Introduction to Corporate Finance,Third Canadian Edition by Laurence Booth amd Sean Cleary Solution

Introduction to Corporate Finance,Third Canadian Edition BY Laurence Booth amd Sean Cleary

Email: Richard@qwconsultancy.com

Introduction to Corporate Finance, Third Edition

Booth, Cleary

Chapter 1: An Introduction to Finance Multiple Choice Questions 1. Section: 1.1 Real versus Financial Assets Learning objective: 1.1 Level of Difficulty: Easy Solution: A 2. Section: 1.1 Real versus Financial Assets Learning objective: 1.2 Level of Difficulty: Medium Solution: C Net worth = Assets – Debts. Examples of real assets are residential structures, non-residential structures, machinery and equipment, durables, inventories, and land.

3. Section: 1.2 The Financial System Learning objective: 1.3 Level of Difficulty: Easy Solution: B 4. Section: 1.2 The Financial System Learning objective: 1.3 Level of Difficulty: Medium Solution: A In the financial system, households are the primary fund providers to the government and businesses.

5. Section: 1.2 The Financial System Learning objective: 1.3 Level of Difficulty: Medium Solution: C Banks, pension funds, and insurance firms do transform the nature of their underlying financial securities. However, mutual funds do not transform the nature of the underlying financial securities.

6. Section: 1.3 Financial Instruments and Markets Learning objective: 1.4 Level of Difficulty: Medium Solution: C 7. Section 1.4 The Global Financial Community Learning objective: 1.5 Level of Difficulty: Medium Solution: C 8. Section 1.4 The Global Financial Community

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Learning objective: 1.5 Level of Difficulty: Medium Solution: D Practice Problems 9. Section: 1.1 Real versus Financial Assets Learning objective: 1.2 Level of Difficulty: Medium Solution: Balance sheet: Residential structures: $1,000+ $3,000+$1,500 = $5,500 As there are no foreign assets or liabilities, the net worth or equity of the island is $5,500 To deal with Fred and Robinson’s debts: Assets Fred House Debt to Friday Robinson House Debt to Friday Friday House Loan to Fred Loan to Robinson Totals

Liabilities

$1,000 $500 $3,000 $2,000 $1,500 $ 500 $2,000 $8,000

$2,500

As net worth equals assets minus liabilities, the net worth of the economy equals total assets minus total liabilities or $5,500.

10. Section: 1.2 The Financial System Learning objective: 1.3 Level of Difficulty: Medium Solution: In the financial system, there are mainly four major sectors: Households, Government, Business, and Non-Residents. Within the field of finance there are four major areas: personal finance, government finance, corporate finance, and international finance. They closely interrelate to each other. Because they are all major parts of the whole financial system, what happens in one market will affect all the other markets.

11. Section: 1.2 The Financial System Learning objective: 1.3 Level of Difficulty: Medium Solution: Banks take in deposits and loan them out to fund borrowers. Pension funds take in pension contributions and pay out pensions to plan participants when they retire. Insurance firms Solutions Manual ..

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take in premiums and pay out when a certain event occurs. Mutual funds pool small funds together and make investments that small investors cannot make. Mutual funds also offer investment expertise to ordinary investors.

12. Section: 1.2 The Financial System Learning objective: 1.3 Level of Difficulty: Medium Solution: Five main reasons why financial and market intermediaries exist are: i) They provide anonymousness and convenience to all transaction parties. ii) They efficiently match the needs of the participants in the financial market and aggregate all the small transactions. iii) They have procedures for documentation of legal contracts to ensure security. iv) The risk of non-payment is alleviated by maintaining credit ratings and by controlling other accounts. v) Financial institutions transform the nature of the underlying financial securities.

13. Section: 1.2 The Financial System Learning objective: 1.3 Level of Difficulty: Medium Solution: A “credit crunch” refers to a situation when financial intermediaries such as banks and other lenders are either unable or unwilling, in general, to offer credit to borrowers. The crunch usually arises due to a lack of confidence, leading people, and other institutions, to be unwilling to lend to the financial intermediary. If very few people are willing to lend to the financial intermediary, then they, in turn, will not have the funds available to lend out and the “crunch” begins.

14. Section: 1.3 Financial Instruments and Markets Learning objective: 1.4 Level of Difficulty: Medium Solution: The two main types of primary market transactions are initial public offerings (IPOs), which are offered to the public by previously private firms, and seasoned equity offerings (SEOs), which are offered by firms already listed on the stock exchange.

15. Section: 1.3 Financial Instruments and Markets Learning objective: 1.4 Level of Difficulty: Difficult Solution: Secondary market transactions are those where ownership of existing shares changes hands, but the corporations or governments who originally issued the securities receive no financing; trading takes place between investors. This is critical to the functioning of the primary markets, because governments and companies would not be able to raise financing if investors were unable to sell their investments if necessary.

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Chapter 2: Business (Corporate) Finance Multiple Choice Questions 1. Section: 2.1 Types of Business Organizations Learning Objective 2.1 Level of difficulty: Medium Solution: D Most partnerships are formed in the professional services areas such as in accounting, investment banking, and medical professions. Factories (including a foundry) are the least likely to be operated as a partnership.

2. Section: 2.1 Types of Business Organizations Learning Objective 2.1 Level of difficulty: Medium Solution: B The limited and general partnerships are generally formed for tax reasons. However, as long as a trust pays out all its income to its income holders, and owns the debt and equity, the use of debt can be maximized to reduce or eliminate corporate income tax.

3. Section: 2.1 Types of Business Organizations Learning Objective 2.1 Level of difficulty: Medium Solution: D In a sole proprietorship, income is taxed at the personal tax rate.

4. Section: 2.1 Types of Business Organizations Learning Objective 2.1 Level of difficulty: Medium Solution: A A trust has more tax advantages than a corporation because income passes through trusts without any corporate tax to the unit owners. Unit holders pay tax on the income received. It avoids the double taxation of a corporation.

5. Section: 2.1 Types of Business Organizations Learning Objective 2.1 Level of difficulty: Medium Solution: A. The corporate form is the most popular form of business. While its ownership and control are separated, it does have double taxation in that both the income of the business and income passed to shareholders are taxed.

6. Section: 2.2 The Goals of the Corporation Learning Objective 2.2 Level of difficulty: Medium Solution: C The goal of a corporation is to maximize shareholders’ wealth.

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7. Section: 2.3 The Role of Management and Agency Issues Learning Objective 2.3 Level of difficulty: Medium Solution: D Market prices are the main concern of shareholders.

8 Section: 2.3 The Role of Management and Agency Issues Learning Objective 2.3 Level of difficulty: Medium Solution: B 9. Section: 2.3 The Role of Management and Agency Issues Learning Objective 2.3 Level of difficulty: Medium Solution: A. 10. Section: 2.4 Corporate Finance Learning Objective 2.5 Level of difficulty: Medium Solution: A All except choice A are concerns of capital budgeting.

11. Section: 2.5 Finance Careers and the Organization of the Finance Function Learning Objective 2.6 Level of difficulty: Easy Solution: B Generally speaking the treasurer does finance-related activities while the controller and accountant do the accounting-related activities.

12. Section: 2.5 Finance Careers and the Organization of the Finance Function Learning Objective 2.6 Level of difficulty: Medium Solution: B The treasurer would usually have the responsibility of credit management.

Practice Problems 13. Section: 2.1 Types of Business Organizations Learning Objective 2.1 Level of difficulty: Easy Solution: The four major forms of business organization are: i) Sole proprietorship – a business owned and operated by one person ii) Partnership – a business owned and operated by two or more people iii) Trust – a legal organization where assets are owned and managed, or controlled by different parties

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iv) Corporation – a business organized as a separate legal entity under corporation law, with ownership divided into transferable shares 14. Section: 2.1 Types of Business Organizations Learning Objective 2.1 Level of difficulty: Medium Solution: The differences are as follows: First, a sole proprietorship is owned and operated by one person, but a partnership is owned and operated by two or more people.

Second, a sole proprietorship is easier to set up than a partnership.

The similarities are as follows: First, in both forms, the owner is not separate from the business and therefore has unlimited liability.

Second, income from the business is taxed at the personal tax rate.

15. Section: 2.1 Types of Business Organizations Learning Objective 2.1 Level of difficulty: Medium Solution: First, a corporation is a distinct legal identity, which means its life can continue on indefinitely. Second, there is a very clear separation between ownership and control of the corporation. Third, corporate owners have limited liability whereas sole proprietors have unlimited liability.

16. Section: 2.1 Types of Business Organizations Learning Objective 2.1 Level of difficulty: Medium Solution: Every director and officer of a corporation in exercising their powers and discharging their duties shall: (a) Act honestly and in good faith with a view to the best interests of the corporation; and (b) Exercise the care, diligence, and skill that a reasonably prudent person would exercise in comparable circumstances.

17. Section: 2.1 Types of Business Organizations Learning Objective 2.1 Topic: Types of Business Organizations Level of difficulty: Medium Solution: The fall in the unit price was mirrored by an increase in the yield. The new yield was ($1.03/$12.26) = 8.4% per year.

18. Section: 2.1 Types of Business Organizations Learning Objective 2.1 Topic: Limited Liability (Types of Business Organizations) Level of difficulty: Medium Solution:

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When operating as a sole proprietorship, all of the assets of the company belong to the owner; the company’s debts are also the owner’s debts. Janice will have to pay her friends and family (the debtholders) the full $100,000 they are owed. This will leave her with $8,000.

A corporation exists independently from its owners. The $108,000 obtained from selling the assets will first be used to pay the debtholders what they are owed. Any remaining funds will be paid to Janice. Because the value of the assets is greater than the money owed to the debtholders, the payments are the same as they were with the sole proprietorship.

19. Section: 2.1 Types of Business Organizations Learning Objective 2.1 Topic: Limited Liability (Types of Business Organizations) Level of difficulty: Medium Solution: The debtholders will receive the entire $93,000 obtained from selling the assets. The remaining $7,000 that they were owed will not be paid because the company has no more funds.

Furthermore, the limited liability of shareholders in a corporation means that the debtholders have no legal right to expect Janice to pay them the rest of the money. Nonetheless, Janice receives nothing from the asset sale.

If the business were a sole proprietorship, the debtholders would receive the $93,000 from the sale of assets. However, they would also have the right to force Janice to pay them the extra $7,000 they were owed. Janice would not only receive no money from the sale of the assets, she would have to pay the extra $7,000!

20. Section: 2.3 The Role of Management and Agency Issues Learning Objective 2.4 Level of difficulty: Medium Solution: They differ in four areas.

1) Performance appraisal: Managers use accounting numbers like the return on investment or cash while shareholders use market prices.

2) Investment analysis: Managers use the IRR of the best division while shareholders use the external WACC. 3) The order of financing: Managers prefer retentions to debt and prefer debt to new equity while shareholders prefer debt first.

4) Risk concern: Managers are concerned with the preservation of the firm while shareholders are concerned about their portfolios.

21. Section: 2.3 The Role of Management and Agency Issues Learning Objective 2.4 Topic: Agency Issues Level of difficulty: Medium Solution: Dan is likely to prefer Project A because it will result in a $5,000 annual bonus for him, whereas Project B would provide only a $4,000 annual bonus. On the other hand, you (the owner) would be better off choosing Project B as it creates more value.

22. Section: 2.3 The Role of Management and Agency Issues

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Learning Objective 2.4 Topic: Agency Issues Level of Difficulty: Difficult Solution: Referring to Table 2-3, the major components of income are straight salary, annual bonus, share receipts or options, and other. Notice that in all cases, straight salary compensation is relatively low compared with the total package. Annual bonuses are generally somewhat larger, but the largest component by far in most cases is share compensation. This comes in two forms: grants of restricted stock awarded under incentive plans, and stock options, for which if the company’s stock price goes above a certain level, the executive gets the right to buy the stock at a fixed lower price.

23. Section: 2.3 The Role of Management and Agency Issues Learning Objective 2.4 Topic: Agency Issues Level of Difficulty: Medium Solution: The idea behind a stock option plan is simply to have the best interests of CEOs and senior managers coincide with those of shareholders. But the actual impact is doubtful. In reality, when a company’s stock falls and makes existing options worthless, new ones are granted to continue to provide incentive for managers.

Additionally, some companies were investigated by regulatory institutions on the “backdating” stock option issue. The fraud was that senior managers would get the compensation committee to award them stock options and then date them to an earlier period when the company’s stock price was low. Effectively, this meant that on the approval date, the stock was already worth a large amount of money, so there was little incentive value to the grant.

24. Section: 2.4 Corporate Finance Learning Objective 2.5 Topic: Corporate Finance Level of Difficulty: Medium Solution: Capital budgeting considers some basic questions: 1. How does a firm decide to expand its existing buildings or to construct or buy another building?

2. How does a firm decide to replace machinery and equipment? Just because it still works, does this mean that the firm should still use it?

3. How does a firm decide whether to buy or lease machinery and equipment?

4. How much stock or inventory should a firm carry? Should it keep stocks to meet every contingency or perhaps use just-in-time methods to reduce the investment?

25. Section: 2.4 Corporate Finance Learning Objective 2.5 Topic: Corporate Finance Level of Difficulty: Medium Solution:

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Financial management includes the following areas.

1. How do firms decide to extend credit to customers to purchase their product?

2. How do firms manage their cash? This is a non-interest-bearing asset, so it seems that it should be minimized, but corporations have considerable amounts of money on deposit at banks.

3. How do firms manage any temporary surplus cash?

4. Finally, why do firms take minority stakes in other firms, or more generally, how do they decide to buy 100 percent or less of another firm? This question leads us into corporate acquisitions and valuation.

26. Section: 2.4 Corporate Finance Learning Objective 2.5 Topic: Corporate Finance Level of Difficulty: Medium Solution: Corporate financing considers the following basic questions.

1. How does a firm decide between raising money through debt or equity?

2. In terms of equity how does it raise the equity: through retaining earnings or through issuing new equity?

3. In fact, how does a firm decide to go public and issue shares to the general public versus remaining a non-traded private company?

4. If it decides to issue debt, what determines whether this is bank debt or bonds issued to the public debt market?

5. What determines whether firms access the short-term money market versus borrowing from a bank?

27. Section: 2.5 Finance Careers and the Organization of the Finance Function Learning Objective 2.6 Topic: Finance career and the organization of the finance function Level of Difficulty: Medium Solution: The major jobs available in the financial industry include analysts, associates, managers, account managers, banking associates, security analysts, sales and trading people, private bankers, retail bankers, financial and investment analysts, portfolio managers, fixed income or equity traders, corporate finance associates and consultants. With financial innovations, more jobs are created.

28. Section: 2.5 Finance Careers and the Organization of the Finance Function Learning Objective 2.6 Level of difficulty: Medium Solution: The most senior person is the chief financial officer (CFO), or in more traditional companies, the senior vice-president of finance. Under the CFO are the two main finance jobs: the treasurer and the controller. The treasurer is responsible for forecasting, pension management, capital budgeting, cash management, credit management, financing, and risk management. The controller focuses on accounting issues such as compliance, tax management, internal auditing, and budgeting.

29. Section: 2.5 Finance Careers and the Organization of the Finance Function

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Learning Objective 2.6 Topic: Corporate Finance and Finance Careers Level of Difficulty: Medium Solution: The controller’s numbers indicate that the computer system will add ($60,000 – $50,000) = $10,000 of value to the firm. That would indicate that you should proceed with the purchase.

In general, the corporate treasurer has responsibility for capital budgeting decisions of this sort, including estimating costs and savings, determining the need for financing, and considering any risks involved. In this case, the interest expense identified by the treasurer brings the net value created down to –$1,000. It would be best to heed the treasurer and not purchase the computer system.

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Chapter 3: Financial Statements Multiple Choice Questions 1. Section: 3.1 Accounting Principles Learning Objective: 3.2 Level of difficulty: Medium Solution: A 2. Section: 3.2 Organizing a Firm’s Transactions Learning Objective: 3.2 Level of difficulty: Easy Solution D Choice D is correct. As a result of the transaction, inventories increase (debit) and accounts payable increases (credit). Note that cash and inventories are both on the assets side of the balance sheet.

3. Section: 3.2 Organizing a Firm’s Transactions Learning Objective: 3.2 Level of difficulty: Medium Solution: A. The CICA Handbook contains GAAP in Canada.

4. Section: 3.2 Organizing a Firm’s Transactions Learning Objective: 3.2 Level of difficulty: Medium Solution: D Revenues are only recognized when there is a verifiable sale, which may or may not take place at the same time cash is exchanged.

5. Section: 3.3 Preparing Accounting Statements Learning Objective: 3.3 Level of difficulty: Easy Solution: A Land is not applicable to CCA. 6. Section: 3.3 Preparing Accounting Statements Learning Objective: 3.3 Level of difficulty: Medium Solution: A Remember that decreases of assets and increases of liabilities are cash inflows, and vice versa.

Payment of a dividend is a cash outflow.

7. Section: 3.3 Preparing Accounting Statements Learning Objective: 3.3 Level of difficulty: Easy Solution: C

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Amortization (depreciation) is the most common non-cash item. The other choices are cash items.

8. Section: 3.3 Preparing Accounting Statements Learning Objective: 3.3 Level of difficulty: Medium Solution: C 9. Section: 3.3 Preparing Accounting Statements Learning Objective: 3.3 Level of difficulty: Easy Solution: D Purchase of inventory is a cash flow from operations, not financing.

10. Section: 3.3 Preparing Accounting Statements Learning Objective: 3.3 Level of difficulty: Medium Solution: D Remember that decreases (increases) of assets and increases (decreases) of liabilities are cash inflows (cash outflows). Only the decrease of accounts payable decreases cash flow.

11. Section: 3.3 Preparing Accounting Statements Learning Objective: 3.3 Level of difficulty: Medium Solution: A. The issuance of long-term bonds is a financing activity, not an operating activity.

12. Section: 3.4 Tim Hortons Inc. Accounting Statements Learning Objective: 3.4 Level of difficulty: Medium Solution: C A firm that controls 80% of another firm consolidates all of the controlled firm and then separates out the minority part that it does not control (20%).

13. Section: 3.4 Tim Hortons Inc. Accounting Statements Learning Objective: 3.4 Level of difficulty: medium Solution: D Current assets are assets that can be converted to cash within one year or liquid assets. Land is difficult to convert to cash, so it is considered a long-term asset. Bonds of other companies held as short-term investments are considered as current assets. Bonds issued by a company must be treated as long-term liabilities.

14. Section: 3.5 The Canadian Tax System Learning Objective: 3.5 Level of difficulty: Medium

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Solution: B If the selling price is greater than the original capital cost, a capital gain arises.

15. Section: 3.5 The Canadian Tax System Learning Objective: 3.5 Level of difficulty: Medium Solution: D The provincial tax rates and structures in Ontario and Quebec are very different.

Practice Problems 16. Section: 3.2 Organizing a Firm’s Transactions Learning Objective: 3.2 Level of difficulty: Easy Solution: Some basic principles of the CICA Handbook are: the going concern principle (the firm is not in imminent threat of bankruptcy); a period of analysis (a year-end balance sheet); the matching principle (revenues must be matched with the costs that generated those revenues); and revenue recognition principles (when there is a verifiable sale).

17. Section: 3.2 Organizing a Firm’s Transactions Learning Objective: 3.2 Level of difficulty: Easy Solution: Total Assets = Total Liabilities + Shareholders’ Equity Shareholders’ Equity = $429,500 – $379,000 = $50,500 18. Section: 3.3 Preparing Accounting Statements Learning Objective: 3.3 Level of difficulty: Easy Solution: Retained Earnings (Ending) = Retained Earnings (Beginning) + Net Income – Dividends = 5,000 + 7,500 – 4,000 = $8,500 19. Section: 3.3 Preparing Accounting Statements Learning Objective: 3.3 Level of difficulty: Easy Solution: a. With a five-year life and straight-line amortization (based on “equal value each year”), the annual charge to amortization will be $2,400 / 5 = $480 (total for all six boats). b.

Year Amortization Book Value (net) 0 – 2,400 1 480 1,920 2 480 1,440 3 480 960 4 480 480

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480

0

c With a five-year life and straight-line amortization (based on “equal value each year”), the annual charge to amortization will be ($2,400 – $400)/ 5 = $400 (total for all six boats).

20. Section: 3.5 The Canadian Tax System Learning Objective: 3.5 Level of difficulty: Medium Solution: Year 1: ½ Capital Cost CCA = $1,200x15%

Year 2:

Year 3: Year 4: Year 5:

UCC (end of Year 1) Add ½ Capital Cost UCC (start of Year 2) CCA = $2,220.00x15% UCC CCA = $1,887.00x15% UCC CCA = $1,603.95x15% UCC CCA = $1,363.36x15% UCC

$1,200.00 180.00 1,020.00 1,200.00 2,220.00 333.00 1,887.00 283.05 1,603.95 240.59 1,363.36 204.50 1,158.86

21. Section: 3.2 Organizing a Firm’s Transactions Learning Objective: 3.2 Level of difficulty: Medium Solution: The correct entries are as follows: Debit accounts receivable by $70,000 Credit sales revenue by $70,000 Debit cost of goods sold (COGS) by $40,000 Credit inventories by $40,000 22. Section: 3.3 Learning Objective: 3.3 Level of difficulty: Medium Solution: Total Shareholders’ Equity ($50,500) = Capital Stock + Retained Earnings ($8,500).

Therefore, Capital Stock = $42,000 23. Section: 3.3 Preparing Accounting Statements Learning Objective: 3.3 Level of difficulty: Medium Solution: Balance Sheet for Finns’ Fridges Assets Liabilities and Owners’ Equity

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Current assets Property and equipment (net) Total assets

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2,000 Interest payable 4,000 Other current liabilities Long-term liabilities Owners’ equity Total liabilities and owners’ 6,000 equity

200 800 3,200 1,800 6,000

Income Statement for Finns’ Fridges Revenues Less: expenses Amortization expense Interest expense

2,000 (1,000) ( 200)

Net income

$800

24. Section: 3.3 Preparing Accounting Statements Learning Objective: 3.3 Level of difficulty: Medium Solution: Working Capital = Current Assets – Current Liabilities = $2,000 – ($200 + $800) = $1,000 25. Section: 3.3 Preparing Accounting Statements Learning Objective: 3.3 Level of difficulty: Medium Solution: From question 23, net income (before tax) is $800. At a tax rate of 30 percent, the income tax payable is 0.30 x $800 = $240. Net income (after tax) = $ 800 – $240 = $560.

26. Section: 3.3 Preparing Accounting Statements Learning Objective: 3.3 Level of difficulty: Medium Solution: There are 100 shares outstanding at the moment. Based on the net income from question 23, EPS = Net income / Shares outstanding = $800 / 100 = $8 per share.

27. Section: 3.2 Organizing a Firm’s Transactions Learning Objective: 3.2 Level of difficulty: Difficult Solution: Canadian GAAP uses historic cost accounting. The fact that the retailer has raised the price for this equipment will not be reflected on the balance sheet of Finns’ Fridges. Therefore, the correct amount of property and equipment (gross) is 25 refrigerators x $200 each = $5,000.

The amortization expense for the first year was $1,000 so that property and equipment (net) = $4,000, as previously given.

28. Section: 3.3 Preparing Accounting Statements Learning Objective: 3.3 Level of difficulty: Difficult Solution: The lost rental income will reduce the company’s revenues (in practice, this might Solutions Manual ..

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show up as “Bad Debt Expense,” but we will simply alter the revenues.) Reduction = 5 students x $10 = $50.

Income Statement for Finns’ Fridges (Revised) Revenues 1,950 Amortization expense 1,000 Interest expense 200 Net income

750

The stolen refrigerator “impairs” the value of property and equipment. The value of one fridge is $4,000/25 = $160. Current assets will also be reduced because of the lost revenues. On the right side of the balance sheet, owners’ equity will change so that the “balance” is maintained.

Balance Sheet for Finns’ Fridges (Revised) Assets Liabilities and Owners’ Equity Current assets 1,950 Interest payable 200 Property and equipment 3,840 Other current liabilities 800 (net) Long-term liabilities 3,200

Total assets

Owners’ equity 5,790 Total liabilities equity

and owners’

1,590 5,790

29. Section: 3.3 Preparing Accounting Statements Learning Objective: 3.3 Level of difficulty: Medium Solution: The cash flow from financing is the total amount raised by issuing stock (or debt) less any dividends paid (or stock or debt repurchased). For Corine’s Candies Inc., cash flow from financing in 2012 = $1.3 million – $1.2 million = $0.1 million. That is, financing activities generated cash.

30. Section: 3.3 Preparing Accounting Statements Learning Objective: 3.3 Level of difficulty: Medium Solution: a.

Revenue 90,000.00 Cost of sales 40,000.00 Rent 10,000.00 Depreciation 2,000.00 Interest 2,000.00 Income before tax 36,000.00 Taxes paid 12,600.00 Net income 23,400.00

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b. Dividends = net income × dividend payout ratio = 23,400 × 30 percent = 7,020 Retained earnings = net income – dividends = 23,400 – 7,020 = 16,380.

31. Section: 3.3 Preparing Accounting Statements Learning Objective: 3.3 Level of difficulty: Difficult Solution: Remember that decreases (increases) of assets and increases (decreases) of liabilities are cash inflows (cash outflows).

Net income Depreciation Deferred income taxes Decrease in inventories Decrease in accounts receivable Decrease in accounts payable Decrease in accruals Decrease in prepaids Cash Flow from Operations

+80,000 +6,000 +2,000 +10,000 +2,000 -1,500 -2,200 +3,600 99,900

32. Section: 3.3 Preparing Accounting Statements Learning Objective: 3.3 Level of difficulty: Difficult Solution: Net Income Depreciation Deferred income taxes Increase in inventories Decrease in accounts receivable Increase in accounts payable Decrease in accruals Decrease in prepaids Cash flow from operations

$90,000 +10,000 +5,000 –20,000 +1,000 +2,000 –2,500 +5,000 90,500

Remember that decreases (increases) of assets and increases (decreases) of liabilities are cash inflows (cash outflows).

33. Section: 3.3 Preparing Accounting Statements Learning Objective: Level of Difficulty: Easy Solution: Total liabilities = total assets – common equity – retained earnings = 425,600 – 125,000 – 85,000 = 215,600 34. Section: 3.3 Preparing Accounting Statements Solutions Manual ..

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Learning Objective: 3.3 Level of Difficulty: Easy Solution: Additional retained earnings = net income × (1 – dividend payout ratio) = 9,300 × (1 – 25 percent) = 6,975.

Ending retained earnings = beginning retained earnings + additional retained earnings = 8,000 + 6,975 = 14,975 35. Section: 3.3 Preparing Accounting Statements Learning Objective: 3.3 Level of Difficulty: Easy Solution: EPS = earnings/number of shares outstanding = $105 million/50 million = $2.10 36. Section: 3.3 Preparing Accounting Statements Learning Objective: 3.3 Level of Difficulty: Easy Solution: cash flow from financing = debt – interest – dividends = $2 million – $2 million × 10 percent – $1 × 0.5 million = $1.3 million NOTE: in cash flow statement preparation, the interest expense is generally considered a cash flow from operations, not financing. Using the indirect method, the cash flow from operations begins with net income, from which interest has already been deducted. Given this, the alternative solution of $2 million - $500,000 = $1.5 million is perfectly acceptable.

37. Section: 3.3 Preparing Accounting Statements Learning Objective: 3.3 Level of Difficulty: Medium Solution: Current assets in year 1 = cash and equivalents + accounts receivable + inventory = 100,000 + 25,000 + 13,000 = 138,000 Current assets in year 2 = 80,000 + 20,000 + 15,000 = 115,000 The change in dollar amount = 115,000 – 138,000 = –23,000 The change in percentage = –23,000/138,000 = –16.67 percent 38. Section: 3.3 Preparing Accounting Statements Learning Objective: Level of difficulty: Easy Solution: Net working capital in year 2 = current assets – current liabilities = 781 – 720 = 61 39. Section: 3.3 Preparing Accounting Statements Learning Objective: Level of difficulty: Medium Solution: Net working capital in year 1 = current assets – current liabilities = 840 – 790 = 50 Changes in net working capital = 61 – 50 = 11 40. Section: 3.3 Preparing Accounting Statements

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Learning Objective: Level of difficulty: Difficult Solution: Additions in retained earnings = 800 – 556 = 244 Net income = additions in retained earnings/(1 – dividend payout ratio) = 244/(1 – 40%) = 406.67 41. Section: 3.3 Preparing Accounting Statements Learning Objective: Level of difficulty: Medium EPS = net income/number of shares outstanding = 406.67/150 = 2.71 42. Section: 3.4 Tim Hortons Inc. Accounting Statements Learning Objective: 3.4 Level of difficulty: Medium Solution: The earnings (net income) figure is $382.812 million, and the earnings per common share (EPS) is reported as $2.36. Therefore, there must have been 382.812 million / 2.36 = 162,208,475 shares outstanding at the end of 2011.

43. Section: 3.4 Tim Hortons Inc. Accounting Statements Learning Objective: 3.4 Level of difficulty: Medium Solution:

Cash and cash equivalents Restricted cash and cash equivalents Restricted investments Account receivable, net Notes receivable, net Deferred income taxes Inventories and other, net Advertising fund restricted assets Total current assets

01-Jan-12 02-Jan-11 Change ($) 126,497 574,354 –447,857 130,613 – 173,667 10,144 5,281 136,999 37,765 620,966

67,110 37,970 182,005 12,543 7,025 100,712 27,402 1,009,121

63,503 –37,970 –8,338 –2,399 –1,744 36,287 10,363 –388,155

Change (%) –78% 95% –100% –5% –19% –25% 36% 38% –38%

Except for increases in restricted cash and cash equivalents, net inventories and other, and advertising fund restricted assets, all current asset items decreased. Cash and cash equivalents decreased by the largest amount in dollar value. However, restricted investments experienced the largest decreases in terms of percent.

44. Section: 3.4 Tim Hortons Inc. Accounting Statements Learning Objective: 3.4 Level of difficulty: Medium

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Solution: Dividend payments = 110.187 million. At $0.68 per share, there were 110.187 million / 0.68 = 162,039,706 shares outstanding during 2011. This figure is slightly lower than what we calculated in question 42. The difference could be due to rounding of the figures, or may have resulted because extra shares were issued after the dividends were paid.

Also note that dividends are paid at a point in time whereas earnings per share are calculated using a weighted average. Tim Hortons repurchased its own shares as well. The weighted average would almost never equal the number of shares outstanding on dividend dates under that scenario.

45. Section: 3.4 Tim Hortons Inc. Accounting Statements Learning Objective: 3.4 Level of difficulty: Medium Solution: average tax rate is $157.854 million/$543.602 million=29.04 percent.

46. Section: 3.4 Tim Hortons Inc. Accounting Statements Learning Objective: 3.4 Level of difficulty: Medium Solution: The sales growth rate in 2011 is $2,012,170/$1,755,244 – 1 = 14.64%.

The sales growth rate in 2010 is $1,755,244/$1,704,065 – 1 = 3%.

The sales growth rate increased by almost five times from 2010 to 2011.

47. Section: 3.5 The Canadian Tax System Learning Objective: 3.5 Level of difficulty: Easy Solution: 46.41 percent. The top personal tax rate in Ontario is 46.41 percent.

48. Section: 3.5 The Canadian Tax System Learning Objective: 3.5 Level of difficulty: Medium Solution: a. The sale price is greater than the original capital cost (purchase price), so there is a capital gain of $30,000 – $25,000 = $5000.

Reducing the asset pool by $25,000 (lesser of the capital cost and selling price) would leave $25,000 – $15,000 = $10,000. This positive value means there will be a CCA recapture of $10,000. b. There is no capital gain as the sale price is less than the purchase price.

Reducing the asset pool by the $20,000 proceeds from the sale would leave $5,000. Again, the positive value indicates a CCA recapture, this time for $5,000. c. As in part (b), there is no capital gain.

Reducing the asset pool by the $10,000 proceeds from the sale would leave − $5,000. As there are no further assets in the pool, its value must fall to zero; a terminal loss of $5,000 will be claimed.

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49. Section: 3.5 The Canadian Tax System Learning Objective: 3.5 Level of difficulty: Medium Solution: The actual tax to be paid will be based on CCA claimed, not the reported amortization.

For firm A, earnings before tax on its tax statements will be $1 million – $200,000 (CCA) = $800,000. At a tax rate of 30 percent, it will pay $240,000 in taxes.

Firm B will have earnings before tax of $1 million – $400,000 = $600,000. It will therefore pay $600,000 x 30% = $180,000 in taxes.

50. Section: 3.5 The Canadian Tax System Learning Objective: 3.5 Level of difficulty: Medium Solution: Net income (before tax) will be $1 million – $200,000 (amortization) = $800,000 for both firms (on their public financial statements).

Firm A, having paid $240,000 in taxes (see Practice Problem 49) appears to have paid $240,000 / $800,000 = 30%.

Firm B appears to have paid $180,000 / $800,000 = 22.5%. This lower apparent tax rate is the direct result of the higher CCA claim.

51. Section: 3.5 The Canadian Tax System Learning Objective: 3.5 Level of difficulty: Difficult Solution: GG Inc. Income Statement for Y2012 Revenue $90,000 Cost of sales 10,000 Rent 10,000 Depreciation 1,500 Interest 2,000 Salary 4,000 Taxable income 62,500 Taxes paid (30%) 18,750 Net income 43,750 52. Section: 3.5 The Canadian Tax System Learning Objective: 3.5 Level of difficulty: Medium Solution: Year 1: ½ Capital Cost of 1st plane CCA = $35,000 x 25% UCC (end of Year 1) Year 2: Add ½ Capital Cost of 1st plane Add ½ Capital Cost of 2nd plane UCC (start of Year 2) CCA = $106,250 x 25% Solutions Manual ..

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$35,000.00 8,750.00 26,250.00 35,000.00 45,000.00 106,250.00 26,562.50 Chapter 3

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UCC (end of Year 2) Add ½ Capital Cost of 2nd plane UCC (start of Year 3) CCA = $124,687.50 x 25% UCC

79,687.50 45,000.00 124,687.50 31,171.88 93,515.62

53. Section: 3.5 The Canadian Tax System Learning Objective: 3.5 Level of difficulty: Medium Solution: In Year 2, the value of “Net additions” to the asset pool will be $90,000 – 50,000 = 40,000.

Year 1:

Year 2:

Year 3:

½ Capital Cost of 1st plane CCA = $35,000 x 25% UCC (end of Year 1) Add ½ Net Additions UCC (start of Year 2) CCA = $46,250 x 25% UCC (end of Year 2) Add ½ Net Additions UCC (start of Year 3) CCA = $54,687.50 x 25% UCC

$35,000.00 8,750.00 26,250.00 20,000.00 46,250.00 11,562.50 34,687.50 20,000.00 54,687.50 13,671.88 41,015.62

54. Section: 3.5 The Canadian Tax System Learning Objective: 3.5 Level of difficulty: Medium Solution: Since the selling price is higher than the original cost, there is a capital gain.

Capital gain = selling price – original cost = 40,000 – 30,000 = $10,000.

CCA recapture (terminal loss) = lower of selling price and original cost – UCC = 30,000 – 5,000 = $25,000.

The number is positive, so it represents a CCA recapture of $25,000.

55. Section: 3.5 The Canadian Tax System Learning Objective: 3.5 Level of difficulty: Difficult Solution: a. Yes. Firms apply GAAP when reporting public financial statements, but have to use CCA when reporting to CRA. b. Firm A pays higher tax. It has lower CCA, and thus higher taxable income. c. The actual tax to be paid will be based on CCA claimed, not the reported amortization. For firm A, earnings before tax on its tax statements will be $10 million – $1 million in CCA = $9 million. At a tax rate of 30 percent, it will pay $2.7 million in taxes.

Firm B will have earnings before tax of $10 million – $2 million = $8 million. It will therefore pay $8 million x 30% = $2.4 million in taxes. d. Firm A: net income = earnings before tax – tax=$9 million – $2.7 million = $6.3 million.

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Firm B: net income = earnings before tax – tax = $8 million – $2.4 million = $5.6 million.

56. Section: 3.3 Preparing Accounting Statements Learning Objective: 3.3 Topic: Corporate Tax Level of Difficulty: Difficult a) The beginning UCC, CCA, and ending UCC in year 1 to 3 for the first machine are as follows. beginning year UCC CCA ending UCC 1 750,000.00

112,500.00 637,500.00

2 637,500.00

191,250.00 446,250.00

3 446,250.00

133,875.00 312,375.00

b) The beginning UCC, CCA, and ending UCC in years 2 and 3 for the second machine are as follows. beginning year UCC CCA ending UCC 2 625,000.00

93,750.00

531,250.00

3 531,250.00

159,375.00 371,875.00

c) In the third year the total ending UCC = 312,375 + 371,875 = 684,250.

57. Section: 3.5 The Canadian Tax System Learning Objective: 3.5 Level of Difficulty: Easy Solution: Kash Kow will pay 25 percent tax or $0.25 on each $1 of net income, leaving $0.75 to be paid as a dividend. When the high-income Ontario resident receives this dividend, it will be subject to tax at the personal rate of 31.34 percent; a further 0.3134 x $0.75 = $0.23505 will be paid as personal income tax leaving $0.51495. Of the original $1 of net income earned by Kash Kow, the government’s cut is $0.48505, or nearly half!

58. Section: 3.5 The Canadian Tax System Learning Objective: 3.5 Level of difficulty: Easy Solution: 1 CCA1 =  2,000  0.45 = 450 2 UCC1 = 2,000 − 450 = 1,550 CCA2 = 0.45  1,550 = 697.50

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Chapter 4: Financial Statement Analysis and Forecasting Multiple Choice Questions 1. Section: 4.1 Consistent Financial Analysis Learning Objective: 4.1 Level of difficulty: Easy Solution: A Accounting standards are different across countries. Even if the input data are the same, the ratios for companies across countries may be different. Thus, we cannot directly compare ratios from annual reports of companies across countries. Debt ratio has different definitions across countries.

2. Section: 4.2 A Framework for Financial Analysis Learning Objective: 4.2 Level of difficulty: Medium Solution: D NI NI Sales Assets =   = (Net Profit Margin)(Asset Turnover)(Leverage) E Sales Assets Equity NI NI Assets =  = ROI * Leverage E Assets Equity 3. Section: 4.2 A Framework for Financial Analysis Learning Objective: 4.2 Level of difficulty: Difficult Solution: B Net profit margin = NI/Sales = (2,090)(1 – 0.4)/(5,600) = 1,254/5,600 = 22.39% Asset Turnover = Sales/Assets = 5,600/ (30,900 + 16,500) = 5,600/47,400 = 11.81% Leverage = Assets/Equity = 47,400/16,500 = 2.87 4. Section: 4.2 A Framework for Financial Analysis Learning Objective: 4.2 Level of difficulty: Difficult Solution: C To increase return on equity (ROE), we could decrease equity, increase debt level, decrease corporate tax rate (increase NI), or increase earnings after tax (NI), holding all the others unchanged.

5. Section: 4.3 Leverage Ratios Learning Objective: 4.3 Level of difficulty: Medium Solution: D Liabilities 500,000 + 90,000 + 150,000 + 2,000,000 2,740,000 = = = 0.49 Debt Ratio = TA 5,630,000 5,630,000 6. Section: 4.3 Leverage Ratios Solutions Manual ..

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Learning Objective: 4.3 Level of difficulty: Medium Solution: C D 2,000,000 = = 0.69 Debt-Equity Ratio = SE 2,800,000 + 90,000 EBIT 360,000 + 150,000 = = 3.4 Times Interest Earned Ratio = I 150,000 7. Section: 4.4 Efficiency Ratios Learning Objective: 4.4 Level of difficulty: Medium Solution: B Sales − COGS 1,090,000 − 380,000 710,000 = = = 65% Gross Profit Margin = Sales 1,090,000 1,090,000 EBIT 1,090,000 − 380,000 − 200,000 510,000 = = = 47% Operating Margin = Sales 1,090,000 1,090,000 8. Section: 4.5 Productivity Ratios Learning Objective: 4.5 Level of difficulty: Medium Solution: A INV 250,000 = = 84days Days Sales in Inventory = ADS 1,090,000 / 365 9. Section: 4.6 Liquidity Ratios Learning Objective: 4.6 Level of difficulty: Medium Solution: C CA 400,000 + 500,000 + 250,000 = = 20.4% Working Capital Ratio = TA 5,630,000 10. Section: 4.3 Leverage Ratios Learning Objective: 4.3 Level of difficulty: Medium Solution: D Invested Capital = Interest-bearing debt+ SE = 2,000,000 + (2,800,000 + 90,000) = $4,890,000 11. Section: 4.3 Leverage Ratios Learning Objective: 4.3 Level of difficulty: Easy Solution: D Times interest earned is measured as EBIT divided by interest.

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Learning Objective: 4.6 Level of difficulty: Easy Solution: B Current ratio indicates how many dollars of current assets are available for one dollar of current liabilities.

13. Section: 4.4 Efficiency Ratios Learning Objective: 4.4 Level of difficulty: Easy Solution: A Gross profit margin indicates how much gross profit is generated from one dollar of sales.

14. Section: 4.5 Productivity Ratios Learning Objective: 4.5 Level of difficulty: Easy Solution: A Average collection period measures the average number of days to collect accounts receivable.

15. Section: 4.7 Valuation Ratios Learning Objective: 4.7 Level of difficulty: Easy Solution: A Dividend yield is the only financial ratio that relates dividend policy to external stock market performance.

Practice Problems 16. Section: 4.2 A Framework for Financial Analysis Learning Objective: 4.2 Level of difficulty: Easy Solution: The financial statements for Finns’ Fridges refer to “Owners’ Equity,” but this is equivalent to shareholders’ equity.

For year 1, ROE = NI / SE = 413/1,213 = 34.0%.

For year 2, ROE = 426/1,429 = 29.8%.

The higher the ROE, the better, so Finns’ Fridges did worse in year 2 than in year 1.

17. Section: 4.2 A Framework for Financial Analysis Learning Objective: 4.2 Level of difficulty: Easy Solution: For year 1, Leverage Ratio = TA / SE = 4,990 / 1,213 = 4.114, while at the end of year 2, Leverage Ratio = TA / SE = 4,381 / 1,429 = 3.066. Thus, Finns’ Fridges is leveraging its owners’ equity much less in year 2.

18. Section: 4.2 A Framework for Financial Analysis Learning Objective: 4.2 Level of difficulty: Easy Solution: ROA = NI / TA

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For year 1, ROA = 413 / 4,990 = 8.28% and for year 2, ROA = 426 / 4,381 = 9.72%. The return on assets for Finn’s Fridges has improved (increased) from year 1 to year 2.

19. Section: 4.3 Leverage Ratios Learning Objective: 4.3 Level of difficulty: Easy Solution: From the year 2 Balance Sheet, Debt Ratio = TL / TA = 2,952 / 4,381 = 0.674 and the Debt-Equity Ratio = D / SE = 2,400 / 1,429 = 1.679. Using either ratio, Finns’ Fridges is much more highly leveraged than its competitor.

20. Section: 4.4 Efficiency Ratios Learning Objective: 4.4 Level of difficulty: Medium Solution: Operating Margin = NOI / S = 4.426 / 30.16 = 14.7% for the large competitor firm.

Operating income is equal to EBIT, so Finns’ ratios will be higher (better): 790/1,950 = 40.5% for year 1 and 768/2,200 = 34.9% for year 2. Even though Finns’ operating margin is on the decline, it is higher than the competitor’s, which means Finns’ has been much more efficient at creating income from its sales.

21. Section: 4.2 A Framework for Financial Analysis Learning Objective: 4.2 Level of difficulty: Medium Solution:

Efficiency Ratio = NI / Sales Productivity Ratio = Sales / TA

Year 1 413 / 1,950 = 21.2%

Year 2 426 / 2,200 = 19.4%

1,950 / 4,990 = 39.1%

2,200 / 4,381= 50.2%

Efficiency fell slightly from year 1 to year 2, but productivity increased significantly; the ROA increased because Finns’ Fridges is generating more sales per dollar of assets (productivity).

22. Section: 4.3 Leverage Ratios Learning Objective: 4.3 Level of difficulty: Medium Solution: For Year 2, CFO = 426 + 1,212 + (–25) = 1,613. The cash flow to debt ratio = CFO / D = 1,613 / 2,400 = 0.672. In other words, the annual cash flow from operations is approximately two-thirds of the total (interest-bearing) debt of the company. If we invert this ratio, 1/ 0.672= 1.488, we find that it would take about one and a half years for the firm to repay its debt.

23. Section: 4.4 Efficiency Ratios Learning Objective: 4.4 Level of difficulty: Medium Solution:

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In year 1, the Operating Margin = NOI / S = 790 / 1,950 = 40.5%, while in year 2, Operating Margin = 768 / 2,200 = 34.9%. Although a decreasing operating margin is a bad sign, the decline from one year to the next may not indicate a trend.

24. Section: 4.5 Productivity Ratios Learning Objective: 4.5 Level of difficulty: Medium Solution: For year 1, fixed asset turnover = S / NFA = 1,950 / 3,840 = 0.508, while for year 2, fixed asset turnover = 2,200 / 3,888 = 0.566. Finns’ Fridges seems to be getting more productive in terms of generating sales from its assets (but two years is insufficient to call this change a trend).

25. Section: 4.6 Learning Objective: 4.6 Liquidity Ratios Level of difficulty: Medium Solution:

Working Capital Ratio = CA / TA Current Ratio = CA / CL

Year 1 1,150 / 4,990 = 23.0%

Year 2 493 / 4,381 = 11.3%

1,150 / (200+177+200) = 1.993 = 199.3%

493 / (160+182+210) = 0.893 = 89.3%

Although Finns’ Fridges experienced a drop in liquidity from year 1 to year 2, it is still much more liquid than its competitor based on either of these two ratios.

26. Section: 4.8 Financial Forecasting Learning Objective: 4.8 Level of difficulty: Medium Solution: Percentage of Sales Balance Sheet for Finns’ Fridges Year 2 Sales Assets Cash Property and equipment (net) Total assets Liabilities and Owners’ Equity Interest payable Tax payable Dividends payable Long-term debt Total liabilities Solutions Manual ..

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% of Sales

2,200 493 3,888 4,381

22.4% 176.7% 199.1%

160 182 210 2,400 2,952

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Common shares Retained earnings Total owners’ equity Total liabilities and owners’ equity

1,000 429 1,429 4,381

45.5% 19.5% 65.0% 199.1%

27. Section: 4.8 Financial Forecasting Learning Objective: 4.8 Level of difficulty: Medium Solution: a.

Forecast of Balance Sheet for Finns’ Fridges % of Sales Sales Assets Cash Property and equipment (net) Total assets Liabilities and Owners’ Equity Interest payable Tax payable Dividend payable Long-term debt Total liabilities Common shares Retained earnings Total owners’ equity Total liabilities and owners’ equity

Year 3 Forecast 2,600

22.4% 176.7% 199.1%

582 4,595 5,177

7.3% 8.3% 9.5% -

189 215 248 2,400 3,052 1,000 429 1,429 4,481

b. External financing will be needed to make up the difference between total assets, and total liabilities and owners’ equity on the initial forecast of the balance sheet. The amount required is therefore $5,177 – $4,481 = $696.

28. Section: 4.8 Financial Forecasting Learning Objective: 4.8 Level of difficulty: Medium Solution: In Year 2, selling expenses were $220 / $2,200 = 10% of revenues. With revenues of $2,600 for Year 3, we can forecast selling expenses to be $260. The other information given is sufficient to create a forecast of the company’s income statement from which we find that the company can expect net income of $559 in year 3.

Forecast of Income Statement for Finns’ Fridges Year 3

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Revenues (net of bad debts) Selling & admin expenses EBITDA Amortization expense EBIT Interest expense Earnings before tax Tax (30%) Net income

2,600 260 2,340 1,422 918 120 798 239 559

29. Section: 4.8 Financial Forecasting Learning Objective: 4.8 Level of difficulty: Medium Solution: For Year 1, Dividend Payout = DPS / EPS = 2.00 / 4.13 = 48.43%, and for Year 2, Dividend Payout = 2.10 / 4.26 = 49.30%. The average value is therefore 48.865%.

With the forecast net income figure of $559, we can estimate the Year 3 dividends as: 48.865% x 559 = $273.16 or $2.73 per share as there are 100 shares outstanding.

30. Section: 4.8 Financial Forecasting Learning Objective: 4.8 Level of Difficulty: Easy Solution: Retained earnings (year 3) = Retained earnings (year 2) + Net income – Dividends = 429 + 559 – 270 = 718 31. Section: 4.8 Financial Forecasting Learning Objective: 4.8 Level of Difficulty: Easy Solution: The external financing requirement is now $5,177 – $4,770 = $407.

32. Section: 4.9 Formula Forecasting Learning Objective: 4.9 Level of difficulty: Difficult Solution: Cash (year 3) = Cash (year 2) + EBITDA – New equipment – year 2 Payables – Debt repayment = 493 + 2,340 – 1,050 – 552 – 800 = $431.

Equipment (year 3) = Equipment (year 2) + New Equipment – Amortization Expense = 3,888 + 1,050 – 1,422 = $3,516.

Interest and Tax Payable are $120 and $239 respectively (see Problem 28). Long-term debt will be 2,400 – 800 = $1,600.

Based on these values the following revised balance sheet can be created.

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Forecast Balance Sheet for Finns’ Fridges (Revised) Year 3 Assets Cash Property and equipment (net) Total assets Liabilities and Owners’ Equity Interest payable Tax payable Dividends payable Long-term debt Total liabilities Common shares Retained earnings Total owners’ equity Total liabilities and owners’ equity

431 3,516 3,947 120 239 270 1,600 2,229 1,000 718 1,718 3,947

Total assets now equal total liabilities and owners’ equity. Therefore, no external financing is required.

33. Section: 4.9 Formula Forecasting Learning Objective: 4.9 Level of Difficulty: Difficult Solution: We can use Equation 4-34 from the text, but we will need to compute the values of the variables from the year 2 financial statements. i) Invested capital as a percentage of sales, a = (Long-Term Debt + Owners’ Equity) / Revenues = (2,400 + 1,429) / 2,200 = 174.0% ii) Retention Ratio, b = (Net Income – Dividends) / Net Income = (426 – 210) / 426 = 50.7% iii) Net Profit Margin, PM = Net Income / Revenues = 426 / 2,200 = 19.4% b  PM 0.507  0.194 g* = = = 0.0599  6% (a − b  PM ) (1.740 − 0.507  0.194) 34. Section: 4.2 A Framework for Financial Analysis Learning Objective: 4.2 Level of difficulty: Easy Solution: The average shareholders’ equity is (13.8 + 16.4)/2 = $15.1 million. The return on equity (ROE) = NI / Average SE = 5.2 / 15.1 = 34.4% 35. Section: 4.4 Efficiency Ratios Learning Objective: 4.4 Level of difficulty: Medium

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Solution: Gross Profit Margin = (S – CGS) / S, so we have 0.75 = (16 – CGS) / 16. Therefore, CGS = 16 – (16 x 0.75) = 4. The company’s income statement would show $4 million for the cost of goods sold.

36. Section: 4.7 Valuation Ratios Learning Objective: 4.7 Level of difficulty: Difficult Solution: The market value of equity is simply the market price of a share times the number of shares outstanding. MVE = $18.20/share x 4 million shares = $72.8 million.

The P/E ratio can be found with the net income and MVE figures, but it is usually calculated using per share amounts. The earnings per share, EPS = $5.2 million / 4 million shares = $1.30 per share. Therefore, P/E = Price / EPS = $18.20 / $1.30 = 14.0 37. Section: 4.7 Valuation Ratios Learning Objective: 4.7 Level of difficulty: Difficult Solution: Re-arranging the P/E ratio equation, we find EPS = P / (P/E ratio). To find the expected EPS (EEPS) for 2013 with this equation, we must use the Forward P/E ratio: EEPS = P / (Forward P/E ratio) = $18.20 / 12.0 = $1.52 (rounded to the nearest cent). Thus, if Corine’s Candies has the same Forward P/E as the industry, it is expected to earn $1.52 per share in 2013.

38. Section: 4.7 Valuation Ratios Learning Objective: 4.7 Level of difficulty: Difficult Solution: We know (see Problem 36) that the market value of equity, MVE = $72.8 million. So, the total enterprise value, TEV = MVE + Market Value of Debt = 72.8 + 20 = $92.8 million.

EBITDA multiple = TEV / EBITDA = 92.8 / 10 = 9.28.

The EBITDA multiple tells us how much value the market is placing on the firm for each dollar of EBITDA. As this multiple is somewhat higher for Corine’s Candies than for other candy producers, the market is valuing Corine’s more highly than its competitors.

39. Section: 4.4 Efficiency Ratios Learning Objective: 4.4 Level of difficulty: Medium Solution: EBT  (1 − T ) = NI NI 685,750 EBT = = = 1,055,000 1 − T (1 − 0.35) CM Sales − VC 5,050,000 − 1,850,000 DTL = = = = 3.03 EBT EBT 1,055,000 FC 2,100,000 = = 3,314,063 Break-Even Point = CM (5,050,000 − 1,850,000) / 5,050,000 40. Section: 4.9 Formula Forecasting Solutions Manual ..

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Learning Objective: 4.9 Level of difficulty: Difficult Solution: InvestedCapital 900,000 + 2,500,000 = = 0.67 a= Sales 5,050,000 NI 685,750 = = 0.1358 PM = Sales 5,050,000 dividend 200,000 = 1− = 0.71 b = 1 − payout = 1 − NI 685,750 EFR S = −b * PM + (a − b * PM ) g

= −(0.71)  (0.1358) + (0.67 − 0.71 0.1358)  0.05 = −0.066 EFR = −b * PM + (a − b * PM ) g = 0 S − 0.71 0.1358 + (0.67 − 0.71 0.1358) g = 0 g * = 16.8% We can re-write the above formula as follows:

EFR = −b * PM + (a − b * PM ) g = −b(1 + g ) * PM + ag S Profit margin ratio is negatively related to EFR, i.e., the higher the profit margin, the lower the EFR. 41. Section: 4.9 Formula Forecasting Learning Objective: 4.9 Level of difficulty: Medium Solution: Use Equation 4-32 from the text. The parameter values were computed in Practice Problem 40: a = 0.67; profit margin = 0.1358; b = 0.71. With the growth rate specified as 30 percent, we have:

EFR = a  S  g − b  PM  (1 + g )  S = 0.67  $5,050,000  0.30 − 0.71 0.1358  (1 + 0.30)  $5,050,000 = $382,066 G.G. Co. will need an additional $382,066 to finance its growth.

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Level of difficulty: Medium Solution: EBT  (1 − T ) = NI NI 180,000 EBT = = = 276,923 1 − T (1 − 0.35) CM Sales − VC 400,088 − 120,000 DTL = = = = 1.01 EBT EBT 276,923 FC 80,000 = = 114,275 Break-Even Point = CM (400,088 − 120,000) / 400,088 43. Section: 4.5 Productivity Ratios Learning Objective: 4.5 Level of difficulty: Difficult Solution: Sales 950,000 = = 1.9 Receivable Turnover = AR 500,000 COGS Sales − GrossProfit 950,000 − 550,000 = = = 0.62 Inventory Turnover = INV INV 650,000 AR 500,000 = = 192 days Collection Period = ADS 950,000 / 365 Interpretation of receivable turnover: on average, the corporation collects all receivables 1.9 times a year.

Interpretation of inventory turnover: on average, the corporation turns over all inventories 0.62 times a year. Note, we use cost of goods sold instead of sales since the data is available. If we use sales for the inventory turnover ratio it is 950,000/650,000 = 1.46X. Interpretation of average collection period: On average, it takes 192 days for the customers to pay their bills after purchase, an unusually high number.

44. Section: 4.7 Valuation Ratios Learning Objective: 4.7 Level of difficulty: Difficult Solution: SE 945,000 = = 1.89 BVPS = # 500,000 DPS 150,000 / 500,000 Dividend yield = = = 3.2% P 9.5 DPS 150,000 / 500,000 = = 34.6% Dividend Payout = EPS 433,000 / 500,000

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P 9.5 = = 5.03 BVPS 1.89 Earnings per share = NI/# = 433,000/500,000 = 0.87 PE ratio = P/EPS = 9.5/0.87 = 10.97

Market-to-Book Ratio =

45. Section: 4.2 A Framework for Financial Analysis Learning Objective: 4.2 Level of Difficulty: Medium Solution: Net profit margin = net income/sales = 829/1,850 = 44.8% Asset turnover = sales/TA = 1,850/2,669 = 0.69 Leverage ratio = TA/SE = 2,669/1,399 = 1.91 46. Section: 4.2 A Framework for Financial Analysis Learning Objective: 4.2 Level of Difficulty: Medium Solution: ROE = NI/SE = 829/1,399 = 0.59 ROE = net profit margin × asset turnover × leverage ratio = 0.448 × 0.69 × 1.91 = 0.59 47 Section: 4.3 Leverage Ratios Learning Objective: 4.3 Level of Difficulty: Medium Solution: In year 1, Debt ratio = TL/TA = (2,396-1,106)/2,396 = 0.54 Debt equity ratio = D/SE = 500/1,106 = 0.45 In year 2, Debt ratio = TL/TA = (2,669 – 1,399)/2,669 = 0.48 Debt equity ratio = D/SE = 550/1,399 = 0.39 The company improved on both leverage ratios in year 2.

48. Section: 4.3 Leverage Ratios Learning Objective: 4.3 Level of Difficulty: Medium Solution: TIE = EBIT/I = 1,065/80 = 13.31 49. Section: 4.4 Efficiency Ratios Learning Objective: 4.4 Level of Difficulty: Medium Solution: Gross profit margin = (S – CGS)/S = (1,850-605)/1,850 = 0.67 EBITDA = net sales-cost of goods sold = 1,850 – 605 = 1,245 Operating margin = NOI/S = (EBITDA – depreciation)/sales = (1,245 – 180)/1,850 = 57.6% Solutions Manual ..

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Gross profit margin excludes the impact of depreciation, while operating margin includes it.

50. Section: 4.5 Productivity Ratios Learning Objective: 4.5 Level of Difficulty: Medium Solution: Receivable turnover = S/AR = 1,850/234 = 7.91 Average collection period = 365/receivable turnover = 365/7.91 = 46.1 days 51. Section: 4.5 Productivity Ratios Learning Objective: 4.5 Level of Difficulty: Medium Solution: Inventory turnover = COGS/inventory = 605/435 = 1.39 Average days of sales in inventory = 365/inventory turnover = 262.6 days 52. Section: 4.5 Productivity Ratios Learning Objective: 4.5 Level of Difficulty: Medium Solution: Net fixed asset turnover = S/NFA = 1,850/1,888 = 0.98 53. Section: 4.6 Liquidity Ratios Learning Objective: 4.6 Level of Difficulty: Medium Solution: Working capital ratio = CA/TA = 781/2,669 = 0.29 Current ratio = CA/CL = 781/720 = 1.08 Quick ratio = (CA–-inventory)/CL = (781–435)/720 = 0.48.

These ratios all indicate whether the corporation is capable of paying its current liabilities.

Working capital ratio measures the percentage of liquid assets amongst all assets. Current ratio indicates whether it can pay off current liabilities using the current assets. Since inventory is the least liquid of the current assets, the quick ratio removes it from the calculation.

54. Section: 4.7 Valuation Ratios Learning Objective: 4.7 Level of Difficulty: Medium Solution: BVPS = SE/# = 1,399/100 = 13.99 Dividend per share = dividend/# = 585/100 = $5.85 Dividend yield = dividend per share/P = 5.85/15 = 0.39 Dividend payout = dividend/NI = 585/829 = 0.71 55. Section: 4.9 Formula Forecasting Learning Objective: 4.9 Level of Difficulty: Medium

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Solution: Expected total dividends = current dividends × (1 + g) = 585 × (1 + 5 percent) = $614.25 56. Section: 4.7 Valuation Ratios Learning Objective: 4.7 Level of Difficulty: Medium Solution: Earnings per share = NI/# = 829/100 = 8.29 PE ratio = 15/8.29 = 1.81 Market-to-book = P/BVPS = 15/13.99 = 1.07 TEV = P × # of shares outstanding + book value of debt = 15 × 100 + 550 = 2,050 EBITDA ratio = TEV/EBITDA = 2,050/1,245 = 1.65 57. Section: 4.9 Formula Forecasting Learning Objective: 4.9 Level of Difficulty: Medium Solution: PM = 44.8% b = 1 – dividend payout ratio = 1 – 0.71 = 0.29 Invested capital = 550 + 1,399 = 1,949 a = invested capital/sales = 1,949/1,850 = 1.0535 g × = (b × PM)/(a – b × PM) = (0.29 × 0.448)/(1.0535 – 0.29 × 0.448) = 14.07% 58. Section: 4.9 Formula Forecasting Learning Objective: 4.9 Level of Difficulty: Medium Solution: EFR = [–b × PM + (a – b × PM) × g] × S = [–0.29 × 0.448 + (1.0535 – 0.29 × 0.448) × 0.05] × 1,850 = –163.35 This corporation has cash surplus of $163.35.

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Chapter 5: Time Value of Money Multiple Choice Questions 1. Section: 5.2 Simple Interest and 5.3 Compound Interest Learning Objective: 5.2 and 5.3 Level of difficulty: Easy Solution: B. Simple interest rate: $1,000 + ($1,000)(8%)(5) = $1,400 Compound interest rate: $1, 000 (1 + .08) = $1, 469.33 5

2. Section: 5.2 Simple Interest and 5.3 Compound Interest Learning Objective: 5.2 and 5.3 Difficulty: Medium Solution: B Simple interest: Total interest paid over three years: $6,100 - $5,000 = $1,100 Annual interest = $1,100/3 = $366.67 $366.67/$5,000 = 7.33% 1

 6100  3 Compound interest:   − 1 = 6.85%  5000  3. Section: 5.2 Simple Interest and 5.3 Compound Interest Learning Objective: 5.2 and 5.3 Difficulty: Medium Solution: B 4. Section: 5.2 Simple Interest and 5.3 Compound Interest Learning Objective: 5.2 and 5.3 Level of difficulty: Easy Solution: C. A) $1,000 + ($1,000)(10%)(5) = $1,500 B) $1,000 + ($1,000)(8%)(10) = $1,800 C) $1,000(1.08)8 = $1,851 D) $1,000(1.07)8 = $1,718 Therefore, C is the largest.

