and maturity of their portfolio to reduce the impact of interest rate increases. When interest rates decline,

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bond prices increase and rise more for longer-term bonds and higher coupon bonds. At such times, CFOs can increase the size and maturity of their portfolios to take advantage of the inverse relationship between interest rates and bond prices. LO: 4 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance AICPA: Risk Analysis

8.6

Explain why bond prices and interest rates are negatively related. What are the roles of the coupon rate and the term to maturity in this relation?

Bond prices and interest rates are negatively related because the market rate varies, while the coupon rate and face value are constant over the life of the bond. Thus, as rates increase, the present value of the interest and principle payments from existing bonds declines. o

For a given change in interest rates, longer-term bonds experience greater price changes (price volatility) than shorter-term bonds. Longer-term bonds have a larger proportion of their cash flows farther in the future, and the change in the present value of those longerterm cash flows will be greater when interest rates change because they are more heavily discounted. In addition, the longer it takes for investors to receive the cash flows, the more uncertainty they have to deal with and hence, the more price-volatile the bond will be.

Lower coupon bonds are more price volatile than higher coupon bonds. The same argument used above also explains this relationship. The lower the coupon on a bond, the greater the proportion of cash flows that investors receive at maturity, as opposed to the higher coupon bonds which give the investors cash flow in higher amounts before maturity.

LO: 4 Level: Basic Bloomcode: Comprehension AASCB: Analytic

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IMA: Corporate Finance AICPA: Measurement

8.7

If interest rates are expected to increase, should investors look to long-term bonds or short-term bonds? Explain.

As interest rates increase, bond prices decrease with longer-term bonds, experiencing a bigger decline than shorter-term bonds. So, investors expecting an increase in interest rates should choose short-term bonds over long-term bonds and reduce their interest rate risk. LO: 4 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

8.8

Explain what you would assume the yield curve would look like during economic expansion and why.

At the beginning of an economic expansion, the yield curve tends to be rather steep as the rates begin to rise once the demand for capital is beginning to pick up due to growing economic activity. The yield curve will retain its positive slope during the economic expansion, which reflects the investors’ expectations that the economy will grow in the future and that the inflation rates will also rise in the future. LO: 5 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

8.9

An investor holds a 10-year bond paying a coupon rate of 9 percent. The yield to maturity of the bond is 7.8 percent. Would you expect the investor to be holding a

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par-value, premium, or discount bond? What if the yield to maturity were 10.2 percent? Explain. Since the bond’s coupon of 9 percent is greater than the yield to maturity, the bond will be a premium bond. As market rates of interest drop below the coupon rate of the 9 percent bond, demand for the bond increases, driving up the price of the bond above face value.

If the yield to maturity is at 10.2 percent, then the bond is paying a lower coupon than the going market rate and will be less attractive to investors. The demand for the 9 percent bond will decline, driving its price below the face value. This will be a discount bond. LO: 2 Level: Basic Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

8.10 a. Investor A holds a 10-year bond, while investor B holds an 8-year bond. If interest rate increases by 1 percent, which investor has the higher interest rate risk? Explain. Since A holds the longer-term bond, he or she will face the higher interest rate risk. Longer-term bonds are more price volatile than shorter-term bonds.

b. Investor A holds a 10-year bond paying 8 percent a year, while investor B also has a 10-year bond that pays a 6 percent coupon. Which investor has the higher interest rate risk? Explain. Investor B will have the higher interest rate risk since lower coupon bonds have a higher interest rate risk than higher coupon bonds of the same maturity. LO: 4 Level: Basic Bloomcode: Analysis AASCB: Analytic

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IMA: Corporate Finance AICPA: Measurement

Questions and Problems BASIC 8.1

Bond price: BA Corp is issuing a 10-year bond with a coupon rate of 8 percent. The interest rate for similar bonds is currently 6 percent. Assuming annual payments, what is the value of the bond?

Solution: Years to maturity = n = 10 Coupon rate = C = 8% Annual coupon = $1,000 × 0.08 = $80 Current market rate = i = 6% Present value of bond = PB 0 6% 1

10 Years

├───┼────┼───┼───┼───┼────┼── $80

$80

─────┤

$80

$80 + $1,000

PB =

C3 C1 C2 + + + 1 2 (1 + i ) (1 + i ) (1 + i)3

C10 + F10 (1 + i)10

1  1    1−  1 − (1 + i )n   Fn (1.06)10  $1,000 = C  = $80  +  + n 10 i   (1 + i )  0.06  (1.06)     = $588.81 + $558.39 = $1,147.20

Financial Calculator Solution:

Enter

PMT

Answer

1,000 PV

-1,147.20

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Solutions Manual

LO: 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

8.2

Bond price: Pierre Dupont just received a cash gift from his grandfather. He plans to invest in a five-year bond issued by Venice Corp. that pays an annual coupon rate of 5.5 percent. If the current market rate is 7.25 percent, what is the maximum amount Pierre should be willing to pay for this bond?

Solution: 0

7.25%

5 Years

├───────┼────────┼───────┼────────┼───────┤ $55

$55

$1,055

Coupon rate = C = 5.5% Annual coupon = $1,000 × 0.055 = $55 Current market rate = i = 7.25% Present value of bond = PB 1  1    1− 5   1 − (1 + i )n   Fn $1,000 (1.0725) PB = C   = $55   + + n 5 i   (1 + i )  0.0725  (1.0725)     = $224.01 + $704.72 = $928.73

Financial Calculator Solution:

Enter

5 N

Answer

7.25

PMT

1,000 PV

-928.73

LO: 2 Bloomcode: Application AASCB: Analytic

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IMA: Corporate Finance AICPA: Measurement

8.3

Bond price: Knight, Inc., has issued a three-year bond that pays a coupon rate of 6.10 percent. Coupon payments are made semiannually. Given the market rate of interest of 5.80 percent, what is the market value of the bond?

Solution: Years to maturity = n = 3 Coupon rate = C = 6.1% Frequency of payment = m = 2 Semiannual coupon = $1,000 × (0.061/2) = $30.50 Current market rate = i = 5.8% Present value of bond = PB 0 5.8%

Periods

├───┼────┼───┼───┼───┼────┤ $30.50 $30.50 $30.50 $30.50 $30.50 $30.50 + $1,000 1   1   2n  1 − 1− i 6 1 +   F2 n (1.029)  $1,000 2 + PB = C   = $30.50   +  2n 6 2 i 0.029 i   (1.029)   1+ 2 2       = $165.77 + $842.38 = $1, 008.15

(

)

(

)

Financial Calculator Solution:

Enter

6 N

Answer

2.9

30.50

PMT

1,000 PV

-1,008.15

LO: 2 Bloomcode: Application AASCB: Analytic

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IMA: Corporate Finance AICPA: Measurement

8.4

Bond price: Regatta, Inc., has seven-year bonds outstanding that pay a 12 percent coupon rate. Investors buying these bonds today can expect to earn a yield to maturity of 8.875 percent. What is the current value of these bonds? Assume annual coupon payments.

Solution: Years to maturity = n = 7 Coupon rate = C = 12% Annual coupon = $1,000 x 0.12 = $120 Current market rate = i = 8.875% Present value of bond = PB 08.875%1

Years

├───┼────┼───┼───┼───┼────┼───┤ $120

$120

$120+ $1,000

1  1    1− 7   1 − (1 + i )n   Fn $1,000 (1.08875) PB = C   = $120   + + n 7 i   (1 + i )  0.08875  (1.08875)     = $606.50 + $551.44 = $1,157.94

Financial Calculator Solution:

Enter

8.875

120

PMT

N Answer

1,000 PV

-1,157.94

LO: 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance

SM 8-18

Fundamentals of Corporate Finance, 5th edition

Solutions Manual

AICPA: Measurement

8.5

Bond price: You are interested in investing in a five-year bond that pays a 7.8 percent coupon rate with interest to be received semiannually. Your required rate of return is 8.4 percent. What is the most you would be willing to pay for this bond?

Solution: Years to maturity = n = 5 Coupon rate = C = 7.8% Frequency of payment = m = 2 Semiannual coupon = $1,000 × (0.078/2) = $39.00 Current market rate = i = 8.4% Present value of bond = PB

0 8.4% 1

10 Periods

├───┼────┼───┼───┼───┼────┼── $39

$39

─────┤

$39

$39+ $1,000

1   1   2n  1 − 1− i 10 1 +   F2 n (1.042)  $1,000 2 + PB = C   = $39   +  2n 10 2 i 0.042 i   (1.042)   1+ 2 2       = $313.20 + $662.71 = $975.91

(

)

(

)

Financial Calculator Solution:

Enter

4.2

PMT

Answer

1,000 PV

-975.91

LO: 2 Bloomcode: Application AASCB: Analytic

SM 8-19

Fundamentals of Corporate Finance, 5th edition

Solutions Manual

IMA: Corporate Finance AICPA: Measurement

8.6

Zero coupon bonds: Diane Carter is interested in buying a five-year zero coupon bond with a face value of $1,000. She understands that the market interest rate for similar investments is 9 percent. Assume annual coupon payments. What is the current value of this bond?

Solution: Years to maturity = n = 5 Coupon rate = C = 0% Current market rate = i = 9% 0 9% 1

5 Years

├───┼────┼───┼───┼───┤ $0

$0+ $1,000

PB =

(

Fmn

1+ i

)

$1,000

(1.09 )

= $649.93

Financial Calculator Solution:

Enter

PMT

Answer

1,000 PV

-649.93

LO: 1, 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

SM 8-20

Fundamentals of Corporate Finance, 5th edition

8.7

Solutions Manual

Zero coupon bonds: Ten-year zero coupon bonds issued by the U.S. Treasury have a face value of $1,000 and interest is compounded semiannually. If similar bonds in the market yield 10.5 percent, what is the value of these bonds?

Solution: Years to maturity = n = 10 Frequency of payment = m = 2 Coupon rate = C = 0% Current market rate = i = 10.5% 010.5%

Periods ├───┼────┼───┼───┼───┼────┼── $0

─────┤

$0 + $1,000

PB =

(

Fmn

1+ i

)

$1,000

(1.0525 )

= $359.38

Financial Calculator Solution:

Enter

5.25

PMT

Answer

1,000 PV

-359.38

LO: 1, 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

8.8

Zero coupon bonds: Northrop Real Estate Company management is planning to fund a development project by issuing 10-year zero coupon bonds with a face value of $1,000. Assuming semiannual compounding, what will be the price of these bonds if the appropriate discount rate is 14 percent?

SM 8-21

Fundamentals of Corporate Finance, 5th edition

Solutions Manual

Solution: Years to maturity = n = 10 Frequency of payment = m = 2 Coupon rate = C = 0% Current market rate = i = 14% 014% 1

20 Periods

this ├───┼────┼───┼───┼───┼────┼── $0

─────┤

$0 + $1,000

PB =

(

Fmn

1+ i

)

$1,000

(1.07 )

= $258.42

Financial Calculator Solution:

Enter

PMT

Answer

1,000 PV

-258.42

LO: 1, 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

8.9

Yield to maturity: Ruth Hornsby is looking to invest in a three-year bond that makes semiannual coupon payments at a rate of 5.875 percent. If these bonds have a market price of $981.13, what yield to maturity can she expect to earn?

SM 8-22

Fundamentals of Corporate Finance, 5th edition

Solutions Manual

Frequency of payment = m = 2 Semiannual coupon = $1,000 × (0.05875/2) = $29.375 Yield to maturity = i Present value of bond = PB = $981.13 Use the trial-and-error approach to solve for YTM. Since the bond is selling at a discount, we know that the yield to maturity is higher than the coupon rate. Try YTM = 6%.

1   2n  1 − 1+ i  F2 n 2 + PB = C    2n 2 i i   1 + 2 2     1   6  1 − (1 + 0.03 )  + $1,000 $981.13  $29.375     (1.03 )6 0.03      $159.13 + $837.48

(

)

(

)

 $996.61 Try a higher rate, say YTM = 6.6%.

1   2n  1 − 1+ i  F2 n 2 + PB = C    2n 2 i i   1 + 2 2     1   6  1 − (1 + 0.033 )  + $1,000 $981.13  $29.375     (1.033 )6 0.033      $157.56 + $823.00

(

)

(

)

 $980.56 The YTM is approximately 6.6 percent. Using a financial calculator provided an exact YTM of 6.58 percent Enter

29.375

-981.13

1,000

SM 8-23

Fundamentals of Corporate Finance, 5th edition

N Answer

Solutions Manual

PMT

3.29 x 2 = 6.58

LO: 3 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement Excel Template available in Wiley Course Resources Excel Template Solution available in Wiley Instructor Resources

8.10

Yield to maturity: Rudy Sandberg wants to invest in four-year bonds that are currently priced at $868.43. These bonds have a coupon rate of 6 percent and make semiannual coupon payments. What is the current market yield on this bond?

Solution: Years to maturity = n = 4 Coupon rate = C = 6% Frequency of payment = m = 2 Semiannual coupon = $1,000 × (0.06/2) = $30 Yield to maturity = i Present value of bond = PB = $868.43 Use the trial-and-error approach to solve for YTM. Since the bond is selling at a discount, we know that the yield to maturity is higher than the coupon rate. Try YTM = 10%.

SM 8-24

Fundamentals of Corporate Finance, 5th edition

Solutions Manual

1   2n  1 − 1+ i  F2 n 2 + C PB =  =  2n 2 i i   1+ 2 2     1   8  1 − (1 + 0.05 )  + $1,000 $868.43  $30     (1.05 )8 0.05      $193.90 + $676.84

(

)

(

)

 $870.74 Try a higher rate, say YTM = 10.1%.

1   2n  1 − 1+ i  F2 n 2 + C PB =   2n 2 i i   1 + 2 2     1   8  1 − (1 + 0.0505 )  + $1,000 $868.43  $30     (1.0505 )8 0.0505      $193.51 + $674.27

(

)

(

)

 $867.78 The YTM is approximately 10.1 percent. Using a financial calculator provided an exact YTM of 10.08 percent. Enter

8 N

Answer

-868.43

1,000

PMT

5.04 x 2 =10.08

LO: 3 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

SM 8-25

Fundamentals of Corporate Finance, 5th edition

8.11

Solutions Manual

Realized yield: Josh Kavern bought 10-year, 12 percent coupon bonds issued by the U.S. Treasury three years ago at $913.44. If he sells these bonds, for which he paid the face value of $1,000, at the current price of $804.59, what is his realized yield on the bonds? Assume similar coupon-paying bonds make annual coupon payments.

Solution: Purchase price of bond = $913.44 Years investment held = n = 3 Coupon rate = C = 12% Frequency of payment = m = 1 Annual coupon = $1,000 × (0.12) = $120 Realized yield = i Selling price of bond = PB = $804.59 To compute the realized return, either the trial-and-error approach or the financial calculator can be used. Since the price has declined, market rates must have increased. So, the realized return is going to be less than the bond’s coupon. Try rates lower than the coupon rate. Try i = 10%.

1    1 − (1 + i )n  Fn PB = C   + n i   (1 + i )   1    1 − (1.10)3  $804.59 $913.44 = $120   + 3  0.10  (1.10)   = $298.42 + $604.50  $902.92 Try a lower rate, i = 9.5%.

SM 8-26

Fundamentals of Corporate Finance, 5th edition

Solutions Manual

1    1 − (1 + i )n  Fn PB = C   + n i   (1 + i )   1    1 − (1.095)3  $804.59 $913.44 = $120   + 3  0.095  (1.095)   = $301.07 + $612.82 = $913.89 The realized rate of return is approximately 9.5 percent. Using a financial calculator provided an exact yield of 9.52 percent. Enter

3 N

Answer

120

-913.44

804.59

PMT

9.52

LO: 3 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

8.12

Realized yield: Four years ago, Lisa Stills bought six-year, 5.5 percent coupon bonds issued by the Fairways Corp. for $947.68. If she sells these bonds at the current price of $894.52, what will be her realized yield on the bonds? Assume similar coupon-paying bonds make annual coupon payments.

Solution: Purchase price of bond = $947.68 Years investment held = n = 4 Coupon rate = C = 5.5% Frequency of payment = m = 1 Annual coupon = $1,000 × (0.055) = $55 Realized yield = i Selling price of bond = PB = $894.52

SM 8-27

Fundamentals of Corporate Finance, 5th edition

Solutions Manual

To compute the realized return, either the trial-and-error approach or the financial calculator can be used. Since the price has declined, market rates must have increased. So, the realized return is going to be less than the bond’s coupon. Try rates lower than the coupon rate. Try i = 5%.

1   1 −  (1 + i )n  Fn PB = C   + n i   (1 + i )   1    1 − (1.05)4  $894.52 $947.68 = $55   + 4  0.05  (1.05)   = $195.03 + $735.92  $930.95 Try a lower rate, i = 4.5%.

1    1 − (1 + i )n  Fn PB = C   + n i   (1 + i )   1    1 − (1.045)4  $894.52 $947.68 = $55   + 4  0.045  (1.045)   = $197.31 + $750.11  $947.42 The realized rate of return is approximately 4.5 percent. Using a financial calculator provided an exact yield of 4.49 percent. Enter

4 N

Answer

-947.68

894.52

PMT

4.49

LO: 3 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

SM 8-28

Fundamentals of Corporate Finance, 5th edition

Solutions Manual

INTERMEDIATE 8.13

Bond price: The International Publishing Group is raising $10 million by issuing 15-year bonds with a coupon rate of 8.5 percent. Coupon payments will be made annually. Investors buying the bonds today will earn a yield to maturity of 8.5 percent. At what price will the bonds sell in the marketplace? Explain.

Solution: Years to maturity = n = 15 Coupon rate = C = 8.5% Annual coupon = $1,000 × 0.085 = $85 Current market rate = i = 8.5% Present value of bond = PB 0 8.5% 1

├───┼────┼───┼───┼─── $85

$85

Year

─────┤

$85

$85+ $1,000

n = 15;

C = 8.5%;

i = YTM = 8.5%

1  1    1− 15   1 − (1 + i )n   Fn $1,000 (1.085) PB = C   = $85   + + n 15 i   (1 + i )  0.085  (1.085)     = $705.86 + $294.14 = $1, 000.00

This answer should have been intuitive. Since the bond is paying a coupon equal to the going market rate of 8.5 percent, the bond should be selling at its par value of $1,000.

Enter

8.5

PMT

Answer

1,000 PV

-1,000

LO: 2 Bloomcode: Application AASCB: Analytic

SM 8-29

Fundamentals of Corporate Finance, 5th edition

Solutions Manual

IMA: Corporate Finance AICPA: Measurement

8.14

Bond Price: Lopez Information Systems management is planning to issue 10-year bonds. The going market yield for such bonds is 8.125 percent. Assume that coupon payments will be made semiannually. Management is trying to whether to issue an 8 percent coupon bond or a zero coupon bond. Lopez needs to raise $1 million. What will be the price of an 8 percent coupon bond, and how many 8 percent coupon bonds will have to be issued? What will be the price of a zero coupon bond, and how many zero coupon bonds will have to be issued?

Solution: 8 percent coupon bonds Years to maturity = n = 10 Frequency of payment = m = 2 Coupon rate = C = 8.00% Semiannual coupon = $1,000 × (0.08/2) = $40 Current market rate = i = 8.125% Present value of bond = PB 0

8.125%

├───────┼────────┼────────┼── $40

$40

20 ─────────┤

$40

$40+ $1,000

1   1   mn  1 − 1− i 20 1 +   F2 n $1,000 (1.040625)  2 + PB = C   = $40   +  mn 2 i 0.040625  (1.040625)20 i    1 + 2 2       = $540.62 + $450.94 = $991.56

(

)

(

)

The firm can sell these bonds at $991.56.

Enter

4.0625

1,000

SM 8-30

Fundamentals of Corporate Finance, 5th edition

Solutions Manual

PMT

Answer

-$991.55

Amount to be raised = $1,000,000 Number of bonds sold = $1,000,000 / $991.55 = 1,009 bond contracts (Rounded)

Zero coupon bonds Years to maturity = n = 10 Coupon rate = C = 0% Current market rate = i = 8.125% 0 8.125%

├───── ┼────┼───┼───┼───┼────┼── $0

─────┤

$0+ $1,000

PB =

(

Fmn 1+ i

Enter

)

$1,000

(1.040625 )

= $450.94

4.0625

PMT

N Answer

1,000 PV

-450.94

Amount to be raised = $1,000,000 Number of bonds sold = $1,000,000 / $450.94 = 2,218 bond contracts (Rounded) LO: 1, 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

8.15

Bond price: Marshall Company is issuing eight-year bonds with a coupon rate of 6.5 percent and semiannual coupon payments. If the current market rate for similar bonds is 8

SM 8-31

Fundamentals of Corporate Finance, 5th edition

Solutions Manual

percent, what will the bond price be? If company management wants to raise $1.25 million, how many bonds does the firm have to sell? Solution: Years to maturity = n = 8 Frequency of payment = m = 2 Coupon rate = C = 6.5% Semiannual coupon = $1,000 × (0.065/2) = $32.50 Current market rate = i = 8% Present value of bond = PB

0 8% 1

├───┼────┼───┼───┼───

$32.50

Period

─────┤

$32.50………..$32.50

$32.50+ $1,000

1   1   mn  1 − 1− 1+ i    F2 n (1.04)16  $1,000 2 PB = C   + = $32.50   +  mn 16 2 i 0.04 i   (1.04)   1 + 2 2       = $378.70 + $533.91 = $912.61

(

)

(

)

To raise $1.25 million, the firm would have to sell: Number of bonds = $1,250,000 / $912.61 = 1,370 bond contracts (Rounded) Enter

32.50

PMT

Answer

1,000 PV

-912.61

LO: 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

SM 8-32

Fundamentals of Corporate Finance, 5th edition

8.16

Solutions Manual

Bond price: Rockne, Inc., has outstanding bonds that will mature in six years and pay an 8 percent coupon semiannually. If you paid $1,036.65 today and your required rate of return was 6.6 percent, did you pay the right price for the bond?

Solution: Years to maturity = n = 6 Frequency of payment = m = 2 Coupon rate = C = 8% Semiannual coupon = $1,000 × (0.08/2) = $40 Current market rate = i = 6.6% Present value of bond = PB 0 6.6%

├───────┼────────┼────────┼── $40

$40

─────────┤

$40

$40+ $1,000

1   1   mn  1 − 1− 12  1+ i    F2 n $1,000 (1.033) 2 PB = C   = $40   + + mn 2 i 0.033  (1.033)12 i    1 + 2 2       = $391.12 + $677.32 = $1, 068.45

(

)

(

)

You paid less at $1,036.65 than what the bond is worth at $1,068.45. That was a good price. Enter

3.3

PMT

Answer

1,000 PV

-1,068.45

LO: 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement Excel Template available in Wiley Course Resources Excel Template Solution available in Wiley Instructor Resources

SM 8-33

Fundamentals of Corporate Finance, 5th edition

8.17

Solutions Manual

Bond price: Nanotech, Inc., has a bond issue maturing in seven years that is paying a coupon rate of 9.5 percent (semiannual payments). Management wants to retire a portion of the issue by buying the securities in the open market. If it can refinance at 8 percent, how much will Nanotech pay to buy back its current outstanding bonds?

Solution: Years to maturity = n = 7 Frequency of payment = m = 2 Coupon rate = C = 9.5% Semiannual coupon = $1,000 × (0.095/2) = $47.50 Current market rate = i = 8%

Present value of bond = PB 0 8%

├───────┼────────┼────────┼── $47.50

$47.50

──────┤

$47.50

$47.50 + $1,000

1   1   mn  1 − 1− 1+ i    F2 n (1.04)14  $1,000 2 PB = C   + = $47.50   +  mn 14 2 i 0.04 i   (1.04)   1 + 2 2       = $501.75 + $577.48 = $1, 079.22

(

)

(

)

The firm will be willing to pay no more than $1,079.23 for their bond.

Enter

47.50

PMT

Answer

1,000 PV

-1,079.22

LO: 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

SM 8-34

Fundamentals of Corporate Finance, 5th edition

8.18

Solutions Manual

Zero coupon bonds: Kintel, Inc., management wants to raise $1 million by issuing sixyear zero coupon bonds with a face value of $1,000. The company’s investment banker states that investors would use an 11.4 percent discount rate to value such bonds. At what price would these bonds sell in the marketplace? How many bonds would the firm have to issue to raise $1 million? Assume semiannual compounding.

Solution: Years to maturity = n = 6 Frequency of payment = m = 2 Coupon rate = C = 0% Current market rate = i = 11.4% Assume semiannual compounding. 0 11.4%

Period ├───┼────┼───┼───┼───┼────┼── $0

─────┤

$0 $1,000

PB =

(

Fmn

1+ i

)

$1,000

(1.057 )

= $514.16

Financial Calculator Solution:

Enter

5.7

PMT

Answer

1,000 PV

514.16

At the price of $514.16, the firm needs to raise $1 million. To do so, the firm will have to issue: Number of bonds

= $1,000,000 / $514.16 = 1,945 bond contracts (Rounded)

SM 8-35

Fundamentals of Corporate Finance, 5th edition

Solutions Manual

IMA: Corporate Finance AICPA: Measurement

8.19

Zero coupon bonds: Rockinghouse Corp. management plans to issue seven-year zero coupon bonds. It has learned that these bonds will sell today at a price of $439.76. Assuming annual compounding, what is the yield to maturity on these bonds?

Solution: Years to maturity = n = 7 Coupon rate = C = 0% YTM = i Present value of bond = PB = $439.76 0i=? 1

├───┼────┼───┼───┼───┼────┼───┤ $0

$0+ $1,000

To solve for the YTM, a trial-and-error approach has to be used. Try YTM = 10%. PB =

(1 + i )

$1,000

(1.10 )

$439.76  $513.16

Try a higher rate, YTM = 12%. PB =

(1 + i )

$1,000

(1.12)

$439.76  $452.35

Try YTM=12.5%. PB =

(1 + i )

$1,000

(1.125 )

$439.76  $438.46

The YTM is approximately 12.5 percent. Enter

7 N

-439.76

1,000

PMT

SM 8-36

Fundamentals of Corporate Finance, 5th edition

Answer

Solutions Manual

12.453

LO: 1, 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

8.20

Yield to maturity: Electrolex, Inc., has four-year bonds outstanding that pay a coupon rate of 6.6 percent and make coupon payments semiannually. If these bonds are currently selling at $914.89, what is the yield to maturity that an investor can expect to earn on these bonds? What is the effective annual yield?

Solution: Years to maturity = n = 4 Frequency of payment = m = 2 Coupon rate = C = 6.6% YTM = i Semiannual coupon payments = $1,000 × (0.066/2) = $33 Present value of bond = PB = $914.89

0i=?

├───────┼────────┼────────┼── $33

$33

8 ─────────┤Yrs. $33+ $1,000

To solve for the YTM, a trial-and-error approach has to be used. Since this is a discount bond, the market rate should be higher than 6.6 percent. Try i = 8% or i/2 = 4%.

SM 8-37

Fundamentals of Corporate Finance, 5th edition

Solutions Manual

1    1 − (1 + i )n  Fn PB = C   + n i   (1 + i )   1    1 − (1.04)8  $1,000 $914.89 = $33   + 8  0.04  (1.04)   = $222.18 + $730.69  $952.87

Try a higher rate, i = 9%, i/2 = 4.5%.

1    1 − (1 + i )n  Fn PB = C   + n i   (1 + i )   1    1 − (1.045)8  $1,000 $914.89 = $33   + 8  0.045  (1.045)   = $217.66 + $703.19  $920.85 Try a higher rate, i = 9.2%, i/2 = 4.6%.

1    1 − (1 + i )n  Fn PB = C   + n i   (1 + i )   1    1 − (1.046)8  $1,000 $914.89 = $33   + 8  0.046  (1.046)   = $216.78 + $697.82  $914.60 The yield to maturity is approximately 9.2 percent. The effective annual yield can be computed as:

SM 8-38

Fundamentals of Corporate Finance, 5th edition

Solutions Manual

EAY = (1 + Quoted rate m)m − 1 = (1.046 ) − 1 2

= 0.0941 = 9.41% Enter

8 N

Answer

-914.89

1,000

PMT

4.5954

The effective annual yield can be computed as:

EAY = (1 + Quoted rate m)m − 1 = (1.045954 ) − 1 2

= 0.09399 = 9.4% LO: 3 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

8.21

Yield to maturity: Serengeti Corp. has five-year bonds outstanding that pay a coupon of 8.8 percent. If these bonds are priced at $1,064.86, what is the yield to maturity on these bonds? Assume semiannual coupon payments. What is the effective annual yield?

Solution: Years to maturity = n = 5 Frequency of payment = m = 2 Coupon rate = C = 8.8% Current market rate = i Semiannual coupon payments = $1,000 x (0.088/2) = $44 Present value of bond = PB = $1,064.86 0 i=?

├───────┼────────┼────────┼── $44

$44

10 ─────────┤Yrs. $44+ $1,000

SM 8-39

Fundamentals of Corporate Finance, 5th edition

Solutions Manual

To solve for the YTM, a trial-and-error approach has to be used. Since this is a premium bond, the market rate should be lower than 8.8 percent. Try i = 7% or i/2 = 3.5%. 1    1 − (1 + i )n  Fn PB = C   + n i   (1 + i )   1    1 − (1.035)10  $1,000 $1,064.86 = $44   + 10  0.035  (1.035)   = $365.93 + $708.92  $1,074.85

Try a higher rate, i = 7.2%, i/2 = 3.6%. 1    1 − (1 + i )n  Fn PB = C   + n i   (1 + i )   1    1 − (1.036)10  $1,000 $1,068.86 = $44   + 10  0.036  (1.036)   = $364.09 + $702.11  $1,066.20

The YTM is approximately 7.2 percent. The effective annual yield can be computed as:

EAY = (1 + Quoted rate m)m − 1 = (1.036 ) − 1 2

= 0.0733 = 7.33% Enter

10 N

Answer

-1,064.86

1,000

PMT

3.6156

The effective annual yield can be computed as:

EAY = (1 + Quoted rate m)m − 1 = (1.036156 ) − 1 2

SM 8-40

Fundamentals of Corporate Finance, 5th edition

Solutions Manual

LO: 3 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

8.22

Yield to maturity: Adrienne Dawson is planning to buy 10-year zero coupon bonds issued by the U.S. Treasury. If these bonds have a face value of $1,000 and are currently selling at $404.59, what is the expected return on them? Assume that interest compounds semiannually on similar coupon paying bonds.

Solution: Years to maturity = n = 10 Frequency of payment = m = 2 Coupon rate = C = 0% Current market rate = i Assume annual coupon payments. Present value of bond = PB = $404.59 0 i=?

Period. ├───────┼────────┼────────┼── $0

─────────┤ $0+ $1,000

To solve for the YTM, a trial-and-error approach has to be used. Try YTM = 10%. PB =

Fmn

(1 + i m )

$1,000

(1.05 )

$404.59  $376.89

Try a lower rate, YTM = 9%.

SM 8-41

Fundamentals of Corporate Finance, 5th edition

PB =

(

Fmn

)

1+ i

m $404.59  $414.64

Solutions Manual

$1,000

(1.045 )

Try YTM=9.25%. PB =

(

Fmn

)

1+ i

m $404.59  $404.85

$1,000

(1.04625 )

The YTM is approximately 9.25 percent.

EAY = (1 + Quoted rate m)m − 1 = (1.04625 ) − 1 2

= 0.09464 = 9.46% The expected return from this investment is 9.46 percent.

Enter

20 N

Answer

-404.59

1,000

PMT

4.63

The effective annual yield can be computed as:

EAY = (1 + Quoted rate m)m − 1 = (1.046283 ) − 1 2

= 0.0947 = 9.47% LO: 3 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

8.23

Realized yield: Brown & Co. issued seven-year bonds two years ago that can be called after two years. The bonds make semiannual coupon payments at a coupon rate of 7.875 percent. Each bond has a market value of $1,053.40, and the call price is $1,078.75. If an

SM 8-42

Fundamentals of Corporate Finance, 5th edition

Solutions Manual

investor purchased the bonds at par value when they were originally issued and the bonds are called by the firm today, what is the investor’s realized yield?

Solution: Purchase price of bond = $1,000 Years investment held = n = 2 Coupon rate = C = 7.875% Frequency of payment = m = 2 Annual coupon = $1,000 × (0.07875/2) = $39.375 Realized yield = i Call price of bond = CP = $1,078.75 Current market value = $1,053.40

To compute the realized return, either the trial-and-error approach or the financial calculator can be used. Since the price has increased, market rates must have decreased. So, the realized return is going to be greater than the bond’s coupon. Try rates higher than the coupon rate. Try i = 10%, or i/2 = 5%. 1   1 − mn  i (1 + )  C CP 2 PB =   +   i 2 (1 + i )mn 2 2     1    1 − (1.05)4  $1,078.75 $1,000 = $39.375   + (1.05)4  0.05    = $139.62 + $887.49  $1,027.11

Try a higher rate, i = 11.48% or i/2 = 5.74%.

SM 8-43

Fundamentals of Corporate Finance, 5th edition

Solutions Manual

1   1 − mn  i (1 + )  C CP 2 PB =   +   i 2 (1 + i )mn 2 2     1    1 − (1.0574)4  $1,078.75 $1,000 = $39.375   + 4  0.0574  (1.0574)   = $137.25 + $862.91  $1,000.16

EAY = (1+ Quoted rate m) m -1 = (1.0574 ) -1 2

= 0.11809 = 11.81% The realized rate of return is approximately 11.81 percent. Using a financial calculator provided an exact yield of 11.49 percent.

Enter

4 N

Answer

39.375

-1,000

1,078.75

PMT

5.74

The effective annual yield can be computed as:

EAY = (1+ Quoted rate m) m -1 = (1.0574 ) -1 2

= 0.1181 = 11.81% LO: 3 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

SM 8-44

Fundamentals of Corporate Finance, 5th edition

8.24

Solutions Manual

Realized yield: Trevor Price bought 10-year bonds issued by Harvest Foods five years ago for $936.05. The bonds make semiannual coupon payments at a rate of 8.4 percent. If the current price of the bonds is $1,048.77, what is the yield that Trevor would earn by selling the bonds today?

Solution: Purchase price of bond = $936.05 Years investment held = n = 5 Coupon rate = C = 8.4% Frequency of payment = m = 2 Annual coupon = $1,000 × (0.084/2) = $42 Realized yield = i Selling price of bond = PB = $1,048.77

1   1 − mn  i (1 + )  C F2 n 2 PB =   +   i 2 (1 + i )mn 2 2     1    1 − (1.055)10  $1,048.77 $936.05 = $42   + 10  0.055  (1.055)   = $316.58 + $613.98  $930.56

Try a lower rate, i = 10.8% or i/2 = 5.4%.

SM 8-45

Fundamentals of Corporate Finance, 5th edition

Solutions Manual

1   1 − mn  i (1 + )  Fn C 2 PB =   +   i 2 (1 + i )mn 2 2     1    1 − (1.054)10  $1,048.77 $936.05 = $42   + 10  0.054  (1.054)   = $318.10 + $619.83  $937.93

EAY = (1 + Quoted rate m)m − 1 = (1.054 ) − 1 2

= 0.1109 = 11.09% The realized rate of return is approximately 11.09 percent. Using a financial calculator provided an exact yield of 11.14 percent.

Enter

10 N

Answer

-936.05

1,048.77

PMT

5.425

The effective annual yield can be computed as:

EAY = (1 + Quoted rate m)m − 1 = (1.05425 ) − 1 2

= 0.1114 = 11.14% LO: 3 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

SM 8-46

Fundamentals of Corporate Finance, 5th edition

8.25

Solutions Manual

Realized yield: You bought a six-year bond issued by Runaway Corp. four years ago. At that time, you paid $974.33 for the bond. The bond pays a coupon rate of 7.375 percent, and coupon payments are made semiannually. Currently, the bond is priced at $1,023.56. What yield can you expect to earn on this bond if you sell it today?

Solution: Purchase price of bond = $974.33 Years investment held = n = 4 Coupon rate = C = 7.375% Frequency of payment = m = 2 Annual coupon = $1,000 × (0.07375/2) = $36.875 Realized yield = i Selling price of bond = PB = $1,023.56 To compute the realized return, either the trial-and-error approach or the financial calculator can be used. Since the price has increased, market rates must have decreased. So, the realized return is going to be greater than the bond’s coupon. Try rates higher than the coupon rate. Try i = 9%, or i/2 = 4.5%.

1   1 − mn  i (1 + )  C F2 n 2 PB =   +   i 2 (1 + i )mn 2 2     1    1 − (1.045)8  $1,023.56 $974.33 = $36.875   + 8  0.045  (1.045)   = $243.22 + $719.75  $962.98 Try a lower rate, i = 8.6% or i/2 = 4.3%.

SM 8-47

Fundamentals of Corporate Finance, 5th edition

Solutions Manual

1   1 − mn  i (1 + )  C F2 n 2 PB =   +   i 2 (1 + i )mn 2 2     1    1 − (1.043)8  $1,023.56 $974.33 = $36.875   + 8  0.043  (1.043)   = $245.22 + $730.87  $976.09

EAY = (1 + Quoted rate m)m − 1 = (1.043 ) − 1 2

= 0.08785 = 8.78% The realized rate of return is approximately 8.78 percent. Using a financial calculator provided an exact yield of 8.84 percent.

Enter

8 N

Answer

36.875

-974.33

1,023.56

PMT

4.327

The effective annual yield can be computed as:

EAY = (1 + Quoted rate m)m − 1 = (1.04327 ) − 1 2

= 0.0884 = 8.84% LO: 3 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

SM 8-48

Fundamentals of Corporate Finance, 5th edition

Solutions Manual

ADVANCED 8.26

Pullman Corp issued 10-year bonds four years ago with a coupon rate of 9.375 percent. At the time of issue, the bonds sold at par. Today bonds of similar risk and maturity must pay an annual coupon of 6.25 percent to sell at par value. Assuming semiannual coupon payments, a. What is the bond’s yield to maturity? b. What will be the current market price of the firm’s bonds?

Solution: a. Given that other bonds with similar risk must pay an annual coupon of 6.25 percent to sell at par, the yield to maturity must be 6.25 percent. b. Years to maturity = n = 6 Frequency of payment = m = 2 Coupon rate = C = 9.375% Semiannual coupon = $1,000 × (0.09375/2) = $46.875 Current market rate = i = 6.25% Present value of bond = PB 0 6.25%

├───┼────┼───┼───┼───

─────┤

$46.875 $46.875………

$46.875+ $1,000

n = 6; m = 2; C = 9.375%; i = YTM = 6.25%

1   1   1− 2n  1 − 12   (1 + i 2)  + F2n = $46.875   (1.03125)  + $1,000 PB = C   12 2   (1 + i 2 )2 n i2  0.03125  (1.03125)       = $463.13 + $691.25 = $1,154.38 Enter

3.125

46.875

PMT

1,000 PV

- 1,154.38 SM 8-49

Fundamentals of Corporate Finance, 5th edition

Solutions Manual

LO: 2 Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

8.27

Showbiz, Inc., has issued eight-year bonds with a coupon of 6.375 percent and semiannual coupon payments. The market’s required rate of return on such bonds is 7.65 percent. a.

What is the market price of these bonds?

If the above bond is callable after five years at an 8.5 percent premium on the face value, what is the expected return?

Solution: a.

Years to maturity = n = 8 Frequency of payment = m = 2 Coupon rate = C = 6.375% Semiannual coupon = $1,000 × (0.06375/2) = $31.875 Current market rate = i = 7.65% Present value of bond = PB

0 7.65%

16 ├───────┼────────┼────────┼── $31.875

$31.875

─────────┤Yrs. $31.875+ $1,000

1   1   mn  1 − 1− 16  1+ i    F2 n $1,000 (1.03825) 2 PB = C   = $31.875   + + mn 16 2 i  0.03825  (1.03825)   1+ i 2 2       = $376.26 + $548.49 = $924.75

(

)

(

)

The firm can sell these bonds at $924.75.

SM 8-50

Fundamentals of Corporate Finance, 5th edition

Solutions Manual

Financial Calculator Solution:

Enter

3.825

31.875

PMT

Answer

1,000 PV

-924.75

Purchase price of bond = $924.75 Years investment held = n = 5 Coupon rate = C = 6.375% Semiannual coupon = $1,000 × (0.06375/2) = $31.875 Frequency of payment = m = 2 Realized yield = i Call price of bond = CP = $1,000 × (1.085) = $1,085.00

To compute the expected return, either the trial-and-error approach or the financial calculator can be used. Try rates higher than the coupon rate. Try i = 8%, or i/2 = 4%.

1   1mn   C CP (1 + i 2) PB =   + mn 2  i2  (1 + i 2)   1    1 - (1.04)10  $1,085 $924.75 = $31.875   + 10  0.04  (1.04)   = $258.54 + $732.99  $991.53 Try a higher rate, i = 9.67% or i/2 = 4.835%.

SM 8-51

Fundamentals of Corporate Finance, 5th edition

Solutions Manual

1   1− mn   C CP (1 + i 2) PB =   + mn 2  i2  (1 + i 2)   1    1 − (1.04835)10  $1,085 $924.75 = $31.875   + 10  0.04835  (1.04835)   = $248.11 + $676.65  $924.76

The realized rate of return is approximately 9.67% percent. Using a financial calculator provided an exact yield of 9.6705 percent.

Enter

10 N

Answer

31.875

-924.75

1,085

PMT

4.835

The effective annual yield can be computed as:

EAY = (1 + Quoted rate m)m − 1 = (1.04835 ) − 1 2

= 0.0990 = 9.90% LO: 2, 3 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

8.28

Peabody Corp. has seven-year bonds outstanding. The bonds pay a coupon of 8.375 percent semiannually and are currently worth $1,063.49. The bonds can be called in three years at price of $1,075. a.

What is the yield to maturity of these bonds?

What is the effective annual yield?

What is the realized yield on the bonds if they are called?

SM 8-52

Fundamentals of Corporate Finance, 5th edition

Solutions Manual

If you plan to invest in one of these bonds today, what is the expected yield on the investment? Explain.

Solution: a.

Years to maturity = n = 7 Frequency of payment = m = 2 Coupon rate = C = 8.375% Current market rate = i Semiannual coupon payments = $1,000 × (0.08375/2) = $41.875 Present value of bond = PB = $1,063.49 0i=?

├───────┼────────┼────────┼── $41.875

$41.875

14 Yrs. ─────────┤ $41.875+ $1,000

To solve for the YTM, a trial-and-error approach has to be used. Since this is a premium bond, the market rate should be lower than 8.375 percent. Try i = 8% or i/2 = 4%. 1   1 − n  i (1 + )  F2 n 2 PB = C   +   i (1 + i )mn 2 2     1    1 − (1.04)14  $1,000 $1,063.49 = $41.875   + 14  0.04  (1.04)   = $442.33 + $577.48  $1,019.81

Try a lower rate, i = 7.2%, or i/2 = 3.6%.

SM 8-53

Fundamentals of Corporate Finance, 5th edition

Solutions Manual

1    1 − (1 + i 2)n  F2 n PB = C   + i   (1 + i 2 )mn 2   1    1 − (1.036)14  $1,000 $1,063.49 = $41.875   + 14  0.036  (1.036)   = $454.24 + $609.49  $1,063.73

The yield-to maturity is approximately 7.2 percent. Financial Calculator Solution:

Enter

14 N

Answer

41.875

-1,063.49

1,000

PMT

3.6 x 2=7.2

The effective annual yield can be computed as:

EAY = (1 + Quoted rate m)m − 1 = (1.036 ) − 1 2

= 0.073296 = 7.3% c.

Purchase price of bond = $1,063.49 Years investment held = n = 3 Coupon rate = C = 8.375% Semiannual coupon payments = $1,000 x (0.08375/2) = $41.875 Frequency of payment = m = 2 Realized yield = i Selling price of bond = PB = $1,075

SM 8-54

Fundamentals of Corporate Finance, 5th edition

Solutions Manual

Try i = 9%, or i/2 = 4.5%. 1   1− mn   F2n C (1 + i 2) PB =   + mn 2  i2  (1 + i 2)   1    1 − (1.045)6  $1,075 $1,063.49 = $41.875   + 6  0.045  (1.045)    $215.99 + $825.49  $1,041.48

Try a lower rate, i = 8.2% or i/2 = 4.1%. 1   1− mn   F2n C (1 + i 2) PB =   + mn 2  i2  (1 + i 2)   1    1 − (1.041)6  $1,075 $1,063.49 = $41.875   + 6  0.041  (1.041)   = $218.80 + $844.70 = $1,063.50

The realized rate of return is approximately 8.37 percent. Using a financial calculator provided an exact yield of 8.2 percent.

Enter

6 N

Answer

41.875

-1,063.49

1,075

PMT

4.1 x 2=8.2

The effective annual yield can be computed as:

EAY = (1 + Quoted rate m)m − 1 = (1.04100 ) − 1 2

= 0.08368 = 8.368%

SM 8-55

Fundamentals of Corporate Finance, 5th edition

Solutions Manual

Purchase price of bond = PB = $1,063.49 Years to maturity = n =7 Coupon rate = C = 8.375% Semiannual coupon payments = $1,000 × (0.08375/2) = $41.875 Frequency of payment = m = 2 Maturity value = FV = $1,000 Use the trial-and-error approach to compute the yield to maturity. Since we have a premium bond, market rates are lower than the bond’s coupon. Try i = 7%, or i/2 = 3.5%. 1   1 −  m  n i F2n C  (1 + 2 )  PB =  +   i 2 (1 + i )mn 2 2     1    1 − (1.035)14  $1,000 $1,063.49 = $41.875   + 14  0.035  (1.035)   = $457.30 + $617.78  $1,075.08

Try a higher rate, i = 7.2%, or i/2 = 3.6%. 1    1 − (1 + i 2)n  F2 n PB = C   + i   (1 + i 2 )mn 2   1    1 − (1.036)14  $1,000 $1,063.49 = $41.875   + 14  0.036  (1.036)   = $454.24 + $609.49  $1,063.73

The expected yield is approximately 7.2 percent which is the same as the yield to maturity obtained in (a). If the bond is not called and is held to maturity, then the expected yield is the yield to maturity.

SM 8-56

Fundamentals of Corporate Finance, 5th edition

Solutions Manual

Financial Calculator Solution:

Enter

14 N

Answer

41.875

-1,063.49

1,000

PMT

3.6 x 2=7.2

EAY = (1 + Quoted rate m)m − 1 = (1.036 ) − 1 2

= 0.073296 = 7.33% The expected yield is approximately 7.33 percent. Using a financial calculator provided an exact yield 7.334 percent. LO: 3 Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

8.29

The Maryland Department of Transportation has issued 25-year bonds that make semiannual coupon payments at a rate of 9.875 percent. The current market rate for similar securities is 11 percent. a.

What is the current market value of one of these bonds?

What will be the bond’s price if rates in the market (i) decrease to 9 percent or (ii) increase to 12 percent?

Refer to your answers in part b. How do the interest rate changes affect premium bonds and discount bonds?

Suppose the bond were to mature in 12 years. How do the interest rate changes in part b affect the bond prices?

SM 8-57

Fundamentals of Corporate Finance, 5th edition

Solutions Manual

Solution: a.

Years to maturity = n = 25 Frequency of payment = m = 2 Coupon rate = C = 9.875% Semiannual coupon = $1,000 × (0.09875/2) = $49.375 Current market rate = i = 11% Present value of bond = PB 0 11%

50 Yrs.

├───────┼────────┼────────┼── $49.375

$49.375

─────────┤

$49.375

$49.375+ $1,000

1   1   2n  1 − 1− 50  1+ i    F2 n $1,000 (1.055) 2 PB = C   = $49.375   + + mn 2 i 0.055  (1.055)50 i    1 + 2 2       = $835.99 + $68.77 = $904.76

(

)

(

)

The Maryland bonds will sell at $904.76.

Enter

5.5

49.375

PMT

Answer

(i)

1,000 PV

-904.76

Current market rate = i = 9%

SM 8-58

Fundamentals of Corporate Finance, 5th edition

Solutions Manual

1   1   2n  1 − 1− i 50 1 +   F2 n (1.045)  $1,000 2 + PB = C   = $49.375   +  mn 50 2 i 0.045 i   (1.045)   1+ 2 2       = $975.75 + $110.71 = $1, 086.46

(

)

(

)

The Maryland bonds will increase in price to sell at $1,086.46.

Enter

4.5

49.375

PMT

Answer

(ii)

1,000 PV

-1,086.46

Current market rate = i = 12% 1   1   2n  1 − 1− i 1 +   F2 n (1.06)50  $1,000 2 + PB = C   = $49.375   +  mn 2 i 0.06 (1.06)50 i     1 + 2 2       = $778.24 + $54.29 = $832.53

(

)

(

)

The Maryland bonds will drop in price to $832.53. Enter

49.375

PMT

Answer

1,000 PV

-832.53

Bonds, in general, decrease in price when interest rates go up. When interest rates decrease, bond prices increase.

(i)

Current market rate = i = 9% Term to maturity = 12 years

SM 8-59

Fundamentals of Corporate Finance, 5th edition

Solutions Manual

1   1   2n  1 − 1− i 24 1 +   F2 n (1.045)  $1,000 2 + PB = C   = $49.375   +  mn 24 2 i 0.045 i   (1.045)   1+ 2 2       = $715.71 + $347.70 = $1, 063.42

(

)

(

)

The Maryland bonds will increase in price to sell at $1,063.42. Enter

4.5

49.375

PMT

Answer

(ii)

1,000 PV

-1,063.42

Current market rate = i = 12% 1   1   2n  1 − 1− i 24 1 +   F2 n (1.06)  $1,000 2 + PB = C   = $49.375   +  mn 24 2 i 0.06 i   (1.06)   1+ 2 2       = $619.67 + $246.98 = $866.65

(

)

(

)

The Maryland bonds will drop in price to $866.65. Enter

49.375

PMT

Answer

1,000 PV

-866.65

With shorter maturity, bond prices react the same way as in part b, but to a lesser extent. When interest rates increase, the bond’s price declines; but the decline in price is less than that for a longer-term bond. Similarly, when interest rates decrease, bond prices increase with both longerterm and shorter-term bonds. However, longer-term bonds increasing more than shorter-term bonds. LO: 2, 3, 4 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance

SM 8-60

Fundamentals of Corporate Finance, 5th edition

Solutions Manual

AICPA: Measurement Excel Template available in Wiley Course Resources Excel Template Solution available in Wiley Instructor Resources

8.30

Rachette Corp. has 18-year bonds outstanding. These bonds, which pay interest semiannually, have a coupon rate of 9.735 percent and a yield to maturity of 7.95 percent.

a. Compute the current price of these bonds. b. If the bonds can be called in five years at a premium of 13.5 percent over par value, what is the investor’s realized yield? c. If you bought one of these bonds today, what is your expected rate of return? Explain.

Solution: a.

Years to maturity = n = 18 Frequency of payment = m = 2 Coupon rate = C = 9.735% Semiannual coupon = $1,000 × (0.09735/2) = $48.675 Current market rate = i = 7.95% Present value of bond = PB 0

├───────┼────────┼────────┼── $48.675

$48.675

36 ─────────┤Yrs.

$48.675

$48.675+ $1,000

1   1 − 1   2n   1− 36  1+ i    F2n $1,000 (1.03975) 2 PB = C   = $48.675   + + 2n 36 2 i  0.03975  (1.03975)   1+ i 2 2       = $923.56 + $245.79 = $1,169.34

(

)

(

)

The bond’s current price is at $1,169.34.

Enter

3.975

48.675

1,000

SM 8-61

Fundamentals of Corporate Finance, 5th edition

Solutions Manual

PMT

Answer

-1,169.34

Purchase price of bond = $1,169.34 (value today); Call price = $1,135

To compute the realized return, either the trial-and-error approach or the financial calculator can be used.

Try rates lower than the coupon rate.

Try i = 8%, or i/2 = 4%. 1   1 −  m  n i F2n C  (1 + 2 )  PB =  +  (1 + i )mn i 2  2 2     1    1 − (1.04)10  $1,135 $1,169.34 = $48.675   + 10  0.04  (1.04)   = $394.80 + $766.77  $1,161.56

Try a lower rate, i = 7.8% or i/2 = 3.9%. 1   1 − mn  i (1 + )  F2n C 2 PB =   +  (1 + i )mn i 2  2 2     1    1 − (1.039)10  $1,135 $1,169.34 = $48.675   + 10  0.039  (1.039)   = $396.77 + $774.18  $1,170.95

SM 8-62

Fundamentals of Corporate Finance, 5th edition

Solutions Manual

EAY = (1 + Quoted rate m)m − 1 = (1.039 ) − 1 2

= 0.07952 = 7.95% The realized rate of return is approximately 7.95 percent. Using a financial calculator provided an exact yield of 7.834 percent.

Enter

10 N

Answer

48.675

-1,169.34

1,135.00

PMT

3.917 x 2 = 7.834

The effective annual yield can be computed as:

EAY = (1 + Quoted rate m)m − 1 = (1.03917 ) − 1 2

= 0.07987 = 7.99% c.

Purchase price of bond = PB = $1,169.34 Years to maturity = n = 18 Coupon rate = C = 9.735% Semiannual coupon = $1,000 × (0.09735/2) = $48.675 Frequency of payment = m = 2 Maturity value = FV = $1,000

Use the trial-and-error approach to compute the yield to maturity. Since we have a premium bond, market rates are lower than the bond’s coupon. Try i = 8%, or i/2 = 4.0%.

SM 8-63

Fundamentals of Corporate Finance, 5th edition

Solutions Manual

1   1 − mn  i (1 + )  F2n C 2 PB =   +   i 2 (1 + i )mn 2 2     1    1 − (1.04)36  $1,000 $1,169.34  $48.675   + 36  0.04  (1.04)    $920.36 + $243.67  $1,164.03

Try i = 7.9%, or i/2 = 3.95%. 1   1 −  m  n i F2n C  (1 + 2 )  PB =  +   i 2 (1 + i )mn 2 2     1    1 − (1.0395)36  $1,000 $1,169.34  $48.675   + 36  0.0395  (1.0395)    $926.77 + $247.92  $1,174.69

Thus the expected yield is between 7.9 percent and 8 percent. Using a financial calculator provided an exact yield of 7.95 percent.

Enter

36 N

Answer

48.675

-1,169.34

1,000

PMT

3.975 x 2= 7.95

The effective annual yield can be computed as:

EAY = (1 + Quoted rate m)m − 1 = (1.03975 ) − 1 2

= 0.08108 = 8.11% LO: 2, 3, 4

SM 8-64

Fundamentals of Corporate Finance, 5th edition

Solutions Manual

Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

8.31

Zippy Corporation just sold $30 million of convertible bonds with a conversion ratio of 40. Each $1,000 bond is convertible into 25 shares of Zippy’s stock. a.

What is the conversion price of Zippy’s stock?

If the current price of Zippy’s stock is $15 and the company’s annual stock return is normally distributed with a standard deviation of $5, what is the probability that investors will find it attractive to convert the bond into Zippy stock in the next year?

Solution: a.

The conversion price is $1,000/40 = $25.

The stock price would have to increase by approximately two standard deviations (2  $5 = $10) for the price to increase to $25 and for conversion to become attractive to the investors. From Chapter 7 we know that 95% of possible outcomes fall within two standard deviations of the mean (average) value in a normal distribution. This means that there is a 5 percent chance that the stock price will move up or down by $10 or more. Since the normal distribution is symmetric, this means that there is only a 2.5 percent chance that Zippy’s stock price will increase enough for it to become attractive for the investors to exercise the conversion option in the next year.

LO: 1 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

SM 8-65

Fundamentals of Corporate Finance, 5th edition

8.32

Solutions Manual

Hastings Corporation has a discount bond making semiannual coupon payments at a rate of 5.2 percent, with 10 years to maturity. The current market rate for similar securities is 6.4 percent. Pivotal Corporation has a premium bond making semiannual coupon payments and a rate of 6.0 percent, with 10 years to maturity. The current market rate for securities similar to the Pivotal bond is 5.2 percent. a.

If interest rates remain unchanged, what do you expect the price of these bonds to be in 1 year? In 3 years? In 7 years? In 10 years?

Explain what is happening to the price of each bond as the time to maturity approaches zero and why.

Solution a

Price of the Hastings bond 1 year from today: Years to maturity = n = 9 Frequency of payment = m = 2 Coupon rate = C = 5.2% Annual coupon = C = = $1,000 × (0.052) = $52.00 Semiannual coupon = $1,000 × (0.052/2) = $26.00 Current market rate = i = 6.4% Present value of bond = PB 6.4%

├───────┼────────┼────────┼── $26.00

$26.00

─────────┤

$26.00

$26.00 + $1,000

1   1   2n  1 − 1− 18   i 1+  (1.032)  + $1,000 F2n 2 + PB = C   = $26.00    mn 2 i   (1.032 )18 0.032   1+ i 2   2       = $351.62 + $567.24 = $918.86

(

Enter

)

(

)

3.2

26.00

PMT

Answer

1,000 PV

-918.86

SM 8-66

Fundamentals of Corporate Finance, 5th edition

Solutions Manual

Price of the Pivotal bond 1 year from today: Years to maturity = n = 9 Frequency of payment = m = 2 Coupon rate = C = 6.0% Annual coupon = C = = $1,000 × (0.06) = $60.00 Semiannual coupon = $1,000 × (0.060/2) = $30.00 Current market rate = i = 5.2% Present value of bond = PB 5.2%

├───────┼────────┼────────┼── $30.00

$30.00

─────────┤

$30.00

$30.00 + $1,000

1   1   2n  1 − 1 − 18   i 1 +  (1.026 )  + $1,000 F2n 2 + PB = C   = $30.00    mn 2 i   (1.026 )18 0.026 i   1 + 2   2       = +$426.91 + $630.01 = $1,056.92

(

Enter

)

(

)

2.6

30.00

PMT

Answer

1,000 PV

-1,056.92

Price of Hastings bond in 3 years: 1   2n  1 − 1     1 + i   14  1 − (1.032)  + $1,000 F2n C  2  PB =    + = $26.00   mn  i   (1.032 )14 2 0.032    1 + i    2    2       = +$289.73 + $643.41 = $933.14

Enter

3.2

26.00

1,000 SM 8-67

Fundamentals of Corporate Finance, 5th edition

Solutions Manual

PMT

Answer

-933.14

Price of Hastings bond in 7 years: 1   2n  1 − 1     1 + i   6  1 − F2n C  2   (1.032 )  + $1,000 PB =    + = $26.00  mn  i  0.032  (1.032 )6 2    1 + i    2    2       = $139.92 + $827.79 = $967.71

Enter

3.2

26.00

PMT

Answer

1,000 PV

-967.71

Price of Hastings bond in 10 years (at maturity): Enter

3.2

26.00

PMT

Answer

1,000 PV

-1,000.00

Price of Pivotal bond in 3 years: 1   2n  1 − 1     1 + i   14  1 − (1.026 )  + $1,000 F2n C  2  PB =    + = $30.00   mn  i   (1.026 )14 2 0.026    1 + i    2    2       = +$348.31 + $698.13 = $1,046.44

Enter

2.6

30.00

1,000

SM 8-68

Fundamentals of Corporate Finance, 5th edition

Solutions Manual

PMT

Answer

-1,046.44

Price of Pivotal bond in 7 years: 1   2n  1 − 1     1 + i   6  1 − F2n C  2   (1.026 )  + $1,000 PB =    + = $30.00  mn  i  0.026  (1.026 )6 2    1 + i    2    2       = +$164.69 + $857.27 = $1,021.96

Enter

2.6

30.00

PMT

Answer

1,000 PV

-1,021.96

Price of Pivotal bond in 10 years (at maturity):

Enter

2.6%

Answer

$30.00 PMT

$1,000 PV

-$1,000.00

As the time to maturity approaches zero, the value of each of the bonds approaches $1,000. The Hastings discount bond increases in value and the Pivotal premium bond decreases in value. In both cases, the largest percentage price changes occur at the shortest maturity lengths, and the price at maturity is simply the bond’s par, or face, value ($1,000). This phenomenon is known as “pull to par”. As the bond approaches maturity, the relative present value of a premium (discount) paid to the coupon approaches zero as the present value of the bond is comprised of fewer and fewer coupon payments relative to the repayment of the face value at maturity.

SM 8-69

Fundamentals of Corporate Finance, 5th edition

Solutions Manual

Sample Test Problems 8.1

Seven years ago Eastern Corporation issued 20-year bonds that had a $1000 face value, paid interest annually, and that had a coupon rate of 7 percent. If the market rate of interest is 5.5 percent today, what is the current market price of an Eastern Corporation bond? Are these bonds selling at a premium or discount?

Solution: Years to maturity = n = 13 Coupon rate = C = 7% Annual coupon payment = $1,000 × 0.07 = $70 Current market rate = i = 5.5% Present value of bond = PB

├───┼────┼───┼───┼─── $70

$70

─────┤

$70

$70 $1,000

1  1    1− 13   1 − (1 + i )n   F $1,000 (1.055) PB = C   = $70   + + n 13 i   (1 + i )  0.055  (1.055)     = $498.56 + $638.19 = $1,136.75

These bonds are selling at a premium. Financial Calculator Solution:

Enter

5.5

PMT

Answer

1,000 PV

-1,136.75

SM 8-70

Fundamentals of Corporate Finance, 5th edition

Solutions Manual

AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

8.2

You are considering investing in a 10-year zero coupon bond that compounds interest semiannually. If the current market rate is 5.65 percent, what is the maximum price you should have to pay for this bond?

Solution: Years to maturity = n = 10 Coupon rate = C = 0% Current market rate = i = 5.65% Frequency of payments = m = 2

├───┼────┼───┼───┼───┼────┼── $0

─────┤

$0 $1,000

PB =

Fmn i   1 + m   

$1,000

(1 + 0.0565/2)

210

= $572.83

Financial Calculator Solution:

Enter

2.825

PMT

Answer

1,000 PV

-527.83

LO: 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance

SM 8-71

Fundamentals of Corporate Finance, 5th edition

Solutions Manual

AICPA: Measurement

8.3

Bigbox, Inc. has bonds outstanding that will mature in eight years. These bonds pay interest semiannually and have a coupon rate of 4.6 percent. If the bonds are currently selling at $888.92, what is the yield to maturity that an investor who buys them today can expect to earn? What is the effective annual yield?

Solution: Years to maturity = n = 8 Coupon rate = C = 4.6% Current market rate = i Semiannual coupon payment = $1,000 × (0.046/2) = 23 Present value of bond = PB = $888.92

├───────┼────────┼────────┼── (888.92)

$23

16 ─────────┤

$23

$23 $1,000

To solve for the YTM, a trial-and-error approach has to be used. Since this bond is selling at a discount, we know that the market rate is higher than 4.6 percent.

Try i = 6% or i/2 = 3%.

1   1 −  n  i (1 + )  Fn 2 PB = C   +   i (1 + i )n 2 2     1    1 − (1.03)16  $1,000 = $23   + 16  0.03  (1.03)   = $288.91 + $623.16 = $912.07  $888.92

SM 8-72

Fundamentals of Corporate Finance, 5th edition

Solutions Manual

Try a higher rate, i = 7%, i/2 = 3.5%.

1   1 −  n (1 + i )  Fn  2 PB = C  +   (1 + i )n i 2 2     1    1 − (1.035)16  $1,000 = $23   + 16  0.035  (1.035)   = $278.17 + $576.71 = $854.57  $888.92

Try a lower rate, i = 6.4%, i/2 = 3.2%.

1    1 − (1 + i )n  Fn PB = C   + n i   (1 + i )   1    1 − (1.032)16  $1,000 $882.92 = $23   + 16  0.032  (1.032)   = $284.54 + $604.12 = $888.66  $888.92

The YTM is approximately 6.4 percent.

Using a financial calculator provides an exact YTM of 6.395 percent Enter

16 N

Answer

$23

-$888.92

$1,000

PMT

6.395%

The effective annual yield can be computed as: EAY=(1 +

Quoted rate −1 m)m

SM 8-73

Fundamentals of Corporate Finance, 5th edition

Solutions Manual

0.06395   = 1 +  −1 2   = (1.03198)2 − 1

= 0.064972 = 6.497% LO: 3 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

8.4

Given a change in market interest rates, which will change more; the market price of a bond with 20 years until maturity or the market price of a bond with 5 years until maturity? Assume all the characteristics of these bonds are identical except the maturity dates.

Solution: The price of the bond with 20 years to maturity will change more. The cash flows from the longer term bond are paid further in the future. As a result, these cash flows are more heavily discounted and therefore more sensitive to interest rate changes. LO: 4 Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

8.5

Which of the following classes of securities is likely to have the lowest corporate borrowing cost? AAA rated bonds. a. A rated bonds. b. BB rated bonds. c. C rated bonds. d. All of the above will have the same corporate borrowing cost.

Solution: a.

SM 8-74

Fundamentals of Corporate Finance, 5th edition

Solutions Manual

The issuers of AAA rated bonds should have the lowest borrowing cost because their default risk premium is lower than issuers with weaker credit ratings. LO: 5 Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

Ethics Case Discussion Questions 1. What were the responsibilities of the mortgage brokers to borrowers? To lenders? To investors? How well did they fulfill their responsibilities? Why? Solution: Mortgage brokers are intermediaries who bring mortgage borrowers together with lenders for a fee. Broker responsibilities to borrowers include collecting and reporting the information needed by lenders to complete a mortgage application and explaining the important and sometimes complex loan terms to borrowers. Lenders rely on mortgage brokers to accurately represent and verify the financial information of borrowers, and obtain appraisals for the properties covered by a loan. While mortgage brokers don’t have any direct responsibilities to investors in mortgage-backed securities (MBS), their role in collecting and verifying the information needed to make sound mortgage loan decisions is essential to investors trying to value MBS. Unfortunately, during the home loan boom of the mid-2000s mortgage brokers didn’t always fulfill their responsibilities to borrowers or lenders. For example, some brokers failed to verify all of the information submitted by borrowers, and in some cases misrepresented or forged borrower documents on loan applications. In their haste to make loans, brokers also failed to carefully inform borrowers about important terms of mortgage loans such as prepayment penalties and teaser rates, and pressured appraisers to artificially inflate home values. This unethical behavior by brokers can largely be traced back to the fees they received to originate home loans. These fees meant that brokers Copyright © 2022 John Wiley & Sons, Inc.

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could earn a lot of money by quickly making loans and ignoring many important quality controls.

2. Did some subprime lenders behave unethically? If so, how? Whose interests did the subprime lenders have a responsibility to represent? Did they adequately represent those interests? Solution: Subprime lenders have a responsibility to ensure that their risky loans are made to qualified borrowers. Unfortunately, with the booming market for securitized sub-prime loans during the mid-2000s, many subprime lenders cut corners by offering low or “nodoc” loans that required little or no documentation of borrower income. Subprime lenders have a responsibility to borrowers to ensure that they receive loans that are suitable given their personal circumstances. In addition, subprime lenders have a responsibility to MBS investors to ensure that the loans they make are completed with appropriate quality controls and credit standards. Given the high default rates on subprime mortgages in the late 2000s, it appears that many subprime lenders failed to behave in the best interests of borrowers and MBS investors.

3. What motivated the investment bankers to get involved in the subprime market? Did they behave appropriately? Why or why not? Solution: Investment banks started the practice of bundling home loans into packages that could be sold to investors as mortgage-backed securities (MBS). In this scenario, the investment bank is responsible for assessing the risk of the mortgages backing these securities and valuing the claims for investors. What is clear from the subprime mortgage meltdown is that investors in MBS securities didn’t fully understand the risks associated with the securities they purchased, and the investment banks are partly responsible for this. While many investment bankers themselves likely misunderstood the risks of these investments, many also likely failed to inform investors of the risks associated with MBS.

4. Should the borrowers (homeowners) share in the blame? If so, how?

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Solution: As with all financial market transactions, borrowers have a responsibility to be aware of their ability to repay a loan, and the agreed upon loan terms. In some cases, however, lenders and brokers failed to adequately disclose important terms of home loans to borrowers.

5. What about the investors in MBSs? What could they have done differently? Solution: Investors in subprime MBS have a responsibility to understand the risks associated with the securities in which they are investing. As such, they largely relied on investment banks and due-diligence firms to properly evaluate the loan quality underlying the MBS investments during the housing boom. While many of these institutions likely didn’t understand the credit quality of the loans bundled into MBS, it is also likely that many investors chose to ignore potential risks given the high promised returns.

6. What can be done to prevent future blowups like the one that occurred in the subprime market? Solution: At a broad level the subprime loan market meltdown was largely attributable to poor incentives and a failure of quality controls during the loan making process. It is also clear that many consumers didn’t fully understand the investment risks.

On the incentive side there are a number of changes that might prevent such events from happening again, some of which were actually implemented following the financial crisis. For example, at some institutions compensation “clawbacks” were introduced. The idea is that if an employee earns compensation based on loans or other actions that turn out to be unethical or fraudulent, then the employer will go after the employee for the undeserved pay ― that is, the employer will attempt to “claw” back payments from the employee. Other institutions have created compensation “holdbacks” where a portion of employee compensation is held by the company until time passes and it is possible to determine that there has been no unethical or fraudulent behavior.

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In terms of quality controls, the current loan market now requires that all mortgage applicants submit financial documentation and that the mortgage brokers and lenders diligently verify that the information provided is correct. Many mortgage brokers now insist that applicants provide bank statements, and proof of financial assets. Additionally, brokers often conduct multiple credit checks and will contact the applicant’s employer to verify that they actually have the job they list in their application. Lenders have also eliminated no- and low-doc mortgage offerings.

Government reforms were also instituted to address many of the problems in the lending market that occurred during the housing boom and subsequent financial crisis. The Dodd Frank Wall Street Reform and Consumer Protection Act (passed into law in 2010) included many new rules and regulations for financial firms to follow. It also created a new federal government agency the Consumer Financial Protection Bureau. The Bureau has the goal of protecting consumers from unfair, deceptive, or abusive practices by lenders and brokers. The Bureau also has the goal of educating consumers to make sure they are informed about the financial products they are being offered, and have the tools needed to make financial decisions.

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Chapter 7

Risk and Return Before You Go On Questions and Answers Section 7.1 Note to instructor: There are no questions for this section.

Section 7.2 1.

What are the two components of a total holding period return? Capital appreciation and income. This can be seen in Equation 7.1.

Section 7.3 1.

How is the expected return on an investment calculated? The expected return is calculated as a weighted average of the possible returns on an investment (outcomes) where the weights are the probabilities that each of the possible returns will be realized.

Section 7.4 1.

What is the relation between the variance and the standard deviation? The standard deviation is the square root of the variance. Alternatively, the variance equals the standard deviation squared.

What relation do we generally observe between risk and return when we examine historical returns? Investments with higher risks tend to have higher returns. This is illustrated in Exhibit 7.3.

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Section 7.5 1.

What type of return tells you the average compounded return earned by an investor? The geometric (compounded) average return.

Section 7.6 1.

What does the coefficient of variation tell us, and how is it related to the Sharpe Ratio? The coefficient of variation is a measure of risk per unit of return. It tells us the amount of risk, defined as the standard deviation of returns, associated with each 1 percent of expected return for an asset. A larger coefficient of variation indicates greater risk for each 1 percent of return. The Sharpe ratio differs from the coefficient of variation in two ways. First, instead of using the total return in the calculation, with the Sharpe ratio we use the difference between the total return and the risk-free rate. Second, the Sharpe ratio is the inverse of the coefficient of variation ratio that would be calculated using this adjusted return. Computing the inverse of the coefficient of variation yields a measure of return per unit of risk, which some investors find more intuitive than a measure of risk for each 1 percent of return.

How would we expect the standard deviation of the return on an individual stock to compare with the standard deviation of the return on a stock index? We would expect that the standard deviation for the returns on individual stocks that do not change in the same way (not directly correlated) will reflect a higher standard deviation of returns than a portfolio of the same stocks. If the returns on the individual stocks added to the portfolio do not change in the same manner, then increasing the number of stocks in the portfolio will reduce the standard deviation of the portfolio returns even further. As more stocks are added, the standard deviation for the portfolio

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gets smaller and smaller but will never become zero, as not all risk can be diversified away.

What are the two components of total risk? The two components of total risk are unsystematic risk and systematic risk. Unsystematic risk is risk that is unique to a particular asset. This is the risk that can be eliminated through diversification. Systematic risk, or undiversifiable risk, is risk that is common to all assets and cannot be eliminated through diversification.

Why does the total risk of a portfolio not approach zero as the number of assets in a portfolio becomes very large? Because the systematic risk associated with the individual assets cannot be diversified away. With a very large number of assets, the total risk of a portfolio will approach the weighted average (where the weights are the fractions of total portfolio value represented by each asset) of the systematic risks associated with each asset. Investors can diversify away risk that is unique to the individual assets, but they cannot diversify away risk that is common to all assets.

Section 7.7 1.

Why are returns on the stock market used as a benchmark in measuring systematic risk? Because the stock market portfolio is the most diversified portfolio for which good return data is available and it is the portfolio that comes closest to eliminating all unique (unsystematic) risk. This makes the returns on the stock market a practical choice as a benchmark for measuring the systematic risk of individual assets.

How is beta estimated? Beta is estimated using regression analysis in which returns for an individual asset are plotted against returns on the market. To quantify the relationship, the slope of the line that represents the relation (line of best fit) is determined. The slope of this regression line is called beta. This is illustrated in Exhibit 7.10.

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How would you interpret a beta of 1.5 for an asset? A beta of 0.75? A beta of 1.5 indicates that the asset has 1.5 times as much systematic risk as the market or simply, the asset has more systematic risk than the market. A beta of 0.75 indicates that the asset has 75 percent as much systematic risk as the market or simply, the asset has less systematic risk than the market.

Section 7.8 1.

How is the expected return on an asset related to its systematic risk? CAPM tells us that there is a linear relation between expected return and systematic risk. With zero systematic risk, the expected return equals the risk-free rate. For systematic risk greater than zero, the expected return on an asset increases as its systematic risk increases and this increase is linear. This relation is illustrated in Equation 7.12.

What name is given to the line on the graph in Exhibit 7.11 that shows the relation between risk and expected return implied by the CAPM? This plot, which reflects a straight-line with a positive slope, is called the Security Market Line, or SML.

If an asset’s expected return does not plot on the line in question 2 above, what does that imply about its price? If the expected return on an asset does not plot on the SML, then this indicates that the expected return on the asset is either too low or too high in view of its systematic risk. If the asset plots below the SML, the expected return is too low, and its price is too high. If the asset plots above the SML, the expected return is too high, and its price is too low.

Self-Study Problems 7.1

Kaaran made a friendly wager with a colleague that involves the result from flipping a coin. If heads comes up, Kaaran must pay her colleague $15; otherwise,

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her colleague will pay Kaaran $15. What is Kaaran’s expected cash flow, and what is the variance of that cash flow if the coin has an equal probability of coming up heads or tails? Suppose Kaaran’s colleague is willing to handicap the bet by paying her $20 if the coin toss results in tails. If everything else remains the same, what are Kaaran’s expected cash flow and the variance of that cash flow? Solution: Part 1: E(cash flow) = (0.5 × –$15) + (0.5 × $15) = 0 σ2cash flow = [0.5 × (–$15 - $0)2] + [0.5 × ($15 – $0)2] = $225 Part 2: E(cash flow) = (0.5 × –$15) + (0.5 × $20) = $2.50 σ2cash flow = [0.5 × (–$15 – $2.50)2] + [0.5 × ($20 – $2.50)2] = $306.25

7.2

You know that the price of CFI, Inc., stock will be $12 exactly one year from today. Today the price of the stock is $11. Describe what must happen to the price of CFI, Inc., today in order for an investor to generate a 20 percent return over the next year. Assume that CFI does not pay dividends.

Solution: The expected return for CFI based on today’s stock price is ($12 – $11)/$11 = 9.09 percent, which is lower than 20 percent. Since the stock price one year from today is fixed, then the only way that you will generate a 20 percent return is if the price of the stock drops today. Consequently, the price of the stock today must drop to $10. It is found by solving the following: 0.2 = ($12 – x)/ x, or x = $10.

7.3

The expected value of a normal distribution of prices for a stock is $50. If you are 90 percent sure that the price of the stock will be between $40 and $60, then what is the variance of the prices for the stock?

Solution: Since you know that 1.645 standard deviations around the expected return captures 90 percent of the distribution, you can set up either of the following equations: $40 = $50 – 1.645σ

$60 = $50 + 1.645σ

and solve for σ. Doing this with either equation yields:

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σ = $6.079 and σ2 = 36.9555

7.4

For each year from 2015 through 2019, the annual returns on small U.S. stocks were −3.60 percent, 25.65 percent, 11.19 percent, −11.60 percent, and 20.63 percent, respectively. What would a $1 investment, made at the beginning of 2015, have been worth at the end of 2019? What average annual return would have been earned on this investment?

Solution: The value in 2019 is: V2019 = $1 × (1 + −0.036) × (1 + 0.2565) × (1 + 0.1119) × (1 + -0.1160) × (1 + 0.2063) = $1.436 Substituting into Equation 7.4 and solving for the geometric average yields: RGeometric average = [(1 + R1) × (1 + R2) × … × (1 + Rn)]1/n – 1 = [$1.436]1/5 - 1 = 0.0751, or 7.51% per year

7.5

You must choose between investing in Stock A and Stock B. You have already used CAPM to calculate the rate of return you should expect to receive for each stock given each one’s systematic risk and decided that the expected return for both exceeds that predicted by CAPM by the same amount. In other words, both are equally attractive investments for a diversified investor. However, since you are still in school and do not have a lot of money, your investment portfolio is not diversified. You have decided to invest in the stock that has the highest expected return per unit of total risk. If the expected return and standard deviation of returns for Stock A are 10 percent and 25 percent, respectively, and the expected return and standard deviation of returns for Stock B are 15 percent and 40 percent, respectively, which should you choose? Assume that the risk-free rate is 5 percent.

Solution: A comparison of the Sharpe ratios for the two stocks will tell you which has the highest expected return per unit of total risk.

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SB =

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E ( R A ) − R rf σRA

E ( R B ) − R rf σ RB

0.10 − 0.05 = 0.20 0.25

0.15 − 0.05 = 0.25 0.40

You should invest in Stock B because it has the highest expected return per unit of risk.

7.6

Viatris, Inc., has a beta of 1.35. If the expected market return is 14.5 percent and the risk-free rate is 5.5 percent, what does CAPM indicate the appropriate expected return for Viatris stock is?

Solution: E(RViatris) = Rrf + Viatris[E(RM) - Rrf] = 0.055 +[1.35 × (0.145 - 0.055)] = 0.1765 or, 17.65%

Questions and Problems, Solution Walkthrough Videos, Learning by Doing Tutorials, and additional study tools and resources are available in Wiley Course Resources.

Discussion Questions 7.1

Suppose that you know the risk and the expected return for two stocks. Discuss the process you might utilize to determine which of the two stocks is a better buy. You may assume that the two stocks will be the only assets held in your portfolio. You should be looking to maximize your expected return on an investment given the level of risk that such an investment requires the investor to bear. Therefore, you should compare the expected return and risk associated with each of the two stocks. If the stocks have the same expected return, then choose the stock with the lower risk. If the stocks have the same risk, then choose the stock with the greatest expected return. If the expected return and risk of the two assets have no common level, perhaps you should compare the ratio of the risk/expected return to see which stock contains the least risk per unit of expected return.

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LO: 1 Level: Basic

7.2

What is the difference between the expected rate of return and the required rate of return? What does it mean if they are different for a particular asset at a particular point in time? The required rate of return is the rate of return that investors require to compensate them for the risk associated with an investment. The expected return will not necessarily equal the required rate of return. The expected return can be lower, in which case the return will not be sufficient to compensate the investor for the risk associated with the investment if the expected return is realized. It can also be higher; in which case the expected return will be greater than that necessary to compensate the investor for the riskiness of the asset.

LO: 7 Level: Basic

7.3

Suppose that the standard deviation of the returns on the shares of stock at two different companies is exactly the same. Does this mean that the required rate of return will be the same for these two stocks? How might the required rate of return on the stock of a third company be greater than the required rates of return on the stocks of the first two companies even if the standard deviation of the returns of the third company’s stock is lower? No, this does not mean that the required rate of return will be the same for these two stocks. Because some risk can be diversified away, it is possible that two stocks with the same standard deviation of returns can have different required rates of return. One of these stocks can have a higher systematic risk than the other stock and, therefore, a higher required rate of return. The third stock can have a higher required rate of return if its systematic risk is greater than the systematic risk of the stock in the other two companies.

LO: 4 Level: Basic

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The correlation between Stocks A and B is 0.50, while the correlation between Stocks A and C is –0.5. You already own Stock A and are thinking of buying either Stock B or Stock C. If you want your portfolio to have the lowest possible risk, would you buy Stock B or C? Would you expect the stock you choose to affect the return that you earn on your portfolio? You would buy Stock C because it would result in your portfolio having a lower beta. If you buy Stock C, the required return for your portfolio would be lower than the required return would be if you bought Stock B. If the expected returns on Stocks C and B equal their required returns, then you would expect your portfolio to earn less with Stock C.

LO: 6 Level: Basic

7.5

The idea that we can know the return on a security for each possible outcome is overly simplistic. However, even though we cannot possibly predict all possible outcomes, this fact has little bearing on the risk-free return. Explain why. The risk-free security delivers the same return in all economic conditions. Even though we do not know all of the possible economic states in future periods, we are reasonably certain that the U.S. government will be able to repay its borrowing in every state. Therefore, the shortcoming of the model does not affect the risk-free security’s return.

LO: 7 Level: Basic

7.6

Which investment category included in Exhibit 7.3 has shown the greatest degree of risk in the United States since 1926? Explain why that makes sense in a world where the value of an asset in this investment category is likely to be more sensitive to changes in market conditions than is the price of a corporate bond. Small stocks have generally been riskier than large stocks, long-term corporate bonds, long-term government bonds, intermediate government bonds, and short-term government bonds. The explanation for this can be best understood if we realize that small stocks will be affected to a greater extent than the list of investments above by

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either good or bad economic conditions of the world. These good and bad effects translate into a distribution with greater spread or greater risk than the other investments. LO: 4 Level: Intermediate

7.7

You are concerned about one of the investments in your fully diversified portfolio. You just have an uneasy feeling about the CFO, Iam Shifty, of that particular firm. You do believe, however, that the firm makes a good product and that it is appropriately priced by the market. Should you be concerned about the effect on your portfolio if Shifty embezzles a portion of the firm’s cash? The risk of Shifty embezzling is a nonsystematic risk that will most likely be offset by a more fortunate event affecting another holding in your portfolio. Therefore, Shifty’s actions should not affect the risk that you bear by investing in your diversified portfolio (systematic risk).

LO: 6, 7 Level: Basic

7.8

The CAPM is used to price the risk (estimate the expected return) for any asset. Our examples have focused on stocks, but we could also use CAPM to estimate the expected rate of return for bonds. Explain why. A firm’s ability to repay its debt obligations will be affected in a very similar, and yet lessened, way than the firm’s stock will be affected. That is, systematic and nonsystematic factors will also affect returns for debt securities. However, if held in a diversified portfolio, then only the systematic risk component will be borne, and require compensation for bearing. Therefore, we can use the CAPM to price debt securities.

LO: 8 Level: Intermediate

7.9

In recent years, investors have agreed that the market portfolio consists of more than just a group of U.S. stocks and bonds. If you are an investor who invests in only U.S. stocks and bonds, describe the effects on the risk in your portfolio.

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If the market portfolio is composed of all assets, then the U.S.-only portfolio will probably have a small amount of unsystematic risk for which there is no additional return. Therefore, the portfolio is bearing too much risk given its expected returns. LO: 6, 7 Level: Basic

7.10

You may have heard the statement that you should not include your home as an asset in your investment portfolio. Assume that your house will comprise up to 75 percent of your assets in the early part of your investment life. Evaluate the implications of omitting it when calculating the risk of your overall investment portfolio. From a systematic risk measurement perspective, omitting the beta of your real estate investment, which does not have a beta equal to zero, could have a serious impact on your portfolio’s perceived systematic risk. In a volatile real estate market, you could be understating the risk in your portfolio, and in a flat real estate market, you could be overestimating the risk in your portfolio.

LO: 8 Level: Intermediate

Questions and Problems BASIC 7.1

Returns: Describe the difference between a total holding period return and an expected return.

LO 2, LO 3 Solution: A holding period return is the total return over some investment or “holding” period. It consists of a capital appreciation component and an income component. A holding period return reflects past performance. The expected return is a weighted average of the

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possible returns from an investment, where each of these returns is weighted by the probability that it will occur. It describes a possible return (or even a return that may not be possible) for a yet- to-occur investment period (future).

7.2

Expected returns: John is watching an old game show rerun called Let’s Make a Deal in which the contestant chooses a prize behind one of two curtains. Behind one of the curtains is a gag prize worth $150, and behind the other is a round-the-world trip worth $7,200. The producer of the game show has placed a subliminal message on the curtain containing the gag prize, which makes the probability of choosing the gag prize equal to 75 percent. What is the expected value of the selection, and what is the standard deviation of that selection?

LO 3 Solution: Expected value: E(prize)

= (0 .75 × $150) + (0.25 × $7,200) = $1,912.50

Variance: σ2prize

= [0.75 × ($150 – $1,912.50)2] + [0.25 × ($7,200 – $1,912.50)2 ]

= $9,319,218.75 Standard deviation: σprize

7.3

= ($9,319,218.75)1/2 = $3,052.74

Expected returns: You have chosen biology as your college major because you would like to be a medical doctor. However, you find that the probability of being accepted to medical school is about 10 percent. If you are accepted to medical school, then your starting salary when you graduate will be $300,000 per year. However, if you are not accepted, then you would choose to work in a zoo, where you will earn $40,000 per year. Without considering the additional years you would spend in school if you study medicine or the time value of money, what is your expected starting salary as well as the standard deviation of that starting salary?

LO 3 Solution: Expected Starting Salary:

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= 0.9($40,000) + (0.1) ($300,000) = $66,000

Variance: σ2salary = 0.9($40,000 – $66,000)2 + (0.1) ($300,000 – $66,000)2 = $6,084,000,000 Standard deviation: σsalary = ($6,084,000,000)1/2 = $78,000

7.4

Historical market: Describe the general relation between risk and return that we observe in the historical bond and stock market data.

LO 3, LO 4 Solution: The general axiom that the greater the risk, the greater the return describes the historical returns of the bond and stock market. If we look at Exhibit 7.3 in the text, we see that small stocks have averaged the greatest returns but that they also have the greatest standard deviation for the returns. When compared to large stocks, the average return and standard deviation of the small stocks are greater. Large stock average returns and standard deviation numbers are larger than those of long-term government bonds, which are larger than those of intermediate-term government bonds, which in turn are larger than those of U.S. Treasury bills. The comparison shows that the riskier the investment category, the greater the average return as well as standard deviation of returns.

7.5

Single-asset portfolios: Stocks A, B, and C have expected returns of 15 percent, 15 percent, and 12 percent, respectively, while their standard deviations are 45 percent, 30 percent, and 30 percent, respectively. If you were considering the purchase of each of these stocks as the only holding in your portfolio and the risk-free rate is 0 percent, which stock should you choose?

LO 4 Solution: Since the holding will be made in a completely undiversified portfolio, then we can calculate the risk per unit of return for each stock, the coefficient of variation, and choose the stock with the lowest value. CV(RA) = 0.45/0.15 = 3.0

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CV(RB) = 0.30/0.15 = 2.0===> Choose B CV(RC) = 0.30/0.12 = 2.5 Alternatively, we could have noted that the expected return for A and B was the same, with A having a greater degree of risk. B and C have the same degree of risk, but B has a greater expected return. This would lead you to the conclusion, just as our coefficient of variation calculations did, that Stock B is superior.

7.6

Arithmetic average: Tanner invested $1,000 in large U.S. stocks at the beginning of 2017. This investment earned 15.98 percent in 2017, 32.41 percent in 2018, 13.69 percent in 2019, and 1.41 percent in 2020. What return did he earn in the average year during the 2017–2020 period?

LO 5 Solution: The answer is the arithmetic average of the four returns, which is calculated using Equation 7.4.

 R = 15.98% + 32.41% + 13.69% + 1.41% = 15.87% = n

R Arithmetic average

i =1

n Excel Template available in Wiley Course Resources

Excel Template Solution available in Wiley Instructor Resources

7.7

Geometric average: What was the average annual return that Tanner earned over the 2017–2020 period in Problem 7.6?

LO 5 Solution: The answer is the geometric average of the four returns, which is calculated using equation 7.5. RGeometric average = [(1 + R1) × (1 + R2) × … × (1 + Rn)]1/n – 1 = [(1 + 0.1598) × (1 + 0.3241) × (1 + 0.1369) × (1 + 0.0141]1/4 – 1 = 0.1535, or 15.35%

Excel Template available in Wiley Course Resources Excel Template Solution available in Wiley Instructor Resources

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Diversification: Describe how investing in more than one asset can reduce risk through diversification.

LO 6 Solution: An investor can reduce the risk of his or her investments by investing in two or more assets whose values do not always move in the same direction at the same time. This is because the movements in the values of the different investments will partially cancel each other out or offset each other.

7.9

Systematic risk: Define systematic risk.

LO 7 Solution: Risk that cannot be diversified away is systematic risk. It is the only type of risk that exists in a diversified portfolio, and it is the only type of risk that is rewarded in asset markets.

7.10

Measuring systematic risk: Susan is expecting the returns on the market portfolio to be negative in the near term. Since she is managing a stock mutual fund, she must remain invested in a portfolio of stocks. However, she is allowed to adjust the beta of her portfolio. What kind of beta would you recommend for Susan’s portfolio?

LO 7 Solution: If we confine our analysis to portfolios with positive beta values, and since beta describes how much and what direction our portfolio is expected to vary with the market portfolio, then Susan should construct a very low beta portfolio. In that case, Susan’s portfolio is not expected to have losses quite as large as that of the market portfolio. A large beta portfolio would have larger losses than that of the market portfolio. If Susan could construct a negative beta portfolio, then she would like to construct as negative a portfolio beta as possible.

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Measuring systematic risk: Describe and justify what the value of the beta of a U.S. Treasury bill should be.

LO 7 Solution: Since the beta of any asset is the slope of the line of best fit for the plot of an asset against that of the market return, then we can use that logic to help us understand the beta of a Tbill. If we purchased a T-bill five years ago and held the same T-bill through each of the last 60 months, then the return for each of those 60 months would be exactly the same. Therefore, the vertical axis coordinates of each of the monthly returns would have the same value and the slope (beta) of the line of best fit would be zero. The meaning of a beta of zero means that our T-bill has no systematic risk. That is logically given that we know that a T-bill has no risk at all since it is a riskless asset.

7.12

Measuring systematic risk: If the expected rate of return for the market is not much greater than the risk-free rate of return, what does this suggest about the general level of compensation for bearing systematic risk?

LO 7 Solution: Such a situation suggests that return compensation for investing in an asset is determined more by the risk-free return than by the market’s compensation for bearing systematic risk. This means that the price for bearing systematic risk is very low. This may be caused by a very low perceived level of risk in the market or by an abundance of funds in the market seeking to be invested in risky assets.

7.13

CAPM: Describe the Capital Asset Pricing Model (CAPM) and what it tells us.

LO 8 Solution: The CAPM describes the relation between systematic risk and the expected return. The model tells us that the expected return on an asset with no systematic risk equals the riskfree rate. As systematic risk increases, the expected return increases linearly with beta. The CAPM is written as E(Ri) = Rrf + β i(E(Rm) – Rrf) .

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The Security Market Line: If the expected return on the market is 10 percent and the risk-free rate is 4 percent, what is the expected return for a stock with a beta equal to 1.5? What is the market risk premium?

LO 8 Solution: Following the CAPM prediction: E(Ri) = Rrf + βi (E(Rm) – Rrf) = 0.04 + [1.5 × (0.1 – 0.04)] = 0.13 The market risk premium is (E(Rm) – Rrf) = 0.06

INTERMEDIATE 7.15

Expected returns: José is thinking about purchasing a soft drink machine and placing it in a business office. He knows that there is a 5 percent probability that someone who walks by the machine will make a purchase from the machine, and he knows that the profit on each soft drink sold is $0.10. If José expects a thousand people per day to pass by the machine and requires a complete return of his investment in one year, then what is the maximum price that he should be willing to pay for the soft drink machine? Assume 250 working days in a year and ignore taxes and the time value of money.

LO 3 Solution: E(Revenue) = 1,000 × 0.05 x $.10 × 250 days = $1,250 Therefore, the most Jose should pay for the machine is $1,250.

7.16

Interpreting the variance and standard deviation: The distribution of grades in an introductory finance class is normally distributed, with an expected grade of 75. If the standard deviation of grades is 7, in what range would you expect 95 percent of the grades to fall?

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75  (1.960 ( 7 ) )

So, the lower end is: 75 – (1.960 × (7)) = 61.28 And the upper end is: 75 + (1.960 × (7)) = 88.72 So, 95 percent of the grades should fall between 61.28 and 88.72. Excel Template available in Wiley Course Resources Excel Template Solution available in Wiley Instructor Resources

7.17

Calculating the variance and standard deviation: Kate recently invested in real estate with the intention of selling the property one year from today. She has modeled the returns on that investment based on three economic scenarios. She believes that if the economy stays healthy, then her investment will generate a 30 percent return. However, if the economy softens, as predicted, the return will be 10 percent, while the return will be -25 percent if the economy slips into a recession. If the probabilities of the healthy, soft, and recessionary states are 0.4, 0.5, and 0.1, respectively, then what are the expected return and the standard deviation of the return on Kate’s investment?

