SOLUTIONS MANUAL for Introduction to Corporate Finance, 4th Canadian Edition by Booth, Cleary and Ra

Chapter 1: An Introduction to Finance Multiple Choice Questions 1. Section: 1.1 Finance Defined Learning objective: 1.1 Level of Difficulty: Basic Solution: A 2. Section: 1.2 Real versus Financial Assets Learning objective: 1.2 Level of Difficulty: Intermediate Solution: C Stocks are financial assets. Examples of real assets are residential structures, non-residential structures, machinery and equipment, durables, inventories, and land.

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

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

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Learning objective: 1.5 Level of Difficulty: Intermediate Solution: D Practice Problems Intermediate 9. Section: 1.2 Real versus Financial Assets Learning objective: 1.2 Level of Difficulty: Intermediate 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: 1.3 The Financial System Learning objective: 1.3 Level of Difficulty: Intermediate 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: 1.3 The Financial System Learning objective: 1.3 Level of Difficulty: Intermediate 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

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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: 1.3 The Financial System Learning objective: 1.3 Level of Difficulty: Intermediate 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: 1.3 The Financial System Learning objective: 1.3 Level of Difficulty: Intermediate 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: 1.4 Financial Instruments and Markets Learning objective: 1.4 Level of Difficulty: Intermediate Solution: There are two major types of secondary markets are exchanges or auction markets and dealer or over-the-counter (OTC) markets. Exchanges have been referred to as auction markets because they involve a bidding process that takes place in a specific location (i.e., similar to an auction). OTC or dealer markets do not have a physical location, but rather consist of a network of dealers who trade directly with one another.

Challenging 15. Section: 1.4 Financial Instruments and Markets Learning objective: 1.4 Level of Difficulty: Challenging 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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Answers to Concept Review Questions 1.2 Real versus Financial Assets Concept review questions 1. What is finance?

Finance in its broadest terms is the study of how and under what terms savings (monies) are allocated between lenders and borrowers.

2. Distinguish between real and financial assets.

Real assets represent the normal tangible things that we think of in terms of personal and business assets. Financial assets are simply what one individual has lent to another, so one person’s positive financial asset is another’s negative financial asset (or liability).

3. Which sector or sectors of the economy are net providers of financing and which are the net users of financing?

Households and non-residents are net providers of financing. Government and business are net users of financing.

1.3The Financial System Concept review questions 1. Identify and briefly describe the three main channels of savings.

In the first channel we have direct intermediation, where the lender provides money directly to the ultimate borrower. The second channel also represents direct intermediation between the lender and borrower, but in this case some help is needed since no one individual can come up with the full amount needed and/or because the borrower is not aware of the available lenders.

The third savings channel is completely different since it represents financial intermediation, where the financial institution or financial intermediary lends the money to the ultimate borrower, but raises the money itself by borrowing directly from other individuals.

2. Distinguish between market and financial intermediaries.

A market intermediary is simply an entity that facilitates the working of markets and helps provide direct intermediation. The financial institution or financial intermediary lends the money to the ultimate borrower, but raises the money itself by borrowing directly from other individuals. In this case, the ultimate lender only has an indirect claim on the ultimate borrower; their direct claim is on the financial institution.

3. Discuss how the three most important types of financial intermediaries operate.

Chartered banks take in deposits and make loans, insurance companies take in premiums and pay off in the event of an incident happening such as a death or fire, while pension funds take in contributions and provide pension payments after plan members retire.

1.4 Financial Instruments and Markets Concept review questions

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1. Distinguish among the various types of financial assets.

The two major categories of financial securities are debt instruments and equity instruments.

2. Identify the major sources of financing used by: (a) governments and (b) businesses.

Governments raise new financing via the debt markets. They issue T-bills as a source of shortterm financing (i.e., less than one year), and they issue traditional bonds and Canada Savings Bonds (CSBs) for long-term financing. Businesses raise short-term financing in the form of debt through the use of loans, or by issuing commercial paper, BAs, etc. (all of which will be discussed in greater detail in later chapters). They raise long-term financing in the form of debt (i.e., through loans, by issuing bonds, or using other long-term debt instruments), or in the form of equity (i.e., by issuing common shares or preferred shares, etc.).

3. Distinguish between primary and secondary markets.

Primary markets involve the issue of new securities by the borrower in return for cash from investors (or lenders). Secondary markets provide trading (or market) environments that permit investors to buy and sell existing securities.

1.5 The Global Financial Community Concept review questions 1. Explain why global financial markets are so important to Canadians.

On aggregate, if we add our foreign borrowings to the amount of direct foreign investment in Canada, it exceeded the sum of what foreigners borrowed from us and the amount that we invested directly abroad.

2. Identify and briefly describe the two major stock markets in the United States.

The New York Stock Exchange (NYSE) is the world’s largest and most famous stock market.

The second largest and most important stock market in the U.S. is the Nasdaq Stock Market SM, or Nasdaq.