5. Section: 5.3 Compound Interest Learning Objective: 5.3 Level of difficulty: Medium Solution: B. Solutions Manual ..

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PV=$15,000,000/(1.05)25=$4,429,541.58 Or using a financial calculator (TI BAII Plus), N=25, I/Y=5, PMT=0, FV=15,000,000, CPT PV= –4,429,541.58 6. Section: 5.2 Simple Interest and 5.3 Compound Interest Learning Objective: 5.2 and 5.3 Level of difficulty: Medium Solution: B. The greater the interest rate, the smaller the present value, given a $100 future value and holding the time period constant.

7. Section: 5.3 Compound Interest Learning Objective: 5.3 Level of difficulty: Medium Solution: A. FV=PV(1+k)n 17,000=10,000(1+ k)8 8ln(1+k)=ln(1.7), therefore k=6.86% Or using a financial calculator (TI BAII Plus), N=8, PV= –10,000, PMT=0, FV=17,000, CPT I/Y=6.86% 8. Section: 5.3 Compound Interest Learning Objective: 5.3 Level of difficulty: Medium Solution: C. FV=PV(1+k)n Assume that the initial investment is $1.

(3)(1)=1 (1.09) n ln(3)=(n)ln(1.09) n=12.7 years Or using a financial calculator (TI BAII Plus), I/Y=9, PV= –1, PMT=0, FV=3, CPT N=12.7 9. Section: 5.4 Annuities and Perpetuities Learning objective: 5.4 Level of difficulty: Medium Solution: D. The annuity due has a greater PV because it pays one year earlier than an ordinary annuity.

10. Section: 5.4 Annuities and Perpetuities Learning Objective: 5.4 Level of difficulty: Difficult Solutions Manual ..

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Solution: C.

 (1 + .15)20 − 1  (1 + k ) 20 − 1 =$ 2 FV20 = PMT  , 000   = 2,000(102.4436) = $204,887  .15 k     Or using a financial calculator (TI BAII Plus), N=20, I/Y=15, PV=0, PMT= -2,000, CPT FV=204,887 11. Section: 5.4 Annuities and Perpetuities Learning Objective: 5.4 Level of difficulty: Medium Solution: B.

1  1    1 − (1.15) 20  1 − (1 + k ) n  PV0 = PMT   = 2,000(6.25933) = $12,519  = $2,000 .15 k         Or using a financial calculator (TI BAII Plus), N=20, I/Y=15, FV=0, PMT= –2,000, CPT PV=12,519 12. Section: 5.4 Annuities and Perpetuities Learning Objective: 5.4 Level of difficulty: Easy Solution: D. PV0=PMT/k=$1,500/.12=$12,500 13. Section: 5.4 Annuities and Perpetuities Learning Objective: 5.4 Level of difficulty: Easy Solution: A. PV0=PMT/k=$1,500/.12 + $1,500 =$14,000 14. Section: 5.6 Loan or Mortgage Arrangements Learning Objective: 5.6 Level of difficulty: Medium Solution: C PV of annuity of 120 remaining payments at 1% per month.

Using a financial calculator (TI BAII Plus), N = 120, I/Y = 1, FV = 0, PMT = -2,752.72, CPT PV = 191,866 15. Section: 5.4 Annuities and Perpetuities Learning Objective: 5.4 Solutions Manual ..

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Level of difficulty: Difficult Solution: A. The future value of a perpetuity cannot be computed as it is infinite.

Practice Problems 16. Section: 5.1 Opportunity Cost Learning Objective: 5.1 Difficulty: Medium Solution: Cost = tuition + textbook + loss of income = $500+$200+$500 = $1,200 The rent and food are expenses that he will be facing regardless of taking the course.

We are, of course, assuming that the extra time he spends studying for the philosophy course will not have any impact on his grades in his other courses and are not placing any value on his enjoyment of the subject.

17. Section: 5.2 Simple Interest Learning Objective: 5.2 Difficulty: Easy Solution: As this is simple interest, Dmitri will earn the same amount of interest each year. The annual amount of interest is 8% * initial investment = .08 * $25,000 = $2,000. a. $2,000 b. $2,000 18. Section: 5.2 Simple Interest Learning Objective: 5.2 Level of difficulty: Easy Solution: a. In one year he will owe P x k = $1,500 x 6% = $90 of interest. b. After three years, the total (principal and interest) owing will be: P + (n x P x k) = $1,500 + (3 x $1,500 x 6%) = $1,770.

19. Section: 5.2 Simple Interest Learning Objective: 5.2 Level of difficulty: Easy Solution: As the exact amount of interest owing each year will be paid, there is no “compounding.” The amount of each annual payment will be P x k = $2,500 x 6% = $150. Unfortunately, these payments never reduce the principal owing, so the loan will never be paid off.

20. Section: 5.2 Simple Interest Solutions Manual ..

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Learning Objective: 5.2 Level of difficulty: Easy Solution: Khalil will be paid interest each month for 12 months, but without compounding. The total interest earned is (n x P x k) = (12 x $1,200 x 0.5%) = $72.

21. Section: 5.3 Compound Interest Learning Objective: 5.3 Level of difficulty: Easy Solution: The payment of compound interest means that we must compound (or find the future value of) the amount invested (the present value):

FV12 months = $1,200  (1 + 0.005)12 = $1,274.01 Of this amount, $1,200 was the original amount invested, so $74.01 of interest will be earned.

22. Section: 5.2 Simple Interest and 5.3 Compound Interest Learning outcome: 5.2 and 5.3 Level of difficulty: Easy Solution: A. Value = P + (n x P x k) = $24 + (387 x $24 x 5%) = $488 B. FV387 years = $24  (1 + 0.05) 387 = $3,806,010,497 23. Section: 5.3 Compound Interest Learning outcome: 5.3 Level of difficulty: Easy Solution: The future value of the loan (the amount to be repaid) is $2,500. The amount that can be borrowed is the present value amount, calculated as:

PV0 = FV1 

1 1 = $2,500  = $2,314.81 1 (1 + k ) (1 + .08)1

Or using a financial calculator (TI BAII Plus), N=1, I/Y=8, PMT=0, FV= -2,500, CPT PV=2,314.81 24. Section: 5.3 Compound Interest Learning Objective: 5.3 Level of difficulty: Easy Solution: Solutions Manual ..

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a. FV1 year = $20,000  (1 + 0.10)1 = $22,000.00 b. FV5 years = $20,000  (1 + 0.10)5 = $32,210.20 c. FV10 years = $20,000  (1 + 0.10)10 = $51,874.85 25. Section: 5.3 Compound Interest Learning Objectives: 5.3 Level of difficulty: Easy Solution: Jon needs $800 in three years; that is the future value amount. The present value equivalent is:

PV0 = FV3 

1 1 = $800  = $691.07 3 (1 + k ) (1 + .05)3

Or using a financial calculator (TI BAII Plus), N=3, I/Y=5, PMT=0, FV= -800, CPT PV=691.07 26. Section: 5.1 Opportunity Cost and 5.3 Compound Interest Learning Objective: 5.1, 5.3 Level of difficulty: Difficult Solution: Find the present value of the money paid back to Veda by each investment, using the interest rate on the alternative (the bank account) as the discount rate.

For Investment A: PV0 =

$500 $800 + = $453.51 + $691.07 = $1144.58 2 (1 + 0.05) (1 + 0.05)3

For Investment B:

PV0 =

$200 $400 $700 + + = $190.48 + $362.81 + $604.69 = $1157.98 1 2 (1 + 0.05) (1 + 0.05) (1 + 0.05) 3

Veda would prefer Investment B, because it has the higher present value.

27. Section: 5.4 Annuities and Perpetuities Learning Objective: 5.4 Level of difficulty: Difficult Solution: The dividends for the first five years form an ordinary annuity. Starting in year 6, the reduced dividend stream can be thought of as a perpetuity. However, the value of this perpetuity, as determined by our formula, occurs at year 5 (one year before the first $2 dividend), and must be discounted to the present: Solutions Manual ..

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 1   1−  5   1 (1 + 0.12)   $2.00  PV0 = $3.00 +  = $10.81 + $16.67  0.5674 = $20.27  5    0.12  (1 + 0.12)  0.12        28. Section: 5.4 Annuities and Perpetuities Learning Objective: 5.4 Level of difficulty: Difficult Solution: 0.0375 kmonthly = = 0.3125% 12 Rent payments are typically made at the start of each month (so this is an annuity due). Over three years, we would expect 36 monthly rent payments. However, the last month’s rent must be paid up front, so the annuity includes only 35 payments; the present value of the last month’s rent is $450 because it will be paid today.

1   1 − (1 + 0.003125)35  PV0 = $450     (1 + 0.003125) + $450 = $15,393.77 0.003125     29. Section: 5.4 Annuities and Perpetuities Learning Objective: 5.4 Level of difficulty: Difficult Solution: It is tempting to view the first option as a perpetuity, but this would be incorrect as the man will die at some time, and the payment will then cease. Thus, option one is an ordinary annuity, with an uncertain number of payments. Option two is much easier to value; it includes exactly 240 monthly payments. kmonthly =

0.06 = 0.5% 12

Using a financial calculator (TI BAII Plus), N = 240, PMT = 3,500, I/Y = 0.5, FV=0, CPT PV = –488,532.70 For the first option to be a better deal, it must include enough payments so that its present value is at least as great as for option two. Again using the calculator, PV = –488,532.70, PMT = 2,785, I/Y = 0.5, CPT N = 420.29 So option one must continue for over 420 monthly payments to equal the value of option two.

This is just over 35 years. Hence, the man must live to be at least 100 years old for option one to Solutions Manual ..

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be a better deal.

30. Section: 5.4 Annuities and Perpetuities Learning outcome: 5.4 Level of difficulty: Easy Solution: Present value of the perpetual scholarship payment:

1  1  PV0 = PMT   = $5000   = $166, 667 k   0.03  31. Section: 5.4 Annuities and Perpetuities Learning outcome: 5.4 Level of difficulty: Medium Solution: Present value of the perpetual scholarship payment at the end of 4 years:

1  1  PV4 = PMT   = $5000   = $166, 667 k   0.03  So present value today is $166,667 / (1.03) 4 = $148,081 .Grace will need to endow $148,081 today for the scholarship to start in 5 years.

32. Section: 5.4 Annuities and Perpetuities Learning outcome: 5.4 Level of difficulty: Medium Solution: Find the present value of the four-year annuity at year 3:

1  1    1 − (1 + k ) n  1 − (1 + 0.07) 4   = $4,000    = $13,548.85 PV3 = PMT  k 0.07         Now, find the present value of this amount today:

 1   1  PV0 = FV  = $13,548.85   = $11,059.90 3 3  (1 + k )   (1.07)  33. Section: 5.4 Annuities and Perpetuities Learning outcome: 5.4 Level of difficulty: Medium Solutions Manual ..

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Solution: To be indifferent between the two options means that the present value of the annuity must equal $40 million (the immediate payout).

1   10   1− (1 + k )  . Solving this using the calculator is the easiest way. N=10, PMT = -5, PV = 40 = 5    k     40, CPT I/Y. We find an interest rate of 4.28%. If the interest rate is greater than 4.28%, I prefer the immediate payout of $40 million. The present value of the 10-year annuity is less than $40 million. If the interest rate is less than 4.28%, I prefer the annuity because the present value will be greater than $40 million.

34. Section: 5.4 Annuities and Perpetuities Learning outcome: 5.4 Level of difficulty: Difficult Solution: Step 1: determine Betty`s annual deposits = $15,051.435. Betty will have to make annual deposits of $15,051.435 per year for 30 years at 5% in order to have $1 million.

Step 2: Abe will be making deposits of 2*15,051.435 = $30,102.87. How many annual deposits will he need to make in order for the future value to be $1 million? (solve for N) The number of deposits is 20.06 Therefore, Abe can afford to wait 10 years before he has to start making his large deposits.

35. Section: 5.1 Opportunity Cost, 5.2 Simple Interest, 5.3 Compound Interest, and 5.4 Annuities and Perpetuities Learning outcome: 5.1, 5.2, 5.3, 5.4 Level of difficulty: Difficult Solution: The manager is confused. To make the choice between the two options you should consider the present value of each set of payments, not the sum of the payments. Summing the payments assumes that the opportunity cost is zero.

For example, if your opportunity cost is 10%, then the PV of Long is $161,009. The value of the house if $250,000 but the cost of the loan (to you) is only $161,009 – a net benefit of $88,991.

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The PV of the Short option is $216,289 – in this case, with an opportunity cost of 10%, the short option costs me $55,280 more.

If instead, your opportunity cost is 1%, then the PV of the Long option is $390,647 while the PV of the Short option is only $333,390. By taking the Short option, you will save $57,257.

36. Section: 5.5 Nominal versus Effective Rates Learning Objective: 5.5 Level of difficulty: Easy Solution: 2

.

0725 0  = 1 + 1 = 7 .

38 %  − For Bank A, k  2 4

.

0720 0  = 1 + 1 = 7 .

40 %  − For Bank B, k 4   12

.

0715 0  = 1 + 1 = 7 .

39 %  − For Bank C, k  12 

Bank B pays the highest effective annual rate.

37. Section: 5.5 Nominal versus Effective Rates Learning Objective: 5.5 Level of difficulty: Easy Solution: a. For annual compounding, the effective annual rate will be the same as the quoted rate. To check this: m

1

 QR   9.5%  k = 1 +  − 1 = 1 +  − 1 = 9.5% m  1   

b. With quarterly compounding, set m=4, 4

 9.5%  k = 1 +  − 1 = 9.84% 4  

c. With monthly compounding, set m=12, 12

 9.5%  k = 1 +  − 1 = 9.92% 12  

38. Section: 5.5 Nominal versus Effective Rates Learning Objective: 5.5 Solutions Manual ..

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Level of difficulty: Easy Solution: a. k = Quoted Rate = 6%  FV1 year = PV0 (1 + k ) = $50,000  (1.06) = $53,000 12

 QR  b. k = 1 +  − 1 = 6.16778%  FV1 year = $50,000  (1.0616778) = $53,083.89 12    QR  c. k = 1 +   365 

365

− 1 = 6.18313%  FV1 year = $50,000  (1.0618313) = $53,091.57

39. Section: 5.5 Nominal versus Effective Rates Learning Objective: 5.5 Level of difficulty: Medium Solution: Step 1: determine monthly effective rate

= 0.66227% Step 2: given the monthly effective rate, determine the quoted rate compounded monthly.

QR monthly = 12 x 0.66227 = 7.94724% Therefore, 8% compounded quarterly is equivalent to 7.94724% compounded monthly.

40. Section: 5.4 Annuities and Perpetuities Learning Objective: 5.4 Level of difficulty: Easy Solution: The value of any perpetual stream of payments can be valued as a perpetuity: PMT $2 PV0 = = = $16.67 k 0.12 Each share is worth $16.67.

41. Section: 5.4 Annuities and Perpetuities Learning Objective: 5.4 Level of difficulty: Easy Solution: Solutions Manual ..

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Because the fees are paid at the start of the year, this is an annuity due.

1   1 − (1 + 0.06) 4    (1 + 0.06) = $21,303.47 PV0 = $5,800   0.06     42. Section: 5.5 Nominal versus Effective Rates Learning Objective: 5.5 Level of difficulty: Medium.

Solution: a. m = 365: k = (1 + .24 ) 365 − 1 = 27.11%.

365

b. m = 4:

k = (1 +

.24 4 ) − 1 = 26.25%.

4

c. m = 3:

k = (1 +

.24 3 ) − 1 = 25.97%.

3

d. m = 2:

k = (1 +

.24 2 ) − 1 = 25.44%.

2

e. Continuous compounding: k = e .24 − 1 = 27.12%. f. The effective monthly rate for a. to d. is: m

a. m=365, f=12

365 QR f .24 12 ) − 1 =2.02% k = (1 + ) − 1= (1 + 365 m

b. m=4, f=12.

k = (1 +

c. m=3, f=12.

3 QR f .24 12 ) − 1 =1.94% k = (1 + ) − 1= (1 + 3 m

d. m=2, f=12.

2 QR f .24 12 ) − 1 =1.91% k = (1 + ) − 1= (1 + 2 m

m

4 QR f .24 12 ) − 1 =1.96% ) − 1= (1 + 4 m

m

m

43. Section: 5.4 Annuities and Perpetuities and 5.5 Nominal versus Effective Rates Learning Objective: 5.4, 5.5 Level of difficulty: Difficult Solution: Step 1: make the payment frequency match the compounding frequency. We need to convert the 6 percent compounded monthly to a quarterly effective rate.

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12

 .06  1 + kannual = 1 +   12 

1 + kquarterly = (1 + kannual ) 4 1

1

 .06 12  4 =  1 +    12   12 4

 .06  = 1 +   12  kquarterly = 1.5075%

Step 2: Now we have an annuity of 5*4 = 20 quarterly payments, a present value of $50,000, and an effective quarterly rate of 1.5075%. Solving for the payments we get $2,914.44.

44. Section: 5.4 Annuities and Perpetuities and 5.5 Nominal versus Effective Rates Learning Objective: 5.4, 5.5 Level of difficulty: Difficult Solution: Step 1: make the payment frequency match the compounding frequency. We need to convert the 6% compounded quarterly to a monthly effective rate.

 .06  1 + kannual = 1 +  4  

4

1 + kmonthly = (1 + kannual ) 12 1

1

 .06 4  12 =  1 +   4     .06  = 1 +  4   kmonthly = 0.4975%

4 12

Step 2: Now we have an annuity of 5*12 = 60 monthly payments, a present value of $150,000 and an effective monthly rate of 0.4975%. Solving for the payments we get $2,897.83.

45. Section: 5.4 Annuities and Perpetuities Learning Objective: 5.4 Level of difficulty: Easy Solution: Solutions Manual ..

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The future value amount is $40,000. The amount to be saved each year is really the payment on an ordinary annuity:

 (1 + 0.07) 8 − 1 $40,000 = PMT    PMT = $3,898.71 0.07   Or using a financial calculator (TI BAII Plus), N=8, I/Y=7, PV=0, FV= -40,000, CPT PMT= 3,898.71 46. Section: 5.4 Annuities and Perpetuities Learning Objective: 5.4 Level of difficulty: Medium Solution: A. The future value of Jane’s account will be:

 (1 + 0.06)17 − 1 FV17 = $1,000    = $28,212.88 0.06   B. The grant has the effect of increasing the amount saved from $1,000 to $1,200. The future value of the account will now be:

 (1 + 0.06)17 − 1 FV17 = $1,200    = $33,855.46 0.06   47. Section: 5.4 Annuities and Perpetuities Learning Objective: 5.4 Level of difficulty: Medium Solution: Find the present value of the four-year annuity due:

1  1    1 − (1 + k ) n  1 − (1 + 0.07) 4   (1 + k ) = $4,000     (1 + 0.07) = $14,497.26 PV0 = PMT  k 0.07         Now, discount this amount back three years:

 1   1  PV0 = FV  = $14,497.26   = $11,834.08 3 3  (1 + k )   (1.07)  48. Section: 5.4 Annuities and Perpetuities Learning Objective: 5.4 Level of difficulty: Medium Solution: Solutions Manual ..

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We have two separate annuities to consider: the tuition payments, and the savings amounts. First, find the present value of the four annual tuition payments (at time 8, when Felix is due to begin university studies):

1   1− 4  (1 + 0.07)  PV8 = $10,000   = $33,872.11   0.07     This is the amount of savings required at time 8. From the perspective of time 0, this is a future value amount (replaces the $40,000 in Problem 45.) Next, find the annual savings amount:

 (1 + 0.07) 8 − 1 $33,872.11 = PMT    PMT = $3,301.44 0.07   49. Section: 5.3 Compound Interest Learning Objective: 5.3, 5.4 Level of difficulty: Difficult Solution: a. We know the future value and present value amounts, as well as the monthly interest rate.

Finding the number of time periods (months) is most easily done with a financial calculator (TI BAII Plus), PV = 15,000, FV = -20,000, I/Y = 0.5, CPT N = 57.68 It will take nearly 58 months, or close to 5 years before Roger can afford to buy the car. b. Solving the following equation for “n” we get:

 (1.005) n − 1 $15,000 $20,000 = + $250  n= 14.86.

(1.005) n  .005  Or using a financial calculator (TI BAII Plus), I/Y=0.5, PV=15,000, FV= -20,000, PMT = 250, CPT N = 14.86 50. Section: 5.3 Compound Interest and 5.5 Nominal versus Effective Rates Learning Objective: 5.3, 5.5 Level of difficulty: Difficult Solution: Let’s assume the present value of the investment is $1. The future value, after doubling, is then $2. a. Annually: With annual compounding, the effective rate is the same as the quoted rate, 9%.

Using a financial calculator (TI BAII Plus), PV = –1, FV = 2, I/Y = 9, CPT N = 8.04 So the investment will double in just over 8 years. b. Quarterly: With quarterly compounding, the effective annual rate is, Solutions Manual ..

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k = (1 +

Booth, Cleary

0.09 4 ) − 1 = 9.3083% , and a financial calculator allows us to find: 4

PV = -1, FV = 2, I/Y = 9.3083, CPT N = 7.79 The higher effective rate means that only 7.79 years are needed to double the value of the investment.

51. Section: 5.4 Annuities and Perpetuities Learning Objectives: 5.4 Level of difficulty: Difficult Solution: a. The present value of the annual payments can be found with a financial calculator, (TI BAII Plus), N=9, PMT = -6,000, I/Y = 5.0, FV=0, CPT PV = 42,646.93 As this is less than $50,000, the immediate payment alternative is better. b. This problem can be solved by trial and error, but the task is much easier with a financial calculator, (TI BAII Plus), N=9, PMT = –6,000, PV = 50,000, FV=0, CPT I/Y = 1.5675%. At an interest rate below 1.5675% per year, the nine-year annuity would be preferable; above the rate the immediate payment is better.

52. Section: 5.5 Nominal versus Effective Rates and 5.6 Loan or Mortgage Arrangements Learning Objective: 5.5, 5.6 Level of difficulty: Difficult Solution: a. First, find the effective interest corresponding to the frequency of Jimmie’s car payments (f =12); with monthly compounding, set m=12,

 QR  k monthly = 1 +  m  

m

f

12

 8.5%  − 1 = 1 +  12  

12

− 1 = 0.70833%

The 60 car payments form an “annuity” whose present value is the amount of the loan (the price of the car):

1   1 −  60  (1 + 0.0070833)  $29,000 = PMT   PMT = $594.98 0.0070833       b. Use the effective monthly interest rate from part A, k=0.70833% Period

(1) Principal Outstanding

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(2) Payment

(3) Interest =k*(1) 16

(4) Principal Repayment =

Ending Principal = (1)-(4) Chapter 5

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1 2 3 4 5 6 7 8 9 10 11 12 13 ...

35 36 37 ...

59 60

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29,000.00 28,610.44 28,218.12 27,823.01 27,425.11 27,024.40 26,620.84 26,214.42 25,805.13 25,392.94 24,977.82 24,559.77 24,138.76

594.98 594.98 594.98 594.98 594.98 594.98 594.98 594.98 594.98 594.98 594.98 594.98 594.98

205.42 202.66 199.88 197.08 194.26 191.42 188.56 185.69 182.79 179.87 176.93 173.97 170.98

(2)-(3) 389.56 392.32 395.10 397.90 400.72 403.56 406.42 409.29 412.19 415.11 418.05 421.01 424.00

14,083.18 13,587.95 13,089.22

594.98 594.98 594.98

99.76 96.25 92.72

495.22 498.73 502.26

13,587.95 13,089.22 12,586.96

1,177.43 590.79

594.98 594.98

8.34 4.18

586.64 590.79

590.79 0.00

28,610.44 28,218.12 27,823.01 27,425.11 27,024.40 26,620.84 26,214.42 25,805.13 25,392.94 24,977.82 24,559.77 24,138.76 23,714.76

The first monthly payment repays $389.56 of the principal amount of the loan and the last payment repays $590.79. c. After three years, or 36 monthly payments, the principal outstanding is $13,089.22 (from the amortization table).The present value of this amount is:   1  = $10,152.19 PV0 = $13,089.22    (1 + 0.0070833) 36   

53. Section: 5.5 Nominal versus Effective Rates and 5.6 Loan or Mortgage Arrangements Learning Objective: 5.5 and 5.6 Level of difficulty: Difficult Solution: The 60 monthly payments form an annuity whose present value is $29,000. Finding the interest rate is most easily done with a financial calculator (TI BAII Plus): N=60, PMT=588.02, PV= -29,000, CPT I/Y = 0.6667% Note that we used N=60 months, so the solution is a monthly interest rate, however, the problem

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asks for the effective annual rate.

k = (1 + kmonthly )12 − 1 = (1 + 0.006667)12 − 1 = 8.30% The quoted rate would be: 1

1

QR = m  [(1 + k ) 12 − 1] = 12  [(1 + 0.0830) 12 − 1] = 8.00%

Or simply: QR = m  kmonthly = 12  0.006667 = 8.00% 54. Section: 5.5 Nominal versus Effective Rates Learning Objective: 5.4, 5.5 Level of difficulty: Medium Solution: Solve the annuity equation to find k, the interest rate:

1   1 −  (1 + k ) 5  k =? $25,000.00 = $6,935.24   k     The calculations are most easily done with a financial calculator (TI BAII Plus), PV = -25,000, PMT=6,935.24, N= 5, FV=0, CPT I/Y = 12% The effective annual interest rate is 12 percent. With annual compounding, the nominal rate (or quoted rate) will also be 12 percent per year.

55. Section: 5.5 Nominal versus Effective Rates Learning Objective: 5.4, 5.5 Level of difficulty: Medium Solution: a. There will be 5 x 12 = 60 monthly payments. The calculations are most easily done with a financial calculator (TI BAII Plus), PV = –25,000, PMT=556.11, N= 60, CPT I/Y = 1.0% Because we used monthly payments, and months as the time period, 1.0% is the effective monthly rate. b. The compounding period matches the payment frequency, so the nominal rate, or quoted rate, is: QR = m  kmonthly = 12  1.0% = 12.0% per year.

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Learning Objective: 5.5 Level of difficulty: Medium Solution: a. Scott will pay interest of ($800–$750) = $50 after one week. This implies a nominal interest rate of $50/$750 = 6.67% per week. With 52 weeks in the year, the nominal rate per year is then 52 x 6.67% = 346.84%. b. The effective annual interest rate is k = (1 + 0.0667) 52 − 1 = 27.7210 = 2,772.10% 57. Section: 5.6 Loan or Mortgage Arrangements Learning Objective: 5.6 Level of difficulty: Medium Solution: a. In Canada, fixed-rate mortgages use semi-annual compounding of interest, so m=2. The effective annual rate is therefore: m

2

 QR   0.064  k = 1 +  − 1 = 1 +  − 1 = 6.5024% m  2   

b. With monthly payments, f=12. We can find the effective monthly interest rate from the effective annual rate, k:

kmonthly = (1 + k ) f − 1 = (1 + 6.5024%) 12 − 1 = 0.5264% 1

1

c. The amortization period is 20 years, or 20 x 12 = 240 months. Josephine’s monthly payments can be computed as:

1   1 −  (1 + 0.005264) 240    PMT = $1,322.69 $180,000 = PMT  0.005264     d. With monthly compounding and payments, the effective monthly interest rate is: m

12

 QR  f  0.0636  12 kmonthly = 1 +  − 1 = 1 +  − 1 = 0.530% m  12    Even though the quoted rate is lower at the Credit Union than at the Bank, the effective rate is higher. Josephine should take the mortgage loan from Providence Bank in this case. The monthly payment for the credit union mortgage would be $1,327.24, which, as expected, is higher than that at Providence Bank.

58. Section: 5.6 Loan or Mortgage Arrangements Learning Objective: 5.6 Level of difficulty: Medium Solutions Manual ..

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Solution: With semi-annual compounding (the norm in Canada) and monthly payments, m=2 and f=12.The effective monthly rate is: m

2

 QR  f  0.039  12 kmonthly = 1 +  − 1 = 1 +  − 1 = 0.3224% m  2    The present value of the mortgage payments over the amortization period (25 years x 12 = 300 months) is:

1   1 − (1 + 0.003224) 300   = $374,553.72 PV0 = $1,950.00   0.003224     In addition, Charlie has $130,000 available as a down payment; the most he can pay for the house is, therefore, $374,553.72 + $130,000 = $504,553.72.

59. Section: 5.6 Loan or Mortgage Arrangements Learning Objective: 5.6 Level of Difficulty: Difficult Solution: Part 1: determine the principal outstanding after the 60th payment (i.e., How much will the next mortgage be for?)

Step 1: determine effective monthly rate: 1

 .06 2  12 kmonthly = 1 +   − 1 = 0.00493862 2    Step 2: determine the monthly payments:

1   1 − (1 + 0.00493862)300  $300, 000 = PMT    0.00493862     PMT = $1,919.4194 Step 3: determine Present Value of remaining (300 – 60) payments of $1,919.4194

1   1 − (1 + 0.00493862)300−60  PV = $1,919.4194    0.00493862     PV = $269,510.0994

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Part 2: determine new payments Step 1: determine new effective monthly rate 1

 .08 2  12 kmonthly = 1 +   − 1 = 0.00655820 2    Step 2: determine the new monthly payment

1   1 − (1 + 0.00655820)300−60  $269,510.0994 = PMT    0.00655820     PV = $2, 232.507688 Franklin’s new payment is $2,232.51, an increase of $313.09.

60. Section: 5.7 Comprehensive Examples Learning Objective: 5.7 Level of difficulty: Medium Solution: a. Timmy’s savings extend right to age 61 (end of each year), so this is an ordinary annuity.

 (1 + 0.10) 40 − 1 FV40 = $3,000    = $1,327,777.67 0.10   Yes, Timmy will achieve his goal by a comfortable margin. b. In the equation for part A set FV = $1,000,000, and solve for the number of years, n. This is easiest done with a financial calculator (TI BAII Plus), FV = –1,000,000, I/Y = 10, PMT = 3,000, CPT N = 37.1.

Timmy will hit the $1 million dollar mark in just over 37 years, or shortly after his 58th birthday.

61. Section: 5.7 Comprehensive Examples Learning Objective: 5.7 Level of difficulty: Easy Solution: This is an ordinary annuity.

 (1 + 0.10)15 − 1 FV15 = $30,000    = $953,174.45 0.10   No, Tommy will not quite achieve his goal before retirement.

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62. Section: 5.7 Comprehensive Examples Learning Objective: 5.7 Level of difficulty: Easy Solution: Annual investment = Annual income – Annual expenditure = $45,000 – $36,000 = $9,000.

This is an annuity due.

 (1 + k )n − 1 FVn = PMT  (1 + k ) k  

 (1 + .126) 35 − 1 = $9,000  (1.126) = (9,000)(497.2749)(1.126) = $5,039,384 .126   Or using a financial calculator (TI BAII Plus), Hit [2nd] [BGN] [2nd] [Set] N=35, I/Y=12.6, PV=0, PMT= -9,000, CPT FV=5,039,384 63. Section: 5.7 Comprehensive Examples Learning Objective: 5.7 Level of Difficulty: Difficult Solution: a. PV=$200,000, monthly rate=12%/12=1%, N = (10)(12)=120 months

1   1 − (1 + .01)120  200,000 = PMT   .01     1   1 −  (1 + .01)120  PMT = 200,000 /   .01     So, PMT=$2,869 Or using a financial calculator (TI BAII Plus), N=120, I/Y=1, PV=-200,000, FV=0, CPT PMT=2,869 b. Remaining months to pay=120 – 18=102 months

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1   1 − (1 + .01)102  PV0 = 2,869  =$182,920 .01     Or using a financial calculator (TI BAII Plus), N=102, I/Y=1, PMT=- 2,869, FV=0, CPT PV=182,920 2

.12 12 ) − 1 =.9759% c. kmonthly= (1 + 2

1   1 − (1 + .009759)120  200,000 = PMT   .009759     1   1 − (1 + .009759)120  PMT = 200,000 /   .009759     So, PMT=$2,836 Or using a financial calculator (TI BAII Plus), N=120, I/Y=.9759, PV=-200,000, FV=0, CPT PMT=2,836 64. Section: 5.7 Comprehensive Examples Learning Objective: 5.7 Level of difficulty: Difficult Solution: Investor A: k=e.15 – 1=16.183424%.

1st, consider an ordinary annuity and the present value of the investment when A turns 25 years old is:

1   1 − 8  (1 + .16183424)  PV25 = $5,500 =$23,749.19   .16183424     Or using a financial calculator (TI BAII Plus), N=8, I/Y=16.183424, PMT=5,500, FV=0, CPT PV=- 23,749.19 Solutions Manual ..

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2nd, discount this amount for five years back to today when she is 20.

PV=FV/(1+k)5=$23,749.19/(1.16183424)5=$11,218.3231 Or, N=5, I/Y=16.183424, PMT=0, FV=- 23,749.19, CPT PV=11,218.3231 Investor B: .16 4 k= (1 + ) − 1 =16.985856% 4

1   1 − 10  (1 + .16985856)  $11,218.3231 = PMT  (1.16985856)   .16985856     PMT=$2,057.38 Or using a financial calculator (TI BAII Plus), Hit [2nd] [BGN] [2nd] [Set] N=10, I/Y=16.985856, PV=11,218.3231, FV=0, CPT PMT= - 2,057.38 Therefore, Investor B has to make a yearly payment of $2,057.38 so that the present value of the two investments is the same.

65. Section: 5.7 Comprehensive Examples Learning Objective: 5.7 Level of difficulty: Medium Solution: a. 1st Calculate their yearly income available for investment Monthly income available = $9,000 – $3,000 – $850 –$1,450 = $3,700 Yearly available = $(3,700)(12) = $44,400 2nd Calculate the FV of their investment when they retire:

 (1 + .1)30 − 1 FV30 = 44,400  =$7,303,535 .1   Or using a financial calculator (TI BAII Plus), N=30, I/Y=10, PV=0, PMT=- 44,400, CPT FV=7,303,535 3rd Calculate the amount they will have when they retire: $7,303,535 + $50,000 = $7,353,535 b. This is an annuity due problem.

PV=7,353,535, k=10%, n=30

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1   1 − (1 + .1)30  7,353,535 = PMT   (1 + .1) .1     So, PMT=$709,143 Or using a financial calculator (TI BAII Plus), Hit [2nd] [BGN] [2nd] [Set] N=30, I/Y=10, PV=- 7,353,535, FV=0, CPT PMT=709,14366. Section: 5.6 Loan or Mortgage Arrangements Learning Objective: 5.6 Level of difficulty: Difficult Solution: a. The effective monthly interest rate is, 2

 0.051  12 kmonthly = 1 +  − 1 = 0.4206% 2   The amount of the mortgage loan will be ($280,000 – $50,000) = $230,000, and there will be 12 x 25 = 300 monthly payments, the value of which can be found with a financial calculator, (TI BAII Plus), N=300, PV = –230,000, I/Y = 0.4206, CPT PMT = 1,350.89. Alysha’s two friends will be paying 2 x $475 = $950 in rent, so she will need an additional $1,350.89 – $950 = $400.89 to make the mortgage payments. b. In two years, Alysha will have made 24 payments, leaving 276. The present value of these payments is the outstanding value of the mortgage loan. Use the calculator again: N=276, I/Y = 0.4206, PMT = 1350.89, CPT PV = 220,336.58.To pay off the loan, and recoup her down payment, Alysha would have to sell the house for at least $220,336.58 + $50,000 = $270,336.58.

67. Section: Appendix 5A: Growing Annuities and Perpetuities Level of difficulty: Easy Solution: 100 = $1, 666.67 . The most I would be willing to pay for the investment is the present .09 − .03 value, therefore, $1,666.67.

PV =

68. Section: Appendix 5A: Growing Annuities and Perpetuities Learning Objective: Appendix Level of difficulty: Medium Solution:

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= $1,816.67 The most I’d pay is the present value of the investment. In this case the cash flows start immediately ($100) and then grow by 3% per year. The present value, or the maximum I’d be willing to pay, is $1,816.67 69. Section: Appendix 5A: Growing Annuities and Perpetuities Learning Objective: Appendix Level of difficulty: Medium Solution: To solve this we need to realize that the present value of a perpetuity (growing or otherwise) occurs one period prior to the first cash flow. Hence, using the growing perpetuity formula will give us the value of the cash flows in year 4. We need to discount those back to time 0.

= $1,180.71 The most I’d be willing to pay for this investment is $1,180.71.

70. Section: Appendix 5A: Growing Annuities and Perpetuities Learning Objective: Appendix Level of difficulty: Medium Solution: Present value of Grow: PVGROW =

100 = $10, 000 .05 − .04

Present value of Shrink: PVSHRINK =

1000 = $14, 285.71 .05 − (−.02)

Grow exceeds the cost by $9,000 while Shrink exceeds the investment cost by $13,285.71 Shrink is preferred, as it exceeds the investment cost by the most.

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71. Section: Appendix 5A: Growing Annuities and Perpetuities Learning Objective: Appendix Level of difficulty: Difficult Solution:

=

PMT1 .02

*1.8946799

The initial deposit is $10,555.87 If Xiang made constant deposits (i.e., no growth), he would have to deposit $15,051.44 per year for the next 30 years.

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Chapter 6: Bond Valuation and Interest Rates Multiple Choice Questions 1. Section: 6.1 The Basic Structure of Bonds Learning Objective: 6.1 Difficulty: Medium Solution: A Mortgages have “blended” payments including interest and principal, not bonds.

2. Section: 6.1 The Basic Structure of Bonds Learning Objective: 6.1 Difficulty: Medium Solution: B Debentures are generally unsecured.

3. Section: 6.2 Bond Valuation Learning Objective: 6.2 Level of difficulty: Medium Solution: C

1   1 − (1 + .10)10  1 B = 8  =49.1565+38.5543=$87.71  + 100  .10 (1 + .10)10     Or, by financial calculator: N = 10; I/Y= 10; PMT = 8; FV = 100; CPT PV = –87.71 4. Section: 6.2 Bond Valuation Learning Objective: 6.2 Difficulty: Medium Solution: D All else being equal, interest rate risk is positively related to term to maturity, but negatively related to coupon rate and market yields. The bond in choice D has the lowest yield, lowest coupon rate and the longest term to maturity relative to the other bonds. Therefore it has the highest interest rate risk.

5. Section: 6.3 Bond Yields Learning Objective: 6.3 Difficulty: Medium Solution: D Coupon = ($1,000) (9%)/2=$45, N=8×2=16, FV=1,000, PV= –980 Using a financial calculator, N=16, PV= –980, PMT=45, FV=1,000 CPT I/Y=4.6804 Therefore, YTM=4.6804%×2=9.36%

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6. Section: 6.3 Bond Yields Learning Objective: 6.3 Difficulty: Medium Solution: D Current yield is the ratio of the annual coupon divided by the current market price. Coupon rate is the ratio of annual coupon divided by the face value. When a bond is at discount, the price is less than the face value. Therefore, the coupon rate is less than the current yield.

Also, when a bond is at a discount, the coupon rate is greater than YTM. 7. Section: 6.4 Interest Rate Determinants Learning Objective: 6.4 Difficulty: Medium Solution: D AAA is rated higher than BB. 8. Section: 6.5 Other Types of Bonds/Debt Instruments Learning Objective: 6.5 Level of difficulty: Medium Solution: C. P =

10,000 10,000 = = $9,804.45 182 1.019945205 (1 + 0.04  ) 365

Because it is quoted on a basis of $100, the quoted price is $98.0445.

9. Section: 6.5 Other Types of Bonds/Debt Instruments Learning Objective: 6.5 Difficulty: Medium Solution: C Floating rate bonds provide protection against increasing interest rates compared to fixed-rate bonds.

10. Section: Appendix 6A: Interest Rate Parity Learning Objective: 6.6A Difficulty: Medium Solution: C Differences in interest rates across countries can be offset by expected changes in exchange rates. If a country has a higher expected inflation rate, its currency will depreciate. IRP states that forward exchange rates locked in today to eliminate foreign exchange risk ensure investors earn the same amount no matter where they invest.

Practice Problems 11. Section: 6.1 The Basic Structure of Bonds Learning Objective: 6.1 Difficulty: Easy

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Solution: Positive covenants require firms to undertake some actions, such as make interest payments and furnish quarterly financial statements. Negative covenants prohibit firms from undertaking some actions, such as restrictions on asset sales, and putting limits on new debt issuance and dividend payments.

12. Section: 6.2 Bond Valuation Learning Objective: 6.2 Difficulty: Easy Solution: When market interest rates increase, prices of bonds decrease. When market interest rates decrease, prices of bonds increase.

13. Section: 6.2 Bond Valuation Learning Objective: 6.2 Difficulty: Medium Solution: Using a financial calculator: A. N = 10; I/Y= 5; PMT = 40; FV = 1,000; CPT PV = –922.78 B. N = 10; I/Y= 4; PMT = 40; FV = 1,000; CPT PV = –1,000 C. N = 10; I/Y= 3; PMT = 40; FV = 1,000; CPT PV = –1,085.30 Clearly, the price of bonds is inversely related to the market yield.

14. Section: 6.2 Bond Valuation Learning Objective: 6.2 Difficulty: Easy Solution: Coupon = ($1,000) (6%) /2=$30, n=10×2=20, k=4%/2=2% By financial calculator: N = 20; I/Y= 2; PMT = 30; FV = 1,000; CPT PV = - 1,163.51 15. Section: 6.2 Bond Valuation Learning Objective: 6.2 Difficulty: Easy Solution: The higher the coupon rate, the higher the market yield, and the lower the term to maturity, the lower the interest rate risk (duration), all else being equal.

16. Section: 6.2 Bond Valuation Learning Objective: 6.2 Difficulty: Medium.

Solution: a. by financial calculator: N = 5; I/Y= 6.5; PMT = 100; FV = 1,000; CPT PV = –1,145.45 b. By financial calculator: N = 10; I/Y= 3.25; PMT = 50; FV = 1,000; CPT PV = –1,147.39 c. By financial calculator: N = 60; I/Y= 0.5416667; PMT = 8.3333; FV = 1,000; CPT PV = - 1,149.07

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Notice that the value of the bond increases with more frequent coupon payments.

17. Section: 6.2 Bond Valuation Learning Objective: 6.2 Difficulty: Medium Solution: The market yield increases to (7% + 100bp) = 8%.

Using a financial calculator, for bond A: N = 10; I/Y= 4; PMT = 30; FV = 1,000; CPT PV = - 918.8910 This represents a decrease in price of (958.42-918.89) = $39.53 or ($39.53/958.42) = 4.12% For bond B: N = 10; I/Y= 4; PMT = 40; FV = 1,000; CPT PV = - 1,000.00 Bond B decreases in price by (1,041.58-1,000) = $41.58 or ($41.58/1,041.58) = 3.99% (The price exactly equals the par value because the market yield now equals the coupon rate).

In general, lower coupon bonds will be impacted more (in percentage terms) than higher coupon bonds.

18. Section: 6.2 Bond Valuation Learning Objective: 6.2 Difficulty: Medium Solution: The market yield increases to (7%+100bp) = 8%.

Using a financial calculator, for bond C: N = 6; I/Y= 4; PMT = 40; FV = 1,000; CPT PV = –1,000.

This is a decrease in price of (1,026.64–1,000) = $26.64 or (26.64/1,026.64) = 2.59% For bond D: N = 16; I/Y= 4; PMT = 40; FV = 1,000; CPT PV = –1,000.00 Bond D decreases in price by (1,060.47-1000) = $60.47 or (60.47/1,060.47) = 5.7% Longer maturity bonds will be impacted more by changes in the market yield.

19. Section: 6.2 Bond Valuation Learning Objective: 6.2 Difficulty: Difficult Solution: With a coupon rate equal to the market yield, the price of the bond is $1,000.

A fall of 50bp results in a market yield of 5.5%. Using a financial calculator (and assuming semi-annual coupon payments): N = 20; I/Y= 2.75; PMT = 30; FV = 1,000; CPT PV = –1,038.07 This is an increase in price of $38.07 or 3.8%.

An increase of 50bp results in a market yield of 6.5% N = 20; I/Y= 3.25; PMT = 30; FV = 1,000; CPT PV = –963.65 This is a price decrease of $36.35 or 3.6% Falling market yields cause larger price impacts than increasing market yields.

20. Section: 6.2 Bond Valuation Learning Objective: 6.2

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Difficulty: Difficult Solution: Using a financial calculator: a. N = 10; I/Y= 3.875; PMT = 32.50; FV = 1,000; CPT PV = –948.99 If the market yield increases to 8.75%, then I/Y = 4.375 and we find PV = –910.43. This is a price decrease of (948.99-910.43)/948.99 = 4.06% b. N = 10; I/Y= 2.625; PMT = 32.50; FV = 1,000; CPT PV = –1,054.35 If the market yield increases to 6.25%, then I/Y = 3.125 and we find PV = 1,010.60. This is a price decrease of (1,054.35 – 1,010.60)/1,054.35 = 4.15% The change in market yield was proportionately larger in part (b) than in (a) leading to a larger price impact.

21. Section: 6.2 Bond Valuation Learning Objective: 6.2 Difficulty: Difficult Solution: Using a financial calculator: a. N = 16; I/Y= 3.875; PMT = 0; FV = 1,000; CPT PV = –544.28 If the market yield increases to 8.75%, then I/Y = 4.375 and we find PV= –504.03. This is a price decrease of (544.28 – 504.03)/544.28 = 7.4% b. N = 16; I/Y= 2.625; PMT = 0; FV = 1,000; CPT PV = –660.62 If the market yield increases to 6.25%, then I/Y = 3.125 and we find PV= –611.19. This is a price decrease of (660.62 – 611.19)/660.62 = 7.48% The change in market yield was proportionately larger in part (b) than in (a) leading to a larger price impact.

22. Section: 6.2 Bond Valuation Learning Objective: 6.2 Difficulty: Medium Solution a. The quoted price can be interpreted as a percentage of face value. Therefore, you would pay 93.863% × $1,000 = $938.63. In addition to the quoted price, however, you pay the accrued interest since the last coupon payment. For U.S. bonds, the day count convention is “30/360”; exactly two months have elapsed since the last coupon payment, so we count 2 x 30 = 60 days out of 360 in the year.

Accrued interest = $1,000 × 5% × (60/360) = $8.33 Cash Price = 938.63 + 8.33 = 946.96 Peter would actually pay $946.96 for this bond. b. The day count convention in Canada is “Actual/365.” From January 1 to March 1, 2013, there are 31 + 28 = 59 days. Accrued interest = $1,000 × 5% × (59/365) = $8.08. You would have to pay 938.63 + 8.08 = $946.71 for this bond.

23. Section: 6.2 Bond Valuation

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Learning Objective: 6.2 Difficulty: Medium B=Par=$1,000 (because coupon rate=market yield=6%) By financial calculator: N = 20; I/Y= 2.5; PMT = 30; FV = 1,000; CPT PV = 1,077.9458. Change in price: ΔB=1,077.9458–1,000= –$77.9458 24. Section: 6.2 Bond Valuation Learning Objective: 6.2 Difficulty: Easy Solution: Cash Price = Quoted price + Accrued interest = $956 + ($1,000)  (0.04)  (31+31+20)/365 = $956 + $8.99 = $964.99 When an investor purchases a bond at a time between the two coupon payment dates, he needs to pay a higher price over the quoted price to compensate the bond seller, who has held the bond for a period of time (in this problem, the whole of July and August plus 20 days in September) since the last coupon payment date but won’t receive the coupon portion if he sells the bond before the next coupon payment date. Therefore the difference between the cash price and the quoted price is the accrued interest to the bondholder.

25. Section: 6.2 Bond Valuation Learning Objective: 6.2 Difficulty: Medium Solution: When the bond was trading at $102.50, the interest rate was lower than the coupon rate. When the bond was trading at $98.50, the interest rate was higher than the coupon rate. Therefore, over that period of time the interest rate went up since the coupon rate does not change.

26. Section: 6.2 Bond Valuation Learning Objective: 6.2 Difficulty: Easy Solution: N = 24; I/Y = 6; PV = –825; FV = 1,000; CPT PMT = 46.06 Semi-annual coupon =$46.06 Annual =$46.06×2 =$92.12 Coupon rate =92.12/1000 = 9.212% 27. Section: 6.3 Bond Yields Learning Objective: 6.3 Difficulty: Difficult Solution: If the YTM were 10%, the bond’s price would be exactly $1,000. We know the price is higher than this, implying a lower yield. Let’s make a “guess” that YTM=8%.

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1   1 − (1 + .04) 2  1 = $1,018.86 B = 50    + 1,000  2 .

04 ( 1 + .

04 )    

This figure is greater than the market price, so we know that the YTM must lie between 8% and 10%. We could continue guessing (e.g., use 9%, calculate the price, and then refine the guess again). However, we can get a good approximation by assuming that the price change is linear with changes in yield: the ratio of changes in yield equals the ratio of changes in price: 10% − YTM $1,000 − $1,010 = 10% − 8% $1,000 − $1,018.86 $1,000 − $1,010 YTM = 10% − (10% − 8%)  $1,000 − $1,018.86

So YTM = 8.94% approximately Checking this result with a financial calculator: N = 2; PMT = 50; FV = 1,000; PV = –1,010; CPT I/Y = 4.4663% This is a ½ year figure, so the YTM = 4.4663%×2 = 8.93% With annual coupon payments, the calculator tells us: N = 1; PMT = 100; FV = 1,000; PV = –1,010; CPT I/Y = 8.91% Assuming the current price is the same, annual coupon payments result in a slightly lower yield.

28. Section: 6.3 Bond Yields Learning Objective: 6.3 Difficulty: Medium Solution: a. N = 2; I/Y = 6; PMT = 70; FV = 1,000; CPT PV = –1,018.33 CY = 70/1,018.33 = 6.87% So, Coupon Rate > CY > YTM when the bond trades at a premium. b. PV = –1,000.00 (because YTM = coupon rate) CY = 70/1000 = 7.0% So, Coupon Rate = CY = YTM when the bond trades at par. c. N = 2; I/Y = 8; PMT = 70; FV = 1,000; CPT PV = –982.17 CY = 70/982.17= 7.13% So, Coupon Rate < CY < YTM when the bond trades at a discount.

29. Section: 6.5 Other Types of Bonds/Debt Instruments Learning Objective: 6.5 Difficulty: Medium Solution: Using a financial calculator: A. N = 20; PMT = 0; FV = 1,000; PV = - 450; CPT I/Y = 4.0733%. YTM=4.0733% × 2 = 8.15% B. I/Y = 3; PMT = 0; FV = 1,000; PV = - 400; CPT N = 31. Number of years=31/2=15.5 years Solutions Manual ..

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C. N = 30; I/Y = 6; PMT = 0; FV = 1,000; CPT PV = $174.11 30. Section: 6.4 Interest Rate Determinants Learning Objective: 6.4 Difficulty: Easy Solution: Using the approximate relationship, 6.75% = Real Rate + 2.5%, so the Real Rate = 4.25%.

(Using the exact relationship, Real Rate = (1+0.0675)/ (1+0.025) – 1 = 4.15%) 31. Section: 6.4 Interest Rate Determinants Learning Objective: 6.4 Difficulty: Easy Solution: The Fisher relationship uses expected inflation figures, not the actual rate of inflation experienced in the past. Therefore, RF = 1.50% +3% = 4.50% (Using the exact relationship, RF = (1+0.015) × (1.03)–1= 4.55% 32. Section: 6.4 Interest Rate Determinants Learning Objective: 6.4 Level of difficulty: Easy Solution: a. We can assume that T-bills (short-term, federal government bonds) have the highest possible credit rating, “AAA”, because they have virtually no default risk. We expect lower rated (riskier) bonds to have a higher yield. For “A” rated bonds, we should expect kb = 6% + 0.45% = 6.45% b. Adding the maturity yield and the “spread” for this bond rating, we find: kb = 6% + 0.50% + 1.10% = 7.60% 33. Section: 6.4 Interest Rate Determinants Learning Objective: 6.4 Level of difficulty: Easy Solution: Exact equation: (1 + RF) = (1 + real rate) (1 + expected inflation rate) Real rate = (1 + RF) / (1 + expected inflation rate) – 1 = (1.09) / (1.045)–1 = 4.31% Approximate equation: RF = real rate + expected inflation rate Real rate = RF – expected inflation rate =9% – 4.5% = 4.5% 34. Section: 6.5 Other Types of Bonds/Debt Instruments Learning Objective: 6.5 Difficulty: Medium Solution: 100 − 97.75 360 k BDY =   100 100 92 Solutions Manual ..

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=8.80% Note the difference between kBEY and kBDY: kBDY uses face value in the denominator instead of price and uses 360 days instead of 365 days.

35. Section: 6.5 Other Types of Bonds/Debt Instruments Learning Objective: 6.5 Difficulty: Medium Solution: a. PMT = 0; N = 20; FV = 1,000; I/Y= 4; Compute PV = –$456.39 b. PV = $760.

PMT = 0; N = 20; FV = 1,000; PV = - 760; Compute I/Y = 1.38% So the annual YTM = 1.38% × 2 = 2.76%.

36. Section: 6.4 Interest Rate Determinants Learning Objective: 6.4 Difficulty: Difficult Solution: For a bond paying a coupon in nominal terms, Sapna requires YTM = 5% + 2.5% = 7.5% (approximately). Thus, using a financial calculator we can find: N = 2; I/Y = 7.5; PMT = 70; FV = 1,000; CPT PV = –991.02 (Using the exact relationship, YTM = (1+0.05) × (1+0.025) –1= 7.625% and B = $988.80) For the Real Return Bond, Sapna requires YTM = 5% N = 2; I/Y = 5; PMT = 45; FV = 1,000; PV = –990.70 Notice that these prices are very similar because the bond paying a “real” coupon rate is valued using the real discount rate and the bond paying a nominal coupon is valued using the nominal discount rate.

37. Section: 6.5 Other Types of Bonds/Debt Instruments Learning Objective: 6.5 Difficulty: Medium Solution: Find the price of the U.S. T-Bill (remembering to use the correct day-count convention and the face value, not the price in the denominator of the yield equation): k BDY = 4.673% =

100 − P 360   100  P = 98.83175 100 90

The yield on an equivalent Canadian T-bill would be: k BEY =

100 − 98.83175 365   100 = 4.794% 98.83175 90

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Learning Objective: 6.2; 6.3; 6.5 Difficulty: Difficult Solution: a. We do not have a yield to maturity figure with which to discount all the cash flows (coupons and face value). Therefore, we must use the market rates implied by the zero coupon bond prices for the appropriate time period. A one-year zero coupon bond will increase from $0.97 to $1 over one year, implying that 0.97×(1+r1) = 1, or r1=3.09%. Similarly, 0.90× (1+r2)2=1 so that r2=5.41%, and 0.81×(1+r3)3=1 so that r3=7.28%. These rates can be used to discount the threeyear coupon bond’s cash flow. (Alternatively, we could use the zero coupon bond prices as given).

B=

$60 $60 $60 $1,000 + + + = $970.72 2 3 1.0309 (1.0541) (1.0728) (1.0728) 3

or B = $60  0.97 + $60  0.90 + $60  0.81 + $1,000  0.81 = $970.80

The difference in these results is due to rounding of the interest rate figures ($970.80 is the correct figure). b. Using a financial calculator: N = 3; PMT = 60; FV = 1,000; PV = -970.80; CPT I/Y = 7.12% c. From part (a), the present values of the coupon payments are: $60×0.97=$58.20 (first coupon), $60×0.90=$54.00 (second coupon) and $60×0.81=$48.60 (third coupon). These are the fair values (market prices) of the coupons today. d. To just break-even, the synthetic zero coupon bond would be sold for: $970.80 – ($58.20 + $54.00 + $48.60) = $810.00. Notice that this is the present value of the face value of the bond: $1,000×0.81 = $810.00 e. $810.00× (1+YTM)3 = $1,000, therefore, YTM = (1,000/810)1/3–1 = 7.28% This is the same figure calculated in (a) as the three-year interest rate. f. The YTM of a coupon-paying bond is an average value (weighted by the dollar amounts) of the yields on all the cash flows (coupons and face value). This average will be lower than the three-year interest rate because the yields are increasing for longer maturities (upward sloping term structure).

39. Section: 6.3 Bond Yields Learning Objective: 6.3 Difficulty: Difficult Solution: We can find the price of the bond using either the YTM or the YTC (but take care to use the correct number of periods and “face value” figures).

Using YTM: N = 20; I/Y = 3.65; PMT = 40; FV = 1,000; CPT PV = –1,049.07 Using YTC: N = 6; I/Y = 3.46; PMT = 40; FV = 1,025; CPT PV = –1,049.20 Solutions Manual ..

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By either measure, the bond’s price is greater than the call price of $1,025. It is, then, likely that the bond will be called. Here we see that YTC<YTM, and the bond is trading based on its YTC. The correct price for the bond is $1,049.20.

40.

Section: 6.5 Other Types of Bonds/Debt Instruments Learning Objective: 6.5 Difficulty: Easy Solution: As a holder of a retractable bond, you will exercise your right if you expect a rise in interest rates.

41.

Section: 6.5 Other Types of Bonds/Debt Instruments Learning Objective: 6.5 Difficulty: Medium Solution: Price of bond =$950 Cost per share through conversion = $950/25 =$38.00 Discount = $40-$38 =$2 Percentage discount = 2/40= 5% 42. Section: 6.4 Interest Rate Determinants Learning Objective: 6.4 Difficulty: Easy Solution: Downgrading implies more risk, which in turn implies more return is required. Therefore the price of the bond is expected to fall.

43. Section: 6.3 Bond Yields Learning Objective: 6.3 Difficulty: Medium Solution: Since the current yield is less than the yield to maturity, the bond is trading at a discount and the coupon rate should be less than 6 percent which is the current yield.

44. Section: 6.3 Bond Yields Learning Objective: 6.3 Difficulty: Medium Solution: We can calculate yield to maturity using the formula below, where r1, r2, ... rn are the spot rate and ytm is the yield to maturity. Yield to maturity is defined as the interest rate that makes price equal the present value of future cash flows. The left hand side of the formula gives the price and the right hand side of the formula gives the present value of future cash flow discounted by yield to maturity.

C/(1+r1)+C/(1+r2)2+C/(1+r3)3…+(C+F/)(1+rn)n=

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C/(1+ytm)+C/(1+ytm)2+C/(1+ytm)3…+(C+F/)(1+ytm)n

45. Section: 6.3 Bond Yields Learning Objective: 6.3 Difficulty: Medium Solution: Bond price = $80×0.91743 + $1,080 ×0.82645 =$965.96 N = 2; PMT = 80; PV = –965.96; FV = 1,000; CPT I/Y = 9.96 46. Section: 6.5 Other Types of Bonds/Debt Instruments Learning Objective: 6.5 Difficulty: Medium Solution: First, since the coupon is higher than the market rate of interest, it implies that the bond is trading at a premium. Then you also know that the company is not doing well so the price of the stock will most probably go further down. Therefore, there is no need to convert the bond into shares.

So the client can keep the bond or sell it but not convert it into shares.

47. Section: Appendix 6A: Interest Rate Parity Learning Objective: 6.6A Difficulty: Medium Solution: Investing funds in the Canadian T-Bill would give $1,000×1.0450 = $1,045 at the end of one year. Knowing that he will have this amount of money available, Adam could buy Australian dollars at the one-year forward rate (he would agree to the conversion rate today, but the actual exchange of CDN$ for AU$ would occur in one year). This transaction will leave Adam with CDN$1,045/0.89829 = AU$1,163.32.

The alternative approach is to convert his funds today (at the spot rate) which would give CDN$1,000/0.90431 = AU$1,105.82. If he invests this amount in an Australian T-bill, at the end of one year he would have AU$1,105.82×1.0520=AU$1,163.32.

As expected from IRP theory, these two approaches will give Adam the same result.

48. Section: Appendix 6A: Interest Rate Parity Learning Objective: 6.6A Difficulty: Difficult Solution: According to IRP, (1 + kdomestic ) (1.05) F =S = ($1.4161)  = $1.3896 / Euro (1 + k foreign ) (1.07) Since $1.3896/Euro ≠$1.4090/Euro, there is an arbitrage opportunity.

Forward rate calculated from IRP ($1.3896/Euro) < the market one-year forward rate ($1.4090/Euro). This means the Euro forward contract is over-priced.

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Bower should sell Euros through the forward contract and buy Euros (underlying asset) today and apply the following transactions: 1st: Borrow $1,000 at 5% (he needs to repay $1,000× (1.05) = $1,050 after one year) Convert $1,000 to Euro at the spot rate ($1.4161/Euro) and get 706.1648 Euros. (i.e., $1,000/($1.4161/Euro) = 706.1648 Euros). Short (sell) Euros through the forward contract.

2nd: Invest 706.1648 Euros in one-year European T-bill at 7%. After one year he will receive 755.5964 Euros. (i.e., 706.1648× (1.07) = 755.5963) 3rd: After one year, convert 755.5963 Euros into CDN$ at the contract forward rate $1.4090/Euro and get $1,064.6352. (i.e., 755.5963 Euros × ($1.4090/Euro) = $1,064.6352).

Repay $1,050 and keep the remainder as his profit.

Arbitrage profit of investing $1,000=$1,064.6352 - $1,050= $14.6352 Explanation: If other investors seize the same arbitrage opportunity as Bower, the forward price would quickly fall to $1.3896/Euro so that IRP holds.

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Chapter 7: Equity Valuation Multiple Choice Questions 1. Section: 7.1 Equity Securities Learning Objective: 7.1 Level of difficulty: Easy Solution: D Jason’s ownership=30,000/2,000,000 = 1.5% 2. Section: 7.1 Equity Securities Learning Objective: 7.1 Level of difficulty: Medium Solution: A Total return = ((2,500 + 400) – 2000)/2000 = 45% 3. Section: 7.1 Equity Securities Learning Objective: 7.1 Level of difficulty: Easy Solution: D Both debt and equity represent ownership of the security. Equity represents ownership of the firm.