LO 4 Solution: E(Ri)

= (0.4)(0.3) + (0.5) (0.1) + (0.1) (–.25) = 0.145

σ2return = (0.4)(0.3 – 0.145)2 + (0.5) (0.1 – 0.145)2 + (0.1) (–0.25 – 0.145)2 = 0.02623 σreturn = (0.02623)1/2 = 0.16194 rounded to 0.162

7.18

Calculating the variance and standard deviation: Barbara is considering investing in a company’s stock and is aware that the return on that investment is particularly sensitive to how the economy is performing. Her analysis suggests that four states of the economy can affect the return on the investment. Using the table of returns and probabilities below, find the expected return and the standard deviation of the return on Barbara’s investment. Probability

Return

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Boom

0.1

25.00%

Good

0.4

15.00%

Level

0.3

10.00%

Slump

0.2

-5.00%

LO 4 Solution: E(Ri) = [0.1 × (0.25)] + [(0.4) × (0.15)] + [(0.3) × (0.1)] + [(0.2) × (–0.05)] = 0.105 σ2return = [0.1 × (0.25 – 0.105)2] + [(0.4) × (0.15 – 0.105)2] + [(0.3) × (0.1 – 0.105)2] + [(0.2) × – (0.05 – 0.105)2]

= 0.00773 σreturn = (0.00773)1/2 = 0.08789

7.19

Calculating the variance and standard deviation: Ben would like to invest in gold and is aware that the returns on such an investment can be quite volatile. Use the following table of states, probabilities, and returns to determine the expected return and the standard deviation of the return on Ben’s gold investment. Probability

Return

Boom

0.1

40.00%

Good

0.2

30.00%

0.3

15.00%

Level

0.2

2.00%

Slump

0.2

-12.00%

LO 4 Solution E(Ri) = [0.1 × (0.4)] + [(0.2) × (0.3)] + [(0.3) × (0.15)] + [(0.2) × (0.02)] + [(0.2) × (–0.12)] = 0.125 σ2return = [0.1 × (0.4 – 0.125)2] + [(0.2) × (0.3 – 0.125)2 + [(0.3) × (0.15 – 0.125)2] + [(0.2) × (0.02 – 0.125)2] + [(0.2) × (–0.12 – 0.125)2 ] = 0.02809 σreturn = (0.02809)1/2 = 0.16759 rounded to 0.168 Excel Template available in Wiley Course Resources

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Excel Template Solution available in Wiley Instructor Resources

7.20

Single-asset portfolios: Using the information from Problems 7.17, 7.18, and 7.19, calculate the coefficient of variation for each of the investments in those problems.

LO 3, LO 4 Solution: Coefficient of variation = σReturn / E(Ri) Problem 17: 0.16194/0.145 = 1.11694 (using the exact values rather than the printed) Problem 18: 0.08789/0.105 = 0.83734 (using the exact values rather than the printed) Problem 19: 0.16759/0.125 = 1.34081 (using the exact values rather than the printed)

7.21

Portfolios with more than one asset: Emmy is analyzing a two-stock portfolio that consists of a utility stock and a commodity stock. She knows that the return on the utility stock has a standard deviation of 40 percent and the return on the commodity stock has a standard deviation of 30 percent. However, she does not know the exact covariance in the returns of the two stocks. Emmy would like to plot the variance of the portfolio for each of three cases—covariance of 0.12, 0, and –0.12—in order to understand what the variance of the portfolio would be for a range of covariances. Do the calculation for all three cases (0.12, 0 and –0.12), assuming an equal proportion of each stock in the portfolio.

LO 6 Solution:

Var ( R 2 asset port ) = x12 12 + x22 22 + 2x1 x2 1,2 Case 1, σ1,2 = 0.12: [(0.5)2 × (0.4)2] + [(0.5)2 × (0.3)2] + [2 × (0.5) × (0.5) × (0.12)] = 0.1225 Case 2, σ1,2 = 0.0: [(0.5)2 × (0.4)2] + [(0.5)2 × (0.3)2] + [2 × (0.5) × (0.5) × (0.0)] = 0.0625 Case 3, σ1,2 = -0.12: [(0.5)2 × (0.4)2] + [(0.5)2 × (0.3)2] + [2 × (0.5) × (0.5) × (-0.12)] = 0.0025

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7.22 Portfolios with more than one asset: Given the returns and probabilities for the three possible states listed below, calculate the covariance between the returns of Stock A and Stock B. For convenience, assume that the expected returns of Stock A and Stock B are 11.75 percent and 18 percent, respectively. Probability

Return on A

Return on B

Good

0.35

0.30

0.50

0.10

Poor

0.15

-0.25

-0.30

LO 6 Solution:

Cov ( RA , RB ) =  AB = 0.35  ( 0.3 − 0.1175 )  ( 0.5 − 0.18 ) + 0.5  ( 0.1 − 0.1175 )  ( 0.1 − 0.18 ) + 0.15  ( −0.25 − 0.1175 )  ( −0.3 − 0.18 ) = 0.0476

7.23

Compensation for bearing systematic risk: You have constructed a diversified portfolio of stocks such that there is no unsystematic risk. Explain why the expected return of that portfolio should be greater than the expected return of a risk-free security.

LO 7 Solution: Your portfolio contains no unsystematic risk but it does contain systematic risk. Therefore, the market should compensate the holder of this portfolio for the systematic risk that the investor bears. A risk-free security has no risk and therefore requires no compensation for risk bearing. The expected return of your portfolio should therefore be greater than the return of the risk-free security.

7.24

Compensation for bearing systematic risk: Write out the equation for the covariance of the returns of two assets, Asset 1 and Asset 2. Using that equation, explain the easiest way for the two asset returns to have a covariance of zero.

LO 7 Solution:

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Cov(Return1 ,Return 2 ) =  R12 n

(

=  pi  (Return1,i − E(Return1 )   (Return 2,i − E(Return 2 )  i =1

)

We know that all stated probabilities must be greater than zero, and thus the source of a zero covariance cannot be from the stated probabilities. The easiest way for the entire probability weighted sum to equal zero is for one of the assets, say Number 1(2), to have a value in all states that is equal to the expected return of Number 1(2). Another way of saying that is for one of the assets to have a constant return in all states. If that occurs, then the second term in the equation will always be equal to zero, causing the sum, or covariance, to be zero.

7.25

Compensation for bearing systematic risk: Evaluate the following statement: “By fully diversifying a portfolio, such as by buying every asset in the market, we can completely eliminate all types of risk, thereby, creating a synthetic Treasury bill.”

LO 7 Solution: The statement is false. A portfolio of all assets would only eliminate unsystematic risk. The systematic risk would remain. If you could eliminate both systematic and unsystematic risk, the expected rate of return on the market portfolio would be equal to the risk-free rate of return, and we know that this is not true.

7.26

CAPM: Damien knows that the beta of his portfolio is equal to 1, but he does not know the risk-free rate of return or the market risk premium. He also knows that the expected return on the market is 8 percent. What is the expected return on Damien’s portfolio?

LO 8 Solution: Following the CAPM prediction: E(Ri) = Rrf + β (E(Rm) – Rrf) = Rrf + E(Rm) – Rrf = E(Rm) = 0.08 = 8.0%

7.27

CAPM: In December 2020, the risk-free rate was 2.97 percent, the market risk premium was 6 percent and the beta for Twitter stock was 0.99. What is the expected return that

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was consistent with the systematic risk associated with the returns on Twitter stock? LO 8 Solution: From Equation 7.12: E(RTwitter stock) = Rrf + βTwitter stock[E(Rm) - Rrf] E(RTwitter stock) = 0.0297 + 0.99[0.06] E(RTwitter stock) = 0.0297 + 0.0594 = 0.0891, or 8.91%

7.28

CAPM: The market risk premium is 6 percent, and the risk-free rate is 5 percent. If the expected return on a bond is 6.5 percent, what is its beta?

LO 8 Solution: From Equation 7.12, we can calculate the beta of the bond as: E(Rbond) = Rrf + β bond × [E(Rm) - Rrf] 0.065 = 0.050 + (β bond × 0.06) β bond = (0.065 – 0.050)/0.060 = 0.25

ADVANCED

7.29

David is going to purchase two stocks to form the initial holdings in his portfolio. Iron stock has an expected return of 15 percent, while Copper stock has an expected return of 20 percent. If David plans to invest 30 percent of his funds in Iron and the remainder in Copper, what will be the expected return from his portfolio? What if David invests 70 percent of his funds in Iron stock?

LO 3 Solution: Part 1: E(Rport) = [(0.3) × (0.15)] + [(0.7) × (0.2)] = 0.185 = 18.5% Part 2: E(Rport) = [(0.7) × (0.15)] + [(0.3) × (0.2)] = 0.165 = 16.5%

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Peter knows that the covariance in the return on two assets is –0.0025. Without knowing the expected return of the two assets, explain what that covariance means.

LO 3, LO 6 Solution: The covariance measure is dependent on the expected return of the two assets but without knowing the expected return of the two assets, it is difficult to characterize the scale of the covariance. However, since the covariance is negative, we can say that generally the two assets move in opposite directions, with respect to their own means, from each other in given states of nature.

7.31

In order to fund her retirement, Glenda needs her portfolio to have an expected return of 12 percent per year over the next 30 years. She has decided to invest in Stocks 1, 2, and 3, with 25 percent in Stock 1, 50 percent in Stock 2, and 25 percent in Stock 3. If Stocks 1 and 2 have expected returns of 9 percent and 10 percent per year, respectively, then what is the minimum expected annual return for Stock 3 that is likely to enable Glenda to achieve her investment requirement?

LO 3, LO 6 Solution: The formula for the expected return of a three-stock portfolio is:

(

)

E R3 asset port = x1E ( R1 ) + x2 E ( R2 ) + x3 E ( R3 )

Therefore, we can solve as in the following: 0.12 = [0.25 × (0.09)] + [0.5 × (0.1)] + [0.25 × E(R3)] E(R3) = 0.19 or 19.0%

7.32

Tonalli is putting together a portfolio of 10 stocks in equal proportions. What is the relative importance of the variance for each stock versus the covariance for the pairs of stocks in her portfolio? For this exercise, ignore the actual values of the variance and covariance terms and explain their importance conceptually.

LO 4, LO 6 Solution:

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The variance of the portfolio will be composed of 10 (n = 10) individual stock variance terms and 45 ((n2 –n)/2) covariance terms. Therefore, the vast majority of the portfolio variance calculation will be determined by the covariance terms of the portfolio in most cases.

7.33

Explain why investors who have diversified their portfolios will determine the price and, consequently, the expected return on an asset.

LO 3, LO 6 Solution: If all investors require returns that compensate them for the level of risk that they bear, then undiversified investors will require a greater return for a given investment than diversified investors will. In other words, diversified investors will be willing to pay a higher price for an asset than will undiversified investors. Therefore, a diversified investor is the marginal investor whose purchase will determine the price, and therefore, the expected return for an asset.

7.34

Brad is about to purchase an additional asset for his well-diversified portfolio. He notices that when he plots the historical returns of the asset against those of the market portfolio, the line of best fit tends to have a large amount of prediction error for each data point (the scatter plot is not very tight around the line of best fit). Do you think that this will have a large or a small impact on the beta of the asset? Explain your opinion.

LO 6 Solution: It will have no effect on the beta of the asset. The beta measures only the systematic risk or variation in the returns of the asset. The prediction error reflects the unsystematic risk inherent in the returns of the asset and will consequently, not affect the beta of the asset.

7.35

Draw the Security Market Line (SML) for the case where the market risk premium is 5 percent and the risk-free rate is 7 percent. Now suppose an asset has a beta of –1.0 and an expected return of 4 percent. Plot it on your graph. Is the security properly priced? If not,

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explain what we might expect to happen to the price of this security in the market. Next, suppose another asset has a beta of 3.0 and an expected return of 20 percent. Plot it on the graph. Is this security properly priced? If not, explain what we might expect to happen to the price of this security in the market. LO 8 Solution: The Security Market Line (SML) shows the relationship between an asset’s expected return and its beta. We know the market has a beta of one, and we know the risk-free rate has a beta of zero. The risk-free rate of return is 7 percent, and the market is expected to return 5 percent more than this. Therefore, the expected rate of return for the market (a beta one asset) is 12 percent. To draw this SML, we need only connect the dots:

Expected Return

18% 15% 12% 9% 6% 3% 0% 0

Beta

We can see from the following diagram that an asset with expected return of 4 percent and a beta of –1.0 is underpriced (its expected return is too high). As the market becomes aware of this underpricing, investors will purchase the asset, bidding up its price until its expected return falls on the SML. (Recall that as the initial purchase price of an asset increases, the expected return from purchasing the asset will decrease because you are paying a higher initial cost for the asset.)

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As we can see from the following diagram, an asset with a beta of 3.0 should have an 18%

Expected Return

15%

The investment will fall here in this plot

12%

0% -1

Beta

expected return of 7% + (3)(5%) = 22%. The asset only has an expected return of 20 percent. Therefore, this asset is overpriced. Demand for this asset will be low, driving down its market price, until the asset’s expected return falls on the SML.

23%

Expected Return

18%

14%

The investment will fall here in this plot

0% 0

Beta

7.36

If the CAPM describes the relation between systematic risk and expected returns, can both an individual asset and the market portfolio of all risky assets have negative expected real rates of return? Why or why not?

LO 8 Solution: A negative expected real rate of return implies that the expected total rate of return is less than the risk-free rate.

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1) It is possible for the beta of an individual stock to be negative. Therefore, from CAPM, E[Ri] = Rrf + βi × [E(Rm) - Rrf)], it is also possible for a share of stock to have a negative expected real rate of return. 2) It is not possible for the market portfolio to have a negative expected real rate of return since the beta for the market equals 1.

7.37

You have been provided the following data on the securities of three firms and the market: σRi

Security

E[Ri]

Stock A

0.15

Stock B

0.15

0.18

Stock C

0.10

0.02

Market portfolio

0.10

0.04

Treasury bills

0.05



βi

1.0

1.5

0.5 0.5

Assume the CAPM and SML are true and fill in the missing values in the table. Would you invest in the stock of any of the three firms? If so, which one(s) and why? LO 8 Solution: 1) The missing values in the table are:

 A = RA,M

( RA ) = 1.0 ( RA )  = 0.06  RM ( 0.04 ) RA

B = RB,M ( RB )  RM = 0.5(0.18) (0.04) = 2.25 C = RC,M

( RC ) =   RM

RC, M

 0.02   0.04  RC, M = 1.00  

 R ,M = 1.00;  M = 1.00  R M

T −bill , M

= 0;  T −bill = 0

2) Using Equation 7.12 you can calculate the expected returns for the different shares: E(RA) = 0.05 + [1.5 × (0.10 - 0.05)] = 0.125, or 12.5% E(RB) = 0.05 + [2.25 × (0.10 - 0.05)] = 0.1625, or 16.25%

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E(RC) = 0.05 + [0.5 × (0.10 - 0.05)] = 0.075, or 7.5% A comparison of the expected returns that are given in the table above, with the returns that CAPM predicts (which are calculated above), indicates that you should buy stocks A and C and avoid stock B.

7.38

You have been provided with the following information about the expected returns to Stock A and Stock B for various possible future economic conditions.

Probability of State of

State of

Return for

Economy

Stock A

Stock B

Boom

0.25

0.45

Level

0.60

0.35

0.12

Slump

0.15

0.10

-0.10

The market risk premium is 7 percent, and the risk-free rate is 4 percent. a. Which stock has more systematic risk? b. Which stock has more unsystematic risk? c. Which stock is “riskier” and why? LO8 Solutions: Using Equation 7.2 you can calculate the expected return for both stocks. E(RA) = [(0.25) × (0.25)] + [(0.60) × (0.35)] + [(0.15) × (0.10)] = 0.2875 E(RB) = [(0.25) × (0.45)] + [(0.60) × (0.12)] + [(0.15) × (-0.10)] = 0.1695 To calculate the amount of systematic risk we can use their expected returns and equation 7.12 to solve for the beta of each stock. E(RA) = Rrf + βA (E(Rm) – Rrf) 0.2875 = 0.04 + (βA × 0.07) βA = 3.54 E(RB) = Rrf + βB (E(Rm) – Rrf) 0.1695 = 0.04 + (βB × 0.07)

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βB = 1.85

(a) Stock A has more systematic risk because it has a higher beta. Using Equation 7.3 we can calculate the variance of both stocks. σ2A = [(0.25) × (0.25 – 0.2875)2] + [(0.60) × (0.35 – 0.2875)2] + [(0.15) × (0.10 – 0.2875)2] = 0.0080 σ2B = [(0.25) × (0.45 – 0.1695)2] + [(0.60) × (0.12 – 0.1695)2 ] + [(0.15) × (-0.10 – 0.1695)2] = 0.0320 (b) Stock B has more total risk as measured by the variance of returns; however, Stock B has less systematic risk than Stock A as measured by the beta. Thus, Stock B must have more unsystematic risk that can be diversified away in a large portfolio. (c) Stock A is riskier since it has more systematic risk, which is the measure of risk that investors care about because it can’t be diversified away in a large portfolio.

Sample Test Problems INTERMEDIATE 7.1

Given the following information from Capstone Corporation, what price would the CAPM predict that the company’s stock will trade for 1 year from today? Risk-free rate: 3% Market risk premium: 8% Beta: 0.65 Current stock price: $64.61 Annual dividend: $1.92

LO 2, LO 8 Solution: Using CAPM, we find: E(RCapstone) = Rrf + ßCapstone × (E(Rm) – Rrf) = 0.03 + (0.65 × 0.08)

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= 0.082 or 8.2 percent Using the total holding period return formula (Equation 7.1) we can solve for the stock price in one year:

RT =

7.2.

P1 − P0 + CF1 P − $64.61 + 1.92  0.082 = 1  P1 = $67.99 P0 $64.61

You are considering investing in a mutual fund. The fund is expected to earn a return of 15 percent in the next year. If its annual return is normally distributed with a standard deviation of 6.5 percent, what return would be at the lower end of the 95 percent confidence interval? (Round answer to 2 decimal places, e.g. 52.75%.)

LO 4 Solution: Since the annual returns earned by the mutual fund are normally distributed, a 95 percent confidence level corresponds to 1.96 standard deviations from the mean. Therefore, 95 percent of the time you would expect the annual return for next year to be in the range: 0.15 + (1.96 × 0.065). The lower end of this range is: 0.15 – (1.96 × 0.065) = 0.0226, or 2.61%, which is the return that would be at the lower end of the 95 percent confidence interval.

7.3

You have just invested in a portfolio of three stocks. The amount of money that you invested in each stock and its beta are summarized below. Calculate the beta of the portfolio and use the capital asset pricing model (CAPM) to compute the expected rate of return for the portfolio. Assume that the expected rate of return on the market is 15 percent and that the risk-free rate is 7 percent.

Stock

Investment

Beta

$ 200,000

1.50

300,000

0.65

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1.25

LO 3, LO 8 Solution: Portfolio Beta =  p =  i =1wi i N

$200,000

20%

$300,000

30%

$500,000

50%

Total

$1,000,000

100%

 p = (0.20 × 1.50) + (0.30 × 0.65) + (0.50 × 1.25) = 1.12 E(RPortfolio) = Rrf + βPortfolio (E(RM) – Rrf) = 0.07 + [1.12 × (0.15 - 0.07)] = 0.1596, or 15.96%

7.4

What would you recommend to an investor who is considering making an investment in a stock which plots below the security market line (SML)? Explain.

LO 8 Solution: You should recommend that the investor not make this investment. An investment that plots below the SML has an expected return that is too low to fully compensate the investor for its systematic risk. In other words, its price is so high that it is not expected to yield a sufficiently high return to compensate for its risk. If investors in the market as a whole realize this, they will sell the stock in question, and its price will be driven down by such sales to the point where the expected return fully compensates them for the risk. If the investor you are advising buys the stock now, and its price subsequently declines, he or she will bear the cost of that decline.

7.5

Why does an investor want a diversified portfolio? Can an investor eliminate all risk?

LO 6, LO 7 Solution: An investor of a diversified portfolio reduces total risk by investing in two or more assets whose values do not always move in the same direction at the same time. With enough

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diversification, the investor can eliminate unsystematic or unique risk, but, by definition, will not be able to eliminate systematic, or market risk, so all risk cannot be eliminated.

Ethics Case Discussion questions 1.

Do CEOs make too much money? If you were a corporate director, how would you suggest the company determine the pay of the CEO? Do they make too much money relative to their average worker? It is obvious that CEOs of major public companies make a lot of money, but it is hard to say if they make “too much.” To answer this question, we would need to know how much they should be making based on some sort of benchmark value that considers their experience, skills, network, and other factors that they bring to the company. CEOs compete with other executives in a competitive market and pay packages should reflect the incremental value the board of directors believes they can create for stockholders. In the end, CEOs should be paid for the value they contribute to the company, but this is difficult to objectively observe. This explains why compensation committees rely so heavily on peer group benchmarks.

It is likely the case that CEOs (maybe not all) create more value for their company than the average worker. This is because CEOs make much more significant investment and financing decisions for the company than the average worker. If these decisions create value, then the CEOs incremental contribution to the value of the company is significantly greater than that of the average worker, perhaps by a factor of 300 times or more. Of course, if CEOs consistently make value destroying decisions, the pay ratio is undeserved. This highlights the important consideration that CEO pay should be tied to the performance of their company. 2.

Should companies focus exclusively on performance share targets related to stockholder value such as return on equity and per share earnings, or should they

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include broader targets such as Environmental, Social, and Governance (ESG) goals. Stock-based performance targets are a very straightforward way to align the interests of the CEO with those of stockholders. With these incentives, CEOs can be expected to make decisions that are most likely to increase the value of the company, including investments in ESG and other factors that are tied to the interests of other stakeholders. One potential downside of this incentive strategy, however, is that CEOs may not have a complete view of the strategic value of these stakeholder interests and may be focused more on making large and splashy investments such as big M&A deals. In this case, boards of directors may strategically create incentives for CEOs to accomplish goals of the corporation through more specific performance targets that ultimately enhance stockholder value.

Do you think that Say-on-Pay votes should be binding, and therefore require a response by boards of directors if pay proposals fail to receive a majority of shareholder approval? Proponents of the current Say-on-Pay rules contend that despite the non-binding status of these shareholder votes, boards of directors are concerned with the possibility that a pay package will fail to receive a majority of shareholder votes. Many even contend that the 2010 legislation mandating Say-on-Pay votes moderated the subsequent growth of CEO pay. The evidence, however, indicates that the growth of CEO pay has increased at a steady rate over the last decade, and that shareholders only rarely voice disapproval over their CEO pay packages. It is possible that a binding shareholder vote to approve with create additional incentives for boards of directors to limit the growth of CEO pay and think more carefully about how to benchmark a CEOs contribution to the value of the company. To be sure, given the current average pay of public company CEOs, it is unlikely that these individuals will be able to find more lucrative employment options if the growth in CEO pay is curtailed.

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Chapter 6

Discounted Cash Flows and Valuation

Before You Go On Questions and Answers Section 6.1 1.

Explain how to calculate the future value of a stream of cash flows. It would be helpful to first construct a time line so that we can identify the timing of each cash flow. The next step would be calculating the future value of each individual cash flow. Finally, we would sum up the future values of all the individual cash flows to determine the future value of the cash flow stream.

Explain how to calculate the present value of a stream of cash flows. To calculate the present value of a stream of cash flows, you should first draw a time line ensuring that each cash flow is placed in its correct time period. Then you calculate the present value of each cash flow for its time period. Finally, all these present values are aggregated.

Why is it important to adjust all cash flows to a common date? When making economic decisions, we need to compare “apples to apples.” This is possible only when we convert all the cash flows to a common date, which can either be a present time or some future date. The reason is the time value of money: a dollar today is worth more than a dollar in the future. Thus, when cash flows are converted to the same time period, the time value of money concept holds true, and we can concentrate on the economic aspects of the decision.

Section 6.2

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What is the difference between an ordinary annuity and an annuity due? An ordinary annuity assumes that the cash flows occur at the end of a period. Most types of loans are ordinary annuities. On the other hand, an annuity due is an annuity whose payment is to be made immediately (or at the beginning of a period) instead of at the end of the period. For example, in many leases the first payment is due immediately, and each successive payment must be made at the beginning of the month.

Give one example of an ordinary annuity and one example of an annuity due. An example of an ordinary annuity is a loan payment or a mortgage where the payment and interest is calculated at the end of the period. An example of an annuity due is rent where payments are made at the beginning of every period.

What is the annuity transformation method? The annuity transformation method refers to the conversion of an ordinary annuity to an annuity due. In this process, you first plot all the cash flows on a time line as if the cash flows were an ordinary annuity. Then you calculate the present or future value factor as you would with an ordinary annuity, and finally, you multiple your answer by (1 + i). Conveniently, this relationship works for both present and future value calculations.

Section 6.3 1. What are the differences between an ordinary annuity, an annuity due, and a perpetuity? An ordinary annuity assumes that the cash flows occur at the end of a period. Most types of loans are ordinary annuities. On the other hand, an annuity due is an annuity whose payment is to be made immediately (or at the beginning of a period) instead of at the end of the period. For example, in many leases the first payment is due immediately, and each successive payment must be made at the beginning of the month. A perpetuity is a special case of annuity, and it refers to a constant stream of identical cash flows with no end.

2. Give two examples of perpetuities.

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The text gives the example of British government bonds called consols that have no maturity and have been traded in the markets since the end of the Napoleonic wars. Another example could be a preferred stock of a company that has no maturity and will pay a constant dividend forever.

Section 6.4 1. What is the difference between a growing annuity and a growing perpetuity? A stream of cash flows that is growing at a constant rate over time can be called a growing annuity or growing perpetuity. If the cash flows extend over a finite length of time, then we call it a growing annuity and can use Equation 6.5 to compute the present value. If the growth will continue at a constant rate for a very long time period and perhaps, forever, we refer to it as the growing perpetuity. We would then use Equation 6.6 to estimate the present value of this cash flow stream.

Section 6.5 1.

What is the APR, and why are lending institutions required to disclose this rate? APR, or the annual percentage rate, is the annualized interest rate using simple interest. It is defined as the simple interest charged per period multiplied by the number of periods per year. Lending institutions are mandated by Federal Truth-in-Lending Act regulations to disclose this rate to essentially make it easier for consumers to be exposed to the same kind of rate by all businesses.

What is the correct way to annualize an interest rate in financial decision making? The correct way to annualize interest rates is by computing the effective annual interest rate (EAR). This is the annual growth rate that allows for compounding, which means you earn interest on interest. To calculate the EAR, take the quoted interest rate and divide it by the number of compounding periods (quoted interest rate/m). Then take the resulting interest rate, add 1 to it, and raise it to the power equal to m. Finally, subtract 1 and the result is EAR. The answer requires Equation 6.7: m

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Distinguish between quoted interest rate, interest rate per period, and effective annual interest rate. The quoted interest rate, such as APR, is the interest rate that has been annualized by multiplying the rate per period by the number of compounding periods. The interest rate per period is the quoted rate per period. It can be stated in the form of an APR—in that case, just divide it by the number of compounding periods to obtain the interest rate per period. Finally, the effective annual interest rate (EAR) is the annual rate of interest that accounts for the effects of compounding.

Self-Study Problems 6.1

Kronka, Inc., is expecting cash inflows of $13,000, $11,500, $12,750, and $9,635 over the next four years. What is the present value of these cash flows if the appropriate discount rate is 8 percent?

Solution: The time line for the cash flows and their present value is as follows: 0

Year

├─────────┼─────────┼─────────┼─────────┤ $13,000

PV4 =

$11,500

$12,750

$9,635

$13,000 $11,500 $12,750 $9,635 + + + (1.08) (1.08)2 (1.08)3 (1.08)4

= $12,037.04 + $9,859.40 + $10,121.36 + $7,082.01 = $39, 099.81 Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: Cash Flow (CF)

Frequency (F)

13,000

11,500

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12,750

9,635

Solutions Manual

Then solve by pressing NPV, enter the rate of 8% and compute NPV= 39,099.81 Excel solution method: A

Given information/assumptions 3

Appropriate discount rate

The Timeline 6

Period

Cash Flows

$13,000

$11,500

$12,750

$9,635

Present Value

Present Value using the Formula

Comments

Present Value

=+C7/(1+B3)^C6+D7/(1+B3)^D6+E7/(1+B3)^E6+F7/

$ 39,099.81

(1+B3)^F6 13

Present Value using the NPV Function

Present Value

$ 39,099.81

=NPV(B3,C7:F7)+B7

LO: 4 Level: Basic

6.2

Your grandfather has agreed to deposit a certain amount of money each year into an account paying 7.25 percent annually to help you go to graduate school. Starting next year, and for the following four years, he plans to deposit $2,250, $8,150, $7,675, $6,125, and $12,345 into the account. How much will you have at the end of the five years?

Solution: The time line for the cash flows and their future value is as follows:

7.25%

Year

├────────┼────────┼────────┼─────────┼────────┤ $2,250

$8,150

$7,675

$6,125

$12,345

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FV5 = [$2,250 x (1.0725)4] + [$8,150 x (1.0725)3] + [$7,675 x (1.0725)2] + [$6,125 x 1.0725] + $12,345 = $2,976.95 + $10,054.25 + $8,828.22 + $6,569.06 + $12,345 = $40,773.48 Financial Calculator Solution:

Using a financial calculator, enter the cash flows as follows: Cash Flow (CF)

Frequency (F)

2,250

8,150

7,675

6,125

12,345

Then solve by pressing NPV, enter the rate of 7.25% and compute NPV= 28,733.68.

7.25

28,733.68

PMT

FV -40,773.48

Excel solution method: A

Given information/assumptions 3

Appropriate discount

7.25%

rate

The Timeline 6

Period

Cash Flows

$2,250

$8,150

$7,675

$6,125

$12,345

Future Value

Future Value using the Formula

Comments

Future Value

=+C7*(1+B3)^4+D7*(1+B3)^3+E7*(1+B3)^2+F7*(1+B3)^1+G7

40,773.48

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Since there is no NFV function, must first find NPV, then convert to the FV 14

Present Value using the NPV Function

Present Value

Future Value using the FV Function

Future Value

$28,733.68

=NPV(B3,C7:G7)

$40,773.48 =-FV(B3,G6,0,B15,0)

LO: 2 Level: Basic

6.3

Mike White is planning to save up for a trip to Europe in three years. He will need $7,500 when he is ready to make the trip. He plans to invest the same amount at the end of each of the next three years in an account paying 6 percent. What is the amount he will have to save every year to reach his goal of $7,500 in three years?

Solution: Amount Mike White will need in three years = FVA3 = $7,500 Number of years = n = 3 Interest rate on investment = i = 6.0% Amount needed to be invested every year = PMT = ? 0

Year

├─────────┼──────┼───────┤ CF=?

CF=?

CF=? FVA3 = $7,500

FVA n = CF 

(1 + i )n − 1 i

$7,500 = CF 

(1 + 0.06)3 − 1 0.06

= CF  3.1836 CF =

$7,500 3.1836

= $2, 355.82 Mike will have to invest $2,355.82 every year for the next three years. Financial Calculator Solution:

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7,500 PMT

-2,355.82 Excel solution method: A

Given information/assumptions 3

Appropriate discount rate

The Timeline 6

Period

Cash Flows

Future Value

Cashflows using the Formula

Cash Flows

CF=?

$ 7,500 Comments ($2,355.82)

13 Cashflows using the PMT Function 14

=-+E8/((((1+B3)^E6)-1)/B3) Comments

Cash Flows

($2,355.82)

=PMT(B3,E6,0,E8,0)

LO: 5 Level: Basic

6.4

Becky Scholes has $150,000 to invest. She wants to be able to withdraw $12,500 every year forever without using up any of her principal. What interest rate would her investment have to earn in order for her to be able to do so?

Solution: Present value of Becky Scholes’s investment = $150,000 Amount needed annually = $12,500 This is a perpetuity!

CF i CF $12,500 i= = PVP $150, 000 i = 8.33%

PVP =

LO: 6

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Level: Basic

6.5

Dynamo Corp. is expecting annual payments of $34,225 for the next seven years from a customer. What is the present value of this annuity if the discount rate is 8.5 percent?

Solution: The time line for Dynamo’s cash flows and their present value is as follows: 0 8.5%

PVA = ?

$34,225

$34,225 $34,225 $34,225

Year

$34,225

1 − 1 (1 + i )n PVA7 = CF  i = $34,225 

1 − 1 (1.085)7 0.085

= $34,225  5.1185 = $175,180.66

Financial Calculator Solution:

8.5

-34,225

PMT

PV 175,181.13

Excel solution method: A

Given information/assumptions 3

Appropriate

8.50%

discount rate

The Timeline 6

Period

Cash Flows

$34,225

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Present Value

Present Value of an annuity using the Formula

Present Value

Present Value of an annuity

Present Value

Solutions Manual

$ 175,181

$175,181

Comments =C7*((1-(1/(1+B3))^I6)/B3)

=-PV(B3,I6,C7,0,0)

Financial calculator, Excel and formula solutions differ because of rounding errors. LO: 2 Level: Basic

Discussion Questions 6.1

Identify the steps involved in computing the future value when you have multiple cash flows. First, prepare a time line to identify the size and timing of the cash flows. Second, calculate the present value of each individual cash flow using an appropriate discount rate. Finally, add up the present values of the individual cash flows to obtain the present value of a cash flow stream. This approach is especially useful in the real world where the cash flows for each period are not the same.

LO: 1 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.2

What is the key economic principle involved in calculating the present value or future value of multiple cash flows?

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Regardless of whether you are calculating the present value or the future value of a cash flow stream, the key principle is to discount the cash flows for calculating the present value or compound the cash flows to calculate the future value at a particular point in time. In this way, the time value of money is reflected through the calculations. LO: 1 Level: Basic Bloomcode: Knowledge AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.3

What is the difference between a perpetuity and an annuity? A cash flow stream that consists of the same amount being received or paid on a periodic basis for a limited time period is called an annuity. If the same payments are made periodically forever, the contract is called a perpetuity.

LO: 2 Level: Basic Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.4

Define annuity due. Would an investment be worth more if it were an ordinary annuity or an annuity due? Explain. When annuity cash flows occur at the beginning of each period, it is called an annuity due. An annuity due will result in a bigger investment than an ordinary annuity because each cash flow will accrue an extra interest payment.

LO: 2 Level: Basic

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Bloomcode: Knowledge AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.5

Raymond Bartz is trying to choose between two equally risky annuities, each paying $5,000 per year for five years. One is an ordinary annuity, the other is an annuity due. Which of the following statements is most correct? a. The present value of the ordinary annuity must exceed the present value of the annuity due, but the future value of an ordinary annuity may be less than the future value of the annuity due. b. The present value of the annuity due exceeds the present value of the ordinary annuity, while the future value of the annuity due is less than the future value of the ordinary annuity. c. The present value of the annuity due exceeds the present value of the ordinary annuity, and the future value of the annuity due also exceeds the future value of the ordinary annuity. d. If interest rates increase, the difference between the present value of the ordinary annuity and the present value of the annuity due remains the same. The answer is c. The present value of the annuity due exceeds the present value of the ordinary annuity, and the future value of the annuity due also exceeds the future value of the ordinary annuity.

LO: 2 Level: Basic Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.6

Which of the following investments will have the highest future value at the end of three years? Assume that the effective annual rate for all investments is the same.

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a. You earn $3,000 at the end of three years (a total of one payment). b. You earn $1,000 at the end of every year for the next three years (a total of three payments). c. You earn $1,000 at the beginning of every year for the next three years (a total of three payments). The answer is c. Earning $1,000 at the beginning of each year for the next three years will have the highest future value as it is an annuity due. LO: 2 Level: Intermediate Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.7

Explain whether or not each of the following statements is correct. a. A 15-year mortgage will have larger monthly payments than a 30-year mortgage of the same amount and same interest rate. b. If an investment pays 10 percent interest compounded annually, its effective rate will also be 10 percent. Statement A is a true statement. The 15-year mortgage will have higher monthly payments since more of the principal will have to be paid each month than in the case of a 30-year mortgage. Statement B is true since the frequency of compounding is annual and hence the rate for a single period is the same as the rate for a year.

LO: 2, 4 Level: Intermediate Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

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6.8

Solutions Manual

When will the annual percentage rate (APR) be the same as the effective annual rate (EAR)? The annual percentage rate (APR) will be the same as the effective annual rate only if the compounding period is annual, not otherwise.

LO: 4 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.9

Why is the effective annual rate (EAR) superior to the annual percentage rate (APR) in measuring the true economic cost or return? Unlike the APR, which reflects annual compounding, the EAR takes into account the actual number of compounding periods. For example, suppose there are two investment alternatives that both pay an APR of 10 percent. Assume that the first pays interest annually and that the second pays interest quarterly. It would be a mistake to assume that both investments will provide the same return. The real return on the first one is 10 percent, but the second investment actually provides a return of 10.38 percent because of the quarterly compounding. Thus, this is the superior investment.

LO: 4 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.10

Suppose three investments have equal lives and multiple cash flows. A high discount rate tends to favor: a. The investment with large cash flows early. b. The investment with large cash flows late.

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c. The investment with even cash flows. d. None of the investments since they have equal lives. The correct answer is a. The investment with large cash flows early will be worth more compared to the one with the large cash flows late. The cash flows that come in later will be discounted more due to the high discount rate, thus being worth less today. Thus, the investment with large cash flows early will be favored. LO: 4 Level: Intermediate Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

Questions and Problems BASIC 6.1

Future value with multiple cash flows: Konerko, Inc., management expects the company to earn cash flows of $13,227, $15,611, $18,970, and $19,114 over the next four years. If the company uses an 8 percent discount rate, what is the future value of these cash flows at the end of year 4?

Solution: 0

├───────┼────────┼───────┼────────┤ $13,227

$15,611

$18,970

$19,114

FV4 = [$13, 227  (1.08)3 ] + [$15, 611 (1.08) 2 ] + [$18,970  (1.08)1 + $19,114] = $16, 662.21 + $18, 208.67 + $20, 487.60 + $19,114 = $74, 472.48

Financial Calculator Solution:

Using a financial calculator, enter the cash flows as follows:

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Cash Flow (CF)

Frequency (F)

13,227

15,611

18,970

19,114

Solutions Manual

Then solve by pressing NPV, enter the rate of 8% and compute NPV= - 54,739.50. To get Future Value:

-54,739.50

PMT

FV 74,472.48

Excel solution method: A

Given information/assumptions 3

Appropriate discount

8.00%

rate

The Timeline 6

Period

Cash Flows

$13,227

$15,611

$18,970

$19,114

Future Value

Future Value using the Formula

Comments

Future Value

=+C7*(1+B3)^3+D7*(1+B3)^2+E7*(1+B3)^1+F7*(1+B3)^0

74,472.48

Since there is no NFV function, must first find NPV, then convert to the FV 14

Present Value using the NPV Function

Present Value

Future Value using the FV Function

Future Value

$54,739.50

=NPV(B3,C7:F7)

$74,472.48 =-FV(B3,F6,0,B15,0)

LO: 1

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Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.2

Future value with multiple cash flows: Ben Woolmer has an investment that will pay him the following cash flows over the next five years: $2,350, $2,725, $3,128, $3,366, and $3,695. If his investments typically earn 7.65 percent, what is the future value of the investment’s cash flows at the end of five years?

Solution: 0

7.65%

Year

├───────┼────────┼───────┼────────┼───────┤ $2,350

$2,725

$3,128

$3,366

$3,695

FV5 = $2,350  (1.0765) 4  + $2,725  (1.0765)3  + $3,128  (1.0765) 2  + $3,366  (1.0765)1  + $3,695 = $3,155.91 + $3,399.45 + $3,624.89 + $3,623.50 + $3,695 = $17,498.75

Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: Cash Flow (CF)

Frequency (F)

2,350

2,725

3,128

3,366

3,695

Then solve by pressing NPV, enter the rate of 7.65% and compute NPV= 12,104.22.

To get Future Value:

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7.65

12,104.22

PMT

Solutions Manual

FV -17,498.74

Excel solution method: A

Given information/assumptions 3

Appropriate

7.65%

discount rate

Future Value showing the Timeline 6

Period

Cash Flows

$2,350

$2,725

$3,128

$3,366

$3,695

Future Value

Future Value using the Formula

Comments

Future Value

=+C7*(1+B3)^4+D7*(1+B3)^3+E7*(1+B3)^2+F7*(1+B3)^1+G7*(

17,498.74

1+B3)^0 Since there is no NFV function, must first find NPV, then convert to the FV 15

Present Value using the NPV Function

Present Value

Future Value using the FV Function

Future Value

$12,104.22

=NPV(B3,C7:G7)

$17,498.74 =-FV(B3,G6,0,B16,0)

LO: 1 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.3

Future value with multiple cash flows: You are a freshman in college and are planning a trip to Europe when you graduate from college at the end of four years. You plan to save the following amounts annually, starting today: $625, $700, $700, and $750. If you can earn 5.75 percent annually, how much will you have at the end of four years?

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Solution: 0

5.75%

Year

├───────┼────────┼───────┼────────┤ $625

$700

$750

FV4 = $625(1.0575)4 + $700(1.0575)3 + $700(1.0575)2 + $750(1.0575) = $781.63 + $827.83 + $782.81 + 793.13 = $3,185.40 Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: Cash Flow (CF)

Frequency (F)

625

700

750

Then solve by pressing NPV, enter the rate of 5.75% and compute NPV= 2,547.08. To get Future Value:

5.75

2,547.08

PMT

FV -3,185.40

Excel Template available in Wiley Course Resources Excel Template Solution available in Wiley Instructor Resources LO: 1 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

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Solutions Manual

Present value with multiple cash flows: Saul Cervantes has just purchased some equipment for his landscaping business. For this equipment he must pay the following amounts at the end of each of the next five years: $10,450, $8,500, $9,675, $12,500, and $11,635. If the appropriate discount rate is 10.875%, what is the cost in today’s dollars of the equipment Saul purchased today?

Solution: 0

10.875% 1

Year

├───────┼────────┼───────┼────────┼───────┤ $10,450

PV =

$8,500

$9,675

$12,500

$11,635

$10, 450 $8,500 $9,675 $12,500 $11,635 + + + + 2 3 4 (1.10875) (1.10875) (1.10875) (1.10875) (1.10875)5

= $9, 425.03 + $6,914.35 + $7,098.23 + 8,271.33 + $6,943.82 = $38, 652.76

Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: Cash Flow (CF)

Frequency (F)

10,450

8,500

9,675

12,500

11,635

Then solve by pressing NPV, enter the rate of 10.875% and compute NPV= 38,652.76. Excel solution method: A

Given information/assumptions 3

Appropriate

10.875%

discount rate

Present Value showing the Timeline

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Period

Cash Flows

Present Value

Present Value using the Formula

Present Value

Net Present Value using the Function

Present Value

Solutions Manual

$10,450

$8,500

$9,675

$12,500

$11,635

38,652.76

$38,652.76

Comments =C7/(1+B3)+D7/(1+B3)^2+E7/(1+B3)^3+F7/(1+B3)^4+G7/(1+B3)^5

=NPV(B3, C7:G7)

LO: 1 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.5

Present value with multiple cash flows: Jeremy Fenloch borrowed some money from his friend and promised to repay him $1,225, $1,350, $1,500, $1,600, and $1,600 over the next five years. If the friend normally discounts investments at 8 percent annually, how much did Jeremy borrow?

Solution: 0

Year

├───────┼────────┼───────┼────────┼───────┤ $1,225

PV =

$1,350

$1,500

$1,600

$1,225 $1,350 $1,500 $1,600 $1,600 + + + + (1.08) (1.08)2 (1.08)3 (1.08)4 (1.08)5

= $1,134.26 + $1,157.41 + $1,190.75 + $1,176.05 + $1,088.93 = $5, 747.40

Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows:

Cash Flow (CF)

Frequency (F)

SM 6-21

Parrino et al. Fundamentals of Corporate Finance, 5th edition

1,225

1,350

1,500

1,600

Solutions Manual

Then solve by pressing NPV, enter the rate of 8% and compute NPV= 5,747.40. Excel solution method similar to Problem 6.4. LO: 1 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.6

Present value with multiple cash flows: Biogenesis Inc. management expects the following cash flow stream over the next five years. They discount all cash flows using a 23 percent discount rate. What is the present value of this cash flow stream?

Year

┼────────┼───────┼────────┼───────┤ -$1,133,676

-$978,452

$275,455

$878,326

$1,835,444

Solution: 0

23%

Year

├───────┼────────┼───────┼────────┼───────┤ -$1,133,676

-$978,452

$275,455

$878,326

$1,835,444

− $1,133,676 − $978,452 $275,455 $878,326 $1,835,444 + + + + (1.23) (1.23) 2 (1.23) 3 (1.23) 4 (1.23) 5 = −$921,687.80 − $646,739.37 + $148,025.09 + $383,738.43. + $651,951.94 = −$384,711.72

PV =

Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows:

SM 6-22

Parrino et al. Fundamentals of Corporate Finance, 5th edition

Cash Flow (CF)

Frequency (F)

-1,133,676

-978,452

275,455

878,326

1,835,444

Solutions Manual

Then solve by pressing NPV, enter the rate of 23% and compute NPV= - 384,711.72. Excel solution method similar to Problem 6.4. LO: 1 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.7

Present value of an ordinary annuity: An investment opportunity requires a payment of $750 for 12 years, starting a year from today. If your required rate of return is 8 percent, what is the value of the investment to you today?

Solution: 0

Year

├───────┼────────┼───────┼………………┼───────┤ $750

$750

Annual payment = PMT = $750 No. of payments = n = 12 Required rate of return = 8% Present value of investment = PVA12

SM 6-23

Parrino et al. Fundamentals of Corporate Finance, 5th edition

1−

1 (1 + i )n i

1−

1 (1.08)12 = $750  7.5361 0.08

PVA n = PMT 

= $750 

Solutions Manual

= $5, 652.06 Financial Calculator Solution: 12

750

PMT

-5,652.06 Excel solution method similar to Self-Study Problem 6.5. LO: 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.8

Present value of an ordinary annuity: Dynamics Telecommunications Corp. has made an investment in another company that will guarantee it a cash flow of $22,500 each year for the next five years. If the company uses a discount rate of 15 percent on its investments, what is the present value of this investment?

Solution: 0

15%

├───────┼────────┼───────┼────────┼───────┤ $22,500

$22,500

Annual payment = PMT = $22,500 No. of payments = n = 5 Required rate of return = 15% Present value of investment = PVA5

SM 6-24

Parrino et al. Fundamentals of Corporate Finance, 5th edition

1− PVA n = PMT 

Solutions Manual

1 (1 + i )n i

1− = $22,500 

1 (1.15)5 = $22,500  3.3522 0.15

= $75, 423.49 Financial Calculator Solution: 5

22,500

PMT

-75,423.49

Excel Template available in Wiley Course Resources Excel Template Solution available in Wiley Instructor Resources LO: 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.9

Future value of an ordinary annuity: Robert Hobbes plans to invest $25,000 a year at the end of each year for the next seven years in an investment that will pay him a rate of return of 11.4 percent. How much money will Robert have at the end of seven years?

Solution: 0

11.4%

Year

├───────┼────────┼───────┼………………┼───────┤ $25,000

$25,000

Annual investment = PMT = $25,000 No. of payments = n = 7 Investment rate of return = 11.4% Future value of investment = FVA7

SM 6-25

Parrino et al. Fundamentals of Corporate Finance, 5th edition

Solutions Manual

(1 + i)n − 1 FVA n = PMT  i (1.114)7 − 1 = $25,000  = $25,000  9.9044 0.114 = $247, 609.95 Financial Calculator Solution: 7

11.4

25,000

PMT

FV -247,609.95

Excel solution method: A

Given information/assumptions 3

Appropriate

11.4%

discount rate

Future Value of an Annuity showing the Timeline 6

Period

Cash Flows

Future Value

Future Value of an annuity using the Formula

Future Value

Future Value of an annuity using the FV

$25,000

$247,609.95

=+C7*(((1+B3)^F6)-1)/B3

Function 14

Future Value

$247,609.95

=-FV(B3,F6, C7,0,0)

LO: 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

SM 6-26

Parrino et al. Fundamentals of Corporate Finance, 5th edition

6.10

Solutions Manual

Future value of an ordinary annuity: Cecelia Thomas is a sales executive at a Baltimore firm. She is 25 years old and plans to invest $3,000 every year in an IRA account, beginning at the end of this year until she reaches the age of 65. If the IRA investment will earn 9.75 percent annually, how much will she have in 40 years, when she turns 65?

Solution: 0

9.75%

Year

├───────┼────────┼───────┼………………┼───────┤ $3,000

$3,000

Annual investment = PMT = $3,000 No. of payments = n = 40 Investment rate of return = 9.75% Future value of investment = FVA40

FVA n = PMT 

(1 + i)n − 1 i

= $3,000 

(1.0975)40 − 1 = $3,000  413.5588 0.0975

= $1, 240, 676.41 Financial Calculator Solution: 40

9.75

3,000

PMT

FV -1,240,676.41

Excel solution method similar to Problem 6.9. LO: 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

SM 6-27

Parrino et al. Fundamentals of Corporate Finance, 5th edition

6.11

Solutions Manual

Future value of an annuity due: Refer to Problem 6.10. If Cecelia Thomas invests at the beginning of each year, how much will she have at age 65?

Solution: 0

9.75%

Year

├───────┼────────┼───────┼………………┼───────┤ $3,000

$3,000

Annual investment = PMT = $3,000 No. of payments = n = 40 Type of annuity = Annuity due Investment rate of return = 9.75% Future value of investment = FVA40

FVA n = PMT 

(1 + i )n − 1  (1 + i) i

(1.0975)40 − 1 = $3,000   (1.0975) = $3,000  413.5588  1.0975 0.0975 = $1, 361, 642.36 Financial Calculator Solution: BGN Mode 40

9.75

3,000

PMT

FV -1,361,642.36

Excel solution method: A

Given information/assumptions 3

Appropriate

9.75%

discount rate

Future Value showing the timeline 6

Period

Cash Flows

Future Value

1 $3,000

2-38 $3,000

39 $3,000

40 $3,000

SM 6-28

Parrino et al. Fundamentals of Corporate Finance, 5th edition

Future Value of an annuity due using the Formula

Future Value

Future Value of an annuity due using the Function

Future Value

$1,361,642

Solutions Manual

=+C7*(((1+B3)^F6)-1)/B3*(1+B3)

=-FV(B3,F6, C7,0,1)

LO: 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.12

Computing annuity payment: Kevin Winthrop is saving for an Australian vacation in three years. He estimates that he will need $5,000 to cover his airfare and all other expenses for a week-long holiday in Australia. If he can invest his money in an S&P 500 equity index fund that is expected to earn an average annual return of 10.3 percent over the next three years, how much will he have to save every year if he starts saving at the end of this year?

Solution: 0

10.3%

Year

├───────┼────────┼───────┤ PMT

PMT

FVAn = $5,000

Future value of annuity = FVA = $5,000 Return on investment = i = 10.3% Payment required to meet target = PMT Using the FVA equation:

SM 6-29

Parrino et al. Fundamentals of Corporate Finance, 5th edition

Solutions Manual

(1 + i )n − 1 FVA n = PMT  i $5,000 = PMT  PMT =

(1.103)3 − 1 0.103

$5,000 $5,000 = 3 (1.103) − 1 3.3196 0.103

= $1, 506.20

Kevin has to save $1,506.20 every year for the next three years to reach his target of $5,000. Financial Calculator Solution: 3

10.3

-5,000 PMT

1,506.20 Excel solution method similar to Self-study Problem 6.3. LO: 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.13

Computing annuity payment: The Elkridge Bar & Grill has a seven-year loan of $23,500 with Bank of America. It plans to repay the loan in seven equal installments starting today. If the rate of interest is 8.4 percent, how much will each payment be?

Solution: 0

Year

├───────┼────────┼───────┼………………┼───────┤ PMT PVAn = $23,500

PMT

PMT n = 7;

PMT

i = 8.4%

SM 6-30

Parrino et al. Fundamentals of Corporate Finance, 5th edition

Solutions Manual

Payment required to meet target = PMT Type of annuity = Annuity due Using the PVA equation:

1− PVA n = PMT 

1 (1 + i )n  (1 + i ) i

$23,500 $23,500 = 1 5.1359  1.084 1− 7 (1.084)  (1.084) 0.084

PMT =

= $4, 221.07 Each payment made by Elkridge Bar & Grill will be $4,221.07, starting today. Financial Calculator Solution: 7

8.4

23,500 PMT

-4,221.07 Excel solution method: A

Given information/assumptions 3

Appropriate discount rate

8.4%

Cashflows showing the Timeline 6

Period

Cash Flows

Present Value

Cashflows using the Formula for an annuity due

Comments

Cash Flows

=+B8/((1-((1+B3)^-F6))/B3)/(1+B3)

Cashflows using the PMT Function for an annuity due

Cash Flows

CF=?

2------5 CF=?

6 CF=?

7 CF=?

$23,500

$4,221.07

($4,221.07)

=PMT(B3,F6,B8,0,1)

LO: 2

SM 6-31

Parrino et al. Fundamentals of Corporate Finance, 5th edition

Solutions Manual

Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.14

Perpetuity: Your grandfather is retiring at the end of next year. He would like to ensure that his heirs receive payments of $10,000 a year forever, starting when he retires. If he can earn 6.5 percent annually, how much does your grandfather need to invest to produce the desired cash flow?

Solution: Annual payment needed = PMT = $10,000 Investment rate of return = i = 6.5% Term of payment = Perpetuity Present value of investment needed = PV PV of Perpetuity =

PMT $10,000 = i 0.065

= $153, 846.15

LO: 3 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.15

Perpetuity: Calculate the annual cash flows for each of the following investments: a.

$250,000 invested at 6%

$50,000 invested at 12%

$100,000 invested at 10%

Solution: a.

Annual payment = PMT Investment rate of return = i = 6% Term of payment = Perpetuity

SM 6-32

Parrino et al. Fundamentals of Corporate Finance, 5th edition

Solutions Manual

Present value of investment needed = PV = $250,000

PV of Perpetuity =

PMT i

PMT = PV  i = $250, 000  0.06 . = $15, 000 b.

Annual payment = PMT Investment rate of return = i = 12% Term of payment = Perpetuity Present value of investment needed = PV = $50,000

PV of Perpetuity =

PMT i

PMT = PV  i = $50, 000  0.12 = $6, 000 c.

Annual payment = PMT Investment rate of return = i = 10% Term of payment = Perpetuity Present value of investment needed = PV = $100,000

PV of Perpetuity =

PMT i

PMT = PV  i = $100, 000  0.10 = $10, 000 LO: 3 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.16. Effective annual interest rate: Marshall Chavez bought a Honda Civic for $17,345. He put down $6,000 and financed the rest through the dealer at an APR of 4.9 percent for four years. What is the effective annual interest rate (EAR) if the loan payments are made monthly?

SM 6-33

Parrino et al. Fundamentals of Corporate Finance, 5th edition

Solutions Manual

Solution: Loan amount = PV = $11,345 Interest rate on loan = i = 4.9% Frequency of compounding = m = 12 Effective annual rate = EAR m

i   0.049  EAR = 1 +  − 1 = 1 + −1 12   m  = 1.0501 − 1 = 5.01%

LO: 5 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.17

Effective annual interest rate: Cyclone Rentals borrowed $15,550 from a bank for three years. If the quoted rate (APR) is 6.75 percent, and the compounding is daily, what is the effective annual interest rate (EAR)?

Solution: Loan amount = PV = $15,550 Interest rate on loan = i = 6.75% Frequency of compounding = m = 365 Effective annual rate = EAR m

i   0.0675  EAR = 1 +  − 1 = 1 + 365   m 

365

−1

= 1.0698 − 1 = 6.98%

LO: 5 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

SM 6-34

Parrino et al. Fundamentals of Corporate Finance, 5th edition

6.18

Solutions Manual

Growing perpetuity: You are evaluating a growing perpetuity investment from a large financial services firm. The investment promises an initial payment of $20,000 at the end of this year and subsequent payments that will grow at a rate of 3.4 percent annually. If you use a 9 percent discount rate for investments like this, what is the present value of this growing perpetuity?

Solution: Cash flow at t = 1 = CF1 = $20,000 Annual growth rate = g = 3.4% Discount rate = i = 9% Present value of growing perpetuity = PVA∞ PVA  =

CF1 $20,000 = (i − g) (0.09 − 0.034)

= $357,142.86

LO: 4 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

INTERMEDIATE 6.19

Future value with multiple cash flows: Trigen Corp. management will invest $331,000, $616,450, $212,775, $818,400, $1,239,644, and $1,617,848 in research and development over the next six years. If the appropriate interest rate is 6.75 percent, what is the future value of these investments eight years from today?

Solution: 0

6.75%

├───────┼────────┼───────┼────────┼───────┼────────┤ $331,000

$616,450

$212,775

$818,400

$1,239,644

$1,617,848

SM 6-35

Parrino et al. Fundamentals of Corporate Finance, 5th edition

Solutions Manual

 $331,000  (1.0675)5  + $616, 450  (1.0675)4  + $212,775  (1.0675)3     (1.0675)2 FV8 =    2 1  + $818, 400  (1.0675)  + $1,239,644  (1.0675)  + $1,617,848  = $458,846.49 + $800,514.85 + $258,835.74 + $932,612.84 + $1,323,319.97 + $1,617,848  (1.0675)2 = $5,391,977.89  (1.0675)2 = $6,144, 462.11

Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: Cash Flow (CF)

Frequency (F)

331,000

616,450

212,775

818,400

1,239,644

1,617,848

Then solve by pressing NPV, enter the rate of 6.75% and compute NPV=3,643,684.79. 8

6.75

3,643,684.79

PMT

FV -6,144,462.10

Excel solution method similar to Self-study Problem 6.2. LO: 1 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

SM 6-36

Parrino et al. Fundamentals of Corporate Finance, 5th edition

6.20

Solutions Manual

Future value with multiple cash flows: Stephanie Watson is 20 years old and plans to make the following investments beginning next year. She will invest $3,125 in each of the next three years and will then make investments of $3,650, $3,725, $3,875, and $4,000 over the following four years. If the investments are expected to earn 11.5 percent annually, how much will Stephanie have when she turns 30?

Solution: Expected rate of return = i = 11.5% Investment period = n = 7 years Future value of investment = FV

 $3,125  (1.115)6  + $3,125  (1.115)5  + $616, 450  (1.115)4           (1.115)3 FV7 =   + $3,650  (1.115)3  + $3,725  (1.115)2  + $3,875  (1.115)1  + $4,000         

= $6,004.81 + $5,385.48 + $4,830.03 + $5,059.61 + $4,631.01 + $4,320.63 + $4,000   (1.115)3 = $34,231.57  (1.115)3 = $47, 451.66

Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: Cash Flow (CF)

Frequency (F)

3,125

3,650

3,725

3,875

4,000

Then solve by pressing NPV, enter the rate of 11.5% and compute NPV=15,977.28. 10

11.5

15,977.28

PMT

FV -47,451.66

Excel solution method similar to Self-study Problem 6.2.

SM 6-37

Parrino et al. Fundamentals of Corporate Finance, 5th edition

Solutions Manual

LO: 1 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.21

Present value with multiple cash flows: Carol Jenkins, a lottery winner, will receive the following payments over the next seven years. She has been approached by an investor who will pay Carol a lump sum today for the rights to those future cash flows. If she can invest her cash flows in a fund that will earn 10.5 percent annually, how much should Carol require the investor to pay for the cash flows?

Year

├────┼─────┼─────┼──────┼─────┼──────┼─────┤ $200,000 $250,000 $275,000

$300,000 $350,000

$400,000

$550,000

Solution: Expected rate of return = i = 10.5% Investment period = n = 7 years Future value of investment = FV FV7 =

$200,000 $250,000 $275,000 $300,000 $350,000 $400,000 $550,000 + + + + + + (1.105)1 (1.105)2 (1.105)3 (1.105)4 (1.105)5 (1.105)6 (1.105)7

= $180,995.48 + $204,746.01 + $203,819.56 + $201,220.46 + $212, 449.96 +$219,728.47 + $273, 417.77 = $1, 496, 377.71

Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: Cash Flow (CF)

Frequency (F)

200,000

250,000

SM 6-38

Parrino et al. Fundamentals of Corporate Finance, 5th edition

275,000

300,000

350,000

400,000

550,000

Solutions Manual

Then solve by pressing NPV, enter the rate of 10.5% and compute NPV=1,496,377.71. Excel solution method similar to Self-study Problem 6.1. LO: 1 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.22

Computing annuity payment: Gary Whitmore is a high school sophomore. He currently has $7,500 in a savings account that pays 5.65 percent annually. Gary plans to use his current savings plus what he can save over the next four years to buy a car. He estimates that the car will cost $12,000 in four years. How much money should Gary save each year if he wants to buy the car?

Solution: Cost of car in four years = $12,000 Amount invested in money market account now = PV = $7,500 Return earned by investment = i = 5.65% Value of current investment in 4 years = FV4

FV4 = PV(1 + i)4 = $7,500(1.0565)4 = $9,344.14 Balance of money needed to buy car = $12,000 – $9,344.14 = $2,655.86 = FVA Payment needed to reach target = PMT

SM 6-39

Parrino et al. Fundamentals of Corporate Finance, 5th edition

Solutions Manual

(1 + i)n − 1 FVA = PMT  i PMT =

FVA $2,655.86 $2,655.86 = = n 4 (1 + i) − 1 (1.0565) − 1 4.351949 i 0.0565

= $610.27

Financial Calculator Solution: 4

5.65

-7,500

PMT

FV 9,344.14

Additional amount Gary needs to save in order to purchase the car in four years: $12,000 - $9,3441.14 = $2,655.86

5.65

2,655.86 PMT

-610.27 Excel solution method similar to Self-study Problem 6.3. LO: 1 Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.23

Growing annuity: Modern Energy Company owns several gas stations. Management is looking to open a new station in the western suburbs of Baltimore. One possibility that managers at the company are evaluating is to take over a station located at a site that has been leased from the county. The lease, originally for 99 years, currently has 73 years before expiration. The gas station generated a net cash flow of $92,500 last year, and the current owners expect an annual growth rate of 6.3 percent. If Modern Energy uses a discount rate of 14.5 percent to evaluate such businesses, what is the present value of this growing annuity?

SM 6-40

Parrino et al. Fundamentals of Corporate Finance, 5th edition

Solutions Manual

Time for lease to expire = n = 73 years Last year’s net cash flow = CF0 = $92,500 Expected annual growth rate = g = 6.3% Firm’s required rate of return = i = 14.5% Expected cash flow next year = CF1 = $92,500(1 + g) = $92,500(1.063) = $98,327.50 Present value of growing annuity = PVAn n   1.063 73  CF1   1 + g   $98,327.50 PVA n =  1 −  1 − =  (i − g)   1 + i   (0.145 − 0.063)   1.145  

= $1,199,115.85  0.995593 = $1,193, 831.54 LO: 4 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.24

Future value of an annuity due: Jeremy Denham plans to save $5,000 every year for the next eight years, starting today. At the end of eight years, Jeremy will turn 30 years old and plans to use his savings toward the down payment on a house. If his investment in a mutual fund will earn him 10.3 percent annually, how much will he have saved in eight years when he buys his house?

Solution: 0

10.3%

Year

├───────┼────────┼───────┼………………┼───────┤ $5,000

$5,000

Annual investment = PMT = $5,000 No. of payments = n = 8 Type of annuity = Annuity due

SM 6-41

Parrino et al. Fundamentals of Corporate Finance, 5th edition

Solutions Manual

Investment rate of return = 10.3% Future value of investment = FVA8  (1 + i )n − 1  FVA n = PMT    (1 + i) i    (1.103)8 − 1  = $5,000    (1.103) = $5,000  11.5612  1.103  0.103  = $63, 760.19

Financial Calculator Solution: BGN Mode 8

10.3

5,000

PMT

FV -63,760.19

Excel solution method similar to Problem 6.11. LO: 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.25

Present value of an annuity due: Grant Productions borrowed some money from the California Finance Company at a rate of 17.5 percent for a seven-year period. The loan calls for a payment of $1,540,862.19 each year beginning today. How much did Grant borrow?

Solution: 0

17.5%

├───────┼────────┼───────┼………………┼───────┤ PMT =$1,540,862.19 at the beginning of each year

Annual payment = PMT = $1,540,862.19 Type of annuity = Annuity due No. of payments = n = 7

SM 6-42

Parrino et al. Fundamentals of Corporate Finance, 5th edition

Solutions Manual

Required rate of return = 17.5% Present value of investment = PVA8 1− PVA n = PMT 

1 (1 + i )n  (1 + i) i 1−

= $1,540,862.19 

1 (1.175)7  (1.175) = $1,540,862.19  3.8663  1.175 0.175

= $6, 999, 999.98  $7, 000, 000

Financial Calculator Solution: BGN Mode

17.5

1,540,862.19

PMT

-6,999,999.98 Excel solution method: A

Given information/assumptions 3

Appropriate

17.5%

discount rate

Present Value of an annuity due showing the Timeline 6

Period

Cash Flows

$1,540,862.19

Present Value

Present Value of an annuity due using the Formula

Present Value

Present Value of an annuity due using the Function

Present Value

2…...........5 $1,540,862.19

$1,540,862.19

$7,000,000

=C7*((1-(1/(1+B3))^F6)/B3)*(1+B3)

=-PV(B3,F6,C7,0,1)

LO: 2

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Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.26

Present value of an annuity due: Sharon Kabana has won a state lottery and will receive a payment of $89,729.45 every year, starting today, for the next 20 years. If she invests the proceeds at a rate of 7.25 percent, what is the present value of the cash flows that she will receive? Round to the nearest dollar.

Solution: 0

7.25%

├───────┼────────┼───────┼………………┼───────┤ PMT = $89,729.45

at the beginning of each year

Annual payment = PMT = $89,729.45 Type of annuity = Annuity due No. of payments = n = 20 Required rate of return = 7.25% Present value of investment = PVA20 1− PVA n = PMT 

1 (1 + i)n  (1 + i) i 1−

= $89,729.45 

1 (1.0725)20  (1.0725) = $89,729.45  10.3912  1.0725 0.0725

= $999, 999.95  $1, 000, 000

Financial Calculator Solution: BGN Mode

7,25

89,729.45

PMT

-999,999.95 Excel solution method similar to Problem 6.25.

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LO: 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.27

Present value of an annuity due: You wrote a piece of software that does a better job of allowing computers to network than any other program designed for this purpose. A large networking company wants to incorporate your software into its systems and is offering to pay you $500,000 today, plus $500,000 at the beginning of each of the following six years, for permission to do this. If the appropriate interest rate is 6 percent, what is the present value of the cash flow stream that the company is offering you?

Solution: You are being offered a seven year annuity due. You can solve this problem several different ways. First, you can calculate the present value of each of the individual cash flows and then add the present values together. Second, you can use the annuity transformation method discussed in the chapter. Third, you can calculate the present value of an ordinary six-year annuity and then add $500,000 to that value. Of course you can also use your calculator or Excel to do the calculations for you. Below are the calculations for the annuity transformation method. PVA7 = CF × PV annuity factor = $500,000 × 5.5824 = $2,791,190.72

Annuity value due

= PVA7 × (1 + i) = $2,791,190.72 × 1.06 = $2,958,662.16

Financial Calculator Solution: BGN Mode

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500,000

PMT

PV -2,958,662.16

Excel solution method similar to Problem 6.25. LO: 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.28

Present value of an annuity: Suppose that the networking company in problem 6.27 will not start paying you until the first of new systems that uses your software is sold in two years. What is the present value of that annuity? Assume that the appropriate interest rate is still 6 percent.

Solution: Since the first cash flow will not be received for two years, the present value will be less than in problem 6.27. All you have to do to solve this problem is to discount the answer from problem 6.27 for two years. Annuity value = value of annuity value due/(1 + i)2 = $2,958,662/(1.06)2 = $2,633,198.79 This is also equal to the value of the regular annuity in problem 6.27, PVA7, discounted one year at 6 percent. Financial Calculator Solution: BGN Mode

2,958,662.16

PMT

-2,633,198.79 Excel solution method similar to Problem 6.27 discounted back an additional two years. LO: 2

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Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.29

Perpetuity: Calculate the present value of the following perpetuities: a. $1,250 discounted to the present at 7percent b. $7,250 discounted to the present at 6.33percent c. $850 discounted to the present at 20 percent

Solution: a.

Annual payment = PMT =$1,250 Investment rate of return = i = 7% Term of payment = Perpetuity Present value of investment needed = PV PV of Perpetuity =

PMT $1,250 = i 0.07

= $17, 857.14

Annual payment = PMT =$7,250 Investment rate of return = i = 6.33% Term of payment = Perpetuity. Present value of perpetuity = PV PV of Perpetuity =

PMT $7,250 = i 0.0633

= $114, 533.97

Annual payment = PMT =$850 Investment rate of return = i = 20% Term of payment = Perpetuity. Present value of investment needed = PV PV of Perpetuity =

PMT $850 = i 0.20

= $4, 250

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LO: 3 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.30

Effective annual interest rate: Find the effective annual interest rate (EAR) on each of the following: a. 6 percent compounded quarterly. b. 4.99 percent compounded monthly. c. 7.25 percent compounded semiannually. d. 5.6 percent compounded daily.

Solution: a.

Interest rate = i = 6% Frequency of compounding = m = 4 Effective annual rate = EAR m

i   0.06  EAR = 1 +  − 1 = 1 + −1 4   m  = 1.06136 − 1 = 6.14%

Interest rate = i = 4.99% Frequency of compounding = m = 12 Effective annual rate = EAR m

i   0.0499  EAR = 1 +  − 1 = 1 + −1 12   m  = 1.0511 − 1 = 5.11%

Interest rate = i = 7.25% Frequency of compounding = m = 2 Effective annual rate = EAR m

i   0.0725  EAR = 1 +  − 1 = 1 + −1 2   m  = 1.0738 − 1 = 7.38%

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Interest rate = i = 5.6% Frequency of compounding = m = 365 Effective annual rate = EAR m

i   0.056  EAR = 1 +  − 1 = 1 + 365   m 

365

−1

= 1.0576 − 1 = 5.76%

LO: 5 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.31

Effective annual interest rate: Which of the following investments has the highest effective annual interest rate (EAR)? a. A bank CD that pays 8.25 percent compounded quarterly. b. A bank CD that pays 8.25 percent compounded monthly. c. A bank CD that pays 8.45 percent compounded annually. d. A bank CD that pays 8.25 percent compounded semiannually. e. A bank CD that pays 8 percent compounded daily (on a 365-day per year basis).

Solution: a.

Interest rate on CD = i = 8.25% Frequency of compounding = m = 4 Effective annual rate = EAR m

i   0.0825  EAR = 1 +  − 1 = 1 + −1 4   m  = 1.08509 − 1 = 8.51%

Interest rate on CD = i = 8.25% Frequency of compounding = m = 12 Effective annual rate = EAR

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i   0.0825  EAR = 1 +  − 1 = 1 + −1 12   m  = 1.0857 − 1 = 8.57%

Interest rate on CD = i = 8.45% Frequency of compounding = m = 12 Effective annual rate = EAR m

i   0.0845  EAR = 1 +  − 1 = 1 + −1 1   m  = 1.0845 − 1 = 8.45%

Interest rate on CD = i = 8.25% Frequency of compounding = m = 2 Effective annual rate = EAR m

i   0.0825  EAR = 1 +  − 1 = 1 + −1 2   m  = 1.0842 − 1 = 8.42%

Interest rate on CD = i = 8% Frequency of compounding = m = 365 Effective annual rate = EAR m

i   0.08  EAR = 1 +  − 1 = 1 + 365   m 

365

−1

= 1.0833 − 1 = 8.33%

Investment b. (8.25% monthly) has the highest EAR. LO: 5 Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.32

Effective annual interest rate: You are considering three alternative investments: (1) a three-year bank CD paying 7.5 percent compounded quarterly; (2) a three-year bank CD paying 7.3 percent compounded monthly; and (3) a three-year bank CD paying 7.75

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percent compounded annually. Which investment has the highest effective annual interest rate (EAR)? Solution: (1)

Interest rate on CD = i = 7.5%

Frequency of compounding = m = 4 Effective annual rate = EAR i  EAR = 1 +   m

m1

 0.075  − 1 = 1 + −1 4  

= 1.0771 − 1 = 7.71%

(2)

Interest rate on CD = i = 7.3%

Frequency of compounding = m = 12 Effective annual rate = EAR i  EAR = 1 +   m

m1

 0.073  − 1 = 1 + −1 12  

= 1.0755 − 1 = 7.55%

(3)

Interest rate on CD = i = 7.75% Frequency of compounding = m = 1 Effective annual rate = EAR i  EAR = 1 +   m

m1

 0.0775  − 1 = 1 + −1 1  

= 1.0775 − 1 = 7.75%

Investment (3) The three-year bank CD paying 7.75 percent interest compounded annually has the highest effective yield. LO: 5 Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

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6.33

Solutions Manual

You have been offered the opportunity to invest in a project which is expected to provide you with the following cash flows: $4,000 in one year, $12,000 in two years, and $8,000 in three years. If the appropriate interest rates are 6 percent for the first year, 8 percent for the second year, and 12 percent for the third year, what is the present value of these cash flows?

Solution: The answer is $20,495.15. Calculated as follows:

PV =

$4,000 $12,000 $8,000 + + 1.06 (1.06 )(1.08 ) (1.06 )(1.08 )(1.12 )

= $3,773.58 + $10, 482.18 + $6,239.39 = $20, 495.15 If the interest rate is different each year, then you must perform the calculation in this way. What you are effectively doing here is discounting each cash flow one year at a time using the appropriate rate. For example, you discount the year three cash flow of $8,000 for one year at 12 percent: $8,000/1.12 = $7,142.86 You then discount this result for one year at 8 percent: $7,142.86/1.08 = $6,613.76 Finally, you get the present value of the $8,000 by discounting the above result by 6 percent: $6,613.76/1.06 = $6,239.40 The one cent difference from the number above is due to rounding. Financial calculator solution is not relevant in this case. LO: 1 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.34

Tirade Owens, a professional athlete, currently has a contract that will pay him a large amount in the first year of his contract and smaller amounts thereafter. He and his agent

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have asked the team to restructure the contract. The team, though reluctant, obliged. Tirade and his agent came up with a counteroffer. What are the present values of each of the three alternatives below using a 14 percent discount rate? Which of the three has the highest present value? Year

Current Contract

Team’s Offer

Counteroffer

$8,125,000

$4,000,000.00

$5,250,000.00

$3,650,000

$3,825,000.00

$7,550,000.00

$2,715,000

$3,850,000.00

$3,625,000.00

$1,822,250

$3,925,000.00

$2,800,000.00

Solution: Current Contract

PV =

$8,125,000 $3,650,000 $2,715,000 $1,822,250 + + + (1.14) (1.14)2 (1.14)3 (1.14)4

= $7,127,192.98 + $2,808,556.48 + $1,832,547.67 + $1,078,918.29 = $12, 847, 215.41 Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: Cash Flow (CF)

Frequency (F)

$8,125,000

$3,650,000

$2,715,000

$1,822,250

Then solve by pressing NPV, enter the rate of 14% and compute NPV=12,847,215.41. Team’s Offer

PV =

$4,000,000 $3,825,000 $3,850,000 $3,925,000 + + + (1.14) (1.14)2 (1.14)3 (1.14)4

= $3,508,771.93 + $2,943,213.30 + $2,598,640.34 + $2,323,915.09 = $11, 374, 540.65

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Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: Cash Flow (CF)

Frequency (F)

$4,000,000.00

$3,825,000.00

$3,850,000.00

$3,925,000.00

Then solve by pressing NPV, enter the rate of 14% and compute NPV=11,374,540.65.

Counteroffer

PV =

$5,250,000 $7,550,000 $3,625,000 $2,800,000 + + + (1.14) (1.14)2 (1.14)3 (1.14) 4

= $4,605,263.16 + $5,809, 479.84 + $2, 446,771.75 + $1,657,824.78 = $14, 519, 339.52 Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: Cash Flow (CF)

Frequency (F)

$5,250,000.00

$7,550,000.00

$3,625,000.00

$2,800,000.00

Then solve by pressing NPV, enter the rate of 14% and compute NPV=14,519,339.52. The counteroffer has the best value for the player. Excel solution method similar to Self-study Problem 1. LO: 1

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Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.35

Gary Kornig is 30 years old and wants to retire when he is 65. So far he has saved (1) $6,950 in an IRA account in which his money is earning 8.3 percent annually and (2) $5,000 in a money market account in which he is earning 5.25 percent annually. Gary wants to have $1 million when he retires. Starting next year, he plans to invest a fixed amount every year until he retires in a mutual fund in which he expects to earn 9 percent annually. How much will Gary have to invest every year to achieve his savings goal?

Solution: Investment (1) Balance in IRA investment = PV = $6,950 Return on IRA account = i = 8.3% Time to retirement = n = 35 years Value of IRA at age 65 = FVIRA

FVIRA = PV  (1 + i)n = $6,950  (1.083)35 = $113,235.03 Financial Calculator Solution: 35

8.3

6,950

PMT

FV -113,235.03

Investment (2) Balance in money market investment = PV = $5,000 Return on money market account = i = 5.25% Time to retirement = n = 35 years Value of money market at age 65 = FVMMA

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FVMMA = PV  (1 + i)n = $5,000  (1.0525)35 = $29,973.93 Financial Calculator Solution: 35

5.25

5,000

PMT

FV -29,973.93

Target retirement balance = $1,000,000 Future value of current savings = $113,235.03 + $29,973.93 = $143,208.96 Amount needed to reach retirement target = FVA = $856,774.04 Annual payment needed to meet target = PMT Expected return from mutual fund = i = 9%

 (1 + i )n − 1  FVA = PMT    i   PMT =

FVA $856,791.04 $856,791.04 = = n 215.711  (1 + i ) − 1   (1.09)35 − 1      i    0.09 

= $3, 971.94 Financial Calculator Solution: 35

856,792.04 PMT

-3,971.94 Excel solution method: A

Given information/assumptions 3

Discount rate of investment 1 (IRA)

8.30%

Discount rate of investment 2 (MM)

5.25%

Discount rate of investment 3 (MF)

9.00%

Cash flows shown on the Timeline 8

Period

Investment 1

$6,950

Investment 2

$5,000

32......63

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Additional investment in MF

Future Value desired at retirement

CF?

Solutions Manual

CF?

CF? $1,000,000

Future Value using the Formula

Comments

Future Value of investment 1

$113,235

=B9*(1+B3)^35

Future Value of investment 2

$29,974

=B10*(1+B4)^35

Total Value of investments 1 and 2

$143,209

=SUM(B15:B16)

Future Value using the FV Function 20

Future Value of investment 1

$113,235

=-FV(B3,35,0,B9,0)

Future Value of investment 2

$29,974

=-FV(B4,35,0,B10,0)

Total Value of investments 1 and 2

$143,209

=SUM(B20:B21)

Additional amount needed to reach retirement target

Cash flows using the Formula

$3,971.94

=+C24/(((((1+B5)^35)-1))/B5)

Cash flows using the PMT function

$3,971.94

=-PMT(B5,35,0,C24,0)

$856,791

=+F12-B17

LO: 1, 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.36 The top prize for the state lottery is $100,000,000. You have decided it is time for you to take a chance and purchase a ticket. Before you purchase the ticket, you must decide whether to choose the cash option or the annual payment option. If you choose the annual payment option and win, you will receive $100,000,000 in 25 equal payments of $4,000,000─one payment today and one payment at the end of each of the next 24 years. If you choose the cash payment, you will receive a one-time lump sum payment of $59,194,567.18. If you can invest the proceeds and earn 6 percent, which option should you choose? Solution: You should choose the lump sum option. To see this, all you have to do is calculate the present value of the cash flows from the annual payment option using the 6 percent

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discount rate. Since the annual payment option is like a 25- year annuity due, this value is:

PVA25 = CF × PV annuity factor = $4,000,000 × 12.7834 = $51,133,424.63 Annuity value due

= PVA25 × (1 + i) = $51,133,424.63 × 1.06 = $54,201,430.11

Financial Calculator Solution: BGN Mode 25

-4,000,000

PMT

PV 54,201.430.11

Since this is less than the $59,194,567.18 lump sum, you are better off taking the lump sum. Excel solution method: A

Given information/assumptions 3

Discount rate of annual payment

6.0%

option

Lottery options showing the Timeline 0

2…...........24

$4,000,000

Period

A. Annual Cash Flows

B. Present Value of lump sum

Present Value of an annuity due using the Formula

Present Value of A

Present Value of an annuity due using the Function

Present Value of A

$59,194,567.18

$54,201,430

=C7*((1-(1/(1+B3))^E6)/B3)*(1+B3)

=-PV(B3,E6,C7,0,1)

LO: 2

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Bloomcode: Anlysis AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.37

At what interest rate would you be indifferent between the cash and annual payment options in problem 6.36?

Solution: Using trial and error, you would be indifferent if you could only earn 5 percent from your investments. With this discount rate, the present value of the cash flows from the annual payment option equals the $59,194,567.18 lump sum. Annuity value due

= PVA25 × (1 + i)

$59,194,567.18

= PVA25 × (1.05)

PVA25 = $56,375,778.27

PVA25 = CF × PV annuity factor = $4,000,000 × 14.09394457 = $56,375,778.27 To determine the annuity factor you must use trial and error or use tables for the Present Value Factor for an Ordinary Annuity. The result is an interest rate of 5 percent. If you use your calculator or Excel to calculate the present value of the cash flows from the annual payment option, you will get exactly $59,194,567.18.

Financial Calculator Solution: BGN Mode 25 N

59,194,567.18

-4,000,000

PMT

5 Excel solution method: A

Lottery options showing the Timeline 3

Period

2…...........24

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$4,000,000

Solutions Manual

A. Annual Cash Flows

$4,000,000

B. Present Value of lump sum

Discount Rate that equates the two options using the RATE Function for an annuity due

Discount Rate

$59,194,567.18

5.00%

=RATE(E3,-B4,B5,0,1)

LO: 2 Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.38

Babu Baradwaj is saving for his son’s college tuition. His son is currently 11 years old and will begin college in seven years. Babu has an index fund investment of $7,500 that is earning 9.5 percent annually. Total expenses at the University of Maryland, where his son says he plans to go, currently total $15,000 per year, but are expected to grow at roughly 6 percent each year. Babu plans to invest in a mutual fund that will earn 11 percent annually to make up the difference between the college expenses and his current savings. In total, Babu will make seven equal investments with the first starting today and with the last being made a year before his son begins college. a. What will be the present value of the four years of college expenses at the time that Babu’s son starts college? Assume a discount rate of 5.5 percent. b. What will be the value of the index mutual fund when his son just starts college? c. What is the amount that Babu will have to have saved when his son turns 18 if Babu plans to cover all of his son’s college expenses? d. How much will Babu have to invest every year in order to have enough funds to cover all his son’s expenses?

Solution: Annual cost of college tuition today (t = 0) = $15,000 Expected increase in annual tuition costs = g = 6% a.

Four-year tuition costs (t = 7 to t = 10) Years from now

Future value calculation

Tuition costs

$15,000(1.06)7

$22,554.45

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$15,000(1.06)8

$23,907.72

$15,000(1.06)9

$25,342.18

$15,000(1.06)10

$26,862.72

Discount rate = i = 5.5% Present value of tuition costs = PV

PV =

$22,554.45 $23,907.72 $25,342.18 $26,862.72 + + + (1.055) (1.055)2 (1.055)3 (1.055)4

= $21,378.63 + $21, 479.95 + $21,581.75 + $21,684.03 = $86,124.36 Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: Cash Flow (CF)

Frequency (F)

$22,554.45

$23,907.72

$25,342.18

$26,862.72

Then solve by pressing NPV, enter the rate of 5.5% and compute NPV=86,124.36

Future value of the index mutual fund at t = 7 Present value of index fund investment = PV = $7,500 Return on fund = i = 9.5% Future value of investment = FV

FV = PV  (1 + i)n = $7,500  (1.095)7 = $14,156.64 Financial Calculator Solution: 7

9.5

7,500

PMT

FV -14,156.64

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Target savings needed at t = 7 PV of tuition costs – Future value of investment

= $86,124.36 – $14,156.64 = $71,967.72

Annual savings needed Return on fund = i = 11% Amount that needs to be saved = FVA = $71,967.72 Annuity due payment needed = PMT FVA of annuity due = PMT  PMT =

(1 + i )n − 1  (1 + i ) i

FVA $71,967.72 $71,967.72 = = 7 (1 + i ) − 1 (1.11) − 1 9.7833  1.11  (1 + i )  (1.11) i 0.11 n

= $6, 627.21

Financial Calculator Solution: BGN Mode 7

71,967.72 PMT

-6,627.21 Excel solution method:

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12--------17

Given information/assumptions 3

Discount rate of existing investment (IF)

9.50%

Growth rate of tuition

6.00%

Discount rate of new investment (MF)

11.00%

Discount rate for tuition costs

5.50%

Cash flows shown on the Timeline 9

Period

Investment in Index Fund

$7,500

Current College Tuition

$15,000

Additional investment in MF

Expected College Tuition expenses

a. Present Value of college expenses at time 18

Tuition Expenses

Formula for Tuition Expenses

Present Value using Formula

$86,124.36

=+D16/(1+B6)+E16/(1+B6)^2+F16/(1+B6)^3+G16/(1+B6)^4

Present Value using NPV Function

$86,124.36

=NPV(B6,D16:G16)

b. Future Value of Index Fund at time 18

Future Value using formula at t=7

$14,156.64

=+B10*(1+B3)^7

Future Value using FV Function at t=7

$14,156.64

=-FV(B3,7,0,B10,0)

c. Target of Savings needed at age 18, or t=7

Present Value at t=7

$71,967.73

=+C18-C22

CF?

PMT 19?

PMT 20?

PMT 21?

$22,554

$23,908

$25,342

$26,863

=B11*(1+B4)^7

=B11*(1+B4)^8

=B11*(1+B4)^9

CF? PMT 18?

Comments

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Solutions Manual

d. Additional annual amount needed to make up the difference between college expenses and current savings

Cash flows using the Formula (CF?)

$6,627.21

=+C26/((((1+B5)^7-1)/B5)*(1+B5))

Cash flows using the PMT function (CF?)

$6,627.21

=-PMT(B5,7, 0, C26,1)

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LO: 1, 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.39

You are now 50 years old and plan to retire at age 65. You currently have a stock portfolio worth $150,000, a 401(k)-retirement plan worth $250,000, and a money market account worth $50,000. Your stock portfolio is expected to provide annual returns of 12 percent, your 401(k) investment will earn 9.5 percent annually, and the money market account earns 5.25 percent, compounded monthly. a. If you do not save another penny, what will be the total value of your investments when you retire at age 65? b. Assume you plan to invest $12,000 every year in your 401(k) plan for the next 15 years (starting one year from now). How much will your investments be worth when you retire at age 65? c. Assume that you expect to live 25 years after you retire (until age 90). Today, at age 50, you take all of your investments and place them in an account that pays 8 percent (use the scenario from part b in which you continue saving). If you start withdrawing funds starting at age 66, how much can you withdraw every year (e.g., an ordinary annuity) and leave nothing in your account after a 25th and final withdrawal at age 90? d. You want your current investments, which are described in the problem statement, to support a perpetuity that starts a year from now. How much can you withdraw each year without touching your principal?

Solution: a.

Stock Portfolio Current value of stock portfolio = $150,000 Expected return on portfolio = i = 12% Time to retirement = n = 15 years Expected value of portfolio at age 65 = FVStock

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FVStock = PV  (1 + i)15 = $150,000  (1.12)15 = $821,034.86 Financial Calculator Solution: 15

150,000

PMT

FV -821,034.86

410(k) Investment Current value of 410(k) portfolio = $250,000 Expected return on portfolio = i = 9.5% Time to retirement = n = 15 years Expected value of portfolio at age 65 = FV401k

FV401k = PV  (1 + i)15 = $250,000  (1.095)15 = $975,330.48 Financial Calculator Solution: 15

9.5

250,000

PMT

FV -975,330.48

Money market account Current value of savings = $50,000 Expected return on portfolio = i = 5.25% Time to retirement = n = 15 years Frequency of compounding = m = 12 Expected value of portfolio at age 65 = FVMMA i   FVMMA = PV   1 +   m

mn

1215

 0.0525  = $50,000   1 + 12  

= $50,000  2.1941 = $109,706.14

Financial Calculator Solution: 15*12

5.25/12

50,000

PMT

FV -109,706.14

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Total value of all three investments = $821,034.86 + $975,330.48 + $109,706.14 = $1,906,071.48

Planned annual investment in 401k plan = $12,000 Future value of annuity = FVA  (1 + i )n − 1  FVA n = PMT    i    (1.095)15 − 1  = $12,000    = $12,000  30.5402  0.095  = $366, 482.77

Financial Calculator Solution: 15

9.5

12,000

PMT

FV -366,482.77

Total investment amount at retirement

= $1,906,071.48 + $366,482.77 = $2,272,554.25

Amount available at retirement = PVA = $2,272,554.25 Length of annuity = n = 25 Expected return on investment = i = 8% Annuity amount expected = PMT Using the PVA equation: 1    1 − (1 + i )n  PVA n = PMT    i     PMT =

$2,272,554.25 $2,272,554.25 = 1  10.6748   1 − (1.08)25     0.08   

= $212, 889.63

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Each payment received for the next 25 years will be $212,889.63.

Financial Calculator Solution: 25

-2,272,554.25

0 PMT

212,890.11 The difference is due to rounding.

Type of payment = Perpetuity Present value of perpetuity = PVA = $2,272,554.25 Expected return on investment = i = 8% PV of Perpetuity =

PMT i

$2,272,554.25 =

PMT 0.08

PMT = $2,272,554.25  0.08 = $181, 804.34

You could receive an annual payment of $181,804.34 forever. Excel solution method: A

Given information/assumptions 3

Expected returns on stock

12.00%

portfolio 4

Expected returns on 401(k)

9.50%

Expected returns on Money

5.38%

5.25% monthly annualized = ((1+0.0525/12)^12) - 1

Market Account

Cash flows shown on the Timeline 8

Age

51-------64

67--89

Period

1--------14

17--39

Stock Portfolio

$150,000

401(k)-retirement plan

$250,000

Money Market Fund

$50,000

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$12,000

Solutions Manual

Additional annual investments in 401 (k)

$12,000

Expected lifespan needs

a. Future Value of current savings at age 65, t=15

Future Value using formula

$1,906,071

Future Value using FV

$1,906,071 =-(FV(B3,15,0,B10,0)+FV(B4,15,0,B11,0)+FV(B5,15,0,B12,0))

PMT?

Comments

=+B10*(1+B3)^15+ B11*(1+B4)^15+B12*(1+B5)^15

function 20

b. Future Value of 401(k) at age 65, t= 15, assuming you make an additional annual investment of $12,000

Future Value using formula

$366,483

=+C13*(((1+B4)^15)-1)/B4

Future Value using FV

$366,483

=-FV(B4, 15, C13,0,0)

Function 23

Total Value assuming

$2,272,554

=+B17+B21

additions 25

c. Withdrawals allowed from savings until age 90, t=25 assuming account earns 8%

Cash Flows from annuity

$212,890

=+B23/(((1-(1/((1.08)^25)))/0.08))

$212,890

=-PMT(0.08,25,B23,0,0)

using formula 27

Cash Flows from annuity using PMT function

d. Based on all investments, amount available for a perpetuity assuming account earns 8%

Cash flows using the Formula

$181,804

=+B23*0.08

LO: 1, 2, 3 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.40

Trevor Diaz wants to purchase a Maserati Qattroporte sedan, which has an invoice price of $121,737 and a total cost of $129,482. Trevor plans to put down $20,000 and will pay the rest by taking on a 5.75 percent five-year bank loan. What is the monthly payment on this auto loan? Prepare an amortization table using Excel.

Solution:

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Cost of new car = $129,482 Down payment = $20,000 Loan amount = $129,482 – $20,000 = $109,482 Interest rate on loan = i = 5.75% Term of loan = n = 5 years Frequency of payment = m = 12 Monthly payment on loan = PMT 1− PVA n = PMT  PMT = 1−

1 (1 + i )n i

$109, 482 1

$109, 482 52.0379

125

 0575   1 + 12    0.0575 12

= $2,103.89

Financial Calculator Solution: 60

5.75/12

109,482

0 PMT

2,103.89

Show a portion of an Excel amortization table for this loan as follows:

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Excel solution method: A

End Month

Beg. Bal

Payment

Principal

Interest

Balance

Terms

$109,482.00

$2,103.89

$1,579.29

$524.60

$107,902.71

Rate

$107,902.71

$2,103.89

$1,586.86

$517.03

$106,315.85

Months

$106,315.85

$2,103.89

$1,594.46

$509.43

$104,721.39

Borrowed Amount

$104,721.39

$2,103.89

$1,602.10

$501.79

$103,119.29

$2,103.89

$1,609.78

$494.11

$101,509.52

$2,103.89

$1,617.49

$486.40

$99,892.03

5.75% 60 $109,482

Excel formulae: A

Payment

Principal

Interest

End Balance

Beg. Month

Bal

=+I5

=-PMT($I$3/12,$I$4,$I$5,0,0)

=-PPMT($I$3/12,A3,$I$4,$I$5,0,0)

=-IPMT($I$3/12,A3,$I$4,$I$5,0,0)

=B3-D3

=+F3

=-PMT($I$3/12,$I$4,$I$5,0,0)

=-PPMT($I$3/12,A2,$I$4,$I$5,0,0)

=-IPMT($I$3/12,A4,$I$4,$I$5,0,0)

=B4-D4

=+F4

=-PMT($I$3/12,$I$4,$I$5,0,0)

=-PPMT($I$3/12,A3,$I$4,$I$5,0,0)

=-IPMT($I$3/12,A5,$I$4,$I$5,0,0)

=B5-D5

=+F5

=-PMT($I$3/12,$I$4,$I$5,0,0)

=-PPMT($I$3/12,A4,$I$4,$I$5,0,0)

=-IPMT($I$3/12,A6,$I$4,$I$5,0,0)

=B6-D6

=+G6

=-PMT($I$3/12,$I$4,$I$5,0,0)

=-PPMT($I$3/12,A5,$I$4,$I$5,0,0)

=-IPMT($I$3/12,A7,$I$4,$I$5,0,0)

=B7-D7

=+G7

=-PMT($I$3/12,$I$4,$I$5,0,0)

=-PPMT($I$3/12,A6,$I$4,$I$5,0,0)

=-IPMT($I$3/12,A8,$I$4,$I$5,0,0)

=B8-D8

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LO: 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.41

The Yan family is buying a new 3,500-square-foot house in Muncie, Indiana, and will borrow $237,000 from Bank One at a rate of 6.375 percent for 15 years. What will be their monthly loan payment? Prepare an amortization schedule using Excel.