3. Explain briefly why events in the United States affected countries around the world so drastically.

The world’s money markets and bond markets are very global in nature, with U.S. markets representing the largest and most active debt markets in the world. The U.S. also possesses the largest equity markets in the world.

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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: Intermediate 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: Intermediate 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: Intermediate 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: Intermediate 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: Intermediate 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: Intermediate 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 2.4 Level of difficulty: Intermediate Solution: D Market prices are the main concern of shareholders.

8 Section: 2.3 The Role of Management and Agency Issues Learning Objective 2.4 Level of difficulty: Intermediate Solution: B 9. Section: 2.3 The Role of Management and Agency Issues Learning Objective 2.4 Level of difficulty: Intermediate Solution: A. 10. Section: 2.4 Corporate Finance Learning Objective 2.5 Level of difficulty: Intermediate 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: Basic 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: Intermediate Solution: B The treasurer would usually have the responsibility of credit management.

Practice Problems Basic 13. Section: 2.1 Types of Business Organizations Learning Objective 2.1 Level of difficulty: Basic 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 Intermediate 14. Section: 2.1 Types of Business Organizations Learning Objective 2.1 Level of difficulty: Intermediate 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: Intermediate 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: Intermediate 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 Level of difficulty: Intermediate 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 Level of difficulty: Intermediate 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 Level of difficulty: Intermediate 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: Intermediate Solution: They differ in these 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 Level of difficulty: Intermediate 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 Learning Objective 2.4 Level of Difficulty: Intermediate

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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.

23. Section: 2.4 Corporate Finance Learning Objective 2.5 Level of Difficulty: Intermediate 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?

24. Section: 2.4 Corporate Finance Learning Objective 2.5 Level of Difficulty: Intermediate Solution: 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.

25. Section: 2.4 Corporate Finance Learning Objective 2.5 Level of Difficulty: Intermediate 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. How does a firm decide to go public and issue shares to the general public versus remaining a

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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?

26. Section: 2.5 Finance Careers and the Organization of the Finance Function Learning Objective 2.6 Level of Difficulty: Intermediate 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.

27. Section: 2.5 Finance Careers and the Organization of the Finance Function Learning Objective 2.6 Level of difficulty: Intermediate 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.

28. Section: 2.5 Finance Careers and the Organization of the Finance Function Learning Objective 2.6 Level of Difficulty: Intermediate 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.

Challenging 29. Section: 2.3 The Role of Management and Agency Issues Learning Objective 2.4 Level of Difficulty: Challenging Solution: Referring to Table 2-2, the major components of income are straight salary, annual bonus, share receipts or options, pension value, 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

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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.

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Answers to Concept Review Questions 2.1 Types of Business Organizations Concept review questions 1. Describe the main advantages and disadvantages of sole proprietorships and partnerships.

The big advantage of a sole proprietorship is that setting one up is easy - there is no paperwork involved and all you really have to do is start the business. However, the critical thing is unlimited liability, because you are liable not only to the extent of what you have invested in the business, but also for any other assets you own.

The two main partnership forms are limited liability partnerships (LLP) and limited and general partnerships. LLPs are the new form of organizing professional firms, since each partner has limited liability in terms of a possible suit against the firm. However, as a partnership, the partner’s income is still included as ordinary income and filed with individual tax returns.

Limited and general partnerships are generally used for tax reasons. In this case a general partner operates the business and limited partners are passive investors. As long as the limited partners are not active in the business they have the advantage of limited liability in that all they can lose is their initial investment. The general partner, on the other hand, has unlimited liability and is the operator of the business.

2. How are trusts distinct from corporations?

Trusts are used whenever you want to separate ownership from control. The use of trusts has recently expanded out of their use in personal finance and mutual funds to income and royalty trusts. The essence of income and royalty trusts is that the trust is set up to invest in the shares and debt obligations of a company. Further, since the trust owns both the debt and equity of the company, the use of debt can be maximized to reduce (or eliminate) any corporate income tax, provided the trust pays out most (or all) of its income to unit-holders. In the jargon of finance professionals, trusts are “tax efficient.”

3. What are the main advantages and disadvantages of the corporation structure?

Unlike a partnership or sole proprietorship if you operate a business as a corporation, your personal assets are separate from any malfeasance or failure at the corporate level. The most difficult aspect of corporations is their control and taxation.

2.2 The Goals of the Corporation Concept review questions 1. What is the primary goal of the corporation?

From an economics perspective, the goal of the firm is to maximize its profits. In finance we extend the definition from that used in economics, since what the firm should really do is enhance the owner’s wealth.

2. What role does the board of directors serve?

The Board of Directors in directing the strategy of the firm should only be guided by what creates shareholder values.

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3. Explain the cost imposed on society if firms become too big to fail, and discuss whether the government should break up large firms when they pose such risks.

If firms become too big to fail, it will become the responsibility of the Government to bail firms out and protect the firms from failure and not let the firms fail. After all, firms hold privileged status as corporations, because they act in the owners’ interests, so the government has the right to oversee their actions. Consequently, many argue that corporations should act in the “social interest,” rather than in the interests of their owners.