4. Section: 7.1 Equity Securities Learning Objective: 7.1 Level of difficulty: Easy Solution: B Required rate of return (k) = RF + Risk Premium = 4% + 6.5% = 10.5% 5. Section: 7.3 Common Share Valuation: The Dividend Discount Model (DDM) Learning Objective: 7.3 Level of difficulty: Medium Solution: D Not every firm pays dividends each year. In practice, preferred dividends are paid quarterly.

Preferred shareholders have claims before common shareholders.

6. Section: 7.3 Common Share Valuation: The Dividend Discount Model (DDM) Learning Objective: 7.3 Level of difficulty: Medium Solution: B D0 = $2.00. D1 = $2.00 × (1 + 0.045) = $2.09 k = RF + Risk Premium = 3% + 6.5% = 9.5% P0 = $2.09/(0.095 – .045) = $41.80 7. Section: 7.3 Common Share Valuation: The Dividend Discount Model (DDM) Learning Objective: 7.3 Level of difficulty: Medium

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Solution: B D1 = D0 (1 + g) = $1.50 × (1 + 0.04) = $1.56 k = (D1/P0) + g = (1.56/26) + 4% = 10% 8. Section: 7.2 Preferred Share Valuation Learning Objective: 7.2 Level of difficulty: Medium Solution: C Capital Gain = (37.5 – 34) × 200 = $700 9. Section: 7.1 Equity Securities Learning Objective: 7.1 Level of difficulty: Medium Solution: B Total dollar return = Capital Gain + Dividends = (37.5 – 34) × 200 + 1.5 × 200 = $1,000 10. Section: 7.3 Common Share Valuation: The Dividend Discount Model (DDM) Learning Objective: 7.3 Level of difficulty: Medium Solution: A Payout ratio = D0/EPS0 = $1.5/$9 = 1/6 = 16.67% ROE = NI/E = EPS/BVPS = $9/$36 = 1/4 = 25% g = (1– payout ratio) × ROE = (retention ratio) × ROE = (1 – 1/6) × 25% = 20.83% 11. Section: 7.3 Common Share Valuation: The Dividend Discount Model (DDM) Learning Objective: 7.3 Level of difficulty: Medium Solution: C g = (1 – payout ratio) × ROE = (Retention Ratio) × ROE 12. Section: 7.3 Common Share Valuation: The Dividend Discount Model (DDM) Learning Objective: 7.3 Level of difficulty: Medium Solution: D Firms with negative earnings may continue to pay dividends from external cash inflows such as borrowing through bond issues, institutional lending, new equity issues or sale of assets.

13. Section: 7.4 Using Multiples to Value Shares Learning Objective: 7.4 Level of difficulty: Medium Solution: D Leading P/E ratio = (D1/EPS1)/(kc – g) = (payout ratio)/(kc – g) 14. Section: 7.4 Using Multiples to Value Shares Learning Objective: 7.4 Level of difficulty: Easy

Solutions Manual 2 Chapter 7 Copyright © 2013 John Wiley & Sons Canada, Ltd. Unauthorized copying, distribution, or transmission is strictly prohibited.

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Solution: A Practice Problems 15. Section: 7.2 Preferred Share Valuation Learning Objective: 7.2 Level of difficulty: easy.

Solution: Preferred shares essentially pay a fixed amount just like bonds. Preferred shareholders have claims on the firm’s earnings and assets in the event of liquidation before common shareholders and they seldom have voting rights. Usually no payments can be made to common shareholders until preferred shareholders have been paid the dividends they are due in entirety.

Preferred share prices increase when market rates decline, and vice-versa.

16. Section: 7.3 Common Share Valuation: The Dividend Discount Model (DDM) Learning Objective: 7.3 Level of difficulty: easy.

Solution: Expected dividend, required rate of return, and the constant dividend growth rate.

17. Section: 7.3 Common Share Valuation: The Dividend Discount Model (DDM) Learning Objective: 7.3 Level of difficulty: easy.

Solution: The Constant Growth DDM assumes a constant rate of growth in dividends, which is less than the required rate of return that will hold indefinitely. It discounts all the future expected dividend cash flows to the present to determine the current market share price. It is suitable for well-established companies that pay dividends that grow steadily.

18. Section: 7.3 Common Share Valuation: The Dividend Discount Model (DDM) Learning Objective: 7.3 Level of difficulty: Easy Solution: PVGO mathematically equals P0 – (EPS1/kc). It assesses the market perception of the growth opportunities available to a firm. If the market perceives that a firm has no future growth opportunities, its PVGO will be zero and its market price reflects only its zero-growth component, which equals EPS1/kc. A positive PVGO increases the firm’s share price.

19. Section: 7.2 Preferred Share Valuation Learning Objective: 7.2 Level of difficulty: Easy Solution: Solving these questions involves the algebraic manipulation of the preferred share valuation formula.

Co.

Price

Preferred Shares in Canada Required Par value Dividend rate return

Dividends paid per share

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A

Pps =

$100

8%

5%

$5.00

B

$60

$50

3%

$1.80 = 3.6% $50.00

C

$70

$75

$70 =

D 0.03 D = $1.80 $8.00

$5.00 0.08 = $62.50

$8.00 kp

$8.00 = 10.67% $75.00

$60 =

k p = 11.43% D

$50

$50

$50 =

$7.00 kp

14%

D = .14*50 = $7.00 D 0.07 D = $10.50 $9.50

k p = 14% E

$150

$30

7%

$10.50 = 35% $30.00

F

$9.50 0.04 = $237.50 $18 Pps = 0.07 = $257.14 $18

$100

4%

$9.50 = 9.5% $100

$18 = 9% Par Par = $200 $0.90 = 6% Par Par = $15

7%

9%

$18.00

5%

6%

$18 =

G

H

Pps =

$150 =

D 0.05 D = $0.90

20. Section: 7.1 Equity Securities Learning Objective: 7.1 Level of difficulty: Easy Solution: To determine the risk premium, we need to remember that the required return is equal to the sum of the risk-free rate and the risk premium.

Step 1: calculate the required return: $110 =

Dp kp

=

0.08 *100 kp

k p = 7.27%

Step 2: the risk premium = 7.27% – 2% = 5.27% 21. Section: 7.3 Common Share Valuation: The Dividend Discount Model (DDM) Learning Objective: 7.3 Level of difficulty: Easy Solution: Solutions Manual 4 Chapter 7 Copyright © 2013 John Wiley & Sons Canada, Ltd. Unauthorized copying, distribution, or transmission is strictly prohibited.

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a.

Assuming the dividend is paid annually: D +P D +P 5 + 75 P0 = 1 1 kc = 1 1 − 1 = − 1 = 60% 1+ kc P0 50 b.

kc = c.

P0 =

D1 + P1 5 + 35 −1= − 1 = −20% P0 50

D1 + P1 1 + kc

P1 = P0 (1 + kc ) − D1 = 50 (1 + ( −.04) ) − 5 = 50*.96 − 5 = $43 d.

P1 = 50 1+ .15 − 5 = $52.50

(

)

22. Section: 7.3 Common Share Valuation: The Dividend Discount Model (DDM) Learning Objective: 7.3 Level of difficulty: Medium Solution: a. D1 = D2 = $1.50

D1 D + P2 + 2 (1 + kc ) (1 + kc ) 2 1.50 1.50 + 75 50 = + (1 + kc ) (1 + kc )2 P0 =

Note: the expected annual return, kc, is the IRR. The IRR of this series of cash flows is determined by (Using CF functions on BAII+): CF0 = –50; C01 = 1.5; F01 = 1; C02 = 76.5; F02 = 1 Compute IRR: 25.20% Alternatively: using the TVM functions on the BAII+ N = 2, PV = –50, PMT = 1.5, FV = 75 compute I/Y also gives 25.20%. b. Using the same inputs as in part a (except C02 = 36.5) we compute I/Y as negative 13.05%.

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c. If the actual return was –4%, what was the sale price?

Using TVM functions on BAII+ N = 2, PV = –50, I/Y = –4, PMT = 1.5, compute FV Sale price = FV = $43.14 d. Sale price = $62.90 Using the same inputs as part c (except I/Y = 15) we compute FV = 62.90 23. Section: 7.3 Common Share Valuation: The Dividend Discount Model (DDM) Learning Objective: 7.3 Level of difficulty: Easy Solution: Solving these requires algebraic manipulation of the dividend discount formula.

Co.

Price

A

5.00 .15 − .1111 = $128.57 $600

B

P0 =

Common Shares in Canada Required Dividend Current return growth dividend 15% $4.50 5.00 g= −1 4.50 = 11.1111% 3% 1% 12 D0 = 1.01 = $11.88

Dividend expected in 1 year $5.00

D1 .03 − .01 D1 = 600*(.03 − .01)

$600 =

= $12 C

$70

70 =

8 kc − .05

8 + 3.50 70 = 16.43% 11 55 = kc − .10

5%

$8.00

10%

D1 1+ g 8 = 1.05 = $7.62 $10.00

6%

$9.50

D1 = D0 (1 + g )

kc =

D

$55

11 + 5.50 55 = 30% 14%

D0 =

$11.00

kc =

E

P0 =

(

D0 1 + g

)

kc − g

9.50 *1.06 .14 − .06 = $125.88 =

= 9.50*1.06 = $10.07

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F

G

18 .15 − .0 = $120.00 $40 P0 =

15%

0%

5%

-2%

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$18.00

$18.00

D1 1+ g 2.80 = 1 + −.02

D0 =

(

= $2.86

)

P0 =

D1 kc − g

40 =

D1 .05 − ( −.02 )

D1 = $2.80

24. Section: 7.3 Common Share Valuation: The Dividend Discount Model (DDM) Learning Objective: 7.3 Level of difficulty: Easy Solution: a. The total earnings of ToolWerks is $10 million. The EPS is $10,000,000/2,000,000 shares which equals $5. b. The expected dividends are determined by the dividend payout ratio multiplied by the earnings. The total dividends are 40% of $10 million or $4 million. On a per share basis, the expected dividends per share are $2.00. c. The dividend growth rate expected for ToolWerks is: D1 2.00 P0 = 75 = g = 5.33% kc − g .08 − g d. The present value of growth opportunities for this firm is: The value of the firm, assuming no growth opportunities and 100% dividend payout is $5/.08 = $62.50. PVGO = $75 – $62.50 = $12.50 25. Section: 7.3 Common Share Valuation: The Dividend Discount Model (DDM) Learning Objective: 7.3 Level of difficulty: Easy Solution: Value of firm, assuming no growth opportunities, is 1.85/.08 = $23.13 PVGO = $50 – $23.13 = $26.87 26. Section: 7.3 Common Share Valuation: The Dividend Discount Model (DDM) Learning Objective: 7.3 Level of difficulty: Easy Solution: a. Earnings per share.

Lagging EPS (current earnings per share) are $300,000/50,000 = $6. To calculate the leading EPS, an estimate of the growth rate of the earnings is needed. b. Dividends per share Dividends per share = $175,000/50,000 = $3.50 c. Earnings retention ratio

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Earnings retention ratio = 1 – dividend payout ratio = 1 – 3.50/6 = 41.67% d. Sustainable growth rate The sustainable growth rate equals 41.67% × 12% = 5% 27. Section: 7.3 Common Share Valuation: The Dividend Discount Model (DDM) Learning Objective: 7.3 Level of difficulty: Medium Solution: As indicated by equation P0 =

D0(1+ g) D = 1 , market share price is positively kc − g kc − g

related to the expected dividend D1 and expected growth rate g, but negatively related to the required rate of return kc.

28. Section: 7.2 Preferred Share Valuation Learning Objective: 7.2 Level of difficulty: Medium Solution: Annual dividend = $100 × 7.25% = $7.25 Pps = Dp/kp = 7.25/.105 = $69.05 29. Section: 7.4 Using Multiples to Value Shares Learning Objective: 7.4 Level of difficulty: Medium Solution: Payout = 1 – Retention ratio = 1 – 0.6 = 0.4 Leading P/E = payout ratio/(kc – g) = 0.4/(.10 – 0.05) = 8 30. Sections: 7.1 Equity Securities, 7.2 Preferred Share Valuation, and 7.3 Common Share Valuation: The Dividend Discount Model (DDM) Learning Objectives: 7.1 to 7.3 Level of difficulty: Difficult Solution: a. No growth g = 0, D0 = $2, kc = 10% D18 = D0 = $2

b. Growth:

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g = 5%, D0 = $2, kc = 10% D18 = D0  (1 + g ) = $2  (1 + 0.05 ) = $4.8132 18

P17 =

18

D18 4.8132 = = $96.26 kc − g 0.1 − 0.05

D  (1 + g ) D26 7.1113 P25 = = 0 = = $142.23 kc − g kc − g 0.1 − 0.05 Similarly : 26

D  (1 + g ) D16 $4.3657 P15 = = 0 = = $87.31 kc − g kc − g 0.1 − 0.05 16

31. Section: 7.3 Common Share Valuation: The Dividend Discount Model (DDM) Learning Objective: 7.3 Level of difficulty: Medium Solution: No, my broker is incorrect.

Debt: banks are not immune from failure and default and therefore some risk will always exist.

In fact, in 1985 two Alberta-based banks, the Northlands Bank and the Canadian Commercial Bank, failed.

Preferred stock: there are generally no voting rights associated with preferred stock.

Common stock: there is no legal obligation to pay a dividend and the failure to pay a dividend on common stock does not trigger bankruptcy. The fact that the firm has paid a dividend of $2.50 per year for the past 18 years is irrelevant.

32. Section: 7.3 Common Share Valuation: The Dividend Discount Model (DDM) Learning Objective: 7.3 Level of difficulty: Medium Solution: D1 1.50 = = $37.50 a. P0 = kc − g .07 − .03 b. The expected dividend yield, ( D1 / P0 ) , is 1.50 / 37.50 = 4% c. The expected capital gains yield,

P1 − 1 , is given by the growth rate (g) = 3% P0

d. i) In one year, immediately after the dividend is paid, the price of the stock is:

P1 =

D2 1.50(1.03) = = $38.63 kc − g .07 − .03

ii) The one-year holding period return = (1.50 + 38.63)/37.5 – 1 = 7% Solutions Manual 9 Chapter 7 Copyright © 2013 John Wiley & Sons Canada, Ltd. Unauthorized copying, distribution, or transmission is strictly prohibited.

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iii) The expected dividend yield = D2 / P1 = 1.545 / 38.63 = 4%. The expected capital gains = the expected growth rate of 3%. e. i) In year 10, immediately after the dividend is paid, the price of the stock is: D11 1.50(1.03)10 P10 = = = $50.40 kc − g .07 − .03 ii) The one-year holding period return must equal the required rate of return = 7%. iii) The expected divided yield is 4% and the expected capital gains yield is 3%.

33. Section: 7.4 Using Multiples to Value Shares Learning Objective: 7.4 Level of difficulty: Medium Solution: a. Expected growth rate = 4% i) Today There are two ways to solve this problem: → The long way: determine the price and calculate the P/E ratio.

To determine the leading P/E ratio, we need to calculate the price of the stock today and the estimate of the earnings next period.

P0 =

2.00 = $40 .09 −.04

The firm uses a dividend payout ratio of 25% so the earnings next year must be $8.00 (25% of $8.00 equals the expected dividend of $2.00) Therefore the leading P/E ratio is 40/8 = 5.00 → Alternatively, we can use the P/E ratio approach: P0 EPS1 P0 EPS1

=

=

D1/EPS1 kc – g 0.25 0.09 – 0.04

= 5

ii) In one year (immediately after dividend paid) In one year, the expected dividend will be 2 × 1.04 = $2.08 and the price of the stock will be $41.60. The expected earnings will be 4 × 2.08 = $8.32.

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So in one year, the expected leading P/E ratio will be 41.6/8.32 = 5 b. Expected growth rate = 8% i) Today Using the P/E ratio approach: P/E = .25/(.09-.08) = 25 Alternatively we can solve for the P/E ratio by: The expected price today is:

2.00 = $200 . The expected earnings are still $8 (the payout ratio .09 −.08

hasn’t changed), so the leading P/E ratio is 25.

ii) In one year (immediately after dividend paid) Using the P/E ratio approach: P/E = 0.25/(0.09 – 0.08) = 25.

Alternatively we can solve for the P/E ratio by: 2.00 (1 + .08) = $216 and the expected earnings are 4 × .09 − .08 (2 × 1.08) = $8.64. The leading P/E ratio is 25.

In one year, the price of the stock will be:

c. The P/E ratio will not change over time as long as the dividend payout ratio is constant. The price will grow over time by, (1+ g ) , the capital gains rate. The capital gains rate is exactly the same rate at which dividends and earnings grow. Therefore, the P/E ratio will not change (P and E both grow by the same rate). Note: if the dividend payout ratio changes, then the P/E ratio will also change.

34. Section: 7.3 Common Share Valuation: The Dividend Discount Model (DDM) Learning Objective: 7.3 Level of difficulty: Medium Solution: The first dividend occurs at the end of year 5. The price of the stock at the end of year 4 is D5 1.00 P4 = = = $25 kc − g .10 − .06 To obtain the price today, we discount the price back 4 years to time 0. The discount rate is 10 percent (the required rate of return for the stock).

The current price of the stock is: 25 = $17.08 1.14 35. Section: 7.3 Common Share Valuation: The Dividend Discount Model (DDM)

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Learning Objective: 7.3 Level of difficulty: Medium Solution: The price immediately after the dividend is paid (January 21) is 5.00/0.10 = $50.00 The price just before the dividend is paid (January 19) is $55.00.

Determining the price immediately after the dividend is similar to determining the present value of an ordinary annuity. Determining the price just before the dividend is similar to determining the present value of an annuity due (cash flows at the beginning of the period).

36. Section: 7.3 Common Share Valuation: The Dividend Discount Model (DDM) Learning Objective: 7.3 Level of difficulty: Medium Solution: a. The expected dividend at the end of year 5 is $5.00 (expect no growth during this period) b. The expected dividend at the end of year 6 D6 = D5 (1+ g) = 5.0 *1.02 = $5.10 c. The expected price of the stock at the end of year 5 (immediately after the year 5 dividend) D6 5.10 P5 = = = $63.75 kc − g .1− .02 d. The price of the stock today We must take into account the present values of the dividends during the first 5 years plus the 5

5

t =1

(1.10 )

present value of the stock price in year 5. P0 = 

t

+

63.75

(1.10 )5

Note: the first 5 payments are

an annuity so we can use the TVM function on the BAII+ calculator.

N = 5, PMT = 5.0, FV = $63.75, I/Y = 10%, compute PV. The price of the stock today is: $58.54 37. Section: 7.3 Common Share Valuation: The Dividend Discount Model (DDM) Learning Objective: 7.3 Level of difficulty: Medium Solution: a. The expected dividend at the end of year 5

(

) ( ) 5

5

D5 = D0 1+ g1 = 5 1.08 = $7.35 b. The expected dividend at the end of year 6 D6 = D5 (1 + g2) = D0 (1 + g1)5(1 + g2) = 5(1.08)5(1.02) = $7.49 c. The expected price of the stock at the end of year 5 (immediately after the year 5 dividend) D6 7.4936 P5 = = = $93.67 kc − g2 .1− .02

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d. The price of the stock today: We will use Excel to calculate this.

Year Dividend 5 1 5.4 2 5.832 3 6.29856 4 6.802445 5 7.34664

Stock price at end of year 5

Present value

93.6696649

4.909091 4.819835 4.732201 4.646161 62.72318

Price of stock in year 0

81.83047

The price of the stock today is $81.83 The formulas used in Excel are given below: A B C D 1 Year Dividend Stock price at end of year 5 Present value 2 0 5 3 1 =1.08*B2 =B3/(1+0.1)^A3 4 2 =1.08*B3 =B4/(1+0.1)^A4 5 3 =1.08*B4 =B5/(1+0.1)^A5 6 4 =1.08*B5 =B6/(1+0.1)^A6 7 5 =1.08*B6 =(B7*1.02/(0.1-0.02)) =B7/(1+0.1)^A7+C7/1.1^A7 8 9 Price of stock in year 0: =SUM(D3:D7) 10 38. Section: 7.3 Common Share Valuation: The Dividend Discount Model (DDM) Learning Objective: 7.3 Level of difficulty: Medium Solution: The easiest way to solve this problem is to use Excel.

Year 0 1 2 3 4 5

Growth rate 9% 9% 9% 6% 6%

Dividend 3.6000 3.9240 4.2772 4.6621 4.9418 5.2383

Stock price at Present value of end of year 7 each cash flow 3.5036 3.4097 3.3184 3.1406 2.9724

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6 7 8

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6% 6% 2%

5.5526 5.8858 6.0035

Discount rate:

12%

2.8131 29.8193

60.0352

Price of stock in year 0:

$48.9771

The price of the stock today is $48.98 The Excel formulas: A 1

Year

2 3 4 5 6 7 8 9 10 11 12 13 14

0 =1+A2 =1+A3 =1+A4 =1+A5 =1+A6 =1+A7 =1+A8 =1+A9

B Growth rate 0.09 0.09 0.09 0.06 0.06 0.06 0.06 0.02

Discount rate:

C Dividend

D E Stock price at end Present value of each cash of year 7 flow

3.6 =(1+B3)*C2 =(C3+D3)/(1+C$12)^A3 =(1+B4)*C3 =(C4+D4)/(1+C$12)^A4 =(1+B5)*C4 =(C5+D5)/(1+C$12)^A5 =(1+B6)*C5 =(C6+D6)/(1+C$12)^A6 =(1+B7)*C6 =(C7+D7)/(1+C$12)^A7 =(1+B8)*C7 =(C8+D8)/(1+C$12)^A8 =(1+B9)*C8 =C10/(C12-B10) =(C9+D9)/(1+C$12)^A9 =(1+B10)*C9 0.12

Price of stock in year 0:

=SUM(E3:E9)

39. Section: 7.3 Common Share Valuation: The Dividend Discount Model (DDM) Learning Objective: 7.3 Level of difficulty: Medium Solution: The easiest way to solve this problem is to use Excel; however, we will show how to solve it using the BA II+.

Step 1: determine the value of the stock at the end of year 3.

Expected dividend in year 3 is: D3 = D0 (1+ g1 )3 = 4.00(1+ .25)3 = 7.8125 The expected value of the stock at the end of year 3:

P3 =

D3 (1+ g2 ) 7.8125*1.10 = = $171.875 kc − g 2 .15 − .10

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CF 1 2 3

Calculation 4*1.25 5*1.25 = 6.25 6.25*1.25 plus the stock price at the end of year 3

Booth, Cleary

Value 5 6.25 7.8125+171.875

F 1 1 1

NPV: I = 15; compute NPV = 127.2212 Value of stock today is $127.22 40. Section: 7.3 Common Share Valuation: The Dividend Discount Model (DDM) Learning Objective: 7.3 Level of difficulty: Medium Solution: a. Implied growth rate D1 D 1 P0 =  g = kc − 1 = 0.15 − = 0.1 = 10% kc − g P0 20 b. Share price in recession D1 1 P0 = = = $6.67 kc − g 0.15 − 0 Therefore, as investors change their growth expectations from 10% to 0%, the share price drops from $20 to $6.67. c. Share price in booming scenario D1 1 P0 = = = kc − g 0.15 − 0.15 The formula seems to break down. Looking at it more closely to see what is happening, if the dividends that the firm pays are expected to grow at the expected rate of return, the growth and the discounting simply cancel each other out. Mathematically the scenario reduces to:

Intuitively, the above expression suggests that the conceived situation is unstable and cannot last forever. In other words, the firm cannot grow at a rate that forever matches or exceeds the rate at which the general economy is growing. Conversely, if the general economy starts to grow at a

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higher rate, then investors will start to demand higher rates of return on their investment and thus kc will get upwardly revised.

41. Section: 7.3 Common Share Valuation: The Dividend Discount Model (DDM) Learning Objective: 7.3 Level of difficulty: Difficult Solution:

First payment is at t = 6 The payment from t = 6 to t = 11 represents a growing annuity with g = 10%. The payments starting t = 12 to infinity represent a growing perpetuity.

Step 1: Calculating the present value of the growing annuity: Present value of a growing annuity is given by: t PMT1   1 + g   PV0 =  1−   k − g   1 + k  

  1 + g  (11− 5)    1 + 0.1  6  D6 2 1  PV5 =  1 −  1− = $9.36 =  0.15 − 0.1   1 + 0.15   kc − g1   1 + kc 

Step 2: Calculating the present value of the growing perpetuity: PMT1 PV0 = k−g

D12 2  1.15  1.05 = = 33.82 kc − g 2 0.15 − 0.05 Step 3: Calculate the price of the stock: PV5 PV11 9.36 33.82 P0 = + = + = 11.92 5 11 5 (1 + k ) (1 + k ) (1 + 0.15) (1 + 0.15)11

 PV11 =

Excel Solution:

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42. Section: 7.3 Common Share Valuation: The Dividend Discount Model (DDM) Learning Objective: 7.3 Level of difficulty: Difficult Solution: Time line:

a. Calculating g2

D  (1 + g1 )  (1 + g2 ) D5 P4 = = 0 kc − g2 kc − g2 4

0.5  (1 + 0.05 )  (1 + g2 ) 0.6078  (1 + g2 ) 10 = = 0.15 − g2 0.15 − g2  1.5 − 10  g2 = 0.6078 + 0.6078  g2 0.8922 or : g2 = = 0.0841 = 8.41% 10.6078 4

b. Calculating price of XYZ 5 years from now:

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P5 = P4  (1 + g2 ) = 10  1.0841 = $10.841  $10.84 Alternatively : You can also use the following formula to get the same answer D  (1 + g1 )  (1 + g2 ) D6 P5 = = 0 kc − g2 0.15 − 0.0841 4

2

c. Current price of XYZ will be the present value of the $10 price in year 4 plus the present value of all the dividends paid in years 1 through 4. The payments in year 1 through 4 represent a growing annuity, therefore, using the present value of a growing annuity formula:  1+ g 4 D1 P4 1 P0 =  1 −  +  kc − g1   1 + kc   (1 + kc )4 4 0.5  1.05   1 + 0.05   10  P0 =  1 −  + = $7.32   0.15 − 0.05   1 + 0.15   (1 + 0.15 )4

Excel Solution:

43. Section: 7.3 Common Share Valuation: The Dividend Discount Model (DDM) Learning Objective: 7.3 Level of difficulty: Difficult Solution: Notation: t = 0 is December 31, 2012 t = 5 is December 31, 2017 t = 10 is December 31, 2022 t = 11 is December 31, 2023 (January 1, 2013 is the beginning of “year 1” so it is considered t = 0 just like December 31, 2012.)

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P0 is the PV of a growing annuity (PVGA) with g2 = 6% and consisting of 6 payments (D5 is the first one and D10 is the last) plus the PV of a growing perpetuity (PVGP) with g3 = 2% ( D11 is the first payment in this growing perpetuity).

Calculating D5 and D11: D5 = 0.5 × EPS5 = 0.5 × $5 × 1.155 = $5.028393 D11 = 0.8 × EPS11 = 0.8 × $5 × 1.155 × 1.066 = $11.412594 6 D5   1 + g 2   D11 1 1 P0 = PVGA + PVGP = +    1 −  4 r − g 2   1 + r   (1 + r ) r − g 3 (1 + r )10

P0 =

6 $ 5 .0 2 8 3 93  1.0 6  1 $ 1 1 .4 1 2 5 9 4 1 1 − +  = $7 2.1 1     4 0.1 − 0.0 6   1.1   (1.1) 0.1 − 0.0 2 (1.1)10

44. Section: 7.3 Common Share Valuation: The Dividend Discount Model (DDM) Learning Objective: 7.3 Level of difficulty: Medium Solution:

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 1+ g 5 D1 P5 1 P0 =  1 −  +  kc − g1   1 + kc   (1 + kc )5 Where : P5 =

D6 5 , D6 = D0  (1 + g1 )  (1 + g2 ) kc − g2

D6 = 4  1.09 5  0.99 = $6.093  P0 =

  1 + 0.09  5  4  1.09 6.093  1 −  +   0.08 − 0.09   1 + 0.08   (0.08 + 0.01)  (1 + 0.08 )5

 P0 = $66.64 45. Section: 7.3 Common Share Valuation: The Dividend Discount Model (DDM) Learning Objective: 7.3 Level of difficulty: Medium Solution: a. Current share price of ABC: D5 1 1 P4 = = = = $10 kc − g 0.15 − 0.05 0.1 P4 10  P0 = = $5.72 4 = (1 + kc ) 1.15 4 b. Current share price of XYZ: D1 D  1.01 5  1.01 P0 = = 0 = = $36.07 kc − g kc − g 0.15 − 0.01 c. PVGO of ABC: EPS1 P0 = + PVGO kc

2 + PVGO  PVGOABC = −7.61 0.15  The negative PVGO suggests that ABC's growth is destroying value

 5.72 =

d. PVGO of XYZ: EPS1 P0 = + PVGO kc

5 + PVGO  PVGOXYZ = 2.74 0.15 The positive PVGO suggests that XYZ's growth opportunities are creating value.

 36.07 =

46. Section: 7.3 Common Share Valuation: The Dividend Discount Model (DDM) Learning Objective: 7.3 Solutions Manual 20 Chapter 7 Copyright © 2013 John Wiley & Sons Canada, Ltd. Unauthorized copying, distribution, or transmission is strictly prohibited.

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Level of difficulty: Medium Solution: No. As the dividend payout ratio increases, the percentage change in stock prices decreases.

Dividend payout ratio 5% 10% 15% 20% 25% 30% 35% 40% 45% 50% 55% 60% 65% 70% 75%

Sustainable growth rate 9.50% 9.00% 8.50% 8.00% 7.50% 7.00% 6.50% 6.00% 5.50% 5.00% 4.50% 4.00% 3.50% 3.00% 2.50%

Percentage change Stock price in stock price $19.9091 $18.1667 –8.75% $16.6923 –8.12% $15.4286 –7.57% $14.3333 –7.10% $13.3750 –6.69% $12.5294 –6.32% $11.7778 –6.00% $11.1053 –5.71% $10.5000 –5.45% $9.9524 –5.22% $9.4545 –5.00% $9.0000 –4.81% $8.5833 –4.63% $8.2000 –4.47%

47. Section: 7.4 Using Multiples to Value Shares Learning Objective: 7.4 Level of difficulty: Easy Solution: All else being equal, reasons why one firm may have a higher leading P/E ratio than a comparable firm are that it has: 1. A lower required rate of return 2. A lower retention ratio, or a higher payout ratio 3. A higher expected growth rate 48. Section: 7.3 Common Share Valuation: The Dividend Discount Model (DDM) Learning Objective: 7.3 Level of difficulty: Difficult Solution: D0 = $1.00, D1 = $1.00 × 1.1 = $1.10, D2 = $1.1 × 1.1 = $1.21 D3 = $1.21 × 1.04 = $1.2584. P2 = D3/(kc – g) = 1.2584/(0.11 – 0.04) = $17.98

P0 =

1.10 1.21 + 17.98 + = 0.99 + 15.58 = $16.57 1 (1 + .11) (1 + .11)2

Or, Using a financial calculator (TI BA II Plus): PV(D1): N = 1; I/Y (or i) = 11%; PMT = 0; FV = –1.10; CPT then PV, gives 0.99

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PV(D2 + P2): N = 2; I/Y (or i) = 11%; PMT = 0; FV = –19.19(1.21+17.98); CPT then PV, gives 15.58 P0 = 0.99 + 15.58 = $16.57 49. Section: 7.5 Additional Multiples or Relative Value Ratios Learning Objective: 7.5 Level of difficulty: Difficult Solution: Payout=D0/EPS0 = $4/$5 = 0.8, Retention ratio (b) = 1 – Payout ratio = 1 – 0.8 = 0.2 D/E=0.67, leverage ratio A/E=(D+E)/E=(0.67+1)/1=1.67 ROE = Net profit margin × Asset turnover × leverage ratio = 20% × 1.5 × 1.67 = 50% g = b × ROE = 0.2 × 50% = 10% EPS1 = EPS0 (1 + g) = $5 × 1.1 = $5.5 k = 3% + 12% = 15% Leading P/E = payout/(k – g) = 0.8/(0.15 – 0.10) = 16 P0 = leading P/E × EPS1 = 16 × 5.5 = $88 50. Section: 7.2 Preferred Share Valuation Learning Objective: 7.2 Level of difficulty: Difficult Solution: The required rates of return for the two stocks: D 0.07 * 50 ABC: $70 = p = k p = 5.00% kp kp PWT: $45 =

Dp kp

=

0.04 * 60 kp

k p = 5.33%

As the risk-free rate is the same for both firms, the only way PWT can have a higher required return is if the risk premium is higher. A higher risk premium reflects a higher level of risk; therefore, PWT is the riskier preferred stock.

51. Section: 7.3 Common Share Valuation: The Dividend Discount Model (DDM) Learning Objective: 7.3 Level of difficulty: Difficult Solution:

P0 =

D0 (1 + g ) kc − g

10 (1 + g ) .10 − g 15 − 150 g = 10 + 10 g 5 = 160 g g = 3.13% 150 =

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52. Section: 7.3 Common Share Valuation: The Dividend Discount Model (DDM) Learning Objective: 7.3 Level of difficulty: Difficult Solution: a. To solve this problem we need to determine what the price of the stock should be (if FinCorp’s growth rate is correct) and then compare it to the market price. If the market price is lower than the price based on our analysis, we should buy.

P0 =

(

D0 1 + g kc − g

) = 5.50 *1.05 = $192.50 . .08 − .05

As the market price is lower than the price based on the analysis, FinCorp should buy the stock. b. The stock price can be expected to increase for two reasons: first, as FinCorp starts buying shares, that will increase demand for the stock and the price will rise. Secondly, FinCorp is not the only smart organization examining this company and if anyone else comes to the same conclusion, they will all buy and will push the stock price up until the price reaches the “correct” price of $192.50.

53. Section: 7.4 Using Multiples to Value Shares Learning Objective: 7.4 Level of difficulty: Difficult Solution: There are two problems with the PHD analyst’s statement: first, a constant P/E ratio implies a constant growth over time—the growth could be zero, positive or negative. The more important problem with the statement is that XW is only a good investment if its return is greater than or equal to the required rate of return. If the investment earns less than its required rate of return, then by definition, it is a bad investment regardless of the growth rate of the earnings.

54. Learning Objective: 7.3 Level of difficulty: Difficult Solution: To solve this problem, we must find the inputs to the DDM model.

1. The expected dividend next year: Leading EPS = earnings per share expected next year. We know the dividend payout ratio is 35%, so the expected dividends next year are 0.35 × 2.50 = $0.875.

2. The sustainable growth rate = retention ratio × ROE a. Retention ratio = 1 – dividend payout ratio = 65% b. ROE – using the DuPont system we find that the ROE = 0.10 × 1.8 × 0.30 = 5.40% c. Growth rate = 0.65 × 0.054 = 3.51% Therefore the expected current stock price of XYZ is $58.7248 ($0.875/(0.05 – 0.0351) 55. Section: 7.3 Common Share Valuation: The Dividend Discount Model (DDM) Learning Objective: 7.3 Level of difficulty: Difficult Solutions Manual 23 Chapter 7 Copyright © 2013 John Wiley & Sons Canada, Ltd. Unauthorized copying, distribution, or transmission is strictly prohibited.

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Solution: Year

Growth rate

Dividend

0 1 2 3 4

-4% -4% -4% 0%

4.0000 3.8400 3.6864 3.5389 3.5389

Discount rate:

Stock price at end of year 3

Present value of each cash flow

23.5930

3.3391 2.7874 17.8397

15%

Price of stock in year 0:

$23.9662

56. Section: 7.3 Common Share Valuation: The Dividend Discount Model (DDM) Learning Objective: 7.3 Level of difficulty: Difficult Solution: Begin by determining the sustainable growth rate for the three periods: Years 1 to 5, g1 = 1% × 0.75 × 3.0 × (1 – 0.05) = 2.1375% Years 6 to 10: g2 = 15% × 3.0 × 2.0 × (1 – 0.10) = 81.00% Years 11 to ∞: g2 = 15% × 3.0 × 2.0 × (1 – 0.10) = 81.00% Year 0 1 2 3 4 5 6 7 8 9 10 11

Growth rate

Dividend

2.1375% 2.1375% 2.1375% 2.1375% 2.1375% 81.0000% 81.0000% 81.0000% 81.0000% 81.0000% 3.5000%

3.0000 3.0641 3.1296 3.1965 3.2648 3.3346 6.0357 10.9246 19.7735 35.7900 64.7799 67.0472

Discount rate: Price of stock in year 0:

Stock price at end of year 10

Present value of each cash flow

583.0191

2.6645 2.3664 2.1018 1.8667 1.6579 2.6094 4.1070 6.4640 10.1738 160.1260

15% $194.1373

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Chapter 8: Risk, Return, and Portfolio Theory Multiple Choice Questions 1. Section: 8.1 Measuring Returns Learning Objective: 8.1 Difficulty: Easy Solution: A. Capital gain return = (26 – 25)/25 = 0.04 = 4% 2. Section: 8.1 Measuring Returns Learning Objective: 8.1 Difficulty: Easy Solution: D. Total return = [(4 × 1) + (26 – 25)] / 25 = 0.2 = 20% 3. Section: 8.1 Measuring Returns Learning Objective: 8.2 Difficulty: Medium Solution: B. The arithmetic average is greater than the geometric mean.

4. Section: 8.1 Measuring Returns Learning Objective: 8.2 Difficulty: Easy Solution: C. Expected return = 0.35(30%) + 0.4(40%) + 0.25(15%) = 30.25% 5. Section: 8.2 Measuring Risk Learning Objective: 8.3 Difficulty: Easy Solution: C  = .35(30 − 30.25) 2 + .40( 40 − 30.25) 2 + .25(15 − 30.25) 2

=

0.0219 + 38.025 + 58.1406 =

96.1875 = 9.81%

6. Section: 8.2 Measuring Risk Learning Objective: 8.3 Difficulty: Medium Solution: C The standard deviation of a portfolio is not usually the weighted average of the standard deviations of each asset. Only when the correlation coefficient = +1 is this the case.

7. Section: 8.3 Expected Return and Risk for Portfolios Learning Objective: 8.4 Difficulty: Medium Solution: B The other statements are incorrect. The correlation coefficient equals covariance divided by the product of the individual standard deviations. It has a range from –1 to +1. It shows a stronger relationship between the returns of two securities when its absolute value is closer to 1.

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8. Section: 8.3 Expected Return and Risk for Portfolios Learning Objective: 8.4 Difficulty: Medium Solution: B. It is possible to eliminate all the risk whenever the correlation coefficient equals –1 and there exists one unique weighting scheme for combining the two securities such that we can eliminate all risk.

9. Section: 8.4 The Efficient Frontier Learning Objective: 8.5 Difficulty: Medium Solution: C. Portfolios A, B, and C are attainable, but D is not.

10. Section: 8.3 Diversification Learning Objective: 8.6 Difficulty: Medium Solution: D The lower the correlation coefficient, the lower the portfolio standard deviation. Therefore the lowest correlation coefficient (–0.9) achieves the greatest diversification.

Practice Problems 11. Section: 8.1 Measuring Returns Learning Objective: 8.1 Difficulty: Medium Solution: Capital gain = ($87–$82)×250 = $1,250 Total dollar return = $1,250 + $750 = $2,000 Percentage return = $2,000/($82×250) = 9.76% 12. Section: 8.1 Measuring Returns Learning Objective: 8.1 Difficulty: Medium Solution: P0 = $30,000/1,500 =$20.00 Total dollar return = ($18–$20) ×1,500 + $4,500 = $1,500 Capital gain/(loss) = ($18–$20) ×1,500 = ($3,000) Percentage return = $1,500/$30,000 = 5% Dividend yield = $4,500/$30,000 = 15% 13. Section: 8.1 Measuring Returns Learning Objective: 8.2 Difficulty: Easy

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Solution: We use arithmetic average when we are trying to estimate the typical return for a single time period, such as a month or a year. However, we should use the geometric mean when we are interested in determining the “true” average rate of return over multiple periods so that it reflects the compound rate of growth over time (i.e., the realized change in wealth over multiple periods).

14. Section: 8.4 The Efficient Frontier Learning Objective: 8.5 Difficulty: Easy Solution: 1. Investors are rational decision-makers.

2. Investors are risk averse. They like expected returns, dislike risk, and require compensation to assume additional risk.

3. Investor preferences are based on a portfolio’s expected return and risk, as measured by variance or standard deviation.

15. Section: 8.1 Measuring Returns Learning Objective: 8.1 Difficulty: Difficult Solution:

M

Opening price $100

Dividen d $7

Carraway Corporation Performance Income Closing price Capital Gain Yield $115 7/100 115 −1 = 7% 100 = 15%

Total daily return =7%+15% = 22% Or 115 + 7

−1

100

Tu

$115

$2

X −1 115 X = $123.05

7% = W

$123.05 = closing price on Tuesday

Tr

$127.36

F

$131.18

$8

115 = 1.7391%

X 127.36 X = $5.09

$0

= 22% 123.05 + 2 −1 115 = 8.74%

6.50% = 8/123.05

3.50%=(127 .36– 123.05)/123 .05

10%

3% =

X −1 127.36 X = $131.18

4%

3%

7% = 4% +3%

$150.86 = (1+15%)*131.18

0%

15% = total daily return

15%

X +8 −1 123.05 X = $127.36

10% =

4% =

7%

2

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– dividend return 16. Section: 8.1 Measuring Returns Learning Objective: 8.2 Difficulty: Easy Solution: Calculate the expected price: .35 × $60 + .45 × $110 + .20 × $85 = $87.50 Expected return = (87.50 / 80) –1 = 9.38% 17. Sections: 8.1 Measuring Returns and 8.2 Measuring Risk Learning Objective: 8.2 and 8.3 Difficulty: Medium Solution: a. Geometric mean return: [(1.18)(0.85)(1.08)(1.06)(0.88)]1/5 – 1 =[1.010446]1/5 –1 =0.208%

b. and c.

Using the BAII+ data function to answer b. and c: 2nd DATA 2nd CLR WORK Remember to enter nothing in the Y’s just hit the ↓.

BAII+ X01 X02 X03 X04 X05 Your entry 2nd STAT ↓ ↓

Your response 18 –15 8 6 –12

BAII+ response LIN N=5 =1

↓

<ENTER> ↓↓ <ENTER> ↓↓ <ENTER> ↓↓ <ENTER> ↓↓ <ENTER> ↓↓

Interpretation Sample size is 5 Arithmetic mean of X is 1% (remember we entered the data in percent) Sample standard deviation is 14.0357%

Sx = 14.0357 Sample variance is the sample standard deviation squared = 0.0197. Note: if we just square 14.0357, we get 197 percent squared.

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18. Section: 8.1 Measuring Returns Learning Objective: 8.1 Level of difficulty: Easy Solution: Value at the end of 5 days = $190 × (1–.08)(1+.18)(1–.3)(1+.06)(1+.05) = $160.70 19. Sections: 8.1 Measuring Returns, 8.2 Measuring Risk, and 8.3 Expected Return and Risk for Portfolios Learning Objective: 8.2, 8.3, and 8.4 Difficulty: Medium Solution: a. i) Five-day cumulative return The five-day cumulative return is the value on Friday afternoon of $1 invested on Monday morning.

ABC: $1(1.05)(1.04)(0.82)(1.02)(1.05) = $0.959 So if $1 grows to $0.959 in five days the cumulative return is $0.959 − 1 = −4.10% $1.00 The easy way to calculate this is: DEF: 1.04 × 1.16 × 1.14 × 1.1 × 1.04 – 1 = 57.33% ii) Geometric average daily return ABC: (1 + cumulative return)1/5 –1 = (1 – 0.041)1/5 – 1 = –0.83% DEF: 9.49% iii) Arithmetic mean daily return iv) Standard deviation of daily returns b.

Using the BAII+ to answer a. (iii and iv) and b.: 2nd DATA, 2nd CLR WORK BAII+ X01 Y01 X02 Y02 X03

Your response 5 4 4 16 –18

<ENTER> ↓ <ENTER> ↓ <ENTER> ↓ <ENTER> ↓ <ENTER> ↓

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Y03 X04 Y04 X05 Y05

14 2 10 5 4

Booth, Cleary

<ENTER> ↓ <ENTER> ↓ <ENTER> ↓ <ENTER> ↓ <ENTER> ↓

Remember, you can always go back and check that you have entered the correct data by using the up arrow key.

Your entry 2nd STAT ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓

BAII+ response LIN N=5 = –0.4 sx = 9.9146 σx = 8.8679 Ӯ = 9.6 sy = 5.5498 σy = 4.9639 a = 9.4893 b = –0.2767 r = –0.4943

Interpretation

Additional action

Sample size is 5 Arithmetic mean daily return of ABC is –0.4% (remember we entered the data in percent) Sample standard deviation of ABC is 9.9146% Population standard deviation of ABC is 8.8679% Arithmetic mean daily return of DEF is 9.6%

<STO> 1

Sample standard deviation of DEF is 5.5498% Population standard deviation of DEF is 4.9639% Coefficients of a regression of ABC and DEF. We don’t need this information for this question.

<STO> 2

The sample correlation between ABC and DEF

<STO> 3

The covariance between ABC and DEF is therefore: Cov = rsxsy = –0.4943 × 9.9146 × 5.5498 = –27.2 20. Section: 8.3 Expected Return and Risk for Portfolios Learning Objective: 8.4 Difficulty: Medium Solution:

$ invested in stock 1 $ invested in stock 2 Total $ invested Weight in stock 1

Case 1

Case 2

Case 3

Case 4

Case 5

$500

.2*2,000 =$400

$0

$200

$150

$500

$1,600

$5000

$300

$850

$1,000

$2000

$5000

200 = .4* X X = $500

$1000

50%

20%

0%

40%

15%

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Weight in stock 2 Expected return of stock 1

Booth, Cleary

50%

80%

100%

60%

85%

8%

3%

Cannot be determined

5%

2%

Expected return of stock 2

3%

8% = .2*3% + .8* X 8% − .6% X= .8 = 9.25%

6%

7% = .4*5% + .6* X 7% − 2% X= .6 = 8.33%

10%

Expected return of portfolio

.5*8%+.5*3% = 5.50%

8%

6%

7%

.15*2+.85*10 = 8.80%

Case 2 $ invested in stock 1: 0.2 x 2,000 = $400 Case 3 $ invested in stock 1: 5,000 – 5,000 = $0 Case 5 $ invested in stock 1: 0.15 x 1,000 = $150 Case 2 $ invested in stock 2: 2,000 – 400 = $1,600 Case 4 $ invested in stock 2: (200/0.4) x 0.6 = $300 Case 5 $ invested in stock 2: 1,000 – 150 = $850 Case 1 Total $ invested: 500 + 500 = $1,000 Case 4 Total $ invested: 200 + 300 = $500 Case 1 Weight in stock 1: (500 / 1,000) x 100 = 50% Case 3 Weight in stock 1: (0 / 5,000) x 100 = 0% Case 1 Weight in stock 2: (500 / 1,000) x 100 = 50% Case 2 Weight in stock 2: (1,600 / 2,000) x 100 = 80% Case 3 Weight in stock 2: (5,000 / 5,000) x 100 = 100% Case 4 Weight in stock 2: (300 / 500) x 100 = 60% Case 5 Weight in stock 2: (850 / 1,000) x 100 = 85% Case 3 Expected return of stock 1: Cannot be determined Case 2 Expected return of stock 2: 8% = 0.2 x 3% + 0.8 x X ⇒ X = (8% – 0.6%) / 0.8 ⇒ = 9.25% Case 3 Expected return of stock 2: 6.00% Case 4 Expected return of stock 2: 7% = 0.4 x 5% + 0.6 x X ⇒ X = (7% – 2%) / 0.6 ⇒ = 8.33% Case 1 Expected return of portfolio: 0.5 x 8% + 0.5 x 3% = 5.50% Case 5 Expected return of portfolio: 0.15 x 2 + 0.85 x 10 = 8.80% 21. Section: 8.3 Expected Return and Risk for Portfolios Learning Objective: 8.4 Difficulty: Medium Solution: a. w2 = 1– w1= 1 – .35 = .65 2 σ p = w21σ12+ w22σ22 +2w1w2ρ σ1 σ2 = (.35)2(.06)2 + (.65)2(.2)2 + 2 × .35 × .65 × .75 × .06 × .2 = .000441 + .0169 +.004095 = .021436 Solutions Manual

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σp = 0.1464 The portfolio standard deviation is 14.64% when the correlation is 0.75. b. σ2p = w21σ12+ w22σ22 +2w1w2ρ σ1 σ2 = (.35)2(.06)2 + (.65)2(.2)2 + 2 × .35 × .65 × (–0.75) × .06 × .2 = .000441 + .0169 + –0.004095 = 0.013246 σp = 11.51 The portfolio standard deviation is 11.51% when the correlation is –0.75.

22. Sections: 8.3 Expected Return and Risk for Portfolios Learning Objective: 8.4 Difficulty: Medium Solution: Case 1 75% 25%

Case 2 15% 85%

15%

2%

3%

10%

– 0.2*.15*.03 = –.0009

.40*.02*.10 = 0.0008

–.20

.40

0.012375

0.007438

11.1243%

8.624%

Weight in stock 1 Weight in stock 2 Standard deviation of stock 1 Standard deviation of stock 2 Covariance between stocks 1 and 2 Correlation between stocks 1 and 2 Portfolio variance Portfolio standard deviation

Case 2: portfolio variance σ2p = w21σ12+ w22σ22 +2w1w2ρ σ1 σ2 = (.15)2(.02)2 + (.85)2(.1)2 + 2 × .15 × .85 × (0.40) × .02 × .1 = 0.007438 23. Section: 8.3 Expected Return and Risk for Portfolios Learning Objective: 8.4 Difficulty: Medium Solution: a.

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Daily returns 0% 0%

1%

2%

3%

4%

5%

6%

4%

5%

6%

4%

5%

6%

Returns

-5% -10% -15% -20% XYZ returns ABC

Daily returns

Returns

25% 20% 15% 10% 5% 0% 0%

1%

2%

3% XYZ returns DEF

Returns

Daily returns 8% 6% 4% 2% 0% -2% 0% -4% -6%

1%

2%

3%

XYZ returns GHI

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Returns

Daily returns 8% 7% 6% 5% 4% 3% 2% 1% 0% 0%

1%

2%

3%

4%

5%

6%

4%

5%

6%

XYZ returns JKL

Returns

Daily returns 10% 8% 6% 4% 2% 0% -2% 0% -4% -6%

1%

2%

3%

XYZ returns MNO

b. ABC and DEF are positively correlated with XYZ (the lines slope upwards). c. GHI and JKL are negatively correlated with XYZ. d. MNO appears to have a low correlation with XYZ (it goes up and down as XYZ increases). e. Using the data analysis feature of Excel we get the following correlation matrix:

ABC DEF GHI JKL MNO

Correlation with XYZ 1 0.999133 -0.84867 -0.99485 -0.13484

The results, based on the graphs, are consistent with the calculated correlations.

24. Section: 8.1 Measuring Returns Learning Objective: 8.2 Solutions Manual

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Difficulty: Medium Solution: Total return (year 1) = (35+5–30)/30 = 33.3% Total return (year 2) = (28+5–35)/35 = –5.71% AA = (33.3%–5.71%)/2 = 13.8% G = [(1+.333)(1–.057)]1/2 – 1 = 12.12% Geometric mean is more appropriate here because it reflects the true average return over multiple periods.

25. Section: 8.2 Measuring Risk Learning Objective: 8.3 Difficulty: Medium Solution: k = (50%+ 30%+ 20%+ 35%+ 55%)/5 = 38%

(50 − 38) 2 + (30 − 38) 2 + (20 − 38) 2 + (35 − 38) 2 + (55 − 38) 2 = 5 −1 = 14.40% 26. Section: 8.3 Expected Return and Risk for Portfolios Learning Objective: 8.4 Difficulty: Medium Solution: Stock B = 45,000 – 15,000 – 10,000 = $20,000 w1 = 15,000/45,000 = 1/3 = 33.33% w2 = 10,000/45,000 = 2/9 = 22.22% w3 = 20,000/45,000 = 4/9 = 44.44% ERp = w1ER1+ w2ER2+ w3ER3 =.3333(12%) +.2222(8%) +.4444(20%) = 14.67% 27. Sections: 8.1 Measuring Returns and 8.2 Measuring Risk Learning Objective: 8.2 and 8.3 Difficulty: Medium Solution: a. Expected return = .20 × (–3%) + .50 × 5% + .30 × 8% = 4.3% b.

 2 = .2 ( −0.03 − .043) + .5 (.05 − .043) + .3 (.08 − .043) 2

2

2

= 0.0010658 + .0000245 + .0004107 = 0.001501 Note, we cannot say the variance is 0.15%. If the returns are measured in percent (i.e., 8%) then the units of the variance are percent squared which is difficult to interpret. In contrast, the units of standard deviation are the same as the units of return.

The standard deviation is: 0.038743 = 3.87%

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c. The geometric average quarterly return: = 4 (1 + .02)(1 − .05)(1 + .03)(1 + .08) − 1 =  (1 + .02)(1 − .05)(1 + .03)(1 + .08) 4 − 1 1

= 1.0779156 − 1 14

= 1.8934%

The arithmetic average quarterly return: Using the BAII+ Data function BAII+ keystrokes: 2nd DATA 2nd CLR WORK X01 = 2% <ENTER> ↓ Y01 = 1% (make sure not to enter any of the quarterly returns in Y, don’t need to hit enter as you are not using the Y because you only have one variable) ↓ X02 = –5%, Y02 = 1, X3 = 3%, Y03 = 1, X04 = 8%, Y04 = 1 2nd STAT The BAII+ should say LIN ↓ BAII+ indicates N = 4.0 This indicates that the sample size is 4. ↓ BAII+ indicates x = 2.0 This is the mean of the quarterly returns in percent. If you entered the data as .02, –.05 etc., then the mean will be .02. ↓ BAII+ indicates sx = 5.3541 This is the sample standard deviation in percent. ↓ BAII+ indicates  X = 4.6368 This is the population standard deviation in percent. d. Using the above solution, we see that the ex-post standard deviation of quarterly returns is 5.3541%. e. We were expecting a quarterly return of 4.3 percent with a standard deviation of 3.87 percent.

This indicates that we had some uncertainty about what the quarterly returns would be. Given the level of the standard deviation, observing an actual quarterly return of 2 percent is not very surprising.

28. Section: 8.1 Measuring Returns Solutions Manual

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Learning Objective: 8.2 Difficulty: Medium Solution: January 1: the expected price of GTS in one year is .15 × 150 + .85 × 200 = $192.50 If the market agrees with FinCorp Inc.’s analysis, then we would expect the stock price to be $192.50 discounted back to January 1. As the discount rate is zero, the expected price on January 1 is $192.50.

July 1: the expectations about GTS have changed so we need to determine the new expected price in six months: .35 × 150 + .65 × 200 = $182.50 If the market agrees with FinCorp Inc., then the expected price on July 1 will be $182.50 The expected change in the stock price is a decrease of 5.2% or $10.

29. Section: 8.1 Measuring Returns Learning Objective: 8.2 Difficulty: Medium Solution: To determine what the recommendation should be, we need to determine the expected price in the future: .35 × 220 + .40 × 100 + .25 × 140. = $152.

The recommendation should be changed to “buy”– at the current price of $140, the stock is underpriced.

30. Section: 8.1 Measuring Returns Learning Objective: 8.2 Difficulty: Medium Solution:

.07 = (1 + .16 )(1 + .19 )(1 − .23)(1 + .14 )(1 − .08 )(1 + X )  6 − 1 1

(1.07)6 = 1.114778(1 + X ) X = 34.6215% 31. Section: 8.3 Expected Return and Risk for Portfolios Learning Objective: 8.4 Level of difficulty: Difficult Solution: a.

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Portfolio return 20.00% 18.00% 16.00% 14.00% 12.00% 10.00% 8.00% 6.00% 4.00% 2.00% 0.00% 0%

20%

40%

60%

80%

100%

120%

Weight in DEF Portfolio return

Creating a chart in Excel: Mark the two columns you wish to graph (make sure X and Y are next to each other, with X in the left hand column) and choose Insert → Chart → XY (scatter) → select the following chart type:

Click next and follow the instructions.

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b. For every additional 1% invested in DEF we gain .01 × 18% and give up .01 × 6% for a net increase of 0.12%. We can also do this using calculus: the portfolio return is Rp = w * RY + (1 − w) RX . By taking the first derivative of the portfolio expected return with respect to the weight in DEF, we will find the tradeoff between DEF and ABC. c. My boss and I are both correct. For every 1% decline in the investment in DEF, I will be gaining .01 × 6% and giving up .01 × 18% for a net decrease of 0.12%. If we look at the graph, I’m increasing the weight in DEF (the higher expected return security). My boss is increasing the weight in ABC (the lower expected return security) and consequently his number must be the negative of mine. On the graph, I am moving to the right while my boss is moving to the left.

Using calculus, my boss took the derivative with respect to (1–w) while I took the derivative with respect to w.

32. Section: 8.3 Expected Return and Risk for Portfolios Learning Objective: 8.4 Difficulty: Medium Solution: a. Set w = weight in Encor

16% = w * 2% + (1 − w)* 25% 16% − 25% w= 2% − 25% = 39.1304% b.

 P2 = (.391304 ) (.01) + (.608696 ) (.10 ) + 2*.4* (.391304 )(.608696 )(.01)(.10 ) 2

2

2

2

= 0.00391097  P = 0.062538 = 6.2538% 33. Section: 8.3 Expected Return and Risk for Portfolios Learning Objective: 8.4 Difficulty: Medium Solution: a. Set w = weight in Peledon The easiest way of solving this is to use the Solver function in Excel. The weight in Peledon is 41.7941%.

This can also be solved analytically by: 0.062 = w2(0.01)2 + (1 – w)2(0.10)2 + 2 x 0.4 x (w)(1 –w)(0.01)(0.10) = 0.0001w2 + 0.01 – 0.02w + 0.01w2 + 0.0008w – 0.0008w2 = 0.0093w2 – 0.0192w + 0.01 0 = 0.0093w2 – 0.0192w + 0.0064 Solutions Manual

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w = 0.41794 Note: you will need to use the quadratic formula to solve for w. b. ERP = 0.41794 x 2% + 0.58206 x 25% = 15.3874% 34. Section: 8.3 Expected Return and Risk for Portfolios Learning Objective: 8.4 Difficulty: Medium Solution:

 p = ( wX ) 2 ( X ) 2 + ( wY ) 2 ( Y ) 2 + 2(wX )(wY )(COVX ,Y ) 6 = (0.4) 2 (12) 2 + (0.6) 2 (15) 2 + 2(0.4)(0.6)(COVX ,Y ) 36 = 23.04+81+0.48 COVX,Y COVX,Y = –141.75 %2 COVX ,Y − 141.75  XY = = = –0.7875 (12)(15)  XY 35. Section: 8.3 Expected Return and Risk for Portfolios Learning Objective: 8.4 Difficulty: Difficult Solution: 1st: Calculate ERA = 0.25(40%)+0.2(20%)+0.55(–10%) = 8.5% ERB = 0.25(55%)+0.2(25%)+0.55(–20%) = 7.75% 2nd: Calculate standard deviation of Stock A and Stock B

 A = .25(40 − 8.5) 2 + .20(20 − 8.5) 2 + .55(−10 − 8.5) 2 =

248.0625 + 26.45 + 188.2375 =

462.75 = 21.51%

 B = .25(55 − 7.75) 2 + .20(25 − 7.75) 2 + .55(−20 − 7.75) 2 = 558.1406 + 59.5125 + 423.5344 = 1,041.1875 = 32.27% 3rd: CovAB = 0.25(40–8.5)(55–7.75)+0.2(20–8.5)(25–7.75)+0.55(–10–8.5)(–20–7.75) = 372.09375+39.675+282.35625 = 694.125%2 COVAB 694.125 4th:  AB = = =+1  A B (21.51)(32.27)

36. Section: 8.3 Expected Return and Risk for Portfolios Learning Objective: 8.4 Difficulty: Easy Solutions Manual

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Solution: wA =

B 32.27 = = 0.6  A +B 21.51 + 32.27

wB = 1–wA = 1–0.6 = 0.4 37. Section: 8.3 Expected Return and Risk for Portfolios Learning Objective: 8.4 Difficulty: Difficult Solution: R(A) = [(500)(30) – (500)(22)+(500)(2)(4)]/(500)(22) = 72.7273% R(B) = [(1,000)(30)–(1,000)(30)+(1,000)(1.5)(4)]/(1,000)(30) = 20% wA = (500)(22)/[(500)(22)+(1,000)(30)] = 0.2683 wB = (1,000)(30)/[(500)(22)+(1,000)(30)] = 0.7317 Total return of the portfolio = wAR(A)+wBR(B) = 0.2683(72.7273%)+0.7317(20%) = 34.1467% 38. Section: 8.3 Expected Return and Risk for Portfolios Learning Objective: 8.4 Difficulty: Easy Solution:

 p = (wA ) 2 ( A ) 2 + (wB ) 2 ( B ) 2 + 2( wA )(wB )(  A, B )( A )( B ) =

(0.2683) 2 (20) 2 + (0.7317) 2 (15) 2 + 2(0.2683)(0.7317)(0.3)(20)(15)

= 28.7940 + 120.4616 + 35.3367 = 184.5923 =13.59% 39. Section: 8.3 Expected Return and Risk for Portfolios Learning Objective: 8.4 Difficulty: Difficult Solution:

Weight in stock 1 Weight in stock 2 Standard deviation of stock 1 Standard deviation of stock 2 Covariance between stocks 1 and 2

Case 1 35% 65%

Case 2 40% 60%

3%

51.6236%

25%

20%

.141685*.03*.25 = 0.001063

.022

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Correlation between stocks 1 and 2 Portfolio variance Portfolio standard deviation

.027

.022/(.516236*.20) = 0.21308 .0676

16.4317%

26%

.141685

Case 1: correlation between stocks 1 and 2 .027 = (.35)2 (.03)2 + (.65)2 (.25)2 + 2 x ρ x .35 x .65 x .03 x 0.25 = .00011025 + .02640625 + .0034125 ρ .027 – .00011025 – .02640625 ρ= .0034125 = 0.141685 Case 2: standard deviation of stock 1

.0676 = (.4 ) ( 1 ) + (.6 ) (.2 ) + 2*.022*.4*.6 2

2

2

2

= .16 12 + .0144 + .01056 .0676 − .0144 − .01056 .16 = .2665  1 = 51.6236%

 12 =

40. Section: 8.3 Expected Return and Risk for Portfolios Learning Objective: 8.4 Difficulty: Difficult Solution: The total amount of cash you have to provide is $1,000. When you short sell ABC you will receive $200 and when added to your $1,000 you will have the $1,200 needed to buy DEF. Consequently the weight in DEF is 1,200/1,000 = 1.2; the weight in ABC is –200/1,000 = –0.20.