Solution: Home loan amount = $237,000 Interest rate on loan = i = 6.375% Term of loan = n = 15 years Frequency of payment = m = 12 Monthly payment on loan = PMT 1− PVA n = PMT 

$237,000 1

PMT = 1−

1 (1 + i )n i

1215

0.06375    1 + 12    0.06375 12

$237,000 = $2, 048.27 115.7072

Financial Calculator Solution: 180

6.375/12

-237,000

0 PMT

2,048.27

One can find an Excel amortization table for this loan on multiple websites. Excel Template available in Wiley Course Resources

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Excel Template Solution available in Wiley Instructor Resources LO: 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.42

Assume you are now 21 years old and will start working as soon as you graduate from college. You plan to start saving for your retirement on your 25th birthday and retire on your 65th birthday. After retirement, you expect to live at least until you are 85. You wish to be able to withdraw $40,000 (in today’s dollars) every year from the time of your retirement until you are 85 years old (i.e., for 20 years). The average inflation rate is likely to be 5 percent. a. Calculate the lump sum you need to have accumulated at age 65 to be able to draw the desired income. Assume that your annual return on your investment is likely to be 10 percent. b. What is the dollar amount you need to invest every year, starting at age 26 and ending at age 65 (i.e., for 40 years, to reach the target lump sum at age 65? c. Now answer questions a. and b. assuming the rate of return to be 8 percent per year, then again at 15 percent per year. d. Now assume you start investing for your retirement when you turn 30 years old and analyze the situation under rate of return assumptions of (i) 8 percent, (ii) 10 percent, and (iii) 15 percent. e. Repeat the analysis by assuming that you start investing only when you are 35 years old.

Solution: a. If the student is 21, then the first withdrawal will be 40,000(1+.05)45=$359,400.312. Then, withdrawals grow at 5% per year thereafter (a spreadsheet is helpful here).

Next, find the NPV of the anticipated retirement withdrawals at each anticipated interest rate. This is the lump sum needed at retirement. This can be done with a spreadsheet or

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alternatively, with the formula for the present value of a growing annuity as follows to find the present value of withdrawals: 20 359,400.312   1.05   PVAn = x 1 −    = 4,353,086.79 .1 − .05   1.1  

Financial calculator solution is not possible. b. Find the annuity payment that will generate that lump sum at the end of the student’s working life. Assume 40 years of saving.

PMT = FVAn /[{(1 + i)40 − 1})/i] = $4,353,086.79/[{(1.1)40 − 1}/i] = $4,353,086.79/442.5926 = $9,835.43

Financial Calculator Solution: 40

4,353,086.79 PMT

-9,835.43

For questions c, d, and e, use the spreadsheet for the changing assumptions of 35 years of saving (at age 30) and 30 years of saving (at age 35) at additional interest rates of 8% and 15%.

RETIREMENT ANALYSIS SUMMARY INVESTMENT AGE = 25

INVESTMENT AGE = 30

INVESTMENT AGE = 35

Rate of Return

10%

15%

Inflation

10%

15%

10%

15%

$3,011,353

$5,160,266

$4,353,087

$3,011,353

rate Retirement Income

$40,000

Level

Lump sum

$5,160,266

$4,353,087

$3,011,353

$5,160,266

$4,353,087

needed at age 65

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Annuity payment

$19,919

$9,835

$1,693

$29,946

$16,062

$3,417

$45,552

$26,463

$6,927

needed

LO: 1, 2, 3 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

Sample Test Problems 6.1

Freisinger, Inc., is expecting a new project to start paying off, beginning at the end of next year. It expects cash flows to be as follows:

7.8%

├───────┼────────┼───────┼────────┼───────┤ $433,676

$478,452

$475,455

$478,326

$535,444

If Freisinger can reinvest these cash flows to earn a return of 7.8 percent, what is the future value of this cash flow stream at the end of five years? What is its present value? Solution:

FV5 = $433,676  (1.078)4  + $478, 452  (1.078)3  + $475, 455  (1.078)2  + $478,326  (1.078)1  +$535, 444 = $585,653.08 + $599,369.52 + $552,518.65 + $515,635.43 + $535, 444 = $2, 788, 620.68

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PV= $433,676 / 1.078  + $478, 452 / (1.078)2  + $475, 455 / (1.078)3  + $478,326 / (1.078)4  + [$535, 444 / (1.078)5 ] = $402,296.85 + $411,718.95 + $379,536.14 + $354,200.32 + $367,807.22 = $1, 915, 559.47

Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: Cash Flow (CF)

Frequency (F)

433,676

478,452

475,455

478,326

535,444

Then solve by pressing NPV, enter the rate of 7.8% and compute NPV=1,915,559.47.

7.8

1,915,559.47

PMT

FV -2,788,620.68

Spreadsheet Solution: Since there is no NFV function in an Excel spreadsheet, first use the formula NPV, then FV: =NPV(0.078,433676,478452,475555,478326,535444) to find the present value, and then use the formula =FV(0.078,5,0, -1915559.47)= 2,788,620.68. LO: 1 Level: Intermediate Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

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Compare an annuity due with an ordinary annuity. The payments for both are made annually and are of the same dollar amounts. The two annuities also have the same duration in years and the same discount rate. Which of the following statements is /are correct? a. The present value of the ordinary annuity is greater. b. The present value of the annuity due is greater. c. The future value of the ordinary annuity is greater. d. The future value of the annuity due is greater.

Solution: b and d are both correct The cash flows of the annuity due are received at the beginning of the period, resulting in less discounting and a higher PV, and more compounding resulting in a higher FV. LO: 2 Level: Intermediate Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.3

You plan to set up an endowment at your alma mater that will fund $200,000 of scholarships each year indefinitely. If the principal (the amount you donate) can be invested at 5.5 percent, compounded annually, how much do you need to donate to the university today, so that the first scholarships can be awarded beginning one year from now?

Solution: Annual payment needed = PMT = $200,000 Investment rate of return = i = 5.5% Term of payment = Perpetuity Present value of investment needed =

PV of Perpetuity =

PMT $200,000 = i 0.055

= $3, 636, 363.64

LO: 3

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Level: Intermediate Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.4

Annalise Genric wants to open a restaurant in a historic building. The property can be leased for 20 years, but not purchased. She believes her restaurant can generate a net cash flow of $76,000 the first year and expects an annual growth rate of 4 percent thereafter. If a discount rate of 15 percent is used to evaluate this business, what is the present value of the cash flows that it will generate?

Solution: Length of lease = n = 20 years Next year’s net cash flow = CF1 = $76,000 Expected annual growth rate = g = 4% Required rate of return = i = 15% Present value of growing annuity = PVAn

PVA n =

n   1.04 20  CF1   1 + g   $76,000  1 −  =   1 −  (i − g)   1 + i   (0.15 − 0.04)   1.15  

= $690,909  0.86612 = $598, 410.10 LO: 4 Level: Intermediate Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.5

A credit card offers financing at an APR of 18 percent, with monthly compounding on outstanding charges. What is the effective annual rate (EAR)?

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Solution: Interest rate = i = 18% Frequency of compounding = m = 12 Effective annual rate = EAR m

i   0.18  EAR = 1 +  − 1 = 1 + −1 12   m  = 1.1956 − 1 = 0.1956,or19.56 percent

LO: 5 Level: Intermediate Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.6

Thomas Nguyen currently has $10,000 in the bank earning interest of 6 percent per year, compounded monthly. If he needs $25,000 to purchase a car and can save an additional $100 a month stating at the end of this month, how long will it take him to accumulate the $25,000?

Solution: months 0

├───────┼────────┼───────┼────────┤……………. $10,000

$100

$100 $25,000

Monthly payment = CF = $100 Present Value = PV = 10,000 Future Value = FV = 25,000 Annual rate of return = i = 6% Payments per year = m = 12 Type of annuity = Ordinary Annuity Using the FVA equation and the equation for the FV of a single amount:

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nm   i  nm  1 +  −1  i  m     FV = CF  + PV   1 +  = i    m   m  

  0.06 n  m  −1  nm  1 + 0.06  12      $25,000 = $100  + $10,000   1 + 0.06   12     12  

 0.06  $25,000 = $20,000   1 + 12  

nm

 0.06  $45,000 = $30,000   1 + 12  

nm

 0.06  − $20,000 + $10,000   1 + 12  

nm

 $45,000   0.06  ln  = n  m  ln  1 +  12    $30,000  n m=

ln (1.5 )

ln (1.005 )

= 81.3 months

Solving for n × m yields: n × m = 81.3 months It will take Shannon 81.3 months or 6.8 years to save the $25,000. Financial Calculator Solution:

6/12

10,000

100

-25,000

PMT

81.296

It will take Shannon 81.3 months or 6.8 years to save the $25,000. Spreadsheet Solution: Using a spreadsheet, enter the formula =NPER(0.06/12,-100,-10000,25000). LO: 2 Level: Intermediate

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Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

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Appendix: Deriving the Formula for the Present Value of an Ordinary Annuity In this chapter we showed that the formula for a perpetuity can be obtained from the formula for the present value of an ordinary annuity if n is set equal to ∞. It is also possible to go the other way. In other words, the present value of an ordinary annuity formula can be derived from the formula for a perpetuity. In fact, this is how the annuity formula was originally obtained. To see how this was done, assume that someone has offered to pay you $1 per year forever, beginning next year, but that, in return, you will have to pay that person $1 per year forever, beginning in year n + 1. The cash flows for the perpetuity that will receive is worth: PVPReceive = $1/i = CF/i

The present value of the cash flows for the $1 perpetuity that you will owe or will need to pay discounted for n years: PVPPay = ($1/i)/(1+i)n = (CF/i)/(1+i)n

Solving for the difference between PVPReceive and PVPPay we see that this is the same as Equation 6.1:

PVA n =

CF  1   1 −  i  (1 + i )n   

1   1 − 1 + i n  ( )  = CF     i    

Problem 6A.1

In the chapter text, you saw that the formula for a growing perpetuity can be obtained from the formula for the present value of a growing annuity if n is set equal to ∞. It is also possible to go the other way. In other words, the present value

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of a growing annuity formula can be derived from the formula for a growing perpetuity. In fact, this is how Equation 6.5 was actually derived. Show how Equation 6.5 can be derived from Equation 6.6. Solution: In this problem, you will receive an annual payment that grows at a rate of g forever. In return, you will have to pay that person $1(1 + g)n each year forever, beginning in year n + 1. The cash flows that you will receive can be represented as in the following time line.

n-1

Receive

$1(1+g) $1(1+g)2……$1(1+g)n-2

Pay

n+1

n+2

∞

$1(1+g)n-1 $1(1+g)n $1(1+g)n $1(1+g)n

The first time line shows the cash flows for the perpetuity that you will receive. This perpetuity is worth:

PVReceive =

$1 CF = ( i − g ) (i − g)

The second time line shows the cash flows for the perpetuity that you will pay. The present value of what you owe is:

PVOwe =

$1 (1 + g) n (i - g)

(1 + i )

CF  (1 + g)n (i - g) = (1 + i )n

Notice that if you subtract, year-by-year, the cash flows you would pay from the cash flows you would receive, you get the cash flows for an n-year annuity.

n–1

n+1 n+2

∞

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Solutions Manual

Difference $1 $1(1 + g) $1(1 + g)2………$1(1 + g)n-2 $1(1 + g)n-1 $0

Therefore, the value of the offer equals the value of an n-year growing annuity. Solving for the difference between PVOwe from PVRe ceive ,we see that this is the same as Equation 6.5.

CF(1 + g)n n CF CF   1 + g   (i − g) PVReceive − PVOwe = − =  1 −  (i − g) (1 + i )n (i − g)   1 + i   The limit of [(1+g)/(1+i)]n will be zero. The growth rate in perpetuity must always be less that the interest rate which makes intuitive sense. The numerator therefore will always be less than the denominator and when n is set to infinity the numerator divided by the denominator will tend to zero. Therefore, as n tends to infinity the resultant limit of Equation 6.5 is Equation 6.6. LO: 4 Level: Advanced

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Chapter 5 The Time Value of Money Before You Go On Questions and Answers Learning Objective 5.1 1.

Why is a dollar today worth more than a dollar one year from now? A dollar is worth more today than one year from now, due to its potential earning capacity. If you have the money in your hand today, you have the opportunity to invest it and earn interest or you can purchase goods and services for your immediate consumption. Given that people have a positive preference for consumption, time value of money holds true.

What is a time line, and why is it important in financial analysis? A time line is a horizontal line that starts at time zero (today) and shows cash flows as they occur over time. It is an important tool used to analyze cash flows over certain time periods, as the timing of each cash flow has a big impact on the final amount, and therefore, on the resulting initial investment decision.

Learning Objective 5.2 1.

What is compounding, and how does it affect the future value of an investment? Compounding is the process that refers to converting the initial (principal) amount into a future value. In order to obtain the future value of the principal amount, you calculate what the value of that amount will be at the end of the time period, assuming the initial investment will earn interest and that interest is re-invested and earns additional interest in future periods.

What is the difference between simple interest and compound interest? The effect of compounding, where interest is earned on interest, makes an investment grow to a larger value than it would if it only paid simple interest. Simple interest is interest earned only on the original principal.

How does changing the compounding period affect the amount of interest earned on an investment? The more frequent the compounding schedule, the higher the amount of interest earned. For example, $100 invested for one year at 10 percent compounded annually will earn

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you $10 of interest at the end of the year, but if your bank compounded interest quarterly, your earnings from interest would increase to $10(1+0.10/4)4 = $10.38.

Learning Objective 5.3 1.

What is the present value, and when is it used? Present value is the amount a future sum is worth today, given a certain rate of return. The present value concept should be used when calculating how much money you need today in order to reach your financial goal sometime in the future.

What is the discount rate? How does the discount rate differ from the interest rate in the future value equation? The discount rate is the rate of return used in a discounted cash flow analysis to determine the present value of future cash flows. Both discount and interest rates essentially represent the same concept. The only difference is the context in which they are used.

What is the relation between the present value factor and the future value factor? The present value factor is the reciprocal of the future value factor. To obtain the present value factor, you divide 1 by the future value factor (1 + i)n.

Explain why you would expect the discount factor to be smaller when based on the longer the time to payment. The discount factor will become smaller the longer the time to payment because of the time value of money. The longer you have to wait to obtain the money, the less value it will have to you. Mathematically, the discount factor is calculated as 1/(1 + i)n. The longer the time to payment, the larger n gets, the smaller the discount factor.

Learning Objective 5.4 1.

What is the difference between the interest rate (i) and the growth rate (g) in the future value equation? The interest rate and the growth rate in the future value equation essentially represent the same concept. The growth rate is used when we deal with numerical values such as changes in sales or over time. When referring to money being invested, we use the term interest rate.

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5.1

Amit Patel is planning to invest $10,000 in a bank certificate of deposit (CD) for five years. The CD will pay interest of 9 percent. What is the future value of Amit’s investment? Solution: Present value of the investment = PV = $10,000 Interest rate = i = 9% Number of years = n = 5. 0 i = 9% 1 2 3 4 5 Years ├───┼───┼───┼────┼───┤ -$10,000 FV5=?

FVn = PV(1 + i ) n FV5 = $10,000(1 + 0.09)5 = $15, 386.24 Financial Calculator Solution: 5 N

9 i

-10,000 PV

0 PMT

FV 15,386.24

Excel solution method uses FV formula/function A

Given information/assumptions Present value of the investment

4 5

Interest rate Number of years (n)

8 9 10

Future Value showing the Timeline Period Cash Flows Future Value

Future Value using the Formula

Future Value

$15,386.24

=-$B$9*((1+$B$4)^$G$8)

15 16

Future Value using the FV Function Future Value $15,386.24

=-FV($B$4,$B$5,0,$B$3,0)

$10,000 9% 5

0 ($10,000)

5 ?

Comments

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5.2

Megan Gaumer expects to need $50,000 for a down payment on a house in six years. How much does she need to invest today in an account paying 7.25 percent in order to have $50,000 in six years? Solution: Amount Megan will need in six years = FV6 = $50,000 Number of years = n = 6 Interest rate = i = 7.25% Amount needed to be invested now = PV = ? i = 7.25%

0 1 2 3 4 5 6 Year ├───┼───┼───┼────┼───┼───┤ PV = ? FV6 = $50,000 FV

PV = (1+𝑖)𝑛 𝑛 =

$50,000 (1+0.0725)6

= $32,853.84 Financial Calculator Solution: 6 N

7.25 i

PV -32,853.84

0 PMT

50,000 FV

Excel solution method uses PV formula/function A

Given information/assumptions

3 Future value of the down payment 4 Interest rate 5 Number of years (n)

$50,000 7.25% 6

Present Value showing the Timeline

8 Period 9 Cash Flows 10 Present Value 12 Present Value using the Formula 13 Present Value

6 $50,000

? Comments (32,853.84)

=-$B$3/(1+$B$4)^$B$5

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15 Present Value using the PV Function (32,853.84) 16 Present Value

Solutions Manual

=PV($B$4,$B$5,0,$B$3,0)

5.3

Kelly Martin has $10,000 that she can deposit into a savings account for five years. Bank A pays compounds interest annually, Bank B twice a year, and Bank C quarterly. Each bank has a quoted annual interest rate of 4 percent. What account balance would Kelly have at the end of the fifth year if she left all the interest paid on the deposit in each bank? Solution: Present value of Kelly’s deposit = PV = $10,000 Number of years = n = 5 Interest rate = i = 4% Compound period m: A=1 B=2 C=4 Amount at the end of 5 years = FV5 = ? 0 i = 4% 1 2 3 4 5 Year ├───┼───┼───┼────┼───┤ -$10,000 FV5 = ? A:

FVn FV5

= PV × (1 + i/m)m x n = 10,000 × (1 + 0.04/1)1 x 5 = $12,166.53

FV5

= 10,000 × (1 + 0.04/2)2 x 5 = $12,189.94

FV5

= 10,000 × (1 + 0.04/4)4 x 5 = $12,201.90

Financial Calculator Solution: Bank A: 5 4 -10,000 0 N i PV PMT

FV 12,166.53

Bank B:

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10 N

2 i

-10,000 PV

0 PMT

Bank C: 20 N

1 i

-10,000 PV

0 PMT

Solutions Manual

FV 12,189.94

FV 12,201.90

Excel solution method uses FV formula/function A

3 4 5

Given information/assumptions Present value of the investment Interest rate Number of years (n)

-$10,000 4% 5

6 7 8

Compounding period (m) Bank A Compounding period (m) Bank B Compounding period (m) Bank C

1 2 4

11 12 13

Future Value showing the Timeline Period Cash Flows Future Value

15 16 17 18

Future Value using the Formula Future Value (Bank A) Future Value (Bank B) Future Value (Bank C)

20 21 22 23

Future Value using the FV Function Future Value (Bank A) $12,166.53 Future Value (Bank B) $12,189.94 Future Value (Bank C) $12,201.90

0 ($10,000)

5 ?

$12,166.53 $12,189.94 $12,201.90

Comments =-$B$3*((1+$B$4)^$B$5) =-$B$3*((1+$B$4/$B$7)^($B$5*$B$7)) =-$B$12*((1+$B$4/$B$8)^($B$5*$B$8))

=FV($B$4,$B$5,0,$B$3,0) =FV($B$4/$B$7,$B$5*$B$7,0,$B$3,0) =FV($B$4/$B$8,$B$5*$B$8,0,$B$3,0)

5.4

You have an opportunity to invest $2,500 today and receive $3,000 in three years. What would be the return on your investment if you accepted this opportunity? Solution: Your investment today = PV = $2,500 Amount to be received = FV3= $3,000 Time of investment = n = 3 Return on the investment = i = ?

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0i=? 1 2 3 Year ├───┼────┼───┤ -$2,500 $3,000 F Vn = PV  (1 + i )n $3, 000 = $2,500  (1 + i )3 $3, 000 = (1 + i )3 $2,500 i = 6.27%

Financial Calculator Solution: 3 N

i 6.27

-2,500 PV

0 PMT

3,000 FV

Excel solution method uses RATE formula/function A 3 4 5

Given information/assumptions Present value of investment today Amount to be received in future Time of investment (n)

3 $3,000

$2,500 $3,000 3

The Timeline 8 9 10

Period Cash Flows Present Value

12 13

Return on the investment using the Formula Return on investment 6.27%

Comments =(($B$4/$B$3)^(1/$B$5))-1

15 16

Return on Investment using the RATE Function Return on investment 6.27%

=RATE(B5,0,-B3,B4,0)

5.5

0 ($2,500)

Emily Smith deposits $1,200 in her bank today. (a) If the bank pays 4 percent interest per year without compounding, how much simple interest will she have earned and how much money will she have at the end of five years?

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(b) How much money will she have in five years if the bank pays compound interest with annual compounding? (c) How much of the earnings in part b will be interest on interest? Solution: Emily’s deposit today= PV = $1,200 Interest rate = i = 4% Number of years = n = 5 Amount to be received = FV5 = ? 0 i = 4% 1 2 3 4 5 Year ├───┼───┼───┼────┼───┤ -$1.200 FV5 = ? a. Future value with simple interest Simple interest per year = $1,200 × 0.04 = $48 Simple interest for 5 years = $48 × 5 = $240 FV5 = $1,200 + $240 = $1,440 b. Future value with compound interest FV5 = $1,200 × (1 + 0.04)5 = $1,459.98 c. Simple interest = $240 Interest on interest = $1,459.98 – $1,200 – $240 = $19.98

Discussion Questions 5.1

Explain what is meant by the phrase “a dollar today is worth more than a dollar tomorrow.” The implication is that if one was to receive a dollar today instead of in the future, the dollar could be invested and will be worth more than a dollar tomorrow because of the interest earned during that one day. This makes today’s dollar more valuable than receiving a dollar tomorrow.

LO: 1 Level: Basic Bloomcode: Knowledge AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

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5.2

Solutions Manual

Explain the importance of a time line. Time lines are important tools used to analyze investments that involve cash flow streams over a period of time. They are horizontal lines that start at time zero (today) and show cash flows as they occur over time. Because of time value of money, it is crucial to keep track of not only the size, but also the timing of the cash flows.

LO: 1 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement 5.3

What are the two factors to be considered in time value of money? The factors that are critical in time value of money are the size of the cash flows and the timing of the cash flows.

LO: 1 Level: Basic Bloomcode: Knowledge AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement 5.4

Explain the difference between future value and present value. Future value measures what one or more cash flows will be worth at the end of a specified period, while present value measures what one or more future cash flows are worth today (at time = 0). LO: 2, 3 Level: Basic Bloomcode: Analysis AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement 5.5

Explain the difference between compounding and discounting. The process of converting an amount given at the present time into a future value is called compounding. It is the process of earning interest over time. Discounting is the process of converting future cash flows to their current or present value. In other words, present value is the current value of future cash flows that are discounted at an appropriate interest rate. LO: 2, 3 Level: Basic

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Bloomcode: Analysis AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement 5.6

Explain how compound interest differs from simple interest. Suppose you invest $100 for three years at a rate of 10 percent. Simple interest would imply that you will earn $10 for each of the three years for a total of $30 ($100 x 10% x 3) interest. At the end of three years you would have $130. Compound interest recognizes that the interest earned in years 1 and 2 will also earn interest over the remaining period. Thus, the $10 earned in the first year would earn interest at 10 percent for the next two years, and the $10 earned in the second year would earn interest for the third year. Therefore, the total amount that you would have at the end of three years would be: $100(1.10)3 = $133.10. By compounding, I have earned additional interest of $3.10. The total compound interest is the $33.10 earned on the $100 invested, while the simple interest earned is equal to only $30.00.

LO: 2 Level: Intermediate Bloomcode: Analysis AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement 5.7

If you were given a choice between investing in a savings account that paid quarterly interest and one that paid monthly interest, which one should you choose if they both offered the same quoted annual interest rate and why? The impact of compounding dictates that one should select the account that pays interest more frequently (as long as the interest rates are the same). This allows for the interest earned in the earlier periods to be reinvested, and earn interest, leading to an investment that grows more.

LO: 4 Level: Basic Bloomcode: Analysis AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement 5.8

Compound growth is exponential over time. Explain. Growth rates, as well as interest rates, are not linear, but rather exponential over time. In other words, the growth rate of the invested funds is accelerated by the compounding of interest. Over time, the principal amount gets larger as interest is added due to the compounding effect.

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LO: 4 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement 5.9

What is the Rule of 72? This is a rule of thumb to determine how fast an investment can double. It is a rule that allows you to closely approximate the time that it would take to double your money. It works well with interest rates between 5 and 20 percent, but varies more with higher rates. The Rule of 72 says that the time to double your money (TDM) approximately equals 72/i, where i is the rate of return expressed as a percentage. For example, if a bank paid 10% interest it would take 7.2 (72/10 = 7.2) years to double your money.

LO: 4 Level: Basic Bloomcode: Knowledge AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement 5.10

You are planning to take a spring break trip to Cancun your senior year. The trip is exactly two years away, but you want to be prepared and have enough money when the time comes. Explain how you would determine the amount of money you will have to save today in order to pay for the trip. First, determine how much money you will need for the trip. Second, check how much you already have and how it translates into cash in the future—how much it will be worth in two years. Next, determine how much you will have to deposit today, given the bank’s offered interest rate, to ensure that you will have saved up the difference when the time for your senior spring break comes.

LO: 4 Level: Intermediate Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

Questions and Problems

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BASIC 5.1

Future value: Chuck Tomkovick is planning to invest $25,000 today in a mutual fund that will provide a return of 8 percent each year. What will the value of the investment be in 10 years?

Solution: 0 i = 8% 10 years ├────────────────────┤ PV = -$25,000 FV10 = ? Amount invested today = PV = $25,000 Return expected from investment = i = 8% Duration of investment = n = 10 years Value of investment after 10 years = FV10

FV10 = PV  (1 + i ) n = $25,000  (1.08)10 = $53,973.12 Financial Calculator Solution: 10 N

8 i

-25,000 PV

0 PMT

FV 53,973.12

Excel solution method uses FV formula/function

3 4

A Given information/assumptions Present value of the investment Interest rate

Duration of investment (n)

Future Value showing the Timeline Period

Cash Flows

Future Value

12 13

Future Value using the Formula Future Value

$53,973.12

Comments =-$B$9*((1+$B$4)^$H$8)

15 16

Future Value using the FV Function Future Value

$53,973.12

=-FV(B4,B5,0,B3,0)

$25,000 8%

($25,000) ?

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LO 2 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.2

Future value: Ted Rogers is investing $7,500 in a bank CD that pays a 6 percent annual interest. How much will the CD be worth at the end of five years? Solution: 0 i = 6% 5 years ├────────────────────┤ PV = $7,500 FV5 = ? Amount invested today = PV = $7,500 Return expected from investment = i = 6% Duration of investment = n = 5 years Value of investment after 5 years = FV5

FV5 = PV  (1 + i ) n = $7,500  (1.06) 5 = $10,036.69 Financial Calculator Solution: 5 N

6 i

-7,500 PV

0 PMT

FV 10,036.69

Excel Template available in Wiley Course Resources Excel Template Solution available in Wiley Instructor Resources LO 2 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.3

Future value: Your aunt is planning to invest in a bank CD that will pay 7.5 percent interest compounded semiannually. If she has $5,000 to invest, how much will she have at the end of four years? Solution: 0 i = 7.5% 4 years ├────────────────────┤

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PV = $5,000 FV4 = ? Amount invested today = PV = $5,000 Return expected from investment = i = 7.5% Duration of investment = n = 4 years Frequency of compounding = m = 2 Value of investment after 4 years = FV4 mn

i    0.075  F V4 = PV  1 +  = $5, 000  1 +  2   m  = $5, 000  (1.0375)8 = $6, 712.35

24

Financial Calculator Solution: 8 N

3.75 i

-5,000 PV

0 PMT

FV 6,712.35

Excel solution method uses FV formula/function A Given information/assumptions Amount invested today (PV) Return expected from investment (i)

3 4 5 Duration of investment (n) 6 Frequency of compounding (m)

Future Value showing the Timeline Period Cash Flows

9 10 11 Future Value

$5,000 7.5% 4 2

0 ($5,000)

4 ?

13 Future Value using the Formula 14 Future Value

$6,712.35

Comments =$B$3*((1+($B$4/$B$6))^($B$5*B6))

16 Future Value using the FV Function 17 Future Value

$6,712.35

=-FV($B$4/2, B5*B6, 0, B3,0)

LO 2 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

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5.4

Future value: Kate Eden received a graduation present of $2,000 that she is planning on investing in a mutual fund that earns 8.5 percent each year. How much money will she have in three years? Solution: 0 i = 8.5% 3 years ├────────────────────┤ PV = $2,000 FV3 = ? Amount Kate invested today = PV = $2,000 Return expected from investment = i = 8.5% Duration of investment = n = 3 years Value of investment after 3 years = FV3

FV3 = PV  (1 + i ) n = $2,000  (1.085) 3 = $2,554.58 Financial Calculator Solution: 3 N

8.5 i

-2,000 PV

0 PMT

FV 2,554.58

Excel solution method uses FV formula/function A 3

Given information/assumptions Present value of the investment

4 5

Interest rate Number of years (n)

8 9

Future Value using a Time Line Period Cash Flows

Future Value

12 13

Future Value using the Formula Future Value

Future Value using the FV Function

Future Value

-$2,000 8.5% 3

0 ($2,000)

3 ?

$2,554.58

Comments =-$B$3*((1+$B$4)^$B$5)

$2,554.58

=FV(B4,B5,0,B3,0)

LO 2

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Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.5

Future value: Your bank pays 5 percent interest compounded semiannually on your savings account. You don’t expect to add to the current balance of $2,700 over the next four years. How much money can you expect to have at the end of this period? Solution: 0 i = 5% 4 years ├────────────────────┤ PV = -$2,700 FV4 = ? Amount invested today = PV = $2,700 Return expected from investment = i = 5% Duration of investment = n = 4 years Frequency of compounding = m = 2 Value of investment after 4 years = FV4 mn

i    0.05  FV4 = PV  1 +  = $2, 700  1 +  2   m  = $2, 700  (1.025)8 = $3, 289.69 Financial Calculator Solution: 8 N

2.50 i

-2,700 PV

24

0 PMT

FV 3,289.69 Excel solution method uses FV formula/function A

3 4 5 6

9 10 11

Given information/assumptions Amount invested today (PV) Return expected from investment (i) Duration of investment (n) Frequency of compounding (m) Future Value showing the Timeline Period Cash Flows Future Value

$2,700 5% 4 2

0 ($2,700)

4 ?

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13 Future Value using the Formula 14 Future Value

$3,289.69

Comments =$B$3*((1+($B$4/$B$6))^($B$5*B6))

16 Future Value using the FV Function 17 Future Value

$3,289.69

=-FV($B$4/2, B5*B6, 0, B3,0)

LO 2 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.6

Future value: Your birthday is coming up and instead of other presents, your parents promised to give you $1,000 in cash. Since you have a part time job and thus don’t need the cash immediately, you decide to invest the money in a bank CD that pays 5.2 percent, compounded quarterly, for the next two years. How much money can you expect to earn in this period of time? Solution: 0 i = 5.2% 2 years ├────────────────────┤ PV = -$1,000 FV2 = ? Amount invested today = PV = $1,000 Return expected from investment = i = 5.2% Duration of investment = n = 2 years Frequency of compounding = m = 4 Value of investment after 2 years = FV2 mn

42

i    0.052  F V2 = PV  1 +  = $1, 000  1 +  4   m  = $1, 000  (1.013)8 = $1,108.86 You have earned 108.86 in total compound interest. Financial Calculator Solution: 8 N

1.3 i

-1,000 PV

0 PMT

FV 1,108.86

Excel solution method uses FV formula/function A

Given information/assumptions

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3 4 5

Amount invested today (PV) Return expected from investment (i) Duration of investment (n)

-$1,000 5.2% 2

Frequency of compounding (m)

9 10 11

Future Value showing the Timeline Period Cash Flows Future Value

13 14

Future Value using the Formula Future Value

$1,108.86

Comments =$B$3*((1+($B$4/$B$6))^($B$5*B6))

16 17

Future Value using the FV Function Future Value

$1,108.86

=-FV($B$4/$b$6, B5*B6, 0, B3,0)

0 ($1,000)

2 ?

LO 2 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.7

Multiple compounding periods: Find the future value of a five-year $100,000 investment that pays 8.75 percent and that has the following compounding periods: a. Quarterly. b. Monthly. c. Daily. d. Continuous. Solution: 0 i = 8.75% 5 years ├────────────────────┤ PV = -$100,000 FV5 = ? Amount invested today = PV = $100,000 Return expected from investment = i = 8.75% Duration of investment = n = 5 years a.

Frequency of compounding = m = 4 Value of investment after 5 years = FV5

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Solutions Manual

mn

45

mn

12  5

mn

365  5

i    0.0875  F V5 = PV  1 +  = $100, 000  1 +  4   m  = $100, 000  (1.021875)20 = $154,154.24

Frequency of compounding = m = 12 Value of investment after 5 years = FV5 i    0.0875  F V5 = PV  1 +  = $100, 000  1 +  12   m  = $100, 000  (1.00729)60 = $154, 637.37

Frequency of compounding = m = 365 Value of investment after 5 years = FV5 i    0.0875  F V5 = PV  1 +  = $100, 000  1 +  365   m  = $100, 000  (1.00024)1825 = $154, 874.91

Frequency of compounding = m = Continuous Value of investment after 5 years = FV5 FV5 = PV  ei  n = $100, 000  e0.0875  5

= $100, 000 1.5488303 = $154, 883.03 Financial Calculator Solution: a. Quarterly 20 2.1875 N i

-100,000 0 PV PMT

b. Monthly 60 0.72917 N i

-100,000 PV

0 PMT

c. Daily 1825 0.02397 -100,000 N i PV

0 PMT

FV 154,154.24

FV 154,637.37

FV 154,874.91

d. Continuously NA Excel Template available in Wiley Course Resources Excel Template Solution available in Wiley Instructor Resources

SM 5-19

Parrino et al. Fundamentals of Corporate Finance, 5th edition

Solutions Manual

LO 2 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.8

Growth rates: Carson Kelly, a catcher for the Arizona Diamondbacks, hit 18 home runs in 2019. If his home-run-hitting ability is expected to grow by 12 percent every year for the following five years, how many home runs is he expected to hit in 2024? Solution: 0 g = 12% 5 years ├────────────────────┤ PV = -18 FV5 = ? Number of home runs hit in 2019 = PV = 18 Expected annual increase in home runs hit = g = 12% Growth period = n = 5 years Expected home runs in 2024 = FV5 FV5 = PV × (1 + g)n = 18 × (1.12)5 = 31.72 or about 32 home runs Financial Calculator Solution: 5 N

12 i

-18 PV

0 PMT

FV 31.72

Excel solution method uses FV formula/function A 3 4 5

Given information/assumptions Number of home runs hit in 2019 (PV) Expected annual increase in home runs hit (g) Growth period (n)

-18 12.0% 5

Future Value showing the Time Line 8 9 10

Period Cash Flows Future Value

Future Value using the Formula

0 (18)

5 ? Comments

SM 5-20

Parrino et al. Fundamentals of Corporate Finance, 5th edition

Future Value

Future Value using the FV Function

Future Value

Solutions Manual

31.72

=-$B$3*((1+$B$4)^$B$5)

31.72

=FV(B4,B5,0,B3,0)

LO 4 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.9

Present value: Roy Gross is considering an investment that pays 7.6 percent, compounded annually. How much will he have to invest today so that the investment will be worth $25,000 in six years? Solution: 0 i = 7.6% 6 years ├────────────────────┤ PV = ? FV6 = $25,000 Value of investment after 6 years = FV6 = $25,000 Return expected from investment = i = 7.6% Duration of investment = n = 6 years Amount to be invested today = PV FVn $25,000 PV = = n (1 + i ) (1.076) 6 = $16,108.92 Financial Calculator Solution: 6 N

7.6 i

PV -16,108.92

0 PMT

25,000 FV

Excel solution method uses PV formula/function A

Given information/assumptions

3 Value of investment after 6 years 4 Return expected from investment (i) 5 Number of years (n)

$25,000 7.6% 6

Present Value showing the Timeline

8 Period

SM 5-21

Parrino et al. Fundamentals of Corporate Finance, 5th edition

9 Cash Flows 10 Present Value

Solutions Manual

$25,000 ?

12 Present Value using the Formula 13 Present Value

(16,108.92)

Comments =-$B$3/(1+$B$4)^$B$5

15 Present Value using the PV Function 16 Present Value

(16,108.92)

=PV($B$4,$B$5,0,$B$3,0)

LO 3 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.10

Present value: Maria Addai has been offered a future payment of $750 two years from now. If she can earn an annual rate of 6.5 percent, compounded daily, on her investment, what should she pay for this investment today? Solution: 0 i = 6.5% 2 years x 365 days per year ├────────────────────┤ PV = ? FV2 = $750 Value of investment after 2 years = FV2 = $750 Return expected from investment = i = 6.5%/365 = 0.065/365 = 0.000178 Duration of investment = n = 2 years × 365 days per year = 730 days Amount to be invested today = PV F Vn $750 PV = = n (1 + i ) (1.000178)730 = $658.58

Financial Calculator Solution: 730 N

0.0178 i

PV -658.58

0 PMT

750 FV

Excel solution method uses PV formula/function A Given information/assumptions Value of investment after 2 years

3 4 Return expected from investment (i)

$750 0.0178%

6.5% compounded daily, 6.5%/365

SM 5-22

Parrino et al. Fundamentals of Corporate Finance, 5th edition

5 Duration of investment (n)

Solutions Manual

Present Value showing the Timeline

8 Period 9 Cash Flows 10 Present Value

2 $750

12 Present Value using the Formula 13 Present Value

(658.58)

Comments =-$B$3/((1+B4)^(B5*365))

15 Present Value using the PV Function 16 Present Value

(657.66)

=PV($B$4,$B$5*365,0,$B$3,0)

LO 3 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.11

Present value: Your brother has asked you for a loan and has promised to pay you $7,750 at the end of three years. If you normally invest to earn 6 percent per year, how much will you be willing to lend to your brother if you view this purely as a financial transaction (i.e. you don’t give your brother a special deal)? Solution: 0 i = 6% 3 years ├────────────────────┤ PV = ? FV3 = $7,750 Loan repayment amount after 3 years = FV3 = $7,750 Return expected from investment = i = 6% Duration of investment = n = 3 years Amount to be invested today = PV FVn $7,750 PV = = n (1 + i ) (1.06) 3 = $6,507.05

Financial Calculator Solution: 3 N

6 i

PV -6,507.05

0 PMT

7,750 FV

SM 5-23

Parrino et al. Fundamentals of Corporate Finance, 5th edition

A Given information/assumptions Loan repayment amount after 3 years

3 4 Return expected from investment (i) 5 Duration of investment (n)

Present Value showing the Timeline Period Cash Flows

8 9 10 Present Value

Solutions Manual

3 $7,750

$7,750 6% 3

0 ?

12 Present Value using the Formula 13 Present Value

(6,507.05)

Comments =-$B$3/((1+B4)^B5)

15 Present Value using the PV Function 16 Present Value

(6,507.05)

=PV($B$4,$B$5,0,$B$3,0)

LO 3 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.12

Present value: Tracy Chapman is saving to buy a house in five years. She plans to put 20 percent down at that time, and she believes that she will need $35,000 for the down payment. If Tracy can invest in a fund that pays 9.25 percent annual interest, compounded quarterly, how much will she have to invest today to have enough money for the down payment? When using the formula round to four decimal places. If using the financial calculator, round to two decimal places.

Solution: 0 i = 9.25% 5 years ├────────────────────┤ PV = ? FV5 = $35,000 Amount needed in the future = $35,000 Return expected from investment = i = 9.25/4= 2.31 Duration of investment = n = 5 X 4 = 20 Amount to be invested today = PV

SM 5-24

Parrino et al. Fundamentals of Corporate Finance, 5th edition

FVn

PV =

i   1 +   m

mn

Solutions Manual

$35, 000 (1.0231) 4  5

= $22,166.97

Financial Calculator Solution: 20 N

2.31 i

0 PMT

PV -22,166.97

35,000 FV

Excel Template available in Wiley Course Resources Excel Template Solution available in Wiley Instructor Resources LO 3 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.13

Present value: You want to buy a zero coupon bond that will have a value of $1,000 at the end of seven years. If the appropriate discount rate is 4.5 percent annually, how much should you pay for the bond today? Solution: 0 i = 4.5% 7 years ├────────────────────┤ PV = ? FV7 = $1,000 Face value of bond at maturity = FV7 = $1,000 Appropriate discount rate = i = 4.5% Number of years to maturity = n = 7 years. Present value of bond = PV FVn $1,000 PV = = n (1 + i ) (1.045) 7

= $734.83 Financial Calculator Solution: 7 N

4.5 i

PV -734.83

0 PMT

1000 FV

SM 5-25

Parrino et al. Fundamentals of Corporate Finance, 5th edition

Solutions Manual

Excel solution method uses PV formula/function A

Given information/assumptions

3 Face value of bond at maturity 4 Appropriate discount rate (i) 5 Number of years to maturity (n)

$1,000 4.5% 7

Present Value showing the Timeline

8 Period 9 Cash Flows 10 Present Value

7 $1,000

12 Present Value using the Formula 13 Present Value

(734.83)

=-$B$3/((1+B4)^B5)

15 Present Value using the PV Function 16 Present Value

(734.83)

=PV($B$4,$B$5,0,$B$3,0)

Comments

LO 3 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.14

Present value: Elizabeth Sweeney wants to accumulate $12,000 by the end of 12 years. If the annual interest rate is 7 percent and interest compounds semiannually, how much will she have to invest today to achieve her goal? Solution: 0 i = 7% 12 years × 2 periods per year ├────────────────────┤ PV = ? FV12 = $12,000 Amount Ms. Sweeney wants at end of 12 years = FV12 = $12,000 Interest rate on investment = i = 7%/2 = 0.07/2 = 0.035 Duration of investment = n = 12 years × 2 periods per year = 24 periods Present value of investment = PV F Vn $12, 000 PV = = n (1 + i ) (1.035)24 = $5, 255.49

Financial Calculator Solution:

SM 5-26

Parrino et al. Fundamentals of Corporate Finance, 5th edition

24 N

3.5 i

PV -5,255.49

0 PMT

Solutions Manual

12,000 FV

Excel solution method uses PV formula/function A

3 4 5 6

Given information/assumptions Amount required after 12 years (FV) Return expected from investment (i) Duration of investment (n) Frequency of compounding (m)

$12,000 7% 12 2

Present Value showing the Timeline

9 Period 10 Cash Flows 11 Future Value

12 $12,000

13 Present Value using the Formula 14 Present Value

($5,255.49)

=-B3/((1+(B4/B6))^(B5*B6))

16 Present Value using the PV Function 17 Present Value

($5,255.49)

=PV($B$4/$B$6, B5*B6, 0, B3,0)

Comments

LO 3 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.15

Interest rate: You are in need of cash and turn to your uncle, who has offered to lend you some money. You decide to borrow $1,300 and agree to pay back $1,500 in two years. Alternatively, you could borrow from your bank, which is charging 6.5 percent interest annually. Should you go with your uncle or the bank? Solution: 0 i=? 2 years ├────────────────────┤ PV = -$1,300 FV2 = $1,500 Amount to be borrowed = PV = $1,300 Amount to be paid back after 2 years = FV2 = $1,500 Interest rate on investment = i = ?

SM 5-27

Parrino et al. Fundamentals of Corporate Finance, 5th edition

Solutions Manual

Duration of investment = n = 2 years. Present value of investment = PV FVn PV = (1 + i )n $1,500 $1,300 = (1 + i ) 2 $1,500 (1 + i) 2 = = 1.1538 $1,300 i = 1.1538 − 1 i = 7.42% You should borrow from the bank.

Financial Calculator Solution: 2 N

-1,300 PV

i 7.42

0 PMT

1,500 FV

Excel solution method uses RATE formula/function A

2 $1,500

Given information/assumptions

3 Amount to be borrowed (PV) 4 Amount to be paid back after 2 years 5 Time of investment (n) The Timeline Period Cash Flows

8 9 10 Present Value

$1,300 $1,500 2

0 ($1,300)

12 Return on the investment using the Formula 13 Return on investment 7.42%

Comments =(($B$4/$B$3)^(1/$B$5))-1

15 Return on Investment using the RATE Function 16 Return on investment 7.42%

=RATE(B5,0,-B3,B4,0)

LO 2, 3 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

SM 5-28

Parrino et al. Fundamentals of Corporate Finance, 5th edition

Solutions Manual

5.16

Number of periods: You invest $150 in a mutual fund today that pays 9 percent interest annually. How long will it take to double your money? Solution: 0 i = 9% n years ├────────────────────┤ PV = -$150 FVn = $300 Value of investment today = PV = $150 Interest on investment = i = 9% Future value of investment = FV = $300 Number of years to double investment = n FVn = PV  (1 + i) n $300 = $150  (1.09) n $300 = 2.00 150 n  In(1.09) = In(2.00) (1.09) n =

In(2.00)  8 years In(1.09)

Financial Calculator Solution:

N 8.043

9 i

-150 PV

0 PMT

300 FV

Excel solution method uses NPER formula/function A

3 4 5

Given information/assumptions Value of investment today (PV) Future value of investment (FV) Interest on investment (i)

8 9 10

The Timeline Period Cash Flows Present Value

Number of periods to double using the Formula

Number of periods

-$150 $300 9%

2 $300

($150) Comments 8

=LN(B4/-B3)/LN(1+B5)

SM 5-29

Parrino et al. Fundamentals of Corporate Finance, 5th edition

15 16

Number of periods to double using the NPER Function Number of periods 8

Solutions Manual

=NPER(B5,0,B3,B4,0)

LO 2, 3 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

INTERMEDIATE 5.17

Future value: Your finance textbook sold 53,250 copies in its first year. The publishing company expects the sales to grow at a rate of 20 percent each year for the next three years and by 10 percent in the fourth year. Calculate the total number of copies that the publisher expects to sell in years 3 and 4. Draw a time line to show the sales level for each of the next four years. Solution: Number of copies sold in its first year = PV = 53,250 Expected annual growth in the next 3 years = g = 20% Number of copies sold after 3 years = FV3 = FVn = PV  (1 + g ) n

= 53, 250  (1.20)3 = 92, 016 copies Financial Calculator Solution: 3 N

20 i

-53,250 PV

0 PMT

FV 92,016

Number of copies sold in the fourth year = FV4 FVn = PV  (1 + g )n = 92,016  (1.10)

= 101, 218 copies 0 3 4 years 0 g = 20% 3 g = 10% 4 ├───────────┼────────┤ PV = -53,250 92,016 101,218 copies Financial Calculator Solution:

SM 5-30

Parrino et al. Fundamentals of Corporate Finance, 5th edition

1 N

10 i

-92,016 PV

0 PMT

Solutions Manual

FV 101,218

Excel solution method uses FV formula/function A

3 4 5

Given information/assumptions Number of copies sold in its first year (PV) Expected annual growth in the next 3 years (g) Growth period (n)

-53,250 20% 3

Future Value showing the Timeline

8 Period 9 Cash Flows 10 Future Value

0 (53,250)

5 ?

12 Future Value using the Formula 13 Future Value

92,016

Comments =-$B$3*((1+$B$4)^$B$5)

15 Future Value using the FV Function 16 Future Value

92,016

=FV(B4,B5,0,B3,0)

LO 4 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.18

Future Value: CelebNav, Inc., had sales last year of $700,000, and the analysts are predicting strong future performance for the start-up, with sales growing 20 percent a year for the next three years. After that, the sales should grow 11 percent per year for two years, at which time the owners are planning to sell the company. What are the projected sales for the last year before the sale? Solution: 0 1 2 3 4 5 years ├───────┼────────┼───────┼────────┼───────┤ g1-3 = 20% g4-5 = 11% PV = -$700,000

FV5=?

Sales of CelebNav last year = PV = $700,000

SM 5-31

Parrino et al. Fundamentals of Corporate Finance, 5th edition

Solutions Manual

Expected annual growth in the next 3 years = g1-3 = 20% Expected annual growth in years 4 and 5 = g4-5= 11% Sales in year 5 = FV5

FV5 = PV  (1 + g1 )3  (1 + g2 )2 = $700,000  (1.20)3  (1.11)2 = $1, 490, 348.16 Financial Calculator Solution: 3 N

20 i

-700,000 PV

2 N

11 i

-1,209,600 PV

0 PMT

FV 1,209,600

0 PMT

FV 1,490,348.16

Excel solution method uses FV formula/function A

Given information/assumptions Sales of CelebNav last year (PV)

Expected annual growth in the first 3 years (g1-3)

20%

Expected annual growth in years 4 and 5 (g4-5)

11%

The Timeline Period

Cash Flows

<--------------g1-3-------------->

Present Value

12 13

Future value using the Formula Future value at the end of year 5

Future value using the FV function

16 17

Future value at the end of year 3 Future value at the end of year 5

-$700,000

<------- g4-5----->

($700,000)

$1,490,348.16

Comments =-B3*(1+B4)^3*(1+B5)^2

$1,209,600.00 $1,490,348.16

=FV(B4,3,0,B3,0) =-FV(B5,2,0,B16,0)

LO 4 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

SM 5-32

Parrino et al. Fundamentals of Corporate Finance, 5th edition

Solutions Manual

5.19

Future value: You decide to take advantage of the current online dating craze and start your own dating app. You know that you have 450 people who will sign up immediately and, through careful marketing research and analysis, determine that membership can grow by 27 percent in the first two years, 22 percent in year 3, and 18 percent in year 4. How many members do you expect to have at the end of four years? Solution: 0 1 2 3 4 years ├───────┼────────┼───────┼────────┤ g1-2=27% g3=22% g4=18% PV = -450 FV4 = ? Number of Web site memberships at t = 0 = PV = 450 Expected annual growth in the next 2 years = g1-2 = 27% Expected annual growth in years 3 = g3= 22% Expected annual growth in years 4 = g4= 18% Number of members in year 4 = FV4 FV4 = PV(1 + g1 )2  (1 + g3 )  (1 + g4 ) = 450  (1.27)2  (1.22)  (1.18)

= 1, 045 members Financial Calculator Solution: 2 N

27 i

-450 PV

0 PMT

1 N

22 i

-725.805 PV

0 PMT

1 N

18 i

-885.4821 PV

0 PMT

FV 725.805 FV 885.4821 FV 1044.8689

Since it is impossible to have a fractional member, it is necessary to round up to 1,045 members for the answer. Excel Template available in Wiley Course Resources Excel Template Solution available in Wiley Instructor Resources LO 4

SM 5-33

Parrino et al. Fundamentals of Corporate Finance, 5th edition

Solutions Manual

Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.20

Multiple compounding periods: Find the future value of an investment of $2,500 made today for the following rates and periods: a. 6.25 percent compounded semiannually for 12 years b. 7.63 percent compounded quarterly for 6 years c. 8.9 percent compounded monthly for 10 years d. 10 percent compounded daily for 3 years e. 8 percent compounded continuously for 2 years Solution: a.

 0.0625  F V12 = PV  1 +  2   = $5, 232.09 0.0763   FV6 = PV  1 +  4   = $3,934.48

2  12

46

12  10

0.089   FV10 = PV  1 +  12   = $6,067.86 0.010   FV3 = PV  1 +  365   = $3,374.51

365  3

= $2,500  (2.0928)

= $2,500  (1.5738 )

= $2,500  ( 2.4271)

= $2,500  (1.3498 )

FV2 = PV  ei  n = $2,500  e0.08  2 = $2,500 × 1.1735 = $2,933.78

Financial Calculator Solution: a.

6.25 percent compounded semiannually for 12 years.

SM 5-34

Parrino et al. Fundamentals of Corporate Finance, 5th edition

24 N

3.125 i

-2,500 PV

0 PMT

Solutions Manual

FV 5,232.09

7.63 percent compounded quarterly for 6 years. 24 N

1.9075 i

-2,500 PV

0 PMT

FV 3,934.48

8.9 percent compounded monthly for 10 years. 120 N

0.74166 7 i

-2,500

PMT

FV 6,067.86

10 percent compounded daily for 3 years. 1095 N

0.02739726 i

-2,500 PV

0 PMT

FV 3,374.51

5.21

Multiple compounding periods: Find the present value of $3,500 under each of the following rates and periods. a. 8.9 percent compounded monthly for five years. b. 6.6 percent compounded quarterly for eight years. c. 4.3 percent compounded daily for four years. d. 5.7 percent compounded continuously for three years. Solution: 0 i= n years ├────────────────────┤

SM 5-35

Parrino et al. Fundamentals of Corporate Finance, 5th edition

Solutions Manual

PV = ? FVn = $3,500 Return expected from investment = i = 8.9% Duration of investment = n = 5 years Frequency of compounding = m = 12 Present value of amount = PV F V5 $3,500 PV = = mn 12  5 i    0.089  1 +  1 +  12   m  $3,500 = = $2, 246.57 1.5579 Return expected from investment = i = 6.6% Duration of investment = n = 8 years Frequency of compounding = m = 4 Present Value of amount = PV F V8 $3,500 PV = = mn 48 i    0.066  1 +  1 +  4   m  $3,500 = = $2, 073.16 1.6882 Return expected from investment = i = 4.3% Duration of investment = n = 4 years Frequency of compounding = m = 365 Present Value of amount = PV F V4 $3,500 PV = = mn 365  4 i    0.043  1 +  1 +  365   m  $3,500 = = $2, 946.96 1.1877 Return expected from investment = i = 5.7% Duration of investment = n = 3 years Frequency of compounding = m = Continuous Present value of amount = PV FV $3,500 PV = i  n3 = 0.057  3 e e

$3,500 = $2, 949.88 1.1865

Financial Calculator Solution: a.

8.9 percent compounded monthly for five years.

SM 5-36

Parrino et al. Fundamentals of Corporate Finance, 5th edition

60 N

0.7417 i

PV -2,246.57

Solutions Manual

0 PMT

3,500 FV

6.6 percent compounded quarterly for eight years. 32 N

1.65 i

PV -2,073.16

0 PMT

3,500 FV

4.3 percent compounded daily for four years. 1460 N

0.011781 i

PV -2,946.96

0 PMT

3,500 FV

Excel solution method using PV formula/function A

Given information/assumptions Future Value (FV)

$3,500

4 Return expected from investment (i/m)

8.9%

5 Return expected from investment (i/m)

6.6%

6 Return expected from investment (i/m)

4.3%

365

a. 9 10 11

Frequency of compounding (m) Frequency of compounding (m) Frequency of compounding (m)

Present Value showing the Timeline Period Cash Flows Future Value

5 $3,500

13 Present Value using the Formula 14 Present Value

($2,246.57)

Comments =-B3/((1+(B4/E4))^(E4*F9))

16 Present Value using the PV Function 17 Present Value

($2,246.57)

=PV(B4/E4,F9*E4,0,B3,0)

b. 20 21 22

Present Value showing the Timeline Period Cash Flows Future Value

8 $3,500

SM 5-37

Parrino et al. Fundamentals of Corporate Finance, 5th edition

Solutions Manual

24 Present Value using the Formula 25 Present Value

($2,073.16)

Comments =-$B$3/((1+(B5/C5))^(C5*E20))

27 Present Value using the PV Function 28 Present Value

($2,073.16)

=PV(B5/C5,E20*C5,0,E21,0)

c. 31 32 33

Present Value showing the Timeline Period Cash Flows Future Value

4 $3,500

35 Present Value using the Formula 36 Present Value

($2,946.96)

Comments =-$B$3/((1+B6/D6))^(D6*E31)

38 Present Value using the PV Function 39 Present Value

($2,946.96)

=PV(B6/D6,E31*D6,0,$B$3,0)

LO 3 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.22

Multiple compounding periods: Samantha plans to invest some money so that she has $5,500 at the end of three years. How much should she invest today given the following choices: a. 4.2 percent compounded daily b. 4.9 percent compounded monthly c. 5.2 percent compounded quarterly d. 5.4 percent compounded annually Solution: 0 i= 3 years ├────────────────────┤ PV = ? FV3 = $5,500 a. Return expected from investment = i = 4.2% Duration of investment = n = 3 years Frequency of compounding = m = 365 Present value of amount = PV

SM 5-38

Parrino et al. Fundamentals of Corporate Finance, 5th edition

PV =

F V3

mn

Solutions Manual

$5,500 365  3

i    0.042  1 +  1 +  365   m  $5,500 = = $4, 848.92 1.1343 Samantha should invest $4,848.92 today to reach her target of $5,500 in three years. Return expected from investment = i = 4.9% Duration of investment = n = 3 years Frequency of compounding = m = 12 Present value of amount = PV FV3 $5,500 PV = = mn 12  3 i  0.049    1 +  1 +  m 12    $5,500 = = $4,749.54 1.1580

Samantha should invest $4,749.54 today to reach her target of $5,500 in three years. Return expected from investment = i = 5.2% Duration of investment = n = 3 years Frequency of compounding = m = 4 Present Value of amount = PV F V3 $5,500 PV = = mn 43 i    0.052  1 + 1 +     4   m  $5,500 = = $4, 710.31 1.1677 Samantha should invest $4,710.31 today to reach her target of $5,500 in three years. Return expected from investment = i = 5.4% Duration of investment = n = 3 years Frequency of compounding = m = 1 Present value of amount = PV FV3 $5,500 PV = = = $4, 697.22 3 (1 + i ) (1.054)3 Samantha should invest $4,697.22 today to reach her target of $5,500 in three years.

Financial Calculator Solution: a.

4.20 percent compounded daily.

SM 5-39

Parrino et al. Fundamentals of Corporate Finance, 5th edition

1095 N

0.01151 i

PV -4,848.92

Solutions Manual

0 PMT

5,500 FV

0 PMT

5,500 FV

0 PMT

5,500 FV

0 PMT

5,500 FV

4.90 percent compounded monthly. 36 N

0.408333 i

PV -4,749.54

5.20 percent compounded quarterly. 12 N

1.30 i

PV -4,710.31

5.40 percent compounded annually. 3 N

5.4 i

PV -4,697.22

Excel solution method using PV formula/function A

a. b. c. d.

m= 365 12 4 1

3 4 5 6 7

Given information/assumptions Future Value (FV) Return expected from investment (i/m) Return expected from investment (i/m) Return expected from investment (i/m) Return expected from investment (i/m)

Present Value showing the Timeline

10 11 12

Period Cash Flows Future Value

14 15

Present Value using the Formula Present Value

($4,848.92)

Comments =-B3/((1+(B4/D4))^(D4*E9))

17 18

Present Value using the PV Function Present Value

($4,848.92)

=PV(B4/D4,E10*E4,0,B3,0)

$5,500 4.2% 4.9% 5.2% 5.4%

Frequency of compounding Frequency of compounding Frequency of compounding

3 $5,500

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Parrino et al. Fundamentals of Corporate Finance, 5th edition

Solutions Manual

Present Value showing the Timeline

Period

22 23

Cash Flows Future Value

25 26

Present Value using the Formula Present Value

($4,749.54)

Comments =-$B$3/((1+(B5/D5))^(D5*D21))

28 29

Present Value using the PV Function Present Value

($4,749.54)

=PV(B5/D5,E21*D5,0,E22,0)

3 $5,500

Present Value showing the Timeline

32 33

Period Cash Flows

Future Value

36 37

Present Value using the Formula Present Value

Present Value using the PV Function

Present Value

Present Value showing the Timeline

43 44 45

Period Cash Flows Future Value

47 48

Present Value using the Formula Present Value

($4,697.22)

Comments =-$B$3/((1+B7/D7))^(D7*E43)

50 51

Present Value using the PV Function Present Value

($4,697.22)

=PV(B7/D7,E43*D7,0,$B$3,0)

3 $5,500

($4,710.31)

Comments =-$B$3/((1+B6/D6))^(D6*E32)

($4,710.31)

=PV(B6/D6,E32*D6,0,$B$3,0)

3 $5,500

LO 3 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.23

Time to grow: Zephyr Sales Company has sales of $1.125 million. If the company’s management expects sales to grow 6.5 percent annually, how long will it be before sales double? Use a financial calculator to solve this problem.

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Parrino et al. Fundamentals of Corporate Finance, 5th edition

Solutions Manual

Solution: Current Sales = PV = $1.125 million Expected growth rate of sales = g = 6.5% Expected sales in the future = FV = $2.25 million To calculate the time needed to reach the target FV, we set up the future value equation. FVn = PV x (1+i)n $2.25M = $1.125M x (1.05)n n = ln (2)/ln (1.065) = 11 years Financial Calculator Solution:

N 11.007

6.5 i

-1.125 PV

0 PMT

2.250 FV

Answer: 11 years Excel solution method using NPER formula/function A 3 4 5

Given information/assumptions Value of investment today (PV) Future value of investment (FV) Interest on investment (i)

2 $2.250

-$1.125 $2.250 6.5%

The Timeline 8 9 10

Period Cash Flows Present Value

12 13

Number of periods to double using the Formula Number of periods 11.0

Comments =LN(B4/-B3)/LN(1+B5)

15 16

Number of periods to double using the NPER Function Number of periods 11.0

=NPER(B5,0,B3,B4,0)

-$1.125

LO 4 Bloomcode: Analysis AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

SM 5-42

Parrino et al. Fundamentals of Corporate Finance, 5th edition

Solutions Manual

5.24

Time to grow: You are going to deposit $850 in a bank CD today, and you will withdraw the money only once the balance is $1,000. If the bank pays 5 percent interest, how long will it take for the balance to reach $1,000? Solution: Amount invested today = PV = $850 Expected amount in the future = FV = $1,000 Interest rate on CD = i = 5% To calculate the time needed to reach the target FV, we set up the future value equation. F Vn = PV  (1 + i )n $1, 000 = $850  (1.05)n $1, 000 = 1.1764 $850 n  ln(1.05) = ln(1.1765) (1.05)n =

ln(1.1765) = 3.3 years ln(1.05)

Financial Calculator Solution:

N 3.33

5 i

-850 PV

0 PMT

1000 FV

Excel solution method uses NPER formula/function A

3 4 5

Given information/assumptions Value of investment today (PV) Future value of investment (FV) Interest on investment (i)

8 9 10

The Timeline Period Cash Flows Present Value

Number of periods to double using the Formula

Number of periods

15 16

Number of periods to double using the NPER Function Number of periods 3.3

2 $1,000

-$850 $1,000 5%

0 ($850)

Comments 3.3

=LN(B4/-B3)/LN(1+B5)

=NPER(B5,0,B3,B4,0)

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Parrino et al. Fundamentals of Corporate Finance, 5th edition

Solutions Manual

LO 2, 3 Bloomcode: Analysis AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.25

Time to grow: Neon Lights Company is a private company with sales of $1.3 million a year. Management wants to take the company public but has to wait until the sales reach $2 million. If the sales are expected to grow 12 percent annually, when is the earliest that Neon Lights will go public? Solution: Current level of sales = PV = $1,300,000 Target sales level in the future = FV = $2,000,000 Projected growth rate = g = 12% To calculate the time needed to reach the target FV, we set up the future value equation. F V3 = PV  (1 + 0.12)n $2, 000, 000 = $1,300, 000 1.12 n $2, 000, 000 = 1.5385 $1,300, 000 n  ln(1.12) = ln(1.5385) (1.12)n =

ln(1.5385) = 3.8 years ln(1.12)

Financial Calculator Solution:

N 3.8

12 i

-1,300,000 PV

0 PMT

2,000000 FV

Excel Template available in Wiley Course Resources Excel Template Solution available in Wiley Instructor Resources LO 4 Bloomcode: Analysis AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

SM 5-44

Parrino et al. Fundamentals of Corporate Finance, 5th edition

Solutions Manual

5.26

Time to grow: You have just inherited $550,000. You plan to save this money and continue to live off the money that you are earning in your current job. If you can invest at an interest rate of 4.6 percent annually, how long will it be before your inheritance is worth $1 million? Solution: F Vn = PV  (1+ )n $1, 000, 000 = $550, 000  (1.046)n $1, 000, 000 = (1.046)n $550, 000  $1, 000, 000  ln   = n  ln(1.046)  $550, 000   $1, 000, 000  ln  $550, 000  n=  . ln(1.046) $0.59784 n= $0.04497 n = 13.29 years

Financial Calculator Solution:

N 13.29

4.60 i

-550,000 PV

0 PMT

1,000,000 FV

Excel solution method uses NPER formula/function A

3 4 5

Given information/assumptions Value of investment today (PV) Future value of investment (FV) Interest on investment (i)

8 9 10

The Timeline Period Cash Flows Present Value

12 13

Number of periods to double using the Formula Number of periods 13.29

2 $1,000,000

-$550,000 $1,000,000 4.6%

0 ($550,000)

Comments =LN(B4/-B3)/LN(1+B5)

SM 5-45

Parrino et al. Fundamentals of Corporate Finance, 5th edition

15 16

Solutions Manual

Number of periods to double using the NPER Function Number of periods 13.29

=NPER(B5,0,B3,B4,0)

LO 2, 3 Bloomcode: Analysis AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.27

Growth rates: Xenix Corp had sales of $353,866 in 2017. If management expects its sales to be $476,450 in three years, what is the rate at which the company’s sales are expected to grow? Solution: Sales in 2017 = PV = $353,866 Expected sales three years from now = $476,450 To calculate the expected sales growth rate, we set up the future value equation. FV3 = PV  (1 + g)3

$476, 450 = $353,866  (1 + g) 3 (1 + g)3 =

$476, 450 = 1.3464 $353,866 1

g = (1.3464) 3 − 1 = 10.42% Financial Calculator Solution: 3 N

-353,866 PV

i 10.42

0 PMT

476,450 FV

Excel solution method uses RATE formula/function A

Given information/assumptions Sales in 2017 (PV)

$353,866

4 5

Expected sales three years from now Time of investment (n)

$476,450 3

The Timeline Period

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Parrino et al. Fundamentals of Corporate Finance, 5th edition

Solutions Manual

9 10

Cash Flows Present Value

$476,450

12 13

Return on the investment using the Formula Return on investment 10.42%

Comments =(($B$4/$B$3)^(1/$B$5))-1

15 16

Return on Investment using the RATE Function Return on investment 10.42%

=RATE(B5,0,-B3,B4,0)

($353,866)

LO 4 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.28

Growth rate: Infosys Technologies, Inc., reported net income of $419 million this year. Analysts expect the company’s earnings to be $1.468 billion in five years. What is the expected growth rate in the company’s earnings? Solution: Earnings in current year = PV = $419,000,000 Expected earnings five years from now = $1,468,000,000 To calculate the expected earnings growth rate, we set up the future value equation. FV5 = PV  (1 + g)5

$1, 468,000,000 = $419,000,000  (1 + g)5 (1 + g)5 =

$1, 468,000,000 = 3.5036 $419,000,000 1

g = (3.5036) 5 − 1 = 28.5% Financial Calculator Solution: 5 N

-419,000,000 PV

i 28.5

0 PMT

1,468,000,000 FV

Excel solution method uses RATE formula/function

3 4

Given information/assumptions Earnings in current year (PV) Expected earnings five years from now

$419,000,000 $1,468,000,000

SM 5-47

Parrino et al. Fundamentals of Corporate Finance, 5th edition

Time of investment (n)

Solutions Manual

The Timeline 8 9 10

Period Cash Flows Present Value

12 13

Return on the investment using the Formula Return on investment

15 16

Return on Investment using the RATE Function Return on investment 28.50%

5 $1,468,000,000

($419,000,000)

28.50%

Comments =(($B$4/$B$3)^(1/$B$5))-1

=RATE(B5,0,-B3,B4,0)

LO 4 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.29

Present value: Caroline Weslin needs to decide whether to accept a bonus of $1,820 today or wait two years and receive $2,100 then. She can invest at 6 percent. What should she do? Solution: 0 i = 6% 2 years ├────────────────────┤ PV = ? FV2 = 2,100 Amount to be received in 2 years = FV2 = $2,100 Return expected from investment = i = 6% Duration of investment = n = 2 years Present value of amount today PV = FV2 $2,100 PV = = n (1 + i ) (1.06) 2 = $1,868.99 Since $1,869 is greater than $1,820, Caroline should wait two years unless she needs the money sooner. The financial calculator and Excel solutions indicate that Caroline will earn a higher interest rate of 7.42% by waiting. Financial Calculator Solution:

SM 5-48

Parrino et al. Fundamentals of Corporate Finance, 5th edition

2 N

-1,820 PV

Solutions Manual

0 PMT

2,100 FV

i 7.42 If Caroline waits for two years, she will earn 7.42%, which is more than the expected return of 6% for the investment choice. Excel solution method uses RATE formula/function A

3 4 5 6 7

Given information/assumptions Amount to be received in 2 years (FV) Return expected from investment (i) Duration of investment (n) Present Value of bonus option Present Value of guaranteed amount

10 11 12

The Timeline Period Cash Flows Present Value of guaranteed amount

Return on the investment using the Formula

Return on investment of bonus

7.42%

=((+B3/B6)^(1/B5))-1

17 18

Return on Investment using the RATE Function Return on investment of bonus

7.42%

=RATE(B5,0,-B6,B3,0)

$2,100 6% 2 $1,820.00 -$1,868.99

=+B3/((1+B4)^B5)

2 $2,100

($1,869) Comments

LO 3 Bloomcode: Analysis AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.30. Present value: Congress and the president have decided to increase the federal tax rate in an effort to reduce the budget deficit. Suppose that Caroline Weslin, from problem 5.29, will pay 35 percent of her bonus to the federal government for taxes if she accepts the bonus today and 40 percent if she receives her bonus in two years. Will the increase in tax rates affect her decision? Solution: Yes. It will affect her decision. If Caroline accepts the bonus today, after paying the taxes, she will have $1,820 × (1 - 0.35) = $1,183.00 left over. If she waits two years and pays the high tax rate, the present value of what she will have left over is only $1,869 × (1 - 0.40) = $1,121.40. LO 3

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Parrino et al. Fundamentals of Corporate Finance, 5th edition

Solutions Manual

Bloomcode: Analysis AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

ADVANCED You have $2,500 that you want to invest in your classmate’s start-up business. You believe the business idea to be great and hope to get $3,700 back at the end of three years. If all goes according to the plan, what will the return on your investment be? Solution: 0 i=? 3 years ├────────────────────┤ PV = -$2,500 FV3 = $3,700 Amount invested in project = PV = $2,500 Expected return three years from now = FV =$3,700 To calculate the expected rate of return, we set up the future value equation. FV3 = PV  (1 + i ) 3 5.31

$3,700 = $2,500(1 + i ) 3 (1 + i ) 3 =

$3,700 = 1.4800 $2,500 1

i = (1.4800) 3 − 1 = 0.1396 = 13.96%

Financial Calculator Solution: 3 N

i 13.96

-2500 PV

0 PMT

3700 FV

Excel solution method uses RATE formula/function

A Given information/assumptions Amount invested in project (PV)

4 5

Expected return three years from now (FV) Time of investment (n)

($2,500) $3,700 3

The Timeline

SM 5-50

Parrino et al. Fundamentals of Corporate Finance, 5th edition

8 9 10

Period Cash Flows Present Value

Return on the investment using the Formula

Return on investment

Return on Investment using the RATE Function

Return on investment

Solutions Manual

3 $3,700

($2,500) Comments 13.96%

=((+E9/-B3)^(1/B5))-1

13.96%

=RATE(B5,0,B3,B4,0)

LO 2, 3 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.32

Patrick Seeley has $2,400 to invest. His brother approached him with an investment opportunity that could double his money in four years. What interest rate would the investment have to yield in order for Patrick’s brother to deliver on his promise?

Solution: 0 i=? 4 years ├────────────────────┤ PV = -$2,400 FV4 = $4,800 Amount invested in project = PV = $2,400 Expected return three years from now = FV =$4,800 Investment period = n = 4 years To calculate the expected rate of return, we set up the future value equation. FV4 = PV × (1 + i)4 $4,800 = $2,400 × (1 + i)4 (1 + i)4 =

$4,800 $2,400

= 2.0000

i = (2.000)1/4 – 1 = 0.1892 = 18.92% Financial Calculator Solution:

SM 5-51

Parrino et al. Fundamentals of Corporate Finance, 5th edition

4 N

i 18.92

-2,400 PV

Solutions Manual

0 PMT

4,800 FV

Excel solution method uses RATE formula/function A Given information/assumptions 3 4 5

Amount invested in project (PV) Expected return three years from now (FV) Time of investment (n)

($2,400) $4,800 4

The Timeline 8

Period

9 10

Cash Flows Present Value

Return on the investment using the Formula

Return on investment

Return on Investment using the RATE Function

Return on investment

4 $4,800

($2,400) Comments 18.92%

=((+E9/-B3)^(1/B5))-1

18.92%

=RATE(B5,0,B3,B4,0)

LO 2, 3 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.33

You have $12,000 in cash. You can deposit it today in a mutual fund earning 8.2 percent compounded semiannually, or you can wait, enjoy some of it, and invest $11,000 in your brother’s business in two years. Your brother is promising you a return of at least 10 percent on your investment. Whichever alternative you choose, you will need to cash in at the end of 10 years. Assume your brother is trustworthy and that both investments carry the same risk. Also assume you will not invest the $11,000 in the first two years. Which decision will yield the largest amount in 10 years? Solution: Option 1: Invest in account paying 8.2 percent semiannually for 10 years. 0 i = 8.2% 10 years ├────────────────────┤ PV = -$12,000 FV10 = ?

SM 5-52

Parrino et al. Fundamentals of Corporate Finance, 5th edition

Solutions Manual

Amount invested in project = PV = $12,000 Investment period = n = 10 years Interest earned on investment = i = 8.2% Frequency of compounding = m = 2 Value of investment after 10 years = FV10  0.082  F V10 = PV  1 +  2   = $26, 803.77

2  10

= $12, 000  (2.23365)

Financial Calculator Solution: 20 N

4.1 i

-12,000 PV

0 PMT

FV 26,803.77

Option 2: Invest in brother’s business to earn 10 percent for eight years. 0 i = 10% 8 years ├────────────────────┤ PV = -$11,000 FV8 = ? Amount invested in project = PV = $11,000 Investment period = n = 8 years Interest earned on investment = i = 10% Frequency of compounding = m = 1 Value of investment after 8 years = FV8

FV8 = PV  (1 + 0.10) = $11,000  (2.14359) 8

= $23,579.48 You are better off investing today in the mutual fund and earn 8.2 percent semiannually for 10 years. However, this assumes you get no personal gratification from the $1,000. Financial Calculator Solution: 8 N

10 i

-11,000 PV

0 PMT

FV 23,579.48

Excel Template available in Wiley Course Resources Excel Template Solution available in Wiley Instructor Resources LO 2

SM 5-53

Parrino et al. Fundamentals of Corporate Finance, 5th edition

Solutions Manual

Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.34

When you were born, your parents set up a bank account in your name with an initial investment of $5,000. You are turning 21 in a few days and will have access to all your funds. The account was earning 7.3 percent for the first seven years, but then the rates went down to 5.5 percent for six years. Your account then earned 8.2 percent three years in a row. Unfortunately, the next two years you earned only 4.6 percent. Finally, as the economy recovered, the return jumped to 7.6 percent for the last three years. a. How much money was in your account at the end of Year 16? b. How much money is in your account now, at the end of year 21? c. What would be the balance now if your parents had made another deposit of $1,200 at the end of year 7? Solution: 0 1 7 13 14 15 16 21 years ├───┼∙∙∙∙∙∙∙∙∙∙┼∙∙∙∙∙∙∙∙∙∙∙∙────┼────┼───┼───∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙──┤ PV = -$5,000 FV21 = ? i1-7 = 7.3% i8-13 = 5.5% i14-16 = 8.2% i17-18 = 4.6% i19-21 = 7.6% a. Initial investment = PV = $5,000 Interest rate for first 7 years = i1-7 = 7.3% Interest rate for next 6 years = i8-13 = 5.5% Interest rate for next 3 years = i14-16 = 8.2% Investment value at age 16 years = FV16 FV16 = PV  (1 + i1−7 )7  (1 + i8−13 )6  (1 + i14 −16 )3 = $5, 000  (1 + 0.073 )  (1.055)6  (1.082)3 7

= $5, 000  (1.6376)  (1.3788)  (1.2667) = $14, 300.55 Interest rate for from age 17 to 18 = i4 = 4.6% Interest rate for next 3 years = i5 = 7.6% Investment at start of 16th year = PV = $14,300.55 Investment value at age 21 years = FV21 FV 21 = FV16  (1 + i4 )2  (1 + i5 )3

= $14,300.55  (1 + 0.046 )  (1.076)3 2

= $14,300.55  (1.0941)  (1.2458)) = $19, 492.08 Additional investment at start of 8th year = $1,200

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Parrino et al. Fundamentals of Corporate Finance, 5th edition

Solutions Manual

Total investment for next 7 years = $5,000 x (1 + .073)7 = $8,187.82 + $1,200 = $9,387.82 Interest rate for next 6 years (years 8–13) = i2 = 5.5% Interest rate for years 14 to 16 = i3 = 8.2% Interest rate for from age 17 to 18 = i4 = 4.6% Interest rate for next 3 years = i5 = 7.6% Investment value at age 21 = FV21 FV21 = FV7  (1 + i2 )6  (1 + i3 )3  (1 + i4 ) 2  (1 + i5 )3

= $9,387.82  (1.055)6  (1.082)3  (1.046 )  (1.076)3 2

= $9387.82  (1.3788)  (1.2667)  (1.0941)  (1.2458) = $22, 348.33 Excel Template available in Wiley Course Resources Excel Template Solution available in Wiley Instructor Resources LO 2 Bloomcode: Analysis AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.35

Joe Burrow, the number 1 draft pick of the NFL Cincinnati Bengals in 2020, and his agent are evaluating three contract options. Each option offers a signing bonus and a series of payments over the life of the contract. Burrow uses a 10.25 percent rate of return to evaluate the contracts. Given the cash flows for each option --A, B, and C--, which one should he choose? Year Cash Flow Type Option A Option B Option C 0 Signing Bonus $3,100,000 $4,000,000 $4,250,000 1 Annual Salary $ 650,000 $ 825,000 $ 550,000 2 Annual Salary $ 715,000 $ 850,000 $ 625,000 3 Annual Salary $ 822,250 $ 925,000 $ 800,000 4 Annual Salary $ 975,000 $1,250,000 $ 900,000 5 Annual Salary $1,100,000 $1,000,000 6 Annual Salary $1,250,000 Solution: To decide on the best contract from Joe Burrow’s viewpoint, we need to find the present value of each option. The contracts are not repeatable and the one with the highest present value should be the one chosen. Option A: Discount rate to be used = i= 10.25% Present value of contract = PVA

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$650,000 $715,000 $822,250 $975,000 $1,100,000 $1,250,000 + + + + + (1.1025)1 (1.1025) 2 (1.1025) 3 (1.1025) 4 (1.1025) 5 (1.1025) 6 = $3,100,000 + $589,569 + $588,232 + $613,576 + $659,918 + $675,305 + $696,047 = $6,922,647

PVA = $3,100,000 +

Option B: Discount rate to be used = i= 10.25% Present value of contract = PVB

$825,000 $850,000 $925,000 $1,250,000 + + + (1.1025)1 (1.1025) 2 (1.1025) 3 (1.1025) 4 = $4,000,000 + $748,299 + $699,297 + $690,249 + $846,049 = $6,983,894

PVB = $4,000,000 +

Option C: Discount rate to be used = i= 10.25% Present value of contract = PVC

$550, 000 $625, 000 $800, 000 $900, 000 $1, 000, 000 + + + + (1.1025)1 (1.1025)2 (1.1025)3 (1.1025) 4 (1.1025)5 = $4, 250, 000 + $498,866 + $514,189 + $596,972 + $609,155 + $613,913

PVC = $4, 250, 000 + = $7, 083, 095

Option C is the best choice for Joe Burrow. Financial Calculator Solution: Option A: CF0 = 3,100,000 CF1 = 650,000 F01= 1 CF2 = 715,000 F02 =1 CF3 = 822,250 F03 = 1 CF4 = 975,000 F04 = 1 CF5 = 1,100,000 F05 = 1 CF6 = 1,250,000 F06 = 1 NPV I/Y = 10.25 COMPUTE NPV = 6,922,646.77 Option B: CF0 = 4,000,000 CF1 = 550,000 F01= 1 CF2 = 850,000 F02 =1 Copyright © 2022 John Wiley & Sons, Inc.

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CF3 = 925,000 F03 = 1 CF4 = 1,250,000 F04 = 1 NPV I/Y = 10.25 COMPUTE NPV = 6,983,895 Option C: CF0 = 4,250,000 CF1 = 550,000 F01= 1 CF2 = 625,000 F02 =1 CF3 = 800,000 F03 = 1 CF4 = 900,000 F04 = 1 CF5 = 1,000,000 F05 = 1 NPV I/Y = 10.25 COMPUTE NPV = 7,083,096

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A Given information/assumptions

Year 0 1 2

3 4 5 6

Annual Salary Annual Salary Annual Salary Annual Salary

Return expected from investment (i)

Option A 18 19 20

Solutions Manual

$822,250 $975,000 $1,100,000 $1,250,000

Present Value showing the Timeline Period Cash Flows Present Value

$925,000 $1,250,000

$800,000 $900,000 $1,000,000

1 $650,000

2 $715,000

10.25%

0 $3,100,000 ?

3 $822,250

4 $975,000

5 $1,100,000

6 $1,250,000

Present Value using the Formula

Present Value

$6,922,647

=+B19+C19/(1+$B$15)+D19/(1+$B$15)^D18+E19/(1+$B$15)^E18+F19/(1+$B$15)^F18+G 19/(1+$B$15)^G18+H19/(1+$B$15)^H18

25 26

Present Value using the NPV Function Present Value

$6,922,647

=NPV($B$15,C19:H19)+B19

Present Value showing the Timeline Period Cash Flows

$0 $4,000,000

Option B 29 30

Comments

1 $825,000

2 $850,000

3 $925,000

4 $1,250,000

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Present Value

33 34

Present Value using the Formula Present Value

$6,983,895

=+B30+C30/(1+$B$15)+D30/(1+$B$15)^D29+E30/(1+$B$1 5)^E29+F30/(1+$B$15)^F29

36 37

Present Value using the NPV Function Present Value

$6,983,895

=NPV($B$15,C30:F30)+B30

Present Value showing the Timeline Period Cash Flows Present Value

$0 $4,250,000 ?

Option C 40 41 42

? Comments

1 $550,000

2 $625,000

3 $800,000

4 $900,000

5 $1,000,000

Present Value using the Formula

Comments

Present Value

$7,083,096

=+B41+C41/(1+$B$15)+D41/(1+$B$15)^D40+E41/(1+$B$15)^E40+F41/(1+ $B$15)^F40+G41/(1+$B$15)^G40

16 17

Present Value using the NPV Function Present Value

$7,083,096

=NPV($B$15,C41:G41)+B41

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LO 3 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

Surmec, Inc., reported sales of $2.1 million last year. The company’s primary business is the manufacture of nuts and bolts. Since this is a mature industry, analysts are confident that sales will grow at a steady rate of 7 percent per year. The company’s net income equals 23 percent of sales. Management would like to buy a new fleet of trucks but can only do so once the net income reaches $620,000 a year. At the end of what year will Surmec be able to buy the trucks? What will sales and net income be in that year? Solution: Current level of sales for Surmec = PV = $2,100,000 Profit margin = 23% Net Income for the year = 0.23 x $2,100,000 = $483,000 Target profit level in the future = FV = $620,000 Projected growth rate of sales = g = 7% To calculate the time needed to reach the target FV, we set up the future value equation. 5.36

FVn = PV × (1 + g)n $620,000 = $483,000 × (1.07)n $620,000 (1.07)n = = 1.2836 $483,000 n × ln(1.07) = ln(1.2836) ln(1.2836) n= = 3.69 years ln (1.07) Financial Calculator Solution:

N 3.69

7 i

-483,000 PV

0 PMT

620,000 FV

The company achieves its profit target during the fourth year. Sales level at end of year 4 = FV4 F Vn = PV  (1 + g )n = $2,100, 000  (1.07)4 = $2, 752, 671.62

Profit for the year = $2,752,671.62 x 0.23 = $633,114.47

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Financial Calculator Solution:

4 N

-483,000

PMT

FV 633,114.47

Excel Template available in Wiley Course Resources Excel Template Solution available in Wiley Instructor Resources LO 4 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.37

You will be graduating in two years and are thinking about your future. You know that you will want to buy a house five years after you graduate and that you will want to put down $60,000. As of right now, you have $8,000 in your savings account. You are also fairly certain that once you graduate, you can work in the family business and earn $32,000 a year, with a 5 percent raise every year. You plan to live with your parents for the first two years after graduation, which will enable you to minimize your expenses and put away $10,000 each year. The next three years, you will have to live on your own, as your younger sister will be graduating from college and has already announced her plan to move back into the family house. Thus, you will be able to save only 13 percent of your annual salary. Assume that you will be able to earn 7.2 percent on the savings from your salary. At what interest rate will you need to invest the current savings account balance in order to achieve your goal? Hint: Draw a time line that shows all the cash flows for years 0 through 7. Remember, you want to buy a house seven years from now and your first salary will be in Year 3. Solution: 0 1 2 3 4 5 6 7 ├─────┼──────┼─────┼─────┼──────┼─────┼──────┤ $10,000 $10,000 $4,586.40 $4,815,72 $5,056.48 Starting salary in year 3 = $32,000 Annual pay increase = 5% Savings in first 2 years = $10,000 Savings rate for years 3 to 7 = 13% Year 1 2 3 4 5 6 7 Salary $0 $0 $32,000 $33,600 $35,280 $37,044 $38,896

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Savings $0 $0 $10,000 $10,000 $4,586.40 $4,815.72 $5,056.48 Investment rate = i = 7.2% Future value of savings from salary = FV7 FV7 = $0 + $0 + [$10,000 × (1.072)4 ] + [$10,000 × (1.072)3 ] + [$4,586.40 × (1.072)2] + [$4,815.72 X (1.072)1 ]+ $5,056.48 = $13,206.24 + $12,319.25 + $5,270.62 + $5,162.45 + $5,056.48 = $41,015.04 Financial Calculator Solution: CF0 = 0 CF1 = 0 F01= 1 CF2 = 0 F02 =1 CF3 = 10,000 F03 = 1 CF4 = 10,000 F04 = 1 CF5 = 4,586.40 F05 = 1 CF6 = 4,815.72 F06 = 1 CF7 = 5,056.48 F07 = 1 NPV I/Y = 7.2 COMPUTE NPV = 25,210.39 Question requires the NFV so use the following solution: 7 N

7.2 i

-25,210.39 PV

0 PMT

FV 41,015.04

Target down payment = $60,000 Amount needed to reach target = $60,000 - $41,015.07= FV = $18,984.93 Current savings balance = PV $8,000 Time to achieve target = n = 7 years. To solve for the investment rate needed to achieve target, we need to set up the future value equation: FV = PV × (1 + 𝑖)7 $18, 984.93 = $8,000 × (1 + 𝑖)7 (1 + 𝑖)7 +

$18,984.98 $8,000

= 2.3731 1

i = (2.3731)7 − 1 = 1.1314 − 1 = 13.14%

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Financial Calculator Solution: 7 N

i 13.14

-8,000 PV

0 PMT

18,984.93 FV

Excel Template available in Wiley Course Resources Excel Template Solution available in Wiley Instructor Resources LO 2 Bloomcode: Analysis AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.38

Both Amy and Lauren just received $5,000 signing bonuses. Both women expect to work for 40 years until retirement, and both have set up retirement accounts that they expect will earn 8 percent interest annually on any money they deposit. Amy decides to deposit her signing bonus immediately and intends to keep the full amount invested for the next 40 years. Lauren intends to use the $5,000 to buy some new equipment for her home gym, but plans to make up this amount with a deposit of $5,000 in her retirement account 10 years from today. a. What will be the value of Amy’s deposit after 10 years? b. How much simple interest and interest earned on interest will Amy have earned after 10 years? c. When they retire in 40 years, how much will each of the $5,000 deposits made by Amy and Lauren be worth? Solutions: a) 0 i = 8% 10 years ├────────────────────┤ PV = -$5,000 FV10 = ? Amount Amy invested today = PV = $5,000 Return expected from investment = i = 8% Duration of investment = n = 10 years Value of investment after 10 years = FV10 FV10 = PV × (1 + i)n = $5,000 × (1.08)10

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= $10,794.62 Financial Calculator Solution: 10 N

8 i

-5,000 PV

0 PMT

FV 10,794.62

Total compound interest = Total simple interest + Total interest on interest Total simple interest earned for one year = SI = P0 × i Total simple interest earned for ten years = 10 years × P0 × i = 10 × $5,000 × 0.08 = $4,000 Total interest on interest = Total compound interest – Total simple interest Total compound interest = FV10 – P0 = $10,794.62 - $5,000 = $5,794.62 Total interest on interest = $5,794.62 - $4,000 = $1,794.62

Future value of Amy’s investment

0 i = 8% 40 years ├────────────────────┤ PV = -$5,000 FV40 = ? Amount Amy invested today = PV = $5,000 Return expected from investment = i = 8% Duration of investment = n = 40 years Value of investment after 40 years = FV40 FV40 = PV × (1 + i)n = $5,000 × (1.08)40 = $108,622.61 Financial Calculator Solution:

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40 N

8 i

-5,000 PV

0 PMT

Solutions Manual

FV 108,622.61

Future value of Lauren’s investment 0 i = 8% 30 years ├────────────────────┤ PV = -$5,000 FV30 = ? Amount Lauren will invest 10 years from today = PV = $5,000 Return expected from investment = i = 8% Duration of investment = n = 30 years Value of investment after 30 years = FV30 FV30 = PV × (1 + i)n = $5,000 × (1.08)30 = $50,313.28 Financial Calculator Solution: 30 N

8 i

-5,000 PV

0 PMT

FV 50,313.28

LO 2 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

Excel Template available in Wiley Course Resources Excel Template Solution available in Wiley Instructor Resources 5.39

You want to buy a house three years from today, and you are currently saving for the down payment. You plan to save $6,000 today, and you anticipate that you will make two more annual deposits that will increase by 4 percent per year thereafter. You expect to earn an 8 percent return on your investments. How much will you have for a down payment at the end of year 3?

Solution: 0 1 2 3 years ├───────┼────────┼───────┼ g = 4%

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PV = -$6,000

Solutions Manual

FV3=?

Amount invested today = PV = $6,000 Expected annual growth of additional investments in each of the next 2 years = g = 4% Return expected from investment = i = 8% Amount available for down payment in year 3 = FV3 Additional investment in year 1 = FV1 = PV × (1 + g) = $6,000 × (1.04) = $6,240 Financial Calculator Solution: 1 N

4 i

-6,000 PV

0 PMT

FV 6,240

Additional investment in year 2 = FV1 = PV × (1 + g)2 =$6,000 × (1.04)2 = $6,489.60 Financial Calculator Solution: 2 N

4 i

-6,000 PV

0 PMT

FV 6,489.60

Future value of today’s investment at end of year 3 = PV × (1 + i)n =$6,000 × (1.08)3 =$7,558.27 Financial Calculator Solution: 3 N

4 i

-6,000 PV

0 PMT

FV 7,558.27

Future value of year 1 investment at end of year 3 = PV × (1 + i)n =$6,240 × (1.08)2 = $7,278.34 Financial Calculator Solution: 2 N

4 i

-6,240 PV

0 PMT

FV 7,278.34

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Future value of year 2 investment at end of year 3 = PV × (1 + i)n = $6,489.60 × (1.08)1 = $7,008.77 Financial Calculator Solution: 1 N

4 i

-6,489.60 PV

0 PMT

FV 7,008.77

Total value of investment available for down payment at end of year 3 = $7,558.27 + $7,278.34 + $7,008.77 = $21,845.38 LO 2, 4 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement Excel Template available in Wiley Course Resources Excel Template Solution available in Wiley Instructor Resources

Sample Test Problems 5.1

Holding all else constant, what will happen to the present value of a future amount if you increase the discount rate? What if you increase the number of years? Solution: Holding all else constant, both increasing the discount rate and increasing the number of years, will decrease the present value. LO 3 Bloomcode: Comprehension AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.2

Juliette Bronson anticipates needing $500,000 to start a business. If she can earn 4.5 percent compounded annually on her investments, how much money would Juliette have to invest today to have $500,000 in three years?

Solution: i = 4.5%

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0 3 Year 1 2 ├────────────────────┤ PV = ? FV3 = $500,000 Amount required at end on investment period = FV3 = $500,000 Return expected from investment = i = 4.5% Duration of investment = n = 3 years Amount to be invested today = PV F Vn $500, 000 PV = = n (1 + i ) (1.045)3

= $438,148.30 Financial Calculator Solution: 3 N

4.5 i

PV -438,148.30

0 PMT

500,000 FV

LO 3 Bloomcode: Analysis AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.3

Christopher Thompkins must decide how to invest $10,000 that he just inherited. What would be the future value of his investment after five years under each of the following three investment opportunities? a. 6.28% compounded quarterly. b. 6.20% compounded monthly. c. 6.12% compounded continuously.

Solution: a.

Interest rate on investment = i = 6.28% Frequency of compounding = m = 4 Value of investment after 5 years = FV5 mn

i    0.0628  F V5 = PV  1 +  = $10, 000  1 +  4   m  = $10, 000  (1.01570)20 = $13, 655.55

45

Financial Calculator Solution:

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20 N

1.57 i

-10,000 PV

0 PMT

Solutions Manual

FV 13,655.55

Interest rate on investment = i = 6.20% Frequency of compounding = m = 12 Value of investment after 5 years = FV5 mn

12  5

i    0.0620  F V5 = PV  1 +  = $10, 000  1 +  12   m  = $10, 000  (1.00517)60 = $13, 623.37 Financial Calculator Solution: 60 N

0.51667 i

-10,000 PV

0 PMT

FV 13,623.37

Interest rate on investment = i = 6.12% Frequency of compounding = m = Continuous Value of investment after 5 years = FV5 FV5 = PV  ei  n = $10, 000  e0.0612  5

= $10, 000 1.357982 = $13, 579.82 LO 2 Bloomcode: Analysis AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.4.