4. Should the Government allow one of the Big Six Canadian banks to fail if it loses money on its loan portfolio?

The creation of shareholder value has been widely accepted, not just by academic theorists but also by regulators. In 1994, the TSX issued a report entitled Where Were the Directors, commonly called the Dey Report, after its chairman, Peter Dey. The report’s mandate was to look at the governance of Canadian companies after the serious recession of the early 1990s. The Dey Report concluded in Section 1.11: We recognize the principal objective of the direction and management of a business is to enhance shareholder value, which includes balancing gain with risk in order to enhance the financial viability of the business. (S1.11) As you will see, this is exactly what finance takes as the objective of the firm. By not letting a firm fail, the Government will have reduced the risks for the firm, and management could take on more risk knowing the Government will bail the company out.

2.3 The Role of Management and Agency Issues Concept review questions 1. Describe the nature of the basic owner-manager agency relationship.

For smaller firms, managers and owners are often the same people, so there is no problem. Even for some quite large Canadian companies, there is often a controlling shareholder to make sure that managers act in the shareholder’s best interests. However, for many companies, the shareholders are widely dispersed and the firm’s chief executive officer (CEO) is able to pack the BOD with cronies that will not challenge his or her authority. In other words, the firm has poor governance and few checks on management so it may be run in their interest rather than in the interests of the shareholders.

2. Define agency costs and describe both types.

The costs associated with agency problems are referred to as agency costs. There are two major types of agency costs: (1) direct costs, which arise due to sub-optimal decisions that are made by managers when they act in a manner that is not in the best interests of their company’s shareholders; and, (2) indirect costs, which are those that are incurred in attempting to avoid direct agency costs.

3. How have management compensation schemes been designed to better align owner-manager interests? How well have these schemes performed in this regard?

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The idea behind share incentive plans is simply to have the best interests of CEOs and senior managers coincide with those of stockholders. Often, shares are granted based on reaching certain objectives, such as revenue targets or investment returns. Whether or not share compensation schemes have successfully met their objectives, however, is doubtful.

4. What is moral hazard and why did it become the buzz word of the 2008 financial crisis?

In 1998, the U.S. government bailed out a hedge fund called Long-Term Capital Management (LTCM), because it was deemed to pose a systemic risk to the U.S. financial system—that is, it imposed an externality on others. This resulted in a common understanding that a financial institution could take risks, because, in the event of failure, the U.S. government would bail out the institution. This is the moral hazard problem: knowing that the U.S. government had bailed out LTCM, the behaviour of other institutions changed.

2.4 Corporate Finance Concept review questions 1. Describe the two key decision areas with respect to the financial management of assets?

The combination of the real asset decision and these financial asset acquisition decisions represent acquisition or investment decisions. Generally we talk about investment decisions in terms of financial management.

2. What are some of the key corporate financing decisions made by firms?

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

• In terms of equity how does it raise the equity: through retaining earnings or through new issues of equity?

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

• If it decides to issue debt, what determine whether this is bank debt or bonds issued to the public debt market?

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

3. What are the two key topics covered in the study of corporate finance?

The financial management of assets and corporate financing decisions represent the area of corporate finance.

Introduction to Corporate Finance, Fourth Edition

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Chapter 3: Financial Statements Multiple Choice Questions 1. Section: 3.1 Accounting Principles Learning Objective: 3.2 Level of difficulty: Intermediate Solution: A 2. Section: 3.2 Organizing a Firm’s Transactions Learning Objective: 3.2 Level of difficulty: Basic 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: Intermediate Solution: A. 4. Section: 3.2 Organizing a Firm’s Transactions Learning Objective: 3.2 Level of difficulty: Intermediate 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: Basic Solution: A CCA does not apply to land.

6. Section: 3.3 Preparing Accounting Statements Learning Objective: 3.3 Level of difficulty: Intermediate 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: Basic Solution: C Amortization (depreciation) is the most common non-cash item. The other choices are cash

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items.

8. Section: 3.3 Preparing Accounting Statements Learning Objective: 3.3 Level of difficulty: Intermediate Solution: C 9. Section: 3.3 Preparing Accounting Statements; 3.4 CP’s Accounting Statements Learning Objective: 3.3 Level of difficulty: Basic 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: Intermediate 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: Intermediate Solution: A. The issuance of long-term bonds is a financing activity, not an operating activity.

12. Section: 3.4 CP’s Accounting Statements Learning Objective: 3.4 Level of difficulty: Intermediate 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 CP’s 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.

14. Section: 3.5 The Canadian Tax System Learning Objective: 3.5 Level of difficulty: Intermediate Solution: B If the selling price is greater than the original capital cost, a capital gain arises.

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

Practice Problems Basic 16. Section: 3.2 Organizing a Firm’s Transactions Learning Objective: 3.2 Level of difficulty