The weight in ABC is negative because the market value of ABC is a liability.

The expected return of the portfolio is: –.20 × 3% + 1.2 × 15% = 17.4% The standard deviation of the portfolio is: 2 2 2 2  P2 = ( −.2 ) (.07 ) + (1.2 ) (.35 ) + 2*.4* ( −.2 )(1.2 )(.07 )(.35 ) = 0.000196 + 0.1764 − 0.004704 = 0.171892  P = 41.4599%

41. Section: 8.3 Expected Return and Risk for Portfolios Learning Objective: 8.4 Difficulty: Medium Solution Solutions Manual

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ER = 0.15(–5) + 0.20(1) + 0.40(6) + 0.25(18) = –0.75 + 0.2 + 2.4 + 4.5 = 6.35% Standard deviation = [0.15(–5–6.35)2 + 0.20(1–6.35)2 + 0.40(6–6.35)2 + 0.25(18–6.35)2]1/2 = 7.68% 42. Section: 8.3 Expected Return and Risk for Portfolios Learning Objective: 8.4 Difficulty: Medium Solution: Holdings of ABC stock = 250 ×$8 =$2,000 Holdings of DEF stock = 300 ×$8 =$2,400 Weights of ABC stock = $2,000/($2,000+$2,400) = 45.45% Weights of DEF stock = $2,400/($2,000+$2,400) = 54.55% 43. Section: 8.3 Expected Return and Risk for Portfolios Learning Objective: 8.4 Difficulty: Medium Solution ERp = .35(18)+.65(23) = 21.25% Standard deviation of portfolio = [0.352(12)2 + 0.652(20)2 + 2 × .35 × .65 × .35 × 12 × 20]1/2 = 15% Standard deviation of portfolio = [0.352(12)2 + 0.652(20)2 + 2 × .35 × .65 × (–.35) × 12 × 20]1/2 = 12.18% 44. Section: 8.3 Expected Return and Risk for Portfolios Learning Objective: 8.4 Difficulty: Difficult Solution a. ERp = .25(15)+.75(23) = 21% Standard deviation of portfolio = [0.252(10)2 + 0.752(23)2]1/2 = 17.43% b. ERp = .75(15)+.25(23) = 17% Standard deviation of portfolio = [0.752(10)2 + 0.252(23)2]1/2 = 9.45% c. No , because by trading some ABC for DEF the investor will have a higher expected return and a lower standard deviation compared to 100 percent in ABC. 45. Section: 8.3 Expected Return and Risk for Portfolios Learning Objective: 8.4 Difficulty: Difficult Solution: ERABC = 0.15(-5) + 0.20(-3) + 0.40(5) + 0.25(8) = -0.75 - 0.6 + 2 + 2

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= 2.65% ERDEF= 0.15(-7) + 0.20(0) + 0.40(6) + 0.25(10) = -1.05 + 0.0 + 2.4 + 2.5 = 3.85% ERp = 0.5(2.65) + 0.5(3.85) = 3.25% Standard deviation of ABC = [ 0.15 (–5 – 2.65)2 + 0.20(–3 – 2.65)2 + 0.40(5 – 2.65)2 + 0.25(8 – 2.65)2]1/2 = 4.95% Standard deviation of DEF = [ 0.15(–7 – 3.85)2 + 0.20(0 – 3.85)2 + 0.40(6 – 3.85)2 + 0.25(10 – 3.85)2]1/2 = 5.65% Covariance = 0.15(-5-2.65) × (–7 – 3.85) + 0.20(–3 – 2.65) × (0-3.85) + 0.40(5-2.65) × (6 – 3.85) + 0.25 (8 – 2.65) × (10 – 3.85) = 27.0475 Standard deviation of portfolio = [ (0.5)2(4.95)2 + (0.5)2(5.65)2 +2 × 0.5 × 0.5 × 27.0475]1/2 = 5.26% In the second part we are investing 60 percent in the above portfolio and 40 percent in T-bills.

Thus ER on the new portfolio = 0.6 × 3.25 + 0.4 × 2.5 = 2.95% Since the standard deviation of the T-bill is zero and has no correlation with the other stocks, the second and third terms of Equation 8-11 will be zero.

Standard deviation of the new portfolio = [(0.6)2(5.26)2]1/2 = 3.16% 46. Section: 8.4 The Efficient Frontier Learning Objective: 8.5 Level of difficulty: Difficult Solution: a. The correlation between the two stocks is –0.80 As both stocks have the same expected returns, no matter what weights are used the expected return of the portfolio will be 8%. Therefore, we want to minimize the risk of the portfolio. The weight, w, represents the weight in Alcon.

Approaches: 1. Use calculus to minimize the variance of the portfolio by choice of weight.

2  P2 = w2 12 + (1 − w )  22 + 2  w (1 − w ) 1 2 d P2 = 2 w 12 − 2 (1 − w )  22 + (1 − 2w ) 2  1 2 dw = 2 w ( 12 +  22 − 2  1 2 ) − 2 22 + 2  1 2 w* =

2 22 − 2  1 2 2 ( 12 +  22 − 2  1 2 )

= 63.7931%

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2. Use the solver function in Excel. → Tools → Solver →

Click “solve” and the solution will appear in cell A4. b. The correlation between the two stocks is 0.80.

As the correlation is positive and the weights have to be positive, the minimum variance will be achieved by investing 100% of the portfolio in Alcon. The very high positive correlation between the stocks means that they essentially move together and there is little scope for diversification.

47. Section: 8.4 The Efficient Frontier Learning Objective: 8.5 Difficulty: Difficult Solution: a. The correlation is 0.00 The two companies have the same standard deviation and zero correlation so no matter what weights we choose the portfolio variance will remain the same. Therefore, we will choose the weights that maximize returns: 100 percent in Beldon. b. The correlation is 1.0 With perfect correlation and equal standard deviations and non-negative weights, the portfolio variance simplifies to:

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 P2 = w2 2 + (1 − w )  2 + 2  w (1 − w ) 2

=  2  w2 + (1 − w ) + 2  w (1 − w )    2 2 2 =   2w + 1 − 2 w + 2  w − 2  w  2

=  2 1 Therefore the portfolio I would recommend to maximize returns would be 100% invested in Beldon.

With any other correlations, there will be a tradeoff between risk and return and without knowing the investors’ preferences we cannot recommend a portfolio weight.

48. Section: 8.4 The Efficient Frontier Learning Objective: 8.5 Difficulty: Difficult Solution:

Expected returns

Efficient frontier 11.00% 10.00% 9.00% 8.00% 7.00% 6.00% 5.00% 5.00%

10.00%

15.00%

20.00%

25.00%

Standard deviation Correlation 0

Correlation 0.5

Correlation -0.5

A sample of the data from Excel: Expected returns:

ABC FGI

0.06 0.1 -0.04

ABC FGI

0.1 0.25

Difference in expected returns Standard deviations:

Correlation: Weight in ABC 0

0 0.5 -0.5 Weight in FGI E(returns) Stdev0 Stdev-.5 Stdev.5 1 10.00% 25.00% 25.00% 25.00%

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0.04 0.08 0.12 0.16

Booth, Cleary

0.96 0.92 0.88 0.84

9.84% 9.68% 9.52% 9.36%

24.00% 23.01% 22.03% 21.06%

24.20% 23.41% 22.62% 21.84%

23.80% 22.61% 21.43% 20.25%

49. Sections: 8.4 The Efficient Frontier Learning Objective: 8.5 Difficulty: Difficult Solution: a. To do this, we will use Excel and begin by calculating the average monthly return and then graph the portfolio average return as a function of alternative weights.

Average Standard deviation Row A /Col 1

ABC

DEF

2.67%

0.92%

3.42%

3.26%

B

C Monthly returns

ABC 0.06 –0.03 …

0.05

DEF 0.01 0.03 …

0.02

2 3 4 …

14

January February …

December

15 16 17

Average =AVERAGE(B3:B14) =AVERAGE(C3:C14) Stdeviation =STDEV(B3:B14) = STDEV (C3:C14) Portfolio expected return

Expected return

3.00% 2.50% 2.00% 1.50% 1.00%

0.50% 0.00% 0%

20%

40%

60%

80%

100%

120%

Weight in ABC

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b. To graph the portfolio standard deviation we need either the sample covariance or correlation.

To do this we will use the data analysis feature in Excel.

Ensure that the Analysis tool pack is installed. Go to Tools → Add ins → make sure Analysis ToolPak is checked → Go to Tools → Data Analysis → Correlation → OK

Click ok. The results are: ABC ABC DEF

DEF

1 -0.70389

1

The result is the correlation matrix. The correlation between ABC and DEF is –.70389. Note: if you used the covariance function in Excel, you will get the population covariance and will need to correct to a sample covariance (multiply by n/(n–1); remember from statistics that when you are calculating the variance or covariance with sample data, you divide by n–1. If you are working with a population, you divide by n).

Standard deviation

ABC 3.42%

DEF 3.26% –0.70389

Correlation

Weight in ABC 0 0.1 0.2 0.3 0.4

Weight in DEF 1 0.9 0.8 0.7 0.6

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0.5 0.6 0.7 0.8 0.9 1 Row/ Col 1

2 3 4 5 6

7 8 9 10 11

A

0.5 0.4 0.3 0.2 0.1 0

1.29% 1.46% 1.84% 2.32% 2.86% 3.42%

B ABC

C DEF

Standard deviation 0.0342

0.0326

Correlation

-0.70389

Weight in Weight in ABC DEF 0 =1-A8 =0.1+A8 =1-A9 =0.1+A9 =1-A10 =0.1+A10 =1-A11

Portfolio standard deviation =(A8^2*B$2^2+B8^2*C$2^2+2*C$4*A8*B8*B$2*C$2)^0.5 =(A9^2*B$2^2+B9^2*C$2^2+2*C$4*A9*B9*B$2*C$2)^0.5 =(A10^2*B$2^2+B10^2*C$2^2+2*C$4*A10*B10*B$2*C$2)^0.5 =(A11^2*B$2^2+B11^2*C$2^2+2*C$4*A11*B11*B$2*C$2)^0.5 … and so on

Standard deviation

Portfolio stdeviation

4.00% 3.50% 3.00% 2.50% 2.00% 1.50% 1.00% 0.50% 0.00% 0%

20%

40%

60%

80%

100%

120%

Weight in ABC

Note the linear relationship between the return and the portfolio weight and the nonlinear relationship between the standard deviation and the portfolio weight. c.

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Portfolio Risk/Return tradeoff 3.00%

Portfolio return

2.50%

2.00%

1.50%

1.00%

0.50% 1.25%

1.75%

2.25%

2.75%

3.25%

Portfolio standard deviation

d. The only portfolios that make sense are those on the upper part of the graph—the efficient portfolios. The exact choice of efficient portfolio will depend on your risk preferences. If you are very risk averse you will choose a portfolio towards the left (low risk but lower expected return).

If you have a higher tolerance for risk, you will choose a portfolio towards the right of the graph (higher risk but higher expected returns).

50. Topic: Step 1: Efficient frontier Learning Objective: 8.5 Difficulty: Difficult Solution: a. Using monthly data for these two companies from January 2011 to December 2011, graph the relationship between risk and return.

Monthly adj prices RIM.TO

RY.TO

^GSPTSE

31/12/2010

58.07

49.82

13449.17

31/01/2011

58.99

51.6

13410.2

28/02/2011

64.15

54.59

13867.31

31/03/2011

54.83

57.66

14083.58

29/04/2011

46.09

57.77

13894.4

31/05/2011

41.35

54.88

13829.66

30/06/2011

27.88

53.44

13188.94

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29/07/2011

23.93

50.32

13047.78

31/08/2011

31.68

49.07

12768.7

30/09/2011

21.36

47.05

11623.84

31/10/2011

20.16

48.14

12252.06

30/11/2011

18.38

46.79

12204.11

30/12/2011

14.8 Monthly returns

51.47

11955.09

RIM.TO 31/01/2011 28/02/2011 31/03/2011 29/04/2011 31/05/2011 30/06/2011 29/07/2011 31/08/2011 30/09/2011 31/10/2011 30/11/2011 30/12/2011

Avg stdev

weight in RIM -

RY.TO

^GSPTSE

1.58% 8.75% -14.53% -15.94% -10.28% -32.58% -14.17% 32.39% -32.58% -5.62% -8.83% -19.48%

3.57% 5.79% 5.62% 0.19% -5.00% -2.62% -5.84% -2.48% -4.12% 2.32% -2.80% 10.00%

-9.2733% 17.7837%

0.3859% 5.0327%

-0.29% 3.41% 1.56% -1.34% -0.47% -4.63% -1.07% -2.14% -8.97% 5.40% -0.39% -2.04% -0.9139% 3.6586% corr

10.6412%

portfolio portfolio std exp ret 5.03% 0.39%

0.1

5.04%

-0.58%

0.2

5.65%

-1.55%

0.3

6.70%

-2.51%

0.4

8.02%

-3.48%

0.5

9.50%

-4.44%

0.6

11.07%

-5.41%

0.7

12.70% 14.37%

-6.38% -7.34%

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0.8 0.9

16.07%

-8.31%

1.0

17.78%

-9.27%

b.

The efficient frontier plots the relationship between the expected returns and risks. The graph in part (a) is of observed (ex-post) returns and risks. In order for the above graph to be an efficient frontier, I need to assume that the ex post risk and return equals the ex ante risk and return. c.

I expect the S&P/TSX index to plot above and to the left of the graph (i.e., it is an efficient but unattainable portfolio with just RIM and the Royal Bank). The S&P/TSX index contains most of the stocks on the market and I expect to find that increasing the number of stocks in the portfolio will make me better off (i.e., higher returns and less risk) than holding just two stocks. d.

The average monthly return of the S&P/TSX during this period was –0.9139% with a standard deviation of 3.6586%. As expected the S&P/TSX will plot outside the RIM/RY frontier. e.

Compared to a portfolio of just RIM and the Royal Bank, the S&P/TSX is an efficient portfolio. With just RIM and the Royal Bank, we cannot attain the same average return and risk as the S&P/TSX index.

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f.

As we add more stocks to the portfolio, I would expect the frontier to expand outwards. If adding XYZ to the portfolio makes me worse off (i.e., lower return for the same risk) I don’t have to hold it in my portfolio; I can always have a weight of zero on that stock. So increasing my choices can’t make me worse off so the frontier won’t move inwards. I expect that increasing my choices will give me the opportunity to invest in stocks that will either increase my expected returns for the same risk, or reduce my risk for the same returns, thereby shifting the frontier outwards.

51. Section: 8.3 Diversification Learning Objective: 8.6 Difficulty: Difficult Solution: a. Sample data from Excel: Number of Stdev of stocks portfolio 1 10.00% 2 7.07% 3 5.77% 4 5.00% 5 4.47% 6 4.08% 7 3.78% 8 3.54% 9 3.33% 10 3.16%

The formulas used: Row /col 1 2 3 4 5 6 7 8 9 10 11

A Number of stocks 1 =1+A2 =1+A3 =1+A4 =1+A5 =1+A6 =1+A7 =1+A8 =1+A9 =1+A10

B Stdev of portfolio =(A2*(1/A2)^2*0.1^2)^0.5 =(A3*(1/A3)^2*0.1^2)^0.5 =(A4*(1/A4)^2*0.1^2)^0.5 =(A5*(1/A5)^2*0.1^2)^0.5 =(A6*(1/A6)^2*0.1^2)^0.5 =(A7*(1/A7)^2*0.1^2)^0.5 =(A8*(1/A8)^2*0.1^2)^0.5 =(A9*(1/A9)^2*0.1^2)^0.5 =(A10*(1/A10)^2*0.1^2)^0.5 =(A11*(1/A11)^2*0.1^2)^0.5

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Portfolio standard deviation

Impact on diversification of adding firms to portfolio 12% 10% 8% 6% 4% 2% 0% 0

10

20

30

40

50

60

Number of independent firms in the Portfolio

From the graph it is obvious that the decline in portfolio risk decreases as we add more stocks to the portfolio – when we go from one to two stocks, the risk decreases by almost 30% (from 10% to 7.07%); however, when we go from two to three, the decrease is less than 20% (from 7.07% to 5.77%). b. In this situation (all stocks independent), I expect the risk to continue to decline as we add more stocks. The risk can become close to zero when we have a huge number of stocks in the portfolio. We can see from the portfolio variance formula with independent stocks that the variance is a function of one over the number of stocks in the portfolio. As the number of stocks approaches infinity, the variance will approach zero. The fact the variance approaches zero is because the average covariance between the stocks is zero; if they are not independent, then we cannot remove all risk by having an infinitely large portfolio.

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Chapter 9: The Capital Asset Pricing Model (CAPM) Multiple Choice Questions 1. Section: 9.1 The New Efficient Frontier Learning Objective: 9.1 Difficulty: Medium Solution: B wRF = 2,500/(2,500+7,500) = 0.25 ERP = (wRF)(RF) + (1 – wRF) (ERA) = (0.25)(8%)+(1 – 0.25)(20%) = 17%  p = (1 − wRF )( A ) = (1 – 0.25)(25%) = 18.75% 2.Section: 9.1 The New Efficient Frontier Learning Objective: 9.1 Difficulty: Medium Solution: D. The new efficient frontier is a straight line. All the portfolios along the new efficient frontier dominate those along the original efficient frontier, except the tangency portfolio P. The weight of the risk-free asset is negative when investors buy stock on margin.

3. Section: 9.2 The Capital Asset Pricing Model (CAPM) Learning Objective: 9.2 Difficulty: Medium Solution: D.  ER − RF  k P = RF +  M  P  M  8 − 5 20 = 5 +  ( p )  24  Therefore σp = 120%

4.Section: 9.3 The CAPM and Market Risk Learning Objective: 9.3 Difficulty: Medium Solution: D. The risk measurement in the SML is beta (βi), while the risk measurement in the capital market line (CML) is the standard deviation of the portfolio (σp).

5. Section: 9.3 The CAPM and Market Risk Learning Objective: 9.3 Difficulty: Medium Solution: B. Because Portfolio A lies above the SML it provides investors with an expected return that is higher than the return that is required to provide adequate compensation for risk.

Therefore, its price must be below that which investors would be willing to pay; it is undervalued.

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Difficulty: Medium Solution: C. Only C is not a difference since RF is the y-intercept for both the SML and the CML. The risk measurements of SML and CML are βi and σp, respectively. The slope of SML  ER − RF  and CML are ( ERM − RF ) and (  M  ), respectively. CML only applies to the efficient  M  portfolio, while SML measures all properly valued risky portfolios, including the efficient portfolio.

7.Section: 9.3 The CAPM and Market Risk Learning Objective: 9.3 Difficulty: Easy Solution: A. The market beta equals 1. A portfolio with a beta greater than 1 is more volatile than the market.

8.Section: 9.3 The CAPM and Market Risk Learning Objective: 9.3 Difficulty: Medium Solution: C. The market portfolio is unobservable in reality. Therefore we use a market index as a proxy.

9.Section: 9.3 The CAPM and Market Risk Learning Objective: 9.3 Difficulty: Medium Solution: D. Systematic risk is also called market risk, while non-systematic risk is called unique risk. Systematic risk = total risk – non-systematic risk. Systematic risk changes through time as the risk of the underlying security or portfolio changes.

10. Section: 9.1 The New Efficient Frontier Learning Objective: 9.1 Difficulty: Difficult Solution: Risk-adverse investors are only willing to invest in a risky undertaking if the expected value is sufficiently greater than the cost. The more risk averse, the larger the premium they will demand.

Investment A: expected value = $9; cost $7 → of interest to a risk-averse investor Investment B: this is a risk-free investment and as long as its return is greater than the market risk-free rate, all investors will be interested.

Investment C: expected value = $8; cost $9 → not of interest to risk averse (this security may be very interesting to a risk-averse investor who already holds a well-diversified portfolio—the value of that portfolio will drop if the TSX falls and Investment C will provide a way to avoid the risk →risk-averse people will pay to remove risk!).

Investment D: expected value = $2; cost $0 → of interest to risk averse

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Investment E: expected value = -$2; cost $0 → not of interest to risk averse (no premium) Note: these investments actually exist in the real world – in future chapters you will learn how to price them.

Investment A: call option Investment B: risk-free asset (i.e., t-bill) Investment C: put option Investment D: long position in forward or futures contract Investment E: short position in forward or futures contract 11. Section: 9.1 The New Efficient Frontier Learning Objective: 9.1 Difficulty: Easy Level of difficulty: Medium Solution: a) Risk loving – the expected value from buying a lottery ticket is much less than the cost of the ticket. b) Risk averse – you are willing to pay to reduce a risk you currently face. c) Risk loving – depending on how you evaluate the risk of being hit by a car versus the cost of waiting at the light. d) Risk averse – the time spent backing up the machine is much less than the expected time spent replicating all the work that is on your hard drive (unless your machine will never crash?).

12. Section: 9.1 The New Efficient Frontier Learning Objective: 9.1 Difficulty: Difficult Solution:

Investor

Weight in riskfree asset

$ amount invested in risk-free asset

Expected portfolio return

Portfolio standard deviation =

Charles

20%

.2*1,200=$240

=0.2*6+0.8*10 =9.2%

Sonja

-300/1,200 = -25%

Borrowed $300

11%

8.75%

$300

9%

5.25%

Borrowed $1800

16%

17.5 %

(1 − wR f ) M

= .8*.07 = 5.6%

wR f *.06+(1- wR f )*.1=.09 Fritz

0.1-.04 wR f =.09

wR f = 25% Eddy

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Nellie

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$685.71

7.71%

3%

13. Section: 9.1 The New Efficient Frontier Learning Objective: 9.1 Difficulty: Medium Solution: wRF = -500/1,500 = -0.333; (1 – wRF) = 1 – (-0.333) = +1.33 Therefore, ERP = (-0.333)(8%) + (1.333)(15%) = 17.33%  p = (1.333) (30%) = 40% 14. Section: 9.1 The New Efficient Frontier Learning Objective: 9.1 Difficulty: Difficult Solution: a) i) The easiest way to evaluate the efficiency of the portfolios is to plot them on a graph: The Brokerage Company

Expected return

12.00% 10.00% 8.00%

Amanda

6.00% 4.00%

Xiang

2.00% 0.00% 0.20%

Geeta

Amir

Rina Charles

0.30%

0.40%

0.50%

0.60%

0.70%

0.80%

Standard deviation

Charles is holding an inefficient portfolio (return = 2%, risk = .4%). Portfolio C (Xiang’s) is better—higher return (5%) with lower risk (.3%).

Rina is holding an inefficient portfolio (return = 4%, risk = .6%). Portfolios C (Xiang’s) and E (Amir’s) both provide a higher expected return with lower risk.

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Amanda is holding an inefficient portfolio (return = 7%, risk = .5%). Portfolio E (Amir’s) provides a higher expected return with lower risk. ii) Inefficient portfolios are not of interest to anyone. Risk loving doesn’t imply irrational behaviour; all investors prefer higher returns for the same risk, or lower risk for the same returns. b) The more risk averse an investor, the greater the expected return they will demand per unit of risk. There are three efficient portfolios: C, E, and F (Xiang, Amir, and Geeta respectively).

Assuming that the investors chose these portfolios, then Amir is the most risk averse and Geeta is the least risk averse.

Investor name Xiang Amir Geeta

Expected return 5.00% 9.00% 10.00%

Standard deviation 0.30% 0.45% 0.70%

Return / Risk 16.67 20.00 14.29

15. Section: 9.1 The New Efficient Frontier Learning Objective: 9.1 Difficulty: Difficult Solution: a) No. To recommend a portfolio for these people one would need to know their levels of risk aversion. For example, if Jean is much more risk averse than Evan, I would recommend different portfolios. b)With a risk-free asset, I will now recommend that the friends invest in a combination of the market or tangency portfolio (entirely risky assets) and the risk-free asset. The market portfolio will be the same for all the friends; however, the fraction they invest in the market portfolio will differ depending on their risk aversion. c)

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Rf = 2%

Expected return

17% 15% 13% 11% 9% 7% 5% 3%

1% 0%

2%

4%

6%

8%

10%

12%

Standard deviation B

C

A

Rf+A

Rf+B

Rf+C

To create this chart in Excel (note: setting it up this way makes it very easy to redo the calculations for different risk-free rates).

Portfolio

Standard deviation

Expected return

A B C

0.05 0.07 0.11

0.08 0.13 0.17

Rf Rf = 2% Standard deviation

0.02 Rf+A

Rf+B

Rf+C

Expected return

Expected return

Expected return

=$B$7+(($C$2$B$7)/$B$2)*A10 =$B$7+(($C$2$B$7)/$B$2)*A11 =$B$7+(($C$2$B$7)/$B$2)*A12

=$B$7+(($C$3$B$7)/$B$3)*A10 =$B$7+(($C$3$B$7)/$B$3)*A11 =$B$7+(($C$3$B$7)/$B$3)*A12 and so on …

=$B$7+(($C$4$B$7)/$B$4)*A10 =$B$7+(($C$4$B$7)/$B$4)*A11 =$B$7+(($C$4$B$7)/$B$4)*A12

0 =0.01+A10 =0.01+A11

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A B C

5.00% 7.00% 11.00%

Booth, Cleary

8.00% 13.00% 17.00%

Rf 2.00% Rf = 2% Rf+A Rf+B Rf+C Standard Expected Expected Expected deviation return return return 0.00% 2.00% 2.00% 2.00% 1.00% 3.20% 3.57% 3.36% 2.00% 4.40% 5.14% 4.73% 3.00% 5.60% 6.71% 6.09% 4.00% 6.80% 8.29% 7.45% And so on…

To get Excel to graph just the points (portfolios A, B, and C) you will need to adjust the “source data” section in the graph.

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d) We can see from the graph above that everyone will be better off (able to achieve a higher return for the same risk) by combining the risk-free asset with risky portfolio B. 16. Section: 9.1 The New Efficient Frontier Learning Objective: 9.1 Difficulty: Easy Solution: Yes; remember the market portfolio is the tangency point on the efficient frontier. If we change the risk-free rate, we will change the tangency point. The new tangency portfolio will have a different risk and return than the original market and therefore, will have a different composition.

17. Section: 9.2 The Capital Asset Pricing Model (CAPM) Learning Objective: 9.2 Difficulty: Easy Solution: Any three of the following: 1). All investors have identical (or homogeneous) expectations with respect to expected returns, standard deviations and correlation coefficients for all available individual securities.

2). All investors have the same one-period time horizon.

3). All investors can borrow or lend money at the risk-free rate of return (RF).

4). There are no transaction costs.

5). There are no personal income taxes so that investors are indifferent between capital gains and dividends.

6). There are many investors, and no single investor can affect the price of a stock through his or her buying and selling decisions. Therefore, investors are price-takers.

7). Capital markets are in equilibrium.

18. Section: 9.2 The Capital Asset Pricing Model (CAPM) Learning Objective: 9.2 Difficulty: Medium Solution: Portfolio Portfolio 1

Expected return 14%

Standard deviation 9%

=

Sharpe Ratio ER p − R f

p

= 1.333

Portfolio 2 Portfolio 3 Portfolio 4 Portfolio 5

9% 3% 8% 4%

3% 10% 4% 6%

2.3333 0.1000 1.5000 0.3333

Required rate of return

 ER − R f  E ( Rp ) = R f +  m  p  m   8% − 2%  = 2% +  9%  5%  = 12.80% 5.60% 14.00% 6.80% 9.20%

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Difficulty: Easy Solution: A portfolio or security is correctly valued when the required rate of return is equal to the expected return. The portfolio or security is undervalued (too cheap) when the required rate of return is lower than the expected rate, and is overvalued when the required rate is higher than the expected rate of return.

To see this, assume that the portfolio will be worth $100 in 1 year. The price today should be $100 discounted at the required rate; however, the stock price we actually observe is $100 discounted at the expected rate. Therefore, if the expected rate is greater than the required rate, the observed PV will be lower than it should be and the stock will be undervalued. We are buying the portfolio at too low a price.

Undervalued: Portfolios 1, 2 and 4 Overvalued: Portfolios 3 and 5 20. Section: 9.3 The CAPM and Market Risk Learning Objective: 9.3 Difficulty: Difficult Solution: a. The data is already downloaded in Chapter 8 Question 50. One would expect RIM to have a higher beta than the Royal Bank. The Royal Bank is a very large, stable firm and its basic business should not be very sensitive to market shocks. One would also expect the beta of the Royal Bank to be closer to 1.0 than RIM. The Royal Bank is a very large firm and therefore a more substantial component of the S&P/TSX than RIM and, therefore, the correlation between the Royal Bank and the market should be closer to 1. RIM, in contrast, operates in a more volatile industry and the basic business is much more sensitive to economy-wide shocks. b. Using Excel: Tools → Data Analysis → Covariance The Variance-Covariance Matrix:

RIM returns RY returns TSX returns

RIM returns RY returns TSX returns 0.028990553 0.000873019 0.0023217 0.002774488 0.0007303 0.001226981

The diagonal terms are the variances and the off-diagonal terms are the covariances.

Beta=COV(r, rm)/VARm Beta: RIM RY

2.26 0.60

c. i) Using the monthly returns of the portfolio, the beta is 1.43. ii) Using the equation for the beta of a portfolio, the beta is 1.43. iii) As expected, the two betas are identical.

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21. Section: 9.3 The CAPM and Market Risk Learning Objective: 9.3 Difficulty: Medium Solution:

Case 1 Case 2 Case 3 Case 4 Case 5

Security 1 beta

Security 2 beta

Weight in Security 1

.50

1.50

.60

2.15

0.45

.50

Portfolio beta =.6*.5+.4*1.5 =.9 1.30

2.1 = w *1.1 + (1 − w ) *1.9

1.10

1.90

1.25

0.60

.75

1.0875

1.30

3.3

.15

3.00

2.1 = −.8w + 1.90 w = −.25

2.10

22. Section: 9.3 The CAPM and Market Risk Learning Objective: 9.3 Difficulty: Easy Solution: a. Zero; by definition the return on the risk-free asset is constant and therefore, the covariance between the risk-free asset and any other asset must be zero. b. One; the covariance of an asset with itself equals the variance of the asset. Therefore, the beta of the market must be one.

23. Section: 9.3 The CAPM and Market Risk Learning Objective: 9.3 Difficulty: Medium Solution: a. ρ σ (0.6)(.25) β FM = FM,M FM = = 0.75 σM (.2) b. k FM = RF + ( ERM − RF )  FM = 6.5%+0.75(16% — 6.5%) = 13.625% c. Stock FM has a required rate of return (13.625%), which is lower than the market return (16%) because its beta is lower than the market beta of 1.

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Solution: Expected return = [(P1 – P0)+D]/P0 = [(12.5 —10)+2.5]/10 = 50% Required return = RF + ( ERM − RF )  = 6% + (β)(25%) The market is in equilibrium so the expected return = required return.

50% = 6% + (β)(25%) β= 1.76 25. Section: 9.2 The Capital Asset Pricing Model (CAPM) Learning Objective: 9.3 Difficulty: Medium Solution: Expected Standard Required Security Beta Recommendation return deviation return Sell (I require 9%, but I only ABC 5% 9% 1.5 9.00% expect to get 5%) Buy (I require 7.4%, but I RTS 10% 3% 1.1 expect the security to get 7.40% 10%) DKF 6% 10% 0.95 Sell 6.80% OPL 9% 4% 0.75 Buy 6.00% WEQ 14% 6% 1.25 Buy 8.00% 26. Section: 9.3 The CAPM and Market Risk Learning Objective: 9.3 Difficulty: Easy Solution: No, the total risk has two components – systematic (or market) and unique (nonsystematic). If the total has increased, it doesn’t mean that the market risk (measured by beta) component has necessarily increased.

27. Section: 9.3 The CAPM and Market Risk Learning Objective: 9.3 Difficulty: Medium Solution: a) R = R f +  ( Rm − R f )

= 2% + 1.2*8% = 11.6% b) Here we will need to use the dividend discount model:

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1.25* (1 + .03) .116 − .03 1.2875 = .086 = $14.9709

P0 =

28. Section: 9.3 The CAPM and Market Risk Learning Objective: 9.3 Difficulty: Medium Solution: Market or systematic risk: (a), (c), and (e) Unique or unsystematic risk: (b), (d), and (f) 29. Section: 9.2 The Capital Asset Pricing Model (CAPM) Learning Objective: 9.2 Difficulty: Easy Solution:Determine which line consisting of the security and the RF produces the greatest slope.  ER − RF   20 − 5  slope =  A = 5  = 3   A  

 ER − RF   25 − 5  slope =  B  =  10  = 2   B    ER − RF   30 − 5  slope =  C  =  15  = 1.67   C   Therefore, choose A. 30. Section: 9.3 The CAPM and Market Risk Learning Objective: 9.3 Difficulty: Easy Solution: Expected return = [(P1 – P0)+D]/P0 = [(22 -20)+0.50]/20 = 12.5% Required return = RF + ( ERM − RF )  = 5% + (2.6)(9%—5%) = 15.4% Expected return (12.5%) < Required return (15.4%), so the stock lies below the SML. It is over-valued.

31. Section: 9.3 The CAPM and Market Risk Learning Objective: 9.3 Difficulty: Medium Solution: βM = 1. βRF = 0 β P = w Aβ A + w Bβ B + ... + w nβ n WA = 100/(100+400+300+200) = 0.1 WB = 400/(100+400+300+200) = 0.4 WRF = 300/(100+400+300+200) = 0.3 Solutions Manual ..

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WNEW = 200/(100+400+300+200) = 0.2 1 = 0.1 (0.9)+(0.4)(1.2)+(0.3)(0)+(0.2)(βNEW) 1 = 0.09 +0.48 + 0 +(0.2)(βNEW) βNEW = 2.15 For example, a firm in the materials industry may have a beta of 2.15, such as a steel or precious metal company.

32. Section: 9.3 The CAPM and Market Risk Learning Objective: 9.3 Difficulty: Medium Solution: k A = RF + ( ERM − RF )  A = 5%+1.2(3%) = 5% + 3.6% = 8.6% > 8% k B = RF + ( ERM − RF )  B = 5%+0.9(3%) = 5% + 2.7% = 7.7% < 8% Therefore Portfolio A lies below the SML and is over-valued, while Portfolio B lies above the SML and is under-valued. If the market is efficient, Portfolio A and B will both adjust to the required rate of return according to the SML; they will fall on the SML. Portfolio A’s price will fall and Portfolio B’s price will rise. Thus, you should sell the over-valued Portfolio A and buy the under-valued Portfolio B. 33. Sections: 9.2 The Capital Asset Pricing Model (CAPM) and 9.3 The CAPM and Market Risk Learning Objective: 9.2 and 9.3 Difficulty: Difficult Solution: The client does not understand the difference between the Capital Market Line (CML) and the Security Market Line (SML). The CML represents the relationship between the expected return and risk for efficient portfolios while the SML plots the relationship between the returns of individual securities and the market risk (Beta).

CML cannot be used to value individual securities because individual securities are not efficient portfolios; an efficient portfolio will be a well-diversified portfolio and thereby have relatively little unique risk. A security, in contrast, will potentially have a great deal of idiosyncratic risk.

Consequently, as only the market risk is priced (investors receive a reward for accepting this risk), we value securities using the SML. This security has a lot of idiosyncratic risk, but, as long as the client holds a well diversified portfolio, he can remove the effects of this risk and be left with just the market risk. The required return for a stock with this level of market risk is 9 percent (i.e., k = 4 + (8-4)(1.25) = 9%; however, you are expecting to earn 12 percent by holding the stock.Therefore, buy the stock. In contrast, if we used the CML, we would determine a required return of 16 percent (i.e., k = 4 + (8-4)(9/3) = 16%), which would suggest the stock is overvalued if the expected return is only 12 percent.

34. Section: 9.3 The CAPM and Market Risk Learning Objective: 9.3 Difficulty: Medium Solutions Manual ..

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Solution: Begin with the dividend discount model to determine the required rate of return. Then use that required rate and the CAPM to determine the beta of QTax.

4.50 (1 + .05 ) R − .05 25R − 1.25 = 4.725 R = 0.239 25 =

.239 = .03 +  (.08 − .03) = .03 +  *.05  = 4.18 35. Section: 9.3 The CAPM and Market Risk Learning Objective: 9.3 Difficulty: Difficult Solution: a) To value PVC, find a comparable firm. ABC, while having the same total risk, is not necessarily appropriate because we do not know if the market risk is similar. Remember, we are only rewarded for holding market risk, and if PVC has very different market risk than ABC, we will get an incorrect valuation.

VJK, in contrast, has the same market risk as PVC, so we will use it to determine the required rate of return for PVC. Note, here we are assuming that PVC will be part of a well-diversified portfolio and therefore its unsystematic or unique risk will be diversified away. The required return for VJK, and thereby PVC, is: R = .01 + 0.75(.05) = .0475 b) Now that we have the required rate of return, we can use the dividend discount model to value PVC: 10(1.03) P0 = = $588.57 .0475 − .03

36. Section: 9.3 The CAPM and Market Risk Learning Objective: 9.3 Difficulty: Easy Solution: By having a portfolio of stocks, we can potentially eliminate diversifiable risk.

37. Section: 9.3 The CAPM and Market Risk Learning Objective: 9.3 Difficulty: Medium Solution: Solutions Manual ..

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No. It is not possible because the higher the beta, the higher the required rate of return must be.

According to CAPM stock A must have a higher required rate of return.

38. Section: 9.3 The CAPM and Market Risk Learning Objective: 9.3 Difficulty:Easy Solution: 15= 6+5 ×   = (15-6)/5 = 1.8 39. Section: 9.3 The CAPM and Market Risk Learning Objective: 9.3 Difficulty:Medium Solution: 20= RF +1.8 × ( ERM – RF ) (i) 14= RF +1.2 × ( ERM – RF ) (ii) (i)-(ii) : 6=0.6 × ( ERM – RF ) ( ERM - RF )=10 (iii) Put (iii) in (i): 20 = RF +1.8 × 10 RF =2% ERM -2=10 ERM =12% 40. Section: 9.3 The CAPM and Market Risk Learning Objective: 9.3 Difficulty:Medium Solution: 12= RF +  A × risk premium (i) 8= RF +  B × risk premium (ii) (i)-(ii): 4= 0.2risk premium Risk premium = 4/0.2 = 20% 41. Section: 9.3 The CAPM and Market Risk Learning Objective: 9.3 Difficulty:Medium Solution:  =cov//σ2M= 0.09375/.0625= 1.5 ERABC = 6+1.5 × 8 = 18% 42. Section: 9.3 The CAPM and Market Risk Learning Objective: 9.3 Difficulty:Medium Solution: Beta of the portfolio= .2 × 0.8+.3 × 1.2+.15 × 1.35+.35 × 1.15 Solutions Manual ..

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= 0.16+0.36+0.2025+0.4025 =1.125 ER = 5+1.125 × 8 =14% 43. Section: 9.4 Alternative Asset Pricing Models Learning Objective: 9.4 Difficulty: Easy Solution: Roll argued that CAPM cannot be tested empirically because the market portfolio, which consists of all risky assets, is unobservable. This forces researchers to use market proxies, which may or may not be the optimal mean-variance efficient portfolio. He also argues that tests of the CAPM are actually tests of the mean-variance efficiency of the chosen market portfolio. He shows that the basic CAPM results will hold whenever the chosen proxy is mean-variance efficient, and will not hold if the converse is true.

44. Section: 9.4 Alternative Asset Pricing Models Learning Objective: 9.4 Difficulty: Medium Solution: ERi =8% + (0.4)(10%) + (0.5)(5%) + (1)(9%)+ (1.5)(12%) = 8%+4%+2.5%+9%+18% = 41.5%

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Chapter 10: Market Efficiency Multiple Choice Questions 1. Section: 10.1 The Importance of Market Efficiency Learning Objective: 10.1 Level of difficulty: Easy Solution: D 2. Section: 10.3 The Efficient Market Hypothesis (EMH) Learning Objective: 10.3 Level of difficulty: Easy Solution: C. The three forms of EMH are weak, semi-strong (not semi-weak), and strong.

3. Section: 10.3 The Efficient Market Hypothesis (EMH) Learning Objective: 10.3 Level of difficulty: Medium Solution: C 4. Section: 10.6 Implications of Market Efficiency Learning Objective: 10.6 Level of difficulty: Medium Solution: D. Insider information is considered private information, which is only reflected in the strong form of EMH. Semi-strong form of EMH includes all publicly known and available information. Therefore, trading on past and current published stock price changes, trading volume, and earnings projections is futile because that information is all reflected in the stock price assuming the semi-strong form of EMH. Please note that insider trading is not permitted in order to protect the general investing public.

5. Section: 10.3 The Efficient Market Hypothesis (EMH) Learning Objective: 10.3 Level of difficulty: Medium Solution: B. The strong form of EMH encompasses both the weak and semi-strong forms of EMH. The semi-strong form of EMH encompasses the weak form of EMH. 6. Section: 10.4 Empirical Evidence Regarding Market Efficiency Learning Objective: 10.4 Step 1: Concept of market efficiency Level of difficulty: Medium Solution: C 7. Section: 10.4 Empirical Evidence Regarding Market Efficiency Learning Objective: 10.4 Level of difficulty: Medium Solution: C 8. Section: 10.2 Defining Market Efficiency

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Learning Objective: 10.2 Level of difficulty: Medium Solution: D 9. Section: 10.4 Empirical Evidence Regarding Market Efficiency Learning Objective: 10.4 Level of difficulty: Medium Solution: D 10. Section: 10.4 Empirical Evidence Regarding Market Efficiency Learning Objective: 10.4 Level of difficulty: Medium Solution: D 11. Section: 10.6 Implications of Market Efficiency Learning Objective: 10.6 Level of difficulty: Medium Solution: B. Technical analysis, which involves examining trading data for patterns, is not likely to be rewarded by substantial abnormal returns, because markets appear to be weak form efficient.

12. Section: 10.4 Empirical Evidence Regarding Market Efficiency Learning Objective: 10.4 Level of difficulty: Difficult Solution: C. Value stocks have consistently outperformed growth stocks.

13. Section: 10.4 Empirical Evidence Regarding Market Efficiency Learning Objective: 10.4 Level of difficulty: Difficult Solution: D. The others are all characteristics of value stocks.

14. Section: 10. 4 Empirical Evidence Regarding Market Efficiency Learning Objective: 10.4 Level of difficulty: Easy Solution: A. It supports the semi-strong form of EMH and therefore supports the weak form of EMH because investors could not earn abnormal returns after the information is made public.

However, it contradicts the strong form of EMH because some investors profit from the private information prior to the announcement.

15. Section: 10.5 Behavioural Finance Learning Objective: 10.5 Level of difficulty: Medium Solution: D. Risk aversion is when investors are willing to assume risk where that risk is adequately compensated for with higher expected returns.

16. Section: 10.4 Empirical Evidence Regarding Market Efficiency

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Learning Objective: 10.4 Level of difficulty: Medium Solution: C Practice Problems 17. Section: 10.1 The Importance of Market Efficiency Learning Objective: 10.1 Level of difficulty: Easy Solution: a. This market is likely to suffer from operational inefficiency due to high transaction costs and frequent loss of records. b. This market is likely to suffer from allocational inefficiency as firms have a limited range of securities that they can issue (i.e., limited ways to share risk). c. This market is likely to suffer from informational inefficiency as the stock prices cannot quickly respond to news due to trading limitations.

18. Section: 10.1 The Importance of Market Efficiency Learning Objective: 10.1 Level of difficulty: Easy Solution: a. Yes. All I have to do to consistently beat the market is do the opposite of what my broker advises. b. No. I’m very slow on doing the analysis and there is no reason to expect that every other investor interested in Canada Bank won’t have done their analysis before me. I would expect the stock price to already reflect the information contained in the financial statements and therefore, it is no surprise that I rarely make money. This is an example of semi-strong form efficiency. c. Yes. I’m trading based on past price behaviour. If the market is weak form efficient, I should not be able to consistently make money (on a risk-adjusted basis). d. Yes. The CEO has access to private information and the fact that nearly all of the time he is making money trading on private information suggests that the market is strong form inefficient. e. No. The fact that a skillful analysis was completed before anyone else does not suggest that the market is semi-strong form inefficient. Rather, the money I make is a fair compensation for my skill and speed.

19. Section: 10.4 Empirical Evidence Regarding Market Efficiency Learning Objective: 10.4 Level of difficulty: Easy Solution: Statistical significance simply asks whether or not the observations are likely under the null hypothesis proposed for the situation. Economic significance, in contrast, asks if the observed relationship is large enough that you can make money from it. For example, a February temperature of -25˚ C might be significantly warmer than “normal”, but, it is still too cold for shorts and a t-shirt.

20. Section: 10.2 Defining Market Efficiency Learning Objective: 10.2 Level of difficulty: Easy

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Solution: A sell-side analyst works for the investment banks and brokerage houses who are trying to “sell” the securities; consequently they are most likely to offer their recommendations to the public. In contrast, the buy-side analyst works for an investor (usually a large institution) and will want to keep their recommendations private.

21. Section: 10.4 Empirical Evidence Regarding Market Efficiency Learning Objective: 10.4 Level of difficulty: Medium Solution: To test the weak form, one way is to test if price changes are independent of each other.

One common test is the serial correlations test, which measures the correlation between successive price changes for various lags. Another method is the runs test, which classifies each price change by its sign, and tests if there are any “runs” in the series of signs.

To test the semi-strong form, one way is to test the speed of adjustment of stock prices to a new information announcement, using an event study. Another way is to examine the performance of investors to see if they consistently generate abnormal risk-adjusted returns by using publicly available information.

22. Section: 10.2 Defining Market Efficiency Learning Objective: 10.2 Level of difficulty: Medium Solution: Assumption #1: A large number of rational, profit-maximizing investors exist who actively participate in the market by analyzing, valuing, and trading securities. The markets are assumed to be competitive.

Assumption #2: Information is costless and widely available to market participants at the same time.

Assumption #3: Information arrives randomly and therefore announcements are not related to one another.

Assumption #4: Investors react quickly and fully to the new information, which is reflected in stock prices.

23. Section: 10.4 Empirical Evidence Regarding Market Efficiency Learning Objective: 10.4 Level of difficulty: Medium Solution: The momentum effect refers to the fact that stocks that have experienced high returns in previous three to 12 month periods tend to outperform in the subsequent three to 12 month periods. It contradicts weak form efficiency.

24. Section: 10.4 Empirical Evidence Regarding Market Efficiency Learning Objective: 10.4 Level of difficulty: Easy Solution: Weak form and semi-strong form efficiency are both well-supported. It is reasonable to conclude that markets are weak-form efficient; however, more contradictory evidence exists for the semi-strong form than for the weak form. Strong form efficiency is not very well supported by the evidence, and it is reasonable to conclude that markets are not strong form efficient in the strictest sense.

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25. Section: 10.6 Implications of Market Efficiency Learning Objective: 10.6 Level of difficulty: Medium Solution: The evidence may suggest that on average pharmaceutical company stocks do better in the spring, but she needs to keep in mind several things: “On average” does not mean always. There is still likely to be considerable variation in the performance of pharmaceutical company stocks in the spring.

The general evidence indicates that trying to “time” the market is not successful.

What will be the impact on the new product if she waits to raise the capital? For example, possible leaks of information?

26. Section: 10.6 Implications of Market Efficiency Learning Objective: 10.6 Level of difficulty: Medium Solution: Not necessarily. The Board should consider what other information or rumours are circulating. Perhaps the stock has risen sharply because another company is interested in buying Marlin, which is no reason why the CEO should get a raise.

27. Section: 10.6 Implications of Market Efficiency Learning Objective: 10.6 Level of difficulty: Medium Solution: First, if the project is really secret (i.e., no one outside the company knows anything about it) then we wouldn’t expect the market to react unless it was strong form efficient. As we know that the markets are not strong form efficient, it is not surprising that there has been no reaction.

Second, if the project is not really all that secret (i.e., people outside the company know all about it) then we wouldn’t expect much of a reaction. After all, what is new? The market will only react to new information, not old information.

28. Section: 10.6 Implications of Market Efficiency Learning Objective: 10.6 Level of difficulty: Easy Solution: For investors, technical and fundamental analysis both tend to be futile since weak form and semi-strong form of efficiency are both well-supported. Active trading strategies are unlikely to outperform “passive” portfolio management strategies on a consistent basis. Investors should focus on diversifying their portfolios and defining expected returns and acceptable risk levels.

For corporate officers, it is unimportant to time security issues and repurchases. Moreover, they should monitor the market price of the firm’s security, which reflects market opinion of the company’s outlook.

29. Section: 10.6 Implications of Market Efficiency Learning Objective: 10.6 Level of difficulty: Difficult

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Solution: a. The markets are full of investors who are constantly analyzing a firm’s prospects (i.e., growth potential, general economic conditions, actions of competitors and suppliers, etc.) and consequently, if the market is semi-strong form efficient, we expect that the stock price will, on average, reflect the prospects of a firm. Therefore, if the investors are becoming more pessimistic about the firm’s prospects, they will be selling and causing the stock price to decline. b. No, given the beta and the market’s fall (assuming that the risk-free rate hasn’t changed) I would have expected the firm’s stock price to fall 6 percent. The fact that it has fallen less than the predicted 6 percent is actually relatively good news.

30. Section: 10.6 Implications of Market Efficiency Learning Objective: 10.6 Level of difficulty: Difficult Solution: (N.B. If you purchase the dividend on or after the ex-dividend date, you are no longer entitled to the dividend.) a. If the announcement is a surprise, I would expect a reaction on March 15. The sign of the reaction will depend on how the market interprets the news: does starting to pay dividends indicate that the firm has stopped its high growth period (negative) or does it mean that the firm is confident of high future cash flows (positive news)? In general, I would expect a positive reaction. b. I would not expect a reaction; everyone already knows this so the announcement provides no new information. c. The day that the firm goes ex-dividend I expect the stock price to drop by the amount of the dividend. Note that this is not a change in price due to information; everyone knows when the stock will go ex-dividend. Rather, it is a reaction to the fact that the buyer of the stock will no longer be entitled to the dividend and therefore is not willing to pay for it.

31. Section: 10.6 Implications of Market Efficiency Learning Objective: 10.6 Level of difficulty: Difficult Solution: a. The announcement is bad news that the market did not anticipate and therefore the market has to revalue the company. As there was fraud involved, you would expect that the financial statements have been massaged to look better than they should and the value of the firm should drop. Also, now the firm has to look for a new CEO which is always a difficult time for a company. b. The market already anticipated the event. Perhaps there had already been rumours and previous restatements of the financial statements. c. It is actually not uncommon for a stock to rise on bad news. The usual interpretation is that the market sees the news as not as bad as anticipated. For example, the market has been anticipating that the CEO will be arrested, the financials will be restated, or the firm will announce that it has been hit by a massive lawsuit for defective steam engines. However, when the bad news is announced, the “massive lawsuit” is for $1,000, not $1 billion. Therefore, the news wasn’t as bad as expected. An alternative interpretation is that the announcement of the actions indicates that the firm has recognized the problem and is doing something about it.

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32. Section: 10.6 Implications of Market Efficiency Learning Objective: 10.6 Level of difficulty: Medium The efficiency of the market is based upon the continuing services of the analysts and portfolio managers to actively scout the market. If these players are removed from the market, the prices will cease to reflect all the available information. This will consequently lead to markets becoming inefficient.

33. Section: 10.5 Behavioural Finance Learning Objective: 10.5 Level of difficulty: Difficult Solution: a. This is an example where human emotions, more than fundamentals of finance, are at play in the market. At the time the incorrect news hit the market, the atmosphere was already volatile with the Lehman firm going bankrupt and Merrill Lynch in trouble. Investors had seen their investments in Lehman drop from $65 per share to 26 cents a share. The news of another big one falling must have caused a panic sale leading to the massive drop in the share price. b. This is an open-ended question designed to force students to think outside the box. A possible explanation proposed by current research in the field is that investors tend to be more sceptical of bad news than of good news. In the above example, investors react strongly to the bad news by trying to sell the United shares, thereby pushing the prices down. Even after the truth is revealed, the scepticism lingers amongst the investors, resulting in relatively slower recovery. c. Yes, at least in the short run. The prices are seemingly driven by non-informational factors.

34. Section: 10.5 Behavioural Finance Learning Objective: 10.5 Level of difficulty: Difficult Solution: Investors are more likely to be overconfident when the economy is booming. Overconfidence often results from past success, even though the past result might have been reflective of the general state of the economy or even a result of random movements in the market. During a state of boom, investors often attribute the resulting gains to their better understanding of the market, which leads to overconfidence.

35. Section: 10.5 Behavioural Finance Learning Objective: 10.5 Level of difficulty: Difficult Solution: Investors tend to become more overconfident as they accumulate more information and develop familiarity with a given financial asset. To that extent, access to the Internet will, in general, lead to more overconfidence amongst investors.

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Chapter 11: Forward, Futures, and Swaps Multiple Choice Questions 1. Section: 11.1 Forward Contracts Learning Objective: 11.1 Level of difficulty: Medium Solution: B If a Canadian firm has to pay U.S. dollars in the future, it worries about the potential appreciation of the U.S. dollar. Choice A, C, and D are true.

2. Section: 11.1 Forward Contracts Learning Objective: 11.2 Level of difficulty: Medium Solution: A

F=

(1 + kdomestic ) (1 + 0.05) S =  1.25 = CDN $1.26 / US $ (1 + k foreign ) (1 + 0.04)

3. Section: 11.1 Forward Contracts Learning Objective: 11.1 Level of difficulty: Medium Solution: B In order to hedge, you take a short position in the U.S. dollar forward contract if you have a long position in U.S. dollars.

4. Section: 11.1 Forward Contracts Learning Objective: 11.2 Level of difficulty: Medium Solution: C Cost of carry = 1.05/1.04 – 1= 0.96% 5. Section: 11.1 Forward Contracts Learning Objective: 11.2 Level of difficulty: Medium Solution: D The forward rate is the spot rate multiplied by (1 + cost of carry percentage).

6. Section: 11.1 Forward Contracts Learning Objective: 11.1 Level of difficulty: Medium Solution: D. Short means investors owe something.

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7. Section: 11.1 Forward Contracts Learning Objective: 11.1 Level of difficulty: Medium Solution: A. Profit from a long position is positively affected by the spot price.

8. Section: 11.2 Futures Contracts Learning Objective: 11.3 Level of difficulty: Medium Solution: A Futures contracts do not involve credit risk because of the existence of the clearing house, while forward contracts do involve credit risk.

9. Section: 11.2 Futures Contracts Learning Objective: 11.3 Level of difficulty: Medium Solution: C Both the buyer and seller put down a $1,500 deposit. The futures contract is worth $15,000 to the buyer at the end of the first day, but is worth –$15,000 to the seller. At the end of the first day, the buyer’s equity was increased by $15,000, not $45,000. The seller’s equity was decreased by the same amount. Only C is true.

10. Section: 11.2 Futures Contracts Learning Objective: 11.3 Level of difficulty: Medium Solution: C If the buyer gains, the clearinghouse will transfer the gained value from the seller’s account to the buyer’s account.

If the seller gains, the clearinghouse will transfer the gained value from the buyer’s account to the seller’s account.

11. Section: 11.2 Futures Contracts Learning Objective: 11.3 Level of difficulty: Medium Solution: A In practice, most of the futures contracts are closed out with an offsetting transaction before the final day of trading.

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Solution: D To hedge, you should short a Government of Canada bond futures contract when you have the same bonds (you have a long position in the same bonds) to sell in the future so that you are locked into a selling price regardless of how the interest rate is going to change, Or you should long a Government of Canada bond futures contract when you need to buy it in the future.

13. Section: 11.2 Futures Contracts Learning Objective: 11.3 Level of difficulty: Medium Solution: D. All future contracts are marked to market each day, as the value of the contract changes.

14. Section: 11.2 Futures Contracts Learning Objective: 11.3 Level of difficulty: Medium Solution: A. Forwards have less basis risk than futures because unlike futures contracts, forwards are not standardized and can therefore be tailor-made with respect to underlying assets and maturity dates.

15. Section: 11.2 Futures Contracts Learning Objective: 11.3 Level of difficulty: Medium Solution: D. Futures on the S&P 500 Index are traded on the Chicago Mercantile Exchange.

16. Section: 11.2 Futures Contracts Learning Objective: 11.3 Level of difficulty: Medium Solution: A. Futures are traded on exchanges while forwards are traded on a dealer or OTC market. Credit risk is less important for futures because they are guaranteed by the clearinghouse.

Futures are marked to market daily.

17. Section 11.3 Swaps Learning Objective: 11.4 Level of difficulty: Medium Solution: B Net interest rate (ABC) = LIBOR + 9.5% – 9.5% = LIBOR 18. Section 11.3 Swaps Learning Objective: 11.4 Level of difficulty: Difficult Solution: A Solutions Manual ..

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Net interest rate (ABC) = LIBOR (as calculated in Problem 17) ABC saving = (LIBOR + 1%) – LIBOR = 1% Net interest rate (DEF) = (LIBOR + 1.5%) + 9.5% – LIBOR = 11% DEF saving = 12% – 11% = 1% 19. Section 11.3 Swaps Learning Objective: 11.4 Level of difficulty: Medium Solution: C Net cash settlement actually decreases the credit risk of the interest rate swap.

20. Section 11.3 Swaps Learning Objective: 11.4 Level of difficulty: Medium Solution: B 21. Section 11.3 Swaps Learning Objective: 11.4 Level of difficulty: Medium Solution: D. The semi-annual payment from the floating rate payee is the negative of that from the fixed rate payee.

22. Section 11.4 The Financial Crisis and The Credit Default Swap Market Learning Objective 11.5 Level of difficulty: Medium Solution: D. Credit default swaps are traded over the counter.

23. Section: Appendix 11A Level of difficulty: Medium Solution: B FRAs are designed to hedge against exposure to interest rates.

Practice Problems 24. Section 11.1 Forward Contracts Learning Objective: 11.1 Level of difficulty: Medium Solution: a. To hedge the bond portfolio against changes in interest rates, Simon can use the bond futures contract. This will be a good hedge because of the very high correlation between the returns on the portfolio and the 6-percent 10-year Government of Canada bond (the notional underlying asset of the bond futures contract). As the portfolio is long on bonds, Simon would enter into a Solutions Manual ..

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short futures position to protect the portfolio against changes in interest rates. b. As the correlation is actually quite different from 1.0, there will be an imperfect hedge against interest rate risk (Simon will face basis risk) – in other words, the change in the value of the portfolio will not be exactly offset by the hedge. In the worst case, if the portfolio and the futures are not well connected Simon may, in fact, make things worse by trying to hedge. For example, the value of the portfolio may fall $1 million AND the value of the hedge may also fall by $10 million (i.e., if there is a twist in the yield curve). c. If interest rates fall, Simon expects the value of bonds to rise. To speculate on this expectation, Simon would buy bond futures – in the future when the value of the bonds rise, we will make a profit from the difference between the value of the bonds in the spot market and the futures price.

If interest rates rise, the value of bonds will fall and Simon will lose. This is the risk in speculation.

25. Section 11.1 Forward Contracts Learning Objective: 11.1 Level of difficulty: Medium Solution:

Position A B C D E F

Long Short Long Long Long Short

Number of Contracts 1 1 2 3 5 10

Today Cost Spot today (C$/US$) (C$) 1.15 $0 1.15 $0 .80 $0 1.05 $0 1.10 $0 1.00 $0

In one year Forward (C$/US) 1.20 1.20 .60 1.30 1.25 1.05

Spot (C$/US$) in one year 1.40 1.40 .65 1.20 1.41 1.30

Payoff (C$) $200 ($200) $100 ($300) $800 ($2,500)

Profit (Loss) (C$)

$100 ($300) $800 ($2,500)

Note: Because the cost of the forward contract is $0 today, the payoff and the profit will be the same. a. The profit (loss) on the contract is determined by:

= ( ST − F ) n = (1.40 − 1.20 )1 = .2 * value of contract =$200 Intuitively: If I need US$1,000 in one year and I use the forward contract, it will cost me C$1,200. If I use the spot rate in one year, it will cost me C$1,400. The profit on the forward contract is the $200 savings.