Tina DeLeon deposited $2,500 today in an account paying 6 percent interest annually. What would be the simple interest earned on this investment in five years? With annual compounding, how much interest-on-interest would Tina earn in five years?

Solution: 0 5 years 3 1 2 4 ├────────────────────┤ PV = -$2,500 FV5 = ? Amount invested today = PV = $2,500 Return expected from investment = i = 6% Duration of investment = n = 5 years

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Frequency of compounding = m = 1 Value of investment after 5 years = FV5

FV5 = PV  (1 + i) n = $2,500(1.06) 5 = $3,345.56 Financial Calculator Solution: 5 N

6 i

-2,500 PV

0 PMT

FV 3,345.56

Simple interest on investment = $2,500 × 0.06 × 5 = $750 Interest-on-interest = FV5 – PV – simple interest on investment Interest-on-interest = $3,345.56 – $2,500 – $750 = $95.56 LO 2 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.5

The state of Texas had 50,948 active patient care physicians in 2016 and by 2020 this number had grown to 56,765. What was the compound annual growth rate (CAGR) in the number of active care physicians during this period?

Solution: 0 4 years 3 2 1 ├────────────────────┤ PV = -50,948 FV4 = 56,765 Number of physicians in 2016 = PV = 50,948 Number of physicians in 2020 = FV4 = 56,765 Years to maturity = n = 4 years. growth rate = i FVn PV = n (1 + i )

47, 663 (1 + i ) 4 56, 765 (1 + i ) 4 = = 1.1142 50,948

42, 725 =

i = (1.1142)1 4 − 1 i = 0.027397, or 2.74%

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The CAGR was 2.74 percent Financial Calculator Solution: 4 N

i 2.74

-50,984 PV

0 PMT

56,7653 FV

LO 4 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

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Chapter 4

Analyzing Financial Statements Before You Go On Questions and Answers Section 4.1 1.

Why is it important to look at a firm’s historical financial statements? When one does a ratio analysis on a firm, it is important to do the analysis over a three- to five-year period. Looking at the historical financial statements allows one to see the trends on the various ratios—whether they are improving, worsening, or staying the same. It is also useful to compare the firm with other companies in the same industry.

What is the primary concern of a firm’s creditors? The creditors of a firm will want to know if the firm is generating enough cash flows to meet all of its required obligations, like employee wages and trade credit, and still has enough to meet the principal and interest payments due periodically. Their ultimate concern is being paid on time and being repaid in full.

Section 4.2 1.

Why does it make sense to standardize financial statements? Standardized, or common-size, financial statements allow you to make meaningful comparisons of financial statements between two firms that are dramatically different in size and also when comparing financial results over time for the same firm. They also make interpretation of data much easier. Standardized or common-size financial statements are those that are prepared with numbers that have been compiled using a common measure of the firm’s size.

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What are common-size, or standardized, financial statements, and how are they prepared? Typically, balance sheets are standardized by dividing each asset, liability, and equity item by total assets (or total deposits in the case of banks) and expressing it as a percentage of total assets. For income statements the scaling factor is sales or revenue, thus expressing each item as a percentage of sales.

Section 4.3 1.

What are the efficiency ratios, and what do they measure? Why, for some firms, is the total asset turnover more important than the fixed asset turnover? Efficiency ratios (also called turnover ratios) measure how efficiently a firm uses its assets to generate sales. The following ratios were discussed: •

Inventory turnover/days’ sales in inventory—calculated as cost of goods sold divided by inventory; it shows how many times the inventory of a firm is sold and replaced over a specific period.

•

Accounts receivable turnover/days’ sales outstanding—computed as net sales divided by accounts receivable; it is a measure used to quantify a firm’s effectiveness in extending credit and success in collection of debts.

•

Total asset turnover—calculated as net sales divided by total assets; it gives us the amount of sales generated for every dollar’s worth of assets.

•

Fixed asset turnover—calculated by dividing sales by net fixed assets; it shows the amount of sales generated with each dollar of fixed assets.

The fixed asset turnover is not very useful for service-oriented firms with little plant or equipment. Instead, the total asset turnover is more relevant.

List the leverage ratios discussed in this section and explain how they are related. Leverage ratios measure the extent to which a firm uses debt rather than equity financing and show the firm’s ability to meet its long-term financial obligations. The three leverage ratios discussed in this book are total debt ratio (plus its variations of debt-equity ratio and the equity multiplier), times interest earned, and cash coverage ratio. This is how all three ratios are linked together: the total debt ratio indicates what proportion of assets are

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financed from other sources than shareholders, and times interest earned measures how effectively the firm can meet the interest obligations on this financing based on operating earnings (EBIT). Cash coverage takes the analysis a step further, determining whether the firm has enough cash on hand to cover the interest payments.

List the profitability ratios discussed in this section, and explain how they differ from each other. The most commonly used profitability ratios are profit margin (gross profit margin, operating profit margin, and net profit margin), return on assets (ROA), and return on equity (ROE). The profit margin ratios examine the company’s profitability as a percentage of sales, whereas ROE and ROA help us analyze profitability as percentage of an investment, either in assets or in the firm’s equity. In other words, ROA tells us what earnings were generated from invested capital (debt and equity), and ROE indicates how well management is employing the investors’ capital invested in the company.

Section 4.4 1.

What is the purpose of the DuPont system of analysis? The purpose of the DuPont system of analysis is to determine a company’s financial health. It breaks down ROE into three parts: profit margin, total asset turnover, and financial leverage (equity multiplier). If ROE is unsatisfactory, the DuPont equation helps identify which part of the business is underperforming.

What is the equation for ROA in the DuPont system, and how do the factors in that equation influence the ratio? ROA is calculated as net income divided by total assets. Modifying the equation by dividing both the numerator and denominator by net sales and rearranging the terms, we can rewrite the equation as: ROA= Net income/Net sales × Net sales/Total assets or ROA = Net profit margin × Total asset turnover

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Therefore, based on the above equation, we can conclude that ROA is a combination of the firm’s ability to efficiently manage its operating expenses (operating efficiency) and its assets (asset use efficiency). In order for the management to increase ROA, it can increase either the profit margin or asset turnover, or both. The strategies that companies choose to pursue to increase their ROA depend on their business type and long-term goals.

What are the three major shortcomings of ROE? The three major shortcomings of ROE are that it does not consider the size of the initial investment or the size of future cash payments, it ignores risk, and it does not directly consider the cash flow involved in the business decision-making process. However, despite the ratio’s drawbacks, it is a handy tool for measuring a company’s profitability and identifying industry leaders, as long as you know where the numbers are coming from.

Section 4.5 1.

In what three ways can a financial manager choose a benchmark? A financial manager can choose a benchmark based on either of the following methods: trend analysis, industry average analysis, or peer group analysis. Trend analysis uses history as its standard by evaluating the firm’s performance against itself over time. Industry average analysis compares the firm’s performance to the performance of sameindustry companies, and peer group analysis benchmarks the company’s performance to that of its competitors. Most of the time, a combination of all three methods is used when analyzing the company.

Explain what the SIC codes are, and discuss the pros and cons of using them in financial analysis. Standard Industrial Classification (SIC) codes are four-digit numbers that are used to categorize business activities. The first two digits determine the broad type of business, such as mining of metals, and then each additional digit narrows down the industry in greater detail. The advantage of using SIC codes in financial analysis is that the financial

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ratio data can be segmented into six size categories by asset size or by sales, which allows for more meaningful comparisons of like firms. The main drawback to using SIC codes is that companies with similar business lines, but not necessarily similar target markets, often have the same SIC codes (for example, Neiman Marcus and Wal-Mart). Therefore, using SIC codes as a basis for financial analysis requires more thought than just relying on the classification numbers.

Section 4.6 1.

Explain how the DuPont system allows us to evaluate a firm’s performance. The DuPont system, which leads to the measurement of a firm’s return on equity (ROE), allows one to break down the measure into three areas of performance. First, a firm’s operational efficiency is measured by the net profit margin; second, the firm’s efficiency in managing its assets is reflected in its asset turnover ratio; and finally, the impact of financial leverage is shown by the equity multiplier. One is then able to pinpoint areas of strengths and weaknesses by breaking down these measures, which are tied to either the balance sheet and/or the income statement.

What are the limitations of traditional financial statement analysis? There are two main problems with financial statement analysis. The first is that it is based on book values (historical data), it may not reflect a firm’s true economic condition, leading to a lack of economic underpinning for much of the decision rules. Second, it is difficult to say a current ratio of 2.2 is good or that one ratio is more important than another.

List some of the problems that financial analysts confront when analyzing financial statements. Some of the problems that financial analysts run into when analyzing financial statements are: •

Multiple business lines

•

Inflation adjustments

•

Globalization

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•

Seasonality

•

Different accounting principles

Solutions Manual

Therefore, a good analyst does not simply look at the numbers provided in the financial statements, but instead adjusts these numbers for all the above factors to provide a meaningful and value-added analysis.

Self-Study Problems 4.1

The Abercrombie Supply Company reported the following information for its latest fiscal year. Prepare the firm’s common-size income statement.

Abercrombie Supply Company Income Statement($ thousands)

Net sales

$2,110,965

Cost of goods sold

1,459,455

Selling and administrative expenses

312,044

Nonrecurring expenses

27,215

Earnings before interest, taxes, depreciation, and amortization

(EBITDA)

$ 312,251

Depreciation

112,178

Earnings before interest and taxes (EBIT)

$ 200,073

Interest expense

117,587

Earnings before taxes (EBT)

Taxes (35%)

82,486 28,870

Net income

53,616

Solution: The common-size income statement for Abercrombie Supply Company should look like the following one: Abercrombie Supply Company Common-Size Income Statement($ thousands)

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% of Net Sales Net sales

$2,110,965

100.0

Cost of goods sold

1,459,455

69.1

Selling and administrative expenses

312,044

14.8

Nonrecurring expenses

27,215

1.3

(EBITDA)

$ 312,251

14.8

Depreciation

112,178

5.3

$ 200,073

9.5

117,587

5.6

82,486

3.9

28,870

1.4

53,616

2.5

Earnings before interest, taxes, depreciation and amortization

Earnings before interest and taxes (EBIT) Interest expense Earnings before taxes (EBT)

Taxes (35%) Net income

Excel solution method: create partial income statement: Abercrombie Supply Company Common-Size Income Statement ($ thousands) A

% of Description

Values

Net

Comments

Sales 5

Net sales

$2,110,965

100.0

=+B5/$B$5*100

Cost of goods sold

1,459,455

69.1

=+B6/$B$5*100

Selling and administrative expenses

312,044

14.8

=+B7/$B$5*100

Nonrecurring expenses

27,215

1.3

=+B8/$B$5*100

Earnings before interest, taxes, depreciation $312,251

14.8

=+B10/$B$5*100

11 Depreciation

112,178

5.3

=+B11/$B$5*100

12 Earnings before interest and taxes (EBIT)

$200,073

9.5

=+B12/$B$5*100

13 Interest expense

117,587

5.6

=+B13/$B$5*100

14 Earnings before taxes (EBT)

$82,486

3.9

=+B14/$B$5*100

15 Taxes (35%)

28,870

1.4

=+B15/$B$5*100

and amortization (EBITDA)

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16 Net income

Solutions Manual

$53,616

2.5

=+B16/$B$5*100

LO: 2 Level: Basic

4.2

Prepare a common-size balance sheet from the following information for Abercrombie Supply Company. Abercrombie Supply Company Balance Sheet ($ thousands)

Assets:

Liabilities and Equity:

Cash and marketable securities

$ 396,494

Accounts receivable

Accounts payable

708,275

Inventory

1,152,398

$ 817,845

Notes payable

101,229

Accrued income taxes

41,322

Other current assets

42,115

Total current assets

$2,299,282

Total current liabilities

$ 960,396

Net plant and equipment

1,978,455

Long-term debt

1,149,520

Total liabilities

Total assets

$4,277,737

$2,109,916

Common stock

1,312,137

Retained earnings

855,684

Total common equity

$2,167,821

Total liabilities and equity

$4,277,737

Solution: Abercrombie Supply’s common-size balance sheet is as follows:

Abercrombie Supply Company Common-Size Balance Sheet ($ thousands) Assets

% of

Liabilities and Equity:

% of

Assets Cash and marketable sec.

$ 396,494

Assets

9.3 Accounts payable and

$ 817,845

19.1

16.6 Notes payable

101,229

2.4

26.9 Accrued income taxes

41,322

1.0

accruals Accounts receivable Inventory

708,275 1,152,398

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Other current assets

42,115

1.0

Total current assets

$2,299,2

53.7

Solutions Manual

Total current liabilities

$ 960,396

22.5

1,149,520

26.9

$2,109,916

49.3

1,312,137

30.7

82 Net plant and equipment

1,978,455

46.3 Long-term debt Total liabilities Common stock Retained earnings Total common equity

Total assets

$4,277,737

100.0 Total liabilities and

855,684

20.0

$2,167,821

50.7

$4,277,737

100.0

equity

Excel solution method: create balance sheet:

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Abercrombie Supply Company Balance Sheet ($ thousands) A

Assets

C % of

Values

Assets

Comments

Liabilities and Equity:

Values

Cash and marketable

G % of Assets

H Comments

Accounts payable and

sec.

$396,494

9.3

=+B5/$B$14*100

accruals

$817,845

19.1

=+F5/$B$14*100

Accounts receivable

708,275

16.6

=+B6/$B$14*100

Notes payable

101,229

2.4

=+F6/$B$14*100

Inventory

1,152,398

26.9

=+B7/$B$14*100

Accrued income taxes

41,322

1.0

=+F7/$B$14*100

Other current assets

42,115

1.0

=+B8/$B$14*100

Total current liabilities

$960,396

22.5

=+F8/$B$14*100

Total current assets

$2,299,282

53.7

=+B9/$B$14*100

Long-term debt

1,149,520

26.9

=+F9/$B$14*100

1,978,455

46.3 =+B10/$B$14*100

Total liabilities

$2,109,916

49.3 =+F10/$B$14*100

Common stock

1,312,137

30.7 =+F11/$B$14*100

Retained earnings

855,684

20.0 =+F12/$B$14*100

Total common equity

$2,167,821

50.7 =+F13/$B$14*100

$4,277,737

100.0 =+F14/$B$14*100

Net plant and 10 equipment

Total liabilities and 14 Total assets

$4,277,737

100.0 =+B14/$B$14*100

equity

LO: 2 Level: Basic

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Solutions Manual

Using the data above for Abercrombie Supply Company calculate the firm’s current ratio and quick ratio

Solution: Abercrombie Supply’s current ratio and quick ratio are calculated as follows: Current ratio =

Current Assets $2,299,282 = = 2.39 Current Liabilities $960,396

Current杳雼㳯·iorr Quick ratio =

Current杳雼㳯·ets Current杳雼㳯·bilities

$2,299,282 $960,396

= 2.39

Current Assets − Inventory $2,299,282 − $1,152,398 = = 1.19 Current Liabilities $960,396

Current Assets − Inventory $2,299,282 − $1,152,398 Current Liabilities

$960,396

LO: 3 Level: Basic

4.4

Refer again to the balance sheet and income statement for Abercrombie Supply Company and calculate the following ratios: inventory turnover, days’ sales outstanding, total asset turnover, fixed asset turnover, total debt ratio, debt-to-equity ratio, times interest earned, cash coverage.

Solution: The ratios are calculated as shown in the following table: Ratio

Formula

Calculation

Inventory turnover

Cost of Goods Sold/Inventory

$1,459,455 / $1,152,398

Days’ sales outstanding

365 Days/Accts Rec. Turnover

$708,275 / ($2,110,965/365)

Value 1.27 122.5 days

Total asset turnover

Net Sales/Total Assets

$2,110,965 / $4,277,737

0.49

Fixed asset turnover

Net Sales/Net Fixed Assets

$2,110,965 / $1,978,455

1.07

Total debt ratio

Total Debt/Total Assets

$2,109,916 / $4,277,737

0.493

Debt-to-equity ratio

Total Debt/Total Equity

$2,109,916 / $2,167,821

0.973

EBIT/Interest Expense

$200,073 / $117,587

1.7

EBITDA/Interest Expense

$312,251 / $117,587

2.66

Times interest earned Cash coverage

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LO: 3 Level: Basic

4.5

Refer again to the balance sheet and income statement for Abercrombie Supply Company. Use the DuPont equation to calculate the return on equity (ROE). In the process, calculate the following ratios: profit margin, EBIT return on assets, return on assets, equity multiplier, and total asset turnover.

Solution: Following are the calculations for the ROE and associated ratios: Net profit margin =

EBIT ROA =

Net income $53,616 = = 0.0254, or 2.54% Net sales $2,110,965

EBIT $200,073 = = 0.0468, or 4.68% Total assets $4,277,737

Return on assets =

Net income $53,616 = = 0.0125, or 1.25% Total assets $4,277,737

Equity multiplier =

Total assets $4,277,737 = = 1.97 Total equity $2,167,821

Total asset turnover =

Net sales $2,110,965 = = 0.49 Total assets $4,277,737

DuPont identity:

ROE = ROA  Equity multiplier = Net profit margin  Total asset turnover ratio  Equity multiplier =

Net income Net sales Total assets   Net sales Total assets Total equity

= 0.0254  0.49  1.97 = 0.0245, or 2.45%

4.6

Last year ABC companies had accounts receivable turnover of 15, total asset turnover of 4.5, and total assets of $1,000,000. What was the value of ABC’s accounts receivable? What was the value of its net sales?

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Solution: In this problem we can use the accounts receivable turnover equation (Equation 4.5) and total asset turnover equation (Equation 4.7) to solve for the values of accounts receivable and net sales. Accounts receivable =

Net sales Accounts receivable

Total asset turnover =

Net sales Net sales Accounts receivable turnover = Accounts receivable Total assets

Formatted: Font: Liberation Serif Formatted: Font: Liberation Serif Formatted: Font: Liberation Serif

Net sales

Total asset turnover = Total assets Dividing accounts receivable turnover by total asset turnover yields:

Net sales Net sales Total assets / = Accounts receivable Totalassets Accounts receivable =

15 4.5

= 3.333 With total assets of $1,000,000, accounts receivable must equal:

Total assets 3.3333 $1, 000, 000 = 3.3333 = $300, 000

Accounts receivable =

From the total asset turnover equation, net sales equal: Net sales Total assets Net sales 4.5 = $1,000,000

Total asset turnover =

Net sales = ( 4.5 )( $1,000,000 ) = $4,500,000

LO: 3 Level: Basic

4.7

The equity multiplier for Spiffy Corporation is 1.75, its EBIT return on assets (EROA) is 0.07, and the value of its equity is $850,000. What is the value of Spiffy’s total assets? What is the value of its EBIT?

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Solution: In this problem we can use the equity multiplier equation (Equation 4.11) and the EROA equation (Equation 4.17) to solve for the values of total assets and EBIT.

Equity multiplier =

Total assets Total equity

EROA=

EBIT Totalassets

First use the equity multiplier equation to solve for total assets: Equity multiplier =

Total assets Total equity

1.75 =

Total assets $850,000

Total assets = 1.75  $850,000 = $1, 487,500

Next, use the EROA equation to solve for EBIT: EROA =

EBIT Totalassets

0.07 =

EBIT $1,487,500

EBIT = 0.07  $1,487,500 = $104,125

LO: 3 Level: Basic

Discussion Questions 4.1

What does it mean when a company’s return on assets (ROA) is equal to its return on equity (ROE)? When ROA equals ROE, it means that the firm does not use any leverage (debt financing). For firms that do use leverage, ROE will be higher than ROA.

LO: 4

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Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: FSA AICPA: Measurement

4.2

Why is too much liquidity not a good thing? Too much liquidity could mean that a firm is not putting its money to work as the shareholders would like. It could mean that the firm’s managers are being too conservative and investing in low-yielding assets, or it could mean that the firm does not have enough investment opportunities and is therefore, hanging onto its cash. Recently, several firms including Microsoft had several billions of dollars in cash on their books, and, ultimately, Microsoft paid a special dividend to its shareholders. Too much liquidity can also make it a takeover target for firms looking to utilize the debt capacity of the liquid firm.

LO: 3 Level: Intermediate Bloomcode: Comprehension AASCB: Analytic IMA: FSA AICPA: Measurement

4.3

Inventory is excluded when the quick ratio or acid-test ratio is calculated because inventory is the most difficult current asset to convert to cash without loss of value. What types of inventory are likely to be most easily converted to cash without loss of value? For the quick ratio, one uses only the most liquid of all assets—that is, all current assets less inventory, which is not very liquid relative to cash or receivables. While the current ratio assumes that inventory could be sold at book value, the quick ratio assumes that inventory has no value. Hence, this gives a more conservative estimate of a firm’s liquidity than the current ratio, and gives a better estimate of the firm’s ability to meet its

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short-term obligations. Inventories of a raw material commodity, such as gold or crude oil, are more likely to be sold with little loss in value. LO: 3 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: FSA AICPA: Measurement

4.4

What does a very high inventory turnover ratio signify? This could mean a number of things, including that the firm is using up its inventory too fast and is unable to meet the demand for its products, or it has priced its products too low relative to its competitors, or worse, the firm is selling defective products that would eventually be returned, or a highly perishable product, if high turnover is normal.

LO: 3 Level: Basic

4.5

How would one explain a low receivables turnover ratio? A low receivables turnover implies a high DSO. This could mean that the firm’s customers are not paying on time, either because of an inefficient collection system or because of a slowdown in their customers’ business or even in the entire economy.

LO: 3 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: FSA AICPA: Measurement

4.6

What additional information does the fixed asset turnover ratio provide over the total asset turnover ratio? For which industries does it carry greater significance?

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The total asset turnover ratio measures the level of sales per dollar invested in total assets. The higher the number, the more efficiently the management is using the firm’s assets. Too high a number relative to its peers could imply that the firm is reaching its full capacity and may require an additional investment in plant and equipment to generate additional sales. The fixed asset turnover ratio can be utilized to break down the performance of individual manufacturing facilities or a division. This ratio provides significant information for manufacturing firms that are capital-intensive, while it will be of much less significance for the service industry, where there is less reliance on plant and equipment. LO: 3 Level: Intermediate Bloomcode: Analysis AASCB: Analytic IMA: FSA AICPA: Measurement

4.7

How does financial leverage help stockholders? Financial leverage implies the use of debt capital in addition to the owners’ capital to finance the firm. With the addition of debt, the owners’ capital can go a long way in acquiring assets for the firm. Given that creditors only get the fixed-interest payments and do not get any share of the profits from the company, the stockholders gain from the usage of debt. This is called the leverage multiplier effect. As the company’s revenues grow, stockholders benefit more from the profits and the debt holders merely receive their interest payments.

LO: 3 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: FSA AICPA: Measurement

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Why is ROE generally much higher than ROA for banks relative to other industries? Banks have a very small equity base relative to firms in most other industries. Thus, they are highly leveraged with borrowed funds. Since their equity base is small, this magnifies the return on equity, but the return on assets is relatively small for the large asset base.

LO: 3 Level: Intermediate Bloomcode: Analysis AASCB: Analytic IMA: FSA AICPA: Measurement

4.9

Why is the ROE a more appropriate proxy (for stockholder value maximization) for some firms than for other firms? The basis on which any business or investment decisions is evaluated must include the size, timing, and uncertainty of the future cash flows. ROE considers neither the risk of the cash flows nor the size of the initial investment or future cash flows from that investment. While the ROE and shareholder wealth are correlated, this is still a problem in large, well-diversified companies with resources from multiple sources. Smaller firms have fewer resources and sources and can better correlate their ROE to shareholder wealth.

LO: 4 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: FSA AICPA: Measurement

4.10

Why is it not enough for an analyst to look at just the short-term and long-term debt on a firm’s balance sheet when assessing the firm’s fixed obligations?

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The amount of liabilities shown on a firm’s balance sheet is not the total obligation of a firm in any given period. To get a true picture, one needs to look at the financial footnotes that follow the financial statements. This is where you will be able to find the amount of debt repayment that the firm is responsible for in the upcoming years. In addition, off-balance sheet items could reflect certain future liabilities of the firm that do not have to be reported on the balance sheet. One also should look for lease obligations of the firm that are reported on the balance sheet since they represent a fixed obligation that the firm must meet with its cash flows. Thus, it is important for an analyst to look beyond the short-term and long-term debt on the balance sheet to get a true measure of the firm’s financial commitments in any given period. LO: 3, 5 Level: Intermediate Bloomcode: Analysis AASCB: Analytic IMA: FSA AICPA: Measurement

Questions and Problems

BASIC 4.1

Liquidity ratios: Explain why the quick ratio or acid-test ratio is a better measure of a firm’s liquidity than the current ratio.

Solution: The quick ratio is a better or more conservative measure of liquidity than the current ratio. The difference in the measurement of the two is that for the quick ratio we exclude the inventory in accounting of the short-term assets. Thus, the quick ratio is measured as: Quick ratio =

Current assets − Inventory Current assets−Inventory Quick ratio = Current liabilities Current liabilities

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This measure includes only the most liquid of the current assets and hence gives a better measure of liquidity. LO: 3 Bloomcode: Analysis AASCB: Analytic IMA: FSA AICPA: Measurement

4.2

Liquidity ratios: Flying Penguins Corp. has total current assets of $11,845,175, current liabilities of $5,311,020, and a quick ratio of 0.89. How much inventory does it have?

Solution: Current assets = $11,845,175 Current liabilities = $5,311,020 Quick ratio = 0.89 Quick ratio = 0.89 =

Current assets − Inventory Current liabilities $11,845,175 − Inventory $5,311,020

0.89 $5,311,020 = $11,845,175 − Inventory Inventory = $11,845,175 − ( 0.89  $5,311,020 ) = $7,118,367

LO: 3 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

4.3

Efficiency ratio: If Newton Manufacturers has an accounts receivable turnover of 4.8 times and net sales of $7,812,379, what would its receivables be?

Solution: Accounts receivable turnover = 4.8 times

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Net sales = $7,812,379

Net sales Accounts receivable 7,812,379 4.8 = Accounts receivable 7,812,379 Accounts receivable = = $1, 627, 579 4.8

Accounts receivable turnover =

LO: 3 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

4.4

Efficiency ratio: Bummel and Strand Corp. has a gross profit margin of 33.7 percent, sales of $47,112,365, and inventory of $14,595,435. What is its inventory turnover ratio?

Solution: Gross profit margin = 33.7% Sales = $ 47,112,365 Inventory = $14,595,435 Net sales − Cost of goods sold Net sales $47,112,365 − COGS 0.337 = $47,112,365 Cost of goods sold = $47,112,365 – (0.337  $47,112,365) = $31,235, 498

Gross Profit Margin =

Inventory Turnover Ratio =

Cost of goods sold Inventory

Inventory Turnover Ratio =

31,235, 498 = 2.14 times 14,595, 435

LO: 3

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Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

4.5

Efficiency ratio: Sorenson Inc. has sales of $3,112,489, a gross profit margin of 23.1 percent, and inventory of $833,145. What are the company’s inventory turnover ratio and days’ sales in inventory?

Solution: Sales = $3,112,489 Gross profit margin = 23.1% Inventory = $833,145 Gross profit margin = 0.231 =

Net Sales-Cost of goods sold Sales 3,112, 489 − Cost of Goods Sold 3,112,489

Cost of goods sold = 3,112, 489 − (0.231  3,112, 489) = $2,393,504

Inventory turnover ratio =

Cost of goods sold $2,393,504 = Inventory $833,145

= 2.873 times

Day's sales in inventory =

365 365 = Inventory turnover ratio 2.873

= 127.1 days

LO: 3

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Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

4.6

Leverage ratios: Breckenridge Ski Company has total assets of $422,235,811 and a debt ratio of 29.5 percent. Calculate the company’s debt-to-equity ratio and equity multiplier.

Solution: Total assets = $422,235,811 Debt ratio = 29.5% Debt ratio = Total debt/Total assets Total debt = $422,235,811  0.295 = $124,559,564

Total debt = $422,235,811 × 0.295 = $124,559,564

Total equity = Total assets − Total debt = $422, 235,811 − $124,559,564 = $297,676, 247 Debt to equity ratio =

Equity multiplier =

$124,559,564 = 0.42 $297,676,247

Total assets $422,235,811 = = 1.42 Total equity $297,676,247

LO: 3 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

4.7

Leverage ratios: Norton Company has a debt-to-equity ratio of 1.65, ROA of 11.3 percent, and total equity of $1,322,796. What are the company’s equity multiplier, debt ratio, and ROE?

Solution: Debt-to-equity ratio = 1.65

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ROA = 11.3% Total equity = $1,322,796

Equity multiplier = 1 + Debt-to-equity = 1 + 1.65 = 2.65 Equity multiplier =

Total assets Total equity

Total assets = Equity multiplier  Total equity = 2.65  $1,322,796 = $3,505, 409 ROA =

Net income Total assets

Net income = ROA  Total assets = 0.113  3,505, 409 = $396,111 ROE =

Net income $396,111 = = 29.9% Equity $1,322, 796

Debt ratio = 1 − =1−

  Equity 1 = 1 − Total assets  Equity multiplier  1 = 0.623 2.65

LO: 3 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

4.8

DuPont Equation: The Rangoon Timber Company has the following ratios: Net sales/Total assets = 2.23;

ROA = 9.69%;

ROE = 16.4%

What are Rangoon’s profit margin and debt ratios? Solution: Net sales/Total assets = Total assets turnover = 2.23

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ROA = 9.69% ROE = 16.4% ROA = Net profit margin × Total assets turnover ROA 0.0969 = = 0.04345 Total assets turnover 2.23

Profit margin =

= 4.35%

ROE = ROA × Equity multiplier Equity multiplier =

Debt ratio = 1 − =1−

ROE 0.164 = = 1.69 ROA 0.0969

Equity 1 =1− Total assets Equity multiplier 1 = 0.41 1.69

LO: 4 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

4.9

DuPont Equation: Lemmon Enterprises has a total asset turnover of 2.1 and a net profit margin of 7.5%. If its equity multiplier is 1.90, what is the ROE for Lemmon Enterprises?

Solution: Total asset turnover = 2.1 Net profit margin = 7.5% Equity multiplier = 1.90 ROE = ROA × Equity multiplier ROA = Net profit margin × Total asset turnover = 7.5% × 2.1 = 15.75% ROE = 15.75% × 1.9 = 29.93% LO: 4

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Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

4.10

Benchmark analysis: List the ways a company’s financial manager can benchmark the company’s own performance.

Solution: Financial managers can benchmark their firm’s performance by collecting data in three ways: through trend analysis, industry average analysis, and peer group analysis. LO: 5 Bloomcode: Knowledge AASCB: Analytic IMA: FSA AICPA: Measurement

4.11

Benchmark analysis: Trademark Corp.’s financial manager collected the following information for its peer group to compare its performance against that of its peers. Ratios

Trademark

Peer Group

DSO

33.5 days

27.9 days

Total asset turnover

2.3

3.7

Inventory turnover

1.8

2.8

Quick ratio

0.6

1.3

a. Explain how Trademark is performing relative to its peers. b. How do the industry ratios help Trademark’s management? Solution: a.

One can see that Trademark is not doing as well as its competitors. The asset turnover ratio indicates that the firm either needs to increase its sales relative to its level of assets or reduce its assets relative to its level of sales. In addition, the lower quick ratio indicates a lower level of liquidity, perhaps because of too much inventory. A reduction in the inventory would help Trademark improve its performance to a level that is comparable to

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its peer group. In addition, collection of receivables is longer, which could result in cash flow problems and non-payments. b.

Average industry ratios serve as benchmarks for the firm’s management to measure its own performance. While no two firms are identical in any industry, the average ratios across the industry are good target ratios for a firm.

LO: 5 Bloomcode: Analysis AASCB: Analytic IMA: FSA AICPA: Measurement

4.12

Market-value ratios: Rockwell Jewelers management announced that the company had net earnings of $6,481,778 for this year. The company has 2,543,800 shares outstanding, and the year-end stock price is $54.21. What are Rockwell’s earnings per share and P/E ratio?

Solution: Net earnings = $6,481,778 Shares outstanding = 2,543,800 Year-end stock price = $54.21 Earnings per share = EPS =

Net earnings $6, 481,778 = Shares outstanding 2,543,800

= $2.55 Price-earnings ratio =

Price per share $54.21 = Earnings per share $2.55

= 21.26 times

LO: 3 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

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Solutions Manual

Market-value ratios: Chisel Corporation has 3 million shares outstanding at a price per share of $3.25. If the debt-to-equity ratio is 1.7 and total book value of debt equals $12,400,000, what is the market-to-book ratio for Chisel Corporation?

Solution: Shares outstanding = 3,000,000 Market price per share = $3.25 Debt-to-equity ratio = 1.7 Total book value of debt = $12,400,000 Market value of equity = 3,000,000 × $3.25 = $9,750,000 Book value of equity =

$12,400,000 1.7

= $7,294,117.65 Market-to-book =

$9,750,000 $7,294,117.65

= 1.34

LO: 3 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

INTERMEDIATE 4.14

Liquidity ratios: Laurel Electronics has a quick ratio of 1.15, current liabilities of $5,311,020, and inventories of $7,121,599. What is the firm’s current ratio?

Solution: Quick ratio = 1.15 Current liabilities = $5,311,020 Inventory = $7,121,599

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Quick ratio =

Solutions Manual

Current assets − Inventory Current assets − $7,121,599 = Current liabilities $5,311,020

= 1.15 =

Current asset − $7,121,599 $5,311,020

Current assets = (1.15  $5,311,020) + $7,121,599 Current assets = $13,229,272 Current ratio =

Current assets $13,229,272 = = 2.49 Current liabilities $5,311,020

Current ratio =

Current assets Current liabilities

$13,229,272 $5,311,020

= 𝟐. 𝟒𝟗

Excel solution method: A

Given 4

Quick ratio

Current liabilities

$5,311,020

Inventory

$7,121,599

Description

Values

Comments

Current assets

$13,229,272

=(+B5*B4)+B6

10 Current ratio

2.49

1.15

=+B9/B5

LO: 3 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

4.15

Efficiency Ratio: Lambda Corporation has current liabilities of $450,000, a quick ratio of 1.8, inventory turnover of 5.0, and a current ratio of 3.5. What is the cost of goods sold for Lambda Corporation?

Solution:

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Solutions Manual

Current liabilities = $450,000 Quick ratio = 1.8 Inventory turnover ratio = 5.0 Current ratio = 3.5 Current assets = 3.5 × $450,000 = $1,575,000

Quick ratio = 1.8 =

Current assets − Inventory Current liabilities $1,575, 000 − Inventory $450, 000

Inventory = $1, 575,000 – (1.8  $450, 000) = $765,000 Inventory turnover =

Cost of goods sold Inventory

Cost of goods sold = 5.0  $765,000 = $3,825,000 Excel solution method: A

Given 3

Current liabilities

Quick ratio

1.8

(CA-CL)/CL

Inventory turnover ratio

5.0

COGS/Inv

Current ratio

3.5

CA/CL

$450,000

Description

Values

Comments

Current assets

$1,575,000

=+B6*B3

$765,000

=+B9-(B4*B3)

$3,825,000

=+B5*B10

10 Inventory 11 Cost of goods sold LO: 3 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

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4.16

Solutions Manual

Efficiency ratio: Norwood Corp. currently has accounts receivable of $1,223,675 on net sales of $6,216,900. What are its accounts receivable turnover and days’ sales outstanding (DSO)?

Solution: Accounts receivable = $1,223,675 Net sales = $6,216,900 Accounts receivable turnover =

Net sales $6,216,900 = Accounts receivable $1,223,675

= 5.08 times Accounts receivable turnover =

Net sales $6,216,900 = Accounts receivable $1,223,675

= 5.08 times

DSO =

365 365 = = 71.8 days Accounts receivable turnover 5.08

Accounts receivable turnover = 365

Net sales Accounts receivable

$6,216,900 $1,223,675

= 5.08 𝑡𝑖𝑚𝑒𝑠Accounts receivable turnover =

365

Accounts receivable turnover

= 5.08 = 71.9 days

Excel solution method: Given A

Accounts receivable

$1,223,675

Net sales

$6,216,900

Description

Values

Units

Comments

Accounts receivable turnover

5.08

times

=+B4/B3

Days' sales outstanding (DSO)

71.84

days

=365/B7

LO: 3 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

SM 4-31

Net sales Accounts receivable

$6,216,900 $1,223,675

Parrino et al. Fundamentals of Corporate Finance, 5th edition

Solutions Manual

Efficiency ratio: If Norwood Corp.’s management wants to reduce the DSO from that

4.17

calculated in Problem 4.16 to an industry average of 56.3 days and its net sales are expected to decline by about 12 percent, what would be the new level of receivables be? Solution: Target DSO = 56.3 days New level of sales = $6,216,900 x ( 1 - 0.12) = $5,470,872

DSO = 56.3 Days =

365 Net sales/Accounts receivable

Accounts receivable =

DSO  Net sales 365

56.3  $5, 470,872 365

= $843, 863 Excel solution method: Given A

Target Days' sales outstanding 3 (DSO)

56.3

days

4 Original sales

$6,216,900

Description

Values

Comments

$5,470,872

=+B4*0.88

$843,863

=+B3*B6/365

7 New net sales (88% of original) 8 Accounts receivable LO: 3 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

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4.18

Solutions Manual

Coverage ratios: Nimitz Rental Company had depreciation expenses of $108,905, interest expenses of $78,112, and an EBIT of $1,254,338 for the last fiscal year. What are the times interest earned and cash coverage ratios for this company?

Solution: Depreciation = $108,905 Interest expenses = $78,112 EBIT = $1,254,338 Times interest earned =

EBIT $1,254,338 = Interest expense $78,112

= 16.1 times

Cash coverage ratio = =

EBITDA EBIT + Depreciation = Interest expense Interest expense $1,363,243 $78,112

= 17.5 times

Excel solution method: Given A

Depreciation expenses

$108,905

Interest expenses

$78,112

Units

Formula

Comments

EBIT/Interest expense

=+B5/B4

Earnings before interest and taxes

(EBIT)

$1,254,338

Description

Values

Times interest earned

16.1 times

EBITDA/Interest

Cash coverage ratio

17.5 times

expense

=(B5+B3)/B4

LO: 3

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Solutions Manual

Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

4.19

Leverage ratios: Conseco, Inc., has a debt ratio of 0.56. What are the company’s debt-toequity ratio and equity multiplier?

Solution: Debt ratio = 0.56 Debt ratio = Total debt/Total assets Equity ratio = 1 – Total debt/Total assets Equity multiplier = =

Total assets 1 = Total equity Total equity / Total Assets 1 1 = 1 − Total debt / Total assets 1 − 0.56

= 2.27

Equity multiplier = 1 + (Debt to equity ratio) Debt-to-equity ratio = Equity multiplier − 1 = 2.27-1 = 1.27 LO: 3 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

4.20

Profitability ratios: Cisco Systems has total assets of $35.594 billion, total debt of $9.678 billion, and net sales of $22.045 billion. Its net profit margin for the year is 20 percent, while the operating profit margin is 30 percent. What are Cisco’s net income, EROA, ROA, and ROE?

Solution: Total assets = $35.594 billion

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Solutions Manual

Total debt = $9.678 billion Net sales = $22.045 billion Net profit margin = 20% Operating profit margin = 30%

Net profit margin =

Net income Sales

Net income = 0.2  $22.045 billion = $4.409 billion

EBIT Sales EBIT = 0.3  $22.045 billion

Operating profit margin =

= $6.614 billion EROA = ROA = Net income Total assets

EBIT $6.614 = = 18.6% Total assets $35.594

Net income $4.409 EBIT $6.614 = = 12.4% EROA = = $35.594 = 18.6%ROA = Total assets Total assets $35.594

$4.409 $35.594

= 12.4%

Total equity = Total assets – Total debt = $35.594 − $9.678 = $25.916 billion Equity multiplier =

Total assets $35.594 = Total equity $25.916

= 1.37

ROE = ROA  EM = 12.4%  1.37 = 17% Excel solution method: Given A

Total assets

$35.594 billion

Total debt

$9.678 billion

Net sales

$22.045 billion

Net profit margin

20% Net income/Sales

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Operating profit margin

Solutions Manual

30% EBIT/Sales

Description

Values

Formula

Comments

Net income

4.409 Sales x Net Profit Margin

=+B5*B6

Earnings before interest and taxes (EBIT)

6.614 Operating PM x Sales

=+B7*B5

Earnings before interest and taxes (EBIT) 12

ROA

18.58% EBIT/Total assets

=+B11/B3

13 14

Return on Assets (ROA)

12.39% Net income/Total assets

=+B10/B3

Total equity

$25.916 Total assets - Total debt

=+B3-B4

Equity multiplier (EM)

1.37 Total assets/Total equity

=+B3/B14

Return on Equity (ROE)

17% ROA x EM

=+B13*B15

LO: 3 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

4.21

Profitability ratios: Procter & Gamble reported the following information for its fiscal year end: On net sales of $51.407 billion, the company earned net income after taxes of $6.481 billion. It had cost of goods sold of $25.076 billion and EBIT of $9.827 billion. What are the company’s gross profit margin, operating profit margin, and net profit margin?

Solution: Net sales = $51.407 billion Net income = $6.481 billion Cost of goods sold = $25.076 billion EBIT = $9.827 billion

Gross profit margin = =

Net sales − Cost of goods sold Net sales $51.407 − $25.076 = 51.2% $51.407

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Operating profit margin =

EBIT $9.827 = = Net sales $51.407

19.1% Oprerating profit margin =

Net profit margin =

Solutions Manual

EBIT $9.827 = = 19.1% Net sales $51.407

Net income $6.481 Net income = = 12.6% Net profit margin= = Net sales $51.407 Net sales

$6.481 = 12.6% $51.407 Operating profit margin = $𝟗.𝟖𝟐𝟕 $𝟓𝟏.𝟒𝟎𝟕

EBIT Net sales

= 𝟏𝟗. 𝟏%Net profit margin =

𝟏𝟐. 𝟔%Net profit margin =

Net income Net sales

$9.827 $51.407

= 𝟏𝟗. 𝟏%Operating profit margin =

Net income Net sales

$6.481 $51.407

EBIT Net sales

= 12.6%

Excel solution method: A

Known 3

Net sales

$51.407 billion

Net income

$6.481 billion

Cost of goods sold (COGS)

$25.076 billion

Earnings before interest and taxes (EBIT)

$9.827 Net income/Sales

Description

Values

Gross profit margin

51.2% (Net sales - COGS)/Net sales

Formula

Comments =(B3-B5)/B3

10 Operating profit margin

19.1% EBIT/Net Sales

=B6/B3

11 Net profit margin

12.6% Net income/Net sales

=B4/B3

LO: 3 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

4.22

Profitability ratios: WalMart, Inc., has net income of $9,054,000 on net sales of $256,329,812. The company has total assets of $104,912,112 and stockholders’ equity of

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Solutions Manual

$43,623,445. Use the extended DuPont identity to find the return on assets and return on equity for the firm. Solution: Net income = $9,054,000 Net sales = $256,329,812 Total assets = $104,912,112 Stockholders’ equity = $43,623,445 Net income $9,054,000 = = 3.53% Net sales $256,329,812

Profit margin =

Total assets turnover =

Profit margin =

Net sales $256,329,812 = = 2.44 times. Total assets $104,912,112

Net income Net sales

$9,054,000 $256,329,812

3.53%Total assets turnover =

Net sales Total assets

$256,329,812 $104,912,112

= 2.44 times

Return on assets = Profit margin  Total assets turnover = 3.53%  2.44 = 8.61% ROE = ROA  EM = 8.61% 

Total assets Total equity

= 8.61% 

$104,912,112 $43,623, 445

= 20.71%

Excel solution method (adjusts for rounding error above): A

Known 3

Net income

$9,054,000

Net sales

$256,329,812

Total assets

$104,912,112

Stockholders' equity

$43,623,445

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Description 9

Values

Profit margin

Solutions Manual

Formula

Comments

3.53% Net income/Net sales

10 Total assets turnover

=+B3/B4

2.44 Net sales/Total assets

=+B4/B5

11 Return on assets

8.61% Profit margin x Total assets turnover

=+B9*B10

12 Equity multiplier

2.405 Total assets/Total equity

=+B5/B6

13 Return on equity

20.71% ROA x EM

=+B11*B12

Note that both ROA and ROE are slightly different due to Excel rounding differently than manually with a calculator. LO: 3 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

4.23

Profitability ratios: Xtreme Sports Innovations has disclosed the following information: EBIT = $25,664,300

Net income = $13,054,000

Total debt = $20,885,753

Total assets = $71,244,863

Net sales = $83,125,336

Compute the following ratios for this firm using the DuPont Identity: debt-to-equity ratio, EROA, ROA, and ROE. Solution: EBIT = $25,664,300 Net income = $13,054,000 Net sales = $83,125,336 Total debt = $20,885,753 Total assets = $71,244,863 Debt-to-equity = =

Debt Total debt = Equity (Total assets − Total debt)

$20,885,753 Debt Total debt = 0.41 Debt-to-equity = = = Equity (Total assets−Total debt) ($71,244,863 − $20,885,753) $20,885,753

($71,244,863−$20,885,753

= 0.41

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Solutions Manual

Equity multiplier=1 + Debt-to-equity-ratio = 1 + 0.41 = 1.41 Equity multiplier = 1 +

Debt-to-equity-ratio = 1 + 0.41 = 1.41

EROA =

EBIT $25,664,300 = Total assets $71,244,863

= 36.02%

ROA =

Net income $13,054,000 = Total assets $71,244,863

= 18.32% ROE = ROA  EM = 18.32%  1.41 = 25.83% Excel solution method (adjusts for rounding error above): A

Formula

Comments

Known 3

EBIT

$25,664,300

Net income

$13,054,000

Net sales

$83,125,336

Total debt

$20,885,753

Total assets

$71,244,863

Description

Values

=+B6/(B710

Debt-to-equity ratio

0.41 Total debt/(Total assets - Total debt)

Equity multiplier

EROA

36.02% EBIT/Total assets

=+B3/B7

Return on assets (ROA)

18.32% Net income/Total assets

=+B4/B7

Return on equity (ROE)

25.83% ROA x EM

=+B13*B11

1.41 1+ Debt-to-equity ratio

B6) =1+B10

Note that both ROA and ROE are slightly different due to Excel rounding differently than manually with a calculator. LO: 3

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Solutions Manual

Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

4.24

Market-value ratios: Cisco Systems had net income of $4.401 billion and at year end 6.735 billion shares outstanding. Calculate the earnings per share for the company.

Solution: Net income = $4.401 billion Shares outstanding = 6.735 billion Earnings per share =

Net income $4.401 = = $0.65 per share Shares outstanding 6.735

LO: 3 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

4.25

Market-value ratios: Use the information for Cisco Systems in Problem 4.24. In addition, the company’s EBITDA was $6.834 billion, and its share price was $22.36. Compute the firm’s price-earnings ratio.

Solution: EBITDA = $6.834 billion Share price = $22.36

Price − earnings ratio =

$22.36 $22.36 = 34.4 times Price − earnings ratio = = $0.65 $0.65

𝟑𝟒. 𝟒 𝐭𝐢𝐦𝐞𝐬 LO: 3

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Solutions Manual

Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

4.26

DuPont equation: Carter, Inc., a manufacturer of electrical supplies, has an ROE of 23.1 percent, a profit margin (PM) of 4.9 percent, and a total asset turnover (TATO) ratio of 2.6 times. Its peer group also has an ROE of 23.1 percent, but has outperformed Carter with a net profit margin (PM) of 5.3 percent and a total asset turnover (TATO) ratio of 3.0 times. Explain how Carter managed to achieve the same level of profitability as reflected by the ROE.

Solution: Carter Inc: ROE = 23.1%, PM = 4.9%, TATO = 2.6 times

ROA = PM  TATO = 0.049  2.6 = 0.1274

ROE = 0.231 = ROA  EM EM =

0.231 = 1.81 times 0.1274

Peer Group: ROE = 23.1%, PM = 5.3%, TATO = 3 times

ROE = 0.231 = PM  TATO  EM EM =

0.231 = 1.45 times 0.053  3

Carter matched its peer group’s ROE by using a higher degree of financial leverage as indicated by its higher equity multiplier. LO: 4 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

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4.27

Solutions Manual

DuPont equation: Grossman Enterprises has an equity multiplier (EM) of 2.6 times, total assets (TA) of $2,312,000, an ROE of 14.8 percent, and a total asset turnover (TATO) ratio of 2.8 times. Calculate the firm’s sales and ROA.

Solution: EM = 2.6 times TA = $2,312,000 ROE = 14.8% TATO = 2.8 times

Total asset turnover =

Sales Total assets

2.8 =

Sales $2,312,000

Sales = 2.8  $2,312,000 = $6, 473, 600 ROE = ROA  EM ROA = =

ROE EM 0.148 = 0.0569 = 5.69% 2.6

LO: 4 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

ADVANCED 4.28

Complete the balance sheet of Flying Roos Corporation. Flying Roos Corporation Balance Sheet

Assets:

Liabilities and Equity:

Cash and marketable securities

Accounts payable and accruals

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Accounts receivable

Solutions Manual

Notes payable

Inventory

$ 300,000

Total current liabilities

Total current assets Long-term debt Net plant and equipment

$2,000,000

Common stock Retained earnings

Total assets

$8,000,000

$1,250,000

Total liabilities and equity

You have the following information: Debt ratio = 40%

Current ratio = 1.5

Net sales = $2.25 million

DSO = 39 days

Inventory turnover ratio (ITO) = 3.375

Cost of goods sold = $1.6875 million Solution:

Total debt = 0.4  Total assets = 0.4  $8,000,000 = $3,200,000 Accounts payable = Total debt − (Long term debt + Notes payable) = $3,200,000 − ($2,000,000 + $300,000) = $900,000 Inventory turnover ratio =

Inventory =

cost of goods sold Cost of goods sold Inventory turnover ratio = Inventory Inventory

Cost of goods sold $1,687,500 = ITO 3.375

= $500,000

DSO =

Accounts receivable Accounts receivable DSO = Sales/365 Sales/365

Accounts receivable = DSO 

Sales $2,250,000 = 39  365 365

= $240, 411 Current assets = Current ratio  Current liabilities = 1.5  $1,200,000 = $1,800,000

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Solutions Manual

Net plant and equipment (Fixed assets) = Total assets – Total Current assets = $8,000,000 - $1,800,000 = $6,200,000 Cash = Current assets – (Accounts receivable + Inventory) = $1,800,000 – ($240,411 + $500,000) = $1,059,589 Common stock = Total liabilities and Equity – (Total liabilities + Retained earnings) = $8,000,000 – ($3,200,000 + $1,250,000) = $3,550,000 Flying Roos Corporation Balance Sheet Assets

Liabilities and Equity

Cash and marketable securities

$1,059,589

Accounts receivable

240,411

Inventories

500,000

Total current assets

$1,800,000

Net plant and equipment

6,200,000

Total assets

$8,000,000

Accounts payable Notes payable

Total current liabilities

$ 900,000 300,000

$1,200,000

Long-term debt

2,000,000

Common stock

3,550,000

Retained earnings

1,250,000

Total liabilities and equity

$8,000,000

Excel Template available in Wiley Course Resources Excel Template Solution available in Wiley Instructor Resources LO: 3 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

4.29

The Northern Clothing Company has total assets of $87,631,181, ROA of 11.67 percent, ROE of 21.19 percent, and a net profit margin of 11.59 percent. What are the company’s net income and net sales? Calculate the firm’s debt-to-equity ratio.

Solution: Total assets = $87,631,181

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Solutions Manual

ROA = 11.67%, ROE = 21.19%, PM = 11.59% Net Income = Return on Assets  Total Assets = 0.1167  87,631,181 = $10, 226, 559

Net sales = $10,226,559 0.1159

Net Income $10,226,559 Net income = = $88, 236, 057 Net sales = = Profit margin Profit margin 0.1159

= $𝟖𝟖, 𝟐𝟑𝟔, 𝟎𝟓𝟕

Total equity = NI/ROE = $10,226,559 / 0.2119 = $48,261,251 Total debt = Total assets − Total equity = $87,631,181 − $48,261,251 = $39,369,930

Debt to equity ratio =

Total debt $39,369,930 = Equity $48,261,251

= 81.6%

Excel Template available in Wiley Course Resources Excel Template Solution available in Wiley Instructor Resources LO: 3, 4 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

4.30

Blackwell Automotive’ s balance sheet at the end of its most recent fiscal year shows the following information: Blackwell Automotive Balance Sheet

Assets: Cash and marketable sec.

Liabilities and Equity: $

23,015

Accounts payable and accruals

$ 163,257

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Accounts receivable

141,258

Inventory

Notes payable

212,444

Total current assets

Solutions Manual

Total current liabilities

21,115 $ 184,372

$ 376,717 Long-term debt

Net plant and equipment

711,256

Goodwill and other assets

89,879

Total assets

$1,177,852

Total liabilities

168,022 $ 352,394

Common stock

313,299

Retained earnings

512,159

Total liabilities and equity

$1,177,852

In addition, it was reported that the firm had a net income of $156,042 on net sales of $4,063,589. a.

What are the firm’s current ratio and quick ratio?

Calculate the firm’s days’ sales outstanding, total asset turnover ratio, and fixed asset turnover ratio.

Solution:

Current ratio = a.

Current assets $376,717 = Current liabilities $184,372

= 2.04 times

Quick ratio =

Current assets − Inventory $376,717 − $212, 444 = Current liabilities $184,372

= 0.89 times b. DSO =

365 365 = Accounts receivable turnover Net sales/Accounts receivable

365  Accounts receivable 365  $141,258 = Net sales $4,063,589

= 12.69 days

Total asset turnover =

Net sales $4,063,589 = Total assets $1,177,852

= 3.45 times

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Fixed asset turnover =

Solutions Manual

Net sales $4,063,589 = Net fixed assets $711,256

= 5.71 times Excel Template available in Wiley Course Resources Excel Template Solution available in Wiley Instructor Resources LO: 3 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

4.31

The following are the financial statements for Nederland Consumer Products Company for the fiscal year. Nederland Consumer Products Company Income Statement

Net sales

$51,407

Cost of products sold

25,076

Gross profit

$26,331

Marketing, research, administrative exp.

15,746

Depreciation

758

Operating income (loss)

$ 9,827

Interest expense

477

Earnings (loss) before income taxes

$ 9,350

Income taxes

2,869

Net earnings (loss)

$ 6,481

Nederland Consumer Products Company Balance Sheet Assets: Cash and marketable securities

Liabilities and Equity: $ 5,469

Accounts payable

$ 3,617

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Investment securities

423

Accounts receivable Inventory

Solutions Manual

Accrued and other liabilities

7,689

4,062

Taxes payable

2,554

4,400

Debt due within one year

8,287

Total current liabilities

$22,147

Deferred income taxes

958

Prepaid expenses & other

1,803

Long-term debt

12,554

receivables $17,115

Deferred income taxes

2,261

Property, plant, and equip., at cost

Total current assets

25,304

Other noncurrent liabilities

2,808

Less: Accumulated depreciation

11,196

Net property, plant, and equipment

$14,108

Total liabilities Convertible Class A preferred

$39,770 1,526

stock Net goodwill and other intangible

23,900

Common stock

2,141

1,925

Retained earnings

13,611

Total stockholders’ equity

$17,278

Total liabilities and equity

$57,048

assets Other noncurrent assets

Total assets

$57,048

Calculate all the ratios for which industry figures are available below for Nederland and compare the firm’s ratios with the industry ratios. Ratio

Industry Average

Current ratio

2.05

Quick ratio

0.78

Gross margin

23.9%

Net profit margin

12.3%

Debt ratio

0.23

Long-term debt to equity

0.98

Times interest earned

5.62

ROA

5.3%

ROE

18.8%

Solution:

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Nederland

Average Current ratio

2.05

Quick ratio

0.78

0.77 ($17,115/$22,147) Current assets / Current liabilities 0.57 ($17,115/$22,147) (Current assets - Inventory) / Current liabilities

Gross margin

23.9%

51.2% ($26,331/$51,407) Gross profit / Net Sales

Net profit margin

12.3%

12.6% ($ 6,481/$51,407) Net income / Net Sales

Debt ratio

0.23

0.70 ($39,770/$57,048) Total debt / Total assets

Long-term debt-to-equity

0.98

0.73 ($12,554/$17,278) Long-term debt / Total equity

Times interest earned

5.62

19.6

ROA

5.3%

11.4% ($6,481/$57,048) Net income / Total assets

ROE

18.8%

37.5% ($6,481/$17,278)

($9,350/$477) EBIT / Interest Expense

Net income / Total equity

Comparison of Nederland’s ratios with those of the industry average: Current ratio: Nederland is much less liquid than the industry average which suggests potential for bankruptcy. Quick ratio: Even after inventory is eliminated, the firm is still less liquid than the industry average. Gross margin: Nederland has a better gross margin than the industry average suggesting better control of variable costs. Net profit margin: The firm has a slightly higher net profit margin than the industry suggesting good expense control. Debt ratio: The firm has a much higher debt ratio than the industry average. This high level of leverage is dangerous, if the firm has any unexpected changes and cannot meets its debt obligations it can be pushed into bankruptcy. Long-term debt-to-equity: The fact that the long-term debt-to equity ratio is lower than the industry average means that they are not using cheap long-term debt effectively. Combined with the higher debt ratio it suggests they are using too much short-term debt to finance their obligations, a dangerous and risky precedent. Times interest earned: This is better than the industry average implying good coverage of interest expense from earnings before interest and taxes.

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ROA: Much higher than the industry average which implies overall, the firm is doing well and making effective use of total assets. ROE: Much higher than the industry average which implies overall, the firm is doing well and making effective use of its shareholders’ capital.

In general, the company uses too much short-term financing leading to a potential liquidity problem, or difficulty in the ability to cover its current bills.

Excel Template available in Wiley Course Resources Excel Template Solution available in Wiley Instructor Resources LO: 3 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

4.32

Refer to the preceding information for Nederland Consumer Products Company. Compute the firm’s ratios for the following categories and briefly evaluate the company’s performance using these numbers. a.

Efficiency ratios

Asset turnover ratios

Leverage ratios

Coverage ratios

Solution: Efficiency Ratios Inventory turnover ratio

5.70

COGS/Inventory = $25,076/$4,400

Days sales in inventory

64.05 days

365/ITO = 365/5.70

Accounts receivables turnover

12.66 times

Sales/AR = $51,407/$4,062

DSO

28.84 days

365/AR turnover = 365/12.66

0.90 times

Sales/TA = $51,407/$57,048

Asset Turnover Ratios Total asset turnover

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Fixed assets turnover

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Sales/FA (net) = $51,407/$14,108

Leverage Ratios Total debt ratio

0.70

TD/TA = $39,770/$57,048

Debt-to-equity ratio

2.30

D/E = $39,770/$17,278

Equity multiplier

3.30

TA/E = $57,048/$17,278

Times interest earned

19.60

EBIT/Interest = $9,350/$477

Cash coverage

21.19

(EBIT + Depreciation)/Interest =

Coverage Ratios

($9,350 + $758)/$477

Excel Template available in Wiley Course Resources Excel Template Solution available in Wiley Instructor Resources LO: 3 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

4.33

Refer to the earlier information for Nederland Consumer Products Company. Using the DuPont identity, calculate the return on equity for Nederland, after calculating the ratios that make up the DuPont identity.

Solution: (ratio computations from 4.31 and 4.32) Net Profit margin Total assets turnover ratio

12.6%

NI/Sales

0.90 times

Sales/TA

Equity multiplier

3.30

TA/E

Return on assets

11.4%

NI/TA

Return on equity

37.4%

[PM×TATO×EM = 12.6% x .90 x 3.3]

Excel Template available in Wiley Course Resources Excel Template Solution available in Wiley Instructor Resources

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LO: 4 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

4.34

Nugent, Inc., has a gross profit margin of 31.7 percent on net sales of $9,865,214 and total assets of $7,125,852. The company has a current ratio of 2.7 times, accounts receivable of $1,715,363, cash and marketable securities of $315,488, and current liabilities of $870,938. a.

What is Nugent’s total current assets?

How much inventory does the firm have? What is the inventory turnover ratio?

What is Nugent’s days’ sales outstanding?

If management sets a target DSO of 30 days, what should Nugent’s accounts receivable be?

Solution: Cash & marketable securities = $315,488

Accounts receivable

= $1,715,363

Current liabilities = $870,938

Total assets = $7,125,852

Sales = $9,865,214

Gross profit margin = 31.7%

Current ratio = 2.7 a.

Current ratio = 2.7 =

Current assets Current liabilities Current assets $870,938

Current assets = 2.7  $870,938 = $2, 351, 533

Current assets = Cash and marketable securities + Accounts receivable + Inventory $2,351,533

= $315,488 + $1,715,363 + Inventory

Inventory

= $2,351,533– ($315,488 + $1,715,363) = $320,682

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Cost of goods sold = Sales x (1 – Gross PM) = $9,865,214 × (1 – 0.317) = $6,737,941 Inventory turnover ratio = =

Cost of goods sold Inventory $6,737,941 = 21.01 times $320,682

DSO = = d.

365 365  Accounts receivable = Net sales / Accounts receivable Net sales 365  $1,715,363 = 63.5 days $9,865,214

Target DSO = 30 days

Target DSO =

30= Accounts receivable =

365 365  Accounts receivable = Net sales/Accounts receivable Net sales

365×Accounts receivable $9,865,214 30  $9,865,214 = $810, 840 365

The firm must limit its accounts receivable to $810,840 at its current sales level to achieve its target DSO of 30 days. LO: 3 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

4.35

Recreational Supplies Co. has net sales of $11,655,000, an ROE of 17.64 percent, and a total asset turnover (TATO) of 2.89 times. If the firm has a debt-to-equity ratio of 1.43, what is the company’s net income?

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EM = 1 + D/E ratio = 1 + 1.43 = 2.43

ROE = PM  TATO  EM PM =

ROE 0.1764 = TATO  EM 2.89  2.43

= 2.51% NI = Sales  PM = $11,655,000  0.0251 = $292, 540.50

LO: 4 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

4.36

Nutmeg Houseware, Inc., has an operating profit margin of 10.3 percent on revenues of $24,547,125 and total assets of $8,652,352. a.

Calculate the company’s total asset turnover ratio and its operating profit (EBIT).

The company’s management has set a target for the total asset turnover ratio of 3.25 for next year. If there is no change in the total assets of the company, what will the new net sales level have to be next year? Calculate the dollar change in sales necessary and the percentage change in sales necessary.

If the operating profit margin declines to 10 percent, what will be the EBIT at the new level of net sales?

Solution: Operating PM = 10.3% Sales = $24,547,125 Total assets = $8,652,352

TATO = a.

Sales $24,547,125 = Total assets $8,652,352

= 2.84 times

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Operating profit = EBIT = Op. PM  Sales = 0.103  $24,547,125 = $2, 528, 354 b.

New TATO = 3.25 times = New sales/TA New sales = TATO  TA = 3.25  $8,652,352 = $28,120,144 $ Change in Sales = $28,120,144 − $24,547,125 = $3, 573, 019

% Change in sales = $3,573,019/ $24,547,125 = 14.6% c.

Operating PM = 10% Sales = $28,120,144.

New EBIT = Operating profit margin  Sales = 0.10  $28,120,144 = $2, 812, 014 LO: 3 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

4.37

Modern Appliances Corporation has reported its financial results for the latest fiscal year. Modern Appliances Corporation Income Statement Net Sales

$5,398,412,000

Cost of goods sold

3,432,925,255

Gross profit

$1,965,486,745

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Selling, general, and admin. expenses Depreciation

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1,036,311,231 299,928,155

Operating income

$ 629,247,359

Interest expense

35,826,000

EBT

$ 593,421,359

Income taxes

163,104,554

Net earnings

$ 430,316,805

Modern Appliances Corporation Balance Sheet Assets:

Liabilities and Equity:

Cash and cash

$ 514,412,159

Short-term borrowings

$ 117,109,865

1,046,612,233

Trade accounts payable

466,937,985

981,870,990

Other current liabilities

994,289,383

equivalents Accounts receivable Inventory Other current assets

313,621,610

Total current assets

$2,856,516,992

Total current liabilities

$1,578,337,233

Net fixed assets

754,660,275

Long-term debt

1,200,691,565

Goodwill

118,407,710

Common stock

397,407,352

Other assets

665,058,761

Retained earnings

1,218,207,588

Total assets

$4,394,643,738

Total liabilities and equity

$4,394,643,738

Using the information from the financial statements, complete a comprehensive ratio analysis for Modern Appliances Corporation. a.

Calculate these liquidity ratios: current and quick ratios.

Calculate these efficiency ratios: inventory turnover, accounts receivable turnover, DSO.

Calculate these asset turnover ratios: total asset turnover, fixed asset turnover.

Calculate these leverage ratios: total debt ratio, debt-to-equity ratio, equity multiplier.

Calculate these coverage ratios: times interest earned, cash coverage.

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Calculate these profitability ratios: gross profit margin, net profit margin, ROA, ROE.

Use the DuPont identity after calculating the component ratios to compute ROE.

Solution: a.

Liquidity Ratios Current ratio

1.81 Current assets/Current

($2,856,516,992/1,578,337,233) Quick ratio ($2,856,516,992 -

liabilities 1.19 (Current assets-Inventory)

$981,870,990)

/Current liabilities 1,578,337,233)

Efficiency Ratios Inventory turnover ratio

$3,432,925,255

3.50 times

COGS/Inventory

5.16 times

Net sales/AR

70.74 days

365/AR turnover

1.23 times

Net sales/Total assets

7.15 times

Net sales/Fixed assets

0.63

Total debt/Total assets

1.72

Debt/Equity

$981,870,990 Accounts receivable turnover ($5,398,412,000 / $1,046, 612,233) DSO (365/5.16) c.

Asset Turnover Ratios Total asset turnover

$5,398,412,000 $4,394,643,738

Fixed assets turnover

$5,398,412,000

$754,660,275 d.

Leverage Ratios Total debt ratio ($1,578,337,233 + $1,200,691,565) $4,394,643,738 Debt to equity ratio ($1,578,337,233 + $1,200,691,565)

($397,407,352 + $1,218,207,588)

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Equity multiplier

$4,394,643,738

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2.72

Total assets/Equity

17.56

EBIT/Interest

($397,407,352 + $1,218,207,588) e.

Coverage Ratios Times interest earned $629,247,359/$35,826,000 Cash coverage ($629,247,359 +

25.94 (EBIT + Depreciation)/Interest

$299,928,155) $35,826,000 f.

Profitability Ratios Gross profit margin

0.36

Gross profit/Net sales

0.08

Net income/Net sales

ROA $430,316,805/$4,394,643,738

0.10

Net income/Total assets

ROE $430,316,805/($397,407,352 +

0.27

Net income/Equity

$1,965,486,745/$5,398,412,000 Net profit margin $430,316,805/$5,398,412,000

$1,218,207,588) g.

DuPont identity. ROE =

Net income Net Sales



Net Sales Total assets  Total assets Common equity

= 0.08  1.23  2.72 = 0.27 LO: 3, 4 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

CFA PROBLEMS

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4.38

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Common-size analysis is used in financial analysis to: a.

evaluate changes in a company’s operating cycle over time.

predict changes in a company’s capital structure using regression analysis.

compare companies of different sizes or compare a company with itself over time.

restate each element in a company’s financial statement as a proportion of the similar account for another company in the same industry.

Solution: c is correct. The most significant benefit of using common-size statements is scaling, whether for a given company or over time. Common-size analysis allows us to make comparisons of investments, financing, and profitability between companies of different sizes and over time for a single company. LO: 2 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

4.39

The TBI Company has a number of days of inventory of 50. Therefore, the TBI Company’s inventory turnover is closest to: a.

4.8 times.

7.3 times.

8.4 times.

9.6 times.

Solution: b is correct. We perform the calculations using the following relationship: Inventory turnover = Cost of goods sold/Inventory Days’ sales in inventory = 365 days/Inventory turnover Cost of goods sold Inventory  = 365 Cost of goods sold Inventory 365

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Inventory turnover  Number of days inventory = 365.

Inserting the given information, we have Inventory turnover × 50 = 365 and solving for Inventory turnover provides a turnover of 7.3 times. LO: 3 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

4.40

DuPont analysis involves breaking return-on-assets ratios into their: a.

profit components.

marginal and average components.

operating and financing components.

profit margin and turnover components.

Solution: d is correct. This is the DuPont “triangle,” in which profit margins and turnovers are used to explain returns. LO: 4 Bloomcode: Comprehension AASCB: Analytic IMA: FSA AICPA: Measurement

4.41

If a company’s net profit margin is –5 percent, its total asset turnover is 1.5 times, and its financial leverage ratio is 1.2 times, its return on equity is closest to a.

–9.0 percent.

–7.5 percent.

–3.2 percent.

1.8 percent.

Solution: a is correct.

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Net income Average total equity Net income Net sales Average total assets =   Net sales Average total assets Average total equity

Return on equity =

Return on equity = –5% × 1.5 × 1.2 = –9.0% LO: 4 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

Sample Test Problems Greenfern Corporation recently filed the following financial statements with the SEC. Greenfern Corporation Income Statement Net sales

$73,236

Cost of products sold

52,092

Gross profit

$21,144

Selling, general, and administrative expenses

9,333

Depreciation

1,060

Operating income (loss)

$ 10,751

Interest expense

649

Earnings (loss) before income taxes

10,102

Income taxes

3,536

Net earnings (loss)

$ 6,566

Greenfern Corporation Balance Sheet Assets:

Liabilities and Stockholders’ Equity:

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Cash and marketable securities

$ 9,118

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Accounts payable

$ 6,379

Accounts receivable

7,844

Accrued and other liabilities

5,663

Inventory

8,900

Taxes payable

4,821

878

Debt due within one year

10,778

2,803

Total current liabilities

$27,641

Deferred income taxes Prepaid expenses & other receivables Total current assets

$29,543

Long-term debt

24,280

Property, plant, and equipment

62,467

Deferred income taxes

6,903

Less: Accumulated depreciation

22,196

Other non-current liabilities

5,608

Net property plant and equip.

$40,271

Goodwill and other intangible

16,270

Total liabilities

$64,432

Common stock

3,667

Retained earnings

17,985

assets Total stockholders’ equity (deficit)

$21,652

Total liabilities and stockholders’ equity Total assets

4.1

$86,084

Refer to the preceding balance sheet and income statement for Greenfern Corporation. What are the company’s current ratio and quick ratio? What do these ratios tell us about Greenfern?

Solution: Current ratio =

Current assets $29,543 Current assets $29,543 = = 1.07 Current ratio = = $27,641 = Current liabilities Current liabilities $27,641

1.07 Quick ratio =

Current assets − Inventory $29,543 − $8,900 = = 0.75 Quick ratio = Current liabilities $27, 641 Current assets−Inventory $29,543−$8,900 = = 0.75 Current liabilities $27,641

The current ratio of just over 1 tells us that Greenfern’s cash and marketable securities, and other current assets, such as accounts receivable and inventory, if liquidated, will just provide enough proceeds to cover short-term liabilities. The quick ratio of Greenfern indicates that if we exclude inventory, which might be considerably less liquid than other

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current assets, the remaining current assets can cover just 75 percent of the short-term liabilities. LO: 3 Level: Intermediate Bloomcode: Analysis AASCB: Analytic IMA: FSA AICPA: Measurement

4.2

Refer to the preceding balance sheet and income statement for Greenfern Corporation. Calculate the following ratios: a. Inventory turnover b. Days’ sales outstanding. c. Total asset turnover. d. Fixed asset turnover. e. Total debt ratio. f. Debt-to-equity ratio. g. Times interest earned ratio. h. Cash coverage ratio.

Solution: Ratio a. Inventory turnover

Formula

Calculation

Value

Cost of Goods Sold/Inventory

$52,092/$8,900

5.85

b. Days’ sales outstanding 365/Acct. Rec Turnover

$7,844/($73,236/365 days)

39.1 days

Net sales/Total assets

$73,236/$86,084

0.85

d. Fixed asset turnover

Net sales/Total fixed assets

$73,236/$40,271

1.82

e. Total debt ratio

Total debt/Total assets

$64,432/$86,084

0.75

f. Debt-to-equity ratio

Total debt/Total equity

$64,432/$21,652

2.98

g. Times interest earned ratio EBIT/Interest Expense

$10,751/$649

16.57

h. Cash coverage ratio (EBIT + Depn. Exp.)/Interest

($10,751 + $1,060)/$649

18.20

c. Total asset turnover

Expense

LO: 3 Level: Intermediate

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Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

4.3

Refer to the preceding balance sheet and income statement for Greenfern Corporation. Use the DuPont identity to calculate the return on equity (ROE). In the process, calculate the following ratios: net profit margin, total asset turnover, equity multiplier, EBIT return on assets (EROA), and return on assets.

Solution: Net profit margin = Net income/Net sales

= $ 6,566 / $73,236 = 0.0897 or 8.97%

Total asset turnover = Net sales/Total assets = $73,236 / $86,084 = 0.85 Equity multiplier = Total assets/Total equity = $86,084 / $21,652 = 3.98 EROA = EBIT/Total assets = $10,751/$86,084 = 0.1249 or 12.49% Return on assets = Net income/Total assets = $ 6,566 / $86,084 = 0.0763 or 7.63% DuPont identity: ROE = ROA × Equity multiplier = Net profit margin × Total asset turnover × Equity multiplier = 0.0897 × 0.85 × 3.98 = 0.3035 = 30.35% LO: 3, 4 Level: Intermediate Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

4.4

Last year Pontiff Enterprises reported net sales of $13,144,680, a gross profit $4,127,429, EBIT of $2,586,150, and net income of $867,555. Compute Pontiff’s cost of goods sold, gross profit margin, operating profit margin, and net profit margin.

Solution:

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Cost of goods sold = Net sales − Gross profit = $13,144,680 − $4,127,429 = $9,017,251 Gross profit margin = Gross profit/Net sales = $4,127,429/$13,144,680 = 0.3140, or 31.40% Operating profit margin = EBIT/Net sales = $2,586,150/$13,144,680 = 0.1967, or 19.67% Net profit margin = Net income/Net sales = $867,555/$13,144,680 = 0.0660, or 6.60%

Cost of goods sold = Net sales − Gross profit = $13,144,680 − $4,127,429 = $9,017,251Gross profit margin = Gross profit/Net sales = $4,127,429/$13,144,680 = 0.3140,or31.40%Operating profit margin = EBIT/Net sales = $2,586,150/$13,144,680 = 0.1967,or19.67%Net profit margin = Net income/Net sales = $867,555/$13,144,680 = 0.0660,or6.60%LO: 3 Level: Intermediate Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

4.5

National City Bank has 646,749,650 shares of common stock outstanding that are currently selling for $37.55 per share on the New York Stock Exchange. If National City’s net income was $2,780,955,000 in the year that just ended, what was its earnings per share and what is its current price-earnings ratio? If the typical price-earnings ratio for a bank is currently 15, what does the price-earnings ratio for National City tell you about its prospects?

Solution: Earnings per share ( EPS) = =

Net income Shares outstanding $2,780,955,000 = $4.30 646,749,650

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Price-earnings ratio = =

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Share price EPS $37.55 = 8.73 $4.30

The fact that the price-earnings ratio for National City of 8.73 is well below the typical value for a bank tells us that the market places a smaller value on each current dollar of earnings at National City than on each current dollar of earnings at the typical bank. This suggests that the market is less optimistic about National City’s prospects than it is about the prospects of the typical bank. LO: 3 Level: Intermediate Bloomcode: Analysis AASCB: Analytic IMA: FSA AICPA: Measurement

Ethics Case Discussion Questions 1. To what extent do market pressures encourage unethical behavior? Can the demise of Andersen be blamed on the fact that the market began rewarding consulting services of the kind Andersen could provide? This question encourages students to reflect on how a company like Andersen with a history of integrity and ethical conduct could go astray. Expect a debate between those who blame changing demands in the market and those who blame individuals at Andersen for poor judgment and character flaws. Market pressures frequently encourage unethical behavior. The inherent conflict of interest from Andersen wanting to continue the lucrative consulting and audit services are clearly a factor in the demise of Andersen. At a minimum, it called into question their appearance of independence. If market pressures are to blame or are at least partly to blame, students might consider what could be done to mitigate such pressures. This allows for a discussion of the strengths and weaknesses of regulation of the financial markets and allows the

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instructor to indicate just what Sarbanes Oxley (SOX) has done to eliminate some of the pressures by making certain activities on the part of accounting firms illegal.

2. How serious are the kinds of conflicts of interest discussed in this case? Did SarbanesOxley eliminate the most serious conflicts? Companies tendering audits and having firms competing for them has always been a source of conflict of interest and continues today. This question focuses on one of the main ethical breakdowns in the Enron - Andersen saga: conflict of interest. Andersen was involved in numerous conflicts of interest. Some were endemic to the accounting profession such as being paid by the client they audited and the provision of audit services. But other conflicts were especially high profile at Andersen-the revolving door of Andersen employees at Enron and Enron employees at Andersen, the actual participation of Andersen in Enron internal auditing and the constant sharing of resources between the two. Students might discuss which conflicts of interest are potential but without much danger of serious consequences and which conflicts of interest could lead to serious problems. Also conflicts of interest are ethical problems that can be legislated away. This provides a further opportunity for the role of regulation in financial markets. Having a firm "audit itself" which occurs when the audit firm is also providing accounting services is a more serious conflict of interest and one that was eliminated with SOX.

3. Was it fair for the government to destroy an entire company because of the misdeeds of some of its members, or had Anderson become such a serial offender that such action on the part of the government was justified? Question three shifts the ethical issue to the conduct of the government. Was Andersen a serial offender with a corrupt culture or did many Andersen employees suffer for the sins of a few. What is fair in this context? Was the government heavy handed in making an example of Andersen? And of course, such discussions ultimately return to the pros and cons of government oversight and regulation. This question also reminds students that there were a number of stakeholders that assisted Enron. At least 10 financial firms were involved as well as a prestigious law firm. They did not pay as high a price as Andersen. Was that fair? While it is true that there were several significant audit failures around the time of Enron, Andersen was a well- established and highly competent

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firm who may have been unfairly punished compared to the other equally culpable players involved in this situation.

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Chapter 3

Financial Statements, Cash Flows, and Taxes Before You Go On Questions and Answers Section 3.1 1.

What types of information does a firm’s annual report contain? A firm’s annual report is typically divided into three sections: financial tables which contain financial information about the firm and its operations, with an accompanying verbal explanation of the firm’s performance over the past year; a corporate public relations section discussing the firm’s operations, and the audited financial statements (balance sheet, income statement, statement of cash flows, and statement of retained earnings).

What is the realization principle, and why may it lead to a difference in the timing of when revenues are recognized on the books and cash is collected? According to the realization principle, revenue should only be recognized when the earning process is completed and the exchange of goods or services can be determined by an arm’s length transaction. Although this principle works in theory, it still does not specify whether realization should occur at the point when the goods are ordered, when they are shipped, or when the payment is actually received from the customer. Also, not many purchases are paid for in cash any more. Therefore, even if the transaction is recognized at the point at which the customer receives the goods, the actual cash flow might not occur until days later (depending what the terms are).

Section 3.2 1.

What is net working capital? Why might a low value for this number be considered undesirable?

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Net working capital is the difference between total current assets and total current liabilities. A low value for this number is undesirable, because it indicates that the company may not have enough cash on hand or liquid assets to cover its immediate expenses.

Explain the accounting concept behind depreciation. Depreciation in accounting is a noncash expense that helps to allocate the cost of an item over its expected life. It reflects the estimated decrease in the value of an asset due to wear and tear and obsolescence.

What is treasury stock? Treasury stock is the stock that the company repurchased from its investors. These shares do not pay dividends, have no voting rights, and should not be included in sharesoutstanding calculations.

Section 3.3 1.

What is the difference between book value and market value? Book value is the price you paid for a particular asset. This price does not change as long as you own the asset. On the other hand, market value is the price at which you can sell an asset today, as it takes into account how much it can earn in the future.

What are some objections to the preparation of marked-to-market balance sheets? Marked-to-market balance sheets list the firm’s assets and liabilities at their current market values. Even though a balance sheet constructed with actual market values might paint a more accurate picture of the company’s financial situation, current values ofter are difficult to estimate, and a lot of the complicated models are potentially open to abuse. Therefore, as of the present, the norm is to use book values.

Section 3.4 1.

How is net income computed?

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Net income is calculated as revenues minus expenses. It is the most comprehensive accounting measure of a company’s performance because it reflects the firm’s accomplishments (revenues) relative to its efforts (expenses) during a time period.

What is EBITDA, and what does it measure? EBITDA stands for earnings before interest, taxes, depreciation, and amortization. EBIT is defined as earnings before taxes and interest. The main difference between these two figures is that EBITDA shows the income earned purely from operations and reflects how efficiently a firm can manufacture and sell its products without taking into account the cost of the productive asset base.

What accounting events trigger changes to the retained earnings account? Two events will trigger changes to the retained earnings account: (1) a firm’s report of a net income or loss and (2) the board of directors’ declaration of a cash dividend.

Section 3.5 1.

How do increases in fixed assets from one period to the next affect cash holdings for the firm? An increase in fixed assets from one period to the next is a use of cash. If a company purchases fixed assets during the year, it decreases cash because it must use cash to pay for the purchase.

Name two working capital accounts that represent sources of cash for the firm. An increase in current liabilities is a source of cash. Two common current liabilities are accounts and notes payable. An increase in either of these accounts from one period to the next will represent a source of cash for the firm.

Explain the difference between cash flows from financing and investment activities. Cash flows from financing activities occur when cash is obtained from (cash inflow) or paid to (cash outflow) long-term creditors or owners (stockholders). Cash flows from

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investing activities relate to the buying (cash outflow) and selling of long-term assets (cash inflow).

Section 3.6 1.

Explain how the four financial statements are related. The four financial statements are linked together as follows: the ending cash balance from the statement of cash flows is used as the cash balance on the balance sheet, and the net income reported in the income statement is transferred to retained earnings statement and after dividends are deducted, the ending retained earnings balance is then reported on the balance sheet. So as you can see, the balance sheet is the one financial statement that ties all four statements together.

Section 3.7 1.

How does the calculation of net income differ from the calculation of cash flow to investors from operating activity? Net income is calculated as the difference between revenues and expenses from the income statement. Cash flow from operating activity is the firm’s earnings before interest and taxes (EBIT) minus taxes paid in cash plus the firm’s noncash expenses, including depreciation and amortization.

All else being equal, if a firm increases its accounts payable, what effect will this have on cash flow to investors? Changes in net working capital accounts do not impact cash flow to investors.

What does it mean when a firm’s cash flow to investors is negative? When a firm’s investment of cash flow from net working capital and long-term assets exceeds the firm’s cash flow from operating activity, the cash flow to investors will be negative. A negative cash flow to investors means that the firm must raise money from new issues of debt or equity.

Section 3.8

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Why is it important to consider the consequences of taxes when financing a new project? When financing a new project, it is important to consider the consequences of taxes because ultimately these have a significant impact on the company’s income.

Which type of tax rate, marginal or average, should be used in analyzing the expansion of a product line, and why? When analyzing the expansion of a product line, the marginal tax rate should be considered because it is the amount paid on an additional dollar of income earned. Since expansion of a product line is expected to generate new cash flows, the company will be taxed based on the additional earnings. Under a single or “flat” tax system the average and marginal taxe rates will be the same.

What are the tax implications of a decision to finance a project using debt rather than new equity? The difference between debt financing and financing through new equity is in the tax treatment of interest and dividends. While interest payments on debt are tax-deductible business expenses, dividends paid to common or preferred stockholders are not deductible.

Self-Study Problems and Solutions 3.1

The going concern assumption of GAAP implies that the firm: a.

Is going under and needs to be liquidated at historical cost.

Will continue to operate and its assets should be recorded at historical cost.

Will continue to operate and that all assets should be recorded at their cost rather than at their liquidation value.

d. Solution:

Is going under and needs to be liquidated at liquidation value. One of the key assumptions under GAAP is the going concern assumption, which states that the firm:

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(c) will continue to operate and that all assets should be recorded at their cost rather than at their liquidation value. LO: 1 Level: Basic

3.2

The Ellicott City Ice Cream Company management has just completed an assessment of the company’s assets and liabilities and has obtained the following information. The firm has total current assets worth $625,000 at book value and $519,000 at market value. In addition, its long-term assets include plant and equipment valued at market for $695,000, while their book value is $940,000. The company’s total current liabilities are valued at market for $543,000, while their book value is $495,000. Both the book value and the market value of long-term debt is $350,000. If the company’s total assets are equal to a market value of $1,214,000 (book value of $1,565,000), what are the book value and market value of its stockholders’ equity?

Solution:

The book value and market value of stockholders’ equity are shown below (in thousands of dollars): Ellicott City Ice Cream Company Balance Sheet ($ thousands)

Assets

Liabilities and Equity Book

Total current assets Fixed assets

Market

$ 625

$ 519

940

695

Book Total current liabilities

Market

$ 495

$ 543

Long-term debt

350

Stockholders’ equity

720

321

$1,565

$1,214

Total liabilities and Total assets

$1,565

$1,214

stockholders’ equity

Assets = Liabilities + Stockholders’ Equity or restated, Assets – Liabilities = Stockholders’ Equity; $1,565 – ($495 + $350) = $720 (Book); $1,214 – ($543 + $350) = $321 (Market) LO: Level: Basic

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Depreciation and amortization expenses are: a.

Part of current assets on the balance sheet.

After-tax expenses that reduce a firm’s cash flows.

Long-term liabilities that reduce a firm’s net worth.

Noncash expenses that cause a firm’s after-tax cash flows to exceed its net income.

Solution:

Depreciation and amortization expenses are: (d) noncash expenses that cause a firm’s after-tax cash flows to exceed its net income.

LO: 4 Level: Basic

3.4

You are given the following information about Clarkesville Plumbing Company. Revenues in 2020 totaled $896, depreciation expenses $75, costs of goods sold $365, and interest expenses $54. At the end of the year, current assets were $121 and current liabilities were $107. The company has an average tax rate of 29 percent. Calculate its net income by setting up an income statement.

Solution:

Clarkesville’s income statement and net income are as follows: Clarkesville Plumbing Company Income Statement for the Fiscal Year Ending December 31, 2020 Amount Revenues

$896.00

COGS

365.00

EBITDA

$531.00

Depreciation

75.00

EBIT

$456.00

Interest

54.00

EBT

$402.00

Taxes (29%)

116.58

Net income

$285.42

LO: 4

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Level: Basic 3.5

The Huntington Rain Gear Company had $633,125 in taxable income in the year ending September 30, 2020. Calculate the company’s tax using using a flat tax rate of 25%.

Solution:

Huntington’s tax bill is calculated as follows: Tax rate 25%

Income $633,125

Tax $158,281.25

LO: 8 Level: Basic

Discussion Questions 3.1

What is a major reason for the accounting scandals in the early 2000s? How do firms sometimes attempt to meet Wall Street analysts’ earnings projections? Many people believe that managers’ short-term focus is driven by Wall Street’s demand that companies meet or beat the earnings forecasted by stock analysts. Rather than report the actual earnings of the firm, managers try to meet the market’s expectations by starting with the bottom-line number and backing into a sales figure. Thus, the sales may be consistent with the reported earnings figure, but do not represent the true revenue generated by the firm.

LO: 1 Level: Basic Bloomcode: Comprehension AACSB: Communication IMA: Reporting AICPA: Reporting

3.2

Why are taxes and the tax code important for managerial decision making?

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Understanding the tax code is critical to finance managers, since most decisions are made on an after-tax basis. Furthermore, taxes affect any valuation analysis and also determine the bottom-line figure that is of concern to shareholders and managers. LO: 8 Level: Basic Bloomcode: Comprehension AACSB: Analytic IMA: Budget Preparation AICPA: Decision Modeling

3.3

Identify the five fundamental principles of GAAP, and explain briefly their importance. The assumption of arm’s length transaction assumes that all business transactions between two parties are made rationally and independently from an economic perspective and both parties will make the deal that provides them the best value. The cost principle calls for the recognition of all accounting transactions at historic cost, or the amount paid or received when the transaction was concluded at arm’s length. The realization principle implies that revenue should be recognized only at the time of the sale. The matching principle dictates that revenue is first recognized and then is matched with the costs incurred in producing the revenue. Finally, the going concern assumption implies that the firm will continue to operate and that all assets should be recorded at their cost rather than at their liquidation value.

LO: 1 Level: Basic Bloomcode: Comprehension AACSB: Communication IMA: Reporting AICPA: Reporting

3.4

Explain why firms prefer to use accelerated depreciation methods over the straightline method for tax purposes.

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When a firm uses accelerated depreciation, the depreciation expense is higher in earlier years than with the straight-line method. This reduces the taxable income and the amount of tax paid by the firm. As a result of this higher noncash expense, early in the life of the asset, the firm’s cash flow is higher. LO: 2 Level: Basic Bloomcode: Comprehension AACSB: Communication IMA: Budget Preparation AICPA: Reporting

3.5

What is treasury stock? Why do firms have treasury stock? Any shares repurchased by the company in the open market are recorded as treasury stock in the shareholders’ equity account in the balance sheet. The most common reason for firms doing this is to reduce the number of shares outstanding in the market when the management believes that its firm’s stock is undervalued. This reduction in the number of shares outstanding is expected to boost the share price.

LO: 2 Level: Basic Bloomcode: Comprehension AACSB: Analytic IMA: Coorporate Finance AICPA: Resource Management

3.6

Define book-value accounting and market-value accounting. Book-value accounting implies that all assets and liabilities are recorded and reported at the historical cost when they were acquired. Market-value accounting requires that all assets and liabilities are reported at their current market value.

LO: 3 Level: Basic Bloomcode: Knowledge

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AACSB: Analytic IMA: Reporting AICPA: Reporting

3.7

Compare and contrast depreciation expense and amortization expense. Depreciation expense is the amount by which a firm’s fixed assets are written down in a period during which the assets are utilized for generating cash flows. Amortization is the amount by which intangible assets like goodwill, patents, license, copyrights, and trademarks are written down in any period that they are utilized by the firm to generate benefits. Both depreciation and amortization are noncash expenses that will serve to boost the firm’s after-tax cash flows, and generate actual value of the asset at the end of a period.

LO: 4 Level: Basic Bloomcode: Analysis AACSB: Analytic IMA: Corporate Finance AICPA: Measurement

3.8

Why are retained earnings not considered an asset of the firm? Retained earnings are part of shareholders’ equity that has already been utilized by the company. It is an obligation of the company which corresponds to a claim by the firm’s shareholders. The retained earnings reported on the balance sheet have already been allocated by the company among various assets and hence are not available for current or future uses. New retained earnings have to be generated to provide for new uses.

LO: 2 Level: Basic Bloomcode: Comprehension AACSB: Communication IMA: Reporting AICPA: Reporting

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What is the statement of cash flows, and what is its role? This financial statement records both the cash inflows and cash outflows for a period of time. Thus, it reports the changes in the cash position of a firm between successive accounting periods.

LO: 5 Level: Basic Bloomcode: Knowledge AACSB: Communication IMA: Reporting AICPA: Reporting

3.10

How does a firm’s cash flow to investors from operating activity differ from net income, and why? Net income is an accounting figure that includes both cash and noncash expenses. In addition, revenues are frequently recognized before they are collected and expenses are frequently recognized before they are paid. Cash flow from operating activity recognizes that certain revenues and expenses, while recognized for accounting purposes, do not actually involve a cash flow and ignores the effects of these non-cash items on the income statement.

LO: 5 Level: Basic Bloomcode: Comprehension AACSB: Communication IMA: Reporting AICPA: Reporting

Questions and Problems BASIC

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Balance sheet: Elkridge Sporting Goods, Inc., has cash and marketable securities of $25,135, accounts receivable of $43,758, inventory of $167,112, net fixed assets of $325,422, and other assets of $13,125. It had accounts payable of $67,855, notes payable of $36,454, long-term debt of $223,125, and common stock of $150,000. Given this information construct a balance sheet for Elkridge. How much retained earnings did the firm have?

Solution: Elkridge Sporting Goods, Inc. Balance Sheet Assets

Book Value

Liabilities and Stockholders’

Book Value

Equity

Cash and marketable

$ 25,135 Accounts payables

$ 67,855

Accounts receivable

43,758 Notes payables

36,454

Inventory

167,112

Total current assets

$236,005

Net fixed assets

325,422 Long-term debt

223,125

Other assets

13,125 Common stock

150,000

securities

Total current liabilities

Retained earnings

$104,309

97,118

Total liabilities and Total assets

$574,552

stockholders’ equity

$574,552

Retained earnings = Total assets – Total current liabilities – Long-term debt – Common Stock = $574,552 – $104,309 - $223,125 - $150,000 = $97,118 Retained Earnings LO: 2 Bloomcode: Analysis AACSB: Communication IMA: Reporting AICPA: Reporting

3.2

Inventory accounting: What is the difference between FIFO and LIFO accounting.

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Solution: FIFO (first in, first out) refers to the practice of firms, when making sales, assuming that the inventory that came in first (normally at a lower cost) is being sold first. During the period of rising prices, LIFO (last in, last out) implies that a firm is selling the higher cost, newer inventory first, leaving the lower cost, older inventory on the balance sheet. LO: 2 Bloomcode: Comprehension AACSB: Communication IMA: Budget Preparation AICPA: Reporting

3.3

Inventory accounting: Explain how the choice of FIFO versus LIFO can affect a firm’s balance sheet and income statement.

Solution: FIFO makes sense during times of rising prices because it allows the firm to eliminate the lower priced inventory first, resulting in a higher profit margin. This allows the firm to leave higher valued inventory on the balance sheet. During inflationary times, a firm using LIFO would see a lower profit margin and lower values of inventory on the balance sheet. It is important that anyone who is analyzing firms using different accounting methods on inventory recognize the impact on the bottom line (profit margin and net income per the income statement) and on current assets reported on the balance sheet. LO: 2 Bloomcode: Comprehension AACSB: Communication IMA: Budget Preparation AICPA: Reporting

3.4

Market-value accounting: How does the use of market-value accounting help managers?