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what is the profit (loss) on the forward contract from the perspective of a U.S. investor? If the U.S. investor needs C$1,000 in one year they can use the forward contract (costs US$1,000/1.20 = US$833.33) or the spot (cost US$1,000/1.40 = US$714.29). The loss to the U.S. investor is US$119.04. b. The profit (loss) on the contract is determined by: = (F – ST)n = –(ST – F)n = – (1.40 – 1.20)1 = –0.2 × value of contract = ($200) c. The forward rate today is determined by: $100 = (0.65 – F) 2 × 1,000 F = 0.60 d. If the future spot rate is less than the forward rate, long positions lose money and short positions make money. We lost money → long position. e. The spot rate in one year is determined by: $800 = (ST – 1.25) 5 × 1,000 ST = 1.41 f. If the future spot rate is greater than the forward rate, long positions make money and short positions lose money. We lost money → short position. The number of contracts is determined by: –$2,500 = – (1.30 – 1.05) n × 1,000 n = 10 26. Section 11.1 Forward Contracts Learning Objective: 11.2 Level of difficulty: Medium Solution:

A

Spot

Cost of carry

$200

(.08*200 ) + .04*200 200 = 12%

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1 year forward 1 year price interest rate 8% F = (1 + c) S

Annual storage cost 4% of spot

= 1.12*200 = $224

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B

$235

F = (1 + c) S 285 = (1 + c)*235 c = 21.2766%

$285

19.2776%

2% of spot

C

F S= (1 + c) 300 S= 1.10 S = $272.73

.07+.03=10%

$300

7%

3% of spot

D

$350

400 −1 = 14.2857% 350

$400

4%

E

$200

(.09* 200 ) + 20  200 = 19%

$238

9%

10.2857% of spot $20 per ounce

F G

$286.41 $250

4.75% 250(0.08) + 15 = 14% 250

$300 $285

3% 8%

$5 per ounce $15 per ounce

(F) To determine the spot price:

c=

.03* S + 5 S

 .03* S + 5  F = (1 + c) S = 1 + S S   F = S + .03* S + 5 300 = 1.03S + 5 S = $286.41 (G) To determine interest rate: 285 = 250 + 250i + 15 i = .08 27. Section 11.1 Forward Contracts Learning Objective: 11.2 Level of difficulty: Medium Solution: Compare the costs and benefits of using the spot and forward markets:

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a. Using spot market: invest $15,000 to buy copper and store for a total cost in one year = $16,800 or $16.80 per kilo • investment: $15,000 • financing: .04 x 15,000 = $600 • storage: 12 x 100 = $1,200 b. Using the forward market: cost of 1,000 kg in one year: $19,000 In this case, it is cheaper to use the spot market to acquire the copper.

Actually, Health Bracelet could make arbitrage profits by buying copper today, storing the copper, and using a forward contract to sell it in one year.

28. Section 11.1 Forward Contracts Learning Objective: 11.1 Level of difficulty: Medium Solution: a. Profit (loss) long position = [ST− F] × n = [1.4 − 1.50] × C$100,000 = −$10,000 (loss) b. Profit (loss) long position = [ST − F] × n = [1.6 − 1.50] × C$100,000 = $10,000 profit 29. Section 11.1 Forward Contracts Learning Objective: 11.1 Level of difficulty: Medium Solution: a. Profit (loss) short position = [F − ST] × n = [1.50 − 1.4] × C$100,000 = $10,000 profit b. Profit (loss) short position = [F − ST] × n = [1.50 − 1.6] × C$100,000 = −$10,000 (loss) 30. Section 11.1 Forward Contracts Learning Objective: 11.1 Level of difficulty: Medium Solution: a. Because the firm has a short position in the underlying asset (i.e., euros), it should take a long position in the forward contract. To hedge itself for the full amount of its obligation, it needs to enter into a 100,000-euro forward contract. b. i. The cost in Canadian dollars = 100,000 euros × C$1.50 per euro = C$150,000 ii. The cost in Canadian dollars = 100,000 euros × C$1.50 per euro = C$150,000 Notice that the cost is the same regardless of what the six-month spot rate is— thus, the position is hedged.

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a. Because the firm has a long position in the underlying asset (i.e., euros), it should take a short position in the forward contract. To hedge itself for the full amount, it needs to enter into a 100,000-euro forward contract. b. i. The proceeds in Canadian dollars = 100,000 euros × C$1.50 per euro = C$150,000 ii. The proceeds in Canadian dollars = 100,000 euros × C$1.50 per euro = C$150,000 Notice that the proceeds are the same regardless of what the six-month spot rate is—thus, the position is hedged.

32. Section 11.1 Forward Contracts Learning Objective: 11.1 Level of difficulty: Difficult Solution: CanComp faces two main risks: a. The German firm may not pay: credit risk The Canadian dollar may have appreciated relative to the U.S. dollar (for the same number of US$, CanComp will receive fewer Canadian dollars): currency risk. b. CanComp will be long US$ in 6 months when the German firm pays. Therefore, CanComp should sell US$ (or conversely buy Canadian $) using a 6-month forward contract to counter its long US$ and short Canadian position. This will fix the CAD/US exchange rate and eliminate the currency risk. c. i) In six months, CanComp will convert its US$1.5 million into Canadian $ using the forward rate and receive 1.5m × 1.25=CAD$1.875 million. If they had not hedged, they could have converted at the spot and obtained 1.5m × 0.75=CAD$1.125 million. Therefore, the profit on the hedge is: (1.25 –.75) x 1.5million = CAD$750,000 ii) In six months, CanComp will convert its US$1.5 million into Canadian $ using the forward rate and receive 1.5m × 1.25=CAD$1.875 million. If they had not hedged, they could have converted at the spot and obtained 1.5m × 1.5=CAD$2.25 million. Therefore, the loss on the hedge is: (1.25 –1.5) x 1.5million = -CAD$375,000 d. Yes, it should hedge. At the time CanComp enters the forward contract (today) they have no idea what the exchange rate will be in the future. If they knew what the future exchange rate would be, then there would be no currency risk (by definition) and hedging is unnecessary.

Hedging decisions are made ex-ante to remove risk.

33. Section 11.1 Forward Contracts Learning Objective: 11.2 Level of difficulty: Medium Solution: I will receive R3.5 million in one year, so: Borrow the PV of R3.5 million in South Africa (this gives me Rands today) Solutions Manual ..

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Take the proceeds of the loan and convert to CAD$ (gives me CAD$ today) Lend the CAD$ for one year (will give me CAD$ in one year) My synthetic forward consists of: Borrowing R3.2710 million at a rate of 7 percent in South Africa Converting to Canadian at current spot →$1.14486 million Lending $1.14486 million at a rate of 3 percent in Canada (giving me $1.17921 million in one year).

Regardless of the spot rate prevailing in one year, I will have CAD$1.17921 million. I will have eliminated the currency risk by borrowing in South Africa, converting to CAD$, and lending in Canada.

34. Section 11.1 Forward Contracts Learning Objective: 11.2 Level of difficulty: Difficult Solution: a. Bert has not taken into account the link between the spot and the forward price. If the forward price increases and the spot and cost of carry don’t change, then there is an arbitrage opportunity.

For example, the spot price is $100 and the cost of carry is 10 percent. The theoretical forward price is $110.

If only the forward price changes to $200 due to the change in supply in the future, an investor can do the following transaction: Buy 1 unit of oil for $100, store it for 1 period; total spent by the end of 1 period: $110 Today, sell 1 unit of oil in forward market for $200.

In one year, take the stored oil and deliver it to satisfy the forward contract; guaranteed profit = $90, risk zero.

The result of people doing this type of transaction → spot price will rise b. In this question, the impact is on the cost of carry and the spot price. Once again, we will have a difference between the theoretical and observed forward price (theoretical will be greater than forward).

For example, before hurricane Katrina the spot price is $100 and the cost of carry is 10 percent.

The theoretical forward price is $110. After hurricane Katrina, the spot price is now $200 and the cost of carry is 25 percent. Now the theoretical forward price is $250, however, the observed forward price is still only $110. Consider an oil company in Alberta that has oil and under normal conditions would have stored it for future delivery.

Now, post hurricane Katrina, the oil company can: Sell oil today at $200.

Buy oil using a forward contract at $110 (if it had kept its oil and stored it, the opportunity cost would have been $250>$110).

Net effect: the forward price of oil will rise due to the change in conditions in the spot market.

35. Section 11.2 Futures Contracts Solutions Manual ..

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Learning Objective: 11.3 Level of difficulty: Easy Solution: Each day, any profits and losses will be credited to an investor’s account to calculate the equity balance. The investor may withdraw the profits, or on the other hand, he has to contribute more money to keep his equity above the maintenance margin after he receives a margin call.

36. Section 11.2 Futures Contracts Learning Objective: 11.3 Level of difficulty: Easy Solution: The number of futures contracts outstanding represents open interest, which reflects the true amount of futures market activity. When a buyer and a seller enter into a futures contract, there is only one contract counted as open interest.

37. Section 11.2 Futures Contracts Learning Objective: 11.3 Level of difficulty: Medium Solution: Forwards Contracts Customized Trading Dealer or OTC Markets Default (credit) risk Important Initial deposit

Not required

Settlement

On maturity date

Futures Standardized Exchanges Unimportant—guaranteed by clearinghouse Initial margin and maintenance margin required Marked to market daily

38. Section 11.2 Futures Contracts Learning Objective: 11.3 Level of difficulty: Medium Solution: Basis risk is the risk associated with a hedged position that is attributable to the fact that the asset to be hedged is not identical to the asset used as the hedge. As a result, it may be impossible to create a perfectly hedged position because changes in the price of the underlying asset in the contract will not move in a totally predictable manner with respect to changes in the price of the asset position to be hedged. One of the advantages of forward contracts is that they can be structured to minimize (or even eliminate) basis risk. This is because, unlike futures contracts, forwards are not standardized and can therefore be tailor-made with respect to underlying assets and maturity dates.

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39. Section 11.3 Swaps Learning Objective:11.4 Level of difficulty: Easy Solution One counterparty has a comparative advantage in the fixed rate market. In contrast, the other firm has a comparative advantage in borrowing in the floating rate market.

40. Section 11.2 Futures Contracts Learning Objective: 11.3 Level of difficulty: Medium Solution:

Day 0 1 2 3 4 5

Spot price $100 $75 $50 $80 $130 $100

Ethel Daily profit (loss) ($25,000) ($25,000) $30,000 $50,000 ($30,000)

Equity position (margin balance) $30,000 $5,000 –$20,000 $10,000 $60,000 $30,000

Egbert Daily profit (loss) $25,000 $25,000 ($30,000) ($50,000) $30,000

Equity position (margin balance) $30,000 $55,000 $80,000 $50,000 $0 $30,000

41. Section 11.2 Futures Contracts Learning Objective: 11.3 Level of difficulty: Medium Solution: Day 0 1 2 3 4 5

Spot price 20.00 20.50 20.75 21.00 19.75 19.25

Daily profit 0 25,000 12,500 12,500 -62,500 -25,000

Equity position (margin balance) 50,000 75,000 87,500 100,000 37,500 12,500

42. Section 11.2 Futures Contracts Learning Objective: 11.3 Level of difficulty: Medium Solution:

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Day 0 1 2 3 4 5

Spot price 20.00 20.50 20.75 21.00 19.75 19.25

Daily profit 0 -25,000 -12,500 -12,500 62,500 25,000

Booth, Cleary

Equity position (margin balance) 50,000 25,000 12,500 0 62,500 87,500

43. Section 11.2 Future Contracts Learning Objective: 11.3 Level of difficulty: Medium Solution:

Day

Spot price

Daily profit (loss)

0 1 2 3 4 5

$100 $92 $95 $103 $90 $100

0 −$8,000 3000 8000 -13000 10000

Equity position before cash deposit $0 $22,000 $25,500 $33,500 $20,500 $32,500

Margin call?

Cash deposit

No Yes No No Yes No

$30,000 $500 0 0 2000 0

Net pay % 0% .5% –.5% –1.5%

Net pay $ $0 $5,000 –$5,000 –$15,000

Equity position (margin balance) $30,000 $22,500 $25,500 $33,500 $22,500 $32,500

44. Section 11.3 Swaps Learning Objective: 11.4 Level of difficulty: Medium Solution: Start of Period 1 2 3 4

LIBOR % 4% 5% 3% 1%

Floating pay % 3% 3.5% 2.5% 1.5%

Fixed pay % –3% –3% –3% –3%

45. Section 11.3 Swaps Learning Objective: 11.4 Level of difficulty: Difficult Solutions Manual ..

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Solution: a. As Anthony’s income is very closely tied to market interest rates, he would prefer the floating rate mortgage. An increase in mortgage payments would occur at the same time as his income rises; and conversely, a decrease in his income would occur at the same time as a decrease in mortgage payments.

Joyce, in contrast, has an income that is fixed so a floating rate mortgage would expose her to interest rate risk. A fixed rate mortgage would remove the risk (at least until the mortgage has to be renegotiated). b. i) My swap agreement calls for Joyce to pay a fixed rate of 5 percent and receive the rate of prime + 2 percent on a notional value of $100,000. I’m assuming that Anthony is able to obtain some benefits from his higher credit quality. ii) This is called a plain vanilla interest rate swap. Anthony will pay the floating rate to Joyce who will pay the fixed rate to Anthony.

The two parties to this swap are exposed to credit risk – one may default (i.e., not make the promised payment). One way that has evolved to limit this risk is to only pay the net amount—this means that if one party defaults, the other only loses the net difference. iii) 1.

The net cash flows for Joyce (the fixed payer): Start of Period

PRIME Floating % pay %

1 2 3 4

3% 5% 4% 2%

5% 7% 6% 4%

Fixed pay % -5% -5% -5% -5%

Net pay % 0% 2% 1% -1%

Net pay on swap $ $0 $2,000 $1,000 -$1,000

The net cash flows for Anthony (the fixed receiver): Start of Period

PRIME Floating % pay %

1 2 3 4

3% 5% 4% 2%

-5% -7% -6% -4%

Fixed pay % 5% 5% 5% 5%

Net pay % 0% -2% -1% 1%

Net pay on swap $ $0 -$2,000 -$1,000 $1,000

iii) 2.

Joyce Net cash Period flows from Solutions Manual ..

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Total cash flows Cash flows if (floating + obtained desired 14

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swap

mortgage

swap)

$0 $2,000 $1,000 -$1,000

-$6,000 -$8,000 -$7,000 -$5,000

-$6,000 -$6,000 -$6,000 -$6,000

fixed mortgage (no swap) -$7,000 -$7,000 -$7,000 -$7,000

swap $1,000 $1,000 $1,000 $1,000

Anthony Net cash Period flows from swap

Cash flows on mortgage

Total cash flows by individual under swap

1 2 3 4

-$3,000 -$3,000 -$3,000 -$3,000

-$3,000 -$5,000 -$4,000 -$2,000

$0 -$2,000 -$1,000 $1,000

Cash flows if obtained desired floating mortgage (no swap) -$4,000 -$6,000 -$5,000 -$3,000

Gain from swap $1,000 $1,000 $1,000 $1,000

We can see in the above tables that obtaining a mortgage and then swapping to obtain the desired type of cash flows was cheaper (both ended up paying less—sharing in Anthony’s credit worthiness) than directly obtaining the desired type of mortgage. Basically, Anthony gave part of his benefits of credit worthiness to Joyce in return for obtaining his desired pattern of cash flows.

46. Section 11.3 Swaps Learning Objective: 11.4 Level of difficulty: Difficult Solution:

ABC Inc. DEF Inc. Spreads

Fixed rate 9.5% 12% 2.5%

Floating rate L + 1% L + 1.5% 0.5%

The spread in spreads 2.5% – 0.5% = 2% The spread in spreads is, in principle, shared between the two parties, i.e., 1 percent for each in this case.

ABC Inc. has the absolute advantage in borrowing both at the fixed rate and floating rate markets because 9.5% < 12% and (L + 1%) < (L + 1.5%).

ABC Inc. has the comparative advantage in borrowing at the fixed rate, while DEF Inc. has the comparative advantage in borrowing at the floating rate because 2.5% > 0.5%.

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47. Section 11.3 Swaps Learning Objective: 11.4 Level of difficulty: Difficult Solution: To deal with this question, I need to determine my exposures. In one year I will be: Short (owe) €103.5 million Long 1 million ounces of gold Long US$ (after I sell my gold) To determine the best way of hedging the two risks, we will consider two strategies and see which gives us the best results (all contracts are for one year): Strategy 1: Short CAD/€ (buy €, sell CAD); short 1 million oz. gold, long CAD/US (buy CAD, sell US$) Details: Sell CAD $165.6 million at 1.60 CAD/€ Will have to deliver CAD$165.6 million in one year to repay debt of €103.5 million Sell 1 million oz. of gold at US$250 per oz.

Will receive US$250 million in one year Sell US$250 million at 1.05 CAD/US Will receive CAD$262.50 million NET EFFECT: receive $96.90 million Canadian (262.5 – 165.6) in one year Strategy 2: Short US/€ (buy € with US$), short 1 million oz. gold, long CAD/US (buy CAD, sell US) Details: Sell US$113.85 million at 1.10 US/€ Will have to deliver US$ 113.85 million to repay € debt Sell 1 million oz. of gold at US$250 per oz.

Will receive US$250 million in one year Sell US$136.15 million at 1.05 CAD/US. Proceeds of gold sale less US$ used to repay debt Will receive CAD$142.9575 NET EFFECT: receive $142.9575 million Canadian in one year The reason for this result is that there is an arbitrage opportunity in the forward currency markets—in a real market, we would not expect to see this occur.

48. Section 11.3 Swaps Learning Objective: 11.4 Level of difficulty: Difficult Solution: One way that swaps, especially currency swaps, can make both parties better off is by improving the allocational efficiency of the market. Remember, we talked about different types of Solutions Manual ..

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efficiency—operational, allocational, and informational efficiency. A currency swap allows two parties to enter into what is effectively a series of forward rate agreements for a custom set of dates and currencies. The swap can have a longer term than a bank may be willing to offer on forward contracts, thereby allowing both firms to better manage their risk. The swap will improve the allocational efficiency of the market by either offering a new security or a cheaper way of buying a set of forward contracts.

Interest rate swaps allow firms to benefit from their comparative advantage in borrowing. The comparative advantage could arise from a lack of information in the debt market (remember much of this market is over-the-counter), firms’ private information about each other, etc. We also see in the history of the swap market that the huge benefits obtained in the early 1980s have largely disappeared as the swap market has become more efficient and information about the market has become more available to participants.

49. Section 11.4 The Financial Crisis and the Credit Default Swap Market Learning Objective: 11.5 Level of difficulty: Easy Solution: In the total return swap, one party receives a fixed or floating rate on a notional amount, while another party receives the total return (capital gain/loss + interest/dividends) from a reference asset, such as the S&P500 index or the TSX 60 index.

50. Section 11.4 The Financial Crisis and the Credit Default Swap Market Learning Objective: 11.5 Level of difficulty: Medium Solution: There are two big differences between a CDS and insurance. First, the risk attached to regular insurance, such as house or car insurance, is essentially random since the risk depends on factors unique to an individual. As a result, by pooling several of these unique risks, the insurer’s exposure becomes predictable. In contrast, for a CDS the underlying risk depends on the economy, as defaults tend to be clustered during a slowdown or recession, when individuals and companies are more likely to reorganize or go bankrupt. As a result, CDS contracts have market risk.

The second problem is that the CDS market is simply part of the swaps market, and, as an OTC market, everything depends on the two counterparties fulfilling their promise. Unlike a heavily regulated insurance company that is required to keep reserves to ensure it can fulfill its promises, in the swap market this risk is mitigated by restricting counterparty risk to large stable financial companies, such as American International Group (AIG), and requiring them to put up “margin” or other collateral should their financial health decline. However, these measures proved inadequate simply because of the size of the market and the limited number of major participants.

51. Appendix 11A Learning Objective 11.6 Solutions Manual ..

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Level of difficulty: Medium Solution: 1 year forward rate expected in

Implied one year forward rate %

1 year

(1.05) − 1 = 7.0388% F = 2

2

1.03

2 years

(1.07 ) − 1 = 11.1150% F3 = 2 (1.05)

3 years

(1.06 ) − 1 = 3.0557% F4 = 3 (1.07 )

4 years

(1.05) − 1 = 1.0935% F5 = 4 (1.06 )

5 years

Cannot be determined

3

4

5

52. Appendix 11A Learning Objective 11.6 Level of difficulty: Medium Solution:

(1 + 2.65%) 2 = (1 + 2.10%)  (1 + F1 ) F1 = 3.20%

(1 + 3.25%)3 = (1 + 2.65%) 2 (1 + F2 ) F2 = 4.46% (1 + 3.75%) 4 = (1 + 3.25%)3  (1 + F3 )

F3 = 5.26% 53. Appendix 11A Learning Objective 11.6 Level of difficulty: Difficult Solution: a. At the end of year 2, bond C will have one year to maturity. To obtain the price of bond C at the end of year 2, we need the implied forward rate for year 3 (end of year 2 to end of year 3).

The implied forward rate is:

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(1.10 ) − 1 = 16.2547% F3 = 2 (1.07 ) 3

The value of bond C will be $1,000/1.162547 = $860.18 b. This bond will have coupons at the end of years 1, 2, and 3. The cash flows in years 1 and 2 are $70 and the cash flow at the end of year 3 is $1,070. We need to discount each cash flow back to today at the appropriate rate. The easiest way to solve this is to synthetically create this coupon bond by buying: 7 percent of bond A, 7 percent of bond B, and 107 percent of Bond C—the price of the new bond must equal the sum of these three components. If not, we have an arbitrage opportunity. The price of the new bond is then:

P = .07 PA + .07 PB + 1.07 PC  1000   1000   1000  = .07  + .07 + 1.07       (1.07 )2   (1.10 )3   1.05      = 66.6667 + 61.1407 + 803.9068 = $931.7142

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Chapter 12: Options Multiple Choice Questions 1. Section: 12.1 Call Options Learning Objective: 12.1 Level of Difficulty: Easy Solution: B A call option is in the money if the asset price is greater than the strike price.

2. Section: 12.1 Call Options Learning Objective: 12.1 Level of Difficulty: Medium Solution: B Time value = Market value – Intrinsic value = $19 – $13 = $6 The market value of the option is usually called the option premium, not option price.

3. Section: 12.1 Call Options Learning Objective: 12.1 Level of Difficulty: Medium Solution: C The value of a call option is positively related to the price of the underlying asset, the remaining time to expiration, and the volatility of the price of the underlying asset, but is negatively related to the dividend paid if the underlying asset is a company’s stock.

4. Section: 12.2 Put Options Learning Objective: 12.2 Level of Difficulty: Medium Solution: D Put option prices are positively related to the strike price, time to expiration, the volatility of the underlying asset price, and dividend payments (as dividend payments increase, put prices increase).

Put option prices are negatively related to the underlying asset price and interest rates.

5. Section: 12.3 Put-Call Parity Learning Objective: 12.3 Level of Difficulty: Medium Solution: D According to put-call parity: C +

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X = P+S (1 + r ) t

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We can rewrite it as

Booth, Cleary

X = P + S −C (1 + r ) t

This means that you could create a loan by doing the following: Long a put, long the underlying asset, and short a call.

6. Sections: 12.1 Call Options and 12.2 Put Options Learning Objective: 12.1 and 12.2 Level of Difficulty: Medium Solution: B IVPut = Max(X – S, 0) = Max[(45 –40), 0] = 5 IVCall = Max(S – X, 0) = Max[(40 –45), 0] = 0 7. Sections: 12.1 Call Options and 12.2 Put Options Learning Objective: 12.1 and 12.2 Level of Difficulty: Medium Solution: B Recall the payoff diagrams of the call buyer, call writer, put buyer, and put writer. Their maximum profits/losses are as follows (C0 and P0 are the option premiums.): Buy a call: Maximum profit = +∞; Maximum loss = C0 Short a call: Maximum profit = +C0; Maximum loss = ∞ Buy a put: Maximum profit = X– P0; Maximum loss = P0 Short a put: Maximum profit = +P0; Maximum loss = X–P0 Clearly, short a call is the most risky.

8. Section: 12.4 Option Pricing Learning Objective: 12.4 Level of Difficulty: Medium Solution: C N(d1) is the cumulative probability of being in the money.

9. Section: 12.5 Options Markets Learning Objective: 12.1 and 12.5 Level of Difficulty: Medium Solution: D A is incorrect because the market maker’s profit should be the spread between the bid and ask, which is 2.05 – 1.85 = 0.20.

B is incorrect because Put B IV = Max [(X–S), 0] = 1. Therefore time value = (1.10 + 1.35)/2 – 1 = 0.225.

C is incorrect because the time value for a put is usually lower than that for a call in that expected rates of return are positive and prices are expected to increase.

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Only D is correct.

10. Section: Appendix 12A Binomial Option Pricing and Risk-Neutral Probabilities Level of Difficulty: Medium Solution: C. PU − PD 52 − 45 h= = = 1.75 PU − S 52 − 48 11. Section: Appendix 12A Binomial Option Pricing and Risk-Neutral Probabilities Level of Difficulty: Medium Solution: A A hedge ratio of 1/3 means short one call to hedge a long position of three units of the underlying asset.

12. Section: Appendix 12A Binomial Option Pricing and Risk-Neutral Probabilities Level of Difficulty: Medium Solution: B The actual probability of an asset price going up and down is not the risk-neutral probability.

Practice Problems 13. Sections: 12.1 Call Options and 12.2 Put Options Learning Objective: 12.1 and 12.2 Level of Difficulty: Medium Solution:

A B C D

Position Long Index Short Index Long Call Short Call

Series 6 3 2 5

Position E Long Put F Short Put G Long Bond H Short Bond

Series 4 8 1 7

14. Sections: 12.1 Call Options and 12.2 Put Options Learning Objective: 12.1, and 12.2 Level of Difficulty: Medium Solution:

Long or Short Long

At expiration Value of Value of Payoff Call or Strike Profit option underlying (intrinsic Put price (loss) today asset value) Call 150 5 175 25 20

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Short Long Short Long Short Long Short

Call Put Put Call Call Put Put

150 150 150 175 175 175 175

5 5 5 5 5 5 5

Booth, Cleary

175 110 110 150 150 200 200

-25 40 -40 0 0 0 0

(20) 35 (35) (5) 5 (5) 5

15. Sections: 12.1 Call Options and 12.2 Put Options Learning Objective: 12.1 and 12.2 Level of Difficulty: Medium Solution:

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16. Sections: 12.1 Call Options and 12.2 Put Options Learning Objective: 12.1 and 12.2 Level of Difficulty: Medium Solution: Call option prices are positively related to the price of the underlying asset, the volatility of the price of the underlying asset, the time to expiration, and increase in interest rates, but negatively related to the strike price and the dividend payment of the underlying asset. Call option prices approach their intrinsic value for deep in and deep out of the money calls.

Put option prices are positively related to the strike price, time to expiration, dividend payments (as dividend payments increase, put prices increase), and the volatility of the underlying asset price.

Put option prices are negatively related to the underlying asset price and interest rates.

17. Section: 12.1 Call Options Learning Objective: 12.1 Level of Difficulty: Medium Solution: Solutions Manual ..

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Possible explanations: 1) The two stocks have different risks; the price of a call, holding all else equal, increases with risk.

2) The prices of the two stocks are different; call prices increase with the price of the underlying asset.

3) The dividend payments of the two stocks are different; call prices decrease as dividend payments increase.

18. Sections: 12.1 Call Options and 12.2 Put Options Learning Objective: 12.1 and 12.2 Level of Difficulty: Medium Solution: a. The individual securities: Long Call(X=25), long put(X=20) 12 10 8 6 4 2 0 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

Call(X=25)

Put(X=20)

The portfolio: Long Call(X=25), long put(X=20) 12 10 8 6 4 2 0 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

Portfolio

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b. The individual securities: Short 1 call(X=25), long 1 put(X=15) 15 10 5 0 5

10

15

20

25

Call(X=25)

Put(X=15)

30

35

30

35

-5

-10 -15

The portfolio: Short 1 call(X=25), long 1 put(X=15) 15 10 5 0 5

10

15

20

25

-5 -10 -15 Portfolio

c. The individual securities:

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Long call(X=25), short put(X=25) 20 15 10

5 0 -5

10

15

20

25

30

35

40

35

40

-10 -15 -20 Call(X=25)

Put(X=15)

The portfolio: Long call(X=25), short put(X=25) 20 15 10 5 0 -5

10

15

20

25

30

-10 -15 -20 Portfolio

Note: the value of the portfolio is the same as being long a share. d. The individual securities:

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Long Call(X=25); short stock 20 10 0 -10

10

15

20

25

30

Call(X=25)

Short stock

35

40

-20 -30 -40 -50

The portfolio: Long Call(X=25); short stock 0 10

15

20

25

30

35

40

-5 -10 -15

-20 -25 -30 Portfolio

e. The individual securities and the portfolio:

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Note: the portfolio payoff diagram is the same as a put. f. The individual securities and the portfolio: Long put(X=25), long stock, short $25 cash 50 40 30

20 10 0 10

15

20

25

Put(X=25)

Stock

30

35

40

-10 -20 -30 Cash

Portfolio

Note: the portfolio graph is the same as the payoff diagram for a call.

19. Sections: 12.1 Call Options and 12.2 Put Options Learning Objective: 12.1 and 12.2 Level of Difficulty: Medium Solution: Solutions Manual ..

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To understand what the investor is thinking we need to determine when the portfolio of 1 call and 1 put will be profitable. Below is the graph of the payoffs (assuming that the strike price is $25 for convenience).

Portfolio Payoff

16 14 12 10 8 6 4 2 0 10

15

20

25

30

35

40

Portfolio

Examining the payoff diagram, we see that the portfolio only makes money if the value of the S&P/TSX is above or below the strike price. Therefore, the investor is expecting the S&P/TSX to be either above or below the strike price—essentially, she is expecting volatility in the market.

20. Sections: 12.1 Call Options and 12.2 Put Options Learning Objective: 12.1 and 12.2 Level of Difficulty: Difficult Solution:

Long or Short A B C D E F G H

Long Long Short Short Long Short Long Long

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Value Call Value of Strike of or underlying price option Put asset today Put 80 .05 80 Call 80 2.00 81 Put 80 .05 79 Call 80 .05 81 Call 99 1.00 125 Put 124 2.00 125 Put 25 2.00 95 Call 25 2.00 95

In/Out of the money At In In In In Out Out In 11

Payoff (intrinsic value of option) 0 1 -1 -1 26 0 0 70

Profit (loss) -.05 -1 -.95 -.95 25 2 -2 68 Chapter 12

Introduction to Corporate Finance, Third Edition

I J K L M N

Long Short Short Long Short Short

Call Put Call Put Call Put

75 75 75 75 110 80

13.00 2.00 5.00 2.00 2.00 3.00

Booth, Cleary

90 90 90 90 <=110 55

In Out In Out At/Out In

15 0 -15 0 0 -25

2 2 -10 -2 2 -22

Notes for solutions: When an option is at the money, the long holder makes a loss equal to the cost of the option and the short position makes a profit equal to the cost (the price at which they originally sold the option).

When an option is out of the money, the long holder makes a loss equal to the cost of the option while the short position makes a profit equal to the cost of the option.

When an option is in the money, the long holder’s profit is equal to the intrinsic value less the cost of the option while the short position makes a loss equal to the intrinsic value less the sale price of the option (their loss is reduced by the sale price of the option).

21. Sections: 12.1 Call Options and 12.2 Put Options Learning Objective: 12.1 and 12.2 Level of Difficulty: Difficult Solution: Mr. Kent is confusing long and short option positions. The holder of a call option has the choice of exercising the call and will only do so if the price of the stock is greater than the strike price.

In contrast, the seller of the put will have to buy the stock from the holder when the holder chooses. The holder of the put will only choose to exercise when the stock price is less than the strike price.

The payoffs to the two positions are summarized below:

S>X S=X S<X

Payoffs Long Call Short Put >0 0 0 0 0 <0

Given the differences in the pattern of payoffs, there is no reason to require the price of a put and a call to be the same.

22. Sections: 12.1 Call Options and 12.2 Put Options Learning Objective: 12.1 and 12.2 Level of Difficulty: Difficult Solutions Manual ..

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Solution: Since you don’t expect the price to go above $105, you should write a call option with an exercise price of $105 or more and since you don’t expect the price to fall below $95, you should write a put option of $95 or less and earn the premiums.

23. Sections: 12.1 Call Options and 12.2 Put Options Learning Objective: 12.1, 12.2 Level of Difficulty: Medium Solution: a. To compare the prices of the options, we need to compare the cash flows of every possible state of the world. Let S* denote the price of the underlying stock at expiration of the options.

S*≤30 0 0 0 0

strategy 1. Buy C1 2. Buy C2 3. Buy C3 4. Buy C4

Cash flows at expiration 30<S*≤40 40<S*≤60 60<S*≤70 0 0 S*-60 0 0 0 0 S*-40 S*-40 S*-30 S*-30 S*-30

S*>70 S*-60 S*-70 S*-40 S*-30

C4 is the most valuable, because, for every possible state of the world (value of S*), it pays at least as much as the other options. Ranking the options by considering their payoffs in each state, we find that C4≥C3≥C1≥C2. Note that this is also in ascending order of strike prices implying that the price of a call increases as the strike price decreases. b.

Action Buy stock buy call Total cash flow Profit c.

Cash flow Cash flow at expiration today S*≤40 S*>40 -50 S* S* C3 0 S*-40 -50-C3

Action Cash flow today Short sell stock 50 Buy 2 calls -2C2 Total cash flow 50-2C2 Solutions Manual ..

S* S*-50-C3

2S*-40 2S*-90-C3

Cash flow at expiration S*≤70 S*>70 -S* 0

-S* 2(S*-70)

-S*

S*-140 13

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Profit d.

Booth, Cleary

-S*+50-2C2

Cash today

Action Buy stock Write 2 calls Total cash flow Profit

S*-90-2C2

flow Cash flow at expiration S*≤30 S*>30 -50 S* S* 2C4 0 2(30-S*)

-50+2C4

S* S*-50+2C4

60-S* 10-S*+2C4

24. Section: 12.1 Call Options Learning Objective: 12.1 Level of Difficulty: Medium Solution: We must first compare the cash flows at expiration of both securities. Define X as the strike price of the call, then in the following table, we see that in every state the cash flow from the stock is greater than the cash flow from the option. Therefore, the value of the stock today must be greater than the value of the option today.

strategy Buy stock Buy call

Cash flow at expiration Cash flow today S*≤X S*>X -S S* S* -C 0 S*-X

25. Section: 12.3 Put-Call Parity Learning Objective: 12.3 Level of Difficulty: Medium Solution:

A B C D E F

XCT stock Price of call price 90 24.57 120 15.15 22.73 85 130

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30 3 5 25 25

Price of put 6 5.24 2 5 30 20

75

Riskfree rate 5%

100 15 25 90 131.25

5% 6% 10% 0.00% 5%

Strike price

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(A) Solving for the price of the call: C = P +S – PV(X) = 6+90-75/1.05 = $24.57 (B) Solving for the price of the put: P = C – S + PV(X) = 30 – 120 + 100/1.05 = $5.24 (C) Solving for the stock price: 15 S = C − P + PV(X) = 3 − 2 + = $15.15 1.06 (D) Solving for the stock price: 25 S = C − P + PV ( X ) = 5 − 5 + = $22.73 1.10 (E) Solving for the risk-free rate: 85 = 25 – 30 + 90/(1+r) 90 = 90/(1+r) 1 + r = 90/90 = 1 r = 0% (F) Solving for the strike price: 130 = 25 − 20 + PV(X) = 25 − 20 +

X 1.05

X 1.05 X = $131.25

125 =

26. Section: 12.4 Option Pricing Learning Objective: 12.4 Level of Difficulty: Medium Solution: Using Appendix I to compute N(d1) and N(d2):

A B C D E F

S 100 100 100 100 100 99

X 98 98 98 99 98 98

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r 0.02 0.02 0.03 0.02 0.02 0.02

σ t 0.03 1 0.04 1 0.03 1 0.03 1 0.03 0.3 0.03 1

d1 1.36 1.02 1.68 1.02 1.6 1.02

N(d1) 0.9131 0.8461 0.9535 0.8461 0.9452 0.8461

d2 1.32 0.98 1.66 0.98 1.58 1 15

N(d2) 0.9066 0.8365 0.9515 0.8365 0.9429 0.8414

Xe-rt 96.05946998 96.05946998 95.10366229 97.03966866 97.41376048 96.05946998

Call 4.222485 4.256253 4.858865 3.436317 2.668565 2.939462 Chapter 12

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Using Excel to compute N(d1) and N(d2):

A B C D E F

S 100 100 100 100 100 99

X 98 98 98 99 98 98

r 0.02 0.02 0.03 0.02 0.02 0.02

σ t d1 0.03 1 1.35509 0.04 1 1.025068 0.03 1 1.688424 0.03 1 1.016678 0.03 0.3 1.602862 0.03 1 1.020079

N(d1) 0.912306 0.847334 0.954335 0.845347 0.945517 0.846155

d2 1.32509 0.985068 1.658424 0.986678 1.58643 0.990079

N(d2) Xe-rt Call 0.9074294 96.05947 4.063373 0.8377046 96.05947 4.263979 0.951384 95.103662 4.9534 0.8380997 97.039669 3.205747 0.9436791 97.41376 2.62441 0.8389323 96.05947 3.181909

27. Section: 12.3 Put-Call Parity Learning Objective: 12.3 Level of Difficulty: Medium Solution:

C+

X = P+S (1 + r ) T

P=C+

X 33 − S ; 10 + − 30 = 7.15 T (1 + r ) (1.05) 4

7.15≠13, therefore put-call parity does not hold.

According to put-call parity, P = $7.15 28. Section: 12.4 Option Pricing Learning Objective: 12.4 Level of Difficulty: Easy Solution: Delta (Δ) is the change in the price of the option with the change in the underlying asset price.

Theta (θ) is the change in the option value with time.

Vega is the change in the option value with respect to the volatility of the underlying asset.

Rho (ρ) is the change in the option value with respect to a change in the interest rate.

29. Section: 12.4 Option Pricing Learning Objective: 12.4 Level of Difficulty: Medium Solution: Using Excel to compute N(d1) and N(d2):

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d1 =

LN ( S / X ) + (r +  2 / 2)t

 t

=

Booth, Cleary

LN (36 / 32) + [0.05 + (0.2  0.2 / 2)]2 0.2 2

= 0.9114

d 2 = d1 −  t = 0.9114 − 0.2  2 = 0.6286 N (d1 ) = 0.8190 N (d 2 ) = 0.7352 C = SN (d1 ) − Xe −rt N (d 2 ) = 36  0.8190 − 32  e −0.052  0.7352 = 8.20 Using Appendix I to compute N(d1) and N(d2): S 36

X r 32 0.05

σ 0.2

t 2

d1 N(d1) d2 N(d2) Xe-rt Call 0.92 0.8212 0.62 0.7324 28.95479738 8.356706

30. Section: 12.1 Call Options Learning Objective: 12.1 Level of Difficulty: Easy Solution Using Excel premium: Intrinsic value = Premium – Time value = 8.20 – 5.00 = $3.20 Using Appendix I premium: Intrinsic value = Premium – Time value = 8.3567 – 5.00 = $3.3567 31. Section: 12.3 Put-Call Parity Learning Objective: 12.3 Level of Difficulty: Medium Solution using the Excel Call price: Using put call parity:

P=C+

X e

rt

32

− S ; 8.20 + e

0.052

− 36 = $1.1548

Note that the risk-free rate used in the Black-Scholes model is continuously compounded.

Solution using the Appendix I Call price: Using put-call parity: X 32 P = C + rt − S ; 8.3567 + 0.052 − 36 = $1.3115 e e 32. Section: 12.4 Option Pricing And Deriving the Put-Call Parity Relationship Learning Objective: 12.3 and 12.4 Level of Difficulty: Medium Solution: Using the Black-Scholes option pricing model: Solutions Manual ..

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d1 =

LN ( S / X ) + (r +  2 / 2)t

 t

=

Booth, Cleary

LN (45 / 50) + [0.05 + (.5 / 2)].5 0.7071 .5

= 0.0893

d 2 = d1 −  t = 0.0893 − 0.7071 .5 = −0.4107 N (d1 ) = 0.5356 N (d 2 ) = 0.3406 C = SN (d1 ) − SX −rt N (d 2 ) = 45  0.5356 − 50  e −0.05.5  0.3406 = 7.49 Then use put-call parity to get the value of the put option 𝑃 = 𝐶 − 𝑆 + 𝑃𝑉(𝑋) = 7.49 − 45 +

50 = 11.29 1.050.5

33. Section: 12.3 Put-Call Parity Learning Objective: 12.3 Level of Difficulty: Medium Solution: To solve this problem, we need to first determine the desired cash flows (i.e., What would the cash flows be if we owned a call with a strike price of $125?).

Action Desired cash flows from synthetic call Buy stock Borrow PV(85) Stock + loan

Cash flow today ?

-100.00 80.95

Future value of stock $85 $135 0 $10 85 -85 0

135 -85 50

The portfolio of a stock and a short bond gives us the same pattern as the call; however, it pays $50 in the up state, not $10. So if we buy 1/5 of a stock and borrow 1/5 of $80.95, we will have the same payoffs as the desired call.

Action

Cash flow today

Desired cash flows from synthetic call Buy 1/5 stock Borrow 1/5 PV(85) Stock + loan

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-20.00 16.19 -3.81

18

Future value of stock $85 $135 0 $10 17 -17 0

27 -17 10

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We see from the above table that the proposed portfolio of long 1/5 of a share and short 1/5 of the PV(85) will exactly replicate the cash flows from the desired call option. The cost of the replicating portfolio is $3.81 (the cash flow is negative meaning that you will be paying $3.81 to acquire the portfolio).

34. Section: 12.4 Option Pricing Learning Objective: 12.3 and 12.4 Level of Difficulty: Difficult Solution: a. Given my compensation, I definitely do not want the portfolio value to drop below $90 billion.

I don’t really care if the value rises above $120 billion (I don’t earn any more money).

To protect the downside, I will buy put options on the index with a strike price of $900. The strike price corresponds to the 10% decline in the value of the portfolio. For every $1 the portfolio drops below $90 billion, the put will pay $1. I’m taking advantage of the fact that the portfolio is very well diversified and has a beta very close to one. If the beta is not close to one, or I’m very risk averse, I may want to have a strike price a little higher than $900.

To finance the puts, I will sell call options with a strike price of $1,200. If the value of the portfolio rises above $120 billion, the gain on the portfolio will be used to cover the loss on the puts. I don’t mind giving up the gain above $120 billion as my compensation doesn’t change if the portfolio value is greater than $120 billion. b. To determine the value of the call (strike=1200) we will use Black-Scholes. To determine the value of the put, we will begin by using the Black-Scholes formula to find the value of a call with a strike of $900 and then use the put-call parity relationship. Using Excel to compute N(d1) and N(d2): S

X

r



T

d1

d2

N ( d1 )

N (d 2 )

Call value

1000 1000

900 1200

3% 3%

0.1 0.1

1 1

1.4036 -1.4732

1.3036 -1.5732

0.9198 0.0703

0.9038 0.0578

130.3881 2.9962

Using put-call parity, we find that the value of the put with a strike of $900 is $3.789

130.3881 − 1000 +

900 e.03x1

= 3.789

With the $100 multiplier and an index value of 1,000, each option will protect $100,000 of value.

As the portfolio has a value of $100 billion, we will need to use 1 million puts and calls.

The cost of the puts: $3.789 million. The proceeds of the sale of the calls: $2.9962 million. The total impact on the portfolio is a cost of $792,800.

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35. Section: 12.3 Put-Call Parity Learning Objective: 12.3 Level of Difficulty: Easy Solution: Using put-call parity, S = C + PV(X) –P = 10 +50/1.05 – 2 = $55.62 36. Section: 12.3 Put-Call Parity Learning Objective: 12.3 Level of Difficulty: Difficult Solution: a. Set up a portfolio consisting of M shares of MCD and S shares of SB such that the cash flows to the portfolio match those of BK provided in the table. If the cost of the portfolio is not the same as the price of BK then there is an arbitrage opportunity.

State 1 State 2

25M+10S 20M+25S

Eq(1)*(-2.5) -62.5M–25S +Eq(2) 20M+25S -42.5M

= =

75 17.50

= = =

-187.50 17.50 -170

Eq(1) Eq(2)

By using the lowest common denominator to multiply through, we find that M= 4, and by substituting back in Equation 1, we find that S= -2.5. Therefore, the replicating portfolio consists of a long position in 4 shares of MCD and short position of 2.5 shares of SB. This portfolio costs (4*15) + (-2.5*5)=$47.5, while 1 share of BK costs $3. Therefore, there is an arbitrage opportunity and we can conclude that the shares are mispriced. Notice, we are only referring to the relative pricing of the different shares and not making any reference to their “fundamental” or “true” underlying values. b. To exploit any arbitrage opportunity, we need to buy low and sell high. In this case, we buy 1 share of BK costing $3 and sell the portfolio for $47.50 and make a profit of $44.50. c. The maximum I would be willing to pay for a share of SB is the cost of the portfolio that replicates 1 share. We know that 4M – 2.5S = B where B represents 1 share of BK. So S = (4M – B)/2.5. The cost of the replicating portfolio is then $22.8, which is the maximum I would be willing to pay.

37. Section: 12.3 Put-Call Parity Learning Objective: 12.3 Level of Difficulty: Difficult Solutions Manual ..

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Solution: The necessary information about the cash flows to the different strategies is summarized below:

Strategy

Cash flow today

Buy Call

-C

Buy S Borrow Portfolio

-75 50/1.05 -27.38

Cash flow at expiration S*=50 S*=100 0 10 50 -50 0

100 -50 50

The portfolio has the same payoffs as 5 calls. Therefore, 5 calls must cost $27.38. The maximum I would be willing to pay for 1 call would be 27.38/5=$5.48.

38. Section: 12.3 Put-Call Parity Learning Objective: 12.3 Level of Difficulty: Medium Solution: Let X be the strike price, then Cash flow at expiration S*≤X S*>X

Strategy

Cash flow today

Short sell stock

S

-S*

-S*

Sell call Borrow Buy put Portfolio

C X/(1+r) -P C+X/(1+r) -P

0 -X X-S* -S*

X-S* -X 0 -S*

Therefore, a portfolio consisting of puts, calls, and borrowing exactly replicates the cash flows to short selling a stock.

39. Section: Appendix 12.A Binomial Option Pricing and Risk-Neutral Probabilities Learning Objective: Appendix 12A and Learning Objective 12.3 Level of Difficulty: Medium Solution: a. First we need to determine the hedge ratio: Solutions Manual ..

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H = (Pu – Pd)/Pu – X) =(105-65)/(105-100) =8 b. Using the binomial option pricing formula: C = (1/h)*[S – Pd/(1+r)] = (1/8)*[80 – 65/1.05] = $2.2619 c. To determine the price of the put, we will use the put-call parity condition: P = C – S + PV(X) = 2.2619 – 80 + 100/1.05 =$17.5 40. Section: Appendix 12A Binomial Option Pricing and Risk-Neutral Probabilities Level of Difficulty: Medium Solution: a.

Cash flow Future value Action today of stock $85 $135 Buy stock -100.00 85 135 Borrow PV(85) 80.95 -85 -85 Sell 2.5 calls 25.00 0 -50 Total cash flows $5.95 0 0 If we buy one share, borrow the present value of the down price and sell 2.5 calls, we get a positive cash flow today and a zero cash flow no matter what happens in the future. This is a classic example of arbitrage. b.

Action

Cash flow today

Buy stock Borrow PV(135) Buy 3.8462 puts Total cash flows

-100.00 128.57 -1.92 $26.65

Future value of stock $85 $135 85 135 -135 -135 50 0 0 0

If we buy one share, borrow the present value of the up price and buy 3.8462 puts, we get a positive cash flow today and a zero cash flow no matter what happens in the future. This is a classic example of arbitrage. To determine the number of puts: with the stock and the bond we have a cash flow of $50 if the stock price is $85 and zero otherwise. Each put will pay $13 if the stock price is $85 and zero otherwise. Therefore, we need 3.8462 puts to have a cash flow of $50 in the down state.

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41. Section: Appendix 12A Binomial Option Pricing and Risk-Neutral Probabilities Level of Difficulty: Medium Solution: a. First we need to determine the hedge ratio: H = (Pu – Pd)/Pu – X) H = (175-125)/(175-165)= 5 Using the binomial option pricing formula: C = 1 / h[S −

Pd 125 ] = (1 / 5) * [150 − ] = $6.19 (1 + r ) (1.05)

b. The delta measures the change in the value of the option for a change in the value of the stock.

In the above case, if the price of the stock goes up $1, we see that the price of the call will increase by 1/h or $0.2.

42. Section: Appendix 12A Binomial Option Pricing and Risk-Neutral Probabilities Learning Objective: Appendix 12A Level of Difficulty: Difficult Solution: a.

Cash flow Future value Action today of stock $85 $190 Buy stock -100.00 85 190 Borrow PV(85) 77.27 -85 -85 Sell 5.25 calls 31.50 0 -105 Total cash flows $8.77 0 0 If we buy the stock, borrow $77.27 and sell 5.25 calls, we will have a positive cash flow today and zero no matter what happens in the future – this is arbitrage. Everyone will start doing this transaction and the price of the stock, risk-free rate, and the price of the call will adjust until the arbitrage opportunity is gone. b. The risk-free rate is 10%, so if we invest $100 we expect to have $110 in one year. Using the up and down prices, we solve for the risk-neutral probabilities:

$110 = pd *85 + (1 − pd )*190 110 = 190 − 105 pd pd = 76.19% The risk-neutral probability of the down state is 76.19% and the risk-neutral probability of the up Solutions Manual ..

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state is 23.81%. c. Using the risk-neutral probabilities, we obtain the expected value of the call option in one year: ( p *0 + (1 − pd )* 20 ) C= d 1.10 = $4.3290 d. The price of the option is based on the no arbitrage argument which is, by definition, a risk-free portfolio’s price must equal a risk-free asset, independent of risk aversion so we need to use the risk-neutral probabilities.

43. Section: Appendix 12A Binomial Option Pricing and Risk-Neutral Probabilities Level of Difficulty: Medium Solution: X = PU −

PU − PD 50 − 42 = 50 − = 46 h 2

44. Section: Appendix 12A Binomial Option Pricing and Risk-Neutral Probabilities Learning Objective: Appendix 12A and 12.3 Level of Difficulty: medium Solution First we calculate the hedge ratio PU − PD 130 − 55 = = 1.875 PU − X 130 − 90 Then using the binomial option pricing formula we calculate the call option value h=

C=

1 PD  1  55   S −  =  98 −  = $24.33 (1 + r )  1.875  1.05  h

And use put-call parity to get the value of the put option 𝑃 = 𝐶 − 𝑆 + 𝑃𝑉(𝑋) = 24.33 − 98 +

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24

90 = $12.04 1.05

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Chapter 13: Capital Budgeting, Risk Considerations, and Other Special Issues Multiple Choice Questions 1. Section: 13.1 Capital Expenditures Learning Objective: 13.1 Difficulty: Medium Solution: C. If a firm fails to invest effectively, its short-term performance and long-term survival will both be affected. Market value of its debt and equity will decline and the cost of capital will increase. The firm will find itself in a competitive disadvantage.

2. Section: 13.1 Capital Expenditures Learning Objective: 13.1 Difficulty: Easy Solution: D. The five factors are entry barriers, threat of substitutes, bargaining power of buyers, bargaining power of suppliers, and rivalry among existing competitors.

3. Section: 13.2 Evaluating Investment Alternatives Learning Objective: 13.2 Difficulty: Medium Solution: A Using a financial calculator (TI BA II Plus): [CF][2nd][CLR WORK] –17,000 [Enter][] 0 [Enter][] [] 8,000 [Enter][] 5 [Enter][] [NPV][20][Enter] [] [CPT] gives $2,937.41 4. Section: 13.2 Evaluating Investment Alternatives Learning Objective: 13.2 Difficulty: Difficult Solution: A. Refer to Figure 13-2. When k < crossover rate, Project A is preferred because it has a higher NPV despite the fact that its IRR is smaller.

5. Section: 13.2 Evaluating Investment Alternatives Learning Objective: 13.2 Difficulty: Difficult Solution: B. Using a financial calculator (TI BA II Plus): Project A: Project B: [CF][2nd][CLR WORK] [CF][2nd][CLR WORK] –2,000 [Enter][] –2,000 [Enter][] 1,000 [Enter][] [] 1,000 [Enter][] [] 2,000 [Enter][] [] 1,000 [Enter][] [] 1,500 [Enter][] [] 4,500 [Enter][] [] Solutions Manual ..

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[NPV][15][Enter] [] [NPV][15][Enter] [] [CPT] gives $1,368.13 [CPT] gives $2,584.53 Since the NPVs of both projects are positive, we should accept both when they are independent and are within the capital budget. However, when they are mutually exclusive, we should accept the project with the higher NPV, which, in this case, is Project B. 6. Section: 13.2 Evaluating Investment Alternatives Learning Objective: 13.2 Difficulty: Medium Solution: B Using a financial calculator (TI BA II Plus): [CF][2nd][CLR WORK] –6,000 [Enter][] 2,500[Enter][] [] 4,000[Enter][] [] 5,000[Enter][] [] [IRR][CPT] gives 35.87% Since 35.87% > 20%, we should accept the project.

7. Section: 13.2 Evaluating Investment Alternatives Learning Objective: 13.2 Difficulty: Medium Solution: D. We reject a project if NPV < 0, or IRR < required rate of return, or discounted payback period > required period, or PI < 1. Otherwise, we accept the project.

8. Section: 13.2 Independent and Interdependent Projects Learning Objective: 13.3 Difficulty: Medium Solution: A. NPV and IRR yield the same ranking when evaluating independent projects. They may have different rankings when evaluating mutually exclusive projects.

9. Section: 13.4 Capital Rationing Learning Objective: 13.4 Difficulty: Difficult.

Solution: D. When a firm uses WACC for a high-risk project, which has a positive NPV using the proper discount rate (k > WACC), then the project would have an even higher NPV. Therefore, it is not possible the firm will reject the project.

10. Section: 13.4 Capital Rationing Learning Objective: 13.4 Difficulty: Medium Solution: B. 11. Section 13.5 International Considerations Learning Objective: 13.5 Solutions Manual ..

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Difficulty: Medium Solution: C. We use the same rules to evaluate FDI and domestic projects while considering unique risks in FDI. 12. Section 13.5 International Considerations Learning Objective: 13.5 Difficulty: Medium Solution: A. Interest rate risk affects the discount rate and is therefore a risk for both FDI and domestic projects.

13. Section 13A The Modified Internal Rate of Return Learning Objective: 13.6 Difficulty: Medium Solution: B. IRR assumes cash flows are invested at IRR. MIRR relaxes this assumption.

14. Section 13A The Modified Internal Rate of Return Learning Objective: 13.6 Difficulty: Medium Solution: C. MIRR is greater than IRR only when cash flows are reinvested at a higher rate than IRR. Practice Problems 15. Section: 13.2 Evaluating Investment Alternatives Learning Objective: 13.2 Difficulty: Easy Solution: a. Payback period: • Determines how long it takes for the project cash flows to add up to the investment • Useful to gauge the possible liquidity impact of the project (how long is the firm’s capital tied up in the project) • Easy to calculate, quick “back of the envelope” type of calculation • Does not take into account the time value of money • Does not account for the cash flows beyond the cut-off date • The choice of the cut-off date is arbitrary IRR (internal rate of return) • Determines the rate of return at which the NPV = 0. Intuitively, it is the rate of return promised by the project • Easy to interpret and compare to other projects Technically, can be very misleading (i.e., project scale, reinvestment rates, multiple solutions) b. The most popular approaches (according to Figure 13-3) are NPV, IRR, and payback period. c. Possible reasons can include: Comfort: CFOs have been using these approaches for many years and have developed “rules of thumb” based on their experience and that, they believe, help them reach good decisions.

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Intuitive nature: both the IRR and the payback methods are easy to understand on an intuitive basis. If you have to explain the decision to a large group (i.e., shareholders) with differing levels of financial education, IRR and payback can be an easily understandable measure.

Ease: Payback is quick and easy to calculate.

16. Section: 13.1 Capital Expenditures Learning Objective: 13.1 Difficulty: Medium Solution: a. Bottom up b. Top down c. Bottom up (unless this reflects a change in the strategic direction of the firm) d. Top down e. Bottom up f. Top down 17. Section: 13.2 Evaluating Investment Alternatives Learning Objective: 13.2 Difficulty: Easy Solution: The payback period does not take into account the time value of money. In addition, it does not account for the cash flows beyond the cut-off date. The choice of the cut-off date is arbitrary.

The discounted payback period has all the drawbacks that the payback period has except that it accounts for the time value of money.

18. Section: 13.2 Evaluating Investment Alternatives Learning Objective: 13.2 Difficulty: Medium Solution: Discounted cash flows Year Project A Project B 0 -1,000.00 -2,000.00 1 467.29 1,401.87 2 873.44 873.44 3 979.56 244.89 4 1,907.24 381.45 5 2,138.96 142.60

NPV IRR Payback period Solutions Manual ..

Project C -8,000.00 1,869.16 1,746.88 6,530.38 1,525.79 1,782.47

Project D -5,000.00 4,485.98 873.44 4,897.79 -2,288.69 -2,851.94

Project E -5,000.00 1,869.16 2,620.32 4,081.49 762.90 2,138.96

Project F Project G -10,000.00 -3,000.00 2,803.74 1,401.87 1,746.88 1,048.13 816.30 244.89 762.90 2,138.96

Project A Project B Project C Project D Project E Project F Project G $5,366.48 $1,044.24 $5,454.68 $116.58 $6,472.82 -$1,731.23 -$305.12 0% 92% 34% 28% 3.5% 47% 0% 3 1.5 1.5 2.5 1.2 2 5

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Discounted payback

1.61

1.68

2.67

1.59

2.13

N/A

Profitability index

6.37

1.52

1.68

1.02

2.29

0.83

N/A 0.90

19. Section: 13.2 Evaluating Investment Alternatives Learning Objective: 13.2 Difficulty: Medium Solution: a. NPV: accept all positive NPV projects → A, B, C, D, and E b. IRR: accept all projects with IRR > 7% → A, B, C, and E (notice that we should exclude D from the IRR consideration due to the change in signs) c. Payback period: Accept all projects with payback less than or equal to 2 years → A, B, D, and E d. Discounted payback period: Accept all projects with discounted payback less than or equal to 2.5 years → A, B, D, and E e. Yes, the payback and discounted payback did not recommend project C. This project took longer to “repay” the capital invested and therefore was rejected by the payback criteria.

According to the NPV criteria, this project would be one of the most profitable (generate a very large NPV). The reason for this contradiction is that the payback and discounted payback use arbitrary criteria; there is no economic reasoning behind using a 2 or 2.5 year cutoff.

20. Section: 13.2 Evaluating Investment Alternatives Learning Objective: 13.2 Difficulty: Medium Solution: a. Take the project with the greatest NPV → E b. Take the project with the greatest IRR that is greater than 7% (the firm’s cost of capital) and excluding D (due to the change in signs) → A c. Take the project with the shortest payback period that is less than 2 years (Note: this criteria is arbitrary) → Project D d. Take the project with the shortest discounted payback period that is less than 2.5 years (Note: this criteria is arbitrary) → Project D e. Take the project with the highest profitability index → Project A f. Many of the results are contradictory. NPV and IRR make completely different recommendations due to scale differences in the projects. The criteria used in the payback and discounted payback criteria are arbitrary. The profitability index recommendation is also very different from the NPV recommendation; again, the criteria didn’t take into account the amount invested and therefore, ignored the total amount of wealth generated by the project.

21. Section: 13.3 Independent and Interdependent Projects Learning Objective: 13.3 Difficulty: Difficult Solution: a. Project D’s life = 5 years, NPV (using discount rate of 7% given earlier) = $116.58. Project H’s life = 3 years, NPV = $ 62.22 Solutions Manual ..

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Annual cash flows Project D Project H Initial investment -$5,000 -3,000 Year 1 4,800 1,500 Year 2 1,000 1,200 Year 3 6,000 750 Year 4 -3,000 Year 5 -4,000 The chain replication will require repeating Project D three times and Project H five times.

Project D: NPVD = 116.58 +

116.58 116.58 + = 116.58 + 83.12 + 59.26 = $258.96 1.075 1.0710

Project H: NPV H = 62.22 +

62.22 1.07

3

+

62.22 1.07

6

+

62.22 1.07

9

+

62.22 1.07 12

= $215.94

The NPV of project D is greater than H, so we would choose D. b.

Project D’s life = 5 years, NPV (using discount rate of 7% given earlier) = $116.58. Project H’s life = 3 years, NPV = $62.22 Project D: find the annuity of 5 years that has the same PV as the project.

N= 5, PV = 116.58, I=7%, solve for PMT. Annuity = $28.43 Project H: N=3, PV = 62.22, I=7%, solve for PMT. Annuity = $23.71 Choose project D as it has the higher equivalent annual NPV. 22. Section: 13.4 Capital Rationing Learning Objective: 13.4 Difficulty: Medium Solution: We begin by determining which projects are valid possibilities by calculating the NPV of each project. As the NPV of projects F and G are negative, we will eliminate them from consideration.

The investment and NPV is summarized in the following table: Project A Project B Project C

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Project D

6

Project E

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Initial -$1,000 investment IRR NPV

-$2,000

Booth, Cleary

-$8,000

-$5,000

-$5,000

92% 34% 28% $5,366.48 $1,044.24 $5,454.68

3.5% $116.58

47% $6,472.82

The investment opportunities available for the $8,000 budget are: C: total NPV = $5,454.58 D+A+B: total NPV = $116.58 + $5,366.48 + $1,044.24 = $6,527.30 E+A+B: total NPV = $6,472.48 + $5,366.48+ $1,044.24 = $12,883.20 Recommendation: that BigCo invest in projects A, B, and E as this results in the greatest increase in wealth for the firm (maximizes the NPV).

23. Section: 13.2 Evaluating Investment Alternatives Learning Objective: 13.2 Difficulty: Medium Solution: In the plot of the three NPV profiles we can see that the NPV ranking of the three projects does not remain constant as discount rates increase. For very low discount rates, Project E dominates A and C, while for very high discount rates, Project A dominates. The reason for the change in rankings is due to the timing of the cash flows and the scale of the investment. For very low discount rates, the higher investment required by Project E is offset by the later, relatively large cash flows. In contrast, when interest rates are very high, cash flows received in the future have very low present values and the relative initial investments dominate (A requires a much lower initial investment than E) hence, A dominates E.

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NPV profiles of Projects C, A, and E $10,000 $8,000 $6,000

NPV

$4,000 $2,000 $0 0

0.1

0.2

0.3

0.4

0.5

($2,000) ($4,000) Discount rates Project C

Project A

Project E

24. Section: 13.2 Evaluating Investment Alternatives Learning Objective: 13.2 Difficulty: Medium Solution: To determine the crossover rate, determine the discount rate at which the NPV of the two projects are equal. One way to solve this is to determine the incremental cash flows and then solve for the IRR. Project annual cash flows

Initial investment Year 1 Year 2 Year 3 Year 4 Year 5

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Project B

Project C

Incremental cash flows: B–C

-$2,000 1,500 1,000 300 500 200

-$8,000 2,000 2,000 8,000 2,000 2,500

$6,000 -$500 -$1,000 -$7,700 -$1,500 -$2,300

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The IRR of the incremental cash flows is: 27.31% To check your result, plot the NPV profiles of the two projects and we can see that the two profiles cross at approximately 27% (hard to see exactly on the graph—hence we need the calculation) NPV profiles of B and C $10,000 $8,000 $6,000

NPV

$4,000 $2,000 $0 0

0.1

0.2

0.3

0.4

0.5

($2,000) ($4,000) Discount rates Project B

Project C

25. Section: 13.4 Capital Rationing Learning Objective: 13.4 Difficulty: Medium Solution: a. As projects A to G are related to satellite launching, we will compute the cost of capital by considering only those firms in the satellite launching industry (they are the closest to the nature of the project). The average cost of capital of the two firms that are in only satellite launching (Crash’n Burn and Liddy’s Launchers) is 23.5%. b. Shareholder value would decrease. The firm would be accepting projects that are too risky; shareholders are demanding a return of 7% for projects that have a risk profile that is comparable to a mix of very risky (satellite launching) and safe (banking). However, the project is very risky and the firm should only accept projects that provide an appropriate risk-adjusted rate of return; failing to do so will increase the riskiness of the firm without a compensating increase in expected returns.

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26. Section: 13.2 Evaluating Investment Alternatives Learning Objective: 13.2 Difficulty: Medium Solution: Yes this is possible. Project D is an example of a project with more than one change of sign so we can have multiple IRRs implying that we cannot rely on the standard result that decreasing the discount rate increases the NPV. We can see this behaviour graphically in the NPV profile of project D:

27. Section: 13.2 Evaluating Investment Alternatives Learning Objective: 13.2 Difficulty: Medium Solution: a. To determine the NPV of the project we need to determine the incremental cash flows: Year 0 1 2

Projected cash flow -20,000 55,000 63,000

Current cash flow 30,000 65,000

Projected – current cash flows -20,000 25,000 -2,000

The NPV of the project is $1,252.42 b. The IRR is a poor choice due to the change in the signs of the incremental cash flows. This may result in multiple IRRs. 28. Section: 13.2 Evaluating Investment Alternatives Learning Objective: 13.2 Difficulty: Medium Solutions Manual ..

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Solution: The PI is calculated as the ratio of the PV of inflows to the PV of outflows. As the firm must choose between the two mutually exclusive projects, the firm would prefer the project with the greatest NPV. The PI provides a relative ranking of the two projects, but not a measure of the absolute increase in wealth generated by the two projects. If the PV of the cash outflows is approximately the same for the two projects, then using the PI provides a sound decision.

However, what if the PV of cash outflows for project 1 is $100 while the PV of cash outflows of project 2 is $1 million (in other words, the amount invested differs substantially between the two projects). The NPV of project 1 will be 2.4*100 – 100 = $2,300 while the NPV of project 2 will be $200,000. The firm will generate the greatest wealth by selecting project 2. Elaine’s recommendation is incomplete. The firm needs to consider more than the PI in choosing projects.

29. Section: 13.2 Evaluating Investment Alternatives Learning Objective: 13.2 Difficulty: Medium Solution: The two projects do not have the same lifetimes and therefore, either a chain-replication or EANPV analysis needs to be done to determine which project is better.

In this case, however, we can reach a conclusion using the chain approach and comparing the NVP of investment 1 and the NPV of investment 2:

1,000 +

1,000

(1 + i )

5

+

1,000

(1 + i )

10

−

700

0

NPV(Investment2) NPV(Investment1)

As long as the discount rate is greater than or equal to zero, the NPV of investment 1 will be greater than investment 2 and Fred’s conclusion is appropriate.

However, what would you conclude if the NPV of investment 2 was $2,000? Now the choice between investments 1 and 2 will depend on the discount rate.

30. Section: 13.2 Evaluating Investment Alternatives Learning Objective: 13.2 Difficulty: Medium Solution: The crossover rate is the discount rate that makes the NPVs of both projects the same.

6,000 9,000 15,600 4,000 8,000 15,000 + + − 23,000 = + + − 20,000 1 2 3 1 2 (1 + k ) (1 + k ) (1 + k ) (1 + k ) (1 + k ) (1 + k ) 3 We can write it in this way to mirror a single project’s cash flows: 2,000 1,000 600 + + − 3,000 = 0 1 2 (1 + k ) (1 + k ) (1 + k ) 3 Using a financial calculator (TI BA II Plus): Solutions Manual ..

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[CF][2nd][CLR WORK] –3,000 [Enter][] 2,000 [Enter][] [] 1,000 [Enter][] [] 600 [Enter][] [] [IRR] [CPT] gives 12.24%.

If you use 12.24% to calculate NPVs of both projects, you will get the same NPV of $522.48 (rounding of $0.02).

31. Section: 13.2 Evaluating Investment Alternatives Learning Objective: 13.2 Difficulty: Medium Solution: PI = PV (cash inflows)/ PV (cash outflows) NPV = - 10,050 + PV (cash inflows) → PV (cash inflows) = NPV + 10,050 = 5,090 + 10,050 = $15,140 → PI = 15,140/10,050 = 1.51 Since PI > 1, we accept the project.

Since NPV > 0, we accept the project as well.

Therefore, in this case, PI and NPV have the same decision.

32. Section: 13.2 Evaluating Investment Alternatives Learning Objective: 13.2 Difficulty: Medium Solution: Project A: 2,500 – (800 + 1,200) = 500 500 ÷ 900 = 0.56 Payback period = 2 + 0.56 = 2.56 years.

Project B: 3,000 – (750 + 1,500) = 750 750 ÷ 1,000 = 0.75 Payback period = 2 + 0.75 = 2.75 years.

Since Payback PeriodA < 2.6 years < Payback PeriodB, Project A will be selected.

33. Section: 13.2 Evaluating Investment Alternatives Learning Objective: 13.2 Difficulty: Medium Solution: Projects

Initial CF CF1

CF2

CF3

CF4

A

2,500

1,200

900

2,000

discounted CF Solutions Manual ..

800

714.2857 956.6327 12

640.6022 1,271.0362 Chapter 13

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B discounted CF

3,000

750

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1,500

1,000

4,000

669.6429 1,195.7908 711.7802 2,542.0723

Project A: 2,500 – 714.2857 – 956.6327 – 640.6022 = 188.4794 188.4794 ÷1,271.0362 = 0.15 Discounted Payback PeriodA = 3 + 0.15 = 3.15 years.

Project B: 3,000 – 669.6429 – 1,195.7908 – 711.7802 = 422.7861 422.7861 ÷2,542.0723 = 0.17 Discounted Payback PeriodB = 3 + 0.17 = 3.17 years.

Since both projects’ discounted payback periods > 2.6 years, neither project will be selected.

34. Section: 13.2 Evaluating Investment Alternatives Learning Objective: 13.2 Difficulty: Medium Solution: Accept the project if: NPV > 0, or IRR > required rate of return, or PI >1, or discounted payback period < the cut-off period.

There might be two IRRs if the sign of cash flows change direction. Moreover, the higher IRR project may have a lower NPV, and vice-versa, depending on the appropriate discount rate, and also depending on the size of the project.

35. Section: 13.2 Evaluating Investment Alternatives Learning Objective: 13.2 Difficulty: Difficult Solution: a. Malcolm is assuming that the investors (or the company) will be able to reinvest any cash generated by the project at 27%. If the investors required a return of 10%, it would seem unlikely that they will be able to find another project that pays 27% with the same risk. For example, investors require 10% for a project with a risk of X. Malcolm is assuming that the investors can find another project with risk X that returns 27%. This is unlikely. b. Malcolm is assuming that the risk of the project is the same as the risk of the firm. If the risk is much higher, which is likely given the high promised rate of return, the investors may be very unhappy. For example, if they require a return of 30% for projects with a comparable level of risk, then they will be very unhappy with the firm accepting a project that is only expected to return 27%.

36. Section: 13.2 Evaluating Investment Alternatives Learning Objective: 13.2 Difficulty: Difficult Solution: a. Begin by determining the required rate of return (WACC) for the firm. The firm generates $1,000 per year which is used to satisfy the shareholders and the debt holders. The combined value of the firm is $13,000 implying that the WACC of the firm is: $1,000/$13,000 = 7.6923% Solutions Manual ..

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The NPV of the project is $610/.076923 – $5,000 = $2,930. As this is a positive NPV, the firm should accept the project.

Alternative approach: the expected return on the project is $610/$5,000 = 12.2%. As the expected return is greater than the required return, the firm should accept the project. b. To demonstrate the impact on the cash flows to shareholders and debt holders begin by determining the capital structure of the firm (to determine how much of the $5,000 will be financed by borrowing).

The firm makes annual debt payments of $300 and its cost of debt is 5%, so the market value of the debt is $300/0.05 = $6,000. The equity value is then $7,000.

To maintain the same capital structure, the firm will finance (7,000/13,000)($5,000) = $2,692.31 using equity, and the remaining $2,307.69 (i.e., $5,000 – $2,692.31) using debt.

Therefore, at a 5% borrowing rate, the firm will have to pay $115.38 (i.e., $2,307.69 × .05) per year in associated interest payments. So, the remaining additional $494.62 (i.e., $610 – $115.38) “belongs” to the equity holders.

Now, we can determine the required rate of return on equity as follows: WACC equals 7.6923%, so we can solve for ke as follows: 7.6923 = (6,000/13,000)(5%) + (7,000/13,000) ke (7,000/13,000) ke = 7.6923 – 2.3077 = 5.3846% So, ke = (13,000/7,000) (5.3846%) = 10.00% So, the shareholder value will be enhanced since the annual (perpetual) return on the extra $2,692.31 of equity equals $494.62 / $2,692.31 = .1837, which is greater than the required return on equity of 10%.

37. Section: 13.2 Evaluating Investment Alternatives Learning Objective: 13.2 Difficulty: Difficult Solution: a. Required return on the entire company is determined using the beta of the firm: 3% + 1.35*5% = 9.75%. As the firm is 100% equity financed, we do not have to worry about the cost of debt. b. To answer this question, first address the fact that the project is of the same risk class as MLTV and therefore we need to determine the required rate of return for MLTV’s assets. Using the comparable firm’s beta of 1.85, we find the required return is 3% + 1.85*5% = 12.25%. As the expected return on the project is only 10%, the company should not undertake the project.

Note: We cannot use the WACC for the entire company to evaluate this project. The risk of the project is not the same as the risk of the overall firm.

38. Section: 13.2 Evaluating Investment Alternatives Learning Objective: 13.2 Difficulty: Difficult Solution: re = 5% + 1.2(8%) = 14.6% WACC = 12% (0.6)(1 -.40) + (14.6%) (0.4) = 10.16% Cost of capital (project) = 10.16% (WACC)

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Using a financial calculator (TI BA II Plus): [CF][2nd][CLR WORK] –120,000 [Enter][] 37,500 [Enter][] 5 [Enter][] [IRR][CPT] gives 16.99% Since 16.99% is greater than 10.16%, the cost of capital of the project, accept the project.

39. Section: 13.2 Evaluating Investment Alternatives Learning Objective: 13.2 Difficulty: Difficult Solution: CF1 CF2 CF3 NPV = + + + ... − CF0 1 2 (1 + k ) (1 + k ) (1 + k )3 CF1 CF2 CF3 0= + + + ... − CF0 − NPV 1 2 (1 + k ) (1 + k ) (1 + k )3 Using a financial calculator (TI BA II Plus) to calculate k by using the same method of calculating IRR: –CF0 – NPV= –50,000 – 200,000 = –250,000 and use 250,000 as an” initial investment” [CF][2nd][CLR WORK] –250,000 [Enter][] 50,000 [Enter][] 50,000 [Enter][] [] 30,000 [Enter][] [] 80,000 [Enter][] [] 60,000 [Enter][] [] 70,000 [Enter][] [] [IRR][CPT] gives 8.82% Therefore, for this project, 8.82% is actually the cost of capital, k.

To test 8.82%:

CF3 CF1 CF2 + + + ... − CF0 1 2 (1 + k ) (1 + k ) (1 + k ) 3 50,000 50,000 30,000 80,000 60,000 70,000 = + + + + + − 200,000 2 3 4 5 1.0882 (1.0882) (1.0882) (1.0882) (1.0882) (1.0882) 6 = 45,947 + 42,223 + 23,281 + 57,050 + 39,319 + 42,155 − 200,000 = 49,975 (Rounding error) NPV =

40. Section: 13.2 Evaluating Investment Alternatives Learning Objective: 13.2 Difficulty: Difficult Solutions Manual ..

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Solution:

PI =

PVCashInflows PVCashOutflow

20,000 40,000 100,000 + + = 17,391 + 30,246 + 57,175 = 104,812 1.15 1.152 1.154 15,000 PVCahOutflows = + 90,000 = 99,863 1.153 104,812 PI = = 1.05  1 99,863 Accept the project.

PVCashInflows =

41. Section: 13.2 Evaluating Investment Alternatives Learning Objective: 13.2 Difficulty: Difficult Solution: a. re = 5% + (1.2)(12% – 5%) = 13.4% WACC = (13.4%)(60%) + (6.5%)(40%) = 10.64% r1 = r2 = r3 = 10.64% r4 = 10.64% + 1% = 11.64% Project 1: n = 3 + (15,067 – 14,078)/ (21,495 – 14,078) = 3.13 years < 3.5 years Project 2: n = 3 + (14,543 – 12,095)/ (19,067 – 12,095) = 3.35 years < 3.5 years Project 3: n = 2 + (8,565– 5,674)/ (9,883 – 5,674) = 2.69 years > 2.25 years Therefore, project 3 is rejected. b. Project 4: PV of annual cash flow in Year 1: 2,955/(1.1164) = 2,647 PV of annual cash flow in Year 2: (4,985 – 2,955)/(1.1164)2 = 1,629 PV of annual cash flow in Year 3: 0 PV of annual cash flow in Year 4: (12,000 – 4,985) /(1.1164)4 = 4,516 n = 3 + (6,500 – 2,647 – 1,629 - 0)/4,516 = 3.49 > 3.25 years Therefore, project 4 should not be accepted.

42. Section: 13.2 Evaluating Investment Alternatives Learning Objective: 13.2 Difficulty: Medium Solution: Project discount rate (k) = WACC + risk premium = 19.4% + 4.6% = 24% Using a financial calculator (TI BA II Plus): [CF][2nd][CLR WORK] –50,000 [Enter][] 18,000 [Enter][] [] 20,000 [Enter][] [] –5,000 [Enter][] []

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40,050 [Enter][] [] 58,000 [Enter][] [] 20,000 [Enter][] [] [NPV][24][Enter] [] [CPT] gives $17,127.06 Since NPV > 0, SK Inc. should accept the project.

43. Section: 13.2 Evaluating Investment Alternatives Learning Objective: 13.2 Difficulty: Medium Solution: Using a financial calculator (TI BA II Plus): [CF][2nd][CLR WORK] –66,777 [Enter][] 20,000 [Enter][] 6 [Enter][] 40,000 [Enter][] [] [NPV][18][Enter] [] [CPT] gives $15,732.05 Since NPV > 0, we should accept the project.

Using a financial calculator (TI BA II Plus): [CF][2nd][CLR WORK] –66,777 [Enter][] 20,000 [Enter][] 6 [Enter][] 40,000 [Enter][] [] [IRR][CPT] gives 25.35% Since IRR > k, we should accept the project.

Therefore, NPV and IRR yield the same decision.

44. Section: 13.2 Evaluating Investment Alternatives Learning Objective: 13.2 Difficulty: Difficult Solution: Time 0 1 2 3 4 5 Cash Inflows 5,000 5,000 5,000 5,000 5,000 Initial cost -12,000 Maintenance cost -1,000 -1,000 -1,000 -1,000 -1,000 Net Cash Flows -13,000 4,000 4,000 4,000 4,000 5,000 Discount Factor 1.00 1.12 1.25 1.40 1.57 1.76 Present Value -13,000 3,571.43 3,188.78 2,847.12 2,542.07 2,837.13 NPV 1,986.53 45. Section: 13.2 Evaluating Investment Alternatives Learning Objective: 13.2 Difficulty: Medium Solutions Manual ..

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Solution: Sell to brother: Cash outflow =$60,000 NPV = –60,000 + 75,000/1.083 = –$462.58 Sell to cousin: NPV = –60,000 + 65,000/1.08 = $185.19 Since the NPV is higher when selling to your cousin, you should sell the truck to your cousin.

46. Section: 13.2 Evaluating Investment Alternatives Learning Objective: 13.2 Difficulty: Medium Solution: NPV = PV of cash inflows – initial cash outflow = 10,000/(.11–.05) –150,000 = $166,666.67–$150,000 = $16,666.67 47. Section: 13.2 Evaluating Investment Alternatives Learning Objective: 13.2 Difficulty: Easy Solution: Since the discount rate is zero, the discounted payback period should equal the payback period. Discounted payback = 2 + ($5,000-$2,500-$2,000)/$1,500 = 2.33 years.

48. Section: 13.2 Evaluating Investment Alternatives Learning Objective: 13.2 Difficulty: Medium Solution: When the discount rate is zero, the discounted payback period will be equal to the payback period.

49. Section: 13.2 Evaluating Investment Alternatives Learning Objective: 13.2 Difficulty: Medium Solution: Discounted Discounted Cash Flow Cash Flow Year (A) (B) 0 -150,000 -100,000 1

27,778

55,556

2

25,720

34,294

3

47,630

15,877

4

66,153

14,701

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Project A Payback = 3 + ($150,000-$30,000-$30,000-$60,000)/$90,000 = 3.33 years.

Discounted payback = 3 + ($150,000 – $27,778 – $25,720 – $47,630)/$66,153 = 3.74 years.

Project B Payback = 2 years.

Discounted payback = 2 + ($100,000-$55,556-$34,294)/$15,877 = 2.64 years.

Both methods favour project B. 50. Section: 13.2 Evaluating Investment Alternatives Learning Objective: 13.2 Difficulty: Medium Solution: Payback = N I0=R*N R= I0/N 51. Section: 13.2 Evaluating Investment Alternatives Learning Objective: 13.2 Difficulty: Medium Solution: Present value of cash inflows = 2,000/(.1-.02) = $25,000 NPV = -25,000 + 25,000 = 0 Since NPV is not positive, you should not invest in the project 52. Section: 13.2 Evaluating Investment Alternatives Learning Objective: 13.2 Difficulty: Medium Solution: IRR of a bond is its yield to maturity. Since the bond is trading at par, it implies that the yield is equal to the coupon rate. Therefore the IRR is 10 percent.

53. Section: 13.3 Independent and Interdependent Projects Learning Objective: 13.3 Difficulty: Medium Solution: Independent projects are those that have no relationship with one another. A firm’s decision to accept one project has no impact on its decision to accept another project that is independent of it. The decision rule is to accept projects whenever NPV > 0 or IRR > k, or PI > 1 assuming no capital constraints.

Mutually exclusive projects are those that we must choose between two or more alternatives.

Therefore simply using the decision rules for independent projects may not be sufficient.

Ranking the projects is the best way to choose the one with the highest NPV based on the same time horizon.

54. Section: 13.3 Independent and Interdependent Projects Learning Objective: 13.3

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Difficulty: Medium Solution: a. The two projects are mutually exclusive. This assumes that the cruise line needs to carry a total of 10,000 passengers and/or the ship builder has limited capacity in its dry docks for vessel construction. b. The two projects are mutually exclusive. Waste disposal and hunting lodges cannot (in general) exist in the same place. c. This depends on your assumptions about timing. In general, one would assume that the two projects are independent. The classroom is unlikely to be used for tutorials (or faculty meetings) all the time and so could satisfy both projects. If one assumes that the classroom will be used exclusively for tutorials (or faculty meetings), then the two projects will be mutually exclusive. d. In general, these would be mutually exclusive. Most people do not mix the two drinks. e. This depends on tastes. Some people prefer salad with steak, and others prefer to keep them separate; therefore, the two dishes are independent.

55. Section: 13.3 Independent and Interdependent Projects Learning Objective: 13.3 Difficulty: Difficult Solution: First, note that the life of the two projects is not the same and consequently, we need to do more than just calculate the present value of each project. Second, note that we will be making the lowest cost choice.

There are two approaches: chain replication and the equivalent annual NPV approach.

The NPV of PDX341: = -500,000 + PV of 5 year annuity of -10,000 at 10% + PV of 10 year annuity of -15,000 at 10 % discounted back another 5 years at 10% =-500,000 -37,907.87 -57,229.39 =-$595,137.26 BAII+: using the CF worksheet: CF0 = –500,000 C01 = –10,000 F01 = 5 C02 = –15,000 F02 = 10 NPV → I=10, solve for NPV = –$595,137.26 NPV of PDW581: BAII+: using the CF worksheet: CF0 = –50,000 C01 = –30,000 F01 = 10

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NPV → I=10, solve for NPV = –$234,337.01 Approach 1: The Chain Approach: PDX (repeats twice): =–$595,137.26 –$595,137.26/1.115 =–$595,137.26 –142,471.13 =—737,608.39 PDW (repeats three times):

− 234,337.01 − 234,337.01 + 1.110 1.120 = −234,337.01 − 90,347.06 − 34,832.70 = $359,516.78

− 234,337.01 +

Based on this analysis, we would prefer PDW as its cost is lower.

Approach 2: Using the EANPV approach: Using the BAII+ for the PDX project: N= 15, I/Y= 10, PV = -595,137.26 solve for PMT. PMT = -$78,244.94 (note: the BAII+ will give you PMT as a positive; as we are dealing with outflows, we have to change the sign of the payments).

Using the BAII+ for the PDW project: N= 10, I/Y= 10, PV = -234,337.01 solve for PMT. PMT = -$38,137.27 (Note: the BAII+ will give you PMT as a positive; as we are dealing with outflows, we have to change the sign of the payments).

Using the EANPV approach, we prefer the PDW machine (lower cost).

56. Section: 13.3 Independent and Interdependent Projects Learning Objective: 13.3 Difficulty: Difficult Solution: Cost of capital (r) = 5% + 1.2*10% = 17%  5,500 6,000 9,500  NPV1 =  + + − 12,095 = 15,015 − 12,095 = +2,920 1 2 (1.17) 3   (1.17) (1.17)

 3,450 3,000  NPV2 =  + − 3,080 = 5,140 − 3,080 = +2,060 1 (1.17) 2   (1.17) Only one of the projects can be chosen.

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 2,920  NPV1 = 2,920 + = 2,920 + 1,823 = $4,743 (1.17) 3    2,060 2,060  NPV2 = 2,060 + + = 2,060 + 1,505 + 1,099 = $4,664 2 (1.17) (1.17) 4   Therefore, project 1 should be chosen.

57. Section: 13.3 Independent and Interdependent Projects Learning Objective: 13.3 Difficulty: Difficult Solution: Cost of capital = 5% + 1.2(10%) = 17%  5,500 6,000 9,500  NPV1 =  + + − 12,095 = 2,920 1 2 (1.17)3   (1.17) (1.17)

 3,450 3,000  NPV2 =  + − 3,080 = 2,060 1 2  (1.17) (1.17)  Solving the problem by financial calculator (TI BA II Plus): Project 1: FV = 0; PV = 2,920; n = 3; I/Y = 17; Compute PMT = -1,322 or, $1,322.

Project 2: FV = 0; PV = 2,060; n = 2; I/Y = 17; Compute PMT = -1,300 or, $1,300.

Therefore, project 1 should be chosen, which is the same result as Problem 56.

58. Section: 13.3 Independent and Interdependent Projects Learning Objective: 13.3 Difficulty: Difficult Solution: Project A: [CF][2nd][CLR WORK] –5,000 [Enter][] 2,500 [Enter][][] 4,050 [Enter][][] [NPV][15][Enter][] [CPT] gives $236.29 Project B: [CF][2nd][CLR WORK] –3,000 [Enter][] 750 [Enter][][] 1,750 [Enter][][] 2,000 [Enter][][] [NPV][15][Enter][] [CPT] gives $290.46 Replicate Project A three times:

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 236.39 236.39  NPVA = 236.39 + + = 236.39 + 178.74 + 135.16 = $550.29 (1.15) 2 (1.15) 4   Replicate Project B twice:  290.46  NPVB = 290.46 + = 290.46 + 190.98 = $481.44 (1.15)3   NPVA > NPVB, therefore choose Project A. 59. Section: 13.3 Independent and Interdependent Projects Learning Objective: 13.3 Difficulty: Difficult Solution: From Problem 58, we get NPVA = $236.39; NPVB = $290.46 Using a financial calculator (TI BA II Plus): Project A: N = 2, I/Y = 15, PV = -236.39, FV = 0, CPT PMT = 145.41 Project B: N = 3, I/Y = 15, PV = -290.46, FV = 0, CPT PMT = 127.21 PMTA > PMTB, therefore choose Project A. 60. Section: 13.4 Capital Rationing Learning Objective: 13.4 Difficulty: Difficult Solution: First calculate each project’s NPV: Project A: [CF][2nd][CLR WORK] –100,000 [Enter][] 80,000 [Enter][][] 80,000 [Enter][][] [NPV][13][Enter][] [CPT] gives $33,448.19 Project B: [CF][2nd][CLR WORK] –75,000 [Enter][] 50,000 [Enter][][] 60,000 [Enter][][] 70,000 [Enter][][] [NPV][13][Enter][] [CPT] gives $64,750.10 Project C: [CF][2nd][CLR WORK] –120,000 [Enter][] Solutions Manual ..

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55,000 [Enter][][] 100,000 [Enter][][] 80,000 [Enter][][] [NPV][13][Enter][] [CPT] gives $62,431.25 Combinations A& B A& C B&C

Total budget Total NPV 175,000 98,198.29 220,000 95,879.44 195,000 127,181.35

Within the budget?

Yes No Yes

Therefore, SK should choose Projects B and C because the total NPV is the greatest and the total budget is within $200,000.

61. Section: 13.4 Capital Rationing Learning Objective: 13.4 Difficulty: Easy Solution: The pure play approach involves finding the beta of a company that operates almost exclusively (i.e., pure play) in the industry associated with the project under consideration and adjusting this company’s beta for the leverage associated with that company.

62. Section: 13.4 Capital Rationing Learning Objective: 13.4 Difficulty: Easy Solution: a. With no capital constraint, the firm should invest in all positive NPV projects; therefore, it should invest in all the projects (A to F) b. The firm has a total of $100 million to invest; it should maximize the NPV earned.

Alternatives: B + A → NPV = $20 million D+C+A+E → NPV = 7+8+5+3=$23 million Recommendation: invest in projects: A, C, D, and E (maximizes the NPV). c. The firm needs to have more funds available to invest. Possible ways to increase available capital are: cut costs elsewhere (i.e., sell unproductive assets); issue equity or debt to raise money; or cut dividends.

63: Section: 13.5 International Considerations Learning Objective: 13.5 Difficulty: Medium Solution: How do we account for the political risk of expropriation or insurrection or the imposition of foreign exchange controls that prevent the firm’s getting its investment back?

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How do we account for other potential legal and regulatory issues where local competitors may have privileged access to cronies in the government?

How do we adjust for foreign exchange risk because cash flows are denominated in a foreign currency?

How do we adjust for the taxes paid in a foreign currency and the possibility that when the profits from the investment are paid back to Canada, they may be taxed again?

How do we finance a foreign project if the local markets are poorly developed?

64: Section: Appendix 13A Modified Internal Rate of Return Learning Objective: 13.6 Difficulty: Difficult Solution: a. IRR is the discount rate that makes the NPV equal to zero for a given set of cash flows. This implies that it is the discount rate that sets the PV of future CFs equal to the initial cash outlay.

Using a financial calculator (TI BA II Plus): [CF][2nd][CLR WORK] –10,000 [Enter][] 5,000[Enter][] [] 3,000[Enter][] [] 4,000[Enter][] [] [IRR][CPT] gives 10.08% IRR assumes that cash flows are reinvested at IRR. b. cf 0 1 2 3

–10,000 5,000 3,000 4,000 sum of FV

FV of cf 5,202 3,060 4,000 12,262

PV = $10,000 FV = $12,262 N=3 Solve for I/Y → I/Y = 7.03 percent So MIRR= 7.03%. c. cf 0 1 2 3

–10,000 5,000 3,000 4,000 sum of FV

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PV = $10,000 FV = $13,072 N=3 Solve for I/Y → I/Y = 9.34 percent So MIRR=9.34%. d. cf 0 1 2 3

–10,000 5,000 3,000 4,000 sum of FV

FV of cf 6,070 3,305 4,000 13,375

PV = $10,000 FV = $13,375 N=3 Solve for I/Y → I/Y = 10.179 percent So MIRR=10.179%.

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Chapter 14: Cash Flow Estimation and Capital Budgeting Decisions Multiple Choice Questions 1. Section: 14.1 General Guidelines for Capital Expenditure Analysis Learning Objective: 14.1 Level of difficulty: Medium Solution: C. Sunk costs are irrelevant and should not be considered.

2. Section: 14.1 General Guidelines for Capital Expenditure Analysis Learning Objective: 14.1 Level of difficulty: Medium Solution: B. Using nominal cash flows and a nominal discount rate should yield the same result as using real cash flows and a real discount rate. Both represent consistent treatments of inflation.

3. Section: 14.1 General Guidelines for Capital Expenditure Analysis Learning Objective: 14.1 Level of difficulty: Easy Solution: A. Cash flow estimation does not include sunk costs, associated interest and dividend payments, or externalities.

4. Section: 14.1 General Guidelines for Capital Expenditure Analysis Learning Objective: 14.1 Level of difficulty: Easy Solution: D. When making capital budgeting decisions, firms should not consider intangible considerations unless their impact on cash flows can be estimated.

5. Section: 14.2 Estimating and Discounting Cash Flows Learning Objective: 14.2 Level of difficulty: Medium Solution: A. R&D costs associated with the project are sunk costs, which should not be considered.

CF0 = C0 + NWC0 + OC = 400,050 – 15,000 + 90,000 + 5,000 = $480,050 Note that inventory decreased instead of increased as a result of the project.

6. Section: 14.2 Estimating and Discounting Cash Flows Learning Objective: 14.2 Level of difficulty: Easy Solution: D. All of the others items except for operating cash flows are included in the calculation of the ending (or terminal) cash flow (ECFn).

7. Section: 14.2 Estimating and Discounting Cash Flows Learning Objective: 14.2 Level of difficulty: Medium Solution: C CF2 = CFBT2(1 – T) + CCA2(T) = (50,000 – 18,000)(1 – 0.40) + (45,000)(0.40)

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=19,200 + 18,000 = 37,200 8. Section: 14.2 Estimating and Discounting Cash Flows Learning Objective: 14.2 Level of difficulty: Medium Solution: B. CFBT1 (1 − T ) CFBT16 (1 − T ) 1 PV (Operating CFs ) = −  , k−g k−g (1 + k )15

(50,000 − 18,000)(1 − 0.40) (50,000 − 18,000)(1 − 0.40)(1.06)15 1 −  0.20 − 0.06 0.20 − 0.06 (1 + .20)15 19,200 (19,200)(2.396558) = −  (0.064905) = $137,143 − $21,333 = $115,810 0.14 0.14

=

9. Section: 14.2 Estimating and Discounting Cash Flows Learning Objective: 14.2 Level of difficulty: Medium Solution: D. A decrease in the corporate tax rate and/or a decrease in the CCA rate will decrease the present value of the CCA tax shield, while a decrease in the discount rate will increase it.

Personal income tax rate is irrelevant here.

10. Section: 14.2 Estimating and Discounting Cash Flows Learning Objective: 14.2 Level of difficulty: Medium Solution: D. A terminal loss occurs when the salvage value is less than the ending UCC for the asset/asset class.

11. Section: 14.2 Estimating and Discounting Cash Flows Learning Objective: 14.2 Level of difficulty: Medium Solution: A. ECFn = SVn + NWCn = 10,000 + 2,000 = 12,000 12. Section: 14.3 Sensitivity to Inputs Learning Objective: 14.3 Level of difficulty: Easy Solution: A. Sensitivity analysis examines the impact of the change of one input at a time, but scenario analysis examines the impact of the change of multiple inputs at a time.

13. Section: 14.4 Replacement Decisions Learning Objective: 14.4 Level of difficulty: Medium Solution: A C0 = C0New − C0Old = 300,000 − 50,000 = $250,000 CCA1 = d × (1/2)△C0 = 0.20 × (1/2)(250,000) Solutions Manual

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= 25,000 UCC (beginning of year 2) = UCC (beginning of year 1) – CCA1 = 250,000 – 25,000 = 225,000 CCA2 = 225,000×0.20 = 45,000 14. Section: 14.4 Replacement Decisions Learning Objective: 14.4 Level of difficulty: Medium Solution: A. We use incremental cash flow, i.e., the difference between the cash flow generated from the new machine and the cash flow that would be generated from the old machine.

15. Section: 14.5 Inflation and Capital Budgeting Decisions Learning Objective: 14.5 Level of difficulty: Medium Solution: A. We need to discount the nominal cash flow by the nominal discount rate, which is $1,000/(1+5 percent) Practice Problems 16. Section: 14.1 General Guidelines for Capital Expenditure Analysis Learning Objective: 14.1 Level of difficulty: Medium Solution: To evaluate any investment we have to begin by determining the cash flows associated with the project. Depreciation and CCA are non-cash expenses that can have cash flow consequences i) Depreciation: to determine cash flow we can start with net income and then add back the noncash expenses, such as depreciation, to obtain cash flow. ii) CCA: this is a little different than other non-cash expenses because while it is a non-cash expense it has a direct effect on cash flows through its effect on taxes paid.

Interest expenses are a little different from other cash expenses in that they reflect a return paid to the providers of capital. When we discount using WACC or the cost of capital, we are implicitly taking into account the interest expense; in other words, we take care of the cost of debt in the cost of capital and do not need to do so in the cash flow. If we deducted the cost of debt (interest) in the cash flow, then we should not double count and include it in the cost of capital.

Example: The cost of debt is 10 percent, cost of equity is 20 percent, WACC (weighted average cost of capital) is 15 percent. You are evaluating a perpetuity that will pay $1,500 per year forever and costs $9,000. Assume you will need to borrow $4,500 to invest.

Question: How do you evaluate this project?

If we invest the $9,000 using ½ from equity and ½ from debt we need the project to generate the following cash flows every year to satisfy the debt and equity holders: $4,500 * .10 = $450 for debt holders $4,500 * .20 = $900 for equity holders Total required: $1,350 to satisfy all the providers of capital

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Project actually produces: $1,500 → good project.

Calculating the NPV: i) The PV of the cash flows is $1,500/.15 = $10,000>$9,000 cost → positive NPV, good investment. The requirements of both the debt and equity holders are satisfied by setting the cost of capital equal to the discount rate. ii) But, if we deduct the interest from the cash flows: (1,500 – 4,500*10%) = 1,050. Present value of cash flows would then be $1,050/.15 = $7,000<$9,000 project appears to be a bad investment. iii) To calculate the NPV correctly we need to either: a) Use cash flows before interest / WACC (average cost of capital including cost of debt) b) Or use cash flows after interest/cost of equity. (Cost of capital assuming that the firm does not use any debt. Note: it does not equal 20%.)

17. Section: 14.1 General Guidelines for Capital Expenditure Analysis Learning Objective: 14.1 Level of difficulty: Easy Solution: Firm B is half right. To evaluate any project we have to ignore sunk costs (the $600,000 is a sunk cost) and take into account opportunity costs (i.e., projects foregone) in determining the incremental costs. Therefore, the analysis should take into account the initial costs and the foregone rents but not the $600,000 sunk renovation costs.

18. Section: 14.1 General Guidelines for Capital Expenditure Analysis Learning Objective: 14.1 Level of difficulty: Easy Solution: The investor has not taken into account the impact of financial distress on the firm’s decision making. If BathGate is in financial distress, then accepting a negative NPV project may be shareholder wealth maximizing. In this case, the shareholders care about the expected upside (the part of the gains from the project obtained by shareholders) but not about the downside (the shareholders have nothing to lose; the firm is in trouble and they probably would have obtained nothing anyway). Consequently, if the project has good upside potential, it may be shareholder wealth maximizing even though the NPV is negative.

Another explanation: This investment is necessary for other projects with positive NPVs. That is, it is an interdependent project. As long as all projects together have positive NPV, the firm can undertake this investment with negative NPV itself.

19. Section: 14.1 General Guidelines for Capital Expenditure Analysis Learning Objective: 14.1 Level of difficulty: Easy Solution: Sunk costs cannot be included because we are considering future cash flows while sunk costs have occurred in the past and cannot be recovered.

Interest and dividend payments also should be excluded as they have already been included in the discount rate.

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Externalities should be excluded since they are side effects that often result from an investment that may benefit or even harm unrelated third parties. Besides, we should ignore intangible considerations that cannot be measured.

20. Section: 14.1 General Guidelines for Capital Expenditure Analysis Learning Objective: 14.1 Level of difficulty: Medium Solution: a. Not relevant (sunk cost) b. Relevant (project interdependencies) c. Not relevant (sunk cost) d. Relevant (to determine after-tax cash flows) e. Not relevant (need to consider incremental cash flows; this is not changed by the new blender) f. Relevant (project interdependencies, incremental cash flow—foregone coffee revenues) g. Not relevant (not related to cash flow or discount rate) h. Not relevant (sunk cost) 21. Section: 14.2 Estimating and Discounting Cash Flows Learning Objective: 14.2 Level of difficulty: Medium Solution: As it is not known how long the project will continue (we only know that we are in year 5), we will calculate the PV of the year 5 cash flow. The PV of the year 5 cash flow is the present value of CFBT(1-T) discounted back to year 0 at the appropriate discount rate.

CFBT(1-T) A B C D E F

$3,800 $1,710 $5,120 $7,500 $7,650 $14,000

PV of the year 5 cash flow $2,977.40 $1,061.78 $3,484.59 $3,728.83 $1,644.25 $7,943.98

22. Section: 14.2 Estimating and Discounting Cash Flows Learning Objective: 14.2 Level of difficulty: Medium Solution: End of year Opening UCC CCA balance 1 50,000 8,750 2 41,250 14,437.50 3 26,812.50 9,384.38 4 17,428.12 6,099.84

Closing UCC balance 41,250 26,812.50 17,428.12 11,328.28

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Learning Objective: 14.2 Level of difficulty: Medium Solution: Components 1 SV0 dT 1 + .5k (1 + k) n 1+ k d +k 0.954545 0.000000 0.620921 0.938596 117.647059 0.592080 0.976190 291.666667 0.676839 0.946429 69.230769 0.321973 0.962963 118.421053 0.340461 0.934783 100.000000 0.375937 0.971698 0.000000 0.591898

C0 dT d +k $200.45 210.000000 $195.36 282.352941 $1,226.20 1458.333333 $960.54 1038.461538 $1,480.15 1578.947368 $149.36 200.000000 $1,475.77 1518.750000

PV(CCA Tax shields) A B C D E F G

24. Section: 14.2 Estimating and Discounting Cash Flows Learning Objective: 14.2 Level of difficulty: Medium Solution: a. Cash outflow. To increase inventory, the firm will have to invest cash to purchase the inventory. b. Cash inflow. The firm is delaying paying its debts and therefore has more cash on hand. c. Cash outflow. The firm is receiving cash later and therefore has less cash on hand. d. Cash inflow. To decrease inventory, the firm will sell the inventory to generate cash.

25. Section: 14.2 Estimating and Discounting Cash Flows Learning Objective: 14.2 Level of difficulty: Difficult Solution: Step 1: initial cash flow = –CF0 = –$4,000 Step 2: PV of after-tax operating cash flow Discount rate = 0.10, payment = $2,000 * (1 – tax rate) = $2,000 * (1 – 0.4), N = 3, and PV = 2,984.22.

Step 3: PV of CCA tax shield.

There is no capital gain, capital recapture, or terminal loss.

Using Equation [14-7], C0dT/(d + k) = 1,200.00, (1 + 0.5k)/(1 + k) = 0.954545, SVdT/(d + k) = 0, 1/(1 + k)n = 0.751315, and PV of CCA tax shield = 1,145.45 Step 4: PV of ECF Discount rate = 0.10, future value = salvage value = 0 N = 3, and PV = 0 Solutions Manual

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Step 5: PV of capital gains taxes paid = 0 Step 6: Using Equation [14-10], NPV = PV (Operating CFs) + PV (CCA Tax Shield) + PV (ECFn) – PV (Capital Gains Taxes Paid) – CF0 NPV = 129.67 This project has a positive NPV. The company should take it.

26. Section: 14.2 Estimating and Discounting Cash Flows Learning Objective: 14.2 Level of difficulty: Difficult Solution: Step 1: initial cash flow = –CF0 = –$12,000 Step 2: PV of after-tax operating cash flow Discount rate = 0.010, payment = $1,600 * (1 – tax rate) = $1,600 * (1 – 0.4), N = 10, and PV = $5,898.78 Step 3: PV of CCA tax shield.

There is no capital gain, capital recapture, or terminal loss.

Using Equation [14-7], C0dT/(d + k) = 3,200.00, (1 + 0.5k)/(1 + k) = 0.954545, SVdT/(d + k) = 200, 1/(1 + k)n = 0.385543, and PV of CCA tax shield = $2,977.44 Step 4: PV of ECF Discount rate = 0.10, future value = salvage value = 750 N = 10, and PV = $289.16 Step 5: PV of capital gains taxes paid = 0 Step 6: Using Equation [14-10], NPV = PV (Operating CFs) + PV (CCA Tax Shield) + PV (ECFn) – PV (Capital Gains Taxes Paid) – CF0 NPV = –$2,834.62 This project has a negative NPV. The company should not take it.

27. Section: 14.2 Estimating and Discounting Cash Flows Learning Objective: 14.2 Level of difficulty: Difficult Solution: As the asset classes will be terminated when the project ends, we have to consider the treatment of the UCC at the end of the project (terminal recapture or loss?). We will need to use Equation 14-8 to determine the PV (CCA tax shield). This project does not have a capital gain so we do not need to worry about that.

To use Equation 14-8, we need the ending UCC. To calculate the UCC at the end of the project:

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Approach 1: (long way) Example (Project A): UCC beg CCA 1 $40,000.00 $2,000.0 2 $38,000.0 $3,800.0 3 $34,200.0 $3,420.0

UCC end $38,000.0 $34,200.0 $30,780.0

Approach 2: (formula) UCC1 = (1 – d) * 0.5 * C0 + 0.5 C0 UCC2 = (1 – d) * UCC1 UCC3 = (1 – d) * UCC2 = (1 – d)2 UCC1 ….

UCCN = (1 – d)N–1 * UCC1 = (1 – d)N–1 [(1 – d) * 0.5 * C0 + 0.5 C0] Step 1: initial cash flow = –CF0 = –$40,000 Step 2: PV of after-tax operating cash flow Discount rate = 0.08, payment = $15,000 * (1 – tax rate) = $15,000 * (1 – 0.45), N = 3, and PV = $21,261.05 Step 3: PV of CCA tax shield.

Using the ending UCC formula above, the ending UCC = $30,780 The salvage value is less than the ending UCC, and the difference is a terminal loss, which is fully tax deductible.

Using Equation [14-8], C0 d T/(d + k) = 10,000, (1 + 0.5k)/(1 + k) = 0.962963, UCC * dT/( d + k) = 7,695.00, 1/(1 + k)n = 0.793832, (SVn – UCCn)(T)/(1 + k)n = –278.64, and PV of CCA tax shield = $3,799.73 Step 4: PV of ECF Discount rate = 0.08, future value = salvage value = 30,000 N = 3, and PV = $23,814.97 Step 5: PV of capital gains taxes paid = 0 Step 6: Using Equation [14-10] NPV = PV (Operating CFs) + PV (CCA Tax Shield) + PV (ECFn) – PV (Capital Gains Taxes Paid) – CF0 NPV = $8,875.75 This project has a positive NPV. The company should take it.

28. Section: 14.2 Estimating and Discounting Cash Flows Learning Objective: 14.2 Level of difficulty: Difficult

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Solution: As the asset classes will be terminated when the project ends, we have to consider the treatment of the UCC at the end of the project (terminal recapture or loss?). We will need to use Equation 14-8 to determine the PV (CCA tax shield). This project does not have a capital gain so we do not need to worry about that.

To use Equation 14-8, we need the ending UCC. To calculate the UCC at the end of the project: UCC1 = (1 – d) * 0.5 * C0 + 0.5 C0 UCC2 = (1 – d) * UCC1 UCC3 = (1 – d) * UCC2 = (1 – d)2 UCC1 ….

UCCN = (1 – d)N–1 * UCC1 = (1 – d)N–1 [(1 – d) * 0.5 * C0 + 0.5 C0] Step 1: initial cash flow = –CF0 = –$90,000 Step 2: PV of after-tax operating cash flow Discount rate = 0.08, payment = $20,000 * (1 – tax rate) = $20,000 * (1 – 0.45), N = 5, and PV = $43,919.81 Step 3: PV of CCA tax shield Using the ending UCC formula above, the ending UCC = $18,367.65 The salvage value is greater than the ending UCC, and the difference is CCA recapture, which is fully taxable.

Using Equation [14-8], C0dT/(d + k) = 31,973.68, (1 + 0.5k)/(1 + k) = 0.962963, UCC * dT/(d + k) = 6,525.35, 1/(1 + k)n = 0.680583, (SVn – UCCn) (T) /(1 + k)n = 9,687.80, and PV of CCA tax shield = $16,660.63 Step 4: PV of ECF Discount rate = 0.08, future value = salvage value = 50,000 N = 5, and PV = $34,029.16 Step 5: PV of capital gains taxes paid = 0 Step 6: Using Equation [14-10] NPV = PV (Operating CFs) + PV (CCA Tax Shield) + PV (ECFn) – PV (Capital Gains Taxes Paid) – CF0 NPV = $4,609.60 This project has a positive NPV. The company should take it.

29. Section: 14.2 Estimating and Discounting Cash Flows Learning Objective: 14.2 Level of difficulty: Difficult Solution: As the asset classes will be terminated when the project ends, we have to consider the treatment of the UCC at the end of the project (terminal recapture or loss?). We will need to use Equation 14-8 to determine the PV (CCA tax shield). This project does not have a capital gain so we do not need to worry about that.

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To use Equation 14-8, we need the ending UCC. To calculate the UCC at the end of the project: UCC1 = (1 – d) * 0.5 * C0 + 0.5 C0 UCC2 = (1 – d) * UCC1 UCC3 = (1 – d) * UCC2 = (1 – d)2 UCC1 ….

UCCN = (1 – d)N–1 * UCC1 = (1 – d)N–1 [(1 – d) * 0.5 * C0 + 0.5 C0] Step 1: initial cash flow = –CF0 = –$85,000.

Step 2: PV of after-tax operating cash flow Discount rate = 0.08, payment = $32,500 * (1 – tax rate) = $32,500 * (1 – 0.45), N = 6, and PV = $82,633.97 Step 3: PV of CCA tax shield.

Using the ending UCC formula above, the ending UCC = $12,143.06 The salvage value is greater than the ending UCC, and the difference is CCA recapture, which is fully taxable.

Using Equation [14-8], C0dT/(d + k) = 30,197.37, (1 + 0.5k)/(1 + k) = 0.962963, UCC*dT/(d + k) = 4,313.98, 1/(1 + k)n = 0.630170, (SVn–UCCn)(T)/(1 + k)n = 14,988.98, and PV of CCA tax shield = $11,371.43 Step 4: PV of ECF Discount rate = 0.08, future value = salvage value = 65,000 N = 6, and PV = $40,961.03 Step 5: PV of capital gains taxes paid = 0 Step 6: Using Equation [14-10] NPV = PV (Operating CFs) + PV (CCA Tax Shield) + PV (ECFn) – PV (Capital Gains Taxes Paid) – CF0 NPV = $49,966.43 This project has a positive NPV. The company should take it.

30. Section: 14.2 Estimating and Discounting Cash Flows Learning Objective: 14.2 Level of difficulty: Difficult Solution: As the asset classes will be terminated when the project ends, we have to consider the treatment of the UCC at the end of the project (terminal recapture or loss?). We will need to use Equation 14-8 to determine the PV (CCA tax shield). This project does not have a capital gain so we do not need to worry about that.

To use Equation 14-8, we need the ending UCC. To calculate the UCC at the end of the project: UCC1 = (1 – d) * 0.5 * C0 + 0.5 C0 UCC2 = (1 – d) * UCC1

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UCC3 = (1 – d) * UCC2 = (1 – d)2 UCC1 ….

UCCN = (1 – d)N–1 * UCC1 = (1 – d)N–1 [(1 – d) * 0.5 * C0 + 0.5 C0] Step 1: initial cash flow = –CF0 = –$4,000 Step 2: PV of after-tax operating cash flow Discount rate = 0.10, payment = $2,000 * (1 – tax rate) = $2,000 * (1 – 0.40), N = 3, and PV = $2,984.22 Step 3: PV of CCA tax shield.

Using the ending UCC formula above, the ending UCC = $1,666.00 When the salvage value is less than the ending UCC, the difference is a terminal loss, which is fully tax deductible.

Using Equation [14-8], C0dT/( d + k) = 1,200.00, (1 + 0.5k)/(1 + k) = 0.954545, UCC*dT/(d + k) = 499.80, 1/(1 + k)n = 0.751315, (SVn – UCCn) (T) / (1 + k )n = –350.41, and PV of CCA tax shield = $1,120.36 Step 4: PV of ECF Discount rate = 0.10, future value = salvage value = 500 N = 3, and PV = $375.66 Step 5: PV of capital gains taxes paid = 0 Step 6: Using Equation [14-10] NPV = PV (Operating CFs) + PV (CCA Tax Shield) + PV (ECFn) – PV (Capital Gains Taxes Paid) – CF0 NPV = $480.24 This project has a positive NPV. The company should take it.

31. Section: 14.2 Estimating and Discounting Cash Flows Learning Objective: 14.2 Level of difficulty: Difficult Solution: As the asset classes will be terminated when the project ends, we have to consider the treatment of the UCC at the end of the project (terminal recapture or loss?). We will need to use Equation 14-8 to determine the PV (CCA tax shield). This project does not have a capital gain so we do not need to worry about that.

To use Equation 14-8, we need the ending UCC. To calculate the UCC at the end of the project: UCC1 = (1 – d) * 0.5 * C0 + 0.5 C0 UCC2 = (1 – d) * UCC1 UCC3 = (1 – d) * UCC2 = (1 – d)2 UCC1 ….

UCCN = (1 – d)N–1 * UCC1 = (1 – d)N–1 [(1 – d) * 0.5 * C0 + 0.5 C0]

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Step 1: initial cash flow = –CF0 = –$5,700 Step 2: PV of after-tax operating cash flow Discount rate = 0.10, payment = $2,000 * (1 – tax rate) = $2,000 * (1 – 0.40), N = 3, and PV = $2,984.22 Step 3: PV of CCA tax shield.

Using the ending UCC formula above, the ending UCC = $2,374.05 When the salvage value is less than the ending UCC, the difference is terminal loss, which is fully tax deductible.

Using Equation [14-8], C0dT/(d + k) = 1,710.00, (1 + 0.5k)/(1 + k) = 0.954545, UCC*dT/(d + k) = 712.215, 1/(1 + k)n = 0.751315, (SVn – UCCn)(T) /(1 + k)n = –563.20, and PV of CCA tax shield = $1,660.37 Step 4: PV of ECF Discount rate = 0.10, future value = salvage value = 500 N = 3, and PV = $375.66 Step 5: PV of capital gains taxes paid = 0 Step 6: Using Equation [14-10] NPV = PV (Operating CFs) + PV (CCA Tax Shield) + PV (ECFn) – PV (Capital Gains Taxes Paid) – CF0 NPV = –$679.75 This project has a negative NPV. The company should not take it.

32. Section: 14.2 Estimating and Discounting Cash Flows Learning Objective: 14.2 Level of difficulty: Difficult Solution: To solve this problem, begin by considering the various cash flows. Assume that all cash flows occur at the end of the year. i) Living expenses: these are the same regardless of whether or not you go to graduate school, so these can be ignored. ii) To solve this problem, use Excel and the solver function.

Year 1 =1+A2 =1+A3 =1+A4 =1+A5 =1+A6 =1+A7

Salary (ugrad only) 40000 =+(1.05)*B2 =+(1.05)*B3 =+(1.05)*B4 =+(1.05)*B5 =+(1.05)*B6 =+(1.05)*B7

CF (grad school) -8000 -8000 -8000 -8000 100 =+(1.07)*C6 =+(1.07)*C7

PV of ugrad option: PV grad option:

=NPV(0.04,B2:B41) =NPV(0.04,C2:C41)

Difference:

=E2-E3

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=1+A8 =+(1.05)*B8 =1+A9 =+(1.05)*B9 =1+A10 =+(1.05)*B10 =1+A11 =+(1.05)*B11 =1+A12 =+(1.05)*B12 =1+A13 =+(1.05)*B13 =1+A14 =+(1.05)*B14

Booth, Cleary

=+(1.07)*C8 =+(1.07)*C9 =+(1.07)*C10 =+(1.07)*C11 =+(1.07)*C12 =+(1.07)*C13 =+(1.07)*C14

Use solver to determine the starting salary at which you are indifferent between the undergraduate and graduate option:

You will need to have a starting salary after graduate school of $37,275.73 to be indifferent between grad school or not.

33. Section: 14.2 Estimating and Discounting Cash Flows Learning Objective: 14.2 Level of difficulty: Difficult Solution: a.

Annual opportunity cost Opportunity cost:

10.00% 0.007974

Present value of rent paid: Present value of mortgage payments: Value of buying house: PV(of sale price of house) less

$79,846.79 $212,125.00

Down payment PV of mortgage-rent

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108458.844 25000 $132,278.21 Chapter 14

Introduction to Corporate Finance, Third Edition

Booth, Cleary

–$48,819.36

Net value of owning home:

If my investments earn 10% per annum, I’m better off financially by renting than investing. The growth rate of the house investment does not offset the opportunity cost.

Details from calculation: (i)Monthly opportunity cost = (1 + 10%)1/12 – 1 = 0.007974 (ii)Present value of rent paid: Present value of rent paid in the 1st year = $7,980.34 since PMT = 700, I/Y = 0.7974%, and n = 12 Since annual rent increases by 1% a year, the PV of all rent can be considered as PV of growing annuity due with PMT = $7,980.34, k = 10%, g = 1%, n = 20. So Present value of rent paid = $79,846.79. (iii) Present value of mortgage payments PV = –250,000, I/Y =7%/12, n = 20 * 12 – >PMT – >1st term payment, 1,938.25 PMT = 1938.25, I/Y =7%/12, n = 15 * 12 – >PV – > principal after 1st term, 215,641.56 PMT = 1938.25, I/Y =7%/12, n = 5 * 12 – > PV of first term payment at 0, 92,141.37 PV = –215,641.56, I/Y = 7.5%/12, n = 15 * 12 – > PMT – > 2nd term payment, 1,999.02 PMT = 1,999.02, I/Y = 7.5%/12, n = 10 * 12 – > PV – > principal after 2nd term, 168,407.26 PMT = 1,999.02, I/Y = 7.5%/12, n = 5 * 12 – > PV of 2nd term payment at 5 years, 95,030.60 3rd term payment, 2,043.24 Principal after 3rd term, 100,769.63 PV of 3rd term payment at 10 years, 97,132.79 4th term payment, 2,067.44 PV of 4th term payment at 15 years, 98,283.15 PV of all payment at t = 0 212,125.00 = 92,141.37 + 95,030.60/1.15 + 97,132.79/1.110 + 98,283.15/1.115 (iv) PV of sale price of house = 275,000 * 1.0520/1.1020 Details from spreadsheet: Mortgage Mortgage balance at Payments beginning of month

Month

Rent

1

700

=H2

=1+A2 =1+A3

700 700

=C2 =C3

Interest

Mortgage Mortgage balance interest rate per Payment at end of month month

250000

=+D2*G2

=+D2–(C2–E2)

=0.07/12

=F2 =F3

=+D3*G3 =+D4*G4

=+D3–(C3–E3) =+D4–(C4–E4)

=G2 =G3

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Annuity factor

=(1– =D2/I2 1/(1+G2)^(241– A2))/G2

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……. =+D11*G1 =+D11–(C11–E11) 1 =+D12*G1 =+D12–(C12–E12) 2 =+D13*G1 =+D13–(C13–E13) 3 =+D14*G1 =+D14–(C14–E14) 4

=1+A10

700

=C10

=F10

=1+A11

700

=C11

=F11

=1+A12

700

=C12

=F12

=1+A13

=1.01* B2

=C13

=F13

=1.01* B49

=C60

=F60

=+D61*G6 =+D61–(C61–E61) 1

=G10 =G11 =G12 =G13

……. =1+A60

=1.01* =1+A61 B50

=H62

=F61

=+D62*G6 =+D62–(C62–E62) 2

=1.01* B51

=C62

=F62

=+D63*G6 =+D63–(C63–E63) 3

=1+A62

=G60 =0.07/12+((A62 =(1– – =D62/I62 1/(1+G62)^(241– 1)/60*0.005)/12 A62))/G62 =G62

b.

Annual opportunity cost Opportunity cost:

4.00% 0.003274

Present value of rent paid: Present value of mortgage payments: Value of buying house: PV(of sale price of house) less

$126,332.52 $332,328.71

Down payment PV of mortgage-rent

Net value of owning home:

333005.87 25000 $205,996.20 $102,009.67

If my other investments only earned 4%, now the house investment is profitable.

34. Section: 14.2 Estimating and Discounting Cash Flows Learning Objective: 14.2 Level of difficulty: Easy Solution: CF0A = C0 + ΔNWC0 + OC = 200,000 + 5,000 + 50,500 = $255,500 CF0B = C0 + ΔNWC0 + OC = 120,500 + 10,000 – 20,000 + 80,500 = $191,000 CF0A > CF0B →project A requires more initial cash flows.

35. Section: 14.2 Estimating and Discounting Cash Flows Learning Objective: 14.2 Level of difficulty: Easy Solutions Manual

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Solution: CCA recapture or terminal losses may be generated by the sale of an asset (or assets).

These may arise when the asset is the only asset in that asset class for the firm. The firm would have to pay additional taxes on “excess” CCA charged against the asset (or assets) if the salvage value > the ending UCC for the asset (or asset class). The amount by which the salvage value exceeds the UCC is referred to as CCA recapture, and is fully taxable. If the salvage value < the ending UCC, then the amount by which the UCC exceeds the salvage value is referred to as a terminal loss, which is fully tax deductible. Also, CCA recapture may occur even if an asset class is not closed, but an asset is sold for a price that exceeds the remaining UCC for that asset class.

36. Section: 14.2 Estimating and Discounting Cash Flows Learning Objective: 14.2 Level of difficulty: Medium Solution: a. k = 4.5% + 1.2 * 10% = 16.5% b. If the asset class is terminated: k = 4.5% + 1.2(10%) = 16.5%

PV (CCA Tax Shield) (C )(d )(T ) (1 + .5k ) (UCC n )(d )(T ) 1 = 0  −  d +k (1 + k ) (d + k ) (1 + k ) n − =

( SVn − UCC n )(T ) (1 + k ) n

(35,000 − 55,000)(0.4) 300,000  0.3  0.4 (1 + 0.5  0.165) 55,000  0.3  0.4 1  −  − 5 0.3 + 0.165 (1.165) (0.3 + 0.165) (1.165) (1.165) 5

= 71,937 − 6,614 + 3,728 = 69,051 c. If the asset class remains open: PV (CCATaxShield ) SV (d )(T ) 1 = 71,937 − n  d +k (1 + k ) n 35,000x0.3x0.4 1 = 71,937 −  (0.3 + 0.165) (1.165) 5 = 71,937 − 4,209 = $67,728 37. Section: 14.2 Estimating and Discounting Cash Flows Learning Objective: 14.2 Level of difficulty: Medium Solution: a. WACC = (30%)(6%)(1 – 0.4) + (50%)(12%) + (20%)(8%) = 8.68% b. k = 8.68% + 1.5% = 10.18%

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c.

1  1    1 − (1 + k ) n  1 − (1.1018) 6  PV (Operatingcash flows) = CFBT (1 − T )    = [195,000(1 − .40)]    k .1018         = (117,000)  (4.3324) = $506,889 38. Section: 14.2 Estimating and Discounting Cash Flows Learning Objective: 14.2 Level of difficulty: Difficult Solution: Capital Cost = C0 = 1,000,000 + 600,000 = $1,600,000

Initial Cash Outlay = CF0 = C0 + ΔNWC0 + OC = 1,600,000 + 50,000 + 0 = $1,650,000 k = rf + β(rm – rf) = 4.5% + 1.5(9.5 – 4.5) = 12%  (1,600,000)(.30)(.45)  1 + .5(.12)   (20,000)(.30)(.45)   1  PV (CCA Tax Shield) =    1 + .12  −    (1.12) 5  .30 + .12 .30 + .12    = 486,735 − 3,648 = $483,087 ECFn = SVn + NWC n = 20,000 + 50,000 = 70,000

PV ( ECFn ) =

ECFn 70,000 = = 39,720 n (1 + k ) (1.12) 5

PV (OperatingRe venues) =

Re v1 (1 − T ) Re v6 (1 − T ) 1 −  , k−g k−g (1 + k ) 5

(250,000)(1 − 0.45) (250,000)(1 − 0.45)(1.05) 5 1 = −  0.12 − 0.05 0.12 − 0.05 (1 + .12) 5 = $1,964,286 − $1,422,529 = $541,757

PV (Operating Costs) =

Cost1 (1 − T ) Cost6 (1 − T ) 1 −  , k−g k−g (1 + k ) 5

(100,000)(1 − 0.45) (100,000)(1 − 0.45)(1.04) 5 1 −  0.12 − 0.04 0.12 − 0.04 (1 + .12) 5 = $687,500 − $474,624 = $212,876

=

PV(Operating CFs) = $541,757 – $212,876 = $328,881 NPV = PV(Operating CFs) + PV(CCA Tax Shield) + PV(ECFn ) − CF0

= 328,881+ 483,087 + 39,720 − $1,650,000 = −$798,312  0 Therefore, Brigid Co. should not accept this project.