Solution:

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Market-value accounting of both assets and liabilities allows managers to have a more accurate picture of their company’s financial condition and to do a better job of estimating cash flows that the assets would generate. However, marking-to-market is not as easy as it sounds because of the difficulties involved in assigning the correct market value of many assets and liabilities. LO: 3 Bloomcode: Comprehension AACSB: Communication IMA: Reporting AICPA: Reporting

3.5

Working capital: Laurel Electronics reported the following information at its annual meetings: The company had cash and marketable securities worth $1,235,455, accounts payables worth $4,159,357, inventory of $7,121,599, accounts receivables of $3,488,121, short-term notes payable worth $1,151,663, and other current assets of $121,455. What is the company’s net working capital?

Solution: Total current assets = Cash and marketable securities + Accounts Receivable + Inventory + Other current assets = $1,235,455 + $3,488,121 + $7,121, 599 + $121,455 = $11,966,630 Total current liabilities = Accounts Payable + Short-term notes payable = $4,159,357 + $1,151,663 = $5,311,020 Net working capital = Current assets – Current liabilities = $11,966,630 - $5,311,020 = $6,655,610 Excel Template available in Wiley Course Resources Excel Template Solution available in Wiley Instructor Resources LO: 2 Bloomcode: Application AACSB: Analytic IMA: Reporting AICPA: Reporting

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Working capital: The financial information for Laurel Electronics referred to in Problem 3.5 is all at book value. Suppose marking to market reveals that the market value of the firm’s inventory is 20 percent below its book value, its receivables are 25 percent below their book value, and the market value of its current liabilities is identical to the book value. What is the firm’s net working capital using market values? What is the percentage difference in net working capital using market versus book values?

Solution: Market value of inventory = $7,121,599 × (1 - 0.20) = $5,697,279 Market value of receivables = $3,488,121 × (1 - 0.25) = $2,616,091 Total current assets = Cash and marketable securities + Accounts receivable (at market) + Inventory (at market) + Other current assets = $1,235,455 + $2,616,091 + $5,697,279 + $121,455 = $9,670,280 Total current liabilities = Accounts payable + Short-term notes payable = $4,159,357 + $1,151,663 = $5,311,020 Net working capital = Current assets – Current liabilities = $9,670,280 - $5,311,020 = $4,359,260 Percent Change =

$4,359,260 − $6,655,610 $6,655,610

= −𝟑𝟒. 𝟓% LO: 2 Bloomcode: Analysis AACSB: Communication IMA: Reporting AICPA: Reporting

3.7

Income statement: The Oakland Mills Company has disclosed the following financial information in its annual report: sales of $1.45 million, cost of goods sold of $812,500, depreciation expenses of $175,000, and interest expenses of $89,575. Assume that the firm has an average tax rate of 29 percent. What is the company’s net income? Set up an income statement to answer the question.

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Solution: Oakland Mills Company Income Statement

Amount Revenues

$1,450,000.00

COGS

812,500.00

EBITDA

$ 637,500.00

Depreciation EBIT Interest EBT

175,000.00 $ 462,500.00 89,575.00 $ 372,925.00

Taxes (29%)

108,148.25

Net income

$ 264,776.75

LO: 4 Bloomcode: Analysis AACSB: Communication IMA: Reporting AICPA: Reporting

3.8

Cash flow: Describe the organization of the statement of cash flows.

Solution: The statement of cash flows identifies the cash inflows and cash outflows of the firms for a specified period. This allows one to estimate the net cash flows from operations. This financial statement is organized to report the cash flows resulting from the three basic activities in any firm—operating, investing, and financing. The cash flows from operations are the results of netting all revenues and expenses that result from the operating activities of the firm. Buying and selling a firm’s assets lead to cash flows from investing activities. Cash flows from financing activities arise from the firm borrowing from and/or making payments to its lenders and shareholders. LO: 5

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3.9

Cash flows: Last year Towson Recording Company increased its investment in marketable securities by $36,845, funded fixed-assets acquisitions of $109,455, and had marketable securities of $14,215 mature. What is the net cash used in investing activities?

Solution: Long-Term Investing Activities Net property, equipment, and other assets

$(109,455.00)

Redemption of marketable securities (matured)

14,215.00

Investments in marketable securities

(36,845.00)

Net cash used in investing activities

$(132,085.00)

LO: 5 Bloomcode: Comprehension AACSB: Communication IMA: Reporting AICPA: Reporting

3.10

Cash flows: Caustic Chemicals management identified the following cash flows as significant in its year-end meeting with analysts. During the year Caustic had repaid existing debt of $312,080 and raised additional debt of $650,000. It also repurchased stock in the open market for a total of $45,250. What is the net cash provided by financing activities?

Solution: Financing Activities Debt repayment

$(312,080)

Increase in long-term debt

650,000

Purchase of treasury stock

(45,250)

Net cash provided by financing activities

$ 292,670

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LO: 5 Bloomcode: Application AACSB: Communication IMA: Reporting AICPA: Reporting

3.11

Cash flows: Identify and describe the noncash expenses that a firm may incur.

Solution: A firm may have several items on its income statement that did not result in any cash outflow to the firm. The two largest are depreciation expenses and amortization expenses. Other non-cash expenses include deferred taxes and depletion charges, which is similar to depreciation and used for natural resource assets. Gains and losses on disposals of assets also fit into this category as they are reported on the income statement but do not involve cash inflows/outflows. LO: 5 Bloomcode: Comprehension AACSB: Communication IMA: Reporting AICPA: Reporting

3.12 Cash flows: Given the data for Oakland Mills Company in problem 3.7 above, compute the cash flows to investors from operating activity. Solution: CFOA = Net Income + Non-cash expenses = $264,776.75 + $175,000.00 = $439,776.75 LO: 7 Bloomcode: Application AACSB: Communication IMA: Reporting AICPA: Reporting

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3.13 Cash flows: Hillman Corporation reported current assets of $3,495,055 on December 31, 2020 and $3,103,839 on December 31, 2019.

Current liabilities for the firm were

$2,867,225 and $2,760,124 at the end of 2020 and 2019 respectively. Compute the cash flow invested in net working capital at Hillman Corporation during 2020. Solution: CFNWC = NWCcurrent period – NWCprevious period = (Current assets, 2020 – Current liablilities, 2020) - (Current assets, 2019 – Current liablilities, 2019) = ($3,495,055 - $2,867,225) – ($3,103,839 - $2,760,124) = $284,115 LO: 7 Bloomcode: Application AACSB: Communication IMA: Reporting AICPA: Reporting

3.14

Cash flows: Del Bridge Construction had long- term assets before depreciation of $990,560 on December 31, 2019 and $1,211,105 on December 31, 2020. How much cash flow was invested in long-term assets for Del Bridge during 2020?

Solution: CFLTA = Long-term assets current period – Long-term assetsprevious period = $1,211,105 - $990,560 = $220,545. LO: 7 Bloomcode: Application AACSB: Communication IMA: Reporting AICPA: Reporting

3.15

Tax: Define average tax rate and marginal tax rate.

Solution:

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The average tax rate is defined as the total taxes paid divided by taxable income. The marginal tax rate, meanwhile, represents the tax rate that is paid on the last dollar of income earned. LO: 8 Bloomcode: Knowledge AACSB: Communication IMA: Reporting AICPA: Reporting

3.16

Tax: What is the relevant tax rate to use when making financial decisions? Explain why.

Solution: Managers need to use the marginal tax rate for making financial decisions. This is because any additional cash flows that result from a firm’s new projects will be taxed at the firm’s marginal tax rate. Thus, this is the appropriate rate to use. LO: 8 Bloomcode: Comprehension AACSB: Communication IMA: Investment Decisions AICPA: Decision Modeling

3.17

Tax: Manz Property Management Company just announced earnings before taxes of $1,478,936. Calculate its taxes using a flat tax rate of 30 percent.

Solution: Earnings before tax = $1,478,936

Tax rate

Income

30%

$1,478,936

Tax $ 443,680.80

LO: 8 Bloomcode: Application AACSB: Communication

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IMA: Reporting AICPA: Measurement

INTERMEDIATE 3.18

Balance sheet: Tim Dye, the CFO of Blackwell Automotive, Inc., is putting together this year’s financial statements. He has gathered the following balance sheet information. The firm had a cash balance of $23,015, accounts payable of $163,257, common stock of $313,299, retained earnings of $512,159, inventory of $212,444, goodwill and other assets equal to $78,656, net plant and equipment of $711,256, and short-term notes payable of $21,115. It also has accounts receivables of $141,258 and other current assets of $11,223. How much long-term debt does Blackwell Automotive have?

Solution: Blackwell Automotive, Inc. Balance Sheet as of December 31 Liabilities and Stockholders’ Assets Cash

Equity $

23,015

Accounts payable

$ 163,257

Accounts receivable

141,258

Short-term notes payable

21,115

Inventory

212,444

Other current assets

11,223

Total current assets

$ 387,940

Total current liabilities

$ 184,372

Net plant and equipment

711,256

Long-term debt

168,022

Goodwill and other assets

78,656

Total liabilities

$ 352,394

Common stock

313,299

Retained earnings

512,159

Stockholders’ Equity

$ 825,458

Total liabilities and Total assets

$1,177,852

stockholders’ equity

$1,177,852

Long-term debt = Total assets – Total current liabilities – Common stock – Retained earnings = $1,177,852 - $184,372 - $313,299 - $512,159 = $168,022

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LO: 2 Bloomcode: Application AACSB: Analytic IMA: Reporting AICPA: Measurement

3.19

Working capital: Mukhopadhya Network Associates has a current ratio of 1.60, where the current ratio is defined as follows: Current ratio = Current assets/current liabilities. The firm’s current assets are equal to $1,233,265, its accounts payable are $419,357, and its notes payable are $351,663. Its inventory is currently at $721,599. The company plans to raise funds in the short-term debt market and invest the entire amount in additional inventory. How much can notes payable increase without the current ratio falling below 1.50?

Solution: Let x be the amount raised through notes payables. New current liabilities = Accounts payable + Notes payable = $419,357 + $351,663 + x = $771,020 + x New current assets = $1,233,265 + x Current assets $1,233,265 + x = 1.5 = Current liabilities $771,020 + x

1.5 × ($771,020 + x) = $1,233,265 + x $1,156,530 + 1.5 x = $1,233,265 + x 1.5 x – x = $1,233,265 - $1,156,530 0.5 x = $76,735 x = $76,735/0.5 = $153,470 Thus the firm can add up to $153,470 in inventory by raising money through notes payable without changing the ratio of current assets to current liabilities to less than 1.50. (This ratio of current assets to current liabilities is known as the current ratio and will be discussed in the next chapter.) LO: 2 Bloomcode: Analysis

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AACSB: Analytic IMA: Corporate Finance AICPA: Measurement

3.20

Market value: Reservoir Bottling Co. reported the following information at the end of the year. Total current assets are worth $237,513 at book value and $219,344 at market value. In addition, plant and equipment have a market value of $343,222, and a book value of $362,145. The company’s total current liabilities are valued at market for $134,889 and have a book value of $129,175. Both the book value and the market value of long-term debt is $144,000. If the company’s total assets have a market value of $562,566 and a book value of $599,658, what is the difference between the book value and market value of its stockholders’ equity?

Solution: Reservoir Bottling Co. Balance Sheet Assets

Book

Market

Value

Book Value

Market

Liabilities and

Value

stockholders’ equity Total current assets

$237,513

$219,344

Total current liabilities

$129,175

$134,889

Net fixed assets

362,145

343,222

Long-term debt

144,000

Other assets

Common stock

326,483

283,677

Total assets

$599,658

$562,566

Total liabilities and

$599,658

$562,566

stockholders’ equity

Common stock (book value) = Total liabilities and stockholders’ equity (book value) – Total current liabilities (book value) - Long-term debt (book value) = $599,658 - $129,175 - $144,000 = $326,483 Common stock (market value) = Total liabilities and stockholders’ equity (market value) – Total current liabilities (market value) - Long-term debt (market value) = $562,566 - $134,889 - $144,000 = $283,677 Change in value of stockholders’ equity = $283,677 – $326,483 = $(42,806) Excel Template available in Wiley Course Resources

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Excel Template Solution available in Wiley Instructor Resources LO: 3 Bloomcode: Analysis AACSB: Analytic IMA: Corporate finance AICPA: Measurement

3.21

Income statement: Nimitz Rental Company provided the following information to its auditors for the latest fiscal year: the company had revenues of $878,412, general and administrative expenses of $352,666, depreciation expenses of $131,455, leasing expenses of $108,195, and interest expenses equal to $78,122. If the company’s average tax rate is 27 percent, what is its net income after taxes?

Solution: Nimitz Rental Company Income Statement Amount Revenues

$878,412

General and administrative expenses

352,666

Leasing expenses

108,195

EBITDA

$417,551

Depreciation expenses

131,455

EBIT

$286,096

Interest expenses EBT

78,122 $207,974

Taxes (27%)

56,153

Net income

$151,821

Excel Template available in Wiley Course Resources Excel Template Solution available in Wiley Instructor Resources LO: 4 Bloomcode: Analysis AACSB: Analytic

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IMA: Reporting AICPA: Measurement

3.22

Income statement: Sosa Corporation recently reported an EBITDA of $31.3 million and net income of $9.7 million. The company had $6.8 million in interest expense, and its average corporate tax rate was 30 percent. What was its depreciation and amortization expense?

Solution: If we look at the income statement we know EBITDA and Net Income from the question, and we are told the tax rate is 30%. So let’s work backwards from Net Income to find EBT (Step1) , then EBIT (Step 2) and then Depreciation and amortization must be the difference between EBITDA and EBIT: DA as: Depreciation and amortization = EBITDA – EBIT (Step 3).

Amount EBITDA

$31,300,000.00

Less: Depreciation and amortization (Step 3)

EBIT (Step 2) Interest

6,800,000.00

EBT (Step 1)

Taxes (30%) Net income

$ 9,700,000.00

Step 1: Calculate EBT Taxes are 30% or 0.3 of EBT and Net Income is therefore, (1 – 30%) or 70% of EBT. Net Income = EBT – Taxes Net Income = EBT – 0.30 (EBT) Net Income = (1-0.30) (EBT) Net Income = (0.70)(EBT)

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EBT

Solutions Manual

= (Net Income/0.70) = ($9,700,000.00/0.70) = $13,857,142.86

Step 2: Calculate EBIT EBIT = EBT + Interest: EBIT = $13,857,142.86 + $6,800,00.00 = $20,657,142.86 Step 3: Calculate Depreciation and amortization EBIT = EBITDA - Depreciation and amortization. So Depreciation and amortization = EBITDA – EBIT Depreciation and amortization = $31,300,000.00 - $20,657,142.86 = $10,642,857.14

The income statement would be as follows: Amount EBITDA

$31,300,000.00

Less: Depreciation and amortization (Step 3)

$10,642,857.14

EBIT (Step 2)

$20,657,142.86

Interest

6,800,000.00

EBT (Step 1)

$13,857,142.86

Taxes (30%)

4,157,142.86

Net income

$ 9,700,000.00

Excel solution method: create partial income statement: A 1

Description

Earnings before interest, taxes, depreciation and

B Values

C Comments

$31,300,000.00

Given

amortization, EBITDA 3

Less: Depreciation and amortization (Step 3)

10,642,857.14

=B2-B4

Earnings before interest and taxes, EBIT (Step 2)

20,657,142.86

=B5+B6

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Interest expense

6,800,000.00

Given

Earinings before taxes, EBT (Step 1)

13,857142.86

=B8/(1-T)

Taxes (30%)

4,157,142.86

=B6*T

Net income

$9,700,000.00

Given

LO: 4 Bloomcode: Application AACSB: Analytic IMA: Reporting AICPA: Measurement

3.23

Income statement: Fraser Corporation has announced that its net income for the year was $1,353,412. The company had EBITDA of $ 4,967,855, and its depreciation and amortization expense was equal to $1,112,685. The company’s average tax rate is 29 percent. What was its interest expense?

Solution: EBIT - Interest Expense = EBT, Interest Expense= EBIT – EBT. So we need need to calculate both EBIT and EBT. Step 1 : Calculate EBIT EBIT = EBITDA - Depreciation and Amortization = $4,967,855.00 - $1,112,685.00 = $3,855,170.00 Step 2 : Calculate EBT Taxes are 29% of EBT and Net Income is therefore, (1 – 29%) or 71% or 0.71 of EBT. So EBT

= (Net Income/0.71)

EBT

= $1,353,412.00/ (0.71) = $1,906,214.08

Step 3: Calculate Interest Expense Interest Expense = EBIT – EBT = $3,855,170.00 - $1,906,214.08 = $1,948,955.92

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The income statement would be as follows: Amount EBITDA

$4,967,855.00

Depreciation and Amortization

1,112,685.00

EBIT

$3,855,170.00

Interest

1,948,955.92

EBT

$1,906,214.08

Taxes (29%)

552,802.08

Net income

$1,353,412.00

Excel solution method: create partial income statement: A

Description

Values

Comments

Earnings before interest, taxes, depreciation and

$4,967,855.00

Given

amortization, EBITDA 3

Less: Depreciation and amortization

1,112,685.00

Given

Earnings before interest and taxes, EBIT (Step 1)

3,855,170.00

=B2-B3

Interest expense (Step 3)

1,948,955.92

=B4-B6

Earinings before taxes, EBT (Step 2)

1,906,214.08

=B8/(1-T)

Taxes

552,802.08

=B6*T

Net income

$1,353,412.00

Given

LO: 4 Bloomcode: Application AACSB: Analytic IMA: Reporting AICPA: Measurement

3.24

Income Statement/Cash Flow from Operations: For its most recent fiscal year, Carmichael Hobby Shop recorded EBITDA of $512,725.20, EBIT of $362,450.20, zero interest expense, and cash flow from operating activity of $348,461.25. Assuming there are no non-cash revenues recorded on the income statement, what is the firm’s net income after taxes?

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Solution: We are trying to find Net Income After Taxes. If we look at an income statement we can see that EBIT = EBT, but we do not know the tax rate, taxes paid, or Depreciation and Amortization. We do, however, know CFOA. From formula (3.4) CFOA = EBIT – TAXES + Noncash Expenses. So we can use all of the information given to calculate taxes and Net Income after taxes. Step 1: Complete the income statement as far as we can with the basic information provided:

EBITDA

$512,725.20

-Depreciation and Amortization =EBIT

$362,450.20

-Interest

0.00

=EBT

$362,450.20

-Taxes =Net income Step 2: Calculate the firm’s noncash expenses (in this case Deprecation and Amoritization) from the Income Statement as follows: EBITDA – DA = EBIT, Therefore DA = EBITDA – EBIT = $512,725.20 - $362,450.20 = $150,275, this is the value of the firm’s noncash expenses Step 3: Use the equation (3.4) to calculate the firm’s Taxes: We are told that CFOA = $348,461.25, from the Income Statement EBIT = $362,450.20, and we just calculated that Noncash expenses = $150,275. From text equation (3.4) CFOA = EBIT – TAXES + Noncash Expenses Rearranging this we can see that TAXES = EBIT + Noncash Expenses – CFOA TAXES = $362,450.20 + $150,275 - $348,461.25

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= $164,263.95 Therefore Net Income after taxes = EBT – TAXES = $362,450.25- $164,263.95 = $198,186.25 The completed income statement is as follows: EBITDA

$512,725.20

-Depreciation and Amortization

$150,275.00

=EBIT

$362,450.20

-Interest

0.00

=EBT

$362,450.20

-Taxes

164,263.95

=Net income

$198,186.25

Excel solution method: create partial income statement: A Description 1

Earnings before interest, taxes, depreciation and

Values

Comments

$512,725.20

Given

amortization, EBITDA 2

Less: Depreciation and amortization (Step 2)

150,275.00

=B1-B3

Earnings before interest and taxes, EBIT

362,450.20

Given

Interest expense

0.00

Given

Earnings before taxes, EBT

362,450.20

=B3-B4

Taxes (Step 3)

164,263.95

=B3+B9-B10

Net income

$198,186.25

=B5-B6

Noncash revenues

$0.00

Noncash expenses

$150,275.00

=B2

$348,461.25

Given

10 Cash Flow from operation activity (CFOA)

Given

LO: 4, 7 Bloomcode: Analysis

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AACSB: Analytic IMA: Reporting AICPA: Measurement

3.25

Eau Claire Paper Mill, Inc., had, at the beginning of the current fiscal year, retained earnings of $323,325. During the year the company produced net income after taxes of $713,445 and paid out 45 percent of its net income as dividends. Construct a statement of retained earnings and compute the year-end balance of retained earnings.

Solution: Eau Claire Paper Mill, Inc. Statement of Retained Earnings Balance of retained earnings, Beginning of year

$ 323,325.00

Add: Net income

713,445.00

Less: Dividends to common stockholders

(321,050.25)

(Net Income, $713,445 × 45%) Balance of retained earnings, End of year

$ 715,719.75

LO: 4 Bloomcode: Analysis AACSB: Analytic IMA: Reporting AICPA: Measurement

3.26

Cash flow: Refer to the information given in Problem 3.21. What is the cash flow from operating activity for Nimitz Rental?

Solution: Cash flow from operations

Net income + Depreciation

$151,281 + $131,455

$282,736

LO: 5 Bloomcode: Application AACSB: Analytic

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IMA: Reporting AICPA: Measurement

3.27

Tax: Mount Hebron Electrical Company’s financial statements indicated that the company had earnings before interest and taxes of $718,323. The interest rate on its $850,000 debt was 8.95 percent. Calculate the federal taxes the company is likely to owe if the tax rate is a flat 30%. What are the marginal and the average tax rates for this company?

Solution: EBIT

$718,323.00

Interest

76,075.00

($850,000 × 8.95%) EBT

$642,248.00

Tax rate

Income

Tax

30%

$642,248.00

$192,674.40

Marginal tax rate

30%

Average tax rate

Total taxes payable / Taxable income (EBT)

= $192,674.40/ $642,248 =

0.30 or 30%

As there is a flat, or single, tax rate the marginal and average rates are equal at 30%. LO: 8 Bloomcode: Analysis AACSB: Analytic IMA: Budget Preparation AICPA: Measurement

ADVANCED

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3.28

Solutions Manual

The Centennial Chemical Corporation just announced income after taxes of $2,768,028.25 on revenues of $13,144,680. The company’s costs (excluding depreciation and amortization) amounted to 61 percent of sales and it had interest expenses of $392,168. What is the firm’s depreciation and amortization expense if its average tax rate is 34 percent?

Solution: Centennial Chemical Corporation Income statement Amount Revenues

$13,144,680.00

Costs ($13,144, 680 × 61%)

$8,018,254.80

EBITDA

$5,126,425.20

Depreciation and amortization}

$540,275.00

($5,126,425.20 - $4,586,150.20)

EBIT ($4,193,982.20 + $392,168) Interest

$4,586,150.20 $392,168.00

EBT [$2,768,028.25 ÷ (1 – 34%)]

$4,193,982.20

Taxes (34%)

$1,425,953.95

Net income

$2,768,028.25

Excel solution method: create partial income statement: A

Description

Values

Comments

Revenues

$13,144,680.00

Costs

8,018,254.80

Given Given (61% of Sales): =B1*0.61

Earnings before interest, taxes, depreciation and

5,126,425.20

=B1-B2

540,275.00

=B3-B5

4,586,150.20

=B7+B6

392,168.00

Given

amortization, EBITDA 4

Less: Depreciation and amortization

Earnings before interest and taxes, EBIT

Interest expense

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Earnings before taxes, EBT

4,193,982.20

Given at T =34%: =B9/(1-0.34)

Taxes

1,425,953.95

Given at T=34%: =B7*0.34

Net income

$2,768,028.25

Given

LO: 4 Bloomcode: Analysis AACSB: Analytic IMA: Reporting AICPA: Measurement

3.29

Retained earnings: Columbia Construction Company earned $451,888 during the year. After paying out $225,794 in dividends, the balance went into retained earnings. If the firm’s total retained earnings were $846,972 at the end of the year 2020, what were the retained earnings on its balance sheet at the start of the year?

Solution: We have to back out the beginning balance by “reversing” the steps in creating the statement of Retained Earnings. We know that for Retained Earnings the Ending Balance = Beginning Balance + Net Income – Dividends. Therefore, Beginning Balance

= Ending Balance – Net Incomce + Dividends = $846,972 - $451,888 + $225,794 = $620,878

The Statement of Retained Earnings would be as follows: Columbia Construction CompanyStatement of Retained Earnings Ending December 31, 2020 Balance of retained earnings, December 31, 2019

$ 620,878

Add: Net income for the year

451,888

Less: Dividends to common stockholders

(225,794)

Balance of retained earnings, December 31, 2020

$ 846,972

LO: 4

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Bloomcode: Application AACSB: Analytic IMA: Reporting AICPA: Measurement

3.30

Menomonie Casino Company earned $23,458,933 before interest and taxes last year and had interest expenses of $1,645,123. If the firm is taxed at 25% on taxable income up to $15,000,000 and 28% on taxable income above $15,000,000, calculate the firm’s tax obligation. What are the marginal and the average tax rates for this company?

Solution: EBIT

$23,458,933.00

Interest

1,645,123.00

EBT

$21,813,810.00

Tax is 25% on $15,000,000 = $3,750,000 28% on ($21,813,810 – 15,000,000) Tax = 28% ($6,813,810) = $1,907,866.80

Tax Rate

Income taxed at this rate

Tax

25%

15,000,000.00

3,750,000.00

28%

6,813,810.00

1,907,866.80

Total

5,657,866.80

Marginal tax rate

28%

Average tax rate

Total taxes payable / Taxable income

$5,657,866.80/ $21,813,810

25.94%

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Bloomcode: Analysis AACSB: Analytic IMA: Reporting AICPA: Measurement

3.31

Vanderheiden Hog Products Corp. provided the following financial information for its most recent quarter : Net income: $189,425 Depreciation and amortization: $63,114 Increase in receivables: $ 62,154 Increase in inventory: $57,338 Increase in accounts payables: $37,655 Decrease in other current assets: $27,450 What is this firm’s cash flow from operating activities during this quarter?

Solution: Vanderheiden Hog Products Corp. Statement of Cash Flows (Partial)

Operating Activities Net income

$189,425

Additions (sources of cash) Depreciation and amortization

63,114

Increase in accounts payable

37,655

Decrease in other current assets

27,450

Subtractions (uses of cash) Increase in receivable

(62,154)

Increase in inventory

(57,338)

Net cash provided by operating activities

$198,152

LO: 5 Bloomcode: Analysis AACSB: Analytic

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IMA: Reporting AICPA: Measurement

3.32

Cash flows: Analysts following the Tomkovick Golf Company were given the following balance sheet information for the years ended June 30, 2020 and June 30 2019. In addition, it was reported that the company had a net income of $ 3,155,848 and that depreciation expenses were equal to $212,366 during 2020. Assume amortization expense was $0 in 2020.

2020

2019

Assets Cash and marketable securities

33,411

16,566

Accounts receivable

260,205

318,768

Inventory

423,819

352,740

Other current assets

41,251

29,912

Total current assets

$ 758,686

$ 717,986

Plant and equipment

1,931,719

1,609,898

Less: Accumulated depreciation

(419,044)

(206,678)

Net plant and equipment

$1,512,675

$1,403,220

Goodwill and other assets

382,145

412,565

$2,653,506

$2,533,771

2020

2019

$ 378,236

$ 332,004

Notes payable

14,487

7,862

Accrued income taxes

21,125

16,815

$ 413,848

$ 356,681

Long-term debt

679,981

793,515

Total liabilities

$1,093,829

$1,150,196

Common stock (10,000 shares)

10,000

Additional paid-in capital

975,465

Retained earnings

587,546

398,110

Less: Treasury stock

(13,334)

$1,559,677

$1,383,575

Total assets

Liabilities and Equity Accounts payable and accruals

Total current liabilities

Preferred stock

Total common equity

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Total liabilities and equity

Solutions Manual

$2,653,506

$2,533,771

2020

2019

Increase (decrease)

Assets Cash and marketable securities

33,411

16,566

$16,845

Accounts receivable

260,205

318,768

(58,563)

Inventory

423,819

352,740

71,079

Other current assets

41,251

29,912

11,339

Total current assets

$ 758,686

$ 717,986

40,700

Plant and equipment

1,931,719

1,609,898

321,821

Less: Accumulated depreciation

(419,044)

(206,678)

(212,366)

Net plant and equipment

$1,512,675

$1,403,220

109,455

Goodwill and other assets

382,145

412,565

(30,420)

$2,653,506

$2,533,771

119,735

2020

2019

$ 378,236

$ 332,004

$46,232

Notes payable

14,487

7,862

6,625

Accrued income taxes

21,125

16,815

4,310

$ 413,848

$ 356,681

57,167

Long-term debt

679,981

793,515

(113,534)

Total liabilities

$1,093,829

$1,150,196

(56,367)

Common stock (10,000 shares)

10,000

Additional paid-in capital

975,465

Retained earnings

587,546

398,110

189,436

Less: Treasury stock

(13,334)

Total common equity

$1,559,677

$1,383,575

176,102

Total liabilities and equity

$2,653,506

$2,533,771

119,735

Total assets

Liabilities and Equity Accounts payable and accruals

Total current liabilities

Preferred stock

Before doing any computations for the requirements, students should first compute the change in the accounts (increase or decrease) based on the comparative balance sheet given in the problem. a. Construct a 2020 cash flow statement for this firm. b. Calculate the net cash provided by operating activities for the statement of cash flows.

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c. What is the net cash used in investing activities? d. Compute the net cash provided by financing activities. Solution: a. Tomkovick Golf Company Statement of Cash FlowsYear Ended June 30, 2020 Operating Activities Net income

$ 3,155,848.00

Additions (sources of cash) Depreciation

212,366.00

Increase in accounts payable

46,232.00

Decrease in accounts receivable

58,563.00

Increase in accrued income taxes

4,310.00

Subtractions (uses of cash) Increase in other current assets

(11,339.00)

Increase in inventory

(71,079.00)

Net cash provided by operating activities

$ 3,394,901.00

Long-Term Investing Activities Increase in plant and equipment

$ (321,821.00)

Decrease in goodwill and other assets Net cash used in investing activities

30,420.00 $ (291,401.00)

Financing Activities Increase in notes payable

6,625.00

Decrease in long-term debt

(113,534.00)

Payment of cash dividends

(2,966,412.00)

Purchase of treasury stock

(13,334.00)

Net cash provided by financing activities

$(3,086.655.00)

Effect of exchange rates on cash

0.00

Net increase in cash and marketable securities

16,845.00

Cash and marketable securities at beginning of

16,566.00

year Cash and marketable securities at end of year

33,411.00

Net cash provided by operating activities = $3,394,901.00

Net cash used in investing activities = $(291,401.00)

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Net cash provided by financing activities = $(3,086.655.00)

Excel Template available in Wiley Course Resources Excel Template Solution available in Wiley Instructor Resources LO: 5 Bloomcode: Analysis AACSB: Analytic IMA: Reporting AICPA: Measurement

3.33

Cash flows: Based on the financial statements for Tomkovick Golf Company in Problem 3.32, compute the cash flow invested in net working capital and the cash flow invested in long-term assets that you would use in a calculation of the cash flows for 2020.

Solution: CFNWC = (Current assets, 2020 – Current liabilities, 2020) – (Current assets, 2019 – Current liabilities, 2019) = ($758,686 – $413,848) – ($717,986 – $356,681) = -$16,467 CFLTA = (Plant and equipment, 2020 – Plant and equipment, 2019) + (Goodwill and other assets, 2020 - Goodwill and other assets, 2019) = ($1,931,719 – $1,609,898) + ($382,145 - $412,565) = $291,401 LO: 7 Bloomcode: Analysis AACSB: Analytic IMA: Reporting AICPA: Measurement

Sample Test Problems 3.1

What is the matching principle, and how can it cause accounting expenses to differ from actual cash outflows?

Solution:

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The matching principle is an accounting principle under which accountants match revenues with the costs incurred to generate those revenues when they prepare an income statement. Because the actual cash flows associated with expenses might not be incurred in the same period that those expenses are recognized in the income statement, the accounting expenses can differ from actual cash outflows. LO: 1 Level: Intermediate Bloomcode: Knowledge AACSB: Analytic IMA: Budget Preparation AICPA: Measurement

3.2

Wolf Pack Enterprises has total current assets of $346,002 and fixed assets of $476,306. The company also has long-term debt of $276,400, $100,000 in its common stock account, and retained earnings of $187,567. What is the value of its total current liabilities?

Solution: Assets

Liabilities and Equity

Total current assets

$346,002

Total current liabilities

$???????

Fixed assets

$476,306

Long-term debt

$276,400

Common stock

$100,000

Retained earnings

$187,567

Liabilities and Total assets

$???????

stockholders’ equity

$???????

First, calculate total assets: $346,002 + $476,306 = $822,308 From Equation 3.1: $822,308 - $276,400 – 100,000 – 187,567 = $258,341 (total current liabilities) LO: 2 Level: Intermediate

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Bloomcode: Analysis AACSB: Analytic IMA: Reporting AICPA: Measurement

3.3

What is the difference between a book-value balance sheet and a market-value balance sheet? Which provides better information to investors and management?

Solution: A book-value balance sheet is an accounting balance sheet in which asset values are listed at their historical cost. A market-value balance sheet reflects current asset values (what the assets are worth today). Market values provide better economic information for investors and managers than book values. Therefore, a market-value balance sheet provides better decision-making information. LO: Level: Intermediate Bloomcode: Analysis AACSB: Analytic IMA: Reporting AICPA: Reporting

3.4

ACME Corporation had revenues last year of $867,030. It also had expenses (excluding depreciation) of $356,240, depreciation of $103,456, and interest expense of $52,423. What was the company’s net income after taxes if its average tax rate was 29 percent?

Solution: Amount Revenues

$867,030.00

Expenses

356,240.00

EBITDA

$510,790.00

Depreciation

103,456.00

EBIT

$407,334.00

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Interest

52,423.00

EBT

$354,911.00

Taxes (29%)

102,924.19

Net income

$251,986.81

LO: 4 Level: Intermediate Bloomcode: Analysis AACSB: Analytic IMA: Reporting AICPA: Measurement

3.5

Last year, True Blue Company increased its investments in marketable securities by $323,370 and paid $1,220,231 for new fixed assets duringthe year. The company also repaid $779,200 of existing long-term debt while raising $913,455 of new debt. In addition, True Blue had a net cash inflow of $345,002 from the sale of fixed assets, and repurchased stock in the open market for a total of $56,001. What is the net cash used in long term investing activities by True Blue? What is the net cash provided by the company’s financing activities?

Solution: Investing Activities Purchase-property, equipment and other assets

$(1,220,231)

Sale-property, equipment and other assets

345,002

Investments in marketable securities

N/A

Net cash used in long term investing activities

$(875,229)

Financing Activities Long-term debt repayment

$(779,200)

Increase in long-term debt

913,455

Purchase of treasury stock

(56,001)

Net cash provided by financing activities

78,254

LO: 5

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Level: Intermediate Bloomcode: Analysis AACSB: Analytic IMA: Reporting AICPA: Measurement

3.6

Sun Devil Corporation reported EBITDA of $7,300,125 and net income of $3,789,882 last year. The company also had $1,155,378 in interest expense, $1,023,285 in depreciation and amortization expense, and an average corporate tax rate of 26 percent. What was the firm’s cash flow from operating activity during the year?

Solution: CFOA = EBIT – Current taxes + Noncash expenses CFOA = EBITDA – Current taxes CFOA = $7,300,125 – [0.26 × ($7,300,125 - $1,023,285 - $1,155,378)] = $5,968,544.88 LO: 7 Level: Intermediate Bloomcode: Analysis AACSB: Analytic IMA: Reporting AICPA: Measurement

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Chapter 2 The Financial System and the Level of Interest Rates Before You Go On Questions and Answers Section 2.1 1.

What critical economic role does the financial system play in the economy? The financial system is in place to gather money from households, businesses and government with surplus funds to invest and then channel these funds to those who need it. An efficient financial system is essential for a healthy economy. The major players in the U.S. financial system are big institutions such as the New York Stock Exchange, Citigroup, or State Farm Insurance.

What are the two basic ways in which funds flow through the financial system from lender–savers to borrower–spenders? There are two basic mechanisms by which funds flow through the financial system: 1) Funds can flow directly through financial markets, and (2) funds can flow indirectly through financial institutions.

Section 2.2 1.

Why is it difficult for individuals to participate in the direct financial markets? The financial markets where direct transactions take place are wholesale markets with a typical minimum transaction size of $1 million. Major buyers and sellers of securities in direct financial markets include commercial banks and other financial institutions, large corporations, the federal, state and local governments, hedge funds, and some wealthy individuals.

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Why might a firm prefer to have a security issue underwritten by an investment banking firm? In the most common type of underwriting arrangement, called firm-commitment underwriting, the investment banker assumes the risk of buying the new securities from the issuing company and reselling them to investors. The investment banker guarantees to buy the entire security issue from the company at a fixed price.

Section 2.3 1.

What is the difference between primary and secondary markets? Primary markets are markets where new securities are sold for the first time. Secondary markets are those where the owners of outstanding securities can sell them to other investors. They provide the means for investors to sell their securities and secure cash.

How and why do large business firms use money markets? Large businesses use money markets to adjust their liquidity positions. If a firm has idle cash sitting around, it can invest it in negotiable CDs, Treasury bills, or other money market instruments. On the other hand, if a company has a temporary cash shortage, it can borrow in the money markets by selling commercial paper at lower interest rates than it could borrow through a commercial bank.

What are capital markets, and why are they important to corporations? Capital markets refer to the segment of the marketplace where capital goods are financed with long-term debt or equities. The most important capital market instruments are common stocks and corporate bonds. Capital markets are important to corporations because they allow them to obtain necessary financing.

Section 2.4 1.

How does information about a firm’s prospects get reflected in its share price?

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Investors act upon the expectations of a firm’s prospects through trading of the securities. The buying and selling then causes the price of the security to reflect their assessment of its value.

What is strong-form market efficiency? semistrong-form market efficiency? weakform market efficiency? Strong-form market efficiency is a market in which all information, private and public, is reflected in the price of the security. The semistrong-form of market efficiency suggests that all public information is reflected in a security’s price, while the weak-form of market efficiency holds that only information contained in the past price of a security is reflected in its current price (it does not reflect public or private information).

Section 2.5 1.

What is financial intermediation, and why is it important? Financial intermediation is the process by which financial institutions act as intermediaries that convert financial securities with one set of characteristics into securities with another set of characteristics. For example, commercial banks use consumer CD deposits to make loans to small businesses.

What are some services that commercial banks provide to businesses? Commercial banks are the largest financial intermediaries in the economy and offer the widest range of financial services to businesses. Nearly every business has a significant relationship with a commercial bank – usually a checking or transaction account and some type of credit or loan arrangement. In addition, banks do a significant amount of equipment lease financing.

What is an IPO, and what role does an investment banker play in the process? Investment bankers specialize in helping firms to sell their new debt or equity issues in financial markets. In an initial public offering (IPO), the investment banker prepares the new issue for sale and then underwrites the deal. Other functions of the investment banker

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in an IPO process include preparing the prospectus, registering the documentation with the SEC, and providing general financial advice to the issuer.

Section 2.6 1.

Explain how the real rate of interest is determined. The real rate of interest depends on the interaction between the rate of return that businesses can expect to earn on investments in capital projects and savers’ time preference for consumption today versus willingness to save. Therefore, the real rate of interest is determined when the desired saving level equals the desired level of borrowing.

How are inflationary expectations accounted for in the nominal rate of interest? The nominal interest rate is the rate that is actually observed in the financial markets, and it is equal to the real interest rate plus the expected annualized changes in prices, or the rate of inflation. This is commonly reflected in the Fisher equation.

Explain why interest rates follow the business cycle. Interest rates tend to follow the business cycle, rising during economic expansions and declining during recessions. On the one hand, during an expansion, there is upward pressure on interest rates as businesses begin to grow and borrow more money. Conversely, during a recession, the demand for goods and services is lower, businesses borrow less, and as a result the economy slows down and the interest rates decline. Typically, during a recession the Fed also loosens credit to stimulate the economy, which puts further downward pressure on the interest rates.

Self-Study Problems and Solutions 2.1

Economic units that need to borrow money are said to be: a.

Lender–savers

Borrower–spenders

Balanced budget keepers.

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None of the above.

Solution: Such units are said to be (b) Borrower-spenders. LO: 1 Level: Basic

2.2

Explain what the marketability of a security is and how it is determined.

Solution: Marketability refers to the ease with which a security can be sold and converted into cash The level of marketability depends on the cost of trading the security and the cost of searching for information. The lower these costs are, the greater the security’s marketability. LO: 3 Level: Basic

2.3

What are over-the-counter markets (OTCs), and how do they differ from organized exchanges?

Solution: Securities that are not listed on an organized exchange are sold OTC. An OTC market differs from an organized exchange in that there is no central trading location. OTC security transactions are made electronically as opposed to on the floor of an exchange. LO: 3 Level: Basic

2.4

What effect does an increase in the demand for business goods and services have on the real interest rate? What other factors can affect the real interest rate?

Solution: An increase in the demand for business goods and services will cause the borrowing schedule in Exhibit 2.4 to shift to the right, thus increasing the real rate of interest. Other factors that can affect the real interest rate include increases in productivity, changes in

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technology, and changes in the corporate tax rate. Demographic factors, such as growth or age of the population, and cultural differences can also affect the real rate of interest. LO: 6 Level: Intermediate

2.5

How does the business cycle affect the nominal interest rate and inflation rate?

Solution: Both the nominal interest and inflation rates tend to follow the business cycle; that is, they rise with economic expansion and fall during a recession. LO: 6 Level: Basic

2.6

You lent $100 to a friend for one year at a nominal rate of interest of 3 percent. Inflation during that year was 2 percent. Did you experience an increase or decrease in the purchasing power of your money? How much did it increase or decrease?

Solution: Since the interest rate that you received (3 percent) exceeded the rate of inflation, the amount that you received from your friend when the loan was repaid had greater purchasing power than $100. The amount by which the purchasing power increased can be calculated using Equation 2.1: 1 + i = (1 + r) × (1+ ∆Pe) Solving for r yields: r = (1 + i)/(1 + ∆Pe) - 1 r = (1 + 0.03)/(1 + 0.02) - 1 r = 0.0098, or 0.98% Therefore, the purchasing power of your money increased by slightly less than 1 percent. LO: 6 Level: Basic

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Discussion Questions 2.1

Explain why total financial assets in the economy must equal total financial liabilities. Every financial asset must be financed with some type of a claim or liability. Since all of an economy’s financial assets are just a collection of the individual financial assets, then they should also sum to the collective claims on those assets in the economy.

LO: 1 Level: Basic Bloomcode: Comprehension AACSB: Analytic IMA: Corporate Finance; Business Economics AICPA: Resource Management

2.2

Why don’t small businesses make greater use of the direct credit markets, since these markets enable firms to finance their activities at a very low cost? Direct credit markets are geared toward big, established companies since they are wholesale in nature and the minimum transaction size is far beyond the needs of a small business. Small businesses are better off borrowing money from financial intermediaries, such as commercial banks.

LO: 5 Level: Basic Bloomcode: Comprehension AACSB: Analytic IMA: Corporate Finance AICPA: Resource Management

2.3

Explain the economic role of brokers and dealers. How does each make a profit?

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Brokers and dealers play a similar economic role in that they both bring buyers and sellers of a commodity together in a market. However, since brokers only facilitate a transaction by helping the two parties make a transaction they are only compensated for taking on that role. They bear no risk of ownership of securities during the transaction. Dealers on the other hand, take risk in that they will purchase (sell) a commodity from (to) a seller (buyer) without another buyer (seller) necessarily being available. In other words, a dealer will take the risk of purchasing (selling) a commodity and will therefore be compensated for undertaking that risk. LO: 3 Level: Basic Bloomcode: Comprehension AACSB: Analytic IMA: Business Economics AICPA: Resource Management

2.4

Why were commercial banks prohibited from engaging in investment banking activities until 1999? Banks had been barred from investment banking following the Great Depression because it was believed that these activities were too risky for banks. At the time, it was believed that excessive risk taking by banks had resulted in a large number of bank failures, which precipitated the Great Depression. Recent research has exonerated the banking system of this charge.

LO: 2 Level: Basic Bloomcode: Knowledge AACSB: Analytic IMA: FSA AICPA: Legal/Regulatory Perspective

2.5

What are two basic services that investment banks provide in the economy?

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Investment banks specialize in helping companies sell new debt or equity as well as providing other services such as broker and dealer services. LO: 2 Level: Basic Bloomcode: Comprehension AACSB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

2.6

How do large corporations adjust their liquidity in the money markets? Large corporations can take advantage of money markets to adjust for their liquidity by selling or buying short-term financial instruments such as commercial paper, CDs, or Treasury bills. Large corporations with cash surplus can invest in short-term securities, while corporations with cash shortfalls can sell securities or borrow funds on a short-term basis. Money market instruments have a maturity anywhere between one day and one year and therefore are more liquid and less risky than long-term debt.

LO: 3 Level: Basic Bloomcode: Comprehension AACSB: Analytic IMA: Corporate Finance AICPA: Resource Management

2.7

The CFO of a certain company always wears his green suit on a day that the firm is about to release positive information about his company. You believe that you can profit from this information by buying the firm’s shares at the beginning of every day that the CFO shows up wearing this green suit. Describe which form of market efficiency is consistent with your belief. You believe that the CFO’s decision to wear a green suit indicates that positive information will be announced and that the company’s stock price will increase following that announcement. If you are correct, knowing what the CFO is wearing before any

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announcement is valuable private information which should enable you to earn abnormally high returns. Therefore, your belief is consistent with the strong-form of market efficiency – according to which it is possible to earn abnormally high returns by trading on private information. LO: 4 Level: Intermediate Bloomcode: Application AACSB: Analytic IMA: Corporate Finance AICPA: Strategic/Critical Thinking

2.8

Why is the expected rate of inflation (ΔPe) used in finding the nominal rate of interest in Equation 2.1 rather than the actual rate of inflation (ΔPa), which can be easily measured? The nominal rate of interest is a forward-looking measure, and therefore it makes sense that it incorporates the expected rate of inflation as opposed to the actual rate of inflation. The expected rate of inflation is the market’s best estimate of what the inflation rate will be in the future.

LO: 6 Level: Basic Bloomcode: Comprehension AACSB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

2.9

How does Exhibit 2.5 help explain why interest rates were so high during the early 1980s as compared to the relatively low interest rates in the early 1960s? The nominal rate of interest is determined by the real rate of interest plus the expected rate of inflation. During the early 1980s, the U.S. economy experienced a very high rate of inflation and, thus, high interest rates. Looking at Exhibit 2.5, we can see that the inflation increased from less than 2 percent in the 1960s to almost 13 percent in the 1980.

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This was a result of the monetary policy instituted by the U.S. government during this period. LO: 6 Level: Basic Bloomcode: Analysis AACSB: Analytic IMA: Business Economics AICPA: Resource Management

2.10

If businesses are not investing when they have unfunded capital projects whose rate of return exceeds the cost of capital, what does it imply about the real rate of interest? The real rate of interest reflects a complex set of forces that control the desired level of lending and borrowing in the economy. In this example, businesses are not investing in projects where the rate of return exceeds the cost of capital. This means that there is reduced demand for investment funds at the current real interest rate. This will remain so until either the real interest rate changes or until something changes for the firm such as introducing a new technology that will increase the rate of return on projects for the firm.

LO: 6 Level: Basic Bloomcode: Comprehension AACSB: Analytic IMA: Corporate Finance AICPA: Resource Management

Questions and Problems BASIC

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Financial System: What is the role of the financial system, and what are the two major components of the financial system?

Solution: The role of the financial system is to gather money from households, businesses, and governments with surplus funds and channel these funds to those who need them. The financial system consists of financial markets and financial institutions. LO: 1 Bloomcode: Knowledge AACSB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

2.2

Financial System: What does a competitive financial system imply about interest rates?

Solution: If the financial system is competitive, one will receive the highest possible rate for money invested with a bank and the lowest possible interest rate when borrowing money. Also, only firms with good credit ratings and projects with high rates of return will be financed. LO: 1 Bloomcode: Comprehension AACSB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

2.3

Financial System: What is the difference between saver–lenders and borrower–spenders, and who are the major representatives of each group?

Solution: Saver–lenders are those who have more money than they currently need. The principal saver–lenders in the economy are households. Borrower–spenders are those who need the money saver–lenders are offering. The main borrower–spenders in the economy are businesses followed by the federal government, although households are important mortgage borrowers.

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LO: 1 Bloomcode: Analysis AACSB: Reflective Thinking IMA: Business Economics AICPA: Industry/Sector Perspective

2.4

Financial Markets: List the two ways in which a transfer of funds takes place in an economy. What is the main difference between these two?

Solution: Funds can flow directly through financial markets or indirectly through intermediation markets where funds flow first through financial institutions. LO: 3 Bloomcode: Knowledge AACSB: Analytic IMA: Business Economics AICPA: Resource Management

2.5

Financial Markets: Suppose you own a security that you know can be easily sold in the secondary market, but the security will sell at a lower price than you paid for it. What does this imply for the security’s marketability and liquidity?

Solution: As the price of the security is lower than that you paid for it, it has a lower degree of liquidity to you, the owner. That is because the security cannot now be sold without a loss in value to the owner. Marketability refers to the ease with which a security can be sold or converted to cash. The information in the problem mentions that the security could be easily sold in secondary market, which implies it has high degree of marketability to you. LO: 3 Bloomcode: Application AACSB: Analytic IMA: Corporate Finance

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AICPA: Resource Management

2.6

Financial Markets: Why are direct financial markets also called wholesale markets?

Solution: The financial markets are also called wholesale markets because the minimum transaction or security denomination is $1 million or more. LO: 2 Bloomcode: Comprehension AACSB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

2.7

Financial Markets: Trader Inc.is a $300 million company, as measured by asset value, and Horst Corp. is a $35 million company. Both are privately held corporations. Explain which firm more likely to go public and register with the SEC, and why.

Solution: Trader Inc. is more likely to go public because of its larger size. Since the cost of SEC registration and compliance is very high, larger firms can offset these costs by the lower funding cost in public markets. Smaller companies find the cost prohibitive for the dollar amount of securities they sell. LO: 2 Bloomcode: Application AACSB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

2.8

Primary Markets: What is a primary market? What does IPO stand for?

Solution: A primary market is where new securities are sold for the first time. IPO stands for Initial Public Offering. LO: 3

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Bloomcode: Knowledge AACSB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

2.9

Primary Markets: Identify whether the following transactions are primary market or secondary market transactions. a. Jim Hendry bought 300 shares of IBM through his brokerage account. b. Peggy Jones bought $5,000 of General Motors bonds from another investor. c. Hathaway Insurance Company bought 500,000 shares of Trigen Corp. when the company issued new stock.

Solution: a. Secondary market transactions. b. Secondary market transactions. c. Primary market transactions. LO: 3 Bloomcode: Application AACSB: Analytic IMA: Corporate Finance AICPA: Resource Management

2.10

Investment Banking: What does it mean to “underwrite” a new security issue? What compensation does an investment banker get from underwriting a security issue?

Solution: To underwrite a new security issue means that the investment banker buys the entire issue from the firm at a guaranteed price and then resells the security to individual investors or other institutions at a higher price. The difference between the banker’s purchase price and the total resale price is called the underwriting spread, and reflects the banker’s compensation. In addition to underwriting new securities, investment banks also provide other services, such as preparing the prospectus, preparing legal documents to be filed with the SEC, and providing general financial advice to the issuer.

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LO: 2 Bloomcode: Comprehension AACSB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

2.11

Investment Banking: Cranjet Inc. is issuing 10,000 bonds, and its investment banker has guaranteed a price of $985 per bond. If the investment banker sells the entire issue to investors for $10,150,000. a. What is the underwriting spread for this issue? b. What is the percentage underwriting cost? c. How much did Cranjet raise?

Solution: a. $300,000 [$10,150,000 – ($985 x 10,000)] b. 2.96 percent ($300,000/$10,150,000) c. $9,850,000 ($985 x 10,000) LO: 2 Bloomcode: Application AACSB: Analytic IMA: Corporate Finance AICPA: Resource Management

2.12

Financial Institutions: What are some of the ways in which a financial institution or intermediary can raise money?

Solution: A financial intermediary can raise money through the sale of financial products that individuals or businesses will purchase, such as checking and savings accounts, life insurance policies, pension or retirement funds, and can make loans in larger amounts to borrower-spenders. LO: 1 Bloomcode: Application

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AACSB: Analytic IMA: Corporate Finance AICPA: Resource Management

2.13

Financial Institutions: How do financial institutions act as intermediaries to provide services to small businesses?

Solution: Financial intermediaries allow smaller companies to access the financial markets. They do this by converting securities with one set of characteristics into securities with another set of characteristics that meets the needs of smaller companies. By repackaging securities, they are able to meet the needs of different clients. LO: 5 Bloomcode: Comprehension AACSB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

2.14

Financial Institutions: Which financial institution is usually the most important to businesses?

Solution: The primary financial intermediaries are commercial banks, life insurance companies, casualty insurance companies, pension funds, investment funds, and business finance companies. Commercial banks are the largest and most prominent financial intermediaries in the economy and offer the widest range of financial services to businesses. LO: 5 Bloomcode: Comprehension AACSB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

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Financial Markets: What is the main difference between money markets and capital markets?

Solution: Money markets are markets in which short-term debt instruments with maturities of less than one year are bought and sold. Capital markets are markets in which equity securities and debt instruments with maturities of more than one year are bought and sold. LO: 3 Bloomcode: Analysis AACSB: Reflective Thinking IMA: Corporate Finance AICPA: Industry/Sector Perspective

2.16

Money Markets: What is the primary role of money markets? Explain how the money markets work.

Solution: Money markets provide an option for large corporations to adjust their liquidity positions. Since it is rare for cash receipts and cash expenditures to be perfectly synchronized, money markets allow companies to temporarily invest idle cash in Treasury bills or negotiable CDs. If a company is short on cash, it can borrow the money from money markets by selling commercial paper at lower interest rates than those available through commercial banks. LO: 3 Bloomcode: Comprehension AACSB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

2.17

Money Markets: What are the main types of securities in the money markets?

Solution: Treasury bills and commercial paper. LO: 3

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2.18

Capital Markets: How do capital market instruments differ from money market instruments?

Solution: Capital market instruments are less liquid or marketable, they have longer maturities, usually between 1 and 30 years, and carry more financial risk. LO: 3 Bloomcode: Analysis AACSB: Analytic IMA: Corporate Finance AICPA: Resource Management

2.19

Market Efficiency: Describe the informational differences that distinguish the three forms of market efficiency.

Solution: The strong-form of market efficiency states that all information is reflected in the security prices. In other words, there is no private or inside information, that if released would potentially change the price. The semistrong-form holds that all public information available to investors is reflected in the security’s price. Therefore, insiders with access to private information could potentially profit from trading on this knowledge before it becomes public. Finally, the weak-form of market efficiency holds that there is both public and private information that is not reflected in the security’s price and having access to it can lead to abnormal profits. LO: 4 Bloomcode: Comprehension AACSB: Analytic IMA: Corporate Finance

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AICPA: Industry/Sector Perspective

2.20

Market Efficiency: Zippy Computers announced strong fourth quarter results. Sales and earnings were both above analysts’ expectations. You notice in the newspaper that Zippy’s stock price went up sharply on the day of the announcement. If no other information about Zippy became public on the day of the announcement and the overall market was down, is this evidence of market efficiency?

Solution: Yes, if no other information became public and the market was down, the increase in Zippy’s price most likely reflects the effects of investors trading on the good news. This means that the strong form of market efficiency does not hold, but lends credence to the semistrong and weak form of market efficiency. Investors, believing that Zippy is now more valuable than they had thought, are willing to pay a higher price for the shares. LO: 4 Bloomcode: Application AACSB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

2.21

Market Efficiency: In problem 2.20, if the market is efficient, would it have been possible for Zippy’s stock price to go down on the day that the firm announced the strong fourth quarter results?

Solution: Yes. The last sentence in the statement of problem 2.20 suggests why this might happen. If, on the same day of the announcement, some very bad news about the future prospects for Zippy became public or if the market went down substantially, Zippy’s stock price might also have gone down despite the positive sales and earnings announcement. Zippy’s stock price may also go down if strong results were anticipated and this information was already reflected in the stock price, but the actual results were not as strong as anticipated. This is an example of the strong form of market efficiency. LO: 4

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Bloomcode: Application AACSB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

2.22

Market Efficiency: If the market is strong-form efficient, then trading on tips you hear from Jim Cramer (the host of Mad Money on CNBC) will generate no excess returns (i.e., returns in excess of fair compensation for the risk you are bearing). True or false?

Solution: True. If the market is strong-form efficient then all new information gets reflected in stock prices very quickly. In such a market, there is nothing you will hear from Jim Cramer on his TV show that will enable you to consistently earn excess returns. The information in his tips will already be reflected in stock prices by the time you can trade on them. LO: 4 Bloomcode: Application AACSB: Analytic IMA: Corporate Finance AICPA: Resource Management

2.23

Financial Markets: What are the major differences between public and private markets?

Solution: Public markets are organized financial markets (also referred to as Exchanges) where the public buys and sells securities through their stock brokers. The SEC regulates public securities markets in the United States. In contrast, private markets involve direct transactions between two parties. These transactions lack SEC regulation. LO: 3 Bloomcode: Analysis AACSB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

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Financial Instruments: What are the two risk-hedging instruments discussed in the chapter?

Solution: The two risk-hedging instruments discussed are futures and options contracts. LO: 3 Bloomcode: Comprehension AACSB: Analytic IMA: Corporate Finance AICPA: Risk Analysis

2.25

Interest Rates: What is the real rate of interest, and how is it determined?

Solution: The real rate of interest measures the return earned on savings, and it represents the cost of borrowing to finance capital goods. It is the interest rate determined in the absence of inflation. The real rate of interest is determined by the interaction between firms that invest in capital projects and the rate of return businesses can expect to earn on investments in capital goods, and individuals’ time preference for consumption. Graphically, it is that point when the desired saving level equals the desired level of investment in the economy. LO: 6 Bloomcode: Comprehension AACSB: Analytic IMA: Corporate Finance AICPA: Resource Management

2.26

Interest Rates: How does the nominal rate of interest vary over time?

Solution: The nominal rate is the rate that we observe in the marketplace. It is determined by both the real rate as well as expected inflation. Therefore, the nominal rate will fluctuate with changes in the real rate as well as changes in expected inflation.

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LO: 6 Bloomcode: Comprehension AACSB: Analytic IMA: Corporate Finance AICPA: Resource Management

2.27

Interest Rates: What is the Fisher equation, and how is it used?

Solution: The Fisher equation reflects the expected, not the reported or actual, annualized change in commodity prices (∆Pe). It is used to protect the buying power from changes in inflation, and it is incorporated into a loan contract by including the real interest rate that would exist in the absence of inflation. LO: 6 Bloomcode: Knowledge AACSB: Analytic IMA: Corporate Finance AICPA: Resource Management

2.28

Interest Rates: Imagine you borrow $500 from your roommate, agreeing to pay her back $500 plus 7 percent nominal interest in one year. Assume inflation over the life of the contract is expected to be 4.25 percent. What is the total dollar amount you will have to pay her back in a year? What percentage of the interest payment is the result of the real rate of interest?

Solution: You will pay her back $535 ($500 × 1.07) in one year. Given an inflation of rate of 4.25 percent, the real rate of interest is approximately 2.368 percent using the Fisher equation: 1 + i = (1 + r) × (1 + ΔPe) 1 + 0.07 = (1 + r) × (1 + 0.0425) r = (1.07/1.0425) – 1 = 0.02638, or 2.638% This means that $13.19 ($500 × 0.02638) will be a result of the real interest rate

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which is 37.69 percent of the total interest payment. The simplified, or approximate, Fisher equation yields a real interest rate of 2.75 percent: i = r + ΔPe r = 0.07 - 0.0425 = 0.0275, or 2.75% This means that $13.75 ($500 × 0.0275) will be a result of the real interest rate which is 39.29 percent of the total interest payment (use the simplified or approximate Fisher equations). Excel Template available in Wiley Course Resources Excel Template Solution available in Wiley Instructor Resources LO: 6 Bloomcode: Analysis AACSB: Reflective Thinking IMA: Corporate Finance AICPA: Resource Management

2.29

Interest Rates: Your parents have given you $1,000 a year before your graduation so that you can take a trip when you graduate. You wisely decide to invest the money in a bank CD that pays 6.75 percent interest. You know that the trip costs $1,025 right now and that the inflation for the year is predicted to be 4 percent. Will you have enough money in a year to purchase the trip?

Solution: Yes. The CD will be worth $1,067.50 at the end of the year ($1,000 × 6.75% + $1,000), and the price of the trip will be $1,066 ($1,025 × 4% + $1,025). The CD will be able to cover the trip. Excel Template available in Wiley Course Resources Excel Template Solution available in Wiley Instructor Resources LO: 6 Bloomcode: Analysis AACSB: Reflective Thinking IMA: Corporate Finance AICPA: Resource Management

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Interest Rates: When are the nominal and real interest rates equal?

Solution: The only time the nominal and real interest rates are equal is when the expected rate of inflation over the contract period is zero. LO: 6 Bloomcode: Comprehension AACSB: Analytic IMA: Corporate Finance AICPA: Resource Management

Sample Test Problems 2.1

What are the two basic mechanisms through which funds flow through the financial system, and how do they differ?

Solution: The two basic mechanisms are the direct financing mechanism and the indirect financing mechanism. In the direct financing mechanism, issuers of securities (borrower-spenders) sell the securities directly to investors (lender-savers). In the indirect financing mechanism, financial institutions aggregate money from lender-savers and make this capital available through loans to borrower-spenders. LO: 1 Level: Intermediate Bloomcode: Comprehension AACSB: Analytic IMA: Corporate Finance AICPA: Resource Management

2.2

You just purchased a share of IBM stock on the New York Stock Exchange. What kind of transaction was this?

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Primary market transaction.

Secondary market transaction.

Futures market transaction.

Private placement.

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Solution: b. (The secondary market is the one in which owners of outstanding securities sell their securities to other investors.) LO: 3 Level: Intermediate Bloomcode: Application AACSB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

2.3

How are brokers different from dealers?

Solution: Brokers bring buyers and sellers together. They execute a transaction for their client and are compensated with a commission fee. Brokers never own the securities being sold and therefore do not bear any risk of ownership. In contrast, dealers purchase securities and sell them from an inventory that they own. Dealers profit if they are able to sell securities for a price greater than they paid for them. Because they own the securities, dealers face the risk that the prices of the securities in their inventory will fall below what they paid for those securities. LO: 3 Level: Intermediate Bloomcode: Analysis AACSB: Reflective Thinking IMA: Business Economics AICPA: Industry/Sector Perspective

2.4

List the three forms of the efficient market hypothesis, and describe what information is assumed to be reflected in security prices under each of these hypotheses.

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Solution: 1) Strong-Form Efficiency – all information including that which is not known by the general public is reflected in the security prices. 2) Semistrong-Form Efficiency – all public information currently available is reflected in the security prices. 3) Weak-Form Efficiency – all information contained in past prices is reflected in security prices, but not all private nor all public information currently available. LO: 4 Level: Intermediate Bloomcode: Comprehension AACSB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

2.5

If the nominal rate of interest is 4.25 percent and the expected rate of inflation is 1.75 percent, what is the real rate of interest (use the Fisher equation)?

Solution: Using the Fisher equation: i = r + ∆Pe + r ∆Pe where i = 0.0425 and ∆Pe = 0.0175 Solving for r, we get r = 0.02457, or 2.457% LO: 6 Level: Intermediate Bloomcode: Application AACSB: Analytic IMA: Corporate Finance AICPA: Resource Management

2.6

What is the relation between business cycles and the general level of interest rates?

Solution:

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As Exhibit 2.5 shows, interest rates tend to follow the business cycle. The level of interest rates tends to rise during periods of economic expansion and decline during periods of economic contraction. LO: 6 Level: Intermediate Bloomcode: Comprehension AACSB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

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Chapter 1

The Financial Manager and the Firm Before You Go On Questions and Answers Section 1.1 1. What are the three basic types of financial decisions managers must make? The three basic decisions each business must make are the capital budgeting decision, the financing decision, and the working capital management decision. These decisions determine which productive assets to buy, how to pay for or finance these purchases, and how to manage the day-to-day financial matters so the company can pay its bills.

2. Explain why you would make an investment if the value of the expected cash flows exceeds the cost of the project. You would accept an investment project whose cash flows exceed the cost of the project because such projects will increase the value of the firm, making the owners wealthier. Most people start a business to increase their wealth. Remember that the cost of capital (time value of money) will affect the decision about whether to invest.

3. Why are capital budgeting decisions among the most important decisions in the life of a firm? The capital budgeting decisions are considered the most important in the life of the firm because these decisions determine which productive assets the firm purchases, and which assets generate most of the firm’s cash flows. Furthermore, capital budgeting decisions are long-term decisions and if you make a mistake in selecting a productive asset, you are stuck with the decision for a long time.

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1. Why are many businesses operated as sole proprietorships or partnerships? Many businesses elect to operate as sole proprietorships or partnerships because of the small operating scale and capital base of their firms. Both of these forms of business organization are fairly easy to start and impose few regulations on the owners.

2. What are some advantages and disadvantages of operating as a public corporation? The main advantages of operating as a public corporation are the access to the public securities markets, which makes it easier to raise large amounts of capital, and the ease of ownership transfer. All the shareholders have to do is to call their broker to buy or sell shares of stock. Since a public corporation usually has many shares outstanding, large blocks of securities can be purchased or sold without an appreciable impact on the price of the stock. The major disadvantage of corporations is the tax situation. Not only must the corporation pay taxes on its income, but the owners of the corporation get taxed again when dividends are paid to them. This is referred to as double taxation. In addition to taxes, public corporations are subject to stringent reporting requirements, and the incentives may convince managers to focus on shorter-term profitability than longer-term wealth creation. 3. Explain why professional partnerships such as physicians’ groups organize as limited liability partnerships. Professional partnerships such as physicians’ groups desire to organize as limited liability partnerships (LLPs) to take advantage of the tax arrangements of partnerships combined with the advantages of the limited liability of a corporation. By operating as an LLP, the partnership is able to avoid a potential financial disaster resulting from the misconduct of one partner.

Section 1.3 1. What are the major responsibilities of the CFO? The major responsibilities of a CFO include analysis and recommendations for financial decisions. The CFO, who reports directly to the CEO, focuses on managing all aspects of the firm’s finances and works with the CEO on strategic issues. The CFO also interacts with

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staff in other functional areas on a regular basis related to financial issues that affect the business.

2. Identify the financial officers who typically report to the CFO and describe their duties. The financial officers discussed in the chapter who report to the CFO are the controller, the treasurer, the risk manager, and the internal auditor. The controller is the firm’s chief accounting officer, and thus prepares the financial statements and taxes. This position also requires close cooperation with the external auditors. The treasurer’s responsibility is the collection and disbursement of cash, investing excess cash, raising new capital, handling foreign exchange, and overseeing the company’s pension fund management. This individual also assists the CFO in handling important Wall Street relationships. The risk manager monitors and manages the firm’s risk exposure in financial and commodity markets and the firm’s relationships with insurance providers. Finally, the internal auditor is responsible for conducting risk assessment and performing audits of highrisk areas.

3. Why does the internal auditor report to both the CFO and the audit committee of the board of directors? The internal auditor reports to the CFO on a day-to-day basis but is ultimately accountable for reporting any accounting irregularities to the board of directors. The dual reporting system serves as a check to ensure that there are no discrepancies in the company’s financial statements.

Section 1.4 1. Why is profit maximization an unsatisfactory goal for managing a firm? Profit maximization is not a satisfactory goal when managing a firm because it is rather difficult to define profits since accountants can apply and interpret the same accounting principles differently. Also, profit maximization does not define the size, the uncertainty, and the timing of cash flows; it ignores the time value of money concept.

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2. Explain why maximizing the market price of a firm’s stock is an appropriate goal for the firm’s management. Maximizing the current market price of a firm’s stock is an appropriate goal for the firm’s management because it is an unambiguous objective and is easy to measure for a firm whose stock is publicly traded. One can simply look at the value of the company’s stock on any given day to determine whether the market price went up or down. Maximizing the market value of the stock is not inconsistent with maximizing the value of claims to the firm’s other stakeholders. In maximizing the value of the stock, managers must make decisions that account for the interests of all stakeholders. This is also true for firms without publicly traded stocks. In these cases, the statement can be interpreted as maximizing the current value of owner’s equity. 3. What is the fundamental determinant of an asset’s value? The fundamental determinant of an asset’s value is the future cash flows the asset is expected to generate including the size, timing, and riskiness of these cash flows. Other factors that may help determine the price of an asset are internal decisions, such as the company’s expansion strategy, as well as external stimulants, such as the state of the economy.

Section 1.5 1. What are agency conflicts? An agency conflict occurs when the goals of the principals or the stockholders are not aligned with the goals of the agents or the company management. Management is often more concerned with pursuing its own self-interest, and so the maximization of shareholder value is pushed to the side.

2. What are corporate raiders? Corporate raiders can make the company more efficient by keeping top managers on their toes. Top managers know that if the company’s performance declines and its stock slips, it makes itself vulnerable to takeovers by corporate raiders who are just waiting to temporarily acquire a company, turn it around, and sell it for profit. Therefore, the role of the corporate raiders is twofold: first, the fear of takeovers pushes managers to do a better job, and second,

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if managers are not performing up to expectations, the company can be rescued and restructured into becoming a strong performer. However, the threat of a corporate raider could result in an incentive conflict for managers, inducing them to focus on short-term profitability over long-term value creation.

3. List the three main objectives of the Sarbanes-Oxley Act. The three main goals of the Sarbanes-Oxley Act are to reduce agency costs in corporations, to restore ethical conduct within the business sector, and to improve the integrity of accounting reporting systems within firms.

Section 1.6 1. What is a conflict of interest in a business setting? Conflict of interest in the business setting refers to a conflict between an individual’s personal or institutional gain and the obligation to serve the interest of another party. For example, the chapter discussed the problem that arises when the real estate agent helping you buy a house is also the listing agent.

2. How would you define an ethical business culture? An ethical business culture means that people have a set of principles, or a moral compass, that helps them identify moral issues and then make ethical judgments without being told what to do.

Self-Study Problems and Solutions 1.1

Give an example of a capital budgeting decision and a financing decision.

Solution: Capital budgeting involves deciding in which productive assets the firm invests, such as buying a new plant or investing in the renovation of an existing facility. Financing decisions determine how a firm will raise capital. Examples of financing decisions include the decision to borrow from a bank or issue debt in the public capital markets.

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LO: 1 Level: Basic

1.2

What is the appropriate decision criterion for financial managers to use when selecting a capital project?

Solution: Financial managers should select a capital project only if the value of the project’s expected future cash flows exceeds the cost of the project. In other words, managers should only make investments that will increase firm value, and thus increase the stockholders’ wealth. LO: 1 Level: Basic

1.3

What are some of the things that managers do to manage a firm’s working capital?

Solution: Working capital management is the day-to-day management of a firm’s short-term assets and liabilities. Working capital can be managed by maintaining the optimal level of inventory, managing receivables and payables, deciding to whom the firm should extend credit, and making appropriate investments with excess cash. LO: 1 Level: Basic

1.4

Which one of the following characteristics does not pertain to corporations? a.

Can enter into contracts

Can borrow money

Are the easiest type of business to form

Can be sued

Can own stock in other companies

Solution: The answer that does not pertain to corporations is: c. Are the easiest type of business to form.

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LO: 2 Level: Basic

1.5

What are typically the main components of an executive compensation package?

Solution: The three main components of a typical executive compensation package are: base salary, bonus based on accounting performance, and compensation tied to the firm’s stock price. LO: 5 Level: Basic

Discussion Questions and Answers 1.1

Describe the cash flows between a firm and its stakeholders. Cash flows are generated by a firm’s productive assets that were purchased through either issuing debt or raising equity. These assets generate revenues through the sale of goods and services. A portion of this revenue is then used to pay wages and salaries to employees, pay suppliers, pay taxes, and pay interest on the borrowed money. The leftover money, residual cash, is then either reinvested back in the business or is paid out to stockholders in the form of dividends.

LO: 1 Level: Basic Bloomcode: Comprehension AACSB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

1.2

What are the three fundamental decisions the financial manager is concerned with, and how do they affect the firm’s balance sheet? The primary financial management decisions every company faces are capital budgeting decisions, financing decisions, and working capital management decisions. Capital

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budgeting addresses the question of which productive assets to buy; thus, it affects the asset side of the balance sheet. Financing decisions focus on raising the money the firm needs to buy productive assets. These decisions are typically accomplished by issuing long-term debt and equity, which affect both the long-term debt and stockholders’ equity components of the balance sheet. Finally, working capital decisions involve how firms manage their current assets and liabilities. The focus here is ensuring that a firm has enough money to pay its bills, and that any excess money is invested to earn a return. These decisions affect current assets and current liabilities on the balance sheet. LO: 1 Level: Basic Bloomcode: Comprehension AACSB: Analytic IMA: Decision Analysis AICPA: Decision Modeling

1.3

What is the difference between stockholders and stakeholders? Stockholders, also referred to as shareholders, are the owners of the company. A stakeholder, on the other hand, is anyone with a claim on the assets of the firm, including, but not limited to, shareholders. Stakeholders include the firm’s employees, suppliers, creditors, and the government.

LO: 1 Level: Basic Bloomcode: Analysis AACSB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

1.4

Suppose that several accountants wants to start an accounting business. What organizational form would they most likely choose, and why?

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Most lawyers, accountants, and doctors form what are known as limited liability partnerships. This formation combines the tax advantages of partnerships with the limited liability of corporations. LO: 2 Level: Basic Bloomcode: Application AACSB: Analysis IMA: Business Economics AICPA: Industry/Sector Perspective

1.5

Why would the owners of a business choose to form a corporation even though they will face double taxation? Because the benefits, such as limited liability and access to large amounts of capital at relatively low cost in the public markets, outweigh the cost of double taxation (as well as the higher costs associated with forming a corporation).

LO: 2 Level: Basic Bloomcode: Comprehension AACSB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

1.6

Explain why profit maximization is not the best goal for a company. What is a better goal? Although profit maximization appears to be the logical goal for any company, it has many drawbacks. First, profit can be defined in a number of different ways, and variations in net income for similar firms can differ widely. Second, accounting profits do not exactly equal cash flows. Third, profit maximization does not account for timing and ignores risk associated with cash flows. An appropriate goal for financial managers is to maximize the current value of the firm’s stock in the open market.

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LO: 4 Level: Intermediate Bloomcode: Comprehension AACSB: Analytic IMA: Performance Measurement AICPA: Strategic/Critical Thinking

1.7

What are some of the major external and internal factors that affect a firm’s stock price? What is the difference between the two general types of factors? External factors that affect the firm’s stock price are: (1) economic shocks, such as natural disasters or wars, (2) the state of the economy, such as the level of interest rates, and (3) the business environment, such as taxes, antitrust laws or regulations. External factors are variables over which the management has no control. Internal factors that affect the stock price can be controlled by management to some degree, because they are firm specific, such as financial management decisions, product quality and cost, marketing and sales, research and developments, and the line of business, the management has selected to enter. Finally, perhaps the most important internal variable that determines the stock price is the expected stream of cash flows: their magnitude, timing, and riskiness.

LO: 4 Level: Basic Bloomcode: Comprehension AACSB: Analytic IMA: Strategic Marketing AICPA: Measurement

1.8

Identify the sources of agency costs. What are some ways these costs can be controlled in a company? Agency costs are the costs that result from conflicts of interest between an agent and a principal. They can either be direct, such as lavish dinners or trips, or indirect, which are usually missed investment opportunities. A company can control these costs by linking

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management compensation to the company’s performance and by establishing an independent board of directors. Outside factors that contribute to the minimization of agency costs are the threat of corporate raiders that can take over a company that is not performing up to expectations and the competitive nature of the managerial labor market. LO: 5 Level: Basic Bloomcode: Comprehension AACSB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

1.9

What is the Sarbanes-Oxley Act, and what is its focus? Why does it focus in these areas? The Sarbanes-Oxley Act is an act of Congress that was passed in 2002. This act was passed in the aftermath of several corporate scandals that occurred at the turn of the century. The act focuses on (1) reducing agency costs in corporations, (2) restoring ethical conduct within the business sector, and (3) improving the integrity of accounting reporting system within firms. Failures in these areas led to the corporate scandals that preceded passage of Sarbanes-Oxley.

LO: 5 Level: Basic Bloomcode: Knowledge AACSB: Analytic IMA: FSA AICPA: Legal/Regulatory Perspective

1.10

Give an example of a conflict of interest in a business setting, other than the one involving the real estate agent discussed in the chapter text. For example, imagine a situation in which you are a financial officer at a growing software company and your firm has decided to hire outside consultants to formulate a global expansion strategy. Coincidentally, your spouse works for one of the major

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consulting firms that your company is considering hiring. In this scenario, you have a conflict of interest, because instinctively, you might be inclined to give the business to your spouse’s firm, since it may benefit your family’s financial situation, regardless of whether or not it makes the best sense for your firm. LO: 6 Level: Intermediate Bloomcode: Application AACSB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

Questions and Problems and their Solutions BASIC 1.1

Capital: What are the two basic sources of funds for all businesses?

Solution: The two basic sources of funds for all businesses are debt and equity. LO: 1.1 Bloomcode: Knowledge AACSB: Analytic IMA: Investment Decisions; Corporate Finance AICPA: Resource Management

1.2

Management role: What is net working capital?

Solution: Net working capital is the difference between a firm’s total current assets and its total current liabilities. LO: 1.1 Bloomcode: Knowledge AACSB: Analytic

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IMA: Corporate Finance AICPA: Resource Management

1.3

Cash flows: Explain the difference between profitable and unprofitable firms.

Solution: A profitable firm is able to generate enough cash flows from productive assets to cover its operating expenses, taxes, and payments to creditors. Unprofitable firms fail to do this, and therefore, may be forced to declare bankruptcy, or close the business. LO: 1.1 Bloomcode: Analysis AACSB: Analytic IMA: Cost Management AICPA: Measurement

1.4

Management role: What three major decisions are of most concern to financial managers?

Solution: Financial managers are most concerned with the capital budgeting decisions, the financing decisions, and the working capital management decisions. LO: 1.1 Bloomcode: Comprehension AACSB: Analytic IMA: FSA AICPA: Resource Management

1.5

Cash flows: What is the appropriate decision rule for a firm considering undertaking a capital project? Give a real-life example.

Solution: A firm should undertake a capital project only if the value of its future cash flows exceeds the cost of the project. For example, a financial manager would not invest $10,000,000 in a new production line if the net present value of future cash flows from

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that line are expected to be only $9,000,000. That would be like throwing $1,000,000 away. LO: 1.1 Bloomcode: Application AACSB: Analytic IMA: Decision Analysis AICPA: Problem Solving and Decision Making

1.6

Management role: What is a firm’s capital structure, and why is it important?

Solution: Capital structure shows how a company is financed; it is the mix of debt and equity on the liability and stockholders’ equity side of the balance sheet. It is important because it affects the risk and the value of the company. In general, companies with higher debt-toequity proportions are often considered riskier, because debt comes with legal obligations to make periodic payments to creditors and to repay the principal at the end, whereas, equity does not require periodic payments nor a repayment of the invested amount. LO: 1.1 Bloomcode: Comprehension AACSB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

1.7

Management role: What are some of the working capital decisions that a financial manager faces?

Solution: The financial manager must make working capital decisions regarding the level of inventory to hold, the terms of granting credit (accounts receivable), and the firm’s policy on paying accounts payable. LO: 1.1 Bloomcode: Comprehension AACSB: Analytic

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IMA: Decision Analysis AICPA: Strategic/Critical Thinking

1.8

Organizational form: What are the common forms of business organization discussed in this chapter?

Solution: The common forms of business organization discussed are sole proprietorship, partnership, corporation, limited liability company (LLC), and limited liability partnership (LLP). LO: 1.2 Bloomcode: Knowledge AACSB: Reflective Thinking IMA: Business Economics AICPA: Industry/Sector Perspective

1.9

Organizational form: What are the advantages and disadvantages of a sole proprietorship?

Solution: Advantages: •

It is the easiest business organization to start.

•

It is the least regulated.

•

Owners keep all the profits and do not have to share the decision-making authority with anyone.

•

All income is taxed as personal income, which is usually in a lower tax bracket than corporate income.

Disadvantages: •

The proprietor has an unlimited liability for all business debt and financial obligations of the firm.

•

The amount of capital that can be invested in the firm is limited by the proprietor’s wealth.

•

It is difficult to transfer ownership (requires sale of the business).

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LO: 1.2 Bloomcode: Comprehension AACSB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

1.10

Organizational form: What is a partnership, and what is the biggest disadvantage of this form of business organization? How can this disadvantage be avoided?

Solution: A partnership consists of two or more owners legally joined together to manage a business. The major disadvantage to partnerships is that all partners have unlimited liability for the organization’s debts and legal obligations no matter what stake they have in the business. One way to avoid this is to form a limited liability partnership (LLP) in which only general partners have unlimited liability and limited partners are only responsible for business obligations up to the amount of capital they have invested in the partnership. LO: 1.2 Bloomcode: Comprehension AACSB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

1.11

Organizational form: Who are the owners in a corporation, and how is their ownership represented?

Solution: The owners of a corporation are its stockholders or shareholders, and the evidence of their ownership is represented by shares of common stock. Other types of ownership do exist and include preferred stock. LO: 1.2 Bloomcode: Comprehension AACSB: Analytic

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IMA: Business Economics AICPA: Industry/Sector Perspective

1.12

Organizational form: Explain what is meant by stockholders’ limited liability.

Solution: Limited liability for a stockholder means that the stockholder’s legal liability extends only to the capital contributed or the amount invested. LO: 1.2 Bloomcode: Comprehension AACSB: Analytic IMA: Business Economics AICPA: Strategic/Critical Thinking

1.13

Organizational form: What is double taxation?

Solution: Double taxation occurs when earnings are taxed twice. The owners of a C-corporation are subject to double taxation—first at the corporate level when the firm’s earnings are taxed and then again at a personal level when they receive dividends. LO: 1.2 Bloomcode: Comprehension AACSB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

1.14

Organizational form: What is the form of business organization taken by most large companies and why?

Solution: Most large companies prefer to operate as public corporations because large amounts of capital can be raised in public markets at a relatively low cost. LO: 1.2 Bloomcode: Comprehension

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AACSB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

1.15

Finance function: What is the primary responsibility of the board of directors in a corporation?

Solution: The board of directors of a corporation is responsible for serving the interests of stockholders in managing the corporation. It is possible that the interest of managers may deviate from those of the stockholders. The board’s objective is to monitor and correct any management decisions that might not be in the best interest of the stockholders. For example, board duties include hiring and firing the CEO, setting CEO pay, and monitoring the investment decisions of managers. LO: 1.3 Bloomcode: Comprehension AACSB: Analytic IMA: Business Economics AICPA: Resource Management

1.16

Finance function: All public companies must hire a certified public accounting firm to perform an independent audit of their financial statements. What exactly does the term audit mean?

Solution: An independent CPA firm that performs an audit of a firm ensures that the financial information reported fairly presents the financial condition of the business. The audit seeks to improve the accounting reporting integrity by ensuring that generally accepted accounting principles (GAAP) have been adhered to consistently year after year and are not applied in a manner that distorts the firm’s performance. LO: 1.3 Bloomcode: Comprehension AACSB: Analytic

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IMA: FSA; Reporting AICPA: Risk Analysis; Reporting

1.17

Firm’s goal: What are some of the drawbacks to setting profit maximization as the main goal of a company?

Solution: Drawbacks include: •

It is difficult to determine what is meant by “profit”.

•

It does not address the size and timing of cash flows—it does not account for the time value of money.

•

It ignores the uncertainty or risk of cash flows.

LO: 1.4 Bloomcode: Comprehension AACSB: Analytic AICPA: Strategic/Critical Thinking IMA: Corporate Finance

1.18

Firm’s goal: What is the appropriate goal of financial managers? How do managers’ decisions affect how successful the firm is in achieving this goal?

Solution: The appropriate goal of financial managers should be to maximize the current value of the firm’s stock price. Managers’ decisions affect the stock price in many ways as the value of the stock is determined by the future cash flows the firm can generate. Managers can impact the cash flows by, for example, selecting what products or services to produce, what type of assets to purchase, or what advertising campaign to undertake. LO: 1.4 Bloomcode: Comprehension AACSB: Analytic AICPA: Strategic/Critical Thinking IMA: Decision Analysis

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Firm’s goal: What are the major factors that affect a firm’s stock price?

Solution: There are both internal and external factors affecting the stock price. They include the characteristics of the firm, the state of the economy, economic shocks, the business environment, expected cash flows (magnitude, timing and risk), and current market conditions. LO: 1.4 Bloomcode: Comprehension AACSB: Analytic AICPA: Strategic/Critical Thinking IMA: Corporate Finance

1.20

Agency conflicts: What is an agency relationship, and what is an agency conflict? How can agency conflicts be reduced in a corporation?

Solution: Agency relationships develop when a principal hires an agent to perform some service or to represent the firm. An agency conflict arises when the agent’s interests and behaviors are different from those of the principal. Agency conflicts can be reduced through the following three mechanisms: management compensation, control of the firm, and the board of directors. LO: 1.5 Bloomcode: Comprehension AACSB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

1.21

Firm’s goal: What can happen if a firm is poorly managed and its stock price falls substantially below its maximum potential price?

Solution:

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If the stock price falls below its maximum potential price, it attracts corporate raiders, who look for fundamentally sound, but poorly managed companies, they can buy, turn around, and sell for a handsome profit. LO: 1.4 Bloomcode: Comprehension AACSB: Analytic IMA: Corporate Finance AICPA: Strategic/Critical Thinking

1.22

Agency conflicts: What are some of the regulations that pertain to boards of directors that were put in place to reduce agency conflicts?

Solution: Some of the regulations include: •

The majority of board members must be outsiders.

•

A separation of the CEO and chairman of the board positions is recommended.

•

Firm is required to have a code of ethics approved by the board.

LO: 1.5 Bloomcode: Comprehension AACSB: Analytic IMA: FSA AICPA: Legal/Regulatory Perspective

1.23

Business ethics: How can a lack of business ethics negatively affect the performance of an economy? Give an example.

Solution: A lack of business ethics can lead to corruption, which, in turn, creates inefficiencies in an economy, inhibits the growth of capital markets, and slows the rate of overall economic growth. For example, the Russian economy has had a relatively difficult time attracting foreign investment since the fall of the Soviet Union due, in part, to weak ethics and corruption in the business community and local and national governments.

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Lower foreign investment has led to slower overall economic growth than the country might otherwise have enjoyed. LO: 1.6 Bloomcode: Comprehension AACSB: Analytic IMA: Business Economics AICPA: Industry/Global Perspective

1.24

Agency conflicts: What are some ways to resolve a conflict of interest?

Solution: One way to resolve a conflict of interest is by complete disclosure. As long as both parties are aware of the fact that, for example, both parties in a contract negotiation are represented by the same firm, disclosure is sufficient. Another way to avoid a conflict of interest is for the company to remove itself from serving the interest of one of the parties. This is, for example, the case with accounting firms not being allowed to serve as consultants to companies for whom they perform audits. LO: 1.5 Bloomcode: Application AACSB: Analytic IMA: FSA AICPA: Legal/Regulatory Perspective

1.25

Information asymmetry: Describe what an information asymmetry is in a business transaction. Explain how the inequity associated with an information asymmetry might be, at least partially, solved through the market for goods or services.

Solution: An information asymmetry exists when one party to a business transaction possesses information that is not available to the other parties in the transaction. If the parties with less information understand their relative disadvantage, they are likely to pay lower prices for the goods and services they purchase or charge higher prices for the goods and services they sell.

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LO: 1.6 Bloomcode: Comprehension AACSB: Analytic IMA: Strategic Marketing AICPA: Marketing/Client Focus

1.26

Business ethics: What ethical conflict does insider trading present?

Solution: Insider trading is an example of information asymmetry. The main idea is that investment decisions should be made on an even playing field. Insider trading is illegal because it puts one party at a significant disadvantage in trading. If insider trading were allowed, capital transfers would be much more difficult. LO: 1.6 Bloomcode: Comprehension AACSB: Ethics IMA: Business Applications AICPA: Professional Demeanor

Sample Test Problems 1.1

Identify three fundamental types of decisions that financial managers make, and identify which part of the balance sheet each of these decisions affects.

Solution: 1. Capital Budgeting Decisions – identifying the productive assets the firm should buy. These decisions affect long-term assets on the balance sheet. 2. Financing Decisions – determining how the firm should finance or pay for assets. These decisions affect long-term debt and stockholders’ equity on the balance sheet. 3. Working Capital Management Decisions – determining how day-to-day financial matters should be managed. These decisions affect current assets and current liabilities on the balance sheet.

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LO: 1 Level: Intermediate Bloomcode: Comprehension AACSB: Analytic IMA: Decision Analysis AICPA: Decision Modeling

1.2 Advantages of the corporate form of organization include which of the following? a. Reduced start-up costs b. Greater access to capital markets c. Unlimited liability d. Single taxation Solution: b. (Shares in a corporation can be sold to raise capital from investors who are not involved in the business. This greatly increases the amount of capital that can be raised to fund the business.) LO: 2 Level: Intermediate Bloomcode: Comprehension AACSB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

1.3

Why is stock value maximization superior to profit maximization as a goal for management?

Solution: While profit maximization appears to be a logical goal at first glance, it has some serious drawbacks. First, since accounting profit is the difference between revenues and expenses, it can be distorted by accounting decisions. Second, accounting profits are quite different from cash flows. Since cash flows are the focus of investors, they should also be the focus of managers. Third, profit maximization does not account for when cash

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flows actually occur. Finally, profit maximization as a goal ignores the risk involved in generating the cash flows. Stock value maximization is superior to profit maximization because it overcomes all of the listed shortcomings of profit maximization. This is because the value of a firm’s stock is determined by the cash flows that the firm is expected to produce. It accounts for (1) the size of the expected cash flows, (2) the timing of the expected cash flows, and (3) the riskiness of the expected cash flows. LO: 4 Level: Intermediate Bloomcode: Comprehension AACSB: Analytic IMA: Strategic/Critical thinking AICPA: Corporate Finance

1.4

What are agency costs? Explain.

Solution: Agency costs are costs that result from an agency relationship in which there is a conflict of interest between a principal and an agent. An agency relationship exists in a business when a firm’s managers (agents) are not also its owners (principals). Agency costs are incurred when managers act in ways that harm or contradict the owners’ interests. The cost of mechanisms, such as audits, that help control agency conflicts are also agency costs. LO: 5 Level: Intermediate Bloomcode: Comprehension AACSB: Analytic AICPA: Industry/Sector Perspective IMA: Business Economics

1.5

Identify seven mechanisms that can help better align the goals of managers with those of stockholders.

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Solution: Mechanisms that can help align the goals of managers with those of stockholders are as follows: (1) the board of directors, (2) management compensation, (3) the managerial labor market, (4) competition among managers, (5) large stockholders, (6) the takeover market, and (7) the legal and regulatory environment. Boards of directors that are independent from managers can help limit the extent to which managers are able to act solely in their own interest. Firms design compensation plans that are tied to firm performance in order to provide managers with incentives to make decisions consistent with the goal of stockholder value maximization. A third mechanism that helps align the goals of managers is the managerial labor market. It is difficult for poorly performing managers to find a good job elsewhere, and it is difficult for a poorly performing firm to hire good managers, which a firm’s current managers typically want to do. Competition among managers within a firm is a fourth mechanism that helps align the goals of managers with those of stockholders. This is because managers who act in the interest of stockholders are more likely to advance within the firm. Because large stockholders have a lot to gain from aligning the goals of managers with their own, they are likely to expend resources to encourage managers to maximize stock value. Sixth, the threat of a takeover, which leads to firing of poor managers, can provide current managers with incentives to perform well. Finally, laws and regulations limit the ability of managers to make decisions that harm stockholders. LO: 5 Level: Intermediate Bloomcode: Comprehension AACSB: Analytic AICPA: Strategic/Critical Thinking IMA: Performance Measurement

Ethics Case Discussion Questions 1.

Should employee pay be linked to sales targets?

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Students are likely to suggest, if the employee compensation plan been different, we may not have seen such behavior. In general, people do what they are paid for. So, having less of a focus on specific sales goals, or a lower amount of employee pay tied to the sales objectives, might have decreased the chances that employees would have opened fraudulent accounts as they would not benefit financially from doing so.

Should the practice of cross-selling be eliminated? Some students will suggest that the cross-selling strategy and sales goals are not

inherently bad – they can be sound compensation and incentive strategies that encourage employees to work to grow the company and add value for shareholders. However, it would also seem important that the company have well-established procedures to verify that new accounts are legitimate and approved by customers. If employees know that their work will be checked, and that any fraudulent accounts will be discovered, then perhaps they would be less likely to make up accounts in the first place.

What other steps could Wells Fargo have taken ahead of time to avoid the problems that it faced? A number of other suggestions are also likely to come up including employee ethics

training, limiting managers’ ability to pressure employees into aggressive selling, adopting a dismissal policy for unethical behavior, internal and external auditing of accounts, adopting claw back policies for more employees, and requiring independent monitoring of customer complaints.

4. Should senior executives Carrie Tolstedt and John Stumpf have been financially penalized by the company? Many students will suggest that the senior manager of the Community Banking division and the firm’s CEO bear the responsibility for the actions of the employees who work for them. As a result, these managers should also be penalized. Moreover, although it took substantial external pressure before the board of directors decided to claw back compensation, going forward the financial penalties and the potential to be dismissed for such actions, sends a strong message to other employees at the firm that such unethical behavior will not be tolerated.

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Other students might argue that the senior managers might not have been aware of the day-to-day actions of employees engaging in this behavior. Students might also argue that unless executives of a company breach their contract in a way that allows the firm to legally seek a claw back, perhaps there is not much that the company can do. In this case, however, it seems that Wells Fargo’s claw back provision specifying reputational harm to the company provided a sufficient legal basis for the board to act.

5. How important is it to have regulators like the Securities and Exchange Commission or congress involved in the oversight of situations such as that at Wells Fargo? The discussion here might be very broad focusing on whether or not we should even have regulation, or very narrow with students suggesting that we definitely need regulation to protect customers, consumers, and employees who may not be in a position to protect themselves. Some students will also suggest that regulation is more reactive than proactive. That is, once corporate wrongdoing is discovered, politicians usually act to address the issues. Sometimes the focus is on the specific company involved, but other times it entails new laws and regulations that affect many companies (e.g., the Dodd-Frank Act). Moreover, regulatory agencies like the SEC have the authority and the responsibility to act to protect the interests of particular groups, and that can include imposing penalties on firms or executives and seeking compensation for the damaged parties.

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Appendix C The 2017 Tax Cuts and Jobs Act: Implications for Cash Flow to Investors, the Cost of Capital, and Capital Structure Questions and Problems BASIC C.1

Taxes and cash flows: Jiffy Packing Inc. generated $3.45 million in earnings before taxes (EBT) in both fiscal years 2017 and 2018. In which year did Jiff y Packing likely have a higher cash flow from operating activity?

Solution: In 2017, Jiffy Packing Inc. would have paid taxes based on the marginal rate brackets summarized in Exhibit 3.6. The marginal rate for most of the taxable income earned by the firm in 2017 was well above the 21 percent flat tax rate applied to taxable income earned in fiscal year 2018. Given the higher marginal rates, cash flow to operating activity would have been lower in 2017 relative to 2018. LO:

Section: C.1 Level: Basic Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement C.2

Net business interest deduction: Hahn Enterprises has a fiscal year EBIT of $14.3 million and net business interest expense of $4.1 million. What is the maximum amount of pretax interest expense that Hahn Enterprises can recognize after the enactment of the 2017 federal tax legislation?

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Solution: The maximum allowable interest expense is defined as DedMaximum = ATI × 0.30. The maximum pretax net business interest expense is equal to $4.29 million ($14.3 million × 0.30 = $4.29 million). LO:

Section: C.1 Level: Basic Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement C. 3

Depreciation and cash flow: The CFO of Granger Garden Supplies developed a plan to

invest $1.2 million in a new manufacturing facility in 2018. During the planning process, the 2017 federal tax legislation was enacted, increasing the first-year bonus depreciation for facilities like this from 50 percent to 100 percent. The firm has a 23 percent tax rate, $9.8 million in EBITDA, and had no interest expense in 2018. What is the increase in cash flow from operating activity (CFOA) for Granger in 2018 that is attributable to the additional depreciation expense allowed under the 2017 tax legislation? Solution: Granger can fully expense the $1.2 million in depreciation for the manufacturing facility for tax year 2018, but before the tax policy reform, it could have depreciated $600,000 of the investment. Before the reform, the tax benefit of the depreciation expense would have been $138,000 (0.23 × $600,000 = $138,000). With full bonus depreciation, the tax shield from depreciation expense is $276,000 (0.23 × $1.2 million = $276,000); thus, the tax reform increased the depreciation tax shield for Granger Garden Supplies and its CFOA by $138,000 ($276,000 – $138,000 = $138,000) in 2018. LO:

Section: C.1 Level: Basic Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement INTERMEDIATE

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Taxes and the cost of debt: Swift Construction Inc. has 2019 EBIT of $1.6 million, a 23 percent tax rate, a 7 percent rate of interest on its bank loan, and net business interest expense of $650,000. Under the 2017 federal tax legislation, what is the company’s aftertax cost of debt?

Solution: First, determine the maximum amount of deductible interest expense. DedMaximum = ATI × 0.30 = $1.6 million × 0.30 = $0.48 million Second, calculate the percentage of total net business interest expense that is deductible. DedPct = DedMaximum∕NBIE = $0.48 million/0.65 million = 0.7835, or 78.35% Third, calculate the percentage tax shield under the 2017 tax reform legislation. kTax shield = DedPct × t × kDebt pretax = 0.7835 × 0.23 × 0.07 = 0.0126, or 1.26% Finally, calculate the after-tax cost of debt. kDebt after-tax = kDebt pretax – kTax shield = 0.07 – 0.0126 = 0.0574, or 5.74% LO:

Section C.2 Level: Intermediate Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement C.5

After-tax cost of a bond before the 2017 federal tax legislation: a. Perpetual Ltd. has issued 500,000 bonds that never require the principal amount to be repaid to investors. Correspondingly, Perpetual must make interest payments into the infinite future. If the bondholders receive annual payments of $75 and the current price of each of these bonds is $882.35, what is the after-tax cost of this debt for Perpetual if the 2017 federal tax legislation was not adopted and the firm is subject to a 40 percent average and marginal tax rate? Solution: Note: This problem takes Problem 13.16 from the 4th edition and extends it to include calculations that reflect the 2017 federal tax reform legislation.

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Since these are perpetual bonds, we know that the pretax cost of debt can be computed as:

We can then use Equation 13.3 to compute the after-tax cost of the debt. kDebt after-tax = kDebt pretax × (1 − t) kDebt after-tax = 0.085 × (1 − 0.40) = 0.0510, or 5.10% b. After-tax cost of a bond after the 2017 federal tax legislation: The debt issue in part (a) is the only debt that Perpetual Ltd. has outstanding and the company has no interest income. Assume that the 2017 tax legislation just became effective and reduced Perpetual’s average and marginal tax rate to 21 percent. What is the after-tax cost of this debt if the company has adjusted taxable income (ATI) of $90 million? Solution: Perpetual’s net business interest income expense is $75 × 500,000 = $37.5 million. Since the company’s ATI equals $90 million, its net business interest deduction is limited to $27 million ($90 million × 0.30 = $27 million). Using Equation C.1, we compute the after-tax cost of the debt as: kDebt after-tax = kDebt pretax × [1 – {[(ATI × 0.30)/NBIE] × t}] = 0.085 × [1 – {[($90.0 million × 0.30)/$37.5 million] × 0.21}] = 0.0728, or 7.28% LO:

Section C.2 Level: Intermediate Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

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Interest tax shield: JAF, Inc. has $500 million of debt outstanding at an interest rate of 9 percent. Assume that interest payments are fully deductible for tax purposes and that debt is perpetual. a. If the marginal tax rate changes from 30 percent to 21 percent, by what amount would the value of the firm’s tax shield decline? Solution: The present value of JAF’s tax shield at 30 percent is: D × t = $500,000,000 × 0.30 = $150,000,000 If the marginal rate changes to 21 percent, the value of the tax shield would be: D × t = $500,000,000 × 0.21 = $105,000,000 The tax shield is now lower by $45,000,000 ($150,000,000 – 105,000,000 = $45,000,000). b. If the tax rate falls from 30 percent to 21 percent, how will JAF’s value change? Explain your answer. Solution: While the value of the tax shield is lower, at a lower tax rate the firm will pay less tax. This increases cash flows to stockholders and increases firm value. As long as the reduction in taxes is greater than the $45,000,000 decline in the tax shield, firm value will increase.

LO:

Section: C.3 Level: Intermediate Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement ADVANCED C.7

WACC calculation before and after the 2017 federal tax legislation: a. It is 2017 (before the 2017 federal tax legislation takes effect) and the Imaginary Products Co. currently has debt with a market value of $300 million outstanding. The debt consists of 9 percent coupon bonds (semiannual coupon payments), which have a maturity of 15 years and are currently priced at $1,440.03 per bond. The firm also has of 2 million preferred shares outstanding with a market price of $12.00 per share. The

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preferred shares pay an annual dividend of $1.20. Imaginary also has 14 million shares of common stock outstanding with a price of $20.00 per share. The firm is expected to pay a $2.20 common dividend one year from today, and that dividend is expected to increase by 5 percent per year forever. If Imaginary is subject to a 40 percent average and marginal tax rate what is the firm’s weighted average cost of capital? Solution: Note: This problem extends Problem 13.24 from the 4th edition to include calculations that reflect the 2017 federal tax reform legislation. Step 1: Total amount of debt, common equity, and preferred equity: Debt = $300,000,000 (given) Preferred equity = $12 × 2,000,000 = $24,000,000 Common equity = $20 × 14,000,000 = $280,000,000 Total capital = $604,000,000 xDebt = 300 million/604 million = 0.4967 xps = 24 million/604 million = 0.0397 xcs = 280 million/604 million = 0.4636 Step 2: Cost of capital components: Cost of debt: $1,440.03 = $45 × PVIFA (30, YTM/2) + $1,000 × PVIF (30, YTM/2) Solving, we find that YTM = 0.0484 (this is a pretax number). Cost of preferred equity:

Cost of common equity:

Step 3: Combine using the WACC formula. WACC = xDebt KDebt pretax (1 – t) + xps kps + xcs kcs WACC = (0.4967 × 0.0484 × (1 − 0.4)) + (0.0397 × 0.10) + (0.4636 × 0.16) Copyright © 2022 John Wiley & Sons, Inc.

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= 0.0926, or 9.26%

b. Impact on WACC of the reduction in the tax rate due to the 2017 tax legislation: The 2017 federal tax legislation has just passed, reducing the average and marginal tax rate at the Imaginary Products Co. to 25 percent and limiting the net business interest deduction to 30 percent of the adjusted taxable income (ATI). Ignoring the limit of the net interest deduction for the moment, using the financial data for 2017 in part (a), what impact does the reduction in the tax rate alone have on the WACC of the Imaginary Products Co.? Solution: Since the tax rate is only used in the WACC calculation above to compute the after-tax cost of debt, we simply need to change this part of the calculation to reflect the impact of the reduction in the tax rate. The WACC with a 25 percent tax rate is: WACC = (0.4967 × 0.0484 × (1 − 0.25)) + (0.0397 × 0.10) + (0.4636 × 0.16) = 0.0962, or 9.62%

The reduction in the tax rate has increased the after-tax WACC for the firm from 9.26 percent to 9.62 percent, or 0.36 percent.

c. Impact on cost of debt and WACC of the reduction in the tax rate and limit on net business interest deduction due to the 2017 federal tax legislation: If Imaginary’s adjusted taxable income (ATI) equals $40 million, what is the impact of the reduction in the tax rate and limitation on the net business interest deduction to 30 percent of ATI on the cost of debt and the WACC of the Imaginary Products Co.? In these calculations, use the financial data for 2017 that are given in part (a). Solution: If the firm has no interest expense or income other than that associated with the 9 percent coupon bonds, its net business interest expense is simply the dollar value of the interest paid on those bonds. With a current price of $1,440.03 and a market value of $300 million, the firm has 208,329 bonds outstanding ($300 million/$1,440.03 = 208,329) and its net business interest expense equals 0.09 × $1,000 × 208,329 = $18,749,610.

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Therefore, using Equation C.1 to calculate the after-tax cost of debt yields: kDebt after-tax = kDebt pretax × [1 – {[(ATI × 0.30)/NBIETotal] × t}] = 0.0484 × [1 – {[($40.0 million × 0.30)/$18.749610 million] × 0.25}] = 0.0407, or 4.07% This after-tax cost of debt yields a WACC of:

WACC = (0.4967 × 0.0407) + (0.0397 × 0.10) + (0.4636 × 0.16) = 0.0984, or 9.84% The 2017 federal tax legislation increased Imaginary’s WACC by 0.58 percent (9.84 percent – 9.26 percent = 0.58 percent) when we consider both the reduction in the tax rate and the limits it imposed on the net business interest deduction.

LO:

Section: C.2 Level: Advanced Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement C.8

Firm value with limited interest deductibility: You own all of the equity in the Huson Holdings Company. The firm is currently debt free and will generate adjusted taxable income (ATI) of $40 million each year in perpetuity. The return on assets, kAssets, is 10 percent, the tax rate is 21 percent, and the maximum amount of interest that can be deducted for tax purposes is 30 percent of ATI. a. What is the value of the all-equity firm? Solution: With $40 million of ATI, the value of the all-equity firm is determined by the after-tax cash flow discounted at the cost of equity (which is the cost of assets). VFirm = [ATI × (1 – t)]/kcs = [$40 million × (1 – 0.21)]/0.10 = $31.6 million/0.10 = $316 million

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b. If Huson Holdings decides to replace $15 million of equity by borrowing $15 million at an interest rate of 8.5 percent, what would the value of the firm be? Solution: We first need to determine the maximum allowable interest expense. DedMaximum = ATI × 0.30 or $40 million × 0.30 = $12 million The total interest payment on $15 million debt will be 8.5% × $15 million = $12.75 million. As the total interest payment is greater than the maximum deductible interest, the maximum allowable value of debt is: DebtMaximum = $12 million/0.085 = $141.18 million At this debt level the present value of the tax shield is $29.65 million ($141.18 million × 0.21 = $29.65 million). The value of the firm with debt is the value of the all-equity firm plus the present value of the tax shield. VFirm = $316 million + $29.65 million = $345.65 million LO:

Section: C.3 Level: Advanced Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

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Textbook: Fundamentals of Corporate Finance, 5th Edition Authors: Robert Parrino, Thomas Bates, Stuart Gillan, David Kidwell Publisher: Wiley Chapter 21: International Financial Management Excel solutions for selected problems at end of Chapter 21 Problem number 24 28 29

Problem description Forward Premium Cross Exchange Rate Hedging

Worksheet tab name 24_Forward_Premium 28_Cross_Rate 29_Hedging

One way to return to the contents worksheet is to hold down the CTRL key and simultaneously press and hold down the P

eously press and hold down the Page Up key

Chapter 21, Problem 24

Student's Name:

Solution method uses cell formulas.

Guidelines:

<-- To view guidelines, move mouse pointer over cell with red triangle. Red triangle identifies a cel

Problem: Forward premium: The spot rate of the Australian dollar (A$) is A$1.1667/$. The Australian dollar is quoted at a 30-day forward premium of 4.90 percent against the U.S. dollar. What is the 30-day forward quote? Unknown: 30-day forward quote.

Assumption(s): Spot rate is quoted as Australian dollar to U.S. dollar (A$/$).

Given information/inputs/arguments: Australian dollar (A$) spot rate Days for forward contract 30 day forward premium on A$

1.1667 30.0 4.90%

Enter Enter as a as positive a positive number number A$/$A$/$ Enter as a positive number Enter Enter percentage percentage as XX.XX% as XX.XX% or .XXXX or .XXXX

Output, Forward 30 day quote: 30 Day Forward quote

1.1619

Analysis, Forward Rate: Forward Premium(Discount)

Forward Rate = Spot rate F0

- Spot Rate

-0.049

1.1667

1.167

-0.049

1.1667

360 n

360 x 30

1.1667 360

Date:

e. Red triangle identifies a cell comment.

$. The Australian U.S. dollar. What is

.XX% or .XXXX

100

Chapter 21, Problem 28

Student's Name:

Solution method uses cell formulas.

Guidelines:

<-- To view guidelines, move mouse pointer over cell with red triangle. Red triangle identifies a cel

Problem:

Cross rate: Flint Corp. recently purchased auto parts worth 17.5 million Mexican pesos (MP) on credit. Management ne find out the U.S. dollar cost of the purchase. It has access to two quotes for Canadian dollars (C$): C$1.2430/$ and C$0.0 What did it cost Flint to purchase the auto parts?

Unknown: Cost of equipment in US$ given different cross rates.

Assumption(s): Cross rates are provided in Canadian $ to Mexican pesos and Canadian $ to US$ .

Given information/inputs/arguments: Foreign Currency Payables in Mexican pesos Canadian $ to US$ Canadian $ to Mexican pesos

17,500,000 1.2430 0.0620

Analysis & Output, Cross Rates: Foreign Currency Payables Cross Rate (US$/MP) Dollar Cost of Payables

17,500,000 0.0499 872,888

Enter as a positive number, Mexican pesos Enter as a positive number, C$/US$ Enter as a positive number, C$/Mpesos

Date:

d triangle identifies a cell comment.

on credit. Management needs to (C$): C$1.2430/$ and C$0.0620/MP.

number, Mexican pesos

number, C$/Mpesos

Chapter 21, Problem 29

Student's Name:

Solution method uses cell formulas.

Guidelines:

<-- To view guidelines, move mouse pointer over cell with red triangle. Red triangle identifies a cell c

Problem:

Hedging: Tricolor Industries has purchased equipment from a Brazilian firm for a total cost of 272,500 Brazilian reals. The has to pay in 30 days. Citibank has given the firm a 30-day forward quote of $0.1829/real. Assume that on the day the pay is due, the spot rate is expected to be $0.2103/real. How much would Tricolor have saved by hedging with a forward contr

Unknown: Savings based on hedging with a forward contract.

Assumption(s): Forward quote is provided in US$/Brazilian real.

Given information/inputs/arguments: Foreign Currency Payables in Brazilian reals 30 day forward rate Spot rate 30 days from now

272,500 0.1829 0.2103

Analysis & Output, Hedging Strategy: Foreign Currency Payables Spot rate on payment date Dollar cost of payables 30 day forward rate Cost if hedged at forward rate Cost savings if use hedge

272,500 0.2103 57,307 0.1829 49,840 7,466.50

Enter as a positive number, Brazilian real Enter as a positive number, $/real Enter as a positive number, $/real

Date:

e. Red triangle identifies a cell comment.

ost of 272,500 Brazilian reals. The firm l. Assume that on the day the payment d by hedging with a forward contract?

ive number, Brazilian real

Textbook: Fundamentals of Corporate Finance, 5th Edition Authors: Robert Parrino, Thomas Bates, Stuart Gillan, David Kidwell Publisher: Wiley Chapter 20: Options and Corporate Finance Excel solutions for selected problems at end of Chapter 20 Problem number 22 23 24

Problem description Valuation of call option Valuation of put option Valuation of put option

Worksheet tab name 22_Value_Call_Option 23_Value_Put_Option 24_Value_Put_Option

One way to return to the contents worksheet is to hold down the CTRL key and simultaneously press and hold dow

Chapter 20, Problem 22

Student's Name:

Solution method uses cell formulas.

Guidelines:

<-- To view guidelines, move mouse pointer over cell with red triangle. Re

Problem:

Option valuation: Assume that the stock of Socrates Motors is currently trading for $40 and will eit rise to $50 or fall to $35 in one month. The risk-free rate for one month is 1.5 percent. What is the of a one-month call option with a strike price of $25?

Unknown: Value of call option today, given two possible outcomes at expiration.

Assumption(s): Option is an European style option.

Given information/inputs/arguments: Current Stock Price High Price in one month Low Price in one month Strike Price Risk-free rate

$40.00 $50.00 $35.00 $25.00 1.5%

Enter as positive number Enter as positive number Enter as positive number Enter as positive number Enter percentage as XX.X% or .XXX

Output: Call Option Value

$15.37

Analysis, Option Payoff Diagram: Stock (X) $100

Risk-Free (Y) $1

Optio

$35.00

$50.00

$1.015

Equation 1 Equation 2 Difference of Eq 1 -Eq 2 Long X if Pos / Short if Neg

$10.00 $25.00 -$15.00 $1.00

= = = =

$35.00 X $50.00 X -$15.00 X X

+ + +

= = =

$35.00

Lend if Y Pos / Borrow if Y Neg

$10.00 -$25.00 -$24.63

Date:

ver cell with red triangle. Red triangle identifies a cell comment.

rading for $40 and will either s 1.5 percent. What is the value

Option ???

$10.00 $1.015 Y $1.015 Y $0.000

$1.015 Y $1.015 Y Y

$25.00

Chapter 20, Problem 23

Student's Name:

Solution method uses cell formulas.

Guidelines:

<-- To view guidelines, move mouse pointer over cell with red triangle. Red

Problem:

Option valuation: You are considering buying a three-month put option on Wing and a Prayer Const company’s stock currently trades for $10 per share and its price will either rise to $15 or fall to $7 in free rate for three months is 2 percent. What is the appropriate price for a put option with a strike

Unknown: Value of put option today, given two possible outcomes at expiration in three months.

Assumption(s): Option is an European style option.

Given information/inputs/arguments: Current Stock Price High Price in three months Low Price in three months Strike Price 3-month risk-free rate

$10 $15 $7 $9 2.0%

Enter as positive number Enter as positive number Enter as positive number Enter as positive number Enter percentage as XX.X% or .XXX

Output: Put option value

$1.18

Analysis, Option Payoff Diagram: Stock (X)

Risk-Free (Y)

Option

$7.00

$15.00

$1.02

Equation 1 Equation 2 Difference of Eq 1 -Eq 2 Short Sale of X

$2.00 $0.00 $2.00 -$0.25

= = = =

$7.00 X $15.00 X -$8.00 X X

+ + +

= = =

-$1.75

Long Y

$2.00 $3.75 $3.68

Date:

ver cell with red triangle. Red triangle identifies a cell comment.

on Wing and a Prayer Construction stock. The er rise to $15 or fall to $7 in three months. The riskr a put option with a strike price of $9?

Option

$2.00 $1.02 Y $1.02 Y $0.00

$1.02 Y $1.02 Y Y

$0.00

Chapter 20, Problem 24

Student's Name:

Solution method uses cell formulas.

Guidelines:

<-- To view guidelines, move mouse pointer over cell with red triangle. Red

Problem: Option valuation: You hold a European put option on Tubes, Inc., stock, with a strike price of $100. Things haven’t been going too well for Tubes. The current stock price is $2, and you think that it will either rise to $3 or fall to $1.50 at the expiration of your option. The appropriate riskfree rate is 5 percent. What is the value of the option? If this were an American option, would it be worth more?

Unknown: Value of put option today, given two possible outcomes at expiration.

Assumption(s): Option is an European style option.

Given information/inputs/arguments: Current Stock Price High Price at end of period Low Price at end of period Strike Price Risk-free rate

$2.00 $3.00 $1.50 $100.00 5.0%

Enter as positive number Enter as positive number Enter as positive number Enter as positive number Enter percentage as XX.X% or .XXX

Output: Put option value

$93.24

Analysis, Option Payoff Diagram: Stock (X)

Risk-Free (Y)

$1.50

$3.00

Option

$1.05

Equation 1 Equation 2 Difference of Eq 1 -Eq 2 Short Sale of X

$98.50 $97.00 $1.50 -$1.00

= = = =

$1.50 X $3.00 X -$1.50 X X

+ + +

= = =

-$1.50

Long Y

$98.50 $100.00 $95.24

If this were an American option, we could exercise today if we wanted. We would want to do so if the value of exercising greater than the value of the option. Exercising today would allow us to sell for $100 something worth $2, a gain of $98. This is more than $93.24. The American option is worth more.

Date:

ver cell with red triangle. Red triangle identifies a cell comment.

with a strike price of rice is $2, and you think on. The appropriate riskmerican option, would it

Option

$98.50

$1.05 Y $1.05 Y $0.00

$1.05 Y $1.05 Y Y

$97.00

Textbook: Fundamentals of Corporate Finance, 5th Edition Authors: Robert Parrino, Thomas Bates, Stuart Gillan, David Kidwell Publisher: Wiley Chapter 19: Financial Planning and Managing Growth Excel solutions for selected problems at end of Chapter 19 Problem number 20 35 39

Problem description Calculate External Funding Needed, EFN Pro Forma balance sheet & income statement Calculate growth rates and funding needs

One way to return to the contents worksheet is to hold down the CTRL key and simultaneously press and hold dow

David Kidwell

Worksheet tab name 20_External_Funds 35_Pro_Forma_Statements 39_Growth_Rates_and_Funding

ld down the CTRL key and simultaneously press and hold down the Page Up key

Chapter 19, Problem 20

Student's Name: Solution method uses cell formulas.

Date:

Guidelines: <-- To view guidelines, move mouse pointer over cell with red triangle. Red triangle identifies a cell comment. Problem: Percent of sales: Tomey Supply Company’s financial statements for the most recent fiscal year are shown below. The company management projects that sales will increase by 20 percent next year. Assume that all costs and assets increase directly with sales. The company has a constant 33 percent dividend payout ratio and has no plans to issue new equity. Any financing needed will be raised through the sale of long-term debt. Prepare pro forma financial statements for the coming year based on this information, and calculate the EFN for Tomey.

Unknown: Equity funding needed (EFN) based on proforma Balance Sheet and Income Statement.

Assumption(s): All values rounded to nearest dollar.

Given information/inputs/arguments: Expected Sales growth rate Dividend Payout Ratio Tax Rate

20.0% 33.00% 28.00%

Enter percentage as XX.X% or .XXX Enter percentage as XX.X% or .XXX Enter percentage as XX.X% or .XXX

Output, External Funding Needed (EFN): External Funding Needed

(211,801.29)

Analysis, Proforma Balance Sheet and Income Statement: Income Statement Net Sales Costs

Historical 1,768,121 1,116,487

Sales Change 20.0% 20.0%

Proforma 2,121,745 1,339,784

EBT Taxes (35%)

651,634 228,072

781,961 218,949

Net Income

423,562

563,012

Dividends Paid Addition to RE

185,794 377,218

Balance Sheet Assets Current Assets Net Fixed Assets

280,754 713,655

Total Assets

994,409

Liabilities and Equity Current Liabilities

167,326

20.0% 20.0%

336,905 856,386 1,193,291

20.0%

200,791

Long-term Debt Common Stock Retained Earnings

319,456 200,000 307,627

107,655 200,000 684,845

Total Liabilities and Equity

994,409

1,193,291

Chapter 19, Problem 35

Student's Name: Solution method uses cell formulas.

Date:

Guidelines: <-- To view guidelines, move mouse pointer over cell with red triangle. Red triangle identifies a cell comment. Problem: The financial statements for the year ended June 30, 2021, are given below for Morgan Construction Company. The firm’s sales are projected to grow at a rate of 25 percent next year, and all financial statement accounts will vary directly with sales. Based on that projection, develop a pro forma balance sheet and an income statement for the 2022 fiscal year.

Unknown: Proforma Balance Sheet and Income Statement.

Assumption(s):

All values rounded to nearest dollar. Proforma Income Statement and Balance Sheet accounts will grow at same rate as sa

Given information/inputs/arguments: Expected Sales growth rate

25.0%

Enter percentage as XX.X% or .XXX

Output, Proforma Balance Sheet and Income Statement: Income Statement Net Sales Costs

FYE 6/30/21 193,212,500 145,265,625

Sales Change 25.0% 25.0%

Proforma 241,515,625 181,582,031

EBITDA Depreciation

47,946,875 23,318,750

25.0%

59,933,594 29,148,438

EBIT Interest

24,628,125 11,935,869

25.0%

30,785,156 14,919,836

EBT Taxes(28%) Net Income

12,692,256 3,553,832 9,138,424

Balance Sheet Assets Cash Accounts Receivable Inventories

FYE 6/30/21 3,349,239 5,830,754 22,267,674

25.0% 25.0% 25.0%

4,186,549 7,288,443 27,834,593

Total Current Assets Net Fixed Assets Other Assets Total Assets

31,447,667 43,362,482 1,748,906 76,559,055

25.0% 25.0%

39,309,584 54,203,103 2,186,133 95,698,819

Liabilities and Equity Accounts Payable Notes Payable

9,041,679 4,857,496

25.0% 25.0%

11,302,099 6,071,870

25.0%

15,865,320 4,442,290 11,423,030 Proforma

Total Current Liabilities Long-term Debt Common Stock Retained Earnings

13,899,175 29,731,406 19,987,500 12,940,974

Total Liabilities and Equity

76,559,055

25.0% 25.0% 25.0%

17,373,969 37,164,258 24,984,375 16,176,218 95,698,819

Chapter 19, Problem 39

Student's Name: Solution method uses cell formulas.

Guidelines:

<-- To view guidelines, move mouse pointer over cell with red triangle. Red triang

Problem:

Munson Communications Company has just reported earnings for the year ended June 30, 2021. Below are the firm’s inc sheet. The company had a 55 percent dividend payout ratio for the last 10 years and management does not plan to chang internal forecasts, management expects sales growth in 2022 to be 20 percent. Assume that equity accounts and long-ter with sales, but change when retained earnings change or additional capital is issued. a. What is the firm’s internal growth rate (IGR)? b. What is the firm’s sustainable growth rate (SGR)? c. What is the external funding needed (EFN) to accommodate the expected growth? d. Construct the firm’s 2022 pro forma financial statements under the assumption that long-term debt will provide all external funding

Unknown:

Internal growth rate, sustainable growth rate, and equity funding needed (EFN) based on proforma Balance Sheet and Inc

Assumption(s): All values rounded to nearest dollar.

Given information/inputs/arguments: Expected Sales growth rate Dividend Payout Ratio Tax Rate

20.0% 55.00% 35.00%

Enter percentage as XX.X% or .XXX Enter percentage as XX.X% or .XXX Enter percentage as XX.X% or .XXX

Output, External Funding Needed (EFN): Retention Ratio Expected NI in 2022 Addition to RE ROE a. Internal Growth Rate b. Sustainable Growth Rate c. External Funding Needed

45.00% 7,321,747 3,294,786 30.8% 8.16% 13.84% 4,777,333

Analysis, Proforma Balance Sheet and Income Statement: Income Statement Net Sales Costs

FYE 6/30/21 79,722,581 59,358,499

Sales Change 20.0% 20.0%

Pro Forma 95,667,097 71,230,199

EBITDA Depreciation

20,364,082 7,318,750

20.0%

24,436,898 8,782,500

EBIT Interest

13,045,332 3,658,477

20.0%

15,654,398 4,390,172

EBT Taxes(35%) Net Income

9,386,855 3,285,399 6,101,456

20.0%

11,264,226 3,942,479 7,321,747

Balance Sheet Assets Cash Accounts Receivable Inventories

FYE 6/30/21 1,728,639 3,009,421 11,492,993

20.0% 20.0% 20.0%

2,074,367 3,611,305 13,791,592

Total Current Assets Net Fixed Assets Other Assets Total Assets

16,231,053 22,380,636 1,748,906 40,360,595

20.0% 20.0%

19,477,264 26,856,763 2,098,687 48,432,714

Liabilities and Equity Accounts Payable Notes Payable

4,666,673 2,507,094

20.0% 20.0%

5,600,008 3,008,513

Total Current Liabilities Long-term Debt Common Stock Retained Earnings

7,173,767 13,345,242 10,165,235 9,676,351

8,608,520 16,687,821 10,165,235 12,971,137

Total Liabilities and Equity

40,360,595

48,432,714

Date:

r over cell with red triangle. Red triangle identifies a cell comment.

ed June 30, 2021. Below are the firm’s income statement and balance s and management does not plan to change this policy. Based on Assume that equity accounts and long-term debt do not vary directly

the expected growth? er the assumption that long-term debt

based on proforma Balance Sheet and Income Statement.

Textbook: Fundamentals of Corporate Finance, 5th Edition Authors: Robert Parrino, Thomas Bates, Stuart Gillan, David Kidwell Publisher: Wiley Chapter 18: Business Formation, Growth, and Valuation Excel solutions for selected problems at end of Chapter 18 Problem number 20 21 31

Problem description Firm valuation, income approach Firm valuation, privately owned restaurant Equity value of a firm

Worksheet tab name 20_Firm_Valuation 21_Firm_Valuation_Restaurant 31_Equity_Value_of_Firm

One way to return to the contents worksheet is to hold down the CTRL key and simultaneously press and hold down the P

Chapter 18, Problem 20

Student's Name:

Solution method uses cell formulas

Guidelines:

<-- To view guidelines, move mouse pointer over cell with red triangle. Red triangle identifies

Problem:

Income approaches: You are using the FCFF approach to value a business. You have estimated th for next year will be $123.65 million and that it will increase at a rate of 8 percent for each of the four years. After that point, the FCFF will increase at a rate of 3 percent forever. If the WACC for t percent and it has no NOA, what is it worth?

Unknown: Present value of the firm using the growing annuity formula:

PVA n =

n   1+ g CF1   × 1-    (WACC - g )   1+ WACC  

Terminal value of firm using following formula:

Assumption(s) All rates are annual rates with annual compounding. All cash flows are at the end of the year.

Given information/inputs/arguments: FCFF next year Rate of increase in FCFF (g1) Number of years for first growth rate in FCCF Constant growth rate in FCFF (g2) Cost of capital (WACC)

Values 123,650,000 8.0% 4.00 3.0% 10.00%

Excel solution method using cell formulas: PV of annuity growing at g1 Present Value of Terminal Value of Firm Total Value of Firm Today

541,975,672 1,536,968,269 2,078,943,942

Comments Enter amount as positive value Enter rate as percent, XX.XX%, or dec Enter amount as positive value Enter rate as percent, XX.XX%, or dec Enter rate as percent, XX.XX%, or dec

Date:

iangle. Red triangle identifies a cell comment.

ness. You have estimated that the FCFF of 8 percent for each of the following nt forever. If the WACC for this firm is 10

n   1+ g CF1   × 1-    ACC - g )   1+ WACC  

r rate as percent, XX.XX%, or decimal .XXXX

r rate as percent, XX.XX%, or decimal .XXXX r rate as percent, XX.XX%, or decimal .XXXX

Chapter 18, Problem 21

Student's Name:

Solution method uses cell formulas

Guidelines:

<-- To view guidelines, move mouse pointer over cell with red triangle. Red triangle identifies

Problem:

Valuing a private business: You want to estimate the value of a privately-owned restaurant that is equity. Its most recent income statement is below (For Year End). You note that the profitability o significantly lower than that of comparable restaurants, primarily due to high salary and wage exp investigation reveals that the annual salaries for the owner and his wife, the firm’s accountant, ar respectively. These salaries are much higher than the industry median salaries for these two posit $50,000, respectively. Compensation for other employees ($200,000 in total) appears to be consi The median P/E ratio of comparable restaurants with no debt is 10. What is the total value of this

Unknown: Present value of the private company.

Assumption(s): All rates are annual rates with annual compounding. All amounts are rounded to the nearest dollar.

Given information/inputs/arguments: Industry standard management salary and wages Current owners' salary and wages Current salary and wages of other employees Median P/E of restaurant industry

Values 150,000 1,200,000 200,000 10.0

Output, Private Company Valuation: Calculation of Cost of Equity

Analysis of Income Statement: Revenue Cost of goods sold Gross Profit Salaries and wages Selling expenses Operating profit (EBIT) Taxes Net Income

$12,675,000 For Year End 3,000,000 600,000 2,400,000 1,400,000 100,000 900,000 315,000 585,000

Date:

ll with red triangle. Red triangle identifies a cell comment.

e of a privately-owned restaurant that is financed entirely with ar End). You note that the profitability of this restaurant is rimarily due to high salary and wage expenses. Further r and his wife, the firm’s accountant, are $900,000 and $300,000, stry median salaries for these two positions of $100,000 and ($200,000 in total) appears to be consistent with the market rates. ebt is 10. What is the total value of this restaurant?

Comments Enter amount as positive value Enter amount as positive value Enter amount as positive value Enter amount as positive value

Revised 3,000,000 600,000 2,400,000 350,000 100,000 1,950,000 682,500 1,267,500

Chapter 18, Problem 31

Student's Name:

Solution method uses cell formulas.

Guidelines:

<-- To view guidelines, move mouse pointer over cell with red triangle. Red triangle identifies a cell co

Problem:

You own a company that produces and distributes course packets for classes at local universities online. You have asked a to invest $35,000 in the business. Your friend wants to know what the business is worth so that he can determine how mu the equity (e.g., what percentage) ) he should expect to receive for his investment. You offer to help him value the busines The business is expected to generate revenue of $110,000 and incur cash operating expenses of $70,000 next year. Ove the following three years, revenue and cash operating expenses are expected to increase 15 percent, 10 percent, and 7 pe After year 4 they are expected to grow 2 percent per year forever. Depreciation and amortization, capital expenditures, and additions to working capital are expected to equal 5 percent, 6 percent, and 1 percent of revenue, respectively, in the You have determined that a target capital structure of 10 percent debt and 90 percent equity is reasonable for this busine With this capital structure, the pretax cost of debt will be 6 percent and the beta for the equity will be 1.30. The average ta rate for the business is 10 percent, and the marginal rate is 20 percent. The risk-free rate is 4.25 percent, and the market r premium is 6.01 percent. What is a 100 percent equity interest in the business worth? What percentage of the equity shou your friend get for his investment?

Unknown: Equity value of the firm and friend's percentage using the FCFF formula.

Assumption(s): All incremental cash flows are at the end of the year. All values rounded to nearest dollar. Salvage value used in straight line depreciation is zero. Cost of capital is annual rate with annual compounding.

Given information/inputs/arguments: Investment made by friend Revenues next year Cash Operating Expenses Increase in Revenues and Operating Exp Year 1 Increase in Revenues and Operating Exp Year 2 Increase in Revenues and Operating Exp Year 3 Increase in Revenues and Operating Exp Year 4 Depreciation & Amortization as a percentage of Revenues Capital Expenditures as a percentage of Revenues Additions to Working Capital as a percentage of Revenues Target Weight of Debt Pretax Cost of Debt Tax Rate Company Beta Risk-rate of return Expected market risk premium

Values 35,000 110,000 70,000 15.00% 10.00% 7.00% 2.00% 5.00% 6.00% 1.00% 10.00% 6.00% 10.00% 1.30 4.25% 6.01%

Comments Enter account amount as positiv Enter account amount as positiv Enter account amount as positiv Enter percentage as XX.X% or .XX Enter percentage as XX.X% or .XX Enter percentage as XX.X% or .XX Enter account amount as positiv Enter percentage as XX.X% or .XX Enter percentage as XX.X% or .XX Enter percentage as XX.X% or .XX Enter percentage as XX.X% or .XX Enter percentage as XX.X% or .XX Enter percentage as XX.X% or .XX Enter account amount as positiv Enter percentage as XX.X% or .XX Enter percentage as XX.X% or .XX

Output, WACC: Calculation of Cost of Equity After tax Cost of Debt WACC

12.06% 5.40% 11.40%

Analysis, cash flow calculations: Time, years Revenues Operating Costs Depreciation & Amortization Operating Profit Taxes NOPAT Depreciation & Amortization Capital Expenditures Additions to Working Capital FCFF Terminal Value FCFF + Terminal Value PV(FCFF)

1 110,000 70,000 5,500 34,500 3,450 31,050 5,500 6,600 165 29,785

2 126,500 80,500 6,325 39,675 3,968 35,708 6,325 7,590 127 34,316

29,785 26,738

34,316 27,654

Enterprise Value Less: Debt Value Equity Value

393,588 39,359 354,230

Investment made by friend Friend's Percentage of Ownership

35,000 9.88%

Date:

triangle identifies a cell comment.

ties online. You have asked a friend at he can determine how much of

percent, 10 percent, and 7 percent. revenue, respectively, in the future.

25 percent, and the market risk

er account amount as positive value er account amount as positive value er account amount as positive value

er account amount as positive value

3 139,150 88,550 6,958 43,643 4,364 39,278 6,958 8,349 97 37,789 37,789 27,337

4 148,891 94,749 7,445 46,697 4,670 42,028 7,445 8,933 30 40,509 439,721 480,230 311,860

5 151,868 96,643 7,593 47,631 4,763 42,868 7,593 9,112 30 41,319

Textbook: Fundamentals of Corporate Finance, 5th Edition Authors: Robert Parrino, Thomas Bates, Stuart Gillan, David Kidwell Publisher: Wiley Chapter 17: Dividends, Stock Repurchases, and Payout Policy Excel solutions for selected problems at end of Chapter 17 Problem number 28 29 30

Problem description Price per share after repurchase Value of sale after capital gains tax Indifference tax rate on dividends

Worksheet tab name 28_Share_Repurchase_Share_Price 29_Share_Repurchase_Gains 30_Share_Repurchase_Tax_Rate

One way to return to the contents worksheet is to hold down the CTRL key and simultaneously press and hold down the P

eously press and hold down the Page Up key

Chapter 17, Problem 28

Student's Name:

Solution method uses cell formulas

Guidelines:

<-- To view guidelines, move mouse pointer over cell with red triangle. Red triangle identifies

Problem:

Cholla Company currently has 30,000 shares outstanding Each share has a market value of $20. If the fir worth of shares, then what will be the value of each share outstanding after the repurchase? Ignore taxe

Unknown: Value per share after repurchase.

Assumption(s) All values to nearest dollar.

Given information/inputs/arguments: Number of shares outstanding, before repurchase Market value per share Dollar amount firm repurchases

Values 30,000 20 150,000

Excel solution method using cell formula: Market value of all shares before repurchase Number of shares repurchased Value of shares repurchased Value of remaining shares after repurchase Number of shares after repurchase Value per share after repurchase

600,000 7,500 150,000 450,000 22,500 20

Comments Enter number of shares as positive Enter price per share as positive va Enter amount of repurchase as pos

Date:

angle. Red triangle identifies a cell comment.

rket value of $20. If the firm repurchases $150,000 he repurchase? Ignore taxes.

r number of shares as positive value r price per share as positive value r amount of repurchase as positive value

Chapter 17, Problem 29

Student's Name:

Solution method uses cell formulas

Guidelines:

<-- To view guidelines, move mouse pointer over cell with red triangle. Red triangle identifies a

Problem:

You purchased 1,000 shares of Koogal stock five years ago for $30 per share. Today Koogal is repurchasing your shares through a fixed-price tender offer for $80 per share. What are the after-tax proceeds to you if only your capital gain is taxed at a 15 percent rate?

Unknown: After tax proceeds.

Assumption(s) All values rounded to nearest dollar.

Given information/inputs/arguments: Number of shares purchased five years ago Market price per five years ago Market price per share today Capital gains tax rate

Values 1,000 30 80 15.00%

Output, cell formulas: Value of shares purchased five years ago Value of same shares today Capital gain Tax on capital gain After tax proceeds

30,000 80,000 50,000 7,500 72,500

Comments Enter account amount as positive value Enter account amount as positive value Enter account amount as positive value Enter account amount as positive value

Date:

d triangle. Red triangle identifies a cell comment.

re. Today Koogal is repurchasing e the after-tax proceeds to you if

er account amount as positive value er account amount as positive value er account amount as positive value er account amount as positive value

Chapter 17, Problem 30

Student's Name:

Solution method uses cell formulas

Guidelines:

<-- To view guidelines, move mouse pointer over cell with red triangle. Red triangle identifies a

Problem: You purchased 1,000 shares of Zebulon Copper Co. five years ago for $50 per share. Today Zebulon management is trying to decide whether to repurchase shares for $70 per share through a fixed-price tender offer or pay a $70 cash dividend per share. If capital gains are taxed at a 15 percent rate, then at what rate must dividends be taxed for you to be indifferent between receiving the dividend and selling your shares back to Zebulon? Unknown: Tax rate on dividends at point of indifference between receiving the dividend and selling shares back to Zebulon.

Assumption(s) All values rounded to nearest dollar.

Given information/inputs/arguments: Number of shares purchased five years ago Market price per five years ago Repurchase price per share Cash dividend per share Capital gains tax rate

Values 1,000 50 70 70 15.00%

Output, cell formulas: Value of all shares five years ago Value of same shares today Capital gain Tax on capital gain Equivalent tax on dividends

50,000 70,000 20,000 3,000 4.29%

Comments Enter number of shares as a positive valu Enter price per share five years ago as a Enter repurchase price per share as a po Enter cash dividend per share as a positi Enter account amount as positive value

Date:

d triangle. Red triangle identifies a cell comment.

per share. Today Zebulon r share through a fixed-price d at a 15 percent rate, then at eiving the dividend and selling

er number of shares as a positive value er price per share five years ago as a positive value er repurchase price per share as a positive value er cash dividend per share as a positive value er account amount as positive value

Textbook: Fundamentals of Corporate Finance, 5th Edition Authors: Robert Parrino, Thomas Bates, Stuart Gillan, David Kidwell Publisher: Wiley Chapter 16: Capital Structure Policy Excel solutions for selected problems at end of Chapter 16 Problem number 16 28 33

Problem description Calculate cost of equity capital under M&M 1 Value of sale after capital gains tax Indifference tax rate on dividends

Worksheet tab name 16_M&M_1_Cost_of_Equity 28_Value_of_Debt_Tax_Shield 33_M&M_2_with_Taxes

One way to return to the contents worksheet is to hold down the CTRL key and simultaneously press and hold down the P

usly press and hold down the Page Up key

Chapter 16, Problem 16

Student's Name:

Solution method uses cell references and cell formulas

Guidelines:

<-- To view guidelines, move mouse pointer over cell with red triangle. Red triangle identifies

Problem:

M&M Proposition 1: The weighted average cost of capital for a firm (assuming all three Modigliani and Miller Pro apply) is 15 percent. What is the current cost of equity capital for the firm if its cost of debt is 10 percent and the firm value for the firm is 0.5?

Unknown: Current cost of equity capital.

Assumption(s) All rates are annual rates with annual compounding

Given information/inputs/arguments: Weighted Average Cost of Capital, WACC Cost of debt Proportion of debt to total firm value

Values 15% 10% 0.50

Excel solution method using cell formula: Proportion of equity to total value of firm Current cost of equity

0.5 20.00%

Comments Enter number of shares as positive Enter price per share as positive va Enter proportion of debt as a ratio

Date:

ngle. Red triangle identifies a cell comment.

ee Modigliani and Miller Proposition 1 assumptions debt is 10 percent and the proportion of debt to total

r number of shares as positive value r price per share as positive value r proportion of debt as a ratio

Chapter 16, Problem 28

Student's Name:

Solution method uses cell formulas and PV function/formula

Guidelines:

<-- To view guidelines, move mouse pointer over cell with red triangle. Red triangle identifies a

Problem: Finite Corp. has $250 million of debt outstanding at an interest rate of 11 percent. What is the present value of the debt tax shield if the debt will mature in five years (and no new debt will replace the old debt), assuming that Finite is subject to a 40 percent marginal tax rate?

Unknown: Present value of debt tax shield.

Assumption(s) All rates are annual rates with annual compounding. All values to nearest dollar.

Given information/inputs/arguments: Value of debt outstanding Interest rate on debt Maturity of debt, years Marginal tax rate Argument for PV function, fv Argument for PV function, type

Values 250,000,000 11.00% 5 40.00% 0 0

Output, cell formulas and PV function: Annual interest on debt Annual tax savings on interest Present value of tax savings (debt tax shield)

27,500,000 11,000,000 40,654,867.19

Comments Enter value of debt as positive value Enter rate as %, XX.XX5, or decimal, .XX Enter years to maturity of debt as posit Enter rate as %, XX.XX5, or decimal, .XX Enter zero, fv = future value not used Enter zero, for regular annuity

Date:

d triangle. Red triangle identifies a cell comment.

percent. What is the present w debt will replace the old

er value of debt as positive value er rate as %, XX.XX5, or decimal, .XXXX er years to maturity of debt as positive value er rate as %, XX.XX5, or decimal, .XXXX er zero, fv = future value not used

Chapter 16, Problem 33

Student's Name:

Solution method uses cell formulas

Guidelines:

<-- To view guidelines, move mouse pointer over cell with red triangle. Red triangle identifies a

Problem: M&M Proposition 2 with taxes: You own all of the equity in a debt-free app development business that generates cash flows of $400,000 each year in perpetuity. The cost of assets, kAssets, is 10 percent and the tax rate is 25 percent. What is the value of your all-equity firm? If you decide to replace $1 million of equity by borrowing $1 million at an interest rate of 6 percent, how much would the value of the firm increase? What would the kcs and WACC for your business be before and after the proposed financial restructuring? Use M&M Proposition 2 with taxes, Equation 16.5, to determine the expected return on the equity for input to the WACC calculation. Assume that all cash flows are perpetuities and that the second and third M&M conditions hold. Unknown: Value of all equity firm, change after adding debt, cost of equity after adding debt and WACC after adding debt.

Assumption(s) All values rounded to nearest dollar. All cash flow at end of year. Cash flows are a perpetuity. No personal taxes.

Given information/inputs/arguments: Annual before tax cash flow, all equity firm All equity cost of assets Tax rate Amount of debt replacing equity Annual interest rate on debt

Values 400,000 10.00% 25.00% 1,000,000 6.00%

Output, cell formulas Annual after tax cash flow, all equity firm Value of all equity Value of tax savings on debt Value of firm after substituting debt for equity Value of equity after substituting Cost of equity after substituting WACC after substituting debt for equity

300,000 3,000,000 250,000 3,250,000 2,250,000 11.33% 9.23%

Comments Enter annual cash flow as a positive val Enter as a percentage, XX.XX%, or decim Enter as a percentage, XX.XX%, or decim Enter amount of debt as a positive valu Enter as a percentage, XX.XX%, or decim

Date:

d triangle. Red triangle identifies a cell comment.

pp development business that ets, kAssets, is 10 percent and decide to replace $1 million of would the value of the firm after the proposed financial rmine the expected return on re perpetuities and that the

er annual cash flow as a positive value er as a percentage, XX.XX%, or decimal, .XXXX er as a percentage, XX.XX%, or decimal, .XXXX er amount of debt as a positive value er as a percentage, XX.XX%, or decimal, .XXXX

Textbook: Fundamentals of Corporate Finance, 5th Edition Authors: Robert Parrino, Thomas Bates, Stuart Gillan, David Kidwell Publisher: Wiley Chapter 15: How Firms Raise Capital Excel solutions for selected problems at end of Chapter 15 Problem number 20 24 26

Problem Description IPO underpricing, dollar amount IPO issuing costs IPO issuing costs

Worksheet tab name 20_IPO_Underpricing 24_IPO_Issuing_Costs 26_IPO_Issuing_Costs

One way to return to the contents worksheet is to hold down the CTRL key and simultaneously press and hold dow

eously press and hold down the Page Up key

Chapter 15, Problem 20

Student's Name:

Solution method uses formulas

Guidelines:

<-- To view guidelines, move mouse pointer over cell with red triangle. Red triangle identifies

Problem:

IPO: On December 9, 2020, DoorDash completed its IPO of 33 million shares to the initial investors at $102.00 per share. price of the stock that same day was $189.51. What was the dollar value of the underpricing associated with the Google IP

Unknown: Dollar value of underpricing.

Assumption(s) Amounts to nearest dollar.

Given information/inputs/arguments: Number of DoorDash shares to initial investors DoorDash's IPO offering price per share DoorDash's price per share at end of first day of trading

Values 33,000,000 102 189.51

Excel solution method using formulas: Offering value of all shares Value of shares at end of day Dollar value of underpricing

3,366,000,000 6,253,830,000 2,887,830,000

Comments Enter percent as XX.XX% or decima Enter amount as positive value Enter percent as XX.XX% or decima

Date:

ngle. Red triangle identifies a cell comment.

estors at $102.00 per share. The closing associated with the Google IPO?

r percent as XX.XX% or decimal, .XXXX

Chapter 15, Problem 24

Student's Name:

Solution method uses formulas and Round function/formula

Guidelines:

<-- To view guidelines, move mouse pointer over cell with red triangle. Red triangle identifies a

Problem:

IPO: Suppose a biotech company in Boston, Massachusetts, completes an $85 million IPO priced to the p firm receives $72 per share, and the out-of-pocket expenses are $340,000. The stock’s closing price at th $84. What is the total cost to the firm of issuing the securities?

Unknown: Total cost of IPO issuing securities.

Assumption(s) All dollar values rounded to nearest dollar

Given information/inputs/arguments: Amount of IPO IPO offering price per share Amount firm receives per share Out of pocket expenses Stock price per share at end of first day of trading

85,000,000 75 72 340,000 84

Excel solution method using ROUND function and formulas: Number of shares Underwriter's spread First day underpricing Total cost to the frim

1,133,333 3,399,999 10,199,997 13,939,996

Values Enter amount of IPO as positive value Enter IPO offering price as a positive va Enter amount firm receives per share a Enter out of pocket expenses as a posit Enter stock price per share at the end o

Date:

d triangle. Red triangle identifies a cell comment.

$85 million IPO priced to the public at $75 per share. The . The stock’s closing price at the end of the first day is

Comments er amount of IPO as positive value er IPO offering price as a positive value er amount firm receives per share as a positive value er out of pocket expenses as a positive value er stock price per share at the end of first day of trading as a positive value

Chapter 15, Problem 26

Student's Name:

Solution method uses formulas and Round function/formula

Guidelines:

<-- To view guidelines, move mouse pointer over cell with red triangle. Red triangle identifies a

Problem:

IPO underpricing: Suppose that a biotech firm in Pittsburgh raised $120 million in an IPO. The firm receiv stock sold to the public for $25 per share. The firm’s legal fees, SEC registration fees, and other out-of-po The firm’s stock price increased 17.5 percent on the first day. What was the total cost to the firm of issui

Unknown: Total cost to firm of issuing the securities

Assumption(s) Risk free rate and Market risk premium are annual rates with annual compounding

Given information/inputs/arguments: Amount raised in IPO Offering price per share Amount firm received per share Firm's fees and out-of-pocket costs Amount stock price increased on the first day

120,000,000 25 23 270,000 17.50%

Excel solution method using ROUND function and formulas: Number of shares Underwriter's spread Stock price per share end of first day of trading First day underpricing Total cost to the frim

4,800,000 9,600,000 29.3750 21,000,000 30,870,000

Values Enter amount raised in IPO as a positive Enter offering price per share as a posit Enter amount firm received per share a Enter fees and costs as a positive value Enter percentage as percent, XX.XX%, o

Date:

d triangle. Red triangle identifies a cell comment.

illion in an IPO. The firm received $23 per share, and the ation fees, and other out-of-pocket costs were $270,000. he total cost to the firm of issuing the securities?

Comments er amount raised in IPO as a positive value er offering price per share as a positive value er amount firm received per share as a positive value er fees and costs as a positive value er percentage as percent, XX.XX%, or decimal, .XXXX

Textbook: Fundamentals of Corporate Finance, 5th Edition Authors: Robert Parrino, Thomas Bates, Stuart Gillan, David Kidwell Publisher: Wiley Chapter 14: Working Capital Management Excel solutions for selected problems at end of Chapter 14 Problem number 19 29 32

Problem Description Calculate firm's accounts payable Calculate interest rate for line of credit Create a receivables aging schedule

Worksheet tab name 19_Accounts_Payable 29_Line_of_Credit 32_Receivables_Aging

One way to return to the contents worksheet is to hold down the CTRL key and simultaneously press and hold dow

eously press and hold down the Page Up key

Chapter 14, Problem 19

Student's Name:

Solution method uses cell formulas

Guidelines:

<-- To view guidelines, move mouse pointer over cell with red triangle. Red triangle identifies

Problem:

Cash conversion cycle: Joanna Handicrafts, Inc., has net sales of $4.23 million with 50 percent being cred million. The firm’s cash conversion cycle is 47.9 days, and its operating cycle is 86.3 days. What is the firm

Unknown: Firm's accounts payable.

Assumption(s) Same amount of sales on each day. Dollar amounts formatted to nearest dollar

Given information/inputs/arguments: Net sales Percent of net sales that are credit Cost of goods sold Cash conversion cycle, days Operating cycle, days Days in year

Values 4,230,000 50.00% 2,540,000 47.9 86.3 365

Output: Excel solution method using cell formulas: Credit sales Days payables outstanding, DPO Accounts payable

2,115,000 38.40 267,222

Comments Enter net sales as a positive value Enter percent as XX.XX% or decima Enter cost of goods sold as a positiv Enter Cash conversion cycle as a po Enter Operating cycle as a positive Enter days in year as a positive valu

Date:

angle. Red triangle identifies a cell comment.

with 50 percent being credit sales. Its cost of goods sold is $2.54 86.3 days. What is the firm’s accounts payable?

r net sales as a positive value r percent as XX.XX% or decimal, .XXXX r cost of goods sold as a positive value r Cash conversion cycle as a positive value r Operating cycle as a positive value r days in year as a positive value

Chapter 14, Problem 29

Student's Name:

Solution method uses cell formulas

Guidelines:

<-- To view guidelines, move mouse pointer over cell with red triangle. Red triangle identifies a

Problem:

Formal line of credit: Lansdowne Electronics has a formal line of credit of $1 million for up to three years interest rate on the loan is 5.3 percent, and under the agreement, Lansdowne has to pay an annual fee of unused amount. Suppose the firm borrows $675,000 the first day of the agreement. What is the fee the c unused balance? What is the effective interest rate?

Unknown: Fee on unused balance and effective annual interest rate.

Assumption(s) Effective interest rate is effective annual interest rate. Interest on borrowed and unborrowed funds paid at end of year.

Given information/inputs/arguments: Line of credit Length of line of credit, years Annual interest rate on borrowed funds Annual interest rate on unused balance Amount firm borrows

Values 1,000,000 3 5.30% 0.50% 675,000

Output: Excel solution method using cell formulas Annual fee on unused balance Annual amount of interest Effective annual interest rate

1,625.00 35,775.00 5.54%

Comments Enter line of credit as a positive value Enter years for line of credit as a positive Enter percentage as percent, XX.XX%, or Enter percentage as percent, XX.XX%, or Enter amount firm borrows as a positive

Date:

d triangle. Red triangle identifies a cell comment.

$1 million for up to three years with HND Bank. The wne has to pay an annual fee of 50 basis points on the greement. What is the fee the company must pay on the

er line of credit as a positive value er years for line of credit as a positive value er percentage as percent, XX.XX%, or decimal, .XXXX er percentage as percent, XX.XX%, or decimal, .XXXX er amount firm borrows as a positive value

Chapter 14, Problem 32

Student's Name:

Solution method uses cell formulas

Guidelines:

<-- To view guidelines, move mouse pointer over cell with red triangle. Red triangle identifies a

Problem:

Aging schedule: Ginseng Company collects 50 percent of its receivables in 10 days or fewer, 31 percent in in 31 to 45 days, 7 percent in 46 to 60 days, and 5 percent in more than 60 days. The company has $1,21 receivable. Prepare an aging schedule for Ginseng Company.

Unknown: Aging schedule.

Assumption(s) All amounts formatted to nearest dollar.

Given information/inputs/arguments:

Values

First/shortest aging period, number of days or fewer Second aging period, largest number of days Third aging period, largest number of days Fourth aging period, largest number of days Days for start of last aging period Percent of receivables collected during first aging period Percent of receivables collected during second aging period Percent of receivables collected during third aging period Percent of receivables collected during fourth aging period Percent of receivable collected during fifth/last aging period Accounts receivable

10 30 45 60 61 50.00% 31.00% 7.00% 7.00% 5.00% 1,213,000.00

Output: Aging schedule, Excel solution method using cell formulas Aging period First Second Third Fourth Fifth

First day 0 11 31 46 61

Last day 10 30 45 60

% Collected 50.00% 31.00% 7.00% 7.00% 5.00%

Amount 606,500 376,030 84,910 84,910 60,650

Date:

d triangle. Red triangle identifies a cell comment.

n 10 days or fewer, 31 percent in 11 to 30 days, 7 percent 60 days. The company has $1,213,000 in accounts

Comments Enter day number as a positive value Enter day number as a positive value Enter day number as a positive value Enter day number as a positive value Enter day number as a positive value Enter percentage as percent, XX.XX%, or decimal, .XXXX Enter percentage as percent, XX.XX%, or decimal, .XXXX Enter percentage as percent, XX.XX%, or decimal, .XXXX Enter percentage as percent, XX.XX%, or decimal, .XXXX Enter percentage as percent, XX.XX%, or decimal, .XXXX Enter amount of accounts receivable as a positive value

Textbook: Fundamentals of Corporate Finance, 5th Edition Authors: Robert Parrino, Thomas Bates, Stuart Gillan, David Kidwell Publisher: Wiley Chapter 13: The Cost of Capital Excel solutions for selected problems at end of Chapter 13 Problem number 15 24 34

Solution Method Cost of bond/debt WACC, Weighted Average Cost of Capital WACC, Weighted Average Cost of Capital

Worksheet tab name 15_Cost_of_Bond 24_WACC 34_WACC

One way to return to the contents worksheet is to hold down the CTRL key and simultaneously press and hold dow

eously press and hold down the Page Up key

Chapter 13, Problem 15

Student's Name:

Solution method uses PV function/formula

Guidelines:

<-- To view guidelines, move mouse pointer over cell with red triangle. Red triangle identifies

Problem:

Current cost of a bond: You know that the after-tax cost of debt capital for Bubbles Champagne Compan issue of five-year bonds outstanding, what is the current price of the bonds if the coupon rate on those b make semiannual coupon payments and the marginal tax rate is 30 percent.

Unknown: Before tax cost of debt and current price of bond.

Assumption(s) Par or face value of bond is $1,000 After tax cost of debt is an annual rate with semiannual compounding

Given information/inputs/arguments: After tax cost of debt Maturity date, future years Annual coupon rate on bonds Times per year that interest paid Marginal tax rate Par or face value of bond Argument for PV function, type

Values 7.00% 5 10.00% 2 30.00% 1,000 0

Excel solution method using PV function: Before tax cost of debt Price of bond, use PV function

10% 1,000

Comments Enter percent as XX.XX% or decima Enter amount as positive value Enter percent as XX.XX% or decima Compounded semiannually Enter percent as XX.XX% or decima Enter amount as positive value For type enter zero, regular annuity

Date:

angle. Red triangle identifies a cell comment.

ubbles Champagne Company is 7 percent. If the firm has only one the coupon rate on those bonds is 10 percent? Assume the bonds

Chapter 13, Problem 34

Student's Name:

Solution method uses RATE and SUMPRODUCT functions/formulas

Guidelines:

<-- To view guidelines, move mouse pointer over cell with red triangle. Red triangle identifies a

Problem:

WACC: The Imaginary Products Co. currently has debt with a market value of $300 million outstanding. The debt consists 9 coupon bonds (semiannual coupon payments) which have a maturity of 15 years and are currently priced at $1,440.03 per The firm also has an issue of 2 million preferred shares outstanding with a market price of $12.00 per share. The preferred pay an annual dividend of $1.20. Imaginary also has 14 million shares of common stock outstanding with a price of $20.00 The firm is expected to pay a $2.20 common dividend one year from today, and that dividend is expected to increase by 5 per year forever. If Imaginary is subject to a 28 percent marginal tax rate, then what is the firm’s weighted average cost of

Unknown: Weighted Average Cost of Capital = WACC.

Assumption(s) Par or face value of bond is $1,000. Annual growth rate of stock dividend has annual compounding.

Given information/inputs/arguments:

Values 300,000,000 9.00% 2 15.00 1,440.03 1,000 2,000,000.00 12.00 1.20 14,000,000 20.00 2.20 5.00% 28.00% 0

Market value of debt Coupon rate on debt Compounding frequency per year on debt Maturity of debt, years Current price of debt Par/face value of bonds Shares of preferred stock Current price per share of preferred Dividend per year on preferred shares Shares of common stock Current price per share of common stock Next annual dividend, at t = 1 Annual growth rate for common stock, forever Tax rates, average and marginal Argument for rate function, type

Output, Weighted Average Cost of Capital, WACC Weighted average cost of capital, using SumProduct function

9.55%

Analysis Source of funds Bond Preferred stock Common stock

Amount 300,000,000 24,000,000 280,000,000

Weight 0.497 0.040 0.464

Expected return 4.840% 10.000% 16.000%

Cost after tax 3.485% 10.000% 16.000%

Date:

d triangle. Red triangle identifies a cell comment.

llion outstanding. The debt consists 9 percent are currently priced at $1,440.03 per bond. ce of $12.00 per share. The preferred shares ck outstanding with a price of $20.00 per share. dividend is expected to increase by 5 percent s the firm’s weighted average cost of capital?

Comments Enter market value of debt as positive value Enter percentage as XX.XX% or .XXXX Enter account amount as positive value Enter maturity as positive value Enter price as positive value Enter face or par value as positive value Enter shares of preferred as positive value Enter current price of preferred as positive value Enter preferred dividend per share as positive value Enter shares of common as a positive value Enter common price per share as positive value Enter next dividend as positive value Enter percentage as XX.XX% or .XXXX Enter percentage as XX.XX% or .XXXX Enter zero for regular annuity

Chapter 13, Problem 34

Student's Name:

Solution method uses IF and SUMPRODUCT functions/formulas

Guidelines:

<-- To view guidelines, move mouse pointer over cell with red triangle. Red triangle identifies a

Problem:

Hurricane Corporation is financed with debt, preferred equity, and common equity with market values of $20 million, $10 $30 million, respectively. The betas for the debt, preferred stock, and common stock are 0.2, 0.5, and 1.1, respectively. If t rate is 3 percent, the market risk premium is 6 percent, and Hurricane’s average and marginal tax rates are both 30 percen is the company’s weighted average cost of capital?

Unknown: Weighted average cost of capital, WACC

Assumption(s) Risk free rate and Market risk premium are annual rates with annual compounding

Given information/inputs/arguments:

Values 20,000,000 10,000,000 30,000,000 0.20 0.50 1.10 3.00% 6.00% 30.00%

Market value of debt Market value of preferred stock Market value of common stock Beta for debt/bond Beta for preferred stock Beta for common stock Risk free rate Market risk premium Tax rates, average and marginal

Output, Weighted Average Cost of Capital, WACC Weighted average cost of capital, using SumProduct function

6.780%

Analysis Source of funds Bond Preferred stock Common stock

Amount 20,000,000 10,000,000 30,000,000

Weight 0.333 0.167 0.500

Expected return 4.200% 6.000% 9.600%

Cost after tax 2.940% 6.000% 9.600%

Date:

d triangle. Red triangle identifies a cell comment.

th market values of $20 million, $10 million, and are 0.2, 0.5, and 1.1, respectively. If the risk-free marginal tax rates are both 30 percent, what

Comments Enter market value of debt as positive value Enter market value of preferred as positive value Enter market value of common as positive value Enter beta as positive value Enter beta as positive value Enter beta as positive value Enter percentage as XX.XX% or .XXXX Enter percentage as XX.XX% or .XXXX Enter percentage as XX.XX% or .XXXX

Textbook: Fundamentals of Corporate Finance, 5th Edition Authors: Robert Parrino, Thomas Bates, Stuart Gillan, David Kidwell Publisher: Wiley Chapter 12: Evaluating Project Economics Excel solutions for selected problems at end of Chapter 12 Problem number 14 23 27

Solution Method Replace an existing asset Capital budgeting, cash flows and NPV Capital budgeting, cash flows and NPV

Worksheet tab name 14_ EBIT 23_Economic_Break_Even 27_Scenario_Analysis

One way to return to the contents worksheet is to hold down the CTRL key and simultaneously press and hold dow

eously press and hold down the Page Up key

Chapter 12, Problem 14

Student's Name:

Solution method uses cell references and cell formulas

Guidelines:

<-- To view guidelines, move mouse pointer over cell with red triangle. Red triangle identifies

Problem:

EBIT: Duplicate Footballs, Inc., expects to sell 15,000 balls this year. The balls sell for $110 each and have a variable cost p Fixed costs, including depreciation and amortization, are currently $220,000 per year. How much can either the fixed costs the variable cost per unit increase before the company has a negative EBIT?

Unknown: Increase in fixed or variable costs before EBIT is negative (until EBIT is zero)

Assumption(s) All values to nearest dollar Opportunity cost of capital is an annual rate with annual compounding. All costs and future savings occur at the end of the year.

Given information/inputs/arguments: Sales per year, units Sales, price per unit Variable cost per unit Annual fixed costs (with depreciation and amortization)

Values 15,000 110 80 220,000

Excel solution method using formulas and cell references: Revenue per year = price per unit * number of units Costs per year = fixed and variable EBIT per year = revenue - total costs per year Increase in fixed costs before EBIT = 0 Increase in variable cost per unit before EBIT = 0

1,650,000 1,420,000 230,000 230,000 15.33

Comments Enter annual sales as positive valu Enter price per unit as positive val Ener variable cost per unit as posit Enter annual fixed cost as positive

Date:

ngle. Red triangle identifies a cell comment.

ch and have a variable cost per unit of $80. much can either the fixed costs or

r annual sales as positive value r price per unit as positive value variable cost per unit as positive value r annual fixed cost as positive value

Chapter 12, Problem 23

Student's Name: Solution method uses PMT and SLN functions/formulas

Guidelines:

<-- To view guidelines, move mouse pointer over cell with red triangle. Red triangle identifies a

Problem:

Economic break-even point: Rose Weiser Company management is considering a project that will require an initial invest $50,000 and will last for 10 years. No other capital expenditures or increases in working capital are anticipated during the project. What is the annual EBIT that will make the project economically viable if the cost of capital for the project is 9 per the firm will depreciate the investment using straight-line depreciation and a salvage value of $0? Assume that the margin rate is 24 percent.

Unknown: EBIT that gives an NPV equal to zero.

Assumption(s) All values rounded to nearest dollar. Cost of capital is annual rate with annual compounding.

Given information/inputs/arguments: Initial project investment Life of new investment, years Salvage value, used in depreciation Tax rate Annual opportunity cost of capital PMT function, argument, fv PMT Function, argument, type

Values 50,000 10 0 24.00% 9.00% 0 0

Type of depreciation: Straight line

Output, EBIT that gives an NPV = 0, uses PMT and SLN functions: Step 1, pmt when t = 0, is 50,000, Free cash flow Step 2: annual depreciation, use SLN function Step 3: net income, Free cash flow - depreciation Step 4: EBIT = net income/(1 - tax rate)

7,791 5,000 2,791 3,672

Comments Enter project investment as a positive value Enter investment life, years, as a positive value Enter salvage value as zero Enter percentage as XX.XX% or .XXXX Enter percentage as XX.XX% or .XXXX Enter 0, no future value Enter 0 to treat payments as regular annuity

Date:

ngle. Red triangle identifies a cell comment.

that will require an initial investment of pital are anticipated during the life of the of capital for the project is 9 percent and of $0? Assume that the marginal tax

vestment as a positive value nt life, years, as a positive value

e as XX.XX% or .XXXX e as XX.XX% or .XXXX

payments as regular annuity

Chapter 12, Problem 27

Student's Name:

Solution method uses formulas and cell references

Guidelines:

<-- To view guidelines, move mouse pointer over cell with red triangle. Red triangle identifies a

Problem:

Scenario analysis: Chip's Home Brew Whiskey management forecasts that if the firm sells each bottle of Snake-Bite for $2 demand for the product will be 15,000 bottles per year, whereas sales will be 90 percent as high if the price is raised 10 pe Chip's variable cost per bottle is $10, and the total fixed cash cost for the year is $100,000. Depreciation and amortization are $20,000, and the firm has a 30 percent marginal tax rate. Management anticipates n increased working capital need o for the year. What will be the effect of the price increase on the firm's FCF for the year?

Unknown: Effect of a 10 percent price increase on Free Cash Flow per year.

Assumption(s) All values rounded to nearest dollar

Given information/inputs/arguments:

Values

Price of each bottle of Snake-Bite Demand when price @ 20 Percentage or original unit sales when price increases Price increase, percent Variable cost per unit Fixed cash cost per year Depreciation and amortization per year Working capital per year Tax rate

20 15,000 90.00% 10.00% 10 100,000 20,000 3,000 30.00%

Output, change in Free Cash Flow Change in free cash flow with price increase

8,400

Analysis, free cash flow: Revenue Total variable cost Fixed cos Depreciation Earnings before taxes Taxes Net income Net operating cash flow Working capital Free cash flow

Current Price $300,000 150,000 100,000 20,000 30,000 9,000 21,000 41,000 3,000 $38,000

Price increase $297,000 135,000 100,000 20,000 42,000 12,600 29,400 49,400 3,000 $46,400

Date:

h red triangle. Red triangle identifies a cell comment.

e firm sells each bottle of Snake-Bite for $20, then the percent as high if the price is raised 10 percent. $100,000. Depreciation and amortization charges cipates n increased working capital need of $3,000

Comments Enter price of each bottle as a positive value Enter demand as positive value Enter percentage as XX.XX% or .XXXX Enter percentage as XX.XX% or .XXXX Enter variable cost per unit as positive value Enter fixed cost as positive value Enter dep. & amort. as a positive value Enter working capital as a positive value Enter percentage as XX.XX% or .XXXX

Textbook: Fundamentals of Corporate Finance, 5th Edition Authors: Robert Parrino, Thomas Bates, Stuart Gillan, David Kidwell Publisher: Wiley Chapter 11: Cash Flows and Capital Budgeting Excel solutions for selected problems at end of Chapter 11 Problem number 25 32 36

Solution Method Replace an existing asset Capital budgeting, cash flows and NPV Capital budgeting, cash flows and NPV

Worksheet tab name 25_Replace_Asset_NPV 32_Capital_Budgeting_NPV 36_Capital_ Budgeting_NPV

One way to return to the contents worksheet is to hold down the CTRL key and simultaneously press and hold dow

eously press and hold down the Page Up key

Chapter 11, Problem 25

Student's Name:

Solution method uses PV, MAX, INDEX, and MATCH functions/formulas

Guidelines:

<-- To view guidelines, move mouse pointer over cell with red triangle. Red triangle identifies

Problem:

Replace an existing asset: Bell Mountain Vineyards is considering updating its current manual accounting system with a h system. While the new accounting system would save the company money, the cost of the system continues to decline. B opportunity cost of capital is 10 percent, and the costs and values of investments made at different times in the future are Year 0 1 2 3 4 5

Cost $5,000 4,000 4,500 3,600 3,300 3,100

Value of Future Savings (at the time of purchase) $7,000 7,000 7,000 7,000 7,000 7,000

When should Bell Mountain buy the new accounting system?

Unknown: What year to buy a new accounting system.

Assumption(s) All values to nearest dollar Opportunity cost of capital is an annual rate with annual compounding. All costs and future savings occur at the end of the year.

Given information/inputs/arguments:

Values 5,000 4,500 4,000 3,600 3,300 3,100 7,000 10.00% 0 0

Cost, year 0 Cost, year 1 Cost, year 2 Cost, year 3 Cost, year 4 Cost, year 5 Value of future savings, same for every year Opportunity cost of capital Other argument for PV function, pmt Other argument for PF function, type

Excel solution method using SUM function: NPV = pv of (savings - cost) NPV at t = 0 NPV at t = 1 NPV at t = 2

Time, years

Value 0 1 2

2,000 2,273 2,479

Comments Enter amount as positive value Enter amount as positive value Enter amount as positive value Enter amount as positive value Enter amount as positive value Enter amount as positive value Enter amount as positive value Enter as percent, XX.XX, or decimal, .XXX Enter zero, pmt not used Enter zero, type not used

NPV at t = 3 NPV at t = 4 NPV at t = 5 Max NPV Year of Max NPV

3 4 5

2,554 2,527 2,422 2,554 3 Bell Mountain should purchase the system i

Date:

red triangle. Red triangle identifies a cell comment.

nt manual accounting system with a high-end electronic of the system continues to decline. Bell Mountain's ade at different times in the future are as follows:

Chapter 11, Problem 32

Student's Name:

Solution method uses NPV and SLN functions/formulas

Guidelines:

<-- To view guidelines, move mouse pointer over cell with red triangle. Red triangle identifies a

Problem:

Rocky Mountain Lumber, Inc., is considering purchasing a new wood saw that costs $50,000. The saw will generate revenu per year for five years. The cost of materials and labor needed to generate these revenues will total $60,000 per year, and expenses will be $10,000 per year. The machine is expected to sell for $1,000 at the end of its five-year life and will be dep a straight-line basis over five years to zero. Rocky Mountain’s tax rate is 26 percent, and its opportunity cost of capital is 10 Should the company purchase the saw? Explain why or why not?

Unknown: Project NPV

Assumption(s) All incremental cash flows are at the end of the year. All values rounded to nearest dollar. Salvage value used in straight line depreciation is zero. Cost of capital is annual rate with annual compounding.

Given information/inputs/arguments:

Values 50,000 100,000 5 60,000 10,000 1,000 0 26.00% 10.00%

Cost of new wood saw Incremental annual revenue from new saw Investment life, years Annual cost of materials and labor Other annual cash expenses Estimated value of machine at end of life Salvage value, used in depreciation Tax rate Annual opportunity cost of capital

Comments Enter account amount as positiv Enter account amount as positiv Enter account amount as positiv Enter account amount as positiv Enter account amount as positiv Enter account amount as positiv Enter account amount as positiv Enter percentage as XX.XX% or . Enter percentage as XX.XX% or .

Type of depreciation: Straight line

Output, Net Present Value Project NPV

44,471

Analysis, cash flow calculations Time, years Incremental Revenue Material & Labor costs Depreciation Other cash expenses Earnings before taxes

1 100,000 60,000 10,000 10,000 20,000

2 100,000 60,000 10,000 10,000 20,000

3 100,000 60,000 10,000 10,000 20,000

Taxes Net income Net operating cash flow Cost of new machine

5,200 14,800 24,800

24,800

-50,000

Terminal value Market value Book value Taxes Terminal after tax cash flow Free cash flow

-50,000

Date:

angle. Red triangle identifies a cell comment.

00. The saw will generate revenues of $100,000 will total $60,000 per year, and other cash f its five-year life and will be depreciated on s opportunity cost of capital is 10 percent.

Enter account amount as positive value Enter account amount as positive value Enter account amount as positive value Enter account amount as positive value Enter account amount as positive value Enter account amount as positive value Enter account amount as positive value Enter percentage as XX.XX% or .XXXX Enter percentage as XX.XX% or .XXXX

4 100,000 60,000 10,000 10,000 20,000

5 100,000 60,000 10,000 10,000 20,000

5,200 14,800 24,800

1,000 0 260 740 24,800

25,540

Chapter 11, Problem 32

Student's Name:

Solution method uses NPV and SLN functions/formulas

Guidelines:

<-- To view guidelines, move mouse pointer over cell with red triangle. Red triangle identifies a

Problem:

ACME Manufacturing is considering replacing an existing production line with a new line that has a greater output capacity with less labor than the existing line. The new line would cost $1 million, have a five-year life, and be depreciated using the three-year schedule. At the end of five years, the new line could be sold as scrap for $200,000 (in Year 5 dollars). Because the new line is more automated, it would require fewer operators, resulting in a savings of $40,000 per year before tax and for inflation (in today’s dollars). Additional sales with the new machine are expected to result in additional net cash inflows of $60,000 per year (in today’s dollars). If ACME invests in the new line, a one-time investment of $10,000 in additional wo will be required. The working capital investment will be recovered at the end of the project's life. The tax rate is 28 percent opportunity cost of capital is 10 percent, and the annual rate of inflation is 3 percent. What is the NPV of the new producti

Unknown: Project NPV

Assumption(s) All incremental cash flows are at the end of the year All values rounded to nearest dollar Use 3 year MACRS for depreciation - has 4 values Investment in working capital is at t = 0 and recovered at t = 5

Given information/inputs/arguments:

Values 1,000,000 40,000 60,000 5 10,000 200,000 3.00% 28.00% 10.00%

Cost of new line Savings per year, not adjusted for inflation Additional sales per year, not adjusted for inflation Investment life, years Additional investment in working capital Estimated value of investment at end of investment life Annual inflation rate Tax rate Annual opportunity cost of capital Type of depreciation: Macrs

Macrs: year Macrs: percent

1 33.33%

Output, Net Present Value Project NPV

-384,519

Analysis, cash flow calculations Time, years Incremental Revenue

1 61,800

2 63,654

Savings Depreciation Earnings before taxes Taxes Net income Net operating cash flow Cost of new machine Investment in working capital

41,200 333,300 -230,300 -64,484 -165,816 167,484

42,436 444,500 -338,410 -94,755 -243,655 200,845

167,484

200,845

-1,000,000 -10,000

Terminal value Market value Book value Taxes Terminal after tax cash flow Free cash flow

-1,010,000

Date:

th red triangle. Red triangle identifies a cell comment.

new line that has a greater output capacity and operates five-year life, and be depreciated using the MACRS p for $200,000 (in Year 5 dollars). Because a savings of $40,000 per year before tax and unadjusted ected to result in additional net cash inflows, before tax, ime investment of $10,000 in additional working capital the project's life. The tax rate is 28 percent, the rcent. What is the NPV of the new production line?

Comments Enter account amount as positive value Enter account amount as positive value Enter account amount as positive value Enter account amount as positive value Enter account amount as positive value Enter account amount as positive value Enter account amount as positive value Enter percentage as XX.XX% or .XXXX Enter percentage as XX.XX% or .XXXX 2 44.45%

3 14.81%

4 7.41%

3 65,564

4 67,531

5 69,556

43,709 148,100 -38,827 -10,872 -27,956 120,144

45,020 74,100 38,451 10,766 27,685 101,785

46,371 0 115,927 32,460 83,468 83,468

10,000

200,000 0 56,000 144,000 120,144

101,785

237,468

Textbook: Fundamentals of Corporate Finance, 5th Edition Authors: Robert Parrino, Thomas Bates, Stuart Gillan, David Kidwell Publisher: Wiley Chapter 10: The Fundamentals of Capital Budgeting Excel solutions for selected problems at end of Chapter 10. Problem number 21 22 22 38

Problem type Calculate Discounted Payback Calculate MIRR using MIRR function Calculate MIRR using alternative method Calculate Payback, NPV, and IRR

Worksheet tab name 21_Discounted_Payback 22_MIRR 22_MIRR_Alternative 38_Payback_NPV_IRR

One way to return to the contents worksheet is to hold down the CTRL key and simultaneously press and hold dow

eously press and hold down the Page Up key

Chapter 10, Problem 21

Student's Name:

Solution method uses PV, SUM, IF, and AND functions/formulas.

Guidelines:

<-- To view guidelines, move mouse pointer over cell with red triangle. Red triangle identifies

Problem:

Discounted payback: Nugent Communication Corp. is considering an investment in new technologies. The company’s man significant benefits in the first three years after installation, and smaller constant benefits in each of the next four years. U in the following table, calculate the discounted payback period for the project assuming a discount rate of 10 percent? Year 0 1 2 3 07-Apr

Cash Flow ($9,365,000) $2,265,433 $4,558,721 $3,378,911 $1,250,000

Unknown: Discounted Payback Period, years

Assumption(s) Discount rate is annual rate with annual compounding. All cash flows occur at the end of the year.

Given information/inputs/arguments: Cash flow at time t = 0, years Cash flow at time t = 1, years Cash flow at time t = 2, years Cash flow at time t = 3, years Cash flow at time t = 4, years Cash flow at time t = 5, years Cash flow at time t = 6, years Cash flow at time t = 7, years Required annual rate of return Argument for PV function, pmt Argument for PV function, type

Values 9,365,000 2,265,433 4,558,721 3,378,911 1,250,000 1,250,000 1,250,000 1,250,000 10.00% 0 0

Comments Enter amount as positive value Enter amount as positive value Enter amount as positive value Enter amount as positive value Enter amount as positive value Enter amount as positive value Enter amount as positive value Enter amount as positive value Enter rate as percent, XX.XX%, or decimal .XXXX Enter 0, not an annuity problem Enter 0, not an annuity problem

Excel solution method using PV, SUM, IF, and AND functions: Year count 0 1 2 3 4

Cash flow -9,365,000 2,265,433 4,558,721 3,378,911 1,250,000

Present value of cash flow -9,365,000 2,059,485 3,767,538 2,538,626 853,767

Cumulative of pv cash flows -9,365,000 -7,305,515 -3,537,977 -999,352 -145,585

Present value of cash flow 0.00 0.00 0.00 0.00 4.19

5 1,250,000 6 1,250,000 7 1,250,000 Discount Payback Period, years

776,152 705,592 641,448

630,567 1,336,159 1,977,607

0.00 0.00 0.00 4.19

Date:

ngle. Red triangle identifies a cell comment.

hnologies. The company’s management expects each of the next four years. Using the cash flows

Chapter 10, Problem 22

Student's Name:

Solution method uses the MIRR function/formula

Guidelines:

<-- To view guidelines, move mouse pointer over cell with red triangle. Red triangle identif

Problem:

Modified internal rate of return (MIRR): Morningside Bakeries recently purchased equipment at a cost of Management expects the equipment to generate cash flows of $275,000 in each of the next four years. T is 14 percent. What is the MIRR for this project?

Unknown: MIRR = Modified Internal Rate of Return

Assumption(s) All rates are annual rates with annual compounding. Cost of capital is also the reinvestment rate. All cash flows are at the end of the year.

Given information/inputs/arguments: Equipment cost at t = 0 Future cash flows Number of years for future cash flows Cost of capital

Values 650,000.00 275,000.00 4.00 14.00%

Excel solution method using cell formulas: Cash flow at t = 0 Cash flow at t = 1 Cash flow at t = 2 Cash flow at t = 3 Cash flow at t = 4 MIRR

-650,000 275,000 275,000 275,000 275,000 20.1%

Comments Enter amount as positive value Enter amount as positive value Enter amount as positive value Enter rate as percent, XX.XX%, or decimal .XXXX

Date:

cell with red triangle. Red triangle identifies a cell comment.

ently purchased equipment at a cost of $650,000. 75,000 in each of the next four years. The cost of capital

Chapter 10, Problem 22, Alternative solution

Student's Name:

Solution method uses FV, RRI, and SUM functions/formulas

Guidelines:

<-- To view guidelines, move mouse pointer over cell with red triangle. Red triangle identif

Problem:

Unknown: MIRR = Modified Internal Rate of Return

Assumption(s) All rates are annual rates with annual compounding. Cost of capital is also the reinvestment rate

Given information/inputs/arguments: Equipment cost at t = 0 Future cash flows Number of years for future cash flows Cost of capital FV function argument pmt FV function argument type

Values 650,000.00 275,000.00 4.00 14.00% 0 0

Excel solution method using cell formulas: Year counter Cash flow at t = 0 0 Cash flow at t = 1 1 Cash flow at t = 2 2 Cash flow at t = 3 3 Cash flow at t = 4 4 Step 1, PV of negative cash flows Step 2, FV of positive cash flows, t = 1 Step 2, FV of positive cash flows, t = 2 Step 2, FV of positive cash flows, t = 3 Step 2, FV of positive cash flows, t = 4 Future value of all positive cash flows MIRR = Modified Internal Rate of Return

Cash flow -650,000 275,000 275,000 275,000 275,000 -650,000 407,425 357,390 313,500 275,000 1,353,315 20.1%

Comments Enter amount as positive value Enter amount as positive value Enter amount as positive value Enter rate as percent, XX.XX%, or decimal .XXXX Enter zero, this argument in FV function not used Enter zero, this argument in FV function not used

Date:

er cell with red triangle. Red triangle identifies a cell comment.

cently purchased equipment at a cost of $650,000. 275,000 in each of the next four years. The cost of capital

Chapter 10, Problem 38

Student's Name: Solution method uses IF, AND, SUM, NPV and IRR functions/formulas

Guidelines:

<-- To view guidelines, move mouse pointer over cell with red triangle. Red triangle identifies

Problem:

Primus Corp. management is planning to convert an existing warehous into a new plant that will increase its productive ca percent. The cost of this project will be $7,125,000. It will result in additional cash flows of $1,875,000 for each of the nex The discount rate is 12 percent. a. What is the payback period? b. What is the NPV for this project? c. What is the IRR?

Unknown: Project Payback Period, NPV, and IRR

Assumption(s) The discount rate is an annual rate with annual compounding. All future cash flows are at the end of the year.

Given information/inputs/arguments:

Values 7,125,000.00 1,875,000 8 12.00%

Project cost, cash flow at t = 0 Future cash flows Years of future cash flows Discount rate

Comments Enter amount as positive value Enter amount as positive value Enter amount as positive value Enter rate as percent, XX.XX%, or decimal .XXXX

Excel solution method using IF, AND, SUM, NPV, IRR functions and cell formulas: Year counter Cash flow at t = 0 Cash flow at t = 1 Cash flow at t = 2 Cash flow at t = 3 Cash flow at t = 4 Cash flow at t = 5 Cash flow at t = 6 Cash flow at t = 7 Cash flow at t = 8 a. Payback b. NPV = Net Present Value c. IRR = Internal Rate of Return

0 1 2 3 4 5 6 7 8

Cash flow -7,125,000 1,875,000 1,875,000 1,875,000 1,875,000 1,875,000 1,875,000 1,875,000 1,875,000

Cumulative Cash flow -7,125,000 -5,250,000 -3,375,000 -1,500,000 375,000 2,250,000 4,125,000 6,000,000 7,875,000

Payback Calculation 0.00 0.00 0.00 3.80 0.00 0.00 0.00 0.00 0.00 3.80 2,189,325 20.328%

Date:

riangle. Red triangle identifies a cell comment.

at will increase its productive capacity by 45 f $1,875,000 for each of the next eight years.

Textbook: Fundamentals of Corporate Finance, 5th Edition Authors: Robert Parrino, Thomas Bates, Stuart Gillan, David Kidwell Publisher: Wiley Chapter 9: Stock Valuation Excel solutions for selected problems at end of Chapter 9. Problem number 20 20 26 36

Problem type Valuing stock with constant growth Alternative method for constant growth Valuing stock with nonconstant growth Valuing stock with nonconstant growth

Worksheet tab name 20_Constant_Growth 20_Alternative 26_Nonconstant_Growth 36_Nonconstant_Growth

One way to return to the contents worksheet is to hold down the CTRL key and simultaneously press and hold dow

eously press and hold down the Page Up key

Chapter 9, Problem 20

Student's Name:

Solution method uses cell formulas, constant growth model

Guidelines:

<-- To view guidelines, move mouse pointer over cell with red triangle. Red triangle identifies a

Problem:

Constant growth: Jenny Banks is interested in buying the stock of Fervan, Inc., which is increasing its dividends at a consta of 6 percent. The firm recently paid a dividend of $2.65. The required rate of return is 16 percent. What is the current valu this stock? What should be the price of the stock in year 5?

Unknown: Price of stock today and price at end of year 5. Here, price means present value of future dividends.

Assumption(s) All rates are annual rates with annual compounding. All dividends occur at the end of the year.

Given information/inputs/arguments: Dividend last year Years to next stock valuation Annual growth rate of dividends Required annual rate of return

Values 2.65 5.00 6.00% 16.00%

Excel solution method using cell formulas: Current price of stock Price of stock at end of year 5

28.09 37.59

Date:

h red triangle. Red triangle identifies a cell comment.

which is increasing its dividends at a constant rate urn is 16 percent. What is the current value of

of future dividends.

Comments Enter amount as positive value Enter amount as positive value Enter rate as percent, XX.XX%, or decimal .XXXX Enter rate as percent, XX.XX%, or decimal .XXXX

Chapter 9, Problem 20

Student's Name:

Solution method uses NPV function/formula

Guidelines:

<-- To view guidelines, move mouse pointer over cell with red triangle. Red triangle identifies a

Problem:

Unknown: Price of stock today and price at end of year 5. Here, price means present value of future dividends.

Assumption(s) All rates are annual rates with annual compounding. All dividends occur at the end of the year.

Given information/inputs/arguments: Dividend last year Years to next stock valuation Annual growth rate of dividends Required annual rate of return

Values 2.65 5.00 6.00% 16.00%

Excel solution method using NPV function and schedule of future dividends: Current price of stock Price of stock at end of year 5

Schedule Year 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Future Dividends 2.80900 2.97754 3.15619 3.34556 3.54630 3.75908 3.98462 4.22370 4.47712 4.74575 5.03049 5.33232 5.65226 5.99140 6.35088

28.09 37.59

16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62

6.73193 7.13585 7.56400 8.01784 8.49891 9.00884 9.54937 10.12234 10.72968 11.37346 12.05586 12.77922 13.54597 14.35873 15.22025 16.13347 17.10147 18.12756 19.21522 20.36813 21.59022 22.88563 24.25877 25.71429 27.25715 28.89258 30.62614 32.46370 34.41153 36.47622 38.66479 40.98468 43.44376 46.05039 48.81341 51.74221 54.84675 58.13755 61.62580 65.32335 69.24275 73.39732 77.80116 82.46923 87.41738 92.66242 98.22217

63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109

104.11550 110.36243 116.98417 124.00323 131.44342 139.33002 147.68983 156.55121 165.94429 175.90095 186.45500 197.64230 209.50084 222.07089 235.39514 249.51885 264.48998 280.35938 297.18095 315.01180 333.91251 353.94726 375.18410 397.69514 421.55685 446.85026 473.66128 502.08095 532.20581 564.13816 597.98645 633.86564 671.89758 712.21143 754.94412 800.24076 848.25521 899.15052 953.09955 1,010.28553 1,070.90266 1,135.15682 1,203.26623 1,275.46220 1,351.98993 1,433.10933 1,519.09589

110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125

1,610.24164 1,706.85614 1,809.26751 1,917.82356 2,032.89297 2,154.86655 2,284.15854 2,421.20805 2,566.48054 2,720.46937 2,883.69753 3,056.71938 3,240.12255 3,434.52990 3,640.60169 3,859.03780

Date:

h red triangle. Red triangle identifies a cell comment.

which is increasing its dividends at a constant rate urn is 16 percent. What is the current value of

of future dividends.

Comments Enter amount as positive value Enter amount as positive value Enter rate as percent, XX.XX%, or decimal .XXXX Enter rate as percent, XX.XX%, or decimal .XXXX

Chapter 9, Problem 26

Student's Name:

Solution method uses cell formulas

Guidelines:

<-- To view guidelines, move mouse pointer over cell with red triangle. Red triangle identifies a

Problem:

Nonconstant growth: Quansi, Inc., management expects to pay no dividends for the next six years. It has growth rate of 25 percent for the next seven years. After seven years, the firm will grow at a constant rate first dividend, to be paid in Year 7, will be $3.25. If the required rate of return is 24 percent, what is the st

Unknown: Price of stock today.

Assumption(s) All rates are annual rates with annual compounding. All dividends occur at the end of the year.

Given information/inputs/arguments: Current dividend First dividend Year of first dividend Annual growth rate of dividends after year 7 Required annual rate of return Argument in PV function, pmt Argument in PV function, type

Values 0.00 3.25 7.00 5.00% 24.00% 0 0

Excel solution method using cell formulas: Step 1: stock price at end of year 7, using constant growth formula Step 2: Stock price today, using PV function

17.96 4.71

Date:

h red triangle. Red triangle identifies a cell comment.

vidends for the next six years. It has projected a , the firm will grow at a constant rate of 5 percent. Its of return is 24 percent, what is the stock worth today?

Comments Enter amount as positive value Enter amount as positive value Enter amount as positive value Enter rate as percent, XX.XX%, or decimal .XXXX Enter rate as percent, XX.XX%, or decimal .XXXX Enter zero, not an annuity problem Enter zero, not an annuity problem

Chapter 9, Problem 36

Student's Name:

Solution method uses NPV function/formula and cell formulas

Guidelines:

<-- To view guidelines, move mouse pointer over cell with red triangle. Red triangle identifies a

Problem:

Nonconstant growth: Triton Inc., is expected to grow at a rate of 22 percent for the next five years and th constant-growth rate of 6 percent. The company recently paid a dividend of $2.35. The required rate of re a. Find the present value of the dividends during the rapid-growth period if dividends grow at the same ra b. What is the value of the stock at the end of Year 5? c. What is the value of the stock today?

Unknown: Present value of dividends during current growth period, value of stock at end of year 5, value of stock today.

Assumption(s) All rates are annual rates with annual compounding. All dividends occur at the end of the year.

Given information/inputs/arguments: Most recent dividend, at t = 0 Current growth rate of dividend Years of rapid dividend growth Annual growth rate of dividends after year 5 Required annual rate of return

Values 2.35 22.00% 5 6.00% 15.00%

Excel solution method using NPV function and cell formulas: Dividend at end of year = 1 Dividend at end of year = 2 Dividend at end of year = 3 Dividend at end of year = 4 Dividend at end of year = 5 a. PV of dividends during rapid growth, use NPV function b. Value of stock at end of year 5, use constant growth model c. Value of stock today, use NPV function

2.87 3.50 4.27 5.21 6.35 14.08 74.80 51.27

Date:

h red triangle. Red triangle identifies a cell comment.

percent for the next five years and then settle to a end of $2.35. The required rate of return is 15 percent. riod if dividends grow at the same rate as the company.

f year 5, value of stock today.

Comments Enter amount as positive value Enter rate as percent, XX.XX%, or decimal .XXXX Enter amount as positive value Enter rate as percent, XX.XX%, or decimal .XXXX Enter rate as percent, XX.XX%, or decimal .XXXX

Textbook: Fundamentals of Corporate Finance, 5th Edition Authors: Robert Parrino, Thomas Bates, Stuart Gillan, David Kidwell Publisher: Wiley Chapter 8: Bond Valuation and the Structure of Interest Rates Excel solutions for selected problems at end of Chapter 8 Problem number 9 9 16 16 29

Solution Method Use RATE function for bond's yield to maturity Use IRR function for bond's yield to maturity Use PV function for bond's price Use NPV function for bond's price Use PV function for bond's price

Worksheet tab name 9_RATE_function 9_Alternative_IRR_function 16_PV_function 16_Alternative_NPV_function 29_PV_function

One way to return to the contents worksheet is to hold down the CTRL key and simultaneously press and hold dow

eously press and hold down the Page Up key

Chapter 8, Problem 9

Student's Name:

Solution method uses RATE function and EFFECT functions/formulas

Guidelines:

<-- To view guidelines, move mouse pointer over cell with red triangle. Red triangle identifies a

Problem:

Yield to maturity: Ruth Hornsby is looking to invest in a three-year bond that makes semiannual coupon payments at a ra percent. If these bonds have a market price of $981.13, what yield to maturity can she expect to earn?

Unknown: Bond's yield to maturity

Assumption(s) Par or face value of bond is $1,000

Given information/inputs/arguments: Number of periods/years, nper Compounding frequency per year Par value of bond Coupon rate Current bond price Type of annuity

Values 3.00 2.00 1,000.00 5.875% 981.13 0.00

Excel solution method using RATE and EFFECT functions: Yield to maturity, rate per 6 months using RATE function Yield to maturity, annual rate compounded semiannually Yield to maturity, effective annual rate, using EFFECT function

3.289% 6.578% 6.687%

Date:

h red triangle. Red triangle identifies a cell comment.

akes semiannual coupon payments at a rate of 5.875 an she expect to earn?

Comments Enter number of years until bond matures Enter value for compounding semiannually Enter par or face value of bond Enter coupon rate as annual rate, X.XXX% or .XXXXX Enter current price of bond as a positive value Enter 0, regular annuity

Chapter 8, Problem 9

Student's Name: Solution method uses IRR, EFFECT, and IF functions/formulas for bond's price

Guidelines:

<-- To view guidelines, move mouse pointer over cell with red triangle. Red triangle identifies a

Problem:

Unknown: Bond's yield to maturity

Assumption(s) Par value of bond is $1,000

Given information/inputs/arguments: Number of periods/years, nper Compounding frequency per year Par value of bond Coupon rate Current bond price Type of annuity

Values 3.00 2.00 1,000.00 5.875% 981.13 0.00

Excel solution method using IRR, EFFECT and IF functions: Yield to maturity, rate per 6 months using IRR function Yield to maturity, annual rate compounded semiannually Yield to maturity, effective annual rate, using EFFECT function

Cash flows: Time 0 1 2 3 4 5 6

Cash flow -981.13 29.38 29.38 29.38 29.38 29.38 1,029.38

3.289% 6.578% 6.687%

Date:

h red triangle. Red triangle identifies a cell comment.

akes semiannual coupon payments at a rate of 5.875 an she expect to earn?

Chapter 8, Problem 16

Student's Name:

Solution method uses PV function/formula

Guidelines:

<-- To view guidelines, move mouse pointer over cell with red triangle. Red triangle identifies a ce

Problem:

Bond price: Rockne, Inc., has outstanding bonds that will mature in six years and pay an 8 percent coupon semiann $1,036.65 today and your required rate of return was 6.6 percent, did you pay the right price for the bond?

Unknown: Find present value of the bond when required rate of return is 6.6%.

Assumption(s) Required annual rate of return is 6.6 with semiannual compounding Par value of bond is $1,000

Given information/inputs/arguments: Annual interest rate, required rate of return Number of periods/years, nper Compounding frequency per year Par value of bond Coupon rate Current bond price Type of annuity

Values 6.60% 6.00 2.00 1,000.00 8.00% 1,036.65 0.00

Excel solution method using PV function: PV of bond's future cash flows

1,068.45

Comments Enter percentage as percent X.XX%, or Enter number of years until bond matu Enter value for compounding semiann Enter par or face value of bond Enter bonds annual coupon rate, X.XX% Enter current price of bond Enter 0, bond's coupon payments are r

Date:

triangle. Red triangle identifies a cell comment.

d pay an 8 percent coupon semiannually. If you paid the right price for the bond?

Enter percentage as percent X.XX%, or decimal. .XXX Enter number of years until bond matures Enter value for compounding semiannually Enter par or face value of bond Enter bonds annual coupon rate, X.XX% or .XXX

Enter 0, bond's coupon payments are regular annuity

Chapter 8, Problem 16

Student's Name:

Solution method uses NPV and IF functions/formulas

Guidelines:

<-- To view guidelines, move mouse pointer over cell with red triangle. Red triangle identifies a ce

Problem:

Unknown: Find present value of the bond when required rate of return is 6.6%.

Assumption(s) Required annual rate of return is 6.6 with semiannual compounding Par or face value of bond is $1,000

Values 6.60% 6.00 2.00 1,000.00 8.00% 1,036.65 0.00

Excel solution method using PV function: PV of bond's future cash flows

Bond's future cash flows 6 month intervals 1 2 3 4 5 6 7 8 9 10 11 12

Cash flow 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 1,040.00

1,068.45

Comments Enter percentage as percent X.XX%, or Enter number of years for bond's life Enter value for compounding semiann Enter par value of bond, $1,000 Enter first cash flow as positive value Enter current price of bond Enter 0, bond's coupon payments are r

Date:

triangle. Red triangle identifies a cell comment.

d pay an 8 percent coupon semiannually. If you paid the right price for the bond?

Enter percentage as percent X.XX%, or decimal. .XXX Enter number of years for bond's life Enter value for compounding semiannually Enter par value of bond, $1,000 Enter first cash flow as positive value

Enter 0, bond's coupon payments are regular annuity

Chapter 8, Problem 29

Student's Name:

Solution method uses PV function/formula

Guidelines:

<-- To view guidelines, move mouse pointer over cell with red triangle. Red triangle identifies a ce

Problem:

The Maryland Department of Transportation has issued 25-year bonds that make semiannual coupon payments at similar securities is 11 percent. a. What is the current market value of one of these bonds? b. What will be the bond’s price if rates in the market (i) decrease to 9 percent or (ii) increase to 12 percent? c. Refer to your answers in part b. How do the interest rate changes affect premium bonds and discount bonds? d. Suppose the bond were to mature in 12 years. How do the interest rate changes in part b affect the bond prices

Unknown: Find present value (market value) of the bond

Assumption(s) Required annual rate of return is 6.6 with semiannual compounding Par value of bond is $1,000

Given information/inputs/arguments: Current annual market rate for these bonds Annual market rate, decrease Annual market rate, increase Number of periods/years, nper Number of periods/years, nper Compounding frequency per year Par value of bond Coupon rate Current bond price Type of annuity

Values 11.00% 9.00% 12.00% 25.00 12.00 2.00 1,000.00 9.875% 1,036.65 0.00

Excel solution method using PV function, 25 year (parts a & b): a: PV of bond's future cash flows, using current rate b, i: PV of bond's future cash flows, using rate decrease b, ii: PV of bond's future cash flows, using rate increase

904.76 1,086.46 832.53

Excel solution method using PV function, 12 year (part d): a: PV of bond's future cash flows, using current rate b, i: PV of bond's future cash flows, using rate decrease b, ii: PV of bond's future cash flows, using rate increase

Solution (part c - excel not needed): Bonds, in general, decrease in price when interest rates go up When interest rates go down, bond prices increase.

926.02 1,063.42 866.65

Comments Enter percentage as percent X.XX%, or Enter percentage as percent X.XX%, or Enter percentage as percent X.XX%, or Enter number of years to bond's matu Enter number of years to bond's matu Enter value for compounding semiann Enter par value of bond, $1,000 Enter first cash flow as positive value Enter current price of bond Enter 0, not an annuity problem

Date:

triangle. Red triangle identifies a cell comment.

ke semiannual coupon payments at a rate of 9.875 percent. The current market rate for

or (ii) increase to 12 percent? mium bonds and discount bonds? nges in part b affect the bond prices?

Enter percentage as percent X.XX%, or decimal. .XXX Enter percentage as percent X.XX%, or decimal. .XXX Enter percentage as percent X.XX%, or decimal. .XXX Enter number of years to bond's maturity Enter number of years to bond's maturity, part d Enter value for compounding semiannually Enter par value of bond, $1,000 Enter first cash flow as positive value

Enter 0, not an annuity problem

Textbook: Fundamentals of Corporate Finance, 5th Edition Authors: Robert Parrino, Thomas Bates, Stuart Gillan, David Kidwell Publisher: Wiley Chapter 7: Risk and Return Problem number 6&7 16 19 19

Solution Method Calculate average and geometric return Interpret variance and standard deviation Calculate variance and standard deviation Alternative calculation of variance and standard deviation

One way to return to the contents worksheet is to hold down the CTRL key and simultaneously press and hold down the P

Worksheet tab name 6_&_7_Calculate_Return 16_Interpret_Var&Stdev 19_Calculate_Mean&Stdev 19_Calculate_Alternative

TRL key and simultaneously press and hold down the Page Up key

Chapter 7, Problems 6 and 7

Student's Name: Solution method uses Average and GeoMean functions/formulas

Guidelines:

<-- To view guidelines, move mouse pointer over cell with red triangle. Red triangle identifies a

Problem:

7.6 Arithmetic Average: Tanner invested $1,000 in large U.S. stocks at the beginning of 2017. This investment earned 15.9 32.41 percent in 2018, 13.69 percent in 2019, and 1.41 percent in 2020. What return did he earn in the average year durin 7.7 Geometric Average: What was the average annual return that Tanner earned over the 2017–2020 period in Problem

Unknown: Arithmetic and geometric rate of return

Assumption(s) The earnings (rates of return) are annual and have annual compounding

Given information/inputs/arguments: Rate earned in 2017 Rate earned in 2018 Rate earned in 2019 Rate earned in 2020

Values 15.98% 32.41% 13.69% 1.41%

Excel solution method for average and geometric mean return: 7.6 Average return, using Average function 7.6 Average return, using SUM and Count functions 7.7 Geometric return using GeoMean function 7.7 Geometric return using formula and Count function

15.873% 15.873% 15.352% 15.352%

Date:

h red triangle. Red triangle identifies a cell comment.

nning of 2017. This investment earned 15.98 percent in 2017, eturn did he earn in the average year during the 2017–2020 period? ed over the 2017–2020 period in Problem 7.6?

Comments Enter percentage as %, XX.XXX%, or decimal, .XXXXX Enter percentage as %, XX.XXX%, or decimal, .XXXXX Enter percentage as %, XX.XXX%, or decimal, .XXXXX Enter percentage as %, XX.XXX%, or decimal, .XXXXX

Chapter 7, Problem 16

Student's Name:

Solution method uses Norm.S.Inv functions/formulas

Guidelines:

<-- To view guidelines, move mouse pointer over cell with red triangle. Red triangle identifies a

Problem:

Interpreting the variance and standard deviation: The distribution of grades in an introductory finance class is normally d with an expected grade of 75. If the standard deviation of grades is 7, in what range would you expect 95 percent of the g fall?

Unknown: Range (confidence interval) that contains 95% of the scores

Assumption(s) None

Given information/inputs/arguments: Mean, expected grade Standard deviation of grades Range/confidence interval

Values 75 7 95.00%

Excel solution method for average and geometric mean return: Standard deviations above and below mean Lower bound for 95% confidence interval Upper bound for 95% confidence interval

1.960 61.280 88.720

Date:

h red triangle. Red triangle identifies a cell comment.

an introductory finance class is normally distributed, ange would you expect 95 percent of the grades to

Comments Enter as a positive value Enter as a positive value Enter percentage as %, XX.XXX%, or decimal, .XXXXX

Chapter 7, Problem 19 Student's Name: Solution method uses SumProduct and Sqrt functions/formulas

Cell comments (Red triangle in upper right corner of cell identifies a cell comment, to view a comment move mouse p

Problem: 7.19 Calculating the variance and standard deviation: Ben would like to invest in gold and is aware that t investment can be quite volatile. Use the following table of states, probabilities, and returns to determin and the standard deviation of the return on Ben’s gold investment. State Boom Good OK Level Slump

Probability 0.1 0.2 0.3 0.2 0.2

Return 40.00% 30.00% 15.00% 2.00% -12.00%

Given information/inputs/arguments: State Boom Good OK Level Slump

Probability 0.10 0.20 0.30 0.20 0.20

Return 40.00% 30.00% 15.00% 2.00% -12.00%

Deviation2 0.07563 0.03063 0.00062 0.01103 0.06003

Unknown: For the discrete probability distribution data, calculate the mean and standard deviation.

Excel solution method using SumProduct function/formula Mean, m or E(Ri )

0.12500

Variance, s return Standard deviation, sreturn

0.02809 0.16759

Date:

w a comment move mouse pointer over cell):

in gold and is aware that the returns on such an es, and returns to determine the expected return

Chapter 7, Problem 19 Student's Name: Solution method uses Average, Var.P, and StDev.P functions/formulas

Cell comments (Red triangle in upper right corner of cell identifies a cell comment, to view a comment move mouse p

Probability 0.1 0.2 0.3 0.2 0.2

Return 40.00% 30.00% 15.00% 2.00% -12.00%

Given information/inputs/arguments: State Boom Good OK Level Slump

Probability 0.10 0.20 0.30 0.20 0.20

Return 40.00% 30.00% 15.00% 2.00% -12.00%

Unknown: For the discrete probability distribution data, calculate the mean and standard deviation.

Excel solution method using Average, Var.P, and StDev.P functions/formulas Mean, m or E(Ri )

0.12500

Variance, s2return Standard deviation, sreturn

0.02809 0.16759

List of population observations Count to 100

Count of States 1 2 3 4 5 6 7 8 9 10

1 2 3 4 5 6 7 8 9 10

Returns 40.00% 40.00% 40.00% 40.00% 40.00% 40.00% 40.00% 40.00% 40.00% 40.00%

11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

30.00% 30.00% 30.00% 30.00% 30.00% 30.00% 30.00% 30.00% 30.00% 30.00% 30.00% 30.00% 30.00% 30.00% 30.00% 30.00% 30.00% 30.00% 30.00% 30.00% 15.00% 15.00% 15.00% 15.00% 15.00% 15.00% 15.00% 15.00% 15.00% 15.00% 15.00% 15.00% 15.00% 15.00% 15.00% 15.00% 15.00% 15.00% 15.00% 15.00% 15.00% 15.00% 15.00% 15.00% 15.00% 15.00% 15.00%

58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

28 29 30 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

15.00% 15.00% 15.00% 2.00% 2.00% 2.00% 2.00% 2.00% 2.00% 2.00% 2.00% 2.00% 2.00% 2.00% 2.00% 2.00% 2.00% 2.00% 2.00% 2.00% 2.00% 2.00% 2.00% -12.00% -12.00% -12.00% -12.00% -12.00% -12.00% -12.00% -12.00% -12.00% -12.00% -12.00% -12.00% -12.00% -12.00% -12.00% -12.00% -12.00% -12.00% -12.00% -12.00%

Date:

o view a comment move mouse pointer over cell):

nvest in gold and is aware that the returns on such an bilities, and returns to determine the expected return

Textbook: Fundamentals of Corporate Finance, 5th Edition Authors: Robert Parrino, Thomas Bates, Stuart Gillan, David Kidwell Publisher: Wiley Chapter 6: Discounted Cash Flows and Valuation Excel solutions for selected problems at end of Chapter 6 Problem number 3 3 8 8 41 41 41

Solution Method FV function/formula Find future value using Schedule PV function/formula Find present value using schedule Loan payment and Loan Amortization 1 Loan payment and Loan Amortization 2 Loan payment and Loan Amortization 3

Worksheet tab name 3_FV_function 3_Alternative_Schedule 8_PV_function 8_Alternative_Schedule 41_PMT_Loan_Amortization 41_Alternative_1 41_Alternative_2

One way to return to the contents worksheet is to hold down the CTRL key and simultaneously press and hold dow

eously press and hold down the PageUp key

Chapter 6, Problem 3

Student's Name:

Solution method uses FV and SUM functions/formulas

Guidelines:

<-- To view guidelines, move mouse pointer over cell with red triangle. Red triangle identifies a ce

Problem:

Future value with multiple cash flows: You are a freshman in college and are planning a trip to Europe when you gr at the end of four years. You plan to save the following amounts annually, starting today: $625, $700, $700, and $7 5.75 percent annually, how much will you have at the end of four years?

Unknown: Find value of investment with uneven cash flows at the end of four years.

Assumption(s) Assume annual interest rate with annual compounding

Given information/inputs/arguments: Annual interest rate Number of periods/years, nper Compounding frequency per year Annuity payment, pmt Amount of first cash flow Amount of second cash flow Amount of third cash flow Amount of fourth cash flow Time of first cash flow, years Time of second cash flow, years Time of third cash flow, years Time of fourth cash flow, years Type of annuity

Values 5.75% 4.00 1.00 0.00 625.00 700.00 700.00 750.00 0.00 1.00 2.00 3.00 0.00

Excel solution method using FV function: Find future value of first cash flow, Excel FV function = Find future value of first cash flow, Excel FV function = Find future value of first cash flow, Excel FV function = Find future value of first cash flow, Excel FV function = Sum of four future values

781.63 827.83 782.81 793.13 3,185.40

Comments Enter percentage as percent X.XX%, or Enter number of years for investment Enter value for compounding once per Enter zero, not an annuity problem Enter first cash flow as positive value Enter first cash flow as positive value Enter first cash flow as positive value Enter first cash flow as positive value Enter time in years for first cash flow Enter time in years for second cash flo Enter time in years for third cash flow Enter time in years for fourth cash flow Enter 0, not an annuity problem

Date:

triangle. Red triangle identifies a cell comment.

anning a trip to Europe when you graduate from college ting today: $625, $700, $700, and $750. If you can earn

Enter percentage as percent X.XX%, or decimal. .XXX Enter number of years for investment life Enter value for compounding once per year Enter zero, not an annuity problem Enter first cash flow as positive value Enter first cash flow as positive value Enter first cash flow as positive value Enter first cash flow as positive value Enter time in years for first cash flow Enter time in years for second cash flow Enter time in years for third cash flow Enter time in years for fourth cash flow Enter 0, not an annuity problem

Chapter 6, Problem 3

Student's Name: Solution method uses Schedule (cell references and cell formulas, no Excel functions)

Guidelines:

<-- To view guidelines, move mouse pointer over cell with red triangle. Red triangle identifies a ce

Problem:

Unknown: Find value of investment with uneven cash flows at the end of four years.

Assumption(s) Assume annual interest rate with annual compounding

Given information/inputs/arguments:

Values 5.75% 4.00 1.00 0.00 625.00 700.00 700.00 750.00 0.00 1.00 2.00 3.00 0.00

Annual interest rate Number of periods/years, nper Compounding frequency per year Annuity payment, pmt Amount of first cash flow Amount of second cash flow Amount of third cash flow Amount of fourth cash flow Time of first cash flow, years Time of second cash flow, years Time of third cash flow, years Time of fourth cash flow, years Type of annuity

Excel solution method, Schedule: Schedule value at end of year 4

3,185.40

Schedule

Year 1 2 3 4

Value, start of year 0.00 660.94 1,439.19 2,262.19

Investment added start of year 625.00 700.00 700.00 750.00

Interest earned during year 35.94 78.25 123.00 173.20

Value, end of year 660.94 1,439.19 2,262.19 3,185.40

Date:

triangle. Red triangle identifies a cell comment.

anning a trip to Europe when you graduate from college ing today: $625, $700, $700, and $750. If you can earn

Chapter 6, Problem 8

Student's Name:

Solution method uses PV function/formula

Guidelines:

<-- To view guidelines, move mouse pointer over cell with red triangle. Red triangle identifies a ce

Problem:

Present value of an ordinary annuity: Dynamics Telecommunications Corp. has made an investment in another com guarantee it a cash fl ow of $22,500 each year for the next five years. If the company uses a discount rate of 15 per investments, what is the present value of this investment?

Unknown: Present value of ordinary annuity (equal end of year payments, equal intervals, fixed time period, one interest rate)

Assumption(s) Discount rate is annual rate with annual compounding

Given information/inputs/arguments: Annual interest rate Number of periods/years, nper Compounding frequency Annuity payment, pmt Future value Type of annuity

Values 15.00% 5.00 1.00 22,500.00 0.00 0.00

Excel solution method using PV function/formula: Find present value of annuity

75,423.49

Comments Enter percentage as percent XX%, or decimal. .XX Enter number of years Enter compounding frequency Enter annuity payment as a positive value Enter zero, no future value Enter zero for regular/ordinary annuity

Date:

triangle. Red triangle identifies a cell comment.

made an investment in another company that will mpany uses a discount rate of 15 percent on its

d time period, one interest rate)

e as percent XX%, or decimal. .XX

Chapter 6, Problem 8 Student's Name: Solution method uses Schedule (cell references and cell formulas, no Excel functions) Guidelines:

<-- To view guidelines, move mouse pointer over cell with red triangle. Red triangle identifies a ce

Problem:

Unknown: Present value of ordinary annuity (equal end of year payments, equal intervals, fixed time period, one interest rate)

Assumption(s) Discount rate is annual rate with annual compounding

Given information/inputs/arguments: Annual interest rate Number of periods/years, nper Compounding frequency Annuity payment, pmt Future value Type of annuity

Values 15.00% 5.00 1.00 22,500.00 0.00 0.00

Excel solution method using PV function/formula: Find present value of annuity

75,423.49

Date:

triangle. Red triangle identifies a cell comment.

made an investment in another company that will mpany uses a discount rate of 15 percent on its

d time period, one interest rate)

e as percent XX%, or decimal. .XX

Chapter 6, Problem 41

Student's Name: Solution method uses PMT function/formula and cell formulas, works only for end of month payments

Guidelines:

<-- To view guidelines, move mouse pointer over cell with red triangle. Red triangle identifies a ce

Problem:

The Yan family is buying a new 3,500-square-foot house in Muncie, Indiana, and will borrow $237,000 from Bank O 6.375 percent for 15 years. What will be their monthly loan payment? Prepare an amortization schedule using Exce

Unknowns: Find annuity payment for annuity due problem Amortize the loan (determine amount of each payment that is interest and reduction of principal)

Assumption(s) Interest rate is annual rate with monthly compounding Monthly payments are at end of month

Given information/inputs/arguments:

Values 6.375% 15.00 12.00 237,000.00 0.00 0.00

Annual interest rate Number of periods/years, nper Compounding frequency Amount of loan, present value, pv Future value Type of annuity

Comments Enter percentage as percent X.XX%, or decimal. .XXX Enter number of years Enter months in a year Enter amount of loan as positive value Enter 0, no future value Enter 0, regular annuity, assume end of month paymen

Excel solution method using PMT function/formula: Monthly loan payment

2,048.27

Loan amortization

Month 1 2 3 4 5 6 7 8 9 10 11 12 13

Beginning Balance 237,000.00 236,210.79 235,417.39 234,619.77 233,817.91 233,011.80 232,201.40 231,386.69 230,567.66 229,744.28 228,916.52 228,084.37 227,247.79

Monthly Payment 2,048.27 2,048.27 2,048.27 2,048.27 2,048.27 2,048.27 2,048.27 2,048.27 2,048.27 2,048.27 2,048.27 2,048.27 2,048.27

Monthly Monthly reduction of Interest Principal 1,259.06 789.21 1,254.87 793.40 1,250.65 797.62 1,246.42 801.86 1,242.16 806.12 1,237.88 810.40 1,233.57 814.70 1,229.24 819.03 1,224.89 823.38 1,220.52 827.76 1,216.12 832.15 1,211.70 836.58 1,207.25 841.02

End of Month Balance 236,210.79 235,417.39 234,619.77 233,817.91 233,011.80 232,201.40 231,386.69 230,567.66 229,744.28 228,916.52 228,084.37 227,247.79 226,406.77

14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

226,406.77 225,561.29 224,711.31 223,856.81 222,997.78 222,134.18 221,266.00 220,393.20 219,515.76 218,633.67 217,746.89 216,855.39 215,959.16 215,058.17 214,152.40 213,241.81 212,326.38 211,406.09 210,480.91 209,550.82 208,615.79 207,675.78 206,730.79 205,780.77 204,825.71 203,865.57 202,900.33 201,929.97 200,954.45 199,973.75 198,987.83 197,996.68 197,000.27 195,998.56 194,991.53 193,979.15 192,961.39 191,938.22 190,909.62 189,875.55 188,835.99 187,790.91 186,740.28 185,684.06 184,622.23 183,554.77 182,481.63

2,048.27 2,048.27 2,048.27 2,048.27 2,048.27 2,048.27 2,048.27 2,048.27 2,048.27 2,048.27 2,048.27 2,048.27 2,048.27 2,048.27 2,048.27 2,048.27 2,048.27 2,048.27 2,048.27 2,048.27 2,048.27 2,048.27 2,048.27 2,048.27 2,048.27 2,048.27 2,048.27 2,048.27 2,048.27 2,048.27 2,048.27 2,048.27 2,048.27 2,048.27 2,048.27 2,048.27 2,048.27 2,048.27 2,048.27 2,048.27 2,048.27 2,048.27 2,048.27 2,048.27 2,048.27 2,048.27 2,048.27

1,202.79 1,198.29 1,193.78 1,189.24 1,184.68 1,180.09 1,175.48 1,170.84 1,166.18 1,161.49 1,156.78 1,152.04 1,147.28 1,142.50 1,137.68 1,132.85 1,127.98 1,123.09 1,118.18 1,113.24 1,108.27 1,103.28 1,098.26 1,093.21 1,088.14 1,083.04 1,077.91 1,072.75 1,067.57 1,062.36 1,057.12 1,051.86 1,046.56 1,041.24 1,035.89 1,030.51 1,025.11 1,019.67 1,014.21 1,008.71 1,003.19 997.64 992.06 986.45 980.81 975.13 969.43

845.49 849.98 854.49 859.03 863.60 868.19 872.80 877.43 882.10 886.78 891.49 896.23 900.99 905.78 910.59 915.43 920.29 925.18 930.09 935.03 940.00 945.00 950.02 955.06 960.14 965.24 970.37 975.52 980.70 985.91 991.15 996.42 1,001.71 1,007.03 1,012.38 1,017.76 1,023.17 1,028.60 1,034.07 1,039.56 1,045.08 1,050.63 1,056.22 1,061.83 1,067.47 1,073.14 1,078.84

225,561.29 224,711.31 223,856.81 222,997.78 222,134.18 221,266.00 220,393.20 219,515.76 218,633.67 217,746.89 216,855.39 215,959.16 215,058.17 214,152.40 213,241.81 212,326.38 211,406.09 210,480.91 209,550.82 208,615.79 207,675.78 206,730.79 205,780.77 204,825.71 203,865.57 202,900.33 201,929.97 200,954.45 199,973.75 198,987.83 197,996.68 197,000.27 195,998.56 194,991.53 193,979.15 192,961.39 191,938.22 190,909.62 189,875.55 188,835.99 187,790.91 186,740.28 185,684.06 184,622.23 183,554.77 182,481.63 181,402.79

61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107

181,402.79 180,318.22 179,227.88 178,131.76 177,029.81 175,922.01 174,808.32 173,688.72 172,563.16 171,431.63 170,294.09 169,150.50 168,000.84 166,845.07 165,683.16 164,515.08 163,340.80 162,160.27 160,973.47 159,780.37 158,580.93 157,375.12 156,162.90 154,944.24 153,719.11 152,487.47 151,249.29 150,004.53 148,753.15 147,495.13 146,230.42 144,959.00 143,680.82 142,395.85 141,104.06 139,805.40 138,499.84 137,187.35 135,867.88 134,541.41 133,207.89 131,867.28 130,519.55 129,164.66 127,802.58 126,433.25 125,056.66

963.70 957.94 952.15 946.32 940.47 934.59 928.67 922.72 916.74 910.73 904.69 898.61 892.50 886.36 880.19 873.99 867.75 861.48 855.17 848.83 842.46 836.06 829.62 823.14 816.63 810.09 803.51 796.90 790.25 783.57 776.85 770.09 763.30 756.48 749.62 742.72 735.78 728.81 721.80 714.75 707.67 700.54 693.39 686.19 678.95 671.68 664.36

1,084.57 1,090.33 1,096.13 1,101.95 1,107.80 1,113.69 1,119.60 1,125.55 1,131.53 1,137.54 1,143.59 1,149.66 1,155.77 1,161.91 1,168.08 1,174.29 1,180.53 1,186.80 1,193.10 1,199.44 1,205.81 1,212.22 1,218.66 1,225.13 1,231.64 1,238.18 1,244.76 1,251.37 1,258.02 1,264.71 1,271.42 1,278.18 1,284.97 1,291.80 1,298.66 1,305.56 1,312.49 1,319.47 1,326.48 1,333.52 1,340.61 1,347.73 1,354.89 1,362.09 1,369.32 1,376.60 1,383.91

180,318.22 179,227.88 178,131.76 177,029.81 175,922.01 174,808.32 173,688.72 172,563.16 171,431.63 170,294.09 169,150.50 168,000.84 166,845.07 165,683.16 164,515.08 163,340.80 162,160.27 160,973.47 159,780.37 158,580.93 157,375.12 156,162.90 154,944.24 153,719.11 152,487.47 151,249.29 150,004.53 148,753.15 147,495.13 146,230.42 144,959.00 143,680.82 142,395.85 141,104.06 139,805.40 138,499.84 137,187.35 135,867.88 134,541.41 133,207.89 131,867.28 130,519.55 129,164.66 127,802.58 126,433.25 125,056.66 123,672.75

108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154

123,672.75 122,281.49 120,882.83 119,476.75 118,063.20 116,642.13 115,213.52 113,777.32 112,333.49 110,881.99 109,422.77 107,955.81 106,481.05 104,998.46 103,507.99 102,009.60 100,503.26 98,988.91 97,466.51 95,936.03 94,397.41 92,850.63 91,295.62 89,732.36 88,160.79 86,580.87 84,992.56 83,395.81 81,790.57 80,176.81 78,554.48 76,923.52 75,283.91 73,635.58 71,978.50 70,312.61 68,637.87 66,954.24 65,261.66 63,560.09 61,849.48 60,129.78 58,400.94 56,662.93 54,915.67 53,159.14 51,393.27

657.01 649.62 642.19 634.72 627.21 619.66 612.07 604.44 596.77 589.06 581.31 573.52 565.68 557.80 549.89 541.93 533.92 525.88 517.79 509.66 501.49 493.27 485.01 476.70 468.35 459.96 451.52 443.04 434.51 425.94 417.32 408.66 399.95 391.19 382.39 373.54 364.64 355.69 346.70 337.66 328.58 319.44 310.26 301.02 291.74 282.41 273.03

1,391.26 1,398.65 1,406.08 1,413.55 1,421.06 1,428.61 1,436.20 1,443.83 1,451.50 1,459.21 1,466.96 1,474.76 1,482.59 1,490.47 1,498.39 1,506.35 1,514.35 1,522.39 1,530.48 1,538.61 1,546.79 1,555.00 1,563.27 1,571.57 1,579.92 1,588.31 1,596.75 1,605.23 1,613.76 1,622.33 1,630.95 1,639.62 1,648.33 1,657.08 1,665.89 1,674.74 1,683.63 1,692.58 1,701.57 1,710.61 1,719.70 1,728.83 1,738.02 1,747.25 1,756.53 1,765.87 1,775.25

122,281.49 120,882.83 119,476.75 118,063.20 116,642.13 115,213.52 113,777.32 112,333.49 110,881.99 109,422.77 107,955.81 106,481.05 104,998.46 103,507.99 102,009.60 100,503.26 98,988.91 97,466.51 95,936.03 94,397.41 92,850.63 91,295.62 89,732.36 88,160.79 86,580.87 84,992.56 83,395.81 81,790.57 80,176.81 78,554.48 76,923.52 75,283.91 73,635.58 71,978.50 70,312.61 68,637.87 66,954.24 65,261.66 63,560.09 61,849.48 60,129.78 58,400.94 56,662.93 54,915.67 53,159.14 51,393.27 49,618.03

155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180

49,618.03 47,833.35 46,039.19 44,235.50 42,422.23 40,599.32 38,766.73 36,924.41 35,072.30 33,210.35 31,338.50 29,456.71 27,564.93 25,663.10 23,751.16 21,829.06 19,896.76 17,954.18 16,001.29 14,038.02 12,064.33 10,080.15 8,085.42 6,080.10 4,064.13 2,037.45

263.60 254.11 244.58 235.00 225.37 215.68 205.95 196.16 186.32 176.43 166.49 156.49 146.44 136.34 126.18 115.97 105.70 95.38 85.01 74.58 64.09 53.55 42.95 32.30 21.59 10.82

1,784.68 1,794.16 1,803.69 1,813.27 1,822.91 1,832.59 1,842.33 1,852.11 1,861.95 1,871.84 1,881.79 1,891.78 1,901.83 1,911.94 1,922.10 1,932.31 1,942.57 1,952.89 1,963.27 1,973.70 1,984.18 1,994.72 2,005.32 2,015.97 2,026.68 2,037.45

47,833.35 46,039.19 44,235.50 42,422.23 40,599.32 38,766.73 36,924.41 35,072.30 33,210.35 31,338.50 29,456.71 27,564.93 25,663.10 23,751.16 21,829.06 19,896.76 17,954.18 16,001.29 14,038.02 12,064.33 10,080.15 8,085.42 6,080.10 4,064.13 2,037.45 -0.00

Date:

triangle. Red triangle identifies a cell comment.

d will borrow $237,000 from Bank One at a rate of an amortization schedule using Excel.

e as percent X.XX%, or decimal. .XXX

annuity, assume end of month payments

Chapter 6, Problem 41

Student's Name: Solution method uses PMT, IPMT, PPMT, and IF functions/formulas and cell formulas, works for regular annuity and annui

Guidelines:

<-- To view guidelines, move mouse pointer over cell with red triangle. Red triangle identifies a ce

Problem:

Unknowns: Find annuity payment for annuity due problem Amortize the loan (determine amount of each payment that is interest and reduction of principal)

Assumption(s) Interest rate is annual rate with monthly compounding Monthly payment can be either end of beginning of month

Given information/inputs/arguments:

Values 6.375% 15.00 12.00 237,000.00 0.00 1.00

Annual interest rate Number of periods/years, nper Compounding frequency Amount of loan, present value, pv Future value Type of annuity

Comments Enter percentage as percent X.XX%, or decimal. .XXX Enter number of years Enter months in a year Enter amount of loan as positive value Enter 0, no future value Can enter 0 or 1, 0 = end of month payment, 1 = start o

Excel solution method using PMT function/formula: Monthly loan payment, PMT function

2,037.45

Loan amortization

Month 1 2 3 4 5 6 7 8 9 10 11 12 13

Beginning Balance 237,000.00 234,962.55 234,173.34 233,379.94 232,582.32 231,780.46 230,974.35 230,163.95 229,349.24 228,530.21 227,706.83 226,879.07 226,046.92

Monthly Payment 2,037.45 2,037.45 2,037.45 2,037.45 2,037.45 2,037.45 2,037.45 2,037.45 2,037.45 2,037.45 2,037.45 2,037.45 2,037.45

Monthly Monthly reduction of Interest Principal 1,259.06 2,037.45 1,254.87 789.21 1,250.65 793.40 1,246.42 797.62 1,242.16 801.86 1,237.88 806.12 1,233.57 810.40 1,229.24 814.70 1,224.89 819.03 1,220.52 823.38 1,216.12 827.76 1,211.70 832.15 1,207.25 836.58

End of Month Balance 234,962.55 234,173.34 233,379.94 232,582.32 231,780.46 230,974.35 230,163.95 229,349.24 228,530.21 227,706.83 226,879.07 226,046.92 225,210.34

14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

225,210.34 224,369.32 223,523.84 222,673.86 221,819.36 220,960.33 220,096.73 219,228.55 218,355.75 217,478.31 216,596.22 215,709.44 214,817.94 213,921.71 213,020.72 212,114.95 211,204.36 210,288.93 209,368.64 208,443.46 207,513.37 206,578.34 205,638.33 204,693.34 203,743.32 202,788.26 201,828.12 200,862.88 199,892.52 198,917.00 197,936.30 196,950.38 195,959.23 194,962.82 193,961.11 192,954.08 191,941.70 190,923.94 189,900.77 188,872.17 187,838.10 186,798.54 185,753.46 184,702.83 183,646.61 182,584.78 181,517.32

2,037.45 2,037.45 2,037.45 2,037.45 2,037.45 2,037.45 2,037.45 2,037.45 2,037.45 2,037.45 2,037.45 2,037.45 2,037.45 2,037.45 2,037.45 2,037.45 2,037.45 2,037.45 2,037.45 2,037.45 2,037.45 2,037.45 2,037.45 2,037.45 2,037.45 2,037.45 2,037.45 2,037.45 2,037.45 2,037.45 2,037.45 2,037.45 2,037.45 2,037.45 2,037.45 2,037.45 2,037.45 2,037.45 2,037.45 2,037.45 2,037.45 2,037.45 2,037.45 2,037.45 2,037.45 2,037.45 2,037.45

841.02 845.49 849.98 854.49 859.03 863.60 868.19 872.80 877.43 882.10 886.78 891.49 896.23 900.99 905.78 910.59 915.43 920.29 925.18 930.09 935.03 940.00 945.00 950.02 955.06 960.14 965.24 970.37 975.52 980.70 985.91 991.15 996.42 1,001.71 1,007.03 1,012.38 1,017.76 1,023.17 1,028.60 1,034.07 1,039.56 1,045.08 1,050.63 1,056.22 1,061.83 1,067.47 1,073.14

224,369.32 223,523.84 222,673.86 221,819.36 220,960.33 220,096.73 219,228.55 218,355.75 217,478.31 216,596.22 215,709.44 214,817.94 213,921.71 213,020.72 212,114.95 211,204.36 210,288.93 209,368.64 208,443.46 207,513.37 206,578.34 205,638.33 204,693.34 203,743.32 202,788.26 201,828.12 200,862.88 199,892.52 198,917.00 197,936.30 196,950.38 195,959.23 194,962.82 193,961.11 192,954.08 191,941.70 190,923.94 189,900.77 188,872.17 187,838.10 186,798.54 185,753.46 184,702.83 183,646.61 182,584.78 181,517.32 180,444.18

61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107

180,444.18 179,365.34 178,280.77 177,190.43 176,094.31 174,992.36 173,884.56 172,770.87 171,651.27 170,525.71 169,394.18 168,256.64 167,113.05 165,963.39 164,807.62 163,645.72 162,477.63 161,303.35 160,122.82 158,936.02 157,742.92 156,543.48 155,337.67 154,125.45 152,906.79 151,681.66 150,450.02 149,211.84 147,967.08 146,715.70 145,457.68 144,192.97 142,921.55 141,643.37 140,358.40 139,066.61 137,767.95 136,462.39 135,149.90 133,830.43 132,503.96 131,170.44 129,829.83 128,482.10 127,127.21 125,765.13 124,395.80

1,078.84 1,084.57 1,090.33 1,096.13 1,101.95 1,107.80 1,113.69 1,119.60 1,125.55 1,131.53 1,137.54 1,143.59 1,149.66 1,155.77 1,161.91 1,168.08 1,174.29 1,180.53 1,186.80 1,193.10 1,199.44 1,205.81 1,212.22 1,218.66 1,225.13 1,231.64 1,238.18 1,244.76 1,251.37 1,258.02 1,264.71 1,271.42 1,278.18 1,284.97 1,291.80 1,298.66 1,305.56 1,312.49 1,319.47 1,326.48 1,333.52 1,340.61 1,347.73 1,354.89 1,362.09 1,369.32 1,376.60

179,365.34 178,280.77 177,190.43 176,094.31 174,992.36 173,884.56 172,770.87 171,651.27 170,525.71 169,394.18 168,256.64 167,113.05 165,963.39 164,807.62 163,645.72 162,477.63 161,303.35 160,122.82 158,936.02 157,742.92 156,543.48 155,337.67 154,125.45 152,906.79 151,681.66 150,450.02 149,211.84 147,967.08 146,715.70 145,457.68 144,192.97 142,921.55 141,643.37 140,358.40 139,066.61 137,767.95 136,462.39 135,149.90 133,830.43 132,503.96 131,170.44 129,829.83 128,482.10 127,127.21 125,765.13 124,395.80 123,019.21

108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154

123,019.21 121,635.30 120,244.04 118,845.38 117,439.30 116,025.75 114,604.68 113,176.07 111,739.87 110,296.04 108,844.54 107,385.32 105,918.36 104,443.60 102,961.01 101,470.54 99,972.15 98,465.81 96,951.46 95,429.06 93,898.58 92,359.97 90,813.18 89,258.17 87,694.91 86,123.34 84,543.42 82,955.11 81,358.36 79,753.12 78,139.36 76,517.03 74,886.08 73,246.46 71,598.13 69,941.05 68,275.16 66,600.42 64,916.79 63,224.21 61,522.64 59,812.03 58,092.33 56,363.49 54,625.48 52,878.22 51,121.69

1,383.91 1,391.26 1,398.65 1,406.08 1,413.55 1,421.06 1,428.61 1,436.20 1,443.83 1,451.50 1,459.21 1,466.96 1,474.76 1,482.59 1,490.47 1,498.39 1,506.35 1,514.35 1,522.39 1,530.48 1,538.61 1,546.79 1,555.00 1,563.27 1,571.57 1,579.92 1,588.31 1,596.75 1,605.23 1,613.76 1,622.33 1,630.95 1,639.62 1,648.33 1,657.08 1,665.89 1,674.74 1,683.63 1,692.58 1,701.57 1,710.61 1,719.70 1,728.83 1,738.02 1,747.25 1,756.53 1,765.87

121,635.30 120,244.04 118,845.38 117,439.30 116,025.75 114,604.68 113,176.07 111,739.87 110,296.04 108,844.54 107,385.32 105,918.36 104,443.60 102,961.01 101,470.54 99,972.15 98,465.81 96,951.46 95,429.06 93,898.58 92,359.97 90,813.18 89,258.17 87,694.91 86,123.34 84,543.42 82,955.11 81,358.36 79,753.12 78,139.36 76,517.03 74,886.08 73,246.46 71,598.13 69,941.05 68,275.16 66,600.42 64,916.79 63,224.21 61,522.64 59,812.03 58,092.33 56,363.49 54,625.48 52,878.22 51,121.69 49,355.83

155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180

49,355.83 47,580.58 45,795.90 44,001.74 42,198.05 40,384.78 38,561.87 36,729.29 34,886.96 33,034.85 31,172.90 29,301.05 27,419.26 25,527.48 23,625.65 21,713.71 19,791.61 17,859.31 15,916.73 13,963.84 12,000.58 10,026.88 8,042.70 6,047.97 4,042.66 2,026.68

263.60 254.11 244.58 235.00 225.37 215.68 205.95 196.16 186.32 176.43 166.49 156.49 146.44 136.34 126.18 115.97 105.70 95.38 85.01 74.58 64.09 53.55 42.95 32.30 21.59 10.82

1,775.25 1,784.68 1,794.16 1,803.69 1,813.27 1,822.91 1,832.59 1,842.33 1,852.11 1,861.95 1,871.84 1,881.79 1,891.78 1,901.83 1,911.94 1,922.10 1,932.31 1,942.57 1,952.89 1,963.27 1,973.70 1,984.18 1,994.72 2,005.32 2,015.97 2,026.68

47,580.58 45,795.90 44,001.74 42,198.05 40,384.78 38,561.87 36,729.29 34,886.96 33,034.85 31,172.90 29,301.05 27,419.26 25,527.48 23,625.65 21,713.71 19,791.61 17,859.31 15,916.73 13,963.84 12,000.58 10,026.88 8,042.70 6,047.97 4,042.66 2,026.68 -0.00

Date: as, works for regular annuity and annuity due

triangle. Red triangle identifies a cell comment.

d will borrow $237,000 from Bank One at a rate of an amortization schedule using Excel.

e as percent X.XX%, or decimal. .XXX

, 0 = end of month payment, 1 = start of month

Chapter 6, Problem 41

Student's Name: Solution method uses PMT and IF functions/formulas and cell formulas, works for regular annuity and annuity due

Guidelines:

<-- To view guidelines, move mouse pointer over cell with red triangle. Red triangle identifies a ce

Problem:

Unknowns: Find annuity payment for annuity due problem Amortize the loan (determine amount of each payment that is interest and reduction of principal)

Assumption(s) Interest rate is annual rate with monthly compounding Monthly payment can be either end of beginning of month

Given information/inputs/arguments:

Values 6.375% 15.00 12.00 237,000.00 0.00 1.00

Annual interest rate Number of periods/years, nper Compounding frequency Amount of loan, present value, pv Future value Type of annuity

Excel solution method using PMT function/formula: Monthly loan payment, PMT function

2,037.45

Loan amortization

Month 1 2 3 4 5 6 7 8 9 10 11 12 13

Beginning Balance 237,000.00 236,210.79 235,417.39 234,619.77 233,817.91 233,011.80 232,201.40 231,386.69 230,567.66 229,744.28 228,916.52 228,084.37 227,247.79

Monthly Payment 2,037.45 2,037.45 2,037.45 2,037.45 2,037.45 2,037.45 2,037.45 2,037.45 2,037.45 2,037.45 2,037.45 2,037.45 2,037.45

Monthly Monthly reduction of Interest Principal 1,248.24 789.21 1,244.05 793.40 1,239.83 797.62 1,235.59 801.86 1,231.33 806.12 1,227.05 810.40 1,222.75 814.70 1,218.42 819.03 1,214.07 823.38 1,209.69 827.76 1,205.30 832.15 1,200.87 836.58 1,196.43 841.02

End of Month Balance 236,210.79 235,417.39 234,619.77 233,817.91 233,011.80 232,201.40 231,386.69 230,567.66 229,744.28 228,916.52 228,084.37 227,247.79 226,406.77

14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

1,191.96 1,187.47 1,182.95 1,178.42 1,173.85 1,169.26 1,164.65 1,160.01 1,155.35 1,150.67 1,145.96 1,141.22 1,136.46 1,131.67 1,126.86 1,122.02 1,117.16 1,112.27 1,107.36 1,102.41 1,097.45 1,092.45 1,087.43 1,082.39 1,077.31 1,072.21 1,067.08 1,061.93 1,056.75 1,051.54 1,046.30 1,041.03 1,035.74 1,030.42 1,025.07 1,019.69 1,014.28 1,008.85 1,003.38 997.89 992.37 986.82 981.23 975.62 969.98 964.31 958.61

61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107

952.88 947.12 941.32 935.50 929.65 923.76 917.85 911.90 905.92 899.91 893.86 887.79 881.68 875.54 869.37 863.16 856.92 850.65 844.35 838.01 831.64 825.23 818.79 812.32 805.81 799.27 792.69 786.08 779.43 772.74 766.03 759.27 752.48 745.65 738.79 731.89 724.96 717.98 710.97 703.93 696.84 689.72 682.56 675.36 668.13 660.85 653.54

108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154

646.19 638.80 631.37 623.90 616.39 608.84 601.25 593.62 585.95 578.24 570.48 562.69 554.86 546.98 539.06 531.10 523.10 515.05 506.97 498.84 490.66 482.45 474.18 465.88 457.53 449.14 440.70 432.22 423.69 415.12 406.50 397.83 389.12 380.37 371.56 362.71 353.81 344.87 335.88 326.84 317.75 308.62 299.43 290.20 280.92 271.58 262.20

155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180

252.77 243.29 233.76 224.18 214.54 204.86 195.12 185.34 175.50 165.61 155.66 145.66 135.61 125.51 115.35 105.14 94.88 84.56 74.18 63.75 53.27 42.73 32.13 21.48 10.77 -0.00

Date:

egular annuity and annuity due

triangle. Red triangle identifies a cell comment.

d will borrow $237,000 from Bank One at a rate of an amortization schedule using Excel.

e as percent X.XX%, or decimal. .XXX

, 0 = end of month payment, 1 = start of month

Textbook: Fundamentals of Corporate Finance, 5th Edition Authors: Robert Parrino, Thomas Bates, Stuart Gillan, David Kidwell Publisher: Wiley Chapter 5: The Time Value of Money Excel solutions for selected problems at end of Chapter 5. Problem number 2 2 7 7 7 7 12 12 19 19 19 20 20 25 25 33 33 34 34 36 36 37 37

Solution Method FV function/formula Alternative, using schedule FV function/formula Alternative, using schedule, Quarterly Alternative, using schedule, Monthly Alternative, using schedule, Daily PV function/formula Alternative, using schedule FVSchedule function/formula Alternative, using schedule Alternative solution: FV function/formula FV function/formula Alternative, using schedule NPER function/formula Alternative, using schedule FV function/formula Alternative, using schedule FVSchedule Function/formula Alternative, using schedule NPER function/formula Alternative, using schedule FVandRate functions/formula Alternative, using schedule

Worksheet tab name 2_FV_function 2_Alternative_Schedule 7_FV_function 7_Alternative_ScheduleQ 7_Alternative_ScheduleM 7_Alternative_ScheduleD 12_PV_function 12_Alternative_Schedule 19_FVSchedule_function 19_Alternative1_Schedule 19_Alternative2_FV_function 20_FV_function 20_Alternative_Schedule 25_NPER_function 25_Alternative_Schedule 33_FV_Function 33_Alternative_Schedule 34_FVSchedule_Function 34_Alternative_Schedule 36_NPER_function 36_Alternative_Schedule 37_FVandRate_functions 37_Alternative_Schedule

One way to return to the contents worksheet is to hold down the CTRL key and press and hold down the PageUp key

d hold down the PageUp key

Chapter 5, Problem 2

Student's Name:

Solution method uses FV function/formula

Guidelines:

<-- To view guidelines, move mouse pointer over cell with red triangle. Red triangle identifies a ce

Problem: Future value: Ted Rogers is investing $7,500 in a bank CD that pays a 6 percent annual interest. How much will the worth at the end of five years?

Unknown: Value of investment at the end of five years.

Assumption(s) Annual interest rate has annual compounding

Inputs: given information/arguments: Annual interest rate Number of periods/years, nper Compounding frequency per year Annuity payment, pmt Present value, pv Type of annuity

Values 6.00% 5.00 1.00 0.00 $ 7,500.00 0.00

Output: Solution method using FV function: Excel FV function =

10,036.69

Comments Enter percentage as percent XX%, or decimal. .XX Enter investment life in years Enter compounding frequency per year, here annual co Enter zero, not an annuity problem Enter initial investment as positive value Enter 0, not an annuity problem

Date:

triangle. Red triangle identifies a cell comment.

annual interest. How much will the CD be

e as percent XX%, or decimal. .XX nt life in years ding frequency per year, here annual compounding an annuity problem estment as positive value annuity problem

Chapter 5, Problem 2

Student's Name:

Solution method uses schedule method

Guidelines:

<-- To view guidelines, move mouse pointer over cell with red triangle. Red triangle identifies a ce

Problem: Future value: Ted Rogers is investing $7,500 in a bank CD that pays a 6 percent annual interest. How much will the worth at the end of five years?

Unknown: Value of investment at the end of five years.

Assumption(s) Annual interest rate has annual compounding

Given information/inputs/arguments:

Values

Annual interest rate Number of periods/years, nper Compounding frequency per year Annuity payment, pmt Present value, pv Type of annuity

6.00% 5.00 1.00 0.00 7,500.00 0.00

Schedule solution method, no Excel functions Future value, reference cell with value end last year

10,036.69

Schedule

Year 1 2 3 4 5

Value, start of year 7,500.00 7,950.00 8,427.00 8,932.62 9,468.58

Interest earned during year 450.00 477.00 505.62 535.96 568.11

Value, end of year 7,950.00 8,427.00 8,932.62 9,468.58 10,036.69

Comments Enter percentage as percent XX% Enter investment life in years Enter compounding frequency pe Enter zero, not an annuity proble Enter initial investment as positiv Enter 0, not an annuity problem

Date:

gle. Red triangle identifies a cell comment.

ual interest. How much will the CD be

Enter percentage as percent XX%, or decimal. .XX Enter investment life in years Enter compounding frequency per year, here annual compounding Enter zero, not an annuity problem Enter initial investment as positive value Enter 0, not an annuity problem

Chapter 5, Problem 7

Student's Name:

Solution method uses FV and EXP functions/formulas

Guidelines:

<-- To view guidelines, move mouse pointer over cell with red triangle. Red triangle identifies a ce

Problem:

Multiple Compounding Periods: Find the future value of a five-year $100,000 investment that pays 8.75 percent and that the following compounding periods: a. Quarterly b. Monthly c. Daily d. Continuous

Unknown: Value of investment at the end of five years.

Assumption(s) None

Given information/inputs/arguments: Annual interest rate Number of periods/years, nper Compounding frequency a Compounding frequency b Compounding frequency c Compounding frequency d Annuity payment, pmt Present value, pv Type of annuity

$ $

Values 8.75% 5.00 4.00 12.00 365.00 1,000,000 0.00 100,000 0.00

Comments Enter percentage as percent XX%, or decimal. .XX Enter number of years Enter quarters in a year Enter months in a year Enter days in a year Compounded Continuously, to approximate enter 1,0 Ener zero, not an annuity problem Ener initial investment as a positive value Enter 0, not an annuity problem

Excel solution method using FV and EXP functions: a. Excel FV function, quarterly compounding = b. Excel FV function, monthly compounding = c. Excel FV function, daily compounding = d. Excel FV function, continuous compounding, 1,000,000 subperiods = d. Excel FV function, continuous compounding, using formula =

$ 154,154.24 $ 154,637.37 $ 154,874.91 $ 154,883.03 $ 154,883.03

Date:

riangle. Red triangle identifies a cell comment.

ment that pays 8.75 percent and that has

e as percent XX%, or decimal. .XX

ontinuously, to approximate enter 1,000,000

Chapter 5, Problem 7

Student's Name: Solution method uses schedule to find future value when annual rate is 8.75% with quarterly compounding

Guidelines:

<-- To view guidelines, move mouse pointer over cell with red triangle. Red triangle identifies a ce

Problem:

Unknown: Value of investment at the end of five years.

Assumption(s) None

Values

$ $

8.75% 5.00 4.00 12.00 365.00 1,000,000.00 0.00 100,000.00 0.00

Excel solution method using schedule FV at the end of 5 years, 20 quarters

154,154.24

Interest earned during quarter 2,187.50 $ 2,235.35 2,284.25 2,334.22 2,385.28 2,437.46 2,490.78 2,545.26 2,600.94

Value, end of quarter 102,187.50 104,422.85 106,707.10 109,041.32 111,426.60 113,864.05 116,354.83 118,900.09 121,501.03

Schedule for quarterly compounding Quarters 1 $ 2 3 4 5 6 7 8 9

Value, start of quarter 100,000.00 $ 102,187.50 104,422.85 106,707.10 109,041.32 111,426.60 113,864.05 116,354.83 118,900.09

Comments Enter percentage as percent XX%, or de Enter number of years Enter quarters in a year Enter months in a year Enter days in a year Compounded Continuously, to approxim Ener zero, not an annuity problem Ener initial investment as a positive valu Enter 0, not an annuity problem

10 11 12 13 14 15 16 17 18 19 20

121,501.03 124,158.87 126,874.84 129,650.23 132,486.33 135,384.47 138,346.00 141,372.32 144,464.84 147,625.01 150,854.31

2,657.84 2,715.98 2,775.39 2,836.10 2,898.14 2,961.54 3,026.32 3,092.52 3,160.17 3,229.30 3,299.94

124,158.87 126,874.84 129,650.23 132,486.33 135,384.47 138,346.00 141,372.32 144,464.84 147,625.01 150,854.31 154,154.24

Date:

d triangle. Red triangle identifies a cell comment.

stment that pays 8.75 percent and that has

Enter percentage as percent XX%, or decimal. .XX

Compounded Continuously, to approximate enter 1,000,000 Ener zero, not an annuity problem Ener initial investment as a positive value Enter 0, not an annuity problem

Chapter 5, Problem 7

Student's Name: Solution method uses schedule to find future value when annual rate is 8.75% with monthly compounding

Guidelines:

<-- To view guidelines, move mouse pointer over cell with red triangle. Red triangle identifies a cell co

Problem:

Unknown: Value of investment at the end of five years.

Assumption(s) None

$ $

Values 8.75% 5.00 4.00 12.00 365.00 1,000,000 0.00 100,000 0.00

Excel solution method using schedule FV at the end of 5 years, 60 months

154,637.37

Interest earned during month 729.17 $ 734.48 739.84 745.23 750.67 756.14 761.65 767.21 772.80

Value, end of month 100,729.17 101,463.65 102,203.49 102,948.72 103,699.39 104,455.53 105,217.19 105,984.40 106,757.20

Schedule for annual rate with monthly compounding Months 1 $ 2 3 4 5 6 7 8 9

Value, start of month 100,000.00 $ 100,729.17 101,463.65 102,203.49 102,948.72 103,699.39 104,455.53 105,217.19 105,984.40

Comments Enter percentage as percent XX%, or decimal Enter number of years Enter quarters in a year Enter months in a year Enter days in a year Compounded Continuously, to approximate e Ener zero, not an annuity problem Ener initial investment as a positive value Enter 0, not an annuity problem

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56

106,757.20 107,535.64 108,319.75 109,109.58 109,905.17 110,706.56 111,513.80 112,326.92 113,145.97 113,970.99 114,802.03 115,639.13 116,482.33 117,331.68 118,187.23 119,049.01 119,917.07 120,791.47 121,672.24 122,559.43 123,453.10 124,353.28 125,260.02 126,173.37 127,093.39 128,020.11 128,953.59 129,893.88 130,841.02 131,795.07 132,756.07 133,724.09 134,699.16 135,681.34 136,670.68 137,667.24 138,671.06 139,682.21 140,700.72 141,726.67 142,760.09 143,801.05 144,849.60 145,905.79 146,969.69 148,041.34 149,120.81

778.44 784.11 789.83 795.59 801.39 807.24 813.12 819.05 825.02 831.04 837.10 843.20 849.35 855.54 861.78 868.07 874.40 880.77 887.19 893.66 900.18 906.74 913.35 920.01 926.72 933.48 940.29 947.14 954.05 961.01 968.01 975.07 982.18 989.34 996.56 1,003.82 1,011.14 1,018.52 1,025.94 1,033.42 1,040.96 1,048.55 1,056.19 1,063.90 1,071.65 1,079.47 1,087.34

107,535.64 108,319.75 109,109.58 109,905.17 110,706.56 111,513.80 112,326.92 113,145.97 113,970.99 114,802.03 115,639.13 116,482.33 117,331.68 118,187.23 119,049.01 119,917.07 120,791.47 121,672.24 122,559.43 123,453.10 124,353.28 125,260.02 126,173.37 127,093.39 128,020.11 128,953.59 129,893.88 130,841.02 131,795.07 132,756.07 133,724.09 134,699.16 135,681.34 136,670.68 137,667.24 138,671.06 139,682.21 140,700.72 141,726.67 142,760.09 143,801.05 144,849.60 145,905.79 146,969.69 148,041.34 149,120.81 150,208.15

57 58 59 60

150,208.15 151,303.42 152,406.67 153,517.97

1,095.27 1,103.25 1,111.30 1,119.40

151,303.42 152,406.67 153,517.97 154,637.37

Date:

compounding

d triangle identifies a cell comment.

at pays 8.75 percent and that has

e as percent XX%, or decimal. .XX

ontinuously, to approximate enter 1,000,000 n annuity problem stment as a positive value annuity problem

Chapter 5, Problem 7

Student's Name: Solution method uses schedule to find future value when annual rate is 8.75% with daily compounding

Guidelines:

<-- To view guidelines, move mouse pointer over cell with red triangle. Red triangle identifies a ce

Problem:

Unknown: Value of investment at the end of five years.

Assumption(s) None

$ $

Values 8.75% 5.00 4.00 12.00 365.00 1,000,000 0.00 100,000 0.00

Excel solution method using schedule FV at the end of 5 years, 1,825 days

154,874.91

Interest earned during day 23.97 $ 23.98 23.98 23.99 24.00 24.00 24.01 24.01 24.02

Value, end of day 100,023.97 100,047.95 100,071.94 100,095.92 100,119.92 100,143.92 100,167.93 100,191.94 100,215.96

Schedule for annual rate with daily compounding Days 1 $ 2 3 4 5 6 7 8 9

Value, start of day 100,000.00 $ 100,023.97 100,047.95 100,071.94 100,095.92 100,119.92 100,143.92 100,167.93 100,191.94

Comments Enter percentage as percent XX%, or decim Enter number of years Enter quarters in a year Enter months in a year Enter days in a year Compounded Continuously, to approximat Ener zero, not an annuity problem Ener initial investment as a positive value Enter 0, not an annuity problem

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56

100,215.96 100,239.98 100,264.01 100,288.05 100,312.09 100,336.14 100,360.19 100,384.25 100,408.32 100,432.39 100,456.46 100,480.55 100,504.63 100,528.73 100,552.83 100,576.93 100,601.04 100,625.16 100,649.28 100,673.41 100,697.54 100,721.68 100,745.83 100,769.98 100,794.14 100,818.30 100,842.47 100,866.64 100,890.82 100,915.01 100,939.20 100,963.40 100,987.60 101,011.81 101,036.03 101,060.25 101,084.48 101,108.71 101,132.95 101,157.19 101,181.44 101,205.70 101,229.96 101,254.23 101,278.50 101,302.78 101,327.06

24.02 24.03 24.04 24.04 24.05 24.05 24.06 24.06 24.07 24.08 24.08 24.09 24.09 24.10 24.11 24.11 24.12 24.12 24.13 24.13 24.14 24.15 24.15 24.16 24.16 24.17 24.17 24.18 24.19 24.19 24.20 24.20 24.21 24.22 24.22 24.23 24.23 24.24 24.24 24.25 24.26 24.26 24.27 24.27 24.28 24.28 24.29

100,239.98 100,264.01 100,288.05 100,312.09 100,336.14 100,360.19 100,384.25 100,408.32 100,432.39 100,456.46 100,480.55 100,504.63 100,528.73 100,552.83 100,576.93 100,601.04 100,625.16 100,649.28 100,673.41 100,697.54 100,721.68 100,745.83 100,769.98 100,794.14 100,818.30 100,842.47 100,866.64 100,890.82 100,915.01 100,939.20 100,963.40 100,987.60 101,011.81 101,036.03 101,060.25 101,084.48 101,108.71 101,132.95 101,157.19 101,181.44 101,205.70 101,229.96 101,254.23 101,278.50 101,302.78 101,327.06 101,351.35

57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103

101,351.35 101,375.65 101,399.95 101,424.26 101,448.58 101,472.90 101,497.22 101,521.55 101,545.89 101,570.23 101,594.58 101,618.94 101,643.30 101,667.66 101,692.04 101,716.41 101,740.80 101,765.19 101,789.58 101,813.99 101,838.39 101,862.81 101,887.23 101,911.65 101,936.08 101,960.52 101,984.96 102,009.41 102,033.86 102,058.32 102,082.79 102,107.26 102,131.74 102,156.22 102,180.71 102,205.21 102,229.71 102,254.22 102,278.73 102,303.25 102,327.77 102,352.30 102,376.84 102,401.38 102,425.93 102,450.49 102,475.05

24.30 24.30 24.31 24.31 24.32 24.33 24.33 24.34 24.34 24.35 24.35 24.36 24.37 24.37 24.38 24.38 24.39 24.40 24.40 24.41 24.41 24.42 24.43 24.43 24.44 24.44 24.45 24.45 24.46 24.47 24.47 24.48 24.48 24.49 24.50 24.50 24.51 24.51 24.52 24.52 24.53 24.54 24.54 24.55 24.55 24.56 24.57

101,375.65 101,399.95 101,424.26 101,448.58 101,472.90 101,497.22 101,521.55 101,545.89 101,570.23 101,594.58 101,618.94 101,643.30 101,667.66 101,692.04 101,716.41 101,740.80 101,765.19 101,789.58 101,813.99 101,838.39 101,862.81 101,887.23 101,911.65 101,936.08 101,960.52 101,984.96 102,009.41 102,033.86 102,058.32 102,082.79 102,107.26 102,131.74 102,156.22 102,180.71 102,205.21 102,229.71 102,254.22 102,278.73 102,303.25 102,327.77 102,352.30 102,376.84 102,401.38 102,425.93 102,450.49 102,475.05 102,499.61

104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150

102,499.61 102,524.18 102,548.76 102,573.34 102,597.93 102,622.53 102,647.13 102,671.74 102,696.35 102,720.97 102,745.59 102,770.23 102,794.86 102,819.51 102,844.15 102,868.81 102,893.47 102,918.13 102,942.81 102,967.48 102,992.17 103,016.86 103,041.55 103,066.26 103,090.96 103,115.68 103,140.40 103,165.12 103,189.85 103,214.59 103,239.33 103,264.08 103,288.84 103,313.60 103,338.37 103,363.14 103,387.92 103,412.70 103,437.49 103,462.29 103,487.09 103,511.90 103,536.72 103,561.54 103,586.36 103,611.20 103,636.03

24.57 24.58 24.58 24.59 24.60 24.60 24.61 24.61 24.62 24.62 24.63 24.64 24.64 24.65 24.65 24.66 24.67 24.67 24.68 24.68 24.69 24.70 24.70 24.71 24.71 24.72 24.73 24.73 24.74 24.74 24.75 24.76 24.76 24.77 24.77 24.78 24.78 24.79 24.80 24.80 24.81 24.81 24.82 24.83 24.83 24.84 24.84

102,524.18 102,548.76 102,573.34 102,597.93 102,622.53 102,647.13 102,671.74 102,696.35 102,720.97 102,745.59 102,770.23 102,794.86 102,819.51 102,844.15 102,868.81 102,893.47 102,918.13 102,942.81 102,967.48 102,992.17 103,016.86 103,041.55 103,066.26 103,090.96 103,115.68 103,140.40 103,165.12 103,189.85 103,214.59 103,239.33 103,264.08 103,288.84 103,313.60 103,338.37 103,363.14 103,387.92 103,412.70 103,437.49 103,462.29 103,487.09 103,511.90 103,536.72 103,561.54 103,586.36 103,611.20 103,636.03 103,660.88

151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197

103,660.88 103,685.73 103,710.58 103,735.45 103,760.31 103,785.19 103,810.07 103,834.95 103,859.85 103,884.74 103,909.65 103,934.56 103,959.47 103,984.40 104,009.32 104,034.26 104,059.20 104,084.14 104,109.09 104,134.05 104,159.02 104,183.99 104,208.96 104,233.94 104,258.93 104,283.92 104,308.92 104,333.93 104,358.94 104,383.96 104,408.98 104,434.01 104,459.05 104,484.09 104,509.14 104,534.19 104,559.25 104,584.31 104,609.39 104,634.46 104,659.55 104,684.64 104,709.73 104,734.83 104,759.94 104,785.06 104,810.17

24.85 24.86 24.86 24.87 24.87 24.88 24.89 24.89 24.90 24.90 24.91 24.92 24.92 24.93 24.93 24.94 24.95 24.95 24.96 24.96 24.97 24.98 24.98 24.99 24.99 25.00 25.01 25.01 25.02 25.02 25.03 25.04 25.04 25.05 25.05 25.06 25.07 25.07 25.08 25.08 25.09 25.10 25.10 25.11 25.11 25.12 25.13

103,685.73 103,710.58 103,735.45 103,760.31 103,785.19 103,810.07 103,834.95 103,859.85 103,884.74 103,909.65 103,934.56 103,959.47 103,984.40 104,009.32 104,034.26 104,059.20 104,084.14 104,109.09 104,134.05 104,159.02 104,183.99 104,208.96 104,233.94 104,258.93 104,283.92 104,308.92 104,333.93 104,358.94 104,383.96 104,408.98 104,434.01 104,459.05 104,484.09 104,509.14 104,534.19 104,559.25 104,584.31 104,609.39 104,634.46 104,659.55 104,684.64 104,709.73 104,734.83 104,759.94 104,785.06 104,810.17 104,835.30

198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244

104,835.30 104,860.43 104,885.57 104,910.71 104,935.86 104,961.02 104,986.18 105,011.35 105,036.52 105,061.70 105,086.89 105,112.08 105,137.28 105,162.48 105,187.69 105,212.91 105,238.13 105,263.36 105,288.60 105,313.84 105,339.08 105,364.33 105,389.59 105,414.86 105,440.13 105,465.41 105,490.69 105,515.98 105,541.27 105,566.57 105,591.88 105,617.19 105,642.51 105,667.84 105,693.17 105,718.51 105,743.85 105,769.20 105,794.55 105,819.92 105,845.28 105,870.66 105,896.04 105,921.42 105,946.82 105,972.21 105,997.62

25.13 25.14 25.14 25.15 25.16 25.16 25.17 25.17 25.18 25.19 25.19 25.20 25.20 25.21 25.22 25.22 25.23 25.23 25.24 25.25 25.25 25.26 25.26 25.27 25.28 25.28 25.29 25.29 25.30 25.31 25.31 25.32 25.33 25.33 25.34 25.34 25.35 25.36 25.36 25.37 25.37 25.38 25.39 25.39 25.40 25.40 25.41

104,860.43 104,885.57 104,910.71 104,935.86 104,961.02 104,986.18 105,011.35 105,036.52 105,061.70 105,086.89 105,112.08 105,137.28 105,162.48 105,187.69 105,212.91 105,238.13 105,263.36 105,288.60 105,313.84 105,339.08 105,364.33 105,389.59 105,414.86 105,440.13 105,465.41 105,490.69 105,515.98 105,541.27 105,566.57 105,591.88 105,617.19 105,642.51 105,667.84 105,693.17 105,718.51 105,743.85 105,769.20 105,794.55 105,819.92 105,845.28 105,870.66 105,896.04 105,921.42 105,946.82 105,972.21 105,997.62 106,023.03

245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291

106,023.03 106,048.45 106,073.87 106,099.30 106,124.73 106,150.17 106,175.62 106,201.07 106,226.53 106,252.00 106,277.47 106,302.95 106,328.43 106,353.92 106,379.41 106,404.92 106,430.42 106,455.94 106,481.46 106,506.99 106,532.52 106,558.06 106,583.60 106,609.15 106,634.71 106,660.27 106,685.84 106,711.42 106,737.00 106,762.59 106,788.18 106,813.78 106,839.39 106,865.00 106,890.62 106,916.24 106,941.87 106,967.51 106,993.15 107,018.80 107,044.46 107,070.12 107,095.78 107,121.46 107,147.14 107,172.82 107,198.52

25.42 25.42 25.43 25.43 25.44 25.45 25.45 25.46 25.47 25.47 25.48 25.48 25.49 25.50 25.50 25.51 25.51 25.52 25.53 25.53 25.54 25.54 25.55 25.56 25.56 25.57 25.58 25.58 25.59 25.59 25.60 25.61 25.61 25.62 25.62 25.63 25.64 25.64 25.65 25.66 25.66 25.67 25.67 25.68 25.69 25.69 25.70

106,048.45 106,073.87 106,099.30 106,124.73 106,150.17 106,175.62 106,201.07 106,226.53 106,252.00 106,277.47 106,302.95 106,328.43 106,353.92 106,379.41 106,404.92 106,430.42 106,455.94 106,481.46 106,506.99 106,532.52 106,558.06 106,583.60 106,609.15 106,634.71 106,660.27 106,685.84 106,711.42 106,737.00 106,762.59 106,788.18 106,813.78 106,839.39 106,865.00 106,890.62 106,916.24 106,941.87 106,967.51 106,993.15 107,018.80 107,044.46 107,070.12 107,095.78 107,121.46 107,147.14 107,172.82 107,198.52 107,224.21

292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338

107,224.21 107,249.92 107,275.63 107,301.35 107,327.07 107,352.80 107,378.53 107,404.27 107,430.02 107,455.78 107,481.54 107,507.30 107,533.07 107,558.85 107,584.64 107,610.43 107,636.23 107,662.03 107,687.84 107,713.65 107,739.48 107,765.30 107,791.14 107,816.98 107,842.82 107,868.68 107,894.54 107,920.40 107,946.27 107,972.15 107,998.03 108,023.92 108,049.82 108,075.72 108,101.63 108,127.55 108,153.47 108,179.39 108,205.33 108,231.27 108,257.21 108,283.16 108,309.12 108,335.09 108,361.06 108,387.03 108,413.02

25.70 25.71 25.72 25.72 25.73 25.74 25.74 25.75 25.75 25.76 25.77 25.77 25.78 25.78 25.79 25.80 25.80 25.81 25.82 25.82 25.83 25.83 25.84 25.85 25.85 25.86 25.87 25.87 25.88 25.88 25.89 25.90 25.90 25.91 25.91 25.92 25.93 25.93 25.94 25.95 25.95 25.96 25.96 25.97 25.98 25.98 25.99

107,249.92 107,275.63 107,301.35 107,327.07 107,352.80 107,378.53 107,404.27 107,430.02 107,455.78 107,481.54 107,507.30 107,533.07 107,558.85 107,584.64 107,610.43 107,636.23 107,662.03 107,687.84 107,713.65 107,739.48 107,765.30 107,791.14 107,816.98 107,842.82 107,868.68 107,894.54 107,920.40 107,946.27 107,972.15 107,998.03 108,023.92 108,049.82 108,075.72 108,101.63 108,127.55 108,153.47 108,179.39 108,205.33 108,231.27 108,257.21 108,283.16 108,309.12 108,335.09 108,361.06 108,387.03 108,413.02 108,439.01

339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385

108,439.01 108,465.00 108,491.01 108,517.01 108,543.03 108,569.05 108,595.07 108,621.11 108,647.15 108,673.19 108,699.24 108,725.30 108,751.37 108,777.44 108,803.51 108,829.60 108,855.69 108,881.78 108,907.88 108,933.99 108,960.11 108,986.23 109,012.35 109,038.49 109,064.63 109,090.77 109,116.92 109,143.08 109,169.25 109,195.42 109,221.59 109,247.78 109,273.97 109,300.16 109,326.36 109,352.57 109,378.79 109,405.01 109,431.24 109,457.47 109,483.71 109,509.96 109,536.21 109,562.47 109,588.73 109,615.00 109,641.28

26.00 26.00 26.01 26.01 26.02 26.03 26.03 26.04 26.05 26.05 26.06 26.06 26.07 26.08 26.08 26.09 26.10 26.10 26.11 26.11 26.12 26.13 26.13 26.14 26.15 26.15 26.16 26.16 26.17 26.18 26.18 26.19 26.20 26.20 26.21 26.21 26.22 26.23 26.23 26.24 26.25 26.25 26.26 26.26 26.27 26.28 26.28

108,465.00 108,491.01 108,517.01 108,543.03 108,569.05 108,595.07 108,621.11 108,647.15 108,673.19 108,699.24 108,725.30 108,751.37 108,777.44 108,803.51 108,829.60 108,855.69 108,881.78 108,907.88 108,933.99 108,960.11 108,986.23 109,012.35 109,038.49 109,064.63 109,090.77 109,116.92 109,143.08 109,169.25 109,195.42 109,221.59 109,247.78 109,273.97 109,300.16 109,326.36 109,352.57 109,378.79 109,405.01 109,431.24 109,457.47 109,483.71 109,509.96 109,536.21 109,562.47 109,588.73 109,615.00 109,641.28 109,667.56

386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432

109,667.56 109,693.85 109,720.15 109,746.45 109,772.76 109,799.08 109,825.40 109,851.73 109,878.06 109,904.40 109,930.75 109,957.10 109,983.46 110,009.83 110,036.20 110,062.58 110,088.96 110,115.36 110,141.75 110,168.16 110,194.57 110,220.98 110,247.41 110,273.84 110,300.27 110,326.71 110,353.16 110,379.62 110,406.08 110,432.54 110,459.02 110,485.50 110,511.98 110,538.48 110,564.97 110,591.48 110,617.99 110,644.51 110,671.03 110,697.56 110,724.10 110,750.65 110,777.20 110,803.75 110,830.31 110,856.88 110,883.46

26.29 26.30 26.30 26.31 26.32 26.32 26.33 26.33 26.34 26.35 26.35 26.36 26.37 26.37 26.38 26.38 26.39 26.40 26.40 26.41 26.42 26.42 26.43 26.44 26.44 26.45 26.45 26.46 26.47 26.47 26.48 26.49 26.49 26.50 26.51 26.51 26.52 26.52 26.53 26.54 26.54 26.55 26.56 26.56 26.57 26.58 26.58

109,693.85 109,720.15 109,746.45 109,772.76 109,799.08 109,825.40 109,851.73 109,878.06 109,904.40 109,930.75 109,957.10 109,983.46 110,009.83 110,036.20 110,062.58 110,088.96 110,115.36 110,141.75 110,168.16 110,194.57 110,220.98 110,247.41 110,273.84 110,300.27 110,326.71 110,353.16 110,379.62 110,406.08 110,432.54 110,459.02 110,485.50 110,511.98 110,538.48 110,564.97 110,591.48 110,617.99 110,644.51 110,671.03 110,697.56 110,724.10 110,750.65 110,777.20 110,803.75 110,830.31 110,856.88 110,883.46 110,910.04

433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479

110,910.04 110,936.63 110,963.22 110,989.82 111,016.43 111,043.04 111,069.66 111,096.29 111,122.92 111,149.56 111,176.21 111,202.86 111,229.52 111,256.18 111,282.85 111,309.53 111,336.21 111,362.90 111,389.60 111,416.30 111,443.01 111,469.73 111,496.45 111,523.18 111,549.91 111,576.66 111,603.40 111,630.16 111,656.92 111,683.69 111,710.46 111,737.24 111,764.03 111,790.82 111,817.62 111,844.42 111,871.23 111,898.05 111,924.88 111,951.71 111,978.55 112,005.39 112,032.24 112,059.10 112,085.96 112,112.83 112,139.71

26.59 26.59 26.60 26.61 26.61 26.62 26.63 26.63 26.64 26.65 26.65 26.66 26.66 26.67 26.68 26.68 26.69 26.70 26.70 26.71 26.72 26.72 26.73 26.74 26.74 26.75 26.75 26.76 26.77 26.77 26.78 26.79 26.79 26.80 26.81 26.81 26.82 26.82 26.83 26.84 26.84 26.85 26.86 26.86 26.87 26.88 26.88

110,936.63 110,963.22 110,989.82 111,016.43 111,043.04 111,069.66 111,096.29 111,122.92 111,149.56 111,176.21 111,202.86 111,229.52 111,256.18 111,282.85 111,309.53 111,336.21 111,362.90 111,389.60 111,416.30 111,443.01 111,469.73 111,496.45 111,523.18 111,549.91 111,576.66 111,603.40 111,630.16 111,656.92 111,683.69 111,710.46 111,737.24 111,764.03 111,790.82 111,817.62 111,844.42 111,871.23 111,898.05 111,924.88 111,951.71 111,978.55 112,005.39 112,032.24 112,059.10 112,085.96 112,112.83 112,139.71 112,166.59

480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526

112,166.59 112,193.48 112,220.38 112,247.28 112,274.19 112,301.10 112,328.02 112,354.95 112,381.89 112,408.83 112,435.77 112,462.73 112,489.69 112,516.66 112,543.63 112,570.61 112,597.59 112,624.59 112,651.59 112,678.59 112,705.60 112,732.62 112,759.65 112,786.68 112,813.72 112,840.76 112,867.81 112,894.87 112,921.93 112,949.00 112,976.08 113,003.16 113,030.25 113,057.35 113,084.45 113,111.56 113,138.68 113,165.80 113,192.93 113,220.06 113,247.20 113,274.35 113,301.51 113,328.67 113,355.84 113,383.01 113,410.19

26.89 26.90 26.90 26.91 26.92 26.92 26.93 26.93 26.94 26.95 26.95 26.96 26.97 26.97 26.98 26.99 26.99 27.00 27.01 27.01 27.02 27.02 27.03 27.04 27.04 27.05 27.06 27.06 27.07 27.08 27.08 27.09 27.10 27.10 27.11 27.12 27.12 27.13 27.14 27.14 27.15 27.15 27.16 27.17 27.17 27.18 27.19

112,193.48 112,220.38 112,247.28 112,274.19 112,301.10 112,328.02 112,354.95 112,381.89 112,408.83 112,435.77 112,462.73 112,489.69 112,516.66 112,543.63 112,570.61 112,597.59 112,624.59 112,651.59 112,678.59 112,705.60 112,732.62 112,759.65 112,786.68 112,813.72 112,840.76 112,867.81 112,894.87 112,921.93 112,949.00 112,976.08 113,003.16 113,030.25 113,057.35 113,084.45 113,111.56 113,138.68 113,165.80 113,192.93 113,220.06 113,247.20 113,274.35 113,301.51 113,328.67 113,355.84 113,383.01 113,410.19 113,437.38

527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573

113,437.38 113,464.57 113,491.77 113,518.98 113,546.19 113,573.41 113,600.64 113,627.87 113,655.11 113,682.36 113,709.61 113,736.87 113,764.14 113,791.41 113,818.69 113,845.97 113,873.27 113,900.56 113,927.87 113,955.18 113,982.50 114,009.82 114,037.15 114,064.49 114,091.84 114,119.19 114,146.54 114,173.91 114,201.28 114,228.66 114,256.04 114,283.43 114,310.83 114,338.23 114,365.64 114,393.06 114,420.48 114,447.91 114,475.34 114,502.79 114,530.24 114,557.69 114,585.15 114,612.62 114,640.10 114,667.58 114,695.07

27.19 27.20 27.21 27.21 27.22 27.23 27.23 27.24 27.25 27.25 27.26 27.27 27.27 27.28 27.29 27.29 27.30 27.30 27.31 27.32 27.32 27.33 27.34 27.34 27.35 27.36 27.36 27.37 27.38 27.38 27.39 27.40 27.40 27.41 27.42 27.42 27.43 27.44 27.44 27.45 27.46 27.46 27.47 27.48 27.48 27.49 27.50

113,464.57 113,491.77 113,518.98 113,546.19 113,573.41 113,600.64 113,627.87 113,655.11 113,682.36 113,709.61 113,736.87 113,764.14 113,791.41 113,818.69 113,845.97 113,873.27 113,900.56 113,927.87 113,955.18 113,982.50 114,009.82 114,037.15 114,064.49 114,091.84 114,119.19 114,146.54 114,173.91 114,201.28 114,228.66 114,256.04 114,283.43 114,310.83 114,338.23 114,365.64 114,393.06 114,420.48 114,447.91 114,475.34 114,502.79 114,530.24 114,557.69 114,585.15 114,612.62 114,640.10 114,667.58 114,695.07 114,722.57

574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620

114,722.57 114,750.07 114,777.58 114,805.09 114,832.61 114,860.14 114,887.68 114,915.22 114,942.77 114,970.32 114,997.88 115,025.45 115,053.02 115,080.61 115,108.19 115,135.79 115,163.39 115,191.00 115,218.61 115,246.23 115,273.86 115,301.49 115,329.13 115,356.78 115,384.44 115,412.10 115,439.76 115,467.44 115,495.12 115,522.81 115,550.50 115,578.20 115,605.91 115,633.62 115,661.34 115,689.07 115,716.80 115,744.54 115,772.29 115,800.04 115,827.80 115,855.57 115,883.34 115,911.12 115,938.91 115,966.70 115,994.50

27.50 27.51 27.52 27.52 27.53 27.53 27.54 27.55 27.55 27.56 27.57 27.57 27.58 27.59 27.59 27.60 27.61 27.61 27.62 27.63 27.63 27.64 27.65 27.65 27.66 27.67 27.67 27.68 27.69 27.69 27.70 27.71 27.71 27.72 27.73 27.73 27.74 27.75 27.75 27.76 27.77 27.77 27.78 27.79 27.79 27.80 27.81

114,750.07 114,777.58 114,805.09 114,832.61 114,860.14 114,887.68 114,915.22 114,942.77 114,970.32 114,997.88 115,025.45 115,053.02 115,080.61 115,108.19 115,135.79 115,163.39 115,191.00 115,218.61 115,246.23 115,273.86 115,301.49 115,329.13 115,356.78 115,384.44 115,412.10 115,439.76 115,467.44 115,495.12 115,522.81 115,550.50 115,578.20 115,605.91 115,633.62 115,661.34 115,689.07 115,716.80 115,744.54 115,772.29 115,800.04 115,827.80 115,855.57 115,883.34 115,911.12 115,938.91 115,966.70 115,994.50 116,022.31

621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667

116,022.31 116,050.12 116,077.95 116,105.77 116,133.61 116,161.45 116,189.29 116,217.15 116,245.01 116,272.87 116,300.75 116,328.63 116,356.51 116,384.41 116,412.31 116,440.22 116,468.13 116,496.05 116,523.98 116,551.91 116,579.85 116,607.80 116,635.75 116,663.71 116,691.68 116,719.65 116,747.64 116,775.62 116,803.62 116,831.62 116,859.63 116,887.64 116,915.66 116,943.69 116,971.72 116,999.76 117,027.81 117,055.87 117,083.93 117,112.00 117,140.07 117,168.15 117,196.24 117,224.34 117,252.44 117,280.55 117,308.66

27.81 27.82 27.83 27.83 27.84 27.85 27.85 27.86 27.87 27.87 27.88 27.89 27.89 27.90 27.91 27.91 27.92 27.93 27.93 27.94 27.95 27.95 27.96 27.97 27.97 27.98 27.99 27.99 28.00 28.01 28.01 28.02 28.03 28.03 28.04 28.05 28.05 28.06 28.07 28.07 28.08 28.09 28.09 28.10 28.11 28.12 28.12

116,050.12 116,077.95 116,105.77 116,133.61 116,161.45 116,189.29 116,217.15 116,245.01 116,272.87 116,300.75 116,328.63 116,356.51 116,384.41 116,412.31 116,440.22 116,468.13 116,496.05 116,523.98 116,551.91 116,579.85 116,607.80 116,635.75 116,663.71 116,691.68 116,719.65 116,747.64 116,775.62 116,803.62 116,831.62 116,859.63 116,887.64 116,915.66 116,943.69 116,971.72 116,999.76 117,027.81 117,055.87 117,083.93 117,112.00 117,140.07 117,168.15 117,196.24 117,224.34 117,252.44 117,280.55 117,308.66 117,336.78

668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714

117,336.78 117,364.91 117,393.05 117,421.19 117,449.34 117,477.49 117,505.66 117,533.83 117,562.00 117,590.18 117,618.37 117,646.57 117,674.77 117,702.98 117,731.20 117,759.42 117,787.65 117,815.89 117,844.13 117,872.38 117,900.64 117,928.90 117,957.17 117,985.45 118,013.74 118,042.03 118,070.32 118,098.63 118,126.94 118,155.26 118,183.58 118,211.91 118,240.25 118,268.60 118,296.95 118,325.31 118,353.67 118,382.05 118,410.43 118,438.81 118,467.21 118,495.61 118,524.01 118,552.42 118,580.85 118,609.27 118,637.71

28.13 28.14 28.14 28.15 28.16 28.16 28.17 28.18 28.18 28.19 28.20 28.20 28.21 28.22 28.22 28.23 28.24 28.24 28.25 28.26 28.26 28.27 28.28 28.28 28.29 28.30 28.30 28.31 28.32 28.32 28.33 28.34 28.35 28.35 28.36 28.37 28.37 28.38 28.39 28.39 28.40 28.41 28.41 28.42 28.43 28.43 28.44

117,364.91 117,393.05 117,421.19 117,449.34 117,477.49 117,505.66 117,533.83 117,562.00 117,590.18 117,618.37 117,646.57 117,674.77 117,702.98 117,731.20 117,759.42 117,787.65 117,815.89 117,844.13 117,872.38 117,900.64 117,928.90 117,957.17 117,985.45 118,013.74 118,042.03 118,070.32 118,098.63 118,126.94 118,155.26 118,183.58 118,211.91 118,240.25 118,268.60 118,296.95 118,325.31 118,353.67 118,382.05 118,410.43 118,438.81 118,467.21 118,495.61 118,524.01 118,552.42 118,580.85 118,609.27 118,637.71 118,666.15

715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761

118,666.15 118,694.59 118,723.05 118,751.51 118,779.98 118,808.45 118,836.93 118,865.42 118,893.92 118,922.42 118,950.93 118,979.44 119,007.97 119,036.49 119,065.03 119,093.57 119,122.12 119,150.68 119,179.24 119,207.81 119,236.39 119,264.98 119,293.57 119,322.16 119,350.77 119,379.38 119,408.00 119,436.62 119,465.26 119,493.89 119,522.54 119,551.19 119,579.85 119,608.52 119,637.19 119,665.87 119,694.56 119,723.25 119,751.95 119,780.66 119,809.38 119,838.10 119,866.83 119,895.56 119,924.30 119,953.05 119,981.81

28.45 28.45 28.46 28.47 28.47 28.48 28.49 28.50 28.50 28.51 28.52 28.52 28.53 28.54 28.54 28.55 28.56 28.56 28.57 28.58 28.58 28.59 28.60 28.60 28.61 28.62 28.63 28.63 28.64 28.65 28.65 28.66 28.67 28.67 28.68 28.69 28.69 28.70 28.71 28.71 28.72 28.73 28.74 28.74 28.75 28.76 28.76

118,694.59 118,723.05 118,751.51 118,779.98 118,808.45 118,836.93 118,865.42 118,893.92 118,922.42 118,950.93 118,979.44 119,007.97 119,036.49 119,065.03 119,093.57 119,122.12 119,150.68 119,179.24 119,207.81 119,236.39 119,264.98 119,293.57 119,322.16 119,350.77 119,379.38 119,408.00 119,436.62 119,465.26 119,493.89 119,522.54 119,551.19 119,579.85 119,608.52 119,637.19 119,665.87 119,694.56 119,723.25 119,751.95 119,780.66 119,809.38 119,838.10 119,866.83 119,895.56 119,924.30 119,953.05 119,981.81 120,010.57

762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808

120,010.57 120,039.34 120,068.12 120,096.90 120,125.69 120,154.49 120,183.29 120,212.10 120,240.92 120,269.75 120,298.58 120,327.42 120,356.26 120,385.11 120,413.97 120,442.84 120,471.71 120,500.59 120,529.48 120,558.38 120,587.28 120,616.18 120,645.10 120,674.02 120,702.95 120,731.89 120,760.83 120,789.78 120,818.73 120,847.70 120,876.67 120,905.64 120,934.63 120,963.62 120,992.62 121,021.62 121,050.64 121,079.65 121,108.68 121,137.71 121,166.75 121,195.80 121,224.85 121,253.91 121,282.98 121,312.06 121,341.14

28.77 28.78 28.78 28.79 28.80 28.80 28.81 28.82 28.82 28.83 28.84 28.85 28.85 28.86 28.87 28.87 28.88 28.89 28.89 28.90 28.91 28.91 28.92 28.93 28.94 28.94 28.95 28.96 28.96 28.97 28.98 28.98 28.99 29.00 29.01 29.01 29.02 29.03 29.03 29.04 29.05 29.05 29.06 29.07 29.07 29.08 29.09

120,039.34 120,068.12 120,096.90 120,125.69 120,154.49 120,183.29 120,212.10 120,240.92 120,269.75 120,298.58 120,327.42 120,356.26 120,385.11 120,413.97 120,442.84 120,471.71 120,500.59 120,529.48 120,558.38 120,587.28 120,616.18 120,645.10 120,674.02 120,702.95 120,731.89 120,760.83 120,789.78 120,818.73 120,847.70 120,876.67 120,905.64 120,934.63 120,963.62 120,992.62 121,021.62 121,050.64 121,079.65 121,108.68 121,137.71 121,166.75 121,195.80 121,224.85 121,253.91 121,282.98 121,312.06 121,341.14 121,370.23

809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855

121,370.23 121,399.32 121,428.43 121,457.53 121,486.65 121,515.77 121,544.91 121,574.04 121,603.19 121,632.34 121,661.50 121,690.66 121,719.84 121,749.01 121,778.20 121,807.39 121,836.59 121,865.80 121,895.02 121,924.24 121,953.47 121,982.70 122,011.94 122,041.19 122,070.45 122,099.71 122,128.98 122,158.26 122,187.55 122,216.84 122,246.14 122,275.44 122,304.75 122,334.07 122,363.40 122,392.73 122,422.08 122,451.42 122,480.78 122,510.14 122,539.51 122,568.88 122,598.27 122,627.66 122,657.05 122,686.46 122,715.87

29.10 29.10 29.11 29.12 29.12 29.13 29.14 29.14 29.15 29.16 29.17 29.17 29.18 29.19 29.19 29.20 29.21 29.21 29.22 29.23 29.24 29.24 29.25 29.26 29.26 29.27 29.28 29.28 29.29 29.30 29.31 29.31 29.32 29.33 29.33 29.34 29.35 29.35 29.36 29.37 29.38 29.38 29.39 29.40 29.40 29.41 29.42

121,399.32 121,428.43 121,457.53 121,486.65 121,515.77 121,544.91 121,574.04 121,603.19 121,632.34 121,661.50 121,690.66 121,719.84 121,749.01 121,778.20 121,807.39 121,836.59 121,865.80 121,895.02 121,924.24 121,953.47 121,982.70 122,011.94 122,041.19 122,070.45 122,099.71 122,128.98 122,158.26 122,187.55 122,216.84 122,246.14 122,275.44 122,304.75 122,334.07 122,363.40 122,392.73 122,422.08 122,451.42 122,480.78 122,510.14 122,539.51 122,568.88 122,598.27 122,627.66 122,657.05 122,686.46 122,715.87 122,745.29

856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900 901 902

122,745.29 122,774.71 122,804.15 122,833.58 122,863.03 122,892.48 122,921.94 122,951.41 122,980.89 123,010.37 123,039.86 123,069.35 123,098.86 123,128.37 123,157.88 123,187.41 123,216.94 123,246.48 123,276.02 123,305.58 123,335.13 123,364.70 123,394.27 123,423.86 123,453.44 123,483.04 123,512.64 123,542.25 123,571.87 123,601.49 123,631.12 123,660.76 123,690.40 123,720.05 123,749.71 123,779.38 123,809.05 123,838.73 123,868.42 123,898.11 123,927.82 123,957.52 123,987.24 124,016.96 124,046.69 124,076.43 124,106.18

29.43 29.43 29.44 29.45 29.45 29.46 29.47 29.47 29.48 29.49 29.50 29.50 29.51 29.52 29.52 29.53 29.54 29.55 29.55 29.56 29.57 29.57 29.58 29.59 29.60 29.60 29.61 29.62 29.62 29.63 29.64 29.64 29.65 29.66 29.67 29.67 29.68 29.69 29.69 29.70 29.71 29.72 29.72 29.73 29.74 29.74 29.75

122,774.71 122,804.15 122,833.58 122,863.03 122,892.48 122,921.94 122,951.41 122,980.89 123,010.37 123,039.86 123,069.35 123,098.86 123,128.37 123,157.88 123,187.41 123,216.94 123,246.48 123,276.02 123,305.58 123,335.13 123,364.70 123,394.27 123,423.86 123,453.44 123,483.04 123,512.64 123,542.25 123,571.87 123,601.49 123,631.12 123,660.76 123,690.40 123,720.05 123,749.71 123,779.38 123,809.05 123,838.73 123,868.42 123,898.11 123,927.82 123,957.52 123,987.24 124,016.96 124,046.69 124,076.43 124,106.18 124,135.93

903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949

124,135.93 124,165.69 124,195.45 124,225.22 124,255.00 124,284.79 124,314.59 124,344.39 124,374.20 124,404.01 124,433.83 124,463.66 124,493.50 124,523.35 124,553.20 124,583.06 124,612.92 124,642.79 124,672.67 124,702.56 124,732.46 124,762.36 124,792.27 124,822.18 124,852.11 124,882.04 124,911.97 124,941.92 124,971.87 125,001.83 125,031.80 125,061.77 125,091.75 125,121.74 125,151.73 125,181.73 125,211.74 125,241.76 125,271.78 125,301.81 125,331.85 125,361.90 125,391.95 125,422.01 125,452.08 125,482.15 125,512.23

29.76 29.77 29.77 29.78 29.79 29.79 29.80 29.81 29.82 29.82 29.83 29.84 29.84 29.85 29.86 29.87 29.87 29.88 29.89 29.89 29.90 29.91 29.92 29.92 29.93 29.94 29.94 29.95 29.96 29.97 29.97 29.98 29.99 29.99 30.00 30.01 30.02 30.02 30.03 30.04 30.05 30.05 30.06 30.07 30.07 30.08 30.09

124,165.69 124,195.45 124,225.22 124,255.00 124,284.79 124,314.59 124,344.39 124,374.20 124,404.01 124,433.83 124,463.66 124,493.50 124,523.35 124,553.20 124,583.06 124,612.92 124,642.79 124,672.67 124,702.56 124,732.46 124,762.36 124,792.27 124,822.18 124,852.11 124,882.04 124,911.97 124,941.92 124,971.87 125,001.83 125,031.80 125,061.77 125,091.75 125,121.74 125,151.73 125,181.73 125,211.74 125,241.76 125,271.78 125,301.81 125,331.85 125,361.90 125,391.95 125,422.01 125,452.08 125,482.15 125,512.23 125,542.32

950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996

125,542.32 125,572.42 125,602.52 125,632.63 125,662.75 125,692.87 125,723.00 125,753.14 125,783.29 125,813.44 125,843.60 125,873.77 125,903.95 125,934.13 125,964.32 125,994.52 126,024.72 126,054.93 126,085.15 126,115.38 126,145.61 126,175.85 126,206.10 126,236.35 126,266.61 126,296.88 126,327.16 126,357.44 126,387.74 126,418.03 126,448.34 126,478.65 126,508.97 126,539.30 126,569.63 126,599.98 126,630.33 126,660.68 126,691.05 126,721.42 126,751.80 126,782.18 126,812.57 126,842.98 126,873.38 126,903.80 126,934.22

30.10 30.10 30.11 30.12 30.12 30.13 30.14 30.15 30.15 30.16 30.17 30.18 30.18 30.19 30.20 30.20 30.21 30.22 30.23 30.23 30.24 30.25 30.25 30.26 30.27 30.28 30.28 30.29 30.30 30.31 30.31 30.32 30.33 30.33 30.34 30.35 30.36 30.36 30.37 30.38 30.39 30.39 30.40 30.41 30.41 30.42 30.43

125,572.42 125,602.52 125,632.63 125,662.75 125,692.87 125,723.00 125,753.14 125,783.29 125,813.44 125,843.60 125,873.77 125,903.95 125,934.13 125,964.32 125,994.52 126,024.72 126,054.93 126,085.15 126,115.38 126,145.61 126,175.85 126,206.10 126,236.35 126,266.61 126,296.88 126,327.16 126,357.44 126,387.74 126,418.03 126,448.34 126,478.65 126,508.97 126,539.30 126,569.63 126,599.98 126,630.33 126,660.68 126,691.05 126,721.42 126,751.80 126,782.18 126,812.57 126,842.98 126,873.38 126,903.80 126,934.22 126,964.65

997 998 999 1,000 1,001 1,002 1,003 1,004 1,005 1,006 1,007 1,008 1,009 1,010 1,011 1,012 1,013 1,014 1,015 1,016 1,017 1,018 1,019 1,020 1,021 1,022 1,023 1,024 1,025 1,026 1,027 1,028 1,029 1,030 1,031 1,032 1,033 1,034 1,035 1,036 1,037 1,038 1,039 1,040 1,041 1,042 1,043

126,964.65 126,995.09 127,025.53 127,055.98 127,086.44 127,116.91 127,147.38 127,177.86 127,208.35 127,238.84 127,269.35 127,299.85 127,330.37 127,360.90 127,391.43 127,421.97 127,452.51 127,483.07 127,513.63 127,544.20 127,574.77 127,605.36 127,635.95 127,666.54 127,697.15 127,727.76 127,758.38 127,789.01 127,819.64 127,850.28 127,880.93 127,911.59 127,942.25 127,972.92 128,003.60 128,034.29 128,064.98 128,095.68 128,126.39 128,157.10 128,187.83 128,218.56 128,249.29 128,280.04 128,310.79 128,341.55 128,372.32

30.44 30.44 30.45 30.46 30.47 30.47 30.48 30.49 30.50 30.50 30.51 30.52 30.52 30.53 30.54 30.55 30.55 30.56 30.57 30.58 30.58 30.59 30.60 30.60 30.61 30.62 30.63 30.63 30.64 30.65 30.66 30.66 30.67 30.68 30.69 30.69 30.70 30.71 30.72 30.72 30.73 30.74 30.74 30.75 30.76 30.77 30.77

126,995.09 127,025.53 127,055.98 127,086.44 127,116.91 127,147.38 127,177.86 127,208.35 127,238.84 127,269.35 127,299.85 127,330.37 127,360.90 127,391.43 127,421.97 127,452.51 127,483.07 127,513.63 127,544.20 127,574.77 127,605.36 127,635.95 127,666.54 127,697.15 127,727.76 127,758.38 127,789.01 127,819.64 127,850.28 127,880.93 127,911.59 127,942.25 127,972.92 128,003.60 128,034.29 128,064.98 128,095.68 128,126.39 128,157.10 128,187.83 128,218.56 128,249.29 128,280.04 128,310.79 128,341.55 128,372.32 128,403.09

1,044 1,045 1,046 1,047 1,048 1,049 1,050 1,051 1,052 1,053 1,054 1,055 1,056 1,057 1,058 1,059 1,060 1,061 1,062 1,063 1,064 1,065 1,066 1,067 1,068 1,069 1,070 1,071 1,072 1,073 1,074 1,075 1,076 1,077 1,078 1,079 1,080 1,081 1,082 1,083 1,084 1,085 1,086 1,087 1,088 1,089 1,090

128,403.09 128,433.87 128,464.66 128,495.46 128,526.26 128,557.07 128,587.89 128,618.72 128,649.55 128,680.39 128,711.24 128,742.09 128,772.96 128,803.83 128,834.71 128,865.59 128,896.48 128,927.38 128,958.29 128,989.20 129,020.13 129,051.06 129,081.99 129,112.94 129,143.89 129,174.85 129,205.81 129,236.79 129,267.77 129,298.76 129,329.76 129,360.76 129,391.77 129,422.79 129,453.81 129,484.85 129,515.89 129,546.94 129,577.99 129,609.06 129,640.13 129,671.21 129,702.29 129,733.38 129,764.48 129,795.59 129,826.71

30.78 30.79 30.80 30.80 30.81 30.82 30.83 30.83 30.84 30.85 30.86 30.86 30.87 30.88 30.89 30.89 30.90 30.91 30.91 30.92 30.93 30.94 30.94 30.95 30.96 30.97 30.97 30.98 30.99 31.00 31.00 31.01 31.02 31.03 31.03 31.04 31.05 31.06 31.06 31.07 31.08 31.09 31.09 31.10 31.11 31.12 31.12

128,433.87 128,464.66 128,495.46 128,526.26 128,557.07 128,587.89 128,618.72 128,649.55 128,680.39 128,711.24 128,742.09 128,772.96 128,803.83 128,834.71 128,865.59 128,896.48 128,927.38 128,958.29 128,989.20 129,020.13 129,051.06 129,081.99 129,112.94 129,143.89 129,174.85 129,205.81 129,236.79 129,267.77 129,298.76 129,329.76 129,360.76 129,391.77 129,422.79 129,453.81 129,484.85 129,515.89 129,546.94 129,577.99 129,609.06 129,640.13 129,671.21 129,702.29 129,733.38 129,764.48 129,795.59 129,826.71 129,857.83

1,091 1,092 1,093 1,094 1,095 1,096 1,097 1,098 1,099 1,100 1,101 1,102 1,103 1,104 1,105 1,106 1,107 1,108 1,109 1,110 1,111 1,112 1,113 1,114 1,115 1,116 1,117 1,118 1,119 1,120 1,121 1,122 1,123 1,124 1,125 1,126 1,127 1,128 1,129 1,130 1,131 1,132 1,133 1,134 1,135 1,136 1,137

129,857.83 129,888.96 129,920.10 129,951.24 129,982.40 130,013.56 130,044.72 130,075.90 130,107.08 130,138.27 130,169.47 130,200.67 130,231.89 130,263.11 130,294.33 130,325.57 130,356.81 130,388.06 130,419.32 130,450.58 130,481.86 130,513.14 130,544.42 130,575.72 130,607.02 130,638.33 130,669.65 130,700.97 130,732.31 130,763.65 130,794.99 130,826.35 130,857.71 130,889.08 130,920.46 130,951.84 130,983.24 131,014.64 131,046.04 131,077.46 131,108.88 131,140.31 131,171.75 131,203.19 131,234.65 131,266.11 131,297.58

31.13 31.14 31.15 31.15 31.16 31.17 31.18 31.18 31.19 31.20 31.21 31.21 31.22 31.23 31.23 31.24 31.25 31.26 31.26 31.27 31.28 31.29 31.29 31.30 31.31 31.32 31.32 31.33 31.34 31.35 31.35 31.36 31.37 31.38 31.39 31.39 31.40 31.41 31.42 31.42 31.43 31.44 31.45 31.45 31.46 31.47 31.48

129,888.96 129,920.10 129,951.24 129,982.40 130,013.56 130,044.72 130,075.90 130,107.08 130,138.27 130,169.47 130,200.67 130,231.89 130,263.11 130,294.33 130,325.57 130,356.81 130,388.06 130,419.32 130,450.58 130,481.86 130,513.14 130,544.42 130,575.72 130,607.02 130,638.33 130,669.65 130,700.97 130,732.31 130,763.65 130,794.99 130,826.35 130,857.71 130,889.08 130,920.46 130,951.84 130,983.24 131,014.64 131,046.04 131,077.46 131,108.88 131,140.31 131,171.75 131,203.19 131,234.65 131,266.11 131,297.58 131,329.05

1,138 1,139 1,140 1,141 1,142 1,143 1,144 1,145 1,146 1,147 1,148 1,149 1,150 1,151 1,152 1,153 1,154 1,155 1,156 1,157 1,158 1,159 1,160 1,161 1,162 1,163 1,164 1,165 1,166 1,167 1,168 1,169 1,170 1,171 1,172 1,173 1,174 1,175 1,176 1,177 1,178 1,179 1,180 1,181 1,182 1,183 1,184

131,329.05 131,360.53 131,392.02 131,423.52 131,455.03 131,486.54 131,518.06 131,549.59 131,581.13 131,612.67 131,644.22 131,675.78 131,707.35 131,738.92 131,770.50 131,802.09 131,833.69 131,865.29 131,896.90 131,928.52 131,960.15 131,991.78 132,023.42 132,055.07 132,086.73 132,118.39 132,150.07 132,181.75 132,213.43 132,245.13 132,276.83 132,308.54 132,340.26 132,371.98 132,403.72 132,435.46 132,467.21 132,498.96 132,530.73 132,562.50 132,594.28 132,626.06 132,657.86 132,689.66 132,721.47 132,753.28 132,785.11

31.48 31.49 31.50 31.51 31.51 31.52 31.53 31.54 31.54 31.55 31.56 31.57 31.57 31.58 31.59 31.60 31.60 31.61 31.62 31.63 31.63 31.64 31.65 31.66 31.66 31.67 31.68 31.69 31.70 31.70 31.71 31.72 31.73 31.73 31.74 31.75 31.76 31.76 31.77 31.78 31.79 31.79 31.80 31.81 31.82 31.82 31.83

131,360.53 131,392.02 131,423.52 131,455.03 131,486.54 131,518.06 131,549.59 131,581.13 131,612.67 131,644.22 131,675.78 131,707.35 131,738.92 131,770.50 131,802.09 131,833.69 131,865.29 131,896.90 131,928.52 131,960.15 131,991.78 132,023.42 132,055.07 132,086.73 132,118.39 132,150.07 132,181.75 132,213.43 132,245.13 132,276.83 132,308.54 132,340.26 132,371.98 132,403.72 132,435.46 132,467.21 132,498.96 132,530.73 132,562.50 132,594.28 132,626.06 132,657.86 132,689.66 132,721.47 132,753.28 132,785.11 132,816.94

1,185 1,186 1,187 1,188 1,189 1,190 1,191 1,192 1,193 1,194 1,195 1,196 1,197 1,198 1,199 1,200 1,201 1,202 1,203 1,204 1,205 1,206 1,207 1,208 1,209 1,210 1,211 1,212 1,213 1,214 1,215 1,216 1,217 1,218 1,219 1,220 1,221 1,222 1,223 1,224 1,225 1,226 1,227 1,228 1,229 1,230 1,231

132,816.94 132,848.78 132,880.63 132,912.48 132,944.34 132,976.21 133,008.09 133,039.98 133,071.87 133,103.77 133,135.68 133,167.60 133,199.52 133,231.45 133,263.39 133,295.34 133,327.29 133,359.25 133,391.22 133,423.20 133,455.19 133,487.18 133,519.18 133,551.19 133,583.20 133,615.23 133,647.26 133,679.30 133,711.34 133,743.40 133,775.46 133,807.53 133,839.60 133,871.69 133,903.78 133,935.88 133,967.99 134,000.11 134,032.23 134,064.36 134,096.50 134,128.64 134,160.80 134,192.96 134,225.13 134,257.31 134,289.49

31.84 31.85 31.85 31.86 31.87 31.88 31.89 31.89 31.90 31.91 31.92 31.92 31.93 31.94 31.95 31.95 31.96 31.97 31.98 31.99 31.99 32.00 32.01 32.02 32.02 32.03 32.04 32.05 32.05 32.06 32.07 32.08 32.08 32.09 32.10 32.11 32.12 32.12 32.13 32.14 32.15 32.15 32.16 32.17 32.18 32.18 32.19

132,848.78 132,880.63 132,912.48 132,944.34 132,976.21 133,008.09 133,039.98 133,071.87 133,103.77 133,135.68 133,167.60 133,199.52 133,231.45 133,263.39 133,295.34 133,327.29 133,359.25 133,391.22 133,423.20 133,455.19 133,487.18 133,519.18 133,551.19 133,583.20 133,615.23 133,647.26 133,679.30 133,711.34 133,743.40 133,775.46 133,807.53 133,839.60 133,871.69 133,903.78 133,935.88 133,967.99 134,000.11 134,032.23 134,064.36 134,096.50 134,128.64 134,160.80 134,192.96 134,225.13 134,257.31 134,289.49 134,321.69

1,232 1,233 1,234 1,235 1,236 1,237 1,238 1,239 1,240 1,241 1,242 1,243 1,244 1,245 1,246 1,247 1,248 1,249 1,250 1,251 1,252 1,253 1,254 1,255 1,256 1,257 1,258 1,259 1,260 1,261 1,262 1,263 1,264 1,265 1,266 1,267 1,268 1,269 1,270 1,271 1,272 1,273 1,274 1,275 1,276 1,277 1,278

134,321.69 134,353.89 134,386.09 134,418.31 134,450.53 134,482.76 134,515.00 134,547.25 134,579.50 134,611.77 134,644.04 134,676.31 134,708.60 134,740.89 134,773.19 134,805.50 134,837.82 134,870.14 134,902.48 134,934.81 134,967.16 134,999.52 135,031.88 135,064.25 135,096.63 135,129.02 135,161.41 135,193.81 135,226.22 135,258.64 135,291.06 135,323.50 135,355.94 135,388.38 135,420.84 135,453.30 135,485.78 135,518.26 135,550.74 135,583.24 135,615.74 135,648.25 135,680.77 135,713.30 135,745.83 135,778.37 135,810.92

32.20 32.21 32.22 32.22 32.23 32.24 32.25 32.25 32.26 32.27 32.28 32.29 32.29 32.30 32.31 32.32 32.32 32.33 32.34 32.35 32.36 32.36 32.37 32.38 32.39 32.39 32.40 32.41 32.42 32.43 32.43 32.44 32.45 32.46 32.46 32.47 32.48 32.49 32.50 32.50 32.51 32.52 32.53 32.53 32.54 32.55 32.56

134,353.89 134,386.09 134,418.31 134,450.53 134,482.76 134,515.00 134,547.25 134,579.50 134,611.77 134,644.04 134,676.31 134,708.60 134,740.89 134,773.19 134,805.50 134,837.82 134,870.14 134,902.48 134,934.81 134,967.16 134,999.52 135,031.88 135,064.25 135,096.63 135,129.02 135,161.41 135,193.81 135,226.22 135,258.64 135,291.06 135,323.50 135,355.94 135,388.38 135,420.84 135,453.30 135,485.78 135,518.26 135,550.74 135,583.24 135,615.74 135,648.25 135,680.77 135,713.30 135,745.83 135,778.37 135,810.92 135,843.48

1,279 1,280 1,281 1,282 1,283 1,284 1,285 1,286 1,287 1,288 1,289 1,290 1,291 1,292 1,293 1,294 1,295 1,296 1,297 1,298 1,299 1,300 1,301 1,302 1,303 1,304 1,305 1,306 1,307 1,308 1,309 1,310 1,311 1,312 1,313 1,314 1,315 1,316 1,317 1,318 1,319 1,320 1,321 1,322 1,323 1,324 1,325

135,843.48 135,876.04 135,908.62 135,941.20 135,973.79 136,006.38 136,038.99 136,071.60 136,104.22 136,136.85 136,169.48 136,202.13 136,234.78 136,267.44 136,300.10 136,332.78 136,365.46 136,398.15 136,430.85 136,463.55 136,496.27 136,528.99 136,561.72 136,594.46 136,627.20 136,659.96 136,692.72 136,725.49 136,758.26 136,791.05 136,823.84 136,856.64 136,889.45 136,922.26 136,955.09 136,987.92 137,020.76 137,053.61 137,086.46 137,119.32 137,152.20 137,185.07 137,217.96 137,250.86 137,283.76 137,316.67 137,349.59

32.57 32.57 32.58 32.59 32.60 32.60 32.61 32.62 32.63 32.64 32.64 32.65 32.66 32.67 32.67 32.68 32.69 32.70 32.71 32.71 32.72 32.73 32.74 32.75 32.75 32.76 32.77 32.78 32.78 32.79 32.80 32.81 32.82 32.82 32.83 32.84 32.85 32.86 32.86 32.87 32.88 32.89 32.89 32.90 32.91 32.92 32.93

135,876.04 135,908.62 135,941.20 135,973.79 136,006.38 136,038.99 136,071.60 136,104.22 136,136.85 136,169.48 136,202.13 136,234.78 136,267.44 136,300.10 136,332.78 136,365.46 136,398.15 136,430.85 136,463.55 136,496.27 136,528.99 136,561.72 136,594.46 136,627.20 136,659.96 136,692.72 136,725.49 136,758.26 136,791.05 136,823.84 136,856.64 136,889.45 136,922.26 136,955.09 136,987.92 137,020.76 137,053.61 137,086.46 137,119.32 137,152.20 137,185.07 137,217.96 137,250.86 137,283.76 137,316.67 137,349.59 137,382.51

1,326 1,327 1,328 1,329 1,330 1,331 1,332 1,333 1,334 1,335 1,336 1,337 1,338 1,339 1,340 1,341 1,342 1,343 1,344 1,345 1,346 1,347 1,348 1,349 1,350 1,351 1,352 1,353 1,354 1,355 1,356 1,357 1,358 1,359 1,360 1,361 1,362 1,363 1,364 1,365 1,366 1,367 1,368 1,369 1,370 1,371 1,372

137,382.51 137,415.45 137,448.39 137,481.34 137,514.30 137,547.26 137,580.24 137,613.22 137,646.21 137,679.21 137,712.21 137,745.22 137,778.25 137,811.27 137,844.31 137,877.36 137,910.41 137,943.47 137,976.54 138,009.61 138,042.70 138,075.79 138,108.89 138,142.00 138,175.12 138,208.24 138,241.37 138,274.51 138,307.66 138,340.82 138,373.98 138,407.15 138,440.33 138,473.52 138,506.72 138,539.92 138,573.13 138,606.35 138,639.58 138,672.81 138,706.06 138,739.31 138,772.57 138,805.84 138,839.11 138,872.39 138,905.69

32.93 32.94 32.95 32.96 32.97 32.97 32.98 32.99 33.00 33.01 33.01 33.02 33.03 33.04 33.04 33.05 33.06 33.07 33.08 33.08 33.09 33.10 33.11 33.12 33.12 33.13 33.14 33.15 33.16 33.16 33.17 33.18 33.19 33.20 33.20 33.21 33.22 33.23 33.24 33.24 33.25 33.26 33.27 33.28 33.28 33.29 33.30

137,415.45 137,448.39 137,481.34 137,514.30 137,547.26 137,580.24 137,613.22 137,646.21 137,679.21 137,712.21 137,745.22 137,778.25 137,811.27 137,844.31 137,877.36 137,910.41 137,943.47 137,976.54 138,009.61 138,042.70 138,075.79 138,108.89 138,142.00 138,175.12 138,208.24 138,241.37 138,274.51 138,307.66 138,340.82 138,373.98 138,407.15 138,440.33 138,473.52 138,506.72 138,539.92 138,573.13 138,606.35 138,639.58 138,672.81 138,706.06 138,739.31 138,772.57 138,805.84 138,839.11 138,872.39 138,905.69 138,938.98

1,373 1,374 1,375 1,376 1,377 1,378 1,379 1,380 1,381 1,382 1,383 1,384 1,385 1,386 1,387 1,388 1,389 1,390 1,391 1,392 1,393 1,394 1,395 1,396 1,397 1,398 1,399 1,400 1,401 1,402 1,403 1,404 1,405 1,406 1,407 1,408 1,409 1,410 1,411 1,412 1,413 1,414 1,415 1,416 1,417 1,418 1,419

138,938.98 138,972.29 139,005.61 139,038.93 139,072.26 139,105.60 139,138.95 139,172.30 139,205.67 139,239.04 139,272.42 139,305.80 139,339.20 139,372.60 139,406.01 139,439.43 139,472.86 139,506.30 139,539.74 139,573.19 139,606.65 139,640.12 139,673.59 139,707.08 139,740.57 139,774.07 139,807.57 139,841.09 139,874.61 139,908.14 139,941.68 139,975.23 140,008.79 140,042.35 140,075.92 140,109.50 140,143.09 140,176.69 140,210.29 140,243.90 140,277.52 140,311.15 140,344.79 140,378.43 140,412.08 140,445.74 140,479.41

33.31 33.32 33.32 33.33 33.34 33.35 33.36 33.36 33.37 33.38 33.39 33.40 33.40 33.41 33.42 33.43 33.44 33.44 33.45 33.46 33.47 33.48 33.48 33.49 33.50 33.51 33.52 33.52 33.53 33.54 33.55 33.56 33.56 33.57 33.58 33.59 33.60 33.60 33.61 33.62 33.63 33.64 33.64 33.65 33.66 33.67 33.68

138,972.29 139,005.61 139,038.93 139,072.26 139,105.60 139,138.95 139,172.30 139,205.67 139,239.04 139,272.42 139,305.80 139,339.20 139,372.60 139,406.01 139,439.43 139,472.86 139,506.30 139,539.74 139,573.19 139,606.65 139,640.12 139,673.59 139,707.08 139,740.57 139,774.07 139,807.57 139,841.09 139,874.61 139,908.14 139,941.68 139,975.23 140,008.79 140,042.35 140,075.92 140,109.50 140,143.09 140,176.69 140,210.29 140,243.90 140,277.52 140,311.15 140,344.79 140,378.43 140,412.08 140,445.74 140,479.41 140,513.09

1,420 1,421 1,422 1,423 1,424 1,425 1,426 1,427 1,428 1,429 1,430 1,431 1,432 1,433 1,434 1,435 1,436 1,437 1,438 1,439 1,440 1,441 1,442 1,443 1,444 1,445 1,446 1,447 1,448 1,449 1,450 1,451 1,452 1,453 1,454 1,455 1,456 1,457 1,458 1,459 1,460 1,461 1,462 1,463 1,464 1,465 1,466

140,513.09 140,546.77 140,580.47 140,614.17 140,647.88 140,681.59 140,715.32 140,749.05 140,782.79 140,816.54 140,850.30 140,884.07 140,917.84 140,951.62 140,985.41 141,019.21 141,053.01 141,086.83 141,120.65 141,154.48 141,188.32 141,222.17 141,256.02 141,289.88 141,323.75 141,357.63 141,391.52 141,425.42 141,459.32 141,493.23 141,527.15 141,561.08 141,595.01 141,628.96 141,662.91 141,696.87 141,730.84 141,764.81 141,798.80 141,832.79 141,866.79 141,900.80 141,934.82 141,968.85 142,002.88 142,036.92 142,070.97

33.68 33.69 33.70 33.71 33.72 33.73 33.73 33.74 33.75 33.76 33.77 33.77 33.78 33.79 33.80 33.81 33.81 33.82 33.83 33.84 33.85 33.85 33.86 33.87 33.88 33.89 33.90 33.90 33.91 33.92 33.93 33.94 33.94 33.95 33.96 33.97 33.98 33.98 33.99 34.00 34.01 34.02 34.03 34.03 34.04 34.05 34.06

140,546.77 140,580.47 140,614.17 140,647.88 140,681.59 140,715.32 140,749.05 140,782.79 140,816.54 140,850.30 140,884.07 140,917.84 140,951.62 140,985.41 141,019.21 141,053.01 141,086.83 141,120.65 141,154.48 141,188.32 141,222.17 141,256.02 141,289.88 141,323.75 141,357.63 141,391.52 141,425.42 141,459.32 141,493.23 141,527.15 141,561.08 141,595.01 141,628.96 141,662.91 141,696.87 141,730.84 141,764.81 141,798.80 141,832.79 141,866.79 141,900.80 141,934.82 141,968.85 142,002.88 142,036.92 142,070.97 142,105.03

1,467 1,468 1,469 1,470 1,471 1,472 1,473 1,474 1,475 1,476 1,477 1,478 1,479 1,480 1,481 1,482 1,483 1,484 1,485 1,486 1,487 1,488 1,489 1,490 1,491 1,492 1,493 1,494 1,495 1,496 1,497 1,498 1,499 1,500 1,501 1,502 1,503 1,504 1,505 1,506 1,507 1,508 1,509 1,510 1,511 1,512 1,513

142,105.03 142,139.10 142,173.17 142,207.25 142,241.34 142,275.44 142,309.55 142,343.66 142,377.79 142,411.92 142,446.06 142,480.21 142,514.36 142,548.53 142,582.70 142,616.88 142,651.07 142,685.27 142,719.47 142,753.69 142,787.91 142,822.14 142,856.38 142,890.62 142,924.88 142,959.14 142,993.41 143,027.69 143,061.98 143,096.27 143,130.58 143,164.89 143,199.21 143,233.54 143,267.88 143,302.22 143,336.57 143,370.94 143,405.30 143,439.68 143,474.07 143,508.46 143,542.87 143,577.28 143,611.70 143,646.12 143,680.56

34.07 34.07 34.08 34.09 34.10 34.11 34.12 34.12 34.13 34.14 34.15 34.16 34.16 34.17 34.18 34.19 34.20 34.21 34.21 34.22 34.23 34.24 34.25 34.25 34.26 34.27 34.28 34.29 34.30 34.30 34.31 34.32 34.33 34.34 34.35 34.35 34.36 34.37 34.38 34.39 34.39 34.40 34.41 34.42 34.43 34.44 34.44

142,139.10 142,173.17 142,207.25 142,241.34 142,275.44 142,309.55 142,343.66 142,377.79 142,411.92 142,446.06 142,480.21 142,514.36 142,548.53 142,582.70 142,616.88 142,651.07 142,685.27 142,719.47 142,753.69 142,787.91 142,822.14 142,856.38 142,890.62 142,924.88 142,959.14 142,993.41 143,027.69 143,061.98 143,096.27 143,130.58 143,164.89 143,199.21 143,233.54 143,267.88 143,302.22 143,336.57 143,370.94 143,405.30 143,439.68 143,474.07 143,508.46 143,542.87 143,577.28 143,611.70 143,646.12 143,680.56 143,715.00

1,514 1,515 1,516 1,517 1,518 1,519 1,520 1,521 1,522 1,523 1,524 1,525 1,526 1,527 1,528 1,529 1,530 1,531 1,532 1,533 1,534 1,535 1,536 1,537 1,538 1,539 1,540 1,541 1,542 1,543 1,544 1,545 1,546 1,547 1,548 1,549 1,550 1,551 1,552 1,553 1,554 1,555 1,556 1,557 1,558 1,559 1,560

143,715.00 143,749.46 143,783.92 143,818.39 143,852.86 143,887.35 143,921.84 143,956.34 143,990.85 144,025.37 144,059.90 144,094.43 144,128.98 144,163.53 144,198.09 144,232.66 144,267.23 144,301.82 144,336.41 144,371.01 144,405.62 144,440.24 144,474.86 144,509.50 144,544.14 144,578.79 144,613.45 144,648.12 144,682.79 144,717.48 144,752.17 144,786.87 144,821.58 144,856.30 144,891.02 144,925.76 144,960.50 144,995.25 145,030.01 145,064.78 145,099.55 145,134.34 145,169.13 145,203.93 145,238.74 145,273.56 145,308.38

34.45 34.46 34.47 34.48 34.49 34.49 34.50 34.51 34.52 34.53 34.53 34.54 34.55 34.56 34.57 34.58 34.58 34.59 34.60 34.61 34.62 34.63 34.63 34.64 34.65 34.66 34.67 34.68 34.68 34.69 34.70 34.71 34.72 34.73 34.73 34.74 34.75 34.76 34.77 34.78 34.78 34.79 34.80 34.81 34.82 34.83 34.83

143,749.46 143,783.92 143,818.39 143,852.86 143,887.35 143,921.84 143,956.34 143,990.85 144,025.37 144,059.90 144,094.43 144,128.98 144,163.53 144,198.09 144,232.66 144,267.23 144,301.82 144,336.41 144,371.01 144,405.62 144,440.24 144,474.86 144,509.50 144,544.14 144,578.79 144,613.45 144,648.12 144,682.79 144,717.48 144,752.17 144,786.87 144,821.58 144,856.30 144,891.02 144,925.76 144,960.50 144,995.25 145,030.01 145,064.78 145,099.55 145,134.34 145,169.13 145,203.93 145,238.74 145,273.56 145,308.38 145,343.22

1,561 1,562 1,563 1,564 1,565 1,566 1,567 1,568 1,569 1,570 1,571 1,572 1,573 1,574 1,575 1,576 1,577 1,578 1,579 1,580 1,581 1,582 1,583 1,584 1,585 1,586 1,587 1,588 1,589 1,590 1,591 1,592 1,593 1,594 1,595 1,596 1,597 1,598 1,599 1,600 1,601 1,602 1,603 1,604 1,605 1,606 1,607

145,343.22 145,378.06 145,412.91 145,447.77 145,482.64 145,517.51 145,552.40 145,587.29 145,622.19 145,657.10 145,692.02 145,726.95 145,761.88 145,796.82 145,831.78 145,866.73 145,901.70 145,936.68 145,971.66 146,006.66 146,041.66 146,076.67 146,111.69 146,146.71 146,181.75 146,216.79 146,251.84 146,286.91 146,321.97 146,357.05 146,392.14 146,427.23 146,462.33 146,497.44 146,532.56 146,567.69 146,602.83 146,637.97 146,673.12 146,708.29 146,743.46 146,778.63 146,813.82 146,849.02 146,884.22 146,919.43 146,954.65

34.84 34.85 34.86 34.87 34.88 34.88 34.89 34.90 34.91 34.92 34.93 34.93 34.94 34.95 34.96 34.97 34.98 34.98 34.99 35.00 35.01 35.02 35.03 35.04 35.04 35.05 35.06 35.07 35.08 35.09 35.09 35.10 35.11 35.12 35.13 35.14 35.14 35.15 35.16 35.17 35.18 35.19 35.20 35.20 35.21 35.22 35.23

145,378.06 145,412.91 145,447.77 145,482.64 145,517.51 145,552.40 145,587.29 145,622.19 145,657.10 145,692.02 145,726.95 145,761.88 145,796.82 145,831.78 145,866.73 145,901.70 145,936.68 145,971.66 146,006.66 146,041.66 146,076.67 146,111.69 146,146.71 146,181.75 146,216.79 146,251.84 146,286.91 146,321.97 146,357.05 146,392.14 146,427.23 146,462.33 146,497.44 146,532.56 146,567.69 146,602.83 146,637.97 146,673.12 146,708.29 146,743.46 146,778.63 146,813.82 146,849.02 146,884.22 146,919.43 146,954.65 146,989.88

1,608 1,609 1,610 1,611 1,612 1,613 1,614 1,615 1,616 1,617 1,618 1,619 1,620 1,621 1,622 1,623 1,624 1,625 1,626 1,627 1,628 1,629 1,630 1,631 1,632 1,633 1,634 1,635 1,636 1,637 1,638 1,639 1,640 1,641 1,642 1,643 1,644 1,645 1,646 1,647 1,648 1,649 1,650 1,651 1,652 1,653 1,654

146,989.88 147,025.12 147,060.36 147,095.62 147,130.88 147,166.15 147,201.43 147,236.72 147,272.02 147,307.32 147,342.63 147,377.96 147,413.29 147,448.62 147,483.97 147,519.33 147,554.69 147,590.06 147,625.45 147,660.84 147,696.23 147,731.64 147,767.06 147,802.48 147,837.91 147,873.35 147,908.80 147,944.26 147,979.72 148,015.20 148,050.68 148,086.17 148,121.67 148,157.18 148,192.70 148,228.23 148,263.76 148,299.30 148,334.85 148,370.41 148,405.98 148,441.56 148,477.14 148,512.74 148,548.34 148,583.95 148,619.57

35.24 35.25 35.25 35.26 35.27 35.28 35.29 35.30 35.30 35.31 35.32 35.33 35.34 35.35 35.36 35.36 35.37 35.38 35.39 35.40 35.41 35.42 35.42 35.43 35.44 35.45 35.46 35.47 35.47 35.48 35.49 35.50 35.51 35.52 35.53 35.53 35.54 35.55 35.56 35.57 35.58 35.59 35.59 35.60 35.61 35.62 35.63

147,025.12 147,060.36 147,095.62 147,130.88 147,166.15 147,201.43 147,236.72 147,272.02 147,307.32 147,342.63 147,377.96 147,413.29 147,448.62 147,483.97 147,519.33 147,554.69 147,590.06 147,625.45 147,660.84 147,696.23 147,731.64 147,767.06 147,802.48 147,837.91 147,873.35 147,908.80 147,944.26 147,979.72 148,015.20 148,050.68 148,086.17 148,121.67 148,157.18 148,192.70 148,228.23 148,263.76 148,299.30 148,334.85 148,370.41 148,405.98 148,441.56 148,477.14 148,512.74 148,548.34 148,583.95 148,619.57 148,655.20

1,655 1,656 1,657 1,658 1,659 1,660 1,661 1,662 1,663 1,664 1,665 1,666 1,667 1,668 1,669 1,670 1,671 1,672 1,673 1,674 1,675 1,676 1,677 1,678 1,679 1,680 1,681 1,682 1,683 1,684 1,685 1,686 1,687 1,688 1,689 1,690 1,691 1,692 1,693 1,694 1,695 1,696 1,697 1,698 1,699 1,700 1,701

148,655.20 148,690.83 148,726.48 148,762.13 148,797.80 148,833.47 148,869.15 148,904.83 148,940.53 148,976.23 149,011.95 149,047.67 149,083.40 149,119.14 149,154.89 149,190.64 149,226.41 149,262.18 149,297.96 149,333.75 149,369.55 149,405.36 149,441.18 149,477.00 149,512.84 149,548.68 149,584.53 149,620.39 149,656.26 149,692.13 149,728.02 149,763.91 149,799.81 149,835.72 149,871.64 149,907.57 149,943.51 149,979.45 150,015.41 150,051.37 150,087.34 150,123.32 150,159.31 150,195.31 150,231.31 150,267.33 150,303.35

35.64 35.65 35.65 35.66 35.67 35.68 35.69 35.70 35.70 35.71 35.72 35.73 35.74 35.75 35.76 35.76 35.77 35.78 35.79 35.80 35.81 35.82 35.82 35.83 35.84 35.85 35.86 35.87 35.88 35.89 35.89 35.90 35.91 35.92 35.93 35.94 35.95 35.95 35.96 35.97 35.98 35.99 36.00 36.01 36.01 36.02 36.03

148,690.83 148,726.48 148,762.13 148,797.80 148,833.47 148,869.15 148,904.83 148,940.53 148,976.23 149,011.95 149,047.67 149,083.40 149,119.14 149,154.89 149,190.64 149,226.41 149,262.18 149,297.96 149,333.75 149,369.55 149,405.36 149,441.18 149,477.00 149,512.84 149,548.68 149,584.53 149,620.39 149,656.26 149,692.13 149,728.02 149,763.91 149,799.81 149,835.72 149,871.64 149,907.57 149,943.51 149,979.45 150,015.41 150,051.37 150,087.34 150,123.32 150,159.31 150,195.31 150,231.31 150,267.33 150,303.35 150,339.38

1,702 1,703 1,704 1,705 1,706 1,707 1,708 1,709 1,710 1,711 1,712 1,713 1,714 1,715 1,716 1,717 1,718 1,719 1,720 1,721 1,722 1,723 1,724 1,725 1,726 1,727 1,728 1,729 1,730 1,731 1,732 1,733 1,734 1,735 1,736 1,737 1,738 1,739 1,740 1,741 1,742 1,743 1,744 1,745 1,746 1,747 1,748

150,339.38 150,375.42 150,411.47 150,447.53 150,483.60 150,519.67 150,555.75 150,591.85 150,627.95 150,664.06 150,700.17 150,736.30 150,772.44 150,808.58 150,844.73 150,880.89 150,917.06 150,953.24 150,989.43 151,025.63 151,061.83 151,098.05 151,134.27 151,170.50 151,206.74 151,242.99 151,279.24 151,315.51 151,351.78 151,388.07 151,424.36 151,460.66 151,496.97 151,533.28 151,569.61 151,605.95 151,642.29 151,678.64 151,715.00 151,751.37 151,787.75 151,824.14 151,860.54 151,896.94 151,933.35 151,969.78 152,006.21

36.04 36.05 36.06 36.07 36.07 36.08 36.09 36.10 36.11 36.12 36.13 36.14 36.14 36.15 36.16 36.17 36.18 36.19 36.20 36.20 36.21 36.22 36.23 36.24 36.25 36.26 36.27 36.27 36.28 36.29 36.30 36.31 36.32 36.33 36.34 36.34 36.35 36.36 36.37 36.38 36.39 36.40 36.40 36.41 36.42 36.43 36.44

150,375.42 150,411.47 150,447.53 150,483.60 150,519.67 150,555.75 150,591.85 150,627.95 150,664.06 150,700.17 150,736.30 150,772.44 150,808.58 150,844.73 150,880.89 150,917.06 150,953.24 150,989.43 151,025.63 151,061.83 151,098.05 151,134.27 151,170.50 151,206.74 151,242.99 151,279.24 151,315.51 151,351.78 151,388.07 151,424.36 151,460.66 151,496.97 151,533.28 151,569.61 151,605.95 151,642.29 151,678.64 151,715.00 151,751.37 151,787.75 151,824.14 151,860.54 151,896.94 151,933.35 151,969.78 152,006.21 152,042.65

1,749 1,750 1,751 1,752 1,753 1,754 1,755 1,756 1,757 1,758 1,759 1,760 1,761 1,762 1,763 1,764 1,765 1,766 1,767 1,768 1,769 1,770 1,771 1,772 1,773 1,774 1,775 1,776 1,777 1,778 1,779 1,780 1,781 1,782 1,783 1,784 1,785 1,786 1,787 1,788 1,789 1,790 1,791 1,792 1,793 1,794 1,795

152,042.65 152,079.10 152,115.55 152,152.02 152,188.50 152,224.98 152,261.47 152,297.97 152,334.48 152,371.00 152,407.53 152,444.06 152,480.61 152,517.16 152,553.72 152,590.30 152,626.88 152,663.46 152,700.06 152,736.67 152,773.28 152,809.91 152,846.54 152,883.18 152,919.83 152,956.49 152,993.16 153,029.83 153,066.52 153,103.21 153,139.92 153,176.63 153,213.35 153,250.08 153,286.81 153,323.56 153,360.32 153,397.08 153,433.85 153,470.64 153,507.43 153,544.23 153,581.04 153,617.85 153,654.68 153,691.51 153,728.36

36.45 36.46 36.47 36.47 36.48 36.49 36.50 36.51 36.52 36.53 36.54 36.54 36.55 36.56 36.57 36.58 36.59 36.60 36.61 36.61 36.62 36.63 36.64 36.65 36.66 36.67 36.68 36.69 36.69 36.70 36.71 36.72 36.73 36.74 36.75 36.76 36.76 36.77 36.78 36.79 36.80 36.81 36.82 36.83 36.84 36.84 36.85

152,079.10 152,115.55 152,152.02 152,188.50 152,224.98 152,261.47 152,297.97 152,334.48 152,371.00 152,407.53 152,444.06 152,480.61 152,517.16 152,553.72 152,590.30 152,626.88 152,663.46 152,700.06 152,736.67 152,773.28 152,809.91 152,846.54 152,883.18 152,919.83 152,956.49 152,993.16 153,029.83 153,066.52 153,103.21 153,139.92 153,176.63 153,213.35 153,250.08 153,286.81 153,323.56 153,360.32 153,397.08 153,433.85 153,470.64 153,507.43 153,544.23 153,581.04 153,617.85 153,654.68 153,691.51 153,728.36 153,765.21

1,796 1,797 1,798 1,799 1,800 1,801 1,802 1,803 1,804 1,805 1,806 1,807 1,808 1,809 1,810 1,811 1,812 1,813 1,814 1,815 1,816 1,817 1,818 1,819 1,820 1,821 1,822 1,823 1,824 1,825

153,765.21 153,802.07 153,838.94 153,875.82 153,912.71 153,949.61 153,986.51 154,023.43 154,060.35 154,097.28 154,134.22 154,171.17 154,208.13 154,245.10 154,282.08 154,319.06 154,356.06 154,393.06 154,430.07 154,467.09 154,504.12 154,541.16 154,578.21 154,615.27 154,652.33 154,689.40 154,726.49 154,763.58 154,800.68 154,837.79

36.86 36.87 36.88 36.89 36.90 36.91 36.91 36.92 36.93 36.94 36.95 36.96 36.97 36.98 36.99 36.99 37.00 37.01 37.02 37.03 37.04 37.05 37.06 37.07 37.07 37.08 37.09 37.10 37.11 37.12

153,802.07 153,838.94 153,875.82 153,912.71 153,949.61 153,986.51 154,023.43 154,060.35 154,097.28 154,134.22 154,171.17 154,208.13 154,245.10 154,282.08 154,319.06 154,356.06 154,393.06 154,430.07 154,467.09 154,504.12 154,541.16 154,578.21 154,615.27 154,652.33 154,689.40 154,726.49 154,763.58 154,800.68 154,837.79 154,874.91

Date:

red triangle. Red triangle identifies a cell comment.

nvestment that pays 8.75 percent and that has

Enter percentage as percent XX%, or decimal. .XX

Compounded Continuously, to approximate enter 1,000,000 Ener zero, not an annuity problem Ener initial investment as a positive value Enter 0, not an annuity problem

Chapter 5, Problem 12

Student's Name:

Solution method uses PV function/formulas

Guidelines:

<-- To view guidelines, move mouse pointer over cell with red triangle. Red triangle identifies a ce

Problem:

Present value: Tracy Chapman is saving to buy a house in five years. She plans to put 20 percent down at that time she believes that she will need $35,000 for the down payment. If Tracy can invest in a fund that pays 9.25 percent interest, compounded quarterly, how much will she have to invest today to have enough money for the down pay

Unknown: Amount to invest today.

Assumption(s) None

Given information/inputs/arguments: Annual interest rate Number of periods/years, nper Compounding frequency Annuity payment, pmt Future value, fv Type of annuity

Values 9.25% 5.00 4.00 0.00 $ 35,000.00 0.00

Comments Enter percentage as percent XX%, or decimal. .XX Enter number of years Enter quarters in a year Enter zero, not an annuity problem Enter amount needed in 5 years Enter 0, not an annuity problem

Excel solution method using PV function/formula: Excel PV function with quarterly compounding =

22,156.14

Date:

triangle. Red triangle identifies a cell comment.

to put 20 percent down at that time, and est in a fund that pays 9.25 percent annual ve enough money for the down payment?

e as percent XX%, or decimal. .XX

an annuity problem eeded in 5 years annuity problem

Chapter 5, Problem 12

Student's Name: Solution method uses schedule to find present value when annual rate is 9.25% with quarterly compounding

Guidelines:

<-- To view guidelines, move mouse pointer over cell with red triangle. Red triangle identifies a ce

Problem:

Present value: Tracy Chapman is saving to buy a house in five years. She plans to put 20 percent down at that time believes that she will need $35,000 for the down payment. If Tracy can invest in a fund that pays 9.25 percent ann compounded quarterly, how much will she have to invest today to have enough money for the down payment?

Unknown: Amount to invest today.

Assumption(s) None

Given information/inputs/arguments: Annual interest rate Number of periods/years, nper Compounding frequency Annuity payment, pmt Future value, fv Type of annuity

Values 9.25% 5.00 4.00 0.00 35,000.00 0.00

Excel solution method for Present Value using Schedule: Excel schedule solution, using Goal Seek

22,156.14

Interest earned during quarter 512.36 $ 524.21 536.33 548.73 561.42 574.41 587.69 601.28 615.18 629.41 643.97 658.86 674.09 689.68 705.63

Value, end of quarter 22,668.50 23,192.71 23,729.04 24,277.78 24,839.20 25,413.61 26,001.30 26,602.58 27,217.76 27,847.17 28,491.14 29,149.99 29,824.09 30,513.77 31,219.40

Schedule for quarterly compounding Quarters 1 $ 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Value, start of quarter 22,156.14 $ 22,668.50 23,192.71 23,729.04 24,277.78 24,839.20 25,413.61 26,001.30 26,602.58 27,217.76 27,847.17 28,491.14 29,149.99 29,824.09 30,513.77

Comments Enter percentage as percent XX%, or dec Enter number of years Enter quarters in a year Not an annuity problem, thus zero Enter amount needed in 5 years Enter 0, not an annuity problem

16 17 18 19 20

31,219.40 31,941.35 32,679.99 33,435.72 34,208.92

721.95 738.64 755.72 773.20 791.08

31,941.35 32,679.99 33,435.72 34,208.92 35,000.00

Date:

ed triangle. Red triangle identifies a cell comment.

ns to put 20 percent down at that time, and she st in a fund that pays 9.25 percent annual interest, ugh money for the down payment?

Enter percentage as percent XX%, or decimal. .XX

Not an annuity problem, thus zero Enter amount needed in 5 years Enter 0, not an annuity problem

Chapter 5, Problem 19

Student's Name: Solution method uses FVSchedule function/formula

Guidelines:

<-- To view guidelines, move mouse pointer over cell with red triangle. Red triangle identifies a ce

Problem:

Future value: You decide to take advantage of the current online dating craze and start your own dating app. You know th you have 450 people who will sign up immediately and, through careful marketing research and analysis, determine that the membership can grow by 27 percent in the first two years, 22 percent in year 3, and 18 percent in year 4. How many members do you expect to have at the end of four years?

Given information/inputs/arguments: People who sign up immediately Membership growth in year 1 Membership growth in year 2 Membership growth in year 3 Membership growth in year 4

Values 450 27.00% 27.00% 22.00% 18.00%

Comments Number of people at start, present value, principal Enter percentage as percent XX%, or decimal, .XX Four cells for growth rates formatted as 0.00% Do not change this format

Unknown: Number of people at end of four years when annual growth rates change from year to year. Metaphor: An investment with present value of 450, different annual interest/growth rates, and future value is unknown.

Excel solution method using FVSchedule function: Excel Function FVSCHEDULE(Principal, Schedule) = Cell G28, is formatted to zero places, rounds G27 to integer value

1,044.87 1,045

Date:

triangle. Red triangle identifies a cell comment.

start your own dating app. You know that esearch and analysis, determine ar 3, and 18 percent in year 4.

ple at start, present value, principal e as percent XX%,

for growth rates formatted as 0.00% ange this format

th rates, and future value is unknown.

Chapter 5, Problem 19

Student's Name: Solution method uses schedule (no Excel functions/formulas)

Guidelines:

<-- To view guidelines, move mouse pointer over cell with red triangle. Red triangle identifies a ce

Problem:

Given information/inputs/arguments: People who sign up immediately Membership growth in year 1 Membership growth in year 2 Membership growth in year 3 Membership growth in year 4

Values 450 27.00% 27.00% 22.00% 18.00%

Comments Number of people at start, present value, principal Enter percentage as percent XX%, or decimal, .XX Four cells for growth rates formatted as 0.00% Do not change this format

Excel solution method using a schedule Schedule procedure does not use any Excel functions People end of year 1 is same as people start of year 2, and so forth People Annual People People Start of growth gained end Year rate each year of year Year 1 450.00 27.00% 121.50 571.50 2 571.50 27.00% 154.31 725.81 3 725.81 22.00% 159.68 885.48 4 885.48 18.00% 159.39 1,044.87 Cell G32, formatted to zero places, rounds E31 to integer value

1,045.00

Date:

triangle. Red triangle identifies a cell comment.

start your own dating app. You know that esearch and analysis, determine ar 3, and 18 percent in year 4.

ple at start, present value, principal e as percent XX%,

for growth rates formatted as 0.00% ange this format

th rates, and future value is unknown.

Chapter 5, Problem 19

Student's Name: Solution method uses Excel's FV function/formula

Guidelines:

<-- To view guidelines, move mouse pointer over cell with red triangle. Red triangle identifies a ce

Problem:

Given information/inputs/arguments: People who sign up immediately Membership growth in year 1 Membership growth in year 2 Membership growth in year 3 Membership growth in year 4

Values 450 27.00% 27.00% 22.00% 18.00%

Comments Number of people at start, present value, principal Enter percentage as percent XX%, or decimal, .XX Four cells for growth rates formatted as 0.00% Do not change this format

Excel solution method using FV function/formula: Year 1 2 3 4

Inputs: Five arguments for FV function/formula rate nper pmt pv 27.00% 1 0 450.00 27.00% 1 0 571.50 22.00% 1 0 725.81 18.00% 1 0 885.48 Cell G31 = G30, formatted to zero places, rounds G30 to integer value

type 0 0 0 0

Output FV 571.50 725.81 885.48 1,044.87 1,045

Date:

triangle. Red triangle identifies a cell comment.

start your own dating app. You know that esearch and analysis, determine ar 3, and 18 percent in year 4.

ple at start, present value, principal e as percent XX%,

for growth rates formatted as 0.00% ange this format

th rates, and future value is unknown.

Chapter 5, Problem 20

Student's Name:

Solution method uses FV function/formula

Guidelines:

<-- To view guidelines, move mouse pointer over cell with red triangle. Red triangle identifies a ce

Problem:

Multiple compounding periods: Find the future value of an investment of $2,500 made today for the following rate a. 6.25 percent compounded semiannually for 12 years. b. 7.63 percent compounded quarterly for 6 years. c. 8.9 percent compounded monthly for 10 years. d. 10 percent compounded daily for 3 years. e. 8 percent compounded continuously for 2 years.

Unknown: Value of investment at the end of five years.

Assumption(s)

Part e, compounded continuously, for input section and when using FV function use 1,000,000 for compounding frequency

Given information/inputs/arguments: Annual interest rate Number of periods/years, nper Compounding frequency per year Annuity payment, pmt Present value, pv Type of annuity

Values for a 6.25% 12.00 2.00 0.00 2,500.00 0.00

Values for b 7.63% 6.00 4.00 0.00 2,500.00 0.00

Values for c 8.90% 10.00 12.00 0.00 2,500.00 0.00

$5,232.09

$3,934.48

$6,067.86

Excel solution method using FV function: Future values, using Excel FV function = Excel solution for part e, using EXP function Future value, part e, compounded continuously,

Date:

ed triangle identifies a cell comment.

day for the following rates and periods:

for compounding frequency per year Values for d 10.00% 3.00 365.00 0.00 2,500.00 0.00

Values for e 8.00% 2.00 1,000,000.00 0.00 2,500.00 0.00

$3,374.51

$2,933.78

Comments Enter percentage as percent XX%, or decimal. .XX Enter number of years Enter compounding frequency per year Enter zero, not an annuity problem. Enter initial investment as a positive value Enter 0, not an annuity problem

Chapter 5, Problem 20

Student's Name:

Solution method uses the schedule method for part a

Guidelines:

<-- To view guidelines, move mouse pointer over cell with red triangle. Red triangle identifies a ce

Problem:

Unknown: Value of investment at the end of five years.

Assumption(s) None

Given information/inputs/arguments: Annual interest rate Number of periods/years, nper Compounding frequency per year Annuity payment, pmt Present value, pv Type of annuity

Values for a 6.25% 12.00 2.00 0.00 $ 2,500.00 0.00

Excel solution method using schedule FV at the end of 12 years, semiannual

5,232.09

Schedule for semiannual compounding

Semiannual time periods 1 $ 2 3 4 5 6 7 8 9 10

Value, start of semiannual period 2,500.00 $ 2,578.13 2,658.69 2,741.78 2,827.46 2,915.81 3,006.93 3,100.90 3,197.80 3,297.73

Interest earned during Value, end of semiannual semiannual period period 78.13 $ 2,578.13 80.57 2,658.69 83.08 2,741.78 85.68 2,827.46 88.36 2,915.81 91.12 3,006.93 93.97 3,100.90 96.90 3,197.80 99.93 3,297.73 103.05 3,400.79

Comments Enter percentage as percent XX%, or decim Enter number of years Enter compounding frequency per year Enter zero, not an annuity problem. Enter initial investment as a positive value Enter 0, not an annuity problem

11 12 13 14 15 16 17 18 19 20 21 22 23 24

3,400.79 3,507.06 3,616.66 3,729.68 3,846.23 3,966.43 4,090.38 4,218.20 4,350.02 4,485.96 4,626.14 4,770.71 4,919.80 5,073.54

106.27 109.60 113.02 116.55 120.19 123.95 127.82 131.82 135.94 140.19 144.57 149.08 153.74 158.55

3,507.06 3,616.66 3,729.68 3,846.23 3,966.43 4,090.38 4,218.20 4,350.02 4,485.96 4,626.14 4,770.71 4,919.80 5,073.54 5,232.09

Date:

triangle. Red triangle identifies a cell comment.

00 made today for the following rates and periods:

er percentage as percent XX%, or decimal. .XX

er compounding frequency per year er zero, not an annuity problem. er initial investment as a positive value

Chapter 5, Problem 25

Student's Name:

Solution method uses NPER function/formulas

Guidelines:

<-- To view guidelines, move mouse pointer over cell with red triangle. Red triangle identifies a ce

Problem:

Time to grow: Neon Lights Company is a private company with sales of $1.3 million a year. Management wants to t company public but has to wait until the sales reach $2 million. If sales are expected to grow 12 percent annually, w the earliest that Neon Lights will go public?

Unknown: Number of years for annual sales to grow from $1.3 to $2.0 million

Assumption(s) Annual rate with annual compounding Sales occur at end of year

Given information/inputs/arguments: Annual growth rate Compounding frequency Annuity payment, pmt Present value, pv Future value, fv Type of annuity

Values 12.00% 1.00 0.00 1,300,000.00 2,000,000.00 0.00

Excel solution method using NPER function/formula: Excel NPER function =

3.80

Comments Enter percentage as percent X.XX%, or decimal. .XXX Enter compounding frequency for annual growth rate Enter 0, not an annuity problem Enter amount of most recent sales Enter desired amount of sales Ener 0, not an annuity problem

Date:

triangle. Red triangle identifies a cell comment.

llion a year. Management wants to take the ected to grow 12 percent annually, when is

e as percent X.XX%, or decimal. .XXX ding frequency for annual growth rate

Chapter 5, Problem 25

Student's Name:

Solution method uses a Schedule

Guidelines:

<-- To view guidelines, move mouse pointer over cell with red triangle. Red triangle identifies a ce

Problem:

Unknown: Number of years for annual sales to grow from $1.3 to $2.0 million

Assumption(s) Annual rate with annual compounding Sales occur at end of year

Given information/inputs/arguments: Annual growth rate Compounding frequency Annuity payment, pmt Present value, pv Future value, fv Type of annuity

Values 12.00% 1.00 0.00 1,300,000.00 2,000,000.00 0.00

Schedule solution (approximation)

Year

Annual Sales Change in Annual sales previous year Annual Sales end of year 1 $1,300,000.00 $156,000.00 $1,456,000.00 2 1,456,000.00 174,720.00 1,630,720.00 3 1,630,720.00 195,686.40 1,826,406.40 4 1,826,406.40 219,168.77 2,045,575.17

Date:

triangle. Red triangle identifies a cell comment.

llion a year. Management wants to take the ected to grow 12 percent annually, when is

e as percent X.XX%, or decimal. .XXX ding frequency for annual growth rate

Chapter 5, Problem 33

Student's Name:

Solution method uses FV function/formula

Guidelines:

<-- To view guidelines, move mouse pointer over cell with red triangle. Red triangle identifies a ce

Problem:

You have $12,000 in cash. You can deposit it today in a mutual fund earning 8.2 percent compounded semiannually, or you can wait, enjoy some of it, and invest $11,000 in your brother's business in two years. Your brother is promising a return of at least 10 percent on your investment. Whichever alternative you choose, you will need to cash in at the end of 10 years. Assume your brother is trustworthy and that both investments carry the same risk. Also, assume you will not invest the $11,000 in the first two years. Which decision will yield the largest amount in 10 years?

Unknown: Which investment has the larger amount in 10 years.

Assumption(s) Brother promises rate with annual compounding.

Given information/inputs/arguments: Annual interest rate Number of periods/years, nper Compounding frequency per year Annuity payment, pmt Present value, pv Type of annuity

Values, Fund Values, Brother 8.20% 10.00% 10.00 8.00 2.00 1.00 0.00 0.00 12,000.00 11,000.00 0.00 0.00

Excel solution method using FV function: Excel FV function =

26,803.77

23,579.48

Comments Enter percentage as percent XX% Enter number of years for each in Enter compounding frequency (ti Enter 0, not an annuity problem. Enter initial investment as a posit Enter 0, not an annuity problem

Date:

gle. Red triangle identifies a cell comment.

compounded semiannually, or you

rry the same risk. Also, assume

Enter percentage as percent XX%, or decimal. .XX Enter number of years for each investment Enter compounding frequency (times per year) Enter 0, not an annuity problem. Enter initial investment as a positive value Enter 0, not an annuity problem

Chapter 5, Problem 33

Student's Name:

Solution method uses a Schedule

Guidelines:

<-- To view guidelines, move mouse pointer over cell with red triangle. Red triangle identifies a ce

Problem:

You have $12,000 in cash. You can deposit it today in a mutual fund earning 8.2 percent compounded semiannually, or you can wait, enjoy some of it, and invest $11,000 in your brother's business in two years. Your brother is promising a return of at least 10 percent on your investment. Whichever alternative you choose, you will need to cash in at the end of 10 years. Assume your brother is trustworthy and that both investments carry the same risk. Also, assume you will not invest the $11,000 in the first two years. Which decision will yield the largest amount in 10 years?

Unknown: Which investment has the larger amount in 10 years.

Assumption(s) Brother's promises annual rate of return with annual compounding.

Given information/inputs/arguments:

Values, Fund Values, Brother 8.20% 10.00% 10.00 8.00 2.00 1.00 0.00 0.00 12,000.00 11,000.00 0.00 0.00

Annual interest rate Number of periods/years, nper Compounding frequency per year Annuity payment, pmt Present value, pv Type of annuity

Excel solution method using schedule: Schedule, end of year 10

26,803.77

Schedule, Fund

Periods 1 2 3 4 5 6 7 8 9 10 11 12

Investment, Start of year 12,000.00 12,492.00 13,004.17 13,537.34 14,092.37 14,670.16 15,271.64 15,897.78 16,549.58 17,228.12 17,934.47 18,669.78

Interest earned during year 492.00 512.17 533.17 555.03 577.79 601.48 626.14 651.81 678.53 706.35 735.31 765.46

Value of investment end of year 12,492.00 13,004.17 13,537.34 14,092.37 14,670.16 15,271.64 15,897.78 16,549.58 17,228.12 17,934.47 18,669.78 19,435.24

23,579.48

Comments Enter percentage as percent Enter number of years for ea Enter compounding frequen Enter 0, not an annuity prob Enter initial investment as a Enter 0, not an annuity prob

13 14 15 16 17 18 19 20

19,435.24 20,232.09 21,061.60 21,925.13 22,824.06 23,759.85 24,734.00 25,748.10

796.85 829.52 863.53 898.93 935.79 974.15 1,014.09 1,055.67

20,232.09 21,061.60 21,925.13 22,824.06 23,759.85 24,734.00 25,748.10 26,803.77

Investment, Start of year 11,000.00 12,100.00 13,310.00 14,641.00 16,105.10 17,715.61 19,487.17 21,435.89

Interest earned during year 1,100.00 1,210.00 1,331.00 1,464.10 1,610.51 1,771.56 1,948.72 2,143.59

Value of investment end of year 12,100.00 13,310.00 14,641.00 16,105.10 17,715.61 19,487.17 21,435.89 23,579.48

Schedule, Brother

Periods 1 2 3 4 5 6 7 8

Date:

Red triangle identifies a cell comment.

ounded semiannually, or you

Chapter 5, Problem 34

Student's Name:

Solution method uses FVSchedule function/formula

Guidelines:

<-- To view guidelines, move mouse pointer over cell with red triangle. Red triangle identifies a ce

Problem:

Unknown: Value of investment at various future years.

Assumption(s) All interest rates are annual rates with annual compounding.

Given information/inputs/arguments: Initial investment Interest rate in year 1 Interest rate in year 2 Interest rate in year 3 Interest rate in year 4 Interest rate in year 5 Interest rate in year 6 Interest rate in year 7 Interest rate in year 8 Interest rate in year 9 Interest rate in year 10 Interest rate in year 11 Interest rate in year 12 Interest rate in year 13 Interest rate in year 14 Interest rate in year 15 Interest rate in year 16 Interest rate in year 17 Interest rate in year 18 Interest rate in year 19 Interest rate in year 20 Interest rate in year 21 Additional investment, end of year 7

Values 5,000 7.30% 7.30% 7.30% 7.30% 7.30% 7.30% 7.30% 5.50% 5.50% 5.50% 5.50% 5.50% 5.50% 8.20% 8.20% 8.20% 4.60% 4.60% 7.60% 7.60% 7.60% 1,200

Comments Enter as a positive value Enter percentage as percent X.XX%, or .XXX Enter percentage as percent X.XX%, or .XXX Enter percentage as percent X.XX%, or .XXX Enter percentage as percent X.XX%, or .XXX Enter percentage as percent X.XX%, or .XXX Enter percentage as percent X.XX%, or .XXX Enter percentage as percent X.XX%, or .XXX Enter percentage as percent X.XX%, or .XXX Enter percentage as percent X.XX%, or .XXX Enter percentage as percent X.XX%, or .XXX Enter percentage as percent X.XX%, or .XXX Enter percentage as percent X.XX%, or .XXX Enter percentage as percent X.XX%, or .XXX Enter percentage as percent X.XX%, or .XXX Enter percentage as percent X.XX%, or .XXX Enter percentage as percent X.XX%, or .XXX Enter percentage as percent X.XX%, or .XXX Enter percentage as percent X.XX%, or .XXX Enter percentage as percent X.XX%, or .XXX Enter percentage as percent X.XX%, or .XXX Enter percentage as percent X.XX%, or .XXX Enter additional investment as a positive value

Unknown: Value of investment at various future years a, end of year 16; b, at end of year 21; c, end of year 21 if $1,200 added at end of year 7

Excel solution method using FVSchedule function: a) End of year 16, Excel Function FVSCHEDULE b) End of year 21, Excel Function FVSCHEDULE c) End of year 21 if 1,200 added at end of year 7

14,300.94 19,492.38 22,349.16

Date:

triangle. Red triangle identifies a cell comment.

al investment of $5,000. You are ning 7.3 percent for the first seven earned 8.2 percent three years in a economy recovered, the return jumped

of $1,200 at the end of year 7?

investment as a positive value

Chapter 5, Problem 34

Student's Name:

Solution method uses a Schedule

Guidelines:

<-- To view guidelines, move mouse pointer over cell with red triangle. Red triangle identifies a ce

Problem:

Unknown: Value of investment at various future years.

Assumption(s) All interest rates are annual rates with annual compounding.

Values 5,000 7.30% 7.30% 7.30% 7.30% 7.30% 7.30% 7.30% 5.50% 5.50% 5.50% 5.50% 5.50% 5.50% 8.20% 8.20% 8.20% 4.60% 4.60% 7.60% 7.60% 7.60% 1,200

Unknown: Value of investment at various future years a, end of year 16; b, at end of year 21; c, end of year 21 if $1,200 added at end of year 7

Excel solution method using Schedule: a) End of year 16, Schedule b) End of year 21, Schedule c) End of year 21 if 1,200 added at end of year 7, Schedule

14,300.94 19,492.38 22,349.16

Schedules:

Year 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

Value, start of year 5,000.00 5,365.00 5,756.65 6,176.88 6,627.79 7,111.62 7,630.77 8,187.82 8,638.15 9,113.24 9,614.47 10,143.27 10,701.15 11,289.71 12,215.47 13,217.14 14,300.94 14,958.78 15,646.89 16,836.05 18,115.59

Interest earned during year 365.00 391.65 420.24 450.91 483.83 519.15 557.05 450.33 475.10 501.23 528.80 557.88 588.56 925.76 1,001.67 1,083.81 657.84 688.10 1,189.16 1,279.54 1,376.78

Value, end of year 5,365.00 5,756.65 6,176.88 6,627.79 7,111.62 7,630.77 8,187.82 8,638.15 9,113.24 9,614.47 10,143.27 10,701.15 11,289.71 12,215.47 13,217.14 14,300.94 14,958.78 15,646.89 16,836.05 18,115.59 19,492.38

Year 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

Date:

triangle. Red triangle identifies a cell comment.

al investment of $5,000. You are ning 7.3 percent for the first seven earned 8.2 percent three years in a economy recovered, the return jumped

of $1,200 at the end of year 7?

investment as a positive value

Value, start Added of year investment 5,000.00 5,365.00 5,756.65 6,176.88 6,627.79 7,111.62 7,630.77 8,187.82 1,200 9,904.15 10,448.87 11,023.56 11,629.86 12,269.50 12,944.32 14,005.76 15,154.23 16,396.88 17,151.13 17,940.08 19,303.53 20,770.60

Interest earned Value, end during year of year 365.00 5,365.00 391.65 5,756.65 420.24 6,176.88 450.91 6,627.79 483.83 7,111.62 519.15 7,630.77 557.05 8,187.82 516.33 9,904.15 544.73 10,448.87 574.69 11,023.56 606.30 11,629.86 639.64 12,269.50 674.82 12,944.32 1,061.43 14,005.76 1,148.47 15,154.23 1,242.65 16,396.88 754.26 17,151.13 788.95 17,940.08 1,363.45 19,303.53 1,467.07 20,770.60 1,578.57 22,349.16

Chapter 5, Problem 36

Student's Name:

Solution method uses NPER function/formulas

Guidelines:

<-- To view guidelines, move mouse pointer over cell with red triangle. Red triangle identifies a ce

Problem:

Surmec, Inc., reported sales of $2.1 million last year. The company’s primary business is the manufacture of nuts an Since this is a mature industry, analysts are confident that sales will grow at a steady rate of 7 percent per year. The company’s net income equals 23 percent of sales. Management would like to buy a new fleet of trucks but can only once the net income reaches $620,000 a year. At the end of what year will Surmec be able to buy the trucks? What sales and net income be in that year?

Unknown: Number of years before Surmec can buy the trucks, net income reaches $620,000

Assumption(s) Annual sales growth rate is annual rate with annual compounding Sales occur at the end of the year

Given information/inputs/arguments:

Values 7.00% 1.00 0.00 $2,100,000 23.00% $620,000 0.00

Annual sales growth Compounding frequency Annuity payment, pmt Current sales, present value Net income as percent of sales Net income, fv Type of annuity

Comments Enter percentage as percent X.XX%, or decimal. .XXX Enter compounding frequency for annual growth rat Enter 0, not an annuity problem Enter current sales as positive value Enter percentage as percent X.XX%, or decimal. .XXX Enter desired amount of net income Ener 0, not an annuity problem

Excel solution method using NPER function/formula: Excel NPER function = Excel NPER function = Excel function =

3.69 years $2,752,671.62 sales $633,114.47 net income

Date:

angle. Red triangle identifies a cell comment.

ness is the manufacture of nuts and bolts. ady rate of 7 percent per year. The y a new fleet of trucks but can only do so ec be able to buy the trucks? What will

e as percent X.XX%, or decimal. .XXX ding frequency for annual growth rate

e as percent X.XX%, or decimal. .XXX

Chapter 5, Problem 36

Student's Name: Solution method is a schedule which only approximates the number of years

Guidelines:

<-- To view guidelines, move mouse pointer over cell with red triangle. Red triangle identifies a ce

Problem:

Unknown: Number of years before Surmec can buy the trucks, net income reaches $620,000

Assumption(s) Annual sales growth rate is annual rate with annual compounding Sales occur at the end of the year

Given information/inputs/arguments: Annual sales growth Compounding frequency Annuity payment, pmt Current sales, present value Net income as percent of sales Net income, fv Type of annuity

Values 7.00% 1.00 0.00 2,100,000.00 23.00% 620,000.00 0.00

Comments Enter percentage as percent X.XX%, or decimal. .XXX Enter compounding frequency for annual growth rate Enter 0, not an annuity problem Enter current sales as positive value Enter percentage as percent X.XX%, or decimal. .XXX Enter desired amount of net income Ener 0, not an annuity problem

Schedule solution (approximation) Year

Net income Change in previous year Net income 1 483,000 33,810 2 516,810 36,177 3 552,987 38,709 4 591,696 41,419 4 Sales = Net Income/23%

Net income end of year 516,810 552,987 591,696 633,114 Desired Net Income Achieved 2,752,672 Related Sales for Desired Net Income

Date:

triangle. Red triangle identifies a cell comment.

usiness is the manufacture of nuts and bolts. teady rate of 7 percent per year. The uy a new fleet of trucks but can only do so mec be able to buy the trucks? What will

e as percent X.XX%, or decimal. .XXX ding frequency for annual growth rate

e as percent X.XX%, or decimal. .XXX

Chapter 5, Problem 37

Student's Name:

Solution method uses FV, SUM, and RATE functions/formulas

Guidelines:

<-- To view guidelines, move mouse pointer over cell with red triangle. Red triangle identifies a ce

Problem:

You will be graduating in two years and are thinking about your future. You know that you will want to buy a house five ye after you graduate and that you will want to put down $60,000. As of right now, you have $8,000 in your savings account. You are also fairly certain that once you graduate, you can work in the family business and earn $32,000 a year, with a 5 percent raise every year. You plan to live with your parents for the first two years after graduation, which will enable you to minimize your expenses and put away $10,000 each year. The next three years, you will have to live on your own, as your younger sister will be graduating from college and has already announced her plan to move back into the family hous Thus, you will be able to save only 13 percent of your annual salary. Assume that you will be able to earn 7.2 percent on th savings from your salary. At what interest rate will you need to invest the current savings account balance in order to achie your goal? Hint: Draw a time line that shows all the cash flows for years 0 through 7. Remember, you want to buy a house seven years from now and your first salary will be in Year 3.

Unknown: Needed interest rate on savings account.

Assumption(s) All interest rates are annual rates with annual compounding All cash flows take place at a point in time, beginning or end of year

Given information/inputs/arguments:

Values

Years to graduation Years to buy house after graduation Years to buy house from today House down payment Current amount in savings account Starting salary, family business Salary raise per year Savings living with parents Years with parents Savings after living with parents Annual rate earned on savings from salary Compounding frequency Annuity payment Type of annuity

2.00 5.00 7.00 60,000.00 8,000.00 32,000.00 5.00% 10,000.00 2.00 13.00% 7.20% 1.00 0.00 0.00

Comments Enter percentage as percent XX%, or decimal. .XX Enter as a positive value Enter as a positive value Enter as a positive value Enter as a positive value Enter as a positive value Enter percentage as percent XX%, or decimal. .XX Enter as a positive value Enter as a positive value Enter percentage as percent XX%, or decimal. .XX Enter percentage as percent XX%, or decimal. .XX Enter compounding frequency for all invested fun Enter 0, not an annuity problem Enter 0, not an annuity problem

8,000.00 0.00 0.00 10,000.00

Current amount in savings account Enter 0, not working Enter 0, not working Enter savings due to living at home, first year wor

Cash flows before any compounding Cash flow at t = 0 Cash flow at t = 1 Cash flow at t = 2 Cash flow at t = 3

0 1 2 3

Cash flow at t = 4 Cash flow at t = 5 Cash flow at t = 6 Cash flow at t = 7

4 5 6 7

10,000.00 4,586.40 4,815.72 5,056.51

Future value of cash flows, end of year 7 FV of year 3 savings, living at home FV of year 4 savings, living at home FV of year 5 savings, from work FV of year 6 savings, from work FV of year 7 savings, from work Sum of future values, funds from working

13,206.24 12,319.25 5,270.62 5,162.45 5,056.51 41,015.07

Funds needed at end of year 7

60,000.00

Funds to be funded by savings account

18,984.93

Rate needed on savings account, Rate fn.

13.14%

Enter savings due to living at home, second year w Calculate salary savings for year 5 Calculate salary savings for year 6 Calculate savings from earnings

Date:

e. Red triangle identifies a cell comment.

will want to buy a house five years $8,000 in your savings account. earn $32,000 a year, with a 5 duation, which will enable you have to live on your own, as move back into the family house. e able to earn 7.2 percent on the ccount balance in order to achieve

as percent XX%, or decimal. .XX

as percent XX%, or decimal. .XX as percent XX%, or decimal. .XX g frequency for all invested funds

to living at home, first year working

Chapter 5, Problem 37

Student's Name:

Solution method uses a Schedule

Guidelines:

<-- To view guidelines, move mouse pointer over cell with red triangle. Red triangle identifies a ce

Problem:

Unknown: Needed interest rate on savings account.

Assumption(s) All rates are annual rates with annual compounding All cash flows take place at a point in time, beginning or end of year

Given information/inputs/arguments: Years to graduation Funds earned before graduation Years to buy house after graduation Years to buy house from today House down payment Current amount in savings account Starting salary, family business Salary raise per year Savings living with parents Years with parents Savings after living with parents Annual rate earned on savings from salary Compounding frequency Annuity payment Type of annuity

Values 2.00 0.00 5.00 7.00 60,000.00 8,000.00 32,000.00 5.00% 10,000.00 2.00 13.00% 7.20% 1.00 0.00 0.00

Schedule solution, use Goal Seek Annual interest rate on savings account

13.14%

Comments Enter percentage as percent XX%, or decim Enter zero, no funds earned before graduat Enter as a positive value Enter as a positive value Enter as a positive value Enter as a positive value Enter as a positive value Enter percentage as percent XX%, or decim Enter as a positive value Enter as a positive value Enter percentage as percent XX%, or decim Enter percentage as percent XX%, or decim Enter compounded frequency for rate earn Enter 0, not an annuity problem Enter 0, not an annuity problem

Schedule

Time 1 2 3 4 5 6 7

Savings account start of year 8,000.00 9,051.22 10,240.57 11,586.20 13,108.65 14,831.16 16,780.00

Annual Interest earned on savings account 1,051.22 1,189.35 1,345.63 1,522.45 1,722.51 1,948.85 2,204.93

Savings account end of year 9,051.22 10,240.57 11,586.20 13,108.65 14,831.16 16,780.00 18,984.93

Work savings start of year 0.00 0.00 0.00 10,000.00 20,720.00 26,798.24 33,543.43

d triangle. Red triangle identifies a cell comment.

er compounded frequency for rate earned on savings

Date:

Funds from work 0.00 0.00 10,000.00 10,000.00 4,586.40 4,815.72 5,056.51

Interest earned from work 0.00 0.00 0.00 720.00 1,491.84 1,929.47 2,415.13

Value for end of year funds from work 0.00 0.00 10,000.00 20,720.00 26,798.24 33,543.43 41,015.07

Value end of year Savings and work 9,051.22 10,240.57 21,586.20 33,828.65 41,629.40 50,323.44 60,000.00

Textbook: Fundamentals of Corporate Finance, 5th Edition Authors: Robert Parrino, Thomas Bates, Stuart Gillan, David Kidwell, Publisher: Wiley Excel solutions for selected problems at end of Chapter 4 Problem number 28 29 30

Problem Description Complete balance sheet Calculate financial ratios Calculate more financial ratios

Worksheet tab name 28_Balance_Sheet 29_Financial_Ratios 30_Financial_Ratios

One way to return to the contents worksheet is to hold down the CTRL key and simultaneously press and hold dow

eously press and hold down the Page Up key

Chapter 4, Problem 28

Student's Name: Solution method uses SUM function/formula

Guidelines:

<-- To view guidelines, move mouse pointer over cell with red triangle. Red triangle identifies a

Problem: Complete the balance sheet of Flying Roos Corporation.

Assets: Cash and marketable securities Accounts receivable Inventory Total current assets Net plant and equipment

Total assets You have the following information: Debt ratio = 40% DSO = 39 days Cost of goods sold = $1.6875 million

Flying Roos Corporation, Balance Sheet Liabilities and Equity: Accounts payable and accruals Notes payable Total current liabilities Long term debt Total debt Common stock Retained earnings $ 8,000,000 Total liabilities and equity

Current ratio = 1.5 Inventory turnover ratio = 3.375 Net sales = $2.25 million

Unknown: Complete balance sheet

Assumption(s) All values to nearest dollar

Given information/inputs/arguments: Total assets Notes payable Long-term debt Retained earnings Debt ratio DSO Current ratio Inventory turnover Net sales Cost of goods sold Days in a year

Excel solution method using cell references and formulas:

Values 8,000,000 300,000 2,000,000 1,250,000 40.00% 39 1.50 3.38 2,250,000 1,687,500 365

Comments Enter Total sales as a positive value Enter Notes payable as a positive value Enter Long-term debt as a positive value Enter Retained earnings as a positive value Enter percent as XX.XX% or decimal, .XXXX Enter days as a positive value Enter ratio as a positive value Enter turnover as a positive value Enter sales as a positive value Enter amount as a positive value Enter days in year

Flying Roos Corporation, Balance sheet as of December 31, 2017 Assets: Liabilities and Equity: Cash and marketable securities $ 1,059,589 Accounts payable and accruals Accounts receivable 240,411 Notes payable Inventory 500,000 Total current liabilities Total current assets 1,800,000 Long term debt Net plant and equipment 6,200,000 Total debt Common stock Retained earnings Total assets $8,000,000 Total liabilities and equity

Step 1: Use cell references to inputs for Total assets, Notes payable, Long term debt, and Retained earnings. Step 2: Use cell reference for Total Liabilities and equity which equals total assets. Step 3: Use Debt ratio = Total debt/Total assets to calculate Total debt. Step 4: Use Total debt = Total current liabilities + Long term debt to calculate Total current liabilities. Step 5: Use Total current liabilities = Accounts payable and accruals + Notes payable to calculate Accounts payable and acc Step 6: Use Total liabilities and equity = Total debt + Common stock + Retained earnings to calculate Retained earnings. Step 7: Use Current ratio = Total current assets/Total current liabilities to calculate Total current assets. Step 8: Use Inventory turnover ratio = Cost of goods sold/Inventory to calculate inventory. Step 9: Use DSO = Days Sales Outstanding = Account receivable/(Sales/365) to calculate Accounts receivable. Step 10: Use Cash and Marketable securities + Accounts receivable + Inventory to calculate Cash and marketable securities Step 11: Use Total assets = Total current assets + Net plant and equipment to calculate Net plant and equipment.

Date:

triangle. Red triangle identifies a cell comment.

300,000 2,000,000

1,250,000

otal sales as a positive value otes payable as a positive value ong-term debt as a positive value etained earnings as a positive value ercent as XX.XX% or decimal, .XXXX ays as a positive value tio as a positive value urnover as a positive value ales as a positive value mount as a positive value

017 $

900,000 300,000 1,200,000 2,000,000 3,200,000 3,550,000 1,250,000 $8,000,000

and Retained earnings.

rrent liabilities. o calculate Accounts payable and accruals. gs to calculate Retained earnings. tal current assets.

te Accounts receivable. ulate Cash and marketable securities. e Net plant and equipment.

Chapter 4, Problem 29

Student's Name:

Solution method uses formulas and cell references

Guidelines:

<-- To view guidelines, move mouse pointer over cell with red triangle. Red triangle identif

Problem:

Unknown: Company's net income, net sales, debt-to-equity ratio

Assumption(s) All dollar values rounded to nearest dollar

Given information/inputs/arguments: Total assets Return on assets, ROA Return on equity, ROE Net profit margin

Values 87,631,181 11.67% 21.19% 11.59%

Excel solution method using cell references and formulas: Net income, form ROA = Net income/Total assets Net sales, from Profit margin = Net income/Net sales Total equity, from Return on equity = Net income/Total equity Debt to equity ratio

10,226,559 88,236,055 48,261,250 81.6%

Date:

cell with red triangle. Red triangle identifies a cell comment.

7 percent, ROE of 21.19 percent, and a net sales? Calculate the firm’s debt-to-equity ratio.

Comments Enter Total assets as a positive number Enter as percent, XX.XX%, or decimal, .XXXX Enter as percent, XX.XX%, or decimal, .XXXX Enter as percent, XX.XX%, or decimal, .XXXX

Chapter 4, Problem 30

Student's Name: Solution method uses cell references, cell formulas, and SUM function/formula to create an income statement

Guidelines:

<-- To view guidelines, move mouse pointer over cell with red triangle. Red triangle identifies

Problem: Blackwell Automotive’ s balance sheet at the end of its most recent fiscal year shows the following inform ation:

Assets: Cash and marketable securities Accounts receivable Inventory Total current assets Net plant and equipment Goodwill and other assets Total assets

Blackwell Automative, Balance Sheet Liabilities and Equity: $23,015 Accounts payable and accruals 141,258 Notes payable 212,444 Total current liabilities 376,717 Long-tem debt 711,256 Total liabilities 89,879 Common stock Retained earnings $1,177,852 Total liabilities and equity

In addition, it was reported that the firm had a net income of $156,042 on net sales of $4,063,5 89. a. What are the firm’s current ratio and quick ratio? b. Calculate the firm’s days’ sales outstanding, total asset turnover ratio, and fixed asset turnover ratio.

Unknown: Current ratio, Quick ratio, DSO = days sales outstanding, Total asset turnover ratio, and Fixed asset turnover ratio.

Assumption(s) Values to nearest dollar

Given information/inputs/arguments: Net income Net sales Days in year

Values 156,042 4,063,589 365

Comments Enter Net income as a positive value Enter Net sales as positive value Enter days in year

Excel solution method using cell references and formulas: a. Current ratio = Total current assets/Total current liabilities = a. Quick ratio = (Total current assets - Inventory)/Total current liabilities = b. DSO = 365/(Net sales/Accounts receivable) = b.Total asset turnover = Net sales/Total assets = b. Fixed asset turnover = Net sales/Net fixed assets =

Date:

ncome statement

ngle. Red triangle identifies a cell comment.

the following inform ation:

$163,257 21,115 184,372 168,022 352,394 313,299 512,159 $1,177,852

f $4,063,5 89. asset turnover ratio.

asset turnover ratio.

2.04 0.89 12.69 days 3.45 times 5.71 times

Textbook: Fundamentals of Corporate Finance, 5th Edition Authors: Robert Parrino, Thomas Bates, Stuart Gillan, David Kidwell Publisher: Wiley Excel solutions for selected problems at end of Chapter 3 Problem number 5 17 21

Solution Method Calculate net working capital Use VlookUp to calculate taxes Calculate net income

Worksheet tab name 5_Working_Capital 17_Taxes_Vlookup 21_Income_Statement

One way to return to the contents worksheet is to hold down the CTRL key and simultaneously press and hold dow

eously press and hold down the Page Up key

Chapter 3, Problem 5

Student's Name:

Solution method uses SUM function/formula

Guidelines:

<-- To view guidelines, move mouse pointer over cell with red triangle. Red triangle identifies a

Problem:

Working capital: Laurel Electronics reported the following information at its annual meeting: The company had cas securities worth $1,235,455, accounts payables worth $4,159,357, inventory of $7,121,599, accounts receivables o term notes payable worth $1,151,663, and other current assets of $121,455. What is the company’s net working ca

Unknown: Net working capital = current assets minus current liabilities

Assumption(s) All values to nearest dollar

Given information/inputs/arguments: Current asset: Cash and marketable securities Current asset: Accounts receivables Current asset: Inventory Current asset: Other current assets Current liabilities: Accounts payable Current liability: Short-term notes payable

Values 1,235,455 3,488,121 7,121,599 121,455 4,159,357 1,151,663

Excel solution method using SUM function: New working capital = current assets - current liabilities

6,655,610

Date:

h red triangle. Red triangle identifies a cell comment.

annual meeting: The company had cash and marketable y of $7,121,599, accounts receivables of $3,488,121, short5. What is the company’s net working capital?

Chapter 3, Problem 17 Solution method uses cell references and cell formulas.

Guidelines:

<-- To view guidelines, move mouse pointer over cell with red triangle. Red triangle identif

Problem: Tax: Manz Property Management Company just announced earnings before taxes of $1,478,936. Calculate its taxes using a flat tax rate of 30 percent

Unknown: Corporate income taxes with flat tax rate = earnings before taxes x tax rate %

Assumption(s) All values rounded to nearest cent

Given information/inputs/arguments: Taxable income Tax rate

Excel solution method: calculate income taxes Earnings before taxes, EBT Taxes

Values $ 1,478,936.00 30.00%

Student's Name:

cell with red triangle. Red triangle identifies a cell comment.

taxes of $1,478,936.

Comments Enter taxable income as a positive value Enter percentage as X.XXX% or .XXX

$ $

1,478,936.00 443,680.80

Date:

Chapter 3, Problem 21

Student's Name: Solution method uses cell references, cell formulas, and SUM function/formula to create an income statement

Guidelines:

<-- To view guidelines, move mouse pointer over cell with red triangle. Red triangle identifies a

Problem: Income statement: Nimitz Rental Company provided the following information to its auditors for the latest fisca revenues of $878,412, general and administrative expenses of $352,666, depreciation expenses of $131,455, lea

and interest expenses equal to $78,122. If the company’s average tax rate is 27 percent, what is its net income after taxes?

Unknown: Net income after taxes

Assumption(s) Values to nearest dollar

Given information/inputs/arguments: Revenues General and administrative expenses Depreciation expenses Leasing expenses Interest expense Tax rate

Values 878,412 352,666 131,455 108,195 78,122 27.00%

Excel solution method: create income statement: Revenue General and administrative expenses Leasing expenses EBITDA Depreciation expenses Earnings before interest and taxes, EBIT Interest expense Earnings before taxes, EBT Taxes Net income

878,412 352,666 108,195 417,551 131,455 286,096 78,122 207,974 56,153 151,821

Date:

to create an income statement

h red triangle. Red triangle identifies a cell comment.

mation to its auditors for the latest fiscal year: the company had depreciation expenses of $131,455, leasing expenses of $108,195,

percent, what is its net income after taxes?

Textbook: Fundamentals of Corporate Finance, 5th Edition Authors: Robert Parrino, Thomas Bates, Stuart Gillan, David Kidwell Publisher: Wiley Chapter 2: The Financial System and the Level of Interest Rates Excel solutions for selected problems at end of Chapter 2. Problem number 28 29

Problem type Use Fisher equation Calculate value in one year

Worksheet tab name 28_Fisher_Equation 29_Value_in_One_Year

One way to return to the contents worksheet is to hold down the CTRL key and simultaneously press and hold dow

eously press and hold down the Page Up key

Chapter 2, Problem 28

Student's Name:

Solution method uses cell formulas

Guidelines:

<-- To view guidelines, move mouse pointer over cell with red triangle. Red triangle identifies a

Problem:

Interest Rates: Imagine you borrow $500 from your roommate, agreeing to pay her back $500 plus 7 percent nominal inte Assume inflation over the life of the contract is expected to be 4.25 percent. What is the total dollar amount you will have in a year? What percentage of the interest payment is the result of the real rate of interest?

Unknown: Total amount to pay back in one year and what percentage is reat rate.

Assumption(s) All rates are annual rates with annual compounding.

Given information/inputs/arguments: Amount borrowed Annual nominal rate Annual inflation rate

Values 500.00 7.00% 4.25%

Excel solution method using cell formulas: In one year pay back original amount borrowed Also pay interest = amount borrowed * Interest rate Total amount to pay back = amount borrowed + interest Real rate = (1 + Nominal rate)/(1 + Inflation rate) - 1 Dollar interest using real rate = amount borrowed * real rate Real $ interest as percentage of $ total interest paid

$ $ $ $

500.00 35.00 535.00 2.638% 13.19 37.68%

Date:

h red triangle. Red triangle identifies a cell comment.

her back $500 plus 7 percent nominal interest in one year. at is the total dollar amount you will have to pay her back

Comments Enter amount as positive value Enter rate as percent, XX.XX%, or decimal .XXXX Enter rate as percent, XX.XX%, or decimal .XXXX

Chapter 2, Problem 29

Student's Name:

Solution method uses cell formulas

Guidelines:

<-- To view guidelines, move mouse pointer over cell with red triangle. Red triangle identifies a

Problem:

Interest Rates: Your parents have given you $1,000 a year before your graduation so that you can take a trip when you gra You wisely decide to invest the money in a bank CD that pays 6.75 percent interest. You know that the trip costs $1,025 rig and that the inflation for the year is predicted to be 4 percent. Will you have enough money in a year to purchase the trip?

Unknown: Amount of funds available in one year versus cost of trip in one year

Assumption(s) All rates are annual rates with annual compounding. All dividends occur at the end of the year.

Given information/inputs/arguments: Amount of funds from parents today Current cost of trip Annual rate on CD Annual inflation rate

$ $

Values 1,000.00 1,025.00 6.75% 4.00%

Excel solution method using cell formulas: Cost of trip in one year = Current cost * (1 + inflation rate) Value of CD in one year = amount invested * (1 + rate on CD)

$ $

1,066.00 1,067.50

Date:

h red triangle. Red triangle identifies a cell comment.

n so that you can take a trip when you graduate. est. You know that the trip costs $1,025 right now ough money in a year to purchase the trip?

Comments Enter amount as positive value Enter amount as positive value Enter rate as percent, XX.XX%, or decimal .XXXX Enter rate as percent, XX.XX%, or decimal .XXXX