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39. Section: 14.3 Sensitivity to Inputs Learning Objective: 14.3 Level of difficulty: Difficult Solution: Capital Cost = C0 = 1,000,000 + 600,000 = $1,600,000 Initial Cash Outlay = CF0 = C0 + ΔNWC0 + OC = 1,600,000 + 50,000 + 0 = $1,650,000 k = rf + β(rm - rf) = 4.5% + 0.8(9.5 – 4.5) = 8.5%  1  (1,600,000)(.30)(.45)  1 + .5(.085)   (100,000)(.30)(.45)   PV (CCA Tax Shield) =  −  20      .30 + .085 .30 + .085    1 + .085     (1.085)  = 539,063 − 6,859 = $532,204 ECFn = SVn + NWC n = 100,000 + 50,000 = 150,000

PV ( ECFn ) =

ECFn 150,000 = = 29,342 n (1 + k ) (1.085) 20

Re v1 (1 − T ) Re v 21 (1 − T ) 1 −  , k−g k−g (1 + k ) 20 (500,000)(1 − 0.45) (500,000)(1 − 0.45)(1.05) 20 1 = −  0.085 − 0.05 0.085 − 0.05 (1 + .085) 20 = $7,857,143 − $4,078,081 = $3,779,062 PV (OperatingRe venues) =

PV (Operating Costs) =

Cost1 (1 − T ) Cost21 (1 − T ) 1 −  , k−g k−g (1 + k ) 20

(100,000)(1 − 0.45) (100,000)(1 − 0.45)(1.04) 20 1 −  0.085 − 0.04 0.085 − 0.04 (1 + .085) 20 = $1,222,222 − $523,868 = $698,354

=

PV(Operating CFs) = $3,779,062 – $698,354 = $3,080,708 NPV = PV (Operating CFs ) + PV (CCA Tax Shield) + PV ( ECFn ) − CF0

= 3,080,708 + 532,204 + 29,342 − $1,650,000 = 1,992,254  0 Therefore, Brigid Co. should accept this project.

40. Section: 14.2 Estimating and Discounting Cash Flows Learning Objective: 14.2 Level of difficulty: Difficult Solution: Step 1: CCA considerations: The project requires a machine costing $45,000 and installation costs of $15,000 → total cost $60,000.The CCA rate is 25%.

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UCC begin

Year

Booth, Cleary

CCA

UCC end

0 1 60000 7500 52500 2 52500 13125 39375 3 39375 9843.75 29531.25 4 29531.25 7382.813 22148.44 5 22148.44 5537.109 16611.33 Salvage value $2,000 → as the CCA class will not terminate, we can ignore CCA recapture or terminal loss.

Step 2: Opportunity and sunk costs: Environmental assessment costs – sunk; original cost of building and renovation costs – sunk Offer from LeCrook – opportunity cost of $150,000 (value of project must take into account foregone opportunity to sell building) Step 3: Working capital effects: Work-in-progress increase of $2,000 (cash outflow, reversed at end of project) at time 0 Increase in accounts receivable $3,000 (cash outflow at end of year 1, reversed at end of project) Increase in accounts payable $2,000 (cash inflow at end of year 1, reversed at end of project) Step 4: Annual revenues taking into account fixed and variable costs Step 5: Impact on other projects (reduced sales of X-ray glasses and reduced production costs) Step 6: Financing charges—already included in WACC of 10% Summary of cash flows (before taxes):

Year 0 1 2 3 4 5

Working capital effects Operating cash flows Opportunity Invest.

Work-inMachines costs A/R A/P Revenues Costs progress sold –60,000 –150,000 –2,000 –3,000 2,000 25 1250000 155000 30 1500000 180000 40 2000000 230000 40 2000000 230000 2,000 2,000 3,000 –2,000 40 2000000 230000

X-ray Glasses Lost Saved revenues Prod. costs –220000 –220000 –220000 –220000 –220000

20000 20000 20000 20000 20000

Determining after-tax cash flows:

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Year

Booth, Cleary

Nontaxable Taxable cash CCA tax cash flows effects flows 0 –212000 1 –1000 2625 895000 2 0 4593.75 1120000 3 0 3445.313 1570000 4 0 2583.984 1570000 5 5000 1937.988 1570000

Total after-tax cash flows –212,000.00 583,375.00 732,593.75 1,023,945.31 1,023,083.98 1,027,437.99

NPV of the X-ray machine project is $3.03 million. As the NPV is positive, the company should accept the project.

41. Section: 14.2 Estimating and Discounting Cash Flows Learning Objective: 14.2 Level of difficulty: Difficult Solution: Capital Cost = C0 = 40,000 + 1,500 = $41,500 Initial Cash Outlay = CF0 = C0 + NWC0 + OC = 41,500 + 2,000 + 0 = $43,500.

1   1 − (1 + .15)6  PV(Future CFt’s) = 5,600  = (5,600)(3.784483) = $21,193 .15     (C )(d )(T ) (1 + .5k ) (UCC n )(d )(T ) ( SVn − UCC n )(T ) 1 PV (CCA Tax Shield) = 0  −  − n d +k (1 + k ) (d + k ) (1 + k ) (1 + k ) n (41,500)(.30)(.40) (1 + 0.5  0.15) (8,469)(.30)(.40) 1 =  −  .30 + .15 (1.15) .30 + .15 (1.15) 6 (4,000 − 8,469)(.40) − (1.15) 6 = 10,345 − 976 + 773 = $10,142 ECFn = SVn + NWC n = 4,000 + 2,000 = $6,000 Note: Capital gains are not possible because SV < C0.

NPV = PV (Operating CFs ) + PV (CCA Tax Shield) + PV ( ECFn ) − PV (CapitalGainsTaxes Paid ) − CF0 6,000 = 21,193 + 10,142 + + 0 – 43,500 (1 + .15) 6 = – $9,571

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Since NPV < 0, GG Inc. should reject the project.

42. Section: 14.2 Estimating and Discounting Cash Flows Learning Objective: 14.2 Level of difficulty: Difficult Solution: Capital Cost = C0 = 40,000 + 1,500 = $41,500 Initial Cash Outlay = CF0 = C0 + NWC0 + OC = 41,500 + 2,000 + 0 = $43,500.

PV (Operatingcash flows) 1   1 − (1 + k ) n  = CFBT (1 − T )    k     1   1 − (1.15)6  = [(70,000 − 40,000)(1 − .40)]     .15    = (18,000)  (3.784483) = $68,121 Since there is no terminal loss or CCA recapture associated with the termination of this project, we use Equation 14-7 to estimate the present value of the CCA tax shield:

(C0 )(d )(T ) (1 + .5k ) ( SVn )(d )(T ) 1  −  d +k (1 + k ) (d + k ) (1 + k ) n (41,500)(.30)(.40) (1 + .5  .15) (4,000)(.30)(.40) 1 =  −  .30 + .15 1 + .15 .30 + .15 (1.15) 6 = 10,345 − 461 = $9,884 ECFn = SVn + NWCn = 4,000 + 2,000 = $6,000 6,000 PV ( ECFn ) = = $2,594 (1.15) 6 There are no capital gains, so this term is zero, and there is no CCA recapture or terminal loss since the asset class is not closed.

PV (CCA Tax Shield) =

Now we can put these items together to determine the NPV of the project.

NPV = PV (Operating CFs ) + PV (CCA Tax Shield) + PV ( ECFn ) − CF0 = 68,121 + 9,884 + 2,594 − 43,500 = $37,099 Therefore, GG Inc. should go ahead with this project.

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43. Section: 14.2 Estimating and Discounting Cash Flows Learning Objective: 14.2 Level of difficulty: Difficult Solution: C0 = $41,500; CF0 = $43,500; (as in Problem 50)

PV (Operatingcash flows) 1   1 − (1 + k ) n  = CFBT (1 − T )    k     1   1 − (1.15)6  = [(70,000 − 40,000)(1 − .40)]     .15    = (18,000)  (3.784483) = $68,121 Since the asset class is closed, we use Equation 14-8 to estimate the present value of the CCA tax shield: (C )(d )(T ) (1 + .5k ) (UCCn )(d )(T ) 1 PV (CCA Tax Shield) = 0  −  d +k (1 + k ) (d + k ) (1 + k ) n ( SVn − UCCn )(T ) − (1 + k ) n (41,500)(0.30)(0.40) (1.075) (8,469)(0.30)(0.40) 1 =  −  0.30 + 0.15 (1 + .15) (0.30 + 0.15) (1 + .15) 6 (4,000 − 8,469)(0.40) − (1 + .15) 6 = 10,345 – 976 +773 = $10,142 ECFn = SVn + NWC n = 4,000 + 2,000 = $6,000 6,000 PV ( ECFn ) = = $2,594 (1.15) 6 There are no capital gains, so this term is zero.

Now we can put these items together to determine the NPV of the project.

NPV = PV (Operating CFs ) + PV (CCA Tax Shield) + PV ( ECFn ) − CF0 = 68,121 + 10,142 + 2,594 − 43,500 = $37,357 Solutions Manual

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Therefore, GG Inc. should go ahead with this project.

44. Section: 14.2 Estimating and Discounting Cash Flows Learning Objective: 14.2 Level of difficulty: Difficult Solution: k = rf + β(market risk premium) = 3.4% + 1.2 (5.5%) = 10% Capital Cost = C0 = 40,000 + 1,500 = $41,500 Initial Cash Outlay = CF0 = C0 + NWC0 + OC = 41,500 + 2,000 + 0 = $43,500.

PV (Operatingcash flows) 1   1 − (1 + k ) n  = CFBT (1 − T )    k     1   1 − (1.10) 6  = [(70,000 − 40,000)(1 − .40)]     .10    = (18,000)  (4.355261) = $78,395 Since there is no terminal loss or CCA recapture associated with the termination of this project, we use Equation 14-7 to estimate the present value of the CCA tax shield: (C )(d )(T ) (1 + .5k ) ( SVn )(d )(T ) 1 PV (CCA Tax Shield) = 0  −  d +k (1 + k ) (d + k ) (1 + k ) n (41,500)(.30)(.40) (1 + .5  .10) (4,000)(.30)(.40) 1 =  −  .30 + .10 1 + .10 .30 + .10 (1.10)6 = 11,884 − 677 = $11,207 ECFn = SVn + NWCn = 4,000 + 2,000 = $6,000 6,000 PV ( ECFn ) = = $3,387 (1.10)6 There are no capital gains, so this term is zero, and there is no CCA recapture or terminal loss since the asset class is not closed.

Now we can put these items together to determine the NPV of the project.

NPV = PV (Operating CFs ) + PV (CCA Tax Shield) + PV ( ECFn ) − CF0 = 78,395 + 11,207 + 3,387 − 43,500 = $49,489

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Therefore, GG Inc. should go ahead with this project. Δ%NPV =

49,489 − 1 = 33% (Δk = 10% - 15% = -5%) 37,099

45. Section: 14.3 Sensitivity to Inputs Learning Objective: 14.3 Level of difficulty: Difficult Solution: Initial Cash Outlay = CF0 = $43,500. Since there is a terminal loss or CCA recapture associated with the termination of this project, we use Equation 14-8 to estimate the present value of the CCA tax shield: PV (CCA Tax Shield) = =

(C 0 )(d )(T ) (1 + .5k ) (UCC n )(d )(T ) ( SVn − UCC n )(T ) 1  −  − n d +k (1 + k ) (d + k ) (1 + k ) (1 + k ) n (41,500)(.30)(.40) (1 + .5  .15) (8,469)(.30)(.40) (4,000 − 8,469)(.40) 1  −  − 6 .30 + .15 1 + .15 .30 + .15 (1.15) (1.15) 6

= 10,345 − 976 + 773 = $10,142 ECFn = SVn + NWCn = 4,000 + 2,000 = $6,000 6,000 PV ( ECFn ) = = $2,594 (1.15) 6 0 = NPV = PV (Operating CFs ) + PV (CCA Tax Shield) + PV ( ECFn ) − CF0

= PV (Operating CFs ) + 10,142 + 2,594 − 43,500 PV (Operating CFs ) = 30,764 1   1 − (1.15) 6   PV (Operatingcash flows) = [ Break − even Operating CF ]   .15       30,764 = ( Break − even Operating CF )  (3.784483) Break − even Operating CF = $8,129 46. Section: 14.2 Estimating and Discounting Cash Flows Learning Objective: 14.2 Level of difficulty: Medium Solution: k = rf + β(market risk premium) = 8% + 0.8(5.5%) = 12.4%

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PV (OperatingRe venues) =

Booth, Cleary

Re v1 (1 − T ) Re v9 (1 − T ) 1 −  , k−g k−g (1 + k ) 8

(15,000)(1 − 0.40) (15,000)(1 − 0.40)(1.05) 8 1 = −  0.124 − 0.05 0.124 − 0.05 (1 + .124) 8 9,000 13,297 = −  (0.392527) = $121,621.62 − $70,533.38 = $51,088.24 0.074 0.074 PV (Operating Costs) =

Cost1 (1 − T ) Cost9 (1 − T ) 1 −  , k−g k−g (1 + k ) 8

(7,000)(1 − 0.40) (7,000)(1 − 0.40)(1.04) 8 1 −  0.124 − 0.04 0.124 − 0.04 (1 + .124) 8 4,200 (5,748) = −  (0.392527) = $50,000 − $26,860.01 = $23,139.99 0.084 0.084

=

PV (Operating CFs) = $51,088 – $23,140 = $27,948 47. Section: 14.2 Estimating and Discounting Cash Flows Learning Objective: 14.2 Level of difficulty: Medium Solution: a. Year 1 CCA expense is lower due to the half-year rule. Year 2 CCA expense is higher and then CCA expenses decline every year thereafter as the UCC continually declines. b. CCA (year 1) = (C0) × (CCA rate) × (1/2) = (250,000) × (0.2) × (1/2) = $25,000 UCC (beginning of year 2) = UCC (beginning of year 1) – CCA (year 1) = 250,000 – 25,000 = $225,000 CCA (year 2) = (UCC) × (CCA rate) = (225,000) × (0.20) = $45,000 Net cash flow (year 2) = OI (1 – T) + CCA (T) = 150,000 (1 – 0.4) + 45,000 (0.4) = $108,000 48. Section: 14.3 Sensitivity to Inputs Learning Objective: 14.3 Level of difficulty: Easy Solution: Sensitivity analysis examines how an investment’s NPV changes as the value of one input is changed at a time. Scenario analysis examines how an investment’s NPV changes in response to differing scenarios with respect to the values of one or more estimates and it is often conducted in the form of a “what-if” analysis.

49. Section: 14.3 Sensitivity to Inputs Learning Objective: 14.3 Level of difficulty: Difficult Solution: a.

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Year

UCC After-tax cash (close) flow

PV of aftertax cash flow

-$2,500.00 $125.00 2,375 $556.25 $237.50 2,137.50 $610.63 $213.75 1,923.75 $632.25 $192.38 1,731.37 $655.85

-$2,500.00 $519.86 $533.34 $516.10 $500.34

UCC (open)

Cash flow

0 1 2 3 4

Booth, Cleary

-$2,500.00 $700.00 2,500 $735.00 2,375 $771.75 2,137.50 $810.34 1,923.75

CCA

Present value of after-tax cash flows:

-$430.35

The asset will be scrapped (salvage = $0) → zero capital gains. As the asset class is large and will continue we do not have to deal with CCA recapture and terminal loss in year 4. b.

Worst case Year

AfterPV of Cash flow tax cash after-tax flow cash flow

Cash flow

Base case

Best case

AfterPV of tax cash after-tax flow cash flow

PV of Afterafter-tax tax cash cash flow flow

Cash flow

Growth rate

2.00%

5.00%

8.00%

Year 1 cash flow

$300

$700

$ 900

0 1 2 3 4

–2,500 300.00 306.00 312.12 318.36

NPV

–2,500 256.25 288.88 287.53 286.87

–2,500 239.49 252.32 234.71 218.85 – $1,554.63

–2,500 700.00 735.00 771.75 810.34

–2,500 556.25 610.63 632.25 655.85

–2,500 –2,500 –2,500 519.86 900.00 706.25 533.35 972.00 788.38 516.10 1,049.76 840.76 500.34 1,133.74 898.40 –$430.35

–2,500 660.05 688.60 686.31 685.39 $220.35

The expected value of the project is: .3*(–1,554.63) + .55*(–430.35) + .15*(220.35) = –$670.03 c.

Year

PV of cash flows

Growth rate Year 1 cash flow NPV

0.03

0.05

0.07

0.03

0.05

0.07

0.03

0.05

0.07

400

400

400

700

700

700

1,000

1,000

1,000

–1,278.46 –1,248.18 –1,217.13 –483.34 –430.35 –376.01 311.78 387.48 465.12

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Given that this project is only 4 years long, the impact of any errors on the initial cash flow estimate will be more important than growth rate errors. With only 4 years to grow, a small error in the growth rate does not have time to compound into a huge error. d. Using the solver function in Excel, we find that the initial cash flow that results in a breakeven or zero NPV is $857.86

47

B

C

Year

CCA

Growth 48 rate Year 1 49 cash flow 50 0 125 51 1 237.5 52 2 213.75 53 3 192.375 54 4 NPV 55

D

E

Cash flow

After-tax cash flow

F PV of after-tax cash flows

0.05 857.862619935937 –2500 =D50 =+D52*(1+G$17) =+D53*(1+G$17) =+D54*(1+G$17)

–2500 =D52*0.75+$C52*0.25 =D53*0.75+$C53*0.25 =D54*0.75+$C54*0.25 =D55*0.75+$C55*0.25

=E51/(1.07)^$B51 =E52/(1.07)^$B52 =E53/(1.07)^$B53 =E54/(1.07)^$B54 =E55/(1.07)^$B55 =SUM(F51:F55)

50. Section: 14.3 Sensitivity to Inputs Learning Objective: 14.3 Level of difficulty: Easy Solution: ROV can be used in corporate decision making to give the firm the option to defer or delay a project, abandon a project, or switch the use of the asset from producing one product to another. If the assets involve generic modern production equipment, the flexibility involved in closing down an unprofitable project and using the assets elsewhere considerably reduces the project’s risk. In this case, scenario analysis combined with these event-changing parameters gives a more accurate NPV than simply assuming that nothing changes as critical values faced by the project change.

51. Section: 14.3 Sensitivity to Inputs Learning Objective: 14.3 Level of difficulty: Difficult Solution: a. The NPV of the terrestrial alternative: No time limit stated for the radio station. Assume it will also last 12 years (to match space alternative): NPV = $144.27 million b. Expected NPV of the satellite alternative: Forecasted cash flows if satellite successful:

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Note: we have to purchase the satellite today, but, only launch 2 years later at an additional cost of $5 million. Assume that the $5 million is not subject to CCA. Satellite survives UCC begin. CCA

Year 0 1 2 3 4 5 6 7 8 9 10 11 12

250 412.5 268.125 174.2813 113.2828 73.63383 47.86199 31.11029 20.22169 13.1441 8.543664 5.553382

87.5 144.375 93.84375 60.99844 39.64898 25.77184 16.7517 10.8886 7.077592 4.600434 2.990282 1.943684

UCC end

Investment Revenue: -500

412.5 268.125 174.2813 113.2828 73.63383 47.86199 31.11029 20.22169 13.1441 8.543664 5.553382 3.609698

-5

After tax -500 30.625 45.53125 -25 16.59531 -25 5.099453 -25 -2.37286 150 106.5201 150 103.3631 150 101.311 150 99.97716 150 99.11015 150 98.5466 150 98.18029

CCA terminal loss is $3.609698 million.

PV of CCA terminal loss = $0.404852 million.

The NPV of the successful launch: PV of after-tax cash flow + PV of CCA terminal loss = –$284.01 million +$0.404852 million = –$283.61 million c. If the satellite explodes:

Year

Satellite explodes UCC beg CCA UCC end Investment Revenue: After tax 0 –500 –500 1 500 87.5 412.5 30.625 2 412.5 144.375 268.125 –5 45.53125

CCA terminal loss is UCC end at year 2, which is $268.125 million.

NPV = PV of after tax cash flow + PV of CCA terminal loss = –442.86 + 186.1979 = –$256.66 million d. The expected NPV for the satellite = .4*(–256.66) + .6*(–283.61) = –$272.83 million Based on the above analysis, I do not recommend that XK invest in the space project. e. The analysis would have to incorporate the value of the option to wait. It may be that in two years the demand for satellite services will have increased dramatically and the expected revenues will have increased sufficiently to make the project viable.

52. Section: 14.3 Sensitivity to Inputs Solutions Manual

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Learning Objective: 14.3 Level of difficulty: Difficult Solution: a.

Investment today = $200 million In one year: Revenues = $500 * 1 million = $500 million Costs = fixed plus variable = $50 + $250 * 1million = $300 million NPV = –200 + (200/1.15) = –$26.087 million Based on NPV, the mine should not be opened. b. i. the choice of closing the mine changes the value of the asset because it essentially gives the mine operator an option on gold. She can, depending on the price of gold in the future, choose whether or not to produce. ii. We know from option theory that the more volatile the value of the underlying asset, the greater the value of the option.

Intuitively, the more volatile the price of gold, the more valuable the chance to close (or open) the mine becomes. Flexibility becomes much more important and valuable the more uncertain the future. iii.

iv.

Portfolio 1: Action

Cash flow today

Purchase mine –200 Lend PV of $50 –48.54 Total cash flow –248.54

Cash flow in future G=850 (850 – 250)*1-50 +50 (850 – 250)=$600

G=200 –50 (close mine) +50 $0

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Action

Cash flow today

Cash flow in future

Buy .9231m oz gold Borrowing pv 184.6154

–276.9231

G=850 784.6154

G=200 184.6154

179.2382

–184.6154

–184.6154

–97.6849

$600

$0

Putting the two portfolios together, we find that buying the mine with the option to close if the price of gold is too low and lending PV of $50 is the equivalent to buying .9231 million ounces of gold and borrowing PV of $184.6154.

-Mine-48.54 =-97.6849 Mine=97.6849-48.54=$49.15 Therefore, the value of the mine, taking into account the value of the option to close, is $49.15 million.

53. Section: 14.4 Replacement Decisions Learning Objective: 14.4 Level of difficulty: Difficult Solution: The consultant’s approach is incorrect; the appropriate approach is to either use the chain replication approach or the Equivalent Annual PV approach.

Example (for simplicity assume zero taxes, zero investment and a discount rate of 10%): Consider two projects: A – pays $100 per year for 2 years (NPV = $173.5537; NPV/life = 86.7769) and B – pays $101 per year for 6 years (NPV = $439.8813, NPV/life = $73.3136).

Based on the analysis of the consultant, we should accept project A as it has the higher NPV/life, but does this make sense? Which would you prefer: to receive $100 per year for two years or $101 per year for 6 years?

Using the chain replication approach, replicate Project A 3 times for an NPV of $435.5261, which is less than the NPV of B. Using the EANPV approach: Project A Annual Payment: $100 Project B Annual Payment: $101 54. Section: 14.4 Replacement Decisions Learning Objective: 14.4 Level of difficulty: Difficult Solution: Because we are dealing with a replacement problem, we have to examine the incremental cash flows. As the old machine was fully depreciated 8 years ago and will be scrapped if we replace it, we will assume that the UCC for this asset class at time zero is close to zero (i.e., we will not have to deal with any CCA recapture/loss or capital gains at time zero if we replace the old machine).

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New machine CCA schedule UCC Year CCA begin 0 1 2 3 4 5

Booth, Cleary

Old machine New machine

UCC Rev. Maint. Invest. Maint. New - Old end –25000

25000 2500 22500 4500 18000 3600 14400 2880 11520 2304

Incremental after tax CF

22500 1500 18000 1500 14400 1500 11520 1500 9216 1500

–500 –500 –500 –500 –500

5000 6000 7000 8000 9000

–25000 1980 2640 3300 3960 4620

CCA Tax shield 850 1530 1224 979.2 783.36

Total –25000 2830 4170 4524 4939.2 5403.36

The cash flows are given as nominal values so we need to use the appropriate nominal discount rate: the approximation is 7% + 3% = 10%. The more exact value for the nominal rate would be 1.07 * 1.03 – 1 = 10.21% NPV of incremental cash flows: + PV of salvage value of new machine – PV of CCA terminal loss NPV of replacing old machine:

–$8,853.44 3104.60662 890.053461 –$4,858.78

Based on the analysis above, the old machine should not be replaced.

55. Section: 14.4 Replacement Decisions Learning Objective: 14.4 Level of difficulty: Difficult Solution: C0 = C0New − C0Old = 100,000 − 50,000 = $50,000 CF0 = C0 + NWC0 + OC = 50,000 + 4,000 + 0 = $54,000 Δ CFBT =10,000 – 6,000 = $4,000 1   1 − (1 + k ) n   PV (Operating CFs ) = (CFBT )(1 − T )  k    

1   1 − (1.15) 5   = (4,000)(.60)(3.352155) = $8,045 = (4,000)(1 − .40)  .15     Since the asset class is left open and there is no CCA recapture or terminal loss, we can use Equation 14-7: SVn = SVNew − SVOld = 35,000 − 15,000 = 20,000

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PV (CCA Tax Shield) =

Booth, Cleary

(C0 )(d )(T ) (1 + .5k ) (SVn )(d )(T ) 1  −  d +k (1 + k ) (d + k ) (1 + k ) n

 (50,000)(.30)(.40)  1 + .5(.15)   (20,000)(.30)(.40)   1  =   1 + .15  −    (1.15) 5  .30 + .15 .30 + .15    = 12,464 − 2,652 = $9,812 ECFn = SVn + NWCn = 20,000 + 4,000 = 24,000 ECFn 24,000 PV (ECFn ) = = = $11,932 (1 + k ) n (1.15)5 NPV = PV ( Operating CFs ) + PV (CCA Tax Shield) + PV (ECFn ) − CF0 . = 8,045 + 9,812 + 11,932 – 50,000 = –$20,211 Therefore, GG Inc. should not go ahead with this replacement project.

56. Section: 14.5 Inflation and Capital budgeting Decisions Learning Objective: 14.5 Level of difficulty: difficult a. Medium 10, 000*3*(1 − .30) NPV = −15, 000 + = $685, 000 .08 − .05 b. We are expecting unit sales to grow at 5% per year. If prices now grow at 2% per year then the after-inflation expected growth in sales is 7%. To see this: year 1 sales is 10,000 units *$3 = $30,000. In year 2 the unit sales have grown by 5% and the price has increased by 2% resulting in an approximate growth rate of 7%.

NPV = −15, 000 +

10, 000*3*(1 − .30) = $2, 085, 000 .08 − (.05 + .02)

Using nominal values and discount rate, the NPV is now $2,085,000. To be more exact, we could use the exact growth rate of 7.1% (1.05*1.02–1). c. Now we have an inconsistency – the sales number is nominal but the required rate of return is in real terms. Two approaches: convert the sales numbers to real or convert the required rate of return to nominal. In this case, it is easier to convert the required rate of return to nominal → 8% + 2% = 10%. The growth rate is still the 7% from above:

NPV = −15, 000 +

10, 000*3*(1 − .30) = $685, 000 (.08 + .02) − (.05 + .02)

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Chapter 15: Mergers and Acquisitions Multiple Choice Questions 1. Section: 15.1 Types of Takeovers Learning Objective: 15.1 Level of difficulty: Medium Solution: B In mergers, the approval of the target company’s shareholders is required, but the shareholders of the acquiring company do not normally have to give their approval.

2. Section: 15.1 Types of Takeovers Learning Objective: 15.1 Level of difficulty: Medium Solution: D A firm with minimal legal problems is more likely to be a target compared to a firm with many legal problems.

3. Section: 15.2 Securities Legislation Learning Objective: 15.2 Level of difficulty: Medium Solution: D 90% is the threshold for minority squeeze-out.

4. Section: 15.3 Friendly versus Hostile Takeovers Learning Objective: 15.3 Level of difficulty: Medium Solution: B A formal vote by the target shareholders is not required since they merely decide on their own whether or not they want to sell their shares to the acquiring firm.

5. Section: 15.3 Friendly versus Hostile Takeovers Learning Objective: 15.3 Level of difficulty: Medium Solution: D It suggests that the bid is too low rather than too high.

6. Section: 15.3 Friendly versus Hostile Takeovers Learning Objective: 15.3 Level of difficulty: Medium Solution: D The arbitrageurs’ motivation is to extract the highest possible price.

7. Section: 15.3 Friendly versus Hostile Takeovers Learning Objective: 15.3 Level of difficulty: Medium Solution: D

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In a hostile takeover, the target has no desire to be acquired and actively rebuffs the acquirer and refuses to provide any confidential information.

8. Section: 15.4 Motivations for Mergers and Acquisitions Learning Objective: 15.4 Level of difficulty: Easy Solution: C The three types of M&A are horizontal, vertical, and conglomerate M&As. 9. Section: 15.4 Motivations for Mergers and Acquisitions Learning Objective: 15.4 Level of difficulty: Medium Solution: C To be a valid M&A, it must meet the following requirement: ΔV= VA–T – (VA + VT) > 0 Choice A : ΔV= 400,000 – 410,000 <0 Choice B : ΔV= 390,000 – 390,000 = 0 Choice C : ΔV= 410,000 – 390,000 >0 Choice D : ΔV= 600,000 – 610,000 <0 Therefore only C is valid.

10. Section: 15.4 Motivations for Mergers and Acquisitions Learning Objective: 15.4 Level of difficulty: Medium Solution: A Evidence shows that diversification in general is a poor motive for a merger.

11. Section: 15.4 Motivations for Mergers and Acquisitions Learning Objective: 15.4 Level of difficulty: Medium Solution: D Cash flow volatility tends to be lower for larger entities, especially if the cash flows from the two underlying businesses are not highly correlated. This may enable the company to reduce their need for external financing.

12. Section: 15.5 Valuation Issues Learning Objective: 15.5 Level of difficulty: Medium Solution: B Market value of the equity = P/E0 × E0 = P/E0 × E1/(1 + g) = 4.5 × 550,000/(1.05) = $2,357,143 13. Section: 15.5 Valuation Issues Learning Objective: 15.5 Level of difficulty: Easy Solution: B The cash flows used in the DCF valuation approach will be the company’s free cash flows.

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According to the discount rate you use, you could use free cash flows to the firm (use WACC) or free cash flows to equity holders (use cost of the equity).

14. Section: 15.5 Valuation Issues Learning Objective: 15.5 Level of difficulty: Medium Solution: B Liquidation value equals liquidation value of current assets plus market value of tangible assets minus the value of liabilities.

Practice Problems 15. Section: 15.1 Types of Takeovers Learning Objective: 15.1 Level of difficulty: Easy Solution: An acquisition occurs when one firm (the acquiring firm or bidder) completely absorbs another firm (the target firm). Under this arrangement, the acquiring firm retains its identity, while the acquired firm ceases to exist. In contrast, a merger is usually the combination of two firms into a new legal entity.

16. Section: 15.2 Securities Legislation Learning Objective: 15.2 Level of difficulty: Medium Solution: a 50.1% b. 50.1% c. 50.1% d. 90% e. To win a vote on amalgamation, IFC will need to win “majority of minority” shareholders. As Marcel owns 12 percent, other minority shareholders need to hold 12.1 percent. IFC will, therefore, need to hold 100 – 12 – 12.1 = 75.9 percent of the shares. f. 10% 17. Sections: 15.2 Securities Legislation and 15.4 Motivations for Mergers and Acquisitions Learning Objective: 15.2 and 15.4 Level of difficulty: Medium Solution: The board acquired a company solely because it appeared to be “cheap.” Acquisitions need to fit into a sound strategy.

The board considered only one target; most firms will look at many possible targets prior to making an offer. The target may have been cheap, but perhaps there were others that were cheaper or a better fit for a sewing machine company.

The lumber industry is very cyclical, so looking only at the past two years is not appropriate. The board of directors should have tried to determine where the target was in the cycle to better approximate its performance.

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The close relationship between the member of the board and the CEO of the target raises the possibility of a serious conflict of interest.

There is the potential problem of an insider-controlled board of directors.

18. Section: 15.3 Friendly versus Hostile Takeovers Learning Objective: 15.3 Level of difficulty: Easy Solution: Total shares Mr. tendered by VanDuun Vendall tendered shareholders A B C D E F

1000 1000 500 500 500 500

400 300 400 300 100 200

Total number of shares accepted by Bynum 600 600 500 500 500 500

Number of Mr. VanDuun’s shares accepted by Bynum (600/1000) × 400 = 240 (600/1000) × 300 = 180 400 300 100 200

19. Section: 15.3 Friendly versus Hostile Takeovers Learning Objective: 15.3 Level of difficulty: Easy Solution: 1) At first, the acquirer can approach the target, or the target can post an offering memorandum if it decides to sell itself.

2) When serious acquirers express interest, they can access the data room of the target firm by signing a confidentiality agreement.

3) Once the confidential data have been evaluated, the acquirer signs a letter of intent which scopes out the terms of an agreement and allows the acquirer to do the main due diligence.

4) The acquirer completes the due diligence.

5) After everything has worked out to the satisfaction of the acquirer, the final sale agreement is reached.

6) The final sale agreement is ratified or agreed to by both parties.

20. Section: 15.3 Friendly versus Hostile Takeovers Learning Objective: 15.3 Level of difficulty: Easy Solution: Common defensive tactics against a takeover include: a. The Board can recommend rejection of the offer, and shareholders may heed their advice. b. The target firm can try to encourage other “bidders” to enter the fray. c. They can attempt to have a friendly investor (a “white squire”) purchase a significant number of their shares in order to reduce the likelihood of the takeover bid’s success. d. They can try to find a friendly suitor (a “white knight”) to make an offer to acquire the Solutions Manual 4 Chapter 15 Copyright © 2013 John Wiley & Sons Canada, Ltd. Unauthorized copying, distribution, or transmission is strictly prohibited.

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company. e. The firm can undergo a recapitalization and finance a share repurchase using debt. f. They can acquire another firm to make themselves less attractive. g. They can sell off some of their key assets (“crown jewels”) to make themselves less attractive. h. They can establish poison pills, which are provisions that make it prohibitively expensive for the acquiring firm to acquire the target firm. Poison pills are allowed in both U.S. and Canada. It is up to the business judgement of the Board in the U.S., but may be removed by the courts in Canada.

21. Section: 15.3 Friendly versus Hostile Takeovers Learning Objective: 15.3 Level of difficulty: Easy Solution: When a hostile tender offer is launched, external parties always look for certain clues. The most obvious is the behaviour of the market price relative to the offer price. If the market price immediately jumps above the offer price, then the market is saying that a competing offer is likely or that the bid is too low and the bidder will have to increase the offer price. Alternatively, if the market price stays close to the offer price, it indicates that the price is fair and the deal is likely to go through.

22. Section: 15.4 Motivations for Mergers and Acquisitions Learning Objective: 15.4 Level of difficulty: Difficult Solution: a. i) The current price of the target is $20 per share.

The bidder is offering 2 shares valued at $15 for a total of $30.

The offer premium is $30/$20 – 1 = 50% ii) To capture the premium, I will buy the target and short sell 2 bidder shares. iii) To show that my transaction will “lock in” the $10 premium, I will consider several scenarios and consider my profit when the deal is completed. Note: at completion the target must sell at twice the price of the bidder; if not, there is an arbitrage opportunity.

Scenario Bidder price does not change Bidder price rises Bidder price falls

Bidder price

Target price

Profit on long position

Profit on short position

Total profit

$15

$30

$30 – $20 = $10

2(15 – 15) = $0

$10

$30

$60

$60 – $20 = $40

2(15 – 30) = –$30

$10

$5

$10

$10 – $20 = –$10

2(15 – 5) = $20

$10

b. Yes, we have not taken into account any possible margin calls on the short position. The actual return will also change if the terms of the deal are changed or the deal is cancelled. If either of these occurs, we no longer have a hedged position.

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23. Section: 15.4 Motivations for Mergers and Acquisitions Learning Objective: 15.4 Level of difficulty: Easy Solution: Horizontal M&A occurs when two firms in the same industry combine. Vertical M&A occurs when a firm can expand by acquiring a company that is closer to its existing customers (“going forward”) or by acquiring a supplier that provides inputs into its production process (“going backward”).Conglomerate M&A occurs when two firms in unrelated businesses combine. The motivation to create a conglomerate is that the different businesses face different risks, which tend to cancel each other out, lowering the overall risk of the combined company.

24. Section: 15.4 Motivations for Mergers and Acquisitions Learning Objective: 15.4 Level of difficulty: Easy Solution: Economies of scale refer to the benefits of getting bigger.

1) Reducing capacity. It may be, for example, that an industry has grown too big and there are too many firms operating in it. A merger or acquisition in this situation is often called an overcapacity M&A. 2) Spreading fixed costs. Often, significant costs in a business are fixed, independent of scale. By increasing the company’s size, these costs are spread over greater volumes and the firm is more efficient.

3) Geographic synergies. Often an industry is fragmented and ripe for consolidation. A geographic roll-up occurs when a national firm is created out of a series of regional firms.

25. Section: 15.4 Motivations for Mergers and Acquisitions Learning Objective: 15.4 Level of difficulty: Easy Solution: 1) Reduced cash flow variability. Cash flow volatility tends to be lower for larger entities, especially if the cash flows from the two underlying businesses are not highly correlated. This may enable the company to reduce its need for external financing, since future financing needs can be forecast with greater certainty.

2) Increase in debt capacity. Debt capacity may rise due to the increase in size and/or reduction in cash flow volatility of the new company. Riskier firms generally cannot carry as much debt as larger firms and the use of additional debt can provide the firm with greater tax savings.

3) Reduction in average issuing costs. Since most security issues occur in large increments, the average cost of floating new debt or equity will decrease as the firm issues larger amounts.

Additionally, larger firms can access more sources of capital than smaller ones, resulting in cost savings.

4) Fewer information problems. Larger firms usually attract more external security analysts and have greater exposure in the media. The result is that they attract big institutional investors, which lowers their financing costs.

26. Section: 15.4 Motivations for Mergers and Acquisitions Learning Objective: 15.4

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Level of difficulty: Easy Solution: 1) The evidence suggests that the target firm shareholders gain the most. These gains consist of a one-third run-up in the stock price prior to the announcement, plus about a two-thirds gain after the announcement. There is considerable disagreement about the source of the run-up prior to the announcement. On the one hand, some people believe that information about an impending merger is leaked, resulting in insider trading, which is, of course, illegal. On the other hand, many believe that informed industry specialists can make reasonable predictions about takeover activity based on transactions elsewhere.

2) In contrast, the acquiring firm’s shareholders, on average, see no change in their stock price.

In fact, usually the stock price dips marginally on news of the bid. This implies that acquiring firms pay too much for target firms, acquire them for the wrong reasons, and/or overestimate the benefits resulting from the merger. Numerous studies concerning post-merger value indicate there is little or no increase in value; there are no synergistic gains to the acquirer, which is the supposed rationale for mergers.

3) “Shareholder value at risk,” or SVAR, in M&As, illustrates the basic point that, when using cash, the acquirer bears all the risk, whereas when using share swaps, the risk is borne by the shareholders in both companies.

27. Sections: 15.3 Friendly versus Hostile Takeovers; 15.4 Motivations for Mergers and Acquisitions 15.5; and Valuation Issues Learning Objective: 15.3, 15.4, and 15.5 Level of difficulty: Difficult Solution: a. Two possible motives for this acquisition are: 1) Value creation: There may be economies of scope (being able to combine different activities) in the selling and marketing of sausages and buns There may be complementary strengths (one very good at marketing, one very good at distribution) Various other synergies (financing; improved efficiency) Tax benefits 2) Managerial motivations (non-value creation): Increasing firm size (i.e., empire building) Reducing firm risk through diversification (reduced manager income risk) b. There are two ways Carla can structure the deal to limit the risk to Superior Sausage: 1) Stock offer • If B&B turns out to be a bad acquisition, then B&B shareholders will have to share in the downside • Alternatively, if B&B turns out to be a great acquisition, then B&B shareholders will also get to share in the upside.

• Problem: B&B shareholders may feel that Superior is offering stock because Superior feels its stock is overvalued.

2) Earnout • If B&B turns out to be as good as promised, then Superior will pay the full price Solutions Manual 7 Chapter 15 Copyright © 2013 John Wiley & Sons Canada, Ltd. Unauthorized copying, distribution, or transmission is strictly prohibited.

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If B&B does not turn out to be as good as promised, then Superior will pay a lower price Makes B&B “put their money where their mouth is.”

c. i) The takeover is likely to be hostile, given her comments about the management of B&B; it is unlikely that they will be willing to negotiate. ii) If the offer is hostile (i.e., not welcomed by the target management), then Superior will have to go directly to the shareholders. This is the definition of a tender offer. iii) Possible defences: • Using a poison pill • Selling the crown jewels (e.g., selling the hot dog bun plant) • Finding a White Knight (a more appealing buyer) d. i) We expected a return of 0% + 2 × 4% = 8% (using CAPM). ii)The abnormal return is the difference between the observed return and the expected return.

B&B actually earned a return of –2 percent (10 percent less than expected). The abnormal return is –10 percent. iii) This reaction is very unusual. Usually targets rise at the announcement of a takeover offer.

Perhaps the market was expecting a much higher offer and, when the actual offer emerged, had to revise its expectations downward.

28. Section: 15.5 Valuation Issues Learning Objective: 15.5 Level of difficulty: Medium Solution: EBITDA = 1,550,000 – 350,000 = 1,200,000 P = 10 × (1,200,000)/500,000) = $24.00 29. Section: 15.5 Valuation Issues Learning Objective: 15.5 Level of difficulty: Difficult Solution: Assume g = 6% NI = 1,550,000 – 350,000 – 400,000 – 150,000 – 260,000 = 390,000 EPS0 = 390,000/500,000 = 0.78 Trailing P/E: P/E0 = 24/0.78 = 30.8X EPS1 = 0.78 × 1.06 = 0.83 Forward P/E: P/E1 = 24/0.83 = 28.9X 30. Section: 15.5 Valuation Issues Learning Objective: 15.5 Level of difficulty: Difficult Solution: k = RF +β (market risk premium) = 5 + 0.65 (5) = 8.25% payout = 300,000/390,000 = 0.77 Solutions Manual 8 Chapter 15 Copyright © 2013 John Wiley & Sons Canada, Ltd. Unauthorized copying, distribution, or transmission is strictly prohibited.

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P/E1 = payout / (k – g) = 0.77/(8.25% – 6%) = 34.2X P/E0 = P/E1 (1 + g) = 34.2(1.06) = 36.3X 31. Section: 15.5 Valuation Issues Learning Objective: 15.5 Level of difficulty: Difficult Solution: Free cash flow to equity (FCFE0) = 390,000 + 400,000 – 400,000 + 300,000 –100,000 = 590,000 Equity = E0 =

FCFE1 590,000(1.06) 625,400 = = = $27,795,556 k−g .0825 − .06 0.0225

Value of the firm = Market value of (equity + debt) = 27,795,556 + 1,000,000 = $28,795,556 32. Section: 15.5 Valuation Issues Learning Objective: 15.5 Level of difficulty: Difficult Solution: k = 8.25%; FCFE1 = $590,000(1.08) = 637,200; FCFE2 = $637,200(1.08) = 688,176; FCFE3 = $688,176 (1.05) = 722,584.8 CF3 (722,584.8) V2 = = = $22,233,378.46 k − g .0825 − .05 637,200 688,176 22,233,378.46 V0 = + + (1.0825) (1.0825) 2 (1.0825) 2

= 588,637 + 587,278 + 18,973,596 = $20,149,511 Value of the firm = Market value of (equity + debt) = 20,149,511 + 1,000,000 = $21,149,511 33. Section: 15.5 Valuation Issues Learning Objective: 15.5 Level of difficulty: Difficult Solution: (i) Cash: The cost is $22 × 500,000 = $11,000,000 Purchasing DEF by cash would generate an NPV of $15,875,000 – $11,000,000 = +$4,875,000. (ii) Post-merger value of ABC-DEF = Value of ABC + Value of DEF to ABC = (600,000)($18) + 15,875,000 = $26,675,000 Since there will be 600,000 + 500,000(2) = 1,600,000 shares outstanding in the new firm, each share will be worth $26,675,000 /1,600,000 = $16.67 So, the actual cost of giving DEF’s shareholders 1,000,000 shares equals: Cost = (1,000,000 shares)($16.67 per share) = $16,670,000 Thus, the NPV under this scenario would be $15,875,000 – $16,670,000 = – $795,000 Therefore, firm ABC should use cash to purchase DEF.

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34. Section: 15.5 Valuation Issues Learning Objective: 15.5 Level of difficulty: Difficult Solution: Total Earnings = $25,000 + $7,000 = $32,000 Total Shares outstanding = 8,000 (i.e., the number of shares Bidder had outstanding) Post-merger EPS = $32,000/8,000 = $4.00 (well above Bidder’s pre-merger EPS of $3.13).

Notice that if the market was inefficient and the P/E ratio for the Bidder remained at 9, the value of B-T would = EPS  P/E ratio = $4.00  9 = $36.00.

Therefore, the market value of B-T would equal $36.00  8,000 = $288,000 However, according to the fact that no synergies arise, the market value of B-T should equal 236,000 + 42,000 = $278,000 Therefore, P/E = 278,000/32,000 = 8.6875 Post-merger share price = 4.00  8.6875 = $34.75 In conclusion, the post-merger EPS = $4.00; market value of B-T = $278,000; new P/E = 8.69; post-merger share price = $34.75.

35. Section: 15.6 Accounting for Acquisitions Learning Objective: 15.6 Level of difficulty: Medium Solution: Goodwill = Price paid – MV of Target’s equity = Price paid – (MV of target’s assets –MV of target’s liabilities) = 1,250– (2,000– 1,050) = 1,250 – 950 = 300 36. Section: 15.6 Accounting for Acquisitions Learning Objective: 15.6 Level of difficulty: Easy Solution: Under the purchase method, one firm basically assumes all of the assets and liabilities of the other (target) firm and all operating results included from the date of acquisition going forward.

No restatement of prior periods’ results is necessary. At the time of the acquisition, all the assets and liabilities of the target firm are restated to reflect the firm’s FMV as of the acquisition date.

Goodwill will result if the purchase price exceeds the FMV of the target firm’s equity.

37. Section: 15.6 Accounting for Acquisitions Learning Objective: 15.6 Level of difficulty: Difficult Solution: a. Number of shares outstanding for the combined firm: 10,000+.80*5,000 = 14,000 b. The original shareholders of the bidder will own 10,000/14,000 = 71.43% of the combined firm. c. Total paid for target = (.80*5,000)*$20 = $80,000 Value of target = net tangible assets (restated) – debt = $65,000–$19,000 = $46,000 Goodwill on this transaction = $80,000 – $46,000 = $34,000 Solutions Manual 10 Chapter 15 Copyright © 2013 John Wiley & Sons Canada, Ltd. Unauthorized copying, distribution, or transmission is strictly prohibited.

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d. Net tangible assets of combined=book net tangible assets of the bidder + market value of the net tangible assets of the target = $18,000 + $65,000 = $83,000 e.

Combined firm balance sheet as of 31/12/1x Net tangible assets

$83,000

Total debt

$34,000

Goodwill Total assets

37,000 $120,000

Equity Total claims

86,000 $120,000

Net tangible assets of combined: $18,000 + $65,000 = $83,000 Total debt = $15,000 + $19,000 = $34,000 Goodwill on balance sheet: $3,000+$34,000 = $37,000 38. Section: 15.6 Accounting for Acquisitions Learning Objective: 15.6 Level of difficulty: Difficult Solution: Bidder Current assets

25,000

Target (book value) 3,500

Target (FMV) 2,900

B-T(post-merger)

Long-term assets Goodwill Total assets

10,000

1,000

1,300

11,300 300* 37,500

35,000

4,500

4,200

Current liabilities Long-term debt Common stock Retained earnings Total

11,000 5,000 15,000 4,000 35,000

1,500 800 1,800 400 4,500

1,500 1,000 2,000 4,500

25,900

12,500 6,000 15,000 4,000 37,500

*Goodwill = 2,000 (Price paid) – MV (Target’s equity) = 2,000 - [4,200 MV (Target’s assets) – 2,500 MV(Target’s liabilities)] = 2,000 – 1,700 = $300 Note that Cash of $2,000 was paid out to the target’s shareholders.

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Chapter 16: Leasing Multiple Choice Questions 1. Section: 16.1 Leasing Arrangements Learning Objective: 16.1 Level of Difficulty: Medium Solution: B In operating leases, the lessor is responsible for maintaining the asset.

2. Section: 16.1 Leasing Arrangements Learning Objective: 16.1 Level of Difficulty: Medium Solution: A Capital leases tend to be long-term leases. The lessee, not the lessor, is responsible for the maintenance of the assets. The lease covers 75 percent of the economic life of the asset. Only statement A is correct.

3. Section: 16.1 Leasing Arrangements Learning Objective: 16.1 Level of Difficulty: Medium Solution: B The lender receives interest payments from the lessor, not lessee. The other statements are correct.

4. Section: 16.1 Leasing Arrangements Learning Objective: 16.1 Level of Difficulty: Easy Solution: B Universities pay no tax; therefore they could lower the lease payments by selling the asset to the new owner, who could enjoy the tax benefits from the asset’s capital cost allowance.

5. Section: 16.2 Accounting for Leases Learning Objectives: 16.2 Level of Difficulty: Difficult Solution: B The lease is classified as a financial lease if the lessor transfers the ownership of the property to the lessee when the lease expires, or the lease term is 75% or more of the estimated economic life of the asset. In this case, 7.5 ÷ 9 = 83% > 75%. Therefore B is correct and C is incorrect. The lease is classified as a financial lease if the present value of the lease payments is 90% or more of the asset’s fair market value at the lease inception, or the lessee could purchase the asset at a price below the fair market value when the lease expires. In this case, 58,000 ÷ 70,000 = 83% < 90% and the purchase price ($90,000) > FMV ($81,000). Therefore, A and D are incorrect.

6. Section: 16.2 Accounting for Leases Learning Objectives: 16.2 Level of Difficulty: Easy

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Solution: C Note that it is an operating lease, not a capital lease. Under an operating lease, no asset/liability is recognized on the lessee’s balance sheet. The operating lease is revealed off balance sheet.

7. Section: 16.2 Accounting for Leases Learning Objectives: 16.2 Level of Difficulty: Medium Solution: A 1   1   1 − (1 + k ) n  1 − 1.055   (1 + k ) = 15,000 Asset/Liability = PVMLP = PMT   (1.05) = 68,189.26 k 0 .

05         Or, using financial calculator: [2nd][BGN][2nd][SET] N = 5; I/Y = 5%; PMT = $15,000; FV = 0; CPT PV = $68,189.26 Or, by Excel, Input 15,000 into B2 to B6 and 0.05 into B1.

NPV (B1, B2:B6), you could get 64,942.15, which is the NPV of year-end payment.

Therefore, NPV of year-beginning payments = 64,942.15 (1.05) = 68,189.26 8. Section: 16.2 Accounting for Leases Learning Objectives: 16.2 Level of Difficulty: Medium Solution: B Under operating leases, NI is higher in the early years and lower in the later years. CFO is lower since the whole lease payment is deducted from CFO. CFF is higher since there is no deduction from CFF under an operating lease. Depreciation expense is lower under an operating lease since there is no asset recognized. Total cash flow is the same regardless of lease type.

9. Section: 16.2 Accounting for Leases Learning Objectives: 16.2 Level of Difficulty: Medium Solution: B Under financial leases: Current assets are unchanged but current liabilities are higher →current ratio is lower.

Total assets are higher and equity is unchanged→leverage ratio is higher.

NI is lower in early years, but not in later years. Sales are unchanged →NI margin is lower in early years, but higher in later years.

ROE is lower in early years, but higher in later years.

10. Section: 16.2 Accounting for Leases Learning Objectives: 16.2 Level of Difficulty: Medium Solution: C Under financial leases, the leverage ratio is higher, the P/E ratio is higher in the early years, and the asset turnover is lower. Only total cash flow is unchanged compared with an operating lease.

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Practice Problems 11. Section: 16.1 Leasing Arrangements Learning Objective: 16.1 Level of Difficulty: Medium Solution: a. Long-term debt and capital leases in 2011: $3,906. Long-term capital leases = $426. Fraction = 10.91% b. TELUS: Total long-term debt in 2011:$6,574. Capital leases: 0. Fraction: 0%.

Notice the dramatic difference. These two industries are, in general, characterized by very different usage of capital leases.

12. Section: 16.4 Motivation for Leasing Learning Objectives: 16.4 Level of Difficulty: Easy Solution: Firms may enter into lease agreements because of cheaper financing, lower risk of asset ownership, lower or zero maintenance cost, convenience, cancellation options, capital budget restrictions, or better-looking financial statements by using an operating lease.

13. Section: 16.2 Accounting for Leases Learning Objectives: 16.2 Level of Difficulty: Medium Solution: Expected Purchase economic Annual lease Length price at PV of lease payments life of the payments of lease end of asset lease A 10 years

$175,000

8 years $10,000

$933,612.08

B 5 years

$115,000

2 years $900,000

$199,586.78

C 10 years

$30,000

5 years $500,000

$113,723.60

D 9 years

$180,000

8 years $1,000

$960,286.72

E 25 years

$110,000 22 years $8,000

$964,869.43

F 10 years

$195,000

$739,203.42

5 years $800,000

Percentage of acquisition price 93.36% (Financial) 19.96% (Operating) 11.37% (Operating) 96.03% (Financial) 96.49% (Financial) 73.92% (Operating)

For projects A, D, E, the length of lease is more than 75% of the economic life, and the PV of lease payments is more than 90% of acquisition price. Thus they are financial leases.

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14. Section: 16.2 Accounting for Leases Learning Objectives: 16.2 Level of Difficulty: Medium Solution: a. All financial statements contain much more than just the balance sheets, income statements, and statements of cash flows – they also contain important additional information about the firm’s operations. In this case, the notes will also describe the operating leases used by the firm.

This is why operating leases are called “off-balance-sheet financing”. b. Igor should have used the information in the notes to correct the levels of the net income (impact on EPS) to correct the P/E ratio for the operating/financial lease’s effects. c. If we assumed that KW and KT are otherwise identical, then the EPS of KW (the operating lease firm) will appear to be different from KT resulting in an artificially different P/E ratio.

Consequently if we correct for the lease effect, the average P/E ratio will change and so will our estimate of the price for KGC. We cannot tell exactly what the change will be – we need to look at the notes. Remember that in general net income will be higher for operating leases in the early years and that it will generally be lower in the later years. We have no information about the age of the leases so we do not know if the net income is “too high or too low” relative to the financial lease case.

15. Section: 16.2 Accounting for Leases Learning Objectives: 16.2 Level of Difficulty: Difficult Solution: First, we decide the type of lease.

Lease term ÷ economic life = 4 ÷ 5 = 80% > 75% Therefore, it is a capital lease.

1   1   1 − (1 + k ) n  1 − 1.084  Asset/Liability = PVMLP = PMT   (1 + k ) = 10,000  (1.08) = 35,771 k 0 .

08         Or, using financial calculator: [2nd][BGN][2nd][SET] N = 4; I/Y = 8%; PMT = $10,000; FV = 0; CPT PV = $35,771 Or, using Excel Input 10,000 into B2 to B5 and 0.08 into B1, NPV (B1, B2:B5) you get 33,121, which is the NPV of year-end payments.

Therefore, NPV of year-beginning payments = 33,121 (1.08) = 35,771 Annual depreciation expense = 35,771 ÷ 4 = $8,943 Interest expense = 35,771 × 0.08 = 2,862 Principal repayment = 10,000 – 2,862 = 7,138 Total expense = 8,943 + 2,862 = 11,805 (notice it’s greater than 10,000) Change in NI = –$11,805 Change in CFO = –$2,862 Change in CFF = –$7,138 16. Section: 16.2 Accounting for Leases Solutions Manual ..

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Learning Objectives: 16.2 Level of Difficulty: Difficult Solution: Now the lease term ÷ economic life = 4 ÷ 6 = 67% < 75%, therefore the lease is considered an operating lease given the information in the problem.

Under an operating lease, no asset/liability is recognized. The whole lease payment is recognized as rental expense.

Total expense = rental expense = $10,000 Change in NI=–$10,000 Change in CFO=–$10,000 Change in CFF=0 Compared with the NI under financial lease, NI is increased by $1,805 (11,805 – 10,000).

The whole lease payment is deducted from CFO and there is no deduction from CFF. Compared with the NI under financial lease, CFO is decreased by $7,138 (actually the principal repayment deducted from CFF under financial lease is now deducted from CFO).

Compared with the NI under financial lease, CFF is increased by $7,138.

17. Section: 16.2 Accounting for Leases Learning Objectives: 16.2 Level of Difficulty: Difficult Solution: Under a capital lease, the present value of the lease payments is recognized as a long-term asset and a long-term liability; however, the first-year principal repayment is recognized as a current liability.

Change in current assets = 0 Change in long-term assets = + $35,771 Change in the current liability = + $7,138 Change in the long-term liability = + (35,771 – 7,138) = +$28,633 18. Section: 16.2 Accounting for Leases Learning Objectives: 16.2 Level of Difficulty: Medium Solution: There is no change in the balance sheet since operating lease does not affect the balance sheet of the lessee.

19. Section: 16.3 Evaluating the Lease Decision Learning Objectives: 16.3 Level of Difficulty: Difficult Solution: a.

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The real option value arises because at year 10, we can choose to renew the lease, buy the reactor, or walk away depending on the economic conditions. b. Expedic has three alternatives: buy the asset, lease for 10 years and then either renew or purchase. To evaluate this, we will consider the NPV of each alternative.

Alternative 1 – buy asset: Year 0 cash flow: –16 billion Year 0 to 20: CF = – maintenance*(1–T) + CCA*T = –12 million*(.6) + 800 million*.4 =312.8 million at the end of year NPV at 7% = –$12.686 billion Alternative 2 – lease and renew lease in year 10 Years 1 to 10: CF = – lease payment*(1 – T) = –2,500 million*.6 = –1,500 million at the beginning of year Years 11 to 20: CF = –3,000*(1–.4) = –1,800 at the beginning of year NPV = –$18.150 billion Alternative 3 – lease and then purchase Years 1 to 10: CF = –1,500 million at the beginning of year Year 10 purchase: CF = – 3.5 billion (Assume straight-line CCA again) Years 11 to 20 CF = – maintenance*(1–T) + CCA*T = –12 million*.6 + 800 million*.4 = $312.8 million at the end of year NPV at 7% = –$11.935 billion Alternative 3 is the best. It has the lowest cost. Note: even though all three NPVs are negative, we will still choose one; remember we are trying to find the lowest cost alternative. We are assuming that the cash flows earned by the reactor would be the same regardless of how we

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acquire the reactor. Before we make the final decision, we would have to consider the cash earned by the reactor to determine if the overall NPV is positive.

20. Section: 16.3 Evaluating the Lease Decision Learning Objectives: 16.3 Level of Difficulty: Difficult Solution: a.

Firm buys asset Year 1 Cash flow from asset Interest payments Lease payments CCA on asset Tax payment After-tax cash flows

Year 2

Year 3

Year 4

Year 5

800,000 800,000 800,000 800,000 800,000 -150,000 -150,000 -150,000 -150,000 -150,000 0 0 0 0 0 300,000 300,000 300,000 300,000 300,000 140,000 140,000 140,000 140,000 140,000 $510,000 $510,000 $510,000 $510,000 $510,000

Principal repayment -1,500,000

-1,500,000

b.

Firm uses financial lease Year 1

Year 2

Year 3

Year 4

Year 5

Cash flow from asset Interest payments Lease payments CCA on asset Tax payment

800,000 0 500,000 300,000 0

800,000 0 500,000 300,000 0

800,000 0 500,000 300,000 0

800,000 0 500,000 300,000 0

800,000 0 500,000 300,000 0

After-tax cash flows

$300,000 $300,000 $300,000 $300,000 $300,000

Principal repayment 0

c.

Lessor in financial lease

Cash flow from asset Interest payments Lease payments CCA on asset Tax payment After-tax cash flows

Year 1

Year 2

Year 3

Year 4

Year 5

0 -150,000 500,000 0 140,000 210,000

0 -150,000 500,000 0 140,000 210,000

0 -150,000 500,000 0 140,000 210,000

0 -150,000 500,000 0 140,000 210,000

0 -150,000 500,000 0 140,000 210,000

Principal repayment -1,500,000

-1,500,000

d. No; Mr. McKee’s suspicions are not correct. As we can see below, the net effect of the financial lease on tax revenues is zero (compare the total below to the tax payments for the firm Solutions Manual ..

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in case (a)). All the lease has done is shared the tax burden between the lessor and the lessee.

Note that there is no net change in the total after- tax cash flows of the two firms—all that the lease has done is split the cash flows between the two parties.

Lessee Lessor Total

Year 1 0 140,000 140,000

Annual tax payments Year 2 Year 3 Year 4 0 0 0 140,000 140,000 140,000 140,000 140,000 140,000

Year 5 0 140,000 140,000

e. There are several ways that leasing could increase total cash flows (lessee + lessor): i) If the two companies have different tax brackets ii) If the two companies have different borrowing costs ii) If their relative levels of efficiency in using the asset were different (i.e., the lessor could only earn $100,000 using the asset while the lessee could earn $1 million.

The gain arises from the comparative advantages of the lessee and lessor.

21. Section: 16.3 Evaluating the Lease Decision Learning Objectives: 16.3 Level of Difficulty: Difficult Solution: NPV (leasing) = CF0 (purchase price savings) – PV(foregone depreciation tax savings) – PV(foregone salvage value) – PV(after-tax lease payments) CF0 = $800,000; Depreciation tax savings = 0.40 × $80,000 = $32,000 per year.

After-tax cost of borrowing = 8% × (1 – .40) = 4.8%.

1   1 − (1.048) 9  PV(Depreciation tax savings) = 32,000 ×   = $229,490 .048     Or, using financial calculator: N = 9; I/Y = 4.8%; PMT = $32,000; FV = 0; CPT PV = $229,490 Or, using Excel Input 32,000 into B2 to B10 and 0.048 into B1, NPV(B1, B2:B10) you get 229,490.  1  = $52,461 PV(Salvage value) = 80,000 ×  9  (1.048)  Or, using financial calculator: N = 9; I/Y = 4.8%; PMT = 0; FV = 80,000; CPT PV = $52,461 Or, using Excel, PV(0.048,9,0, – 80000), you get 52,461 Solutions Manual ..

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PV(after-tax lease payments) 1   1 − (1.048) 9  = 40,000(1 – 0.4) ×    (1.048) = $180,379 .048     Or, using financial calculator: [2nd][BGN][2nd][SET] N = 9; I/Y = 4.8%; PMT = $24,000; FV = 0; CPT PV = $180,379 Or, using Excel, Input 24,000 into B2 to B10 and 0.048 into B1, NPV (B1, B2:B10) you get 172,117, which is the NPV of year-end payments.

Therefore, NPV of year-beginning payments = 172,117(1.048) = 180,379 NPV(leasing) = CF0 – PV(foregone depreciation tax savings) – PV(foregone salvage value) – PV(after-tax lease payments) = 800,000 – 229,490 – 52,461 – 180,379 = +$337,670 > 0 The firm should lease the equipment instead of purchasing it.

22. Section: 16.3 Evaluating the Lease Decision Learning Objectives: 16.3 Level of Difficulty: Difficult Solution: NPV(leasing) = CF0 (i.e., purchase price savings) + PV(maintenance savings) – PV(foregone depreciation tax savings) – PV(foregone salvage value) – PV(after-tax lease payments) CF0 = $250,000; After-tax borrowing cost = 8%  (1 – 0.40) = 4.8%

1   1 − (1.048) 4  PV(maintenance savings) = 20,000 × (1 – 0.4) ×   = $42,750 .048     Or, using financial calculator: N = 4; I/Y = 4.8%; PMT = $12,000; FV = 0; CPT PV = $42,750 Or, using Excel Input 12,000 into B2 to B5 and 0.048 into B1, NPV (B1, B2:B5) you get 42,750.

Since the salvage value is the ending UCC at the end of four years.

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(C0 )( d )(T ) (1 + .5k ) ( SVn )( d )(T ) 1  −  d +k (1 + k ) (d + k ) (1 + k ) n ( 250,000)(.20)(.40) (1 + .5  .048) (115,200)(.20)(.40) 1 =  −  .20 + .048 (1 + .048) .20 + .048 (1.048) 4 = 78,798 – 30,807 = $47,991  1  PV(Salvage value) = 115,200 ×  = $95,501 4  (1.048)  Or, using financial calculator: N = 4; I/Y = 4.8%; PMT = 0; FV = 115,200; CPT PV = $95,501 Or, using Excel, PV(0.048,4,0, – 115200), you get 95,501.

PV (CCA Tax Shield) =

PV(after-tax lease payments) 1   1 −  (1.048) 4    (1.048) = $67,203 = 30,000 × (1 – 0.4) ×  .048       Or, using financial calculator: [2nd][BGN][2nd][SET] N = 4; I/Y = 4.8%; PMT = $18,000; FV = 0; CPT PV = $67,203 Or, using Excel, Input 18,000 into B2 to B5 and 0.048 into B1, NPV (B1, B2:B5) you get 64,125, which is the NPV of year-end payments.

Therefore, NPV of year-beginning payments = 64,125(1.048) = 67,203.

NPV(leasing) = CF0 + PV(maintenance savings) – PV(foregone depreciation tax savings) – PV(foregone salvage value) – PV(after-tax lease payments) = 250,000 + 42,750 – 47,991 – 95,501 – 67,203 = $82,055 > 0 The firm should lease rather than buy the machine.

23. Section: 16.3 Evaluating the Lease Decision Learning Objectives: 16.3 Level of Difficulty: Difficult Solution: First, we calculate the monthly payments for each option.

Leases: (N.B. Lease payments are usually at the beginning of the month.)

Monthly lease rate = 8% ÷ 12 = 0.67%; Number of monthly payments = 6 years × 12 months = 72

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22,000 = $383.59 1   1 − (1.0067)72   (1.0067) .0067     Loan: (N.B. Loan payments are usually at the end of the month.)

Monthly lease payments =

Monthly loan rate = 7% ÷ 12 = 0.58%; 22,000 = $374.66 Monthly loan payments = 1   1 − (1.0058)72    .0058     Estimate the PV of the beginning-of-month lease payments using the loan rate.

1   1 − (1.0058) 72  (1.0058) = $22,655 PV(lease payments) = 383.59 ×  .0058     This implies that the firm should enter into the loan arrangement, since the effective cost of the asset would be greater than $22,000, which is the cost under the loan arrangement 24. Section: 16.3 Evaluating the Lease Decision Learning Objectives: 16.3 Level of Difficulty: Difficult Solution: NPV(leasing) = CF0 (i.e., purchase price savings) − PV(forgone depreciation tax savings) −PV(forgone salvage value) − PV(after-tax lease payments) CF0 = $1,500,000 Depreciation tax savings = 0.35 × $180,000 = $63,000 per year After-tax cost borrowing cost = 8% x (1–.35) = 5.2%

1   1 −  (1.052) 5  PV (Depreciation tax savings) = $63,000 ×   = $271,255.63 .052     PV (Salvage value) = $800,000 × (1/1.052^5) = $620,885.17

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1   1 − (1.052) 5  PV (after-tax lease payments) = $130,000 ×   × (1.052) = $588,840.00 .052     NPV(leasing) = $1,500,000 – $271,255.63 – $620,885.17 – $588,840.00 = +$19,019.20 It is better to lease since the NPV is positive.

25. Section: 16.3 Evaluating the Lease Decision Learning Objectives: 16.3 Level of Difficulty: Difficult Solution: Setting PV(after-tax lease payments) = CF0 (i.e., purchase price savings) − PV(forgone depreciation tax savings) −PV(forgone salvage value) PV(after-tax lease payments) = $1,500,000 – $271,255.63 – $620,885.17 = $607,859.20 Using the annuity formula with PV = 607,859.20, FV = 0, I/Y = 5.2 and N = 5, we get payment as $134,198.93 Before-tax lease payment = $134,198.93/0.65 = $206,460 26. Section: 16.3 Evaluating the Lease Decision Learning Objectives: 16.3 Level of Difficulty: Medium Solution: University does not pay taxes.

NPV(leasing) = CF0 (i.e., purchase price savings) − PV(lease payments) CF0 = $1,800,000

1   1 −  (1.05) 5  PV(lease payments) = $400,000×    (1.05) = $1,818,380 .05     NPV(leasing) = $1,800,000 – $1,818,380 = -$18,380 Since the NPV is negative it is better to buy the shuttle bus.

27. Section: 16.3 Evaluating the Lease Decision Learning Objectives: 16.3 Level of Difficulty: Difficult

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Solution: NPV(leasing) = CF0 (i.e., purchase price savings) − PV(forgone depreciation tax savings) − PV(after-tax lease payments) CF0 = $1,800,000 After-tax cost of borrowing is 3%.

(C )( d )(T ) (1 + .5k ) PV (CCA Tax Shield) = 0  d +k (1 + k ) (1,800,000)(.25)(.40) (1 + .5  .03) =  .25 + .03 (1 + .03) = $633,495 PV(lease payments) = $400,000×(1 – .04)×[(1 – 1/1.035)/.03] ×1.03 = 1,132,104 NPV(leasing) = $1,800,000 – $633,495 – $1,132,104 =$34,401 Since the NPV is positive it is better to lease the shuttle bus.

28. Section: 16.3 Evaluating the Lease Decision Learning Objectives: 16.3 Level of Difficulty: Difficult Solution: Monthly lease rate = 7% ÷12 = 0.583% Number of monthly payments = 10 years × 12 months = 120 2,500,000 Monthly lease payments = = $28,858.7769 1   1 − (1.00583)120    (1.00583) .00583     Monthly loan rate = 7% ÷12 = .583% 2,500,000 Monthly loan payments = = $29,027.12 1   1 − (1.00583)120    .00583    

1   1 − 120  (1.00583)  (1.00583) =$2,500,000.00 PV(lease payments) = $28,858.7769×  .00583       Since the lease payment is equal to $2,500,000, the firm could take the loan or the lease.

29. Section: 16.3 Evaluating the Lease Decision Solutions Manual ..

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Learning Objectives: 16.3 Level of Difficulty: Difficult Cost of the car =$25,000 Monthly discount rate = 6% ÷ 12 = 0.5% 1   1 −  (1.005) 48   = $27,677 PV of lease = $650×  .005    

1   1− 48     1 (1.005)  = $28,516 PV of loan from father = ($25,000–$5,000) ×  +$300×  48  .005    (1.005)    The present value of the lease is lower, implying the lease is cheaper; therefore, you should take the lease.

30. Section: 16.4 Motivation for Leasing Learning Objectives: 16.4 Level of Difficulty: Easy Solution: Two alternative methods available to Mr. Zhang’s company are (note: solution provides only sample advantages and disadvantages): a) Borrow $250,000 from the bank i) Advantages: will have outright ownership of the assets, so will be able to claim CCA etc. ii) Disadvantages: if Mr. Zhang is like most small- to medium-sized enterprises, the company is not likely to have many assets and consequently without the house as collateral, the cost of borrowing is likely to be high. Also, if business conditions do not turn out well, Mr. Zhang will be stuck with delivery trucks, no business, and likely a depressed resale market. b) Lease the trucks i) Advantages: requires very little capital outlay, may have the flexibility to cancel the lease, fixed payments over life of lease, and may enable Mr. Zhang to upgrade his trucks more easily in the future. ii) Disadvantage: the assets are not owned so will not be able to use them as collateral for future loans.

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Chapter 17: Investment Banking and Securities Law Multiple Choice Questions 1. Section: 17.1 Conflicts between Issuers and Investors Learning Objective: 17.1 Level of difficulty: Easy Solution: D. Due diligence is very time-consuming and very expensive to implement.

2. Section: 17.1 Conflicts between Issuers and Investors Learning Objective: 17.1 Level of difficulty: Medium Solution: B. The used car market is a classic example of information asymmetry; it is cited as the most familiar lemons market.

3. Section: 17.1 Conflicts between Issuers and Investors Learning Objective: 17.1 Level of difficulty: Medium Solution: B. Ponzi schemes are illegal in both the U.S. and Canada.

4. Section: 17.2 A Primer on Securities Legislation in Canada Learning Objective: 17.2 Level of difficulty: Medium Solution: D. The British Columbia Securities Commission has a multitude of requirements dictating what has to be included in a prospectus.

5. Section: 17.2 A Primer on Securities Legislation in Canada Learning Objective: 17.2 Level of difficulty: Easy Solution: C There is no federal securities regulator; this area is a provincial responsibility.

6. Section: 17.2 A Primer on Securities Legislation in Canada Learning Objective: 17.3 Level of difficulty: Medium Solution: A An IPO is assumed to have the greatest information asymmetry.

7. Section: 17.2 A Primer on Securities Legislation in Canada Learning Objective: 17.3 Level of difficulty: Easy Solution: D

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The market for non-registered securities is called the exempt market. The primary market is the market for new securities, which investors purchase from the issuer. The secondary market is the market where investors purchase securities from other investors, not the issuer. Securities in the primary and secondary market are registered.

8. Section: 17.2 A Primer on Securities Legislation in Canada Learning Objective: 17.3 Level of difficulty: Medium Solution: B In the exempt market, the issuer prepares an offering memorandum, instead of a prospectus.

9. Section: 17.2 A Primer on Securities Legislation in Canada Learning Objective: 17.3 Level of difficulty: medium.

Solution: D Private issuers, or closely held issuers, are exempt only if there is no promotion, less than $3 million is raised, and the securities are sold to no more than 35 individuals with the approval of the board of directors.

10. Section: 17.3 IPOs and Investment Banking Learning Objective: 17.4 Level of difficulty: Medium Solution: C Most IPOs are firm commitments offerings.

11. Section: 17.4 Post-IPO Regulation and Seasoned Offerings Learning Objective: 17.5 Level of difficulty: Easy Solution: D The main components of continuous disclosure are the filing of quarterly and annual financial statements, an annual information form (AIF), and proxy and information circulars.

12. Section: 17.4 Post-IPO Regulation and Seasoned Offerings Learning Objective: 17.5 Level of difficulty: Medium Solution: A During the IPO a large amount of information is released. Since seasoned equity offerings occur after an IPO, the firm need not repeat information that had been previously released.

Practice Problems 13. Section: 17.1 Conflicts between Issuers and Investors Learning Objective: 17.1 Level of difficulty: Medium Solution: a. Arthur pays $0.51 x 100,000 = $51,000 for the stamps. He sells them for $0.52 × 100,000 = $52,000, so his profit is $1,000.

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b. Arthur sells the stamps for $0.5125 × 100,000 = $51,250 and pays shipping and insurance, leaving $51,250 – $249 = $51,001. Therefore, his profit is exactly $1. A “quick buck” indeed! c. He makes $52,000 – 51,000 – 249 = $751.

14. Section: 17.1 Conflicts between Issuers and Investors Learning Objective: 17.1 Level of difficulty: Difficult Solution: The probability of a fraudulent bond is 1/5 = 0.2, and the probability of a nonfraudulent bond is 1 – 0.2 = 0.8. We assume the interest on an investment is k.

We have two investment options.

Option 1: invest $1 on a non-fraudulent bond and get 1+0.12 one year later.

Option 2: invest $1 on an investment. One year later, there is 0.2 chance of default when investors get $0, and 0.8 chance of getting 1 + k.

Because there is no risk premium and assuming no arbitrage, the two options should give the same payoff one year later: 0.2*0 + 0.8*(1 + k) = 1.12 Solving the equation above: k = 40%.

15. Section: 17.2 A Primer on Securities Legislation in Canada Learning Objective: 17.2 Level of difficulty: Medium Solution: The OSC is involved in the areas of primary market offerings (IPOs), secondary market trading, activities of investment professionals, insider trading, and takeover bids.

16. Section: 17.2 A Primer on Securities Legislation in Canada Learning Objective: 17.2 Level of difficulty: Medium Solution: The OSC determined three types of security distribution as follows: distribution by the issuer, (who knows best the true value of the security), distribution by a control block, and distribution of restricted shares to the public for the first time.

17. Section: 17.2 A Primer on Securities Legislation in Canada Learning Objective: 17.3 Level of difficulty: Medium Solution: Three major categories of exempt purchasers are: First, accredited investors, such as banks, governments, wealthy investors, investment dealers, and individuals owning control blocks.

Second, government debt issues are exempt, as are debt issues by many financial institutions.

Finally, securities issued as part of takeovers and corporate reorganizations are exempt because they are covered by corporate law requirements to provide proxy circulars and similar documents.

18. Section: 17.3 IPOs and Investment Banking Learning Objective: 17.4 Level of difficulty: Medium

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Solution: Stage 1: Initial discussion with the investment bank, which forms the formal IPO process.

Stage 2: Drafting an initial prospectus (the preliminary prospectus) Stage 3: Finalization of the prospectus; the waiting period for final clearance from the securities commission.

Stage 4: Pricing and distribution of the issue and after-market stabilization.

19. Section: 17.3 IPOs and Investment Banking Learning Objective: 17.4 Level of difficulty: Medium Solution: Limit orders are expressions of interest, but not firm orders. Investors enter into limit orders when they are willing to indicate how much of a certain security they would be willing to buy or sell at a certain price level. Institutional investors are usually interested in limit orders.

Investors enter into market orders when they want a fixed amount of the security, at whatever the final price is. Retail investors are usually interested in market orders.

20. Section: 17.3 IPOs and Investment Banking Learning Objective: 17.4 Level of difficulty: Medium Solution: During the quiet period, the investment dealer cannot issue an analyst report recommending the shares. The underwriter and issuer cannot hype the stock to help sell it, and the underwriters as a group cannot drop the price. The lead underwriter has the right to trade in the shares to maintain an orderly market during this period to ensure the success of the issue.

21. Section: 17.3 IPOs and Investment Banking Learning Objective: 17.4 Level of difficulty: Medium Solution: The four types of public offerings are a best efforts offering, a firm commitment offering, a bought deal, and a standby or rights offering. The last two can only be used with seasoned offerings, and most IPOs are firm commitment offerings.

Best efforts offering: shares that are sold by investment dealers through an agency agreement to do their best, with no guarantee of success; investment dealers are paid an amount for each share they sell.

Firm commitment offering: an offering in which the investment dealer buys the new securities from the issuer and guarantees the sale of a certain number.

Bought Deal: an offering in which the underwriter buys all the shares of a seasoned issue to resell later, even before the drafting of the preliminary prospectus.

Standby or rights offering: an offering of common shares at a discount to investors who already own shares; can only be used with seasoned offerings.

22. Section: 17.3 IPOs and Investment Banking Learning Objective: 17.4 Level of difficulty: Medium Solution:

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Disaster “out” clause: if the state of the financial markets deteriorates so much that the underwriter cannot market the issue profitably, then the issue can be cancelled. Clearly, this is a huge safety net for the underwriter.

23. Section: 17.3 IPOs and Investment Banking Learning Objective: 17.4 Level of difficulty: Medium Solution: An overallotment or green-shoe option gives the underwriter the option of buying more shares from the issuer (usually 15 percent more) if investor demand is strong.

24. Section: 17.3 IPOs and Investment Banking Learning Objective: 17.4 Level of difficulty: Easy Solution: A lock-up period prevents the founders of the company from selling their shares for a given time.

25. Section: 17.3 IPOs and Investment Banking Learning Objective: 17.4 Level of Difficulty: Easy Solution: The waiting period occurs after the preliminary prospectus has been drafted and sent to the securities commission to be examined for deficiencies. During this “wait” time, the investment dealer and the issuer must await final clearance before selling the securities.

26. Section: 17.3 IPOs and Investment Banking Learning Objective: 17.4 Level of difficulty: Medium Solution: The marketing of the issue will involve “road shows” or “dog and pony” shows to describe the issuer and the issue itself in the major financial cities where the issue will be marketed.

Typically, exempt purchasers (i.e., the major financial institutions) will be contacted by different members of the selling group and invited to these presentations by senior management and the lead underwriter.

27: Section: 17.3 IPOs and Investment Banking Learning Objective: 17.4 Level of difficulty: Difficult Solution: There is too little competition for business in Canada, and Canadian firms do not need to tolerate high under-pricing, because they want the best price for their shares.

A large number of reasons have been given for the under-pricing in the U.S. First, (the most obvious) is that it lowers the risk of the underwriter losing money on the issue. However, this answer implies that the U.S. investment banks are more powerful than their equivalents in Canada and although there is anecdotal evidence of this, it is difficult to prove. Second, is the litigious nature of the U.S. economy: if the share price falls someone may mount a class action

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suit against the underwriter for misleading the purchaser. Third, a well-received public offering paves the way for subsequent offerings by the firm and builds momentum into the share price.

However, the relative rarity of the equity issue makes this rational dubious. Fourth, spinning: the underwriter allocates IPOs to favoured clients which is essentially a way of bribing them with millions of dollars to get future investment banking business.

28. Section: 17.3 IPOs and Investment Banking Learning Objective: 17.4 Level of difficulty: Medium Solution: There are 1 million shares outstanding before the IPO, and 250,000 new shares are being issued, bringing the total to 1,250,000. Of these, the brothers will retain 500,000 (half of their original holdings). Therefore, they will own (500,000 / 1,250,000) = 40% of the shares (and of the company).

29. Section: 17.3 IPOs and Investment Banking Learning Objective: 17.4 Level of difficulty: Medium Solution: The IPO is intended to sell 500,000 + 250,000 = 750,000 shares. When investor demand is strong, the “green-shoe” standard overallotment clause means that 750,000 × 15% = 112,500 additional shares will have to be issued by the company. This would raise the total outstanding shares to 1,250,000 + 112,500 = 1,362,500. The Finn brothers will still own 500,000 shares, which would then represent (500,000 / 1,362,500) = 36.7% of the company.

30. Section: 17.3 IPOs and Investment Banking Learning Objective: 17.4 Level of difficulty: Medium Solution: a. To raise $2 million, the equity offering, before fees, will have to be 2,000,000 / (1 – 0.07) = $2,150,537.63. The flotation costs will be this gross figure less the net $2 million, or $150,537.63. b. To raise $2 million, the equity offering, before fees, will have to be 2,000,000 / (1 – 0.05) = $2,105,263.16. The flotation costs will be this gross figure less the net $2 million, or $105,263.16. It saves $45,274.47 on flotation.

31. Section: 17.3 IPOs and Investment Banking Learning Objective: 17.4 Level of difficulty: Easy Solution: The net proceeds were $25 million × (1 – 0.018) – $100,000 = $24,450,000.

Winnipeg Water & Gas paid a total of $550,000 in fees (gross proceeds less the net figure above), which is $550,000 / $25,000,000 = 2.2% of the total issue amount.

32. Section: 17.3 IPOs and Investment Banking Learning Objective: 17.4 Level of Difficulty: Difficult

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Solution: With fees of 5 percent, Lansdowne Ltd. will receive 95 percent of the offer price for each share, or $25 × 0.95 = $23.75. To raise $10 million, the company must issue $10 million / $23.75 = 421,053 shares (rounding up to an integer number of shares).

If Investors think that firms only issue new equity if the stock is overpriced, in order to attract investors, the investment dealer suggests a lower offering price. Also, it is less risky for the underwriters since it will be easier to sell the issue at a lower price.

33. Section: 17.3 IPOs and Investment Banking Learning Objective: 17.4 Level of Difficulty: Difficult Solution: Under Plan I, you will gross $14 × 1 million shares = $14 million and will pay $14 million × 0.065 = $910,000 in fees. The net proceeds are therefore $13,090,000.

Under Plan II, only 95 percent, or 950,000 shares are expected to be sold, so the gross proceeds will be $15 × 950,000 = $14,250,000. After the dealer’s fees, net proceeds will be $14,250,000 – 950,000 = $13,300,000. The investment dealer charges $950,000 Plan II appears to be better as you will receive more money and have sold fewer shares doing so.

However, this option entails more risk for you and the company: if the IPO doesn’t go very well, you may raise far less money (and you will still pay the fixed fee).

34. Section: 17.3 IPOs and Investment Banking Learning Objective: 17.4 Level of Difficulty: Difficult Solution: a. On the undervalued shares, your profit will be 1,000 shares × $1.50 = $1,500. On the overvalued shares, you will lose 1,000 × $1.00 = $1,000. Your net gain is $500. b. You will only receive 500 shares of the undervalued issue, so your profit will be 500 × $1.50 = $750. On the overvalued shares, you will still lose $1,000. In this situation, you will have a net loss of $250. c. You will only receive 200 shares or one fifth of the undervalued issue, so your profit will be 200 x $1.50 = $300. On the overvalued shares, you will still lose $1,000. In this situation, you will have a net loss of $700.

35. Section: 17.3 IPOs and Investment Banking Learning Objective: 17.4 Level of Difficulty: Difficult Solution: a. Working down from the top of the list (highest limit price), selling 800,000 shares means that investors A, B, C, and D would buy the shares (with a partial allotment of 150,000 shares for investor D.) For all these investors to buy the shares, the price can be no higher than $19.25 (the lowest of this group’s indicated limit prices). b. Two-times oversubscription means that expressions of interest for 1,600,000 shares are needed. To get expressions totalling this many shares involves investors A through G (with a partial allotment of 150,000 shares for investor G), and the lowest limit price for this group is $18.50.

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c. According to Table 17-1 in the text, the historical underpricing in Canada has been 6.3%.

Therefore, you would expect the stock to rise to $18.50 x 1.063 = $19.67 on the first day of trading. In the U.S., the first-day return has averaged 18.4%, so you might expect the price to rise to $18.50 × 1.184 = $21.90.

36. Section: 17.4 Post-IPO Regulation and Seasoned Offerings Learning Objective: 17.5 Level of difficulty: Medium Solution: The main components of continuous disclosure are the filing of quarterly and annual financial statements, annual information forms (AIFs), and proxy and information circulars.

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Chapter 18: Debt Instruments Multiple Choice Questions 1. Section: 18.1 What Is Debt?

Learning Objective: 18.1 Level of difficulty: Medium Solution: B 2. Section: 18.1 What Is Debt?

Learning Objective: 18.1 Level of difficulty: Easy Solution: C After-tax cost of debt = 8% (1 – 0.3) = 5.6% 3. Section: 18.2 Short-Term Debt and the Money Market Learning Objective: 18.2 Level of difficulty: Medium Solution: B 1 + kTB 1.02 R= −1 = − 1 = 13.33% P 0.9 4. Section: 18.2 Short-Term Debt and the Money Market Learning Objective: 18.2 Level of difficulty: Medium Solution: D Use the equivalent maturity T-bill yield: 6% – 1% = 5% 5. Section: 18.2 Short-Term Debt and the Money Market Learning Objective: 18.2 Level of difficulty: Medium Solution: B Only firms with very good credit ratings can issue CP, while firms without good ratings can seek bankers’ acceptances.

6. Section: 18.2 Short-Term Debt and the Money Market Learning Objective: 18.2 Level of difficulty: Medium Solution: C While both treasury bills and treasury bonds are issued by the government, the shorter term of Tbills makes them relatively safer.

7. Section: 18.2 Short-Term Debt and the Money Market Learning Objective: 18.2 Level of difficulty: Medium Solution: A Solutions Manual ..

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8. Section: 18.3 Bank Financing Learning Objective: 18.3 Level of difficulty: Medium Solution: D 9. Section: 18.3 Bank Financing Learning Objective: 18.3 Level of difficulty: Medium Solution: D 10. Section: 18.3 Bank Financing Learning Objective: 18.3 Level of difficulty: Medium Solution: B A revolver adds more stability than a line of credit.

11. Section: 18.5 Bond Ratings Learning Objective: 18.5 Level of difficulty: Easy Solution: D Practice Problems 12. Section: 18.1 What Is Debt?

Learning Objective: 18.1 Level of difficulty: Easy Solution: Interest is compensation for the use or retention of money owed to another.

Interest must be referable to a principal sum.

Interest accrues from day to day.

13. Section: 18.2 Short-Term Debt and the Money Market Learning Objective: 18.2 Level of difficulty: Easy Solution: 1,000 1,000 Price = = = $989.75 (1 + K ) (1 + .021 180 / 365) 14. Section: 18.2 Short-Term Debt and the Money Market Learning Objective: 18.2 Level of difficulty: Medium The borrower receives a net amount of $4950. A year later, he must repay $5,000 plus interest of $500. Therefore, the effective interest paid by the borrower is: 5,500 − 4,950 = 11.11% 4,950 Thus, service fees and other costs increase the effective interest rate of a loan.

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15. Section: 18.2 Short-Term Debt and the Money Market Learning Objective: 18.2 Level of difficulty: Easy Solution: The yield spread is the difference between the promised yield (not the expected yield) and the Tbill rate: Yield spread = 9% – 1% = 8%.

16. Section: 18.2 Short-Term Debt and the Money Market Learning Objective: 18.2 Level of difficulty: Easy Solution: The total cost of issuing the commercial paper is 9% + 0.125% + 0.125% = 9.25%. For the BAs, the total cost is 8.75% + 0.325% = 9.075%. The bankers’ acceptances is the better choice as it is slightly less costly overall.

17. Section: 18.2 Short-Term Debt and the Money Market Learning Objective: 18.2 Level of difficulty: Medium Solution: k = 4.8(91)/365 = 1.2% 1,000,000 P= = $988,142 1.012 18. Section: 18.2 Short-Term Debt and the Money Market Learning Objective: 18.2 Level of difficulty: Medium Solution: 500,000(1.05)(0.95) + 0(1 − 0.95) P= = $433,696 1.15 19. Section: 18.2 Short-Term Debt and the Money Market Learning Objective: 18.2 Level of difficulty: Medium They are high quality (low default risk), liquid, and short-term (low interest rate risk).

To complete the answer, the student can reflect on the desirability (on behalf of lenders and borrowers) of each of these characteristics.

20. Section: 18.2 Short-Term Debt and the Money Market Learning Objective: 18.1, 18.2 Level of difficulty: Medium Solution:

EBIT Interest Taxable Income Solutions Manual ..

No Debt $123,500 0 123,500

$150,000 loan at 8% $123,500 12,000 111,500 3

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30,875 92,625

27,875 83,625

The net income for Jackie’s company will fall by (92,625 – 83,675) = $9,000, as shown in the table above. Although the company will pay $12,000 in interest on the loan, these payments are tax deductible. The result is that the company really pays only (1 – Tax Rate) = (1 –25%) = 75% of the interest cost ($12,000 x 75% = 9,000), with the remainder being offset by lower taxes.

21. Section: 18.2 Short-Term Debt and the Money Market Learning Objective: 18.2 Level of difficulty: Medium Solution: Yes; Jackie is correct. The tax-deductibility of interest payments means that the after-tax cost of borrowing is lower than the actual amount of interest paid. Using Equation 18-1, K = Kd(1 – T) = 8%*(1 – 0.25)=6% We could also obtain this result by noting that the impact of the interest payment on net income was $9,000. For a $150,000 loan, this amounts to an interest rate of 9,000/150,000 = 6% 22. Section: 18.2 Short-Term Debt and the Money Market Learning Objective: 18.2 Level of difficulty: Difficult Solution: Michael will pay only his “expected value” for the Collingwood commercial paper, not the full par value amount. Over 60 days, approximately one-sixth of a year, the paper promises a return of (9% / 6) = 1.5%, and Michael requires a (12% / 6) = 2% return. Thus, his expected value is:

Par  (1 + R )  P + Recover  (1 − P) $1,000  (1.015)  0.99 + $800  0.01 = = $992.99 (1 + K ) (1.02) 23. Section: 18.2 Short-Term Debt and the Money Market Learning Objective: 18.2 Level of difficulty: Difficult Solution: At 9% per year, the promised return is 1.5% (approximately) for the 60-day life of the commercial paper. Using a $1,000 figure for the par value (and hence the issue price), the amount recovered in the event of a default is $800. Using Equation 18-2, we find:

1,000  (1.015)  P + 800  (1 − P) (1.01) 1,000  (1.01) − 800 210 P= = = 0.9767 1,000  (1.015) − 800 215

$1,000 =

This is the probability of NOT defaulting. Therefore, the probability of a default is (1 – 0.9767) = 0.0233, or 2.33% Solutions Manual ..

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24. Section: 18.2 Short-Term Debt and the Money Market Learning Objective: 18.2 Level of difficulty: Difficult Solution: A 2-percent chance of default means that the probability of not defaulting is, P = 98%. As in Problem 23, the promised yield is 1.5 percent over the 60-day life of the paper, and the T-bill yield is 1 percent. With V = $1,000, the par-value amount:

1,000  (1.015)  0.98 + Recover  (1 − 0.98) (1.01) 1,000  (1.01) − 1,000  (1.015)  0.98 15.3 Recover = = = 765 (1 − 0.98) 0.02 Thus, investors expect to recover $765 for every $1,000 invested, or 76.5% if Collingwood were to default on the commercial paper. $1,000 =

25. Section: 18.3 Bank Financing Learning Objective: 18.3 Level of difficulty: Medium Solution: Collingwood can borrow up to: 75% x Accounts Receivable + 50% x Inventory = 0.75 x $18,536,000 + 0.50 x $74,196,000 = $51 million.

26. Section: 18.3 Bank Financing Learning Objective: 18.3 Level of difficulty: Easy Solution: The annual interest payment, at the current rate, is 9.75% x $50 million = $4,875,000. To stay on-side with the covenant, Collingwood must earn at least: 2 x $4,875,000 = $9,750,000 this year.

27. Section: 18.4 Long-Term Debt and the Money Market Learning Objective: 18.4 Level of difficulty: Medium Solution: By issuing long-term debt (as opposed to short-term debt), the issuer is betting on interest rates either remaining the same or rising in the future. Long-term financing is less risky for the business as it represents permanent funding, as opposed to short-term financing which is temporary.

28. Section: 18.2 Long-Term Debt and the Money Market Learning Objective: 18.4 Level of difficulty: Medium Solution: The “bullet” payment pays off the entire principal amount of the loan so the annual payments consist of interest only: $5.25 million / $50 million = 10.5% per year.

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This annual interest rate is somewhat higher than the yield on commercial paper or BAs, even including the extra fees for those alternatives (see Problem 16). There are many reasons why longer-term loans may have a higher interest rate than short-term commercial paper (which they usually do). One possibility is that Collingwood’s bank believes the 10-year term increases the risk that the company will default, and the extra yield is compensation for this risk.

29. Section: 18.5 Bond Ratings Learning Objective: 18.5 Level of difficulty: Medium Solution: Core Profitability This is an assessment based on standard profit measures such as the return on equity; return on assets; the “quality” of a firm’s earnings; its cost structure (i.e., whether it is the low cost producer, etc.); its growth opportunities; and its pricing structure.

Asset Quality Assets are made up of many different types, so DBRS looks at the importance of intangibles (for example, how valuable is the goodwill on the firm’s balance sheet); the market value of the firm’s assets; and, its use of derivatives and risk management to see whether it is managing its operational and market risks effectively.

Strategy and Management Strength Ultimately a firm is comprised of assets and management, so that an assessment of a firm’s credit risk is vitally concerned with the capabilities of the senior management group. This is particularly important if the firm is actively involved in mergers and acquisitions where a clear strategic approach and skills at integration of acquired companies is valuable.

Balance Sheet Strength If the lenders have to initiate bankruptcy proceedings, it is important to understand where they stand in the overall liabilities of the firm, so standard debt ratios, coverage tests and the amount of financial flexibility available to the firm is important. The latter includes an assessment of the firm’s reliance on short-term debt, its commitment to a capital expenditure program that cannot be easily stopped, and the support potentially available from other parties such as affiliated companies. Size is important since larger firms are usually less risky and have more market power.

Business Strength Standard issues such as market share; growth prospects for the industry; a defensible base of diversified operations; up to date management information systems; key intangibles such as the quality of its workforce; and, industry issues such as the degree of unionization and competition.

Miscellaneous Issues This is a “catch-all” category, including such issues as the quality of the firm’s accounting statements and whether there have been consistent restatements, the structure of the bond indenture, and the importance of the firm and industry to the province or territory or to Canada.

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30. Section: 18.5 Bond Ratings Learning Objective: 18.5 Level of difficulty: Difficult Solution: a. Table 18-6 shows that the average default rate for BB-rated bonds over 10 years is 8.99%; the probability of not defaulting is therefore 91.01%. b. Using equation 18-2 $1,000  (1.10)  0.9101 + 0 V= = $944.44 (1.06) So Collingwood’s bonds are worth $944.44 per $1000 of face value, or 0.94444 x$50 million = $47,222,000 in total.

31. Section: 18.5 Bond Ratings Learning Objective: 18.5 Level of difficulty: Difficult Solution: From Table 18-7, the default recovery rate on senior unsecured bonds has averaged 40.6%.

Using this in conjunction with the solution to Problem 30,

V =

$1,000  (1.10)  0.9101 + 0.406  1,000  0.0899 = $978.88 (1.06)

The bonds are worth $978.88 per $1,000 of face value, or 0.97888 x $50 million = $48,944,000 in total.

32. Section: 18.5 Bond Ratings Learning Objective: 18.5 Level of difficulty: Difficult Solution: A somewhat open ended question which will force students to think of other factors in the market that might affect the desirability of a particular bond vis-à-vis another. Some of the reasons are: i. Liquidity ii. Interest rate risk iii. How much the investor is likely to get in case of default

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Chapter 19: Equity and Hybrid Instruments Multiple Choice Questions 1. Section: 19.1 Shareholders’ Equity Learning Objective: 19.1 Level of difficulty: Easy Solution: D All of them may appear in a share structure.

2. Section: 19.2 Preferred Share Characteristics Learning Objective: 19.3 Level of difficulty: Medium Solution: C Preferred shares are considered a part of equity; owners cannot bankrupt the firm.

3. Section: 19.3 Warrants and Convertible Securities Learning Objective: 19.4 Level of difficulty: Easy Solution: C 4. Section: 19.3 Warrants and Convertible Securities Learning Objective: 19.4 Level of difficulty: Medium Solution: A The exercise price is paid in cash when warrants are exercised. Debt is not exchanged to common shares when its attached warrant is exercised. A conversion ratio is specified in convertibles.

5. Section: 19.3 Warrants and Convertible Securities Learning Objective: 19.2, 19.4 Level of difficulty: Medium Solution: D 6. Section: 19.3 Warrants and Convertible Securities Learning Objective: 19.4 Level of difficulty: Medium Solution: A 2*(30 – 20) = $20 7. Section: 19.3 Warrants and Convertible Securities Learning Objective: 19.4 Level of difficulty: Medium Solution: B 8. Section: 19.3 Warrants and Convertible Securities Learning Objective: 19.4 Level of difficulty: Medium Solution: A At the time of issuance, the convertible security will be priced higher than its conversion value.

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9. Section: 19.4 Other Hybrids Learning Objective: 19.5 Level of difficulty: Easy Solution: D Permanence, subordination, legal, and subjective are the four factors.

10. Section: 19.4 Other Hybrids Learning Objective: 19.5 Level of difficulty: Medium Solution: D Preferred securities are different from preferred shares because payments of preferred securities are tax-deductible.

11. Section: 19.4 Other Hybrids Learning Objective: 19.5 Level of difficulty: Medium Solution: D See Figure 19-4.

Practice Problems 12. Section: 19.1 Shareholders’ Equity Learning Objective: 19.1 Level of difficulty: Easy Solution: To vote at any meeting of the shareholders of the corporation To receive any dividend declared by the corporation To receive the remaining property of the corporation on dissolution 13. Section: 19.1 Shareholders’ Equity Learning Objective: 19.1 Level of Difficulty: Medium Solution: i. Preferred shares can be a means of raising equity capital without diluting control. ii. Firms issuing preferred shares can avoid the bankruptcy risk that is associated with debt issuance. iii. Firms paying low taxes have little use for the tax shields generated by debt. Preferred shares are attractive to these firms because preferred dividends are a significantly lower financial cost (preferred dividends are lower than interest) and do not have bankruptcy costs.

14. Section: 19.1 Shareholders’ Equity Learning Objective: 19.1 Level of Difficulty: Medium Solution: a. i)The equity holders will receive the “equity”: $1.7 million less $1.5 million owed to creditors, or $200,000. ii). The creditors will receive the $1.2 million proceeds from liquidating the assets (and lose the remaining $300,000 they are owed). Equity holders will get nothing. b. i). Without limited liability, the situation in part A will not change. ii) Now the equity holders would actually have to pay (that is, they would be liable for) an extra $300,000 to satisfy the creditors’ claims.

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15. Section: 19.1 Shareholders’ Equity Learning Objective: 19.1 Level of Difficulty: Medium Solution: a. You own 500 out of 0.5 million shares, or 500/500,000 = 0.1% b. You will purchase 500 / 5 =100 extra shares, giving you 600. In total, the company will sell an additional 500,000 / 5 =100,000 shares, so there are 600,000 outstanding. Your percentage ownership in the firm will not change. c. If you do not buy the new shares, you will still have 500 shares, but there will be 600,000 outstanding. Your percentage share of the firm’s equity has fallen to 500/600,000 = 0.083% 16. Section: 19.1 Shareholders’ Equity Learning Objective: 19.1 Level of Difficulty: Medium Solution: The founder will own 250,000 shares. The total number of shares outstanding will be 250,000 + 750,000 (sold in the IPO) = 1,000,000. Therefore, the founders will own 250,000 / 1,000,000 = 25% of the firm.

The Class A shares owned by the founder give him 2 votes per share, or 500,000 votes in all.

The common shares will have 1 vote each, or 750,000 votes in total. Thus, the founder will have 500,000 / 1,250,000 = 40% of the total votes available.

17. Section: 19.1 Shareholders’ Equity Learning Objective: 19.1 Level of Difficulty: Medium Solution: As the preferred shares are “cumulative,” all the missed dividends must be paid on them before any are paid on the common shares. In six months (2 quarters), dividends of 2% x $25 (par) x 2 = $1.00 would have accumulated for each preferred share. In total, $2 million will have to be paid to the preferred shareholders, leaving $4 million for the common shareholders.

Therefore, a dividend of $4 million / 50,000,000 shares = $0.08 per share will be paid on each common share.

18. Section: 19.1 Shareholders’ Equity Learning Objective: 19.2 Level of Difficulty: Medium Solution: Collingwood Corp. will receive 6.5% x $10 million = $650,000 in dividends, before paying tax.

However, corporations receive dividends from other companies tax-free, so the net income aftertax is still $650,000.

19. Section: 19.1 Shareholders’ Equity Learning Objective: 19.2 Level of Difficulty: Easy Solution: From Equation 19-3, Conversion Price (CP) = Par / Conversion Ratio (CR), therefore CR = Par / CP = $50 / $12.50 = 4. This means that each preferred share will be converted into 4 common shares.

20. Section: 19.1 Shareholders’ Equity Learning Objective: 19.2 Solutions Manual ..

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Level of Difficulty: Easy Solution: From Problem 19, the conversion price of the common stock is $12.50. A 20 percent premium means the price would have to be 0.20 x $12.50 = $2.50 higher, or $15.00 per share before the firm would call (and force conversion of) the preferred shares.

21. Section: 19.1 Shareholders’ Equity Learning Objective: 19.2 Level of Difficulty: Medium Solution: The conversion value, CV = CR x P (where P = the price of the common stock). From Problem 19, CR = 4, therefore CV = 4 x $10 = $40.

The convertible premium uses the price of the preferred shares and the conversion value: Premium = (P – CV) / CV = ($50 – $40) / $40 = 25%.

This figure may be interpreted to mean that the value of the preferred shares is 25 percent more than what they would be without the conversion privilege, or that the common shares must increase in value by 25 percent before conversion would make sense.

22. Section: 19.3 Warrants and Convertible Securities Learning Objective: 19.4 Level of difficulty: Medium Solution: Warrants are usually issued with long-term maturities, while call options have very short-term maturities. Warrants are issued by firms to raise capital, while call options are independent of the underlying asset and involve two parties: one buyer and one seller.

23. Section: 19.3 Warrants and Convertible Securities Learning Objective: 19.4 Level of difficulty: Medium Solution: Conversion Price = $100/4 = $25.

Conversion value = $40(4) = $160 Because 160 > 95 or 40>25, the convertible bonds should be converted.

24. Section: 19.3 Warrants and Convertible Securities Learning Objective: 19.4 Level of Difficulty: Difficult Conversion price: CP=Par/CR = $1,000 / 25.32 = $39.49 Conversion Value: CV = CR*P = $32.50 x 25.32 = $822.90 Value as a straight bond: 1 1     1− 8  1 − 1 + k n   ( b )  + F = 57.50   (1 + 0.09 )  + 1000 = $820.12 SBV= I   8   (1 + kb )n kb 0.09   (1 + 0.09 )         Floor Value: FV = Max(SBV, CV) =$822.90 Thus, these bonds cannot trade at a price lower than $822.90 Conversion premium = (Current Price – FV)/FV=(1,051-822.90)/822.90 = 27.72% 25. Section: 19.3 Warrants and Convertible Securities Learning Objective: 19.4 Level of difficulty: Difficult Solutions Manual ..

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Solution:

m (V + mX ) − mX m+n 100,000 = (10,000,000 + 100,000x$10) − 100,000x$10 100,000 + 900,000 = $100,000

Payoff =

DilutionFactor = =

m m+n

100, 000 = 0.10 100, 000 + 900, 000

26. Section: 19.3 Warrants and Convertible Securities Learning Objective: 19.4 Level of Difficulty: Difficult Solution: a. The market value of Orion’s equity is, V = nP = 12,000,000 (shares) x $4.75 = $57 million b. The warrant holders will pay the strike price, X = $4.00 for each new share. In total, they will pay mX = 3,000,000 x $4.00= $12 million c. The new shares will be purchased from the company, so its value will increase to (V + mX) = $57,000,000 + $12,000,000 = $69 million. The warrant holders will own (m / m+n) = 3,000,000 / 15,000,000 = 20% of the shares. Therefore, in total they will own shares worth 0.20 x $69,000,000 = $13.8 million d. The payoff to the warrant holders is their total value less their cost: $13,800,000 – $12,000,000 = $1.8 million. On a per share basis this is $1,800,000 / 3,000,000 = $0.60. Thus, the fair value (the amount you should be willing to pay) of each warrant is $0.60.

27. Section: 19.3 Warrants and Convertible Securities Learning Objective: 19.4 Level of Difficulty: Difficult Solution: a. We have share price: S= $20, Exercise price of the warrants: X = $18, Number of shares which can be purchased using the warrant: n=2 Floor Value = n  (S − X ) = 2  (20 − 18 ) = $4 b. Suppose that the warrant traded for less than $4, say at $3. An investor would buy a warrant for $3, exercise it, and purchase two shares for a total of 2*18=$36, and immediately sell these shares for 2*$20 = $40, for a riskless profit of $40-$36-$3=$1. Ignoring transaction costs, this arbitrage process would continue until the price of the warrants reached at least $4. c. The minimum value of the warrants: Share Price (+/– 10%) Floor Value %change $18 (Share price = exercise price) $0 –100% $20 (Share price now) 2*(20–18)=$4 0% $22 2*(22–18)=$8 100% 28. Section: 19.3 Warrants and Convertible Securities Learning Objective: 19.4 Level of Difficulty: Difficult Solutions Manual ..

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Solution: With a 6 percent yield, the convertible preferred shares are paying 0.06 x $50 = $3.00 per year in dividends. The price of a straight preferred share paying this same amount of dividend would be, SPV = Div / k = $3.00 / 0.08 = $37.50. We know that the conversion value for these preferred shares is $40. Thus, the Floor Value = Max (SPV, CV) = Max ($37.50, $40) = $40. These convertible preferred shares will not sell for less than $40.

29. Section: 19.4 Other Hybrids Learning Objective: 19.5 Level of Difficulty: Medium Solution: The interest payable is 8% × $25 million (par value) = $2 million.

For normal bonds, this interest payment would be tax deductible. However, income bonds are more like equity (which pays dividends, not interest) than debt, and the interest is therefore not deductible.

EBIT = $3 million; Tax payable = 25% × $3 million = $0.75 million; Earnings after tax = $3 million – $0.75 million = $2.25 million. The “interest” will have to be paid out of this figure leaving just $0.25 million or $250,000 in net earnings for the firm.

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Chapter 20: Cost of Capital Multiple Choice Questions 1. Section: 20.1 Financing Sources Learning Objective: 20.1 Level of difficulty: Medium Solution: D Invested capital = all interest-bearing liabilities + total equity The invested capital is $50,000 if the invested capital (all interest-bearing liabilities + total equity) is $50,000, which is not necessarily equal to total assets.

2. Section: 20.1 Financing Sources Learning Objective: 20.1 Level of difficulty: Easy Solution: A X 2.50 V= = = $25.00 K e 0.10 3. Section: 20.1 Financing Sources Learning Objective: 20.1 Level of difficulty: Medium Solution: B 75,000 EPS = = $7.50 10,000 EPS 7.50 EarningsYield = = = 0.375 P 20.00 4. Section: 20.1 Financing Sources Learning Objective: 20.1 Level of difficulty: Medium Solution: A To satisfy bond holders, 60,000 (5%) = 3,000 To satisfy equity holders, 140,000 (10%) = 14,000 Total minimum earnings = 3,000 + 14,000 = $17,000 5. Section: 20.1 Financing Sources Learning Objective: 20.1 Level of difficulty: Medium Solution: C When ROE > ke, the management is adding value to the firm and the market price goes above the book value of the investment.

When ROE = ke, the management is neither increasing nor destroying the firm’s value.

When ROE < ke, the management is destroying the firm’s value.

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Learning Objective: 20.2 Level of difficulty: Medium Solution: A Market values are used to calculate the weights of equity and debt, not book values.

7. Section: 20.5 Growth Models and the Cost of Common Equity Learning Objective: 20.5 Level of difficulty: Medium Solution: B D1 EPS ( Payout) EPS (1 − b) Recall P = = = ke − g ke − g ke − g To increase P, increase payout, or decrease retention ratio, or decrease cost of equity, or increase g.

8. Section: 20.5 Growth Models and the Cost of Common Equity Learning Objective: 20.5 Level of difficulty: Difficult Solution: A 6 − 3 250,000 g = b  ROE =  = 0.5  0.2 = 0.1 6 1,250,000 D1 3(1.1) P= = = $165.00 k e − b  ROE 0.12 − 0.1 9. Section: 20.5 Growth Models and the Cost of Common Equity Learning Objective: 20.5 Level of difficulty: Medium Solution: A A growth firm is the one that adds value to the firm and has growth opportunities: ROE > ke.

10. Section: 20.5 Growth Models and the Cost of Common Equity Learning Objective: 20.5 Level of difficulty: Medium Solution: C Cash cows do not have significant growth opportunities.

Practice Problems 11. Section: 20.6 Risk-Based Models and the Cost of Common Equity Learning Objective: 20.6 Level of difficulty: Easy Solution: k e = RF +  ( ERM − RF ) = 0.02 + 1.5(0.12 − 0.02) = 17% 12. Section: 20.5 Growth Models and the Cost of Common Equity Level of difficulty: Medium Learning Objective: 20.5 Solutions Manual ..

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Solution: P=

D1 EPS1 (1 − b) EPS1 (1 − 0) NI /# 1,018,600 = = = = = $11.98 ke ke ke ke 500,000  0.17

( g = b  ROE = 0%) P ROE NI / E 1,018,600 = = = = 5.76 BVPS ke ke (950,000 + 90,000)(0.17)

13. Section: 20.1 Financing Sources Learning Objective: 20.1 Level of difficulty: Medium Solution: Invested Capital = short-term debt + long-term debt + total equity = 250,000 + 690,000 + 950,000 + 90,000 = 1,980,000 Before-tax ROI=NI/Invested capital = 1,018,600/1,980,000 = 51.44% 14. Section: 20.3 Estimating the Non-Equity Component Costs Learning Objective: 20.3 Level of difficulty: Medium Solution: i) Flotation costs: Issuing expenses on new securities have to be paid from the gross proceeds of an issue so that the firm’s initial cash inflow doesn’t match the funds provided by investors. ii) Taxes: The tax deductibility of interest payments made by the firm separates the cost of debt from the corresponding market yield.

15. Section: 20.2 The Cost of Capital Learning Objective: 20.2 Level of difficulty: Medium Solution: k e = RF +  ( ERM − RF ) = 0.04 + 0.8(0.10) = 12.00% WACC = 12%

750,000 250,000 + 6%(1 − 0.2) = 10.20% 750,000 + 250,000 750,000 + 250,000

16. Section: 20.5 Growth Models and the Cost of Common Equity Level of difficulty: Medium Learning Objective: 20.5 Solution: Exp( EPS ) 23.50 V fed = = = $626.67 kTbond − 1% 4.75% − 1% 17. Section: 20.5 Growth Models and the Cost of Common Equity Learning Objective: 20.5 Level of difficulty: Medium Solution: Solutions Manual ..

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D1 = D0 (1 + g1) = EPS0 (1 – b)(1 + g1) = ($4.50)(1 – 0.6)(1.1) = 1.98 P0 =

1.98 = $16.50 .17 − .05

18. Section: 20.5 Growth Models and the Cost of Common Equity Learning Objective: 20.5 Level of difficulty: Medium Solution: D1 ke = +g P (1 − F ) 2.75(1.05) = + 0.05 40(1 − 0.03) = 12.44% 19. Section: 20.5 Growth Models and the Cost of Common Equity Learning Objective: 20.5 Level of difficulty: Medium Solution: P0 = D1/(r – g) = D0*(1 + g)/(r – g) Reorganized:.

P0*(r – g) = D0*(1 + g) P0*r – P0*g = D0 + D0*g (D0 + P0)*g = P0*r – D0 G = (P0*r – D0)/(D0 + P0) = (22.75*0.12 – 0.6)/(0.6 + 22.75) g = 9.12% 20. Section: 20.5 Growth Models and the Cost of Common Equity Learning Objective: 20.5 Level of difficulty: Medium Topic: Growth Models and the Cost of Common Equity Solution:

NI EPS 12 = = = 0.25 E BVPS 48 12 − 8.75 g = b  ROE =  0.25 = 0.0677 12 D1 8.75 P= = = $270.90 k e − g 0.1 − 0.0677 ROE =

V = 270.90  10,000 + 500,000 = $3,209,000 21. Section: 20.5 Growth Models and the Cost of Common Equity Learning Objective: 20.5 Solutions Manual ..

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Level of difficulty: Medium Solution: g = b  ROE = (1 − payout)  ROE = (1 − 0.5)12% = 0.06 D 3(1.06) ke = 1 + g = + 0.06 = 19.25% P 24 ROE = 12%  k e = 19.25% Therefore, management is reducing the shareholders’ value.

22. Section: 20.5 Growth Models and the Cost of Common Equity Learning Objective: 20.5 Level of difficulty: Medium Solution:

Po =

ROE1  BVPS Inv  ROE2 − k e  +   ke (1 + k e )  ke 

0.20  10 100  0.25 − 0.1 + 0.1 1.1  0.1  = 20 + 136.36 = $156.36 PVGO = $136.36, PVEO = $20 ROE1 and ROE2 are both greater than cost of equity, therefore this firm has both high PVGO and PVEO. It is a star. =

23. Section: 20.7 The Cost of Capital and Investment Learning Objective: 20.7 Level of difficulty: Medium Solution: The statement is false. The cost of capital for a new project depends on the use of funds, not the source. Even if this particular project will be funded with debt, it is probably only one of many projects that the firm undertakes. No firm is 100% debt financed. Over time, the firm will raise financing through a number of sources, including internal funds, new equity, new preferred shares, and new debt. The source of funding for this project is from the pool of available funds. Therefore the cost of capital for the project should be the WACC, appropriately adjusted for the risk of this particular project.

24. Section: 20.7 The Cost of Capital and Investment Learning Objective: 20.7 Level of difficulty: Medium Solution: The appropriate discount rate should be based on the risk of the project, not on the risk of the individual companies undertaking the project. In this case, the development of a software package would be more closely associated with the risk of the software development firm.

Therefore the appropriate discount rate would be 2 + 2.3(10) = 25%. At this discount rate, the NPV of the project is negative and neither party should proceed with the project.

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25. Section: 20.7 The Cost of Capital and Investment Learning Objective: 20.7 Level of difficulty: Medium Solution: The firm will make both type 1 and type 2 errors. In the first case, it will tend to accept high-risk projects that it should have rejected. Since the project has high risk, using the WACC (which is too low a discount rate given the risk of the project) will overestimate the NPV and will lead management to accept projects that should be rejected. In the second case, the firm may reject low-risk projects that it should have accepted. Again, using the WACC (in this case a discount rate that is too high given the risk) will underestimate the NPV and lead management to reject projects it should have accepted.

26. Section: 20.7 The Cost of Capital and Investment Learning Objective: 20.5, 20.6 and 20.7 Level of difficulty: Difficult Solution: We must first determine the firm’s cost of equity. We have enough information to estimate ke using either the CAPM or the constant dividend growth model.

CAPM ke= RF + B(ERM – RF) = 0.02 + 2.1(0.1 – 0.02) = 18.80% Dividend Growth ke= D1 ÷ P0 + g = 3(1.04)/25 + 0.04 = 16.48% We can now estimate the cost of debt from the information given. kb = (1 – T) × (RF + 3%) = (1 – 0.4)*(2% + 3%) = 3% From the ranges of costs we have derived, we can now solve for the firm’s weighted average cost of capital. k = B × Ki ÷ V + E × Ke ÷ V k = 0.35 × 0.03 + 0.65 × 0.1880 = 13.27% OR k = 0.35 × 0.03 + 0.65 × 0.1648 = 11.76% We can now perform a net present value calculation: NPV = –12 + 2 ÷ 0.1327 = 3.0716 million NPV = –12 + 2 ÷ 0.1176 = 5.0068 million The net present value calculations indicate that the project should be undertaken at both discount rates.

27. Section: 20.7 The Cost of Capital and Investment Learning Objective: 20.5, 20.6 and 20.7 Level of difficulty: Difficult

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Solution: We first compute the costs of each source of funds: Debt: NP = $975; Assuming annual coupons I = (0.075)($1,000) = $75; n = 15 So we have: 1   1 − (1 + K )15  1 i  + 1,000  975 = 75  (1 − .45)  Ki (1 + K i )15     Solving for Ki, as shown in Chapter 6, we get: By financial calculator: PMT = 75(1 –0.45) = $41.25; PV = -975; FV = 1,000; N = 15.

Then compute I/Y will give 4.36%, which is the firm’s annual after-tax cost of debt.

Preferred: kp = Dp ÷ NPp = 0.05 ÷ 0.95 = 5.26% Equity: kne = ke × P0 ÷ NP0 = (0.15) *8/(1 – 0.12) / ( 8) = 17.04% We next compute the market value of each component: Debt: The market value of debt outstanding is: 1   1 − (1 + 0.075)15  1  + 1,000  = $1,220.68 × 1,800 = $2,197,224 B = 100 0.075 (1 + 0.075)15     Preferred: The market value is the total dividend payments divided by the market capitalization rate.

P = 0.06 × ($1,200,000) ÷ 0.05 = $1,440,000 Equity: Shares are currently trading at 8/(1 – 0.12)= $9.09 E = 300,000 ($9.09) = $2,727,000 Note the value of retained earnings is incorporated into the current market price of equity.

Total market value =V=B+P+E = $2,197,224 + 1,440,000 + $2,727,000 = $6,364,224 Finally we can compute the weighted average cost of capital: B P E 2,197,224 1,440,000 2,727,000 WACC = K B + K P + K E = (0.0436) + (0.0526) + (0.1704) = 10.00% V V V 6,364,224 6,364,224 6,364,224 28. Section: 20.7 The Cost of Capital and Investment Learning Objective: 20.5, 20.6 and 20.7 Level of difficulty: Difficult Solution: a.

Cost of Debt: NP = $980; Assuming annual coupons I = (0.05)($1,000) = $50; n = 20 So we have: Solutions Manual ..

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1   1 − (1 + K ) 20  1 i  + 1,000  980 = 50  (1 − .20)  Ki (1 + K i ) 20       Solving for Ki, as shown in Chapter 6, we get: By financial calculator: PMT = 50(1 – .20) = $40; PV = –980; FV = 1,000; N = 20.

Then compute I/Y will give 4.15%, which is the firm’s annual after-tax cost of debt.

Cost of Preferred shares: K= 2/22 = 9.09% Cost of Common Shares: K= 0.01 + 1.10(0.10 – 0.01) = 10.90% Ke= 0.1090(30/28.50) = 11.47% b.

Since they only need $3m in total financing, all of the common equity financing can be raised from internal funds. So, we should use the cost of common equity using internal funds.

WACC= 0.3(0.0415) + 0.1(0.0909) + 0.6(0.1090) = 8.69% c. Since $ 3 m equity = $5 m total financing*0.6 target, the appropriate common equity cost is still the WACC using internal funds: NOTE: if the financing needed exceeded $ 5million, the MCC would be computed using the cost of new equity, or 11.47%: MCC = 0.3(0.0415) + 0.1(0.0909) + 0.6(0.1147) = 9.04% 29. Section: 20.7 The Cost of Capital and Investment Learning Objective: 20.5, 20.6 and 20.7 Level of difficulty: Difficult Solution: a. Cost of LT debt: NP = $996.50; Semi-annual coupons I = (0.115/2)($1,000) = $57.50; n = 25*2 = 50 So we have: 1   1 − (1 + K ) 50  1 i  + 1,000  996.50 = 57.50  (1 − .50)  Ki (1 + K i ) 50       Solving for Ki, as shown in Chapter 6, we get: By financial calculator: PMT = 57.50(1 – .50) = $28.75; PV = –996.5; FV = 1,000; N = 50.

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Then compute I/Y will give 2.89%, which is the firm’s semi-annual after-tax cost of debt.

So, their annual after-tax cost of debt = (1.0289)2 – 1 = 5.86% b. Cost of Preferred Shares: Dp 3 kp = = = 6.12%.

NPp 49 c. and d.

Cost of Common Equity Financing: (i) Dividend Growth Model Approach: D D 1.75 1.75 ke = 1 + g = + 0.06 = 13%, and k ne = 1 + g = + 0.06 = 13.29%.

P0 25 NP 24 (ii) CAPM Approach: k e = RF + [ ERM − RF ] i = 0.11 + 0.95(0.12 − 0.11) = 11.95%

P   25  k ne =  0  k e =   (0.1195) = 12.45%.  24   NP  30. Section: 20.7 The Cost of Capital and Investment Learning Objective: 20.7 Level of difficulty: Difficult Solution: a. Using ke, we get:

B P CE ki + k p + ke V V V = (0.2)(0.0586) + (0.2)(0.0612) + (0.6)(0.15) = 11.40%

WACC =

b.

Break

InternalFundsAvailable $4m = = $6.67m.

CE Po int 0.6 V If the investment is less than or equal to $6.67 million, then all equity can be raised internally. c. Since $10m > break point of $6.67m, kCE = kCS , and we obtain, =

MCC =

B P CE ki + kp + k ne = (0.2)(0.0586) + (0.2)(0.0612) + (0.6)(0.2) = 14.40% V V V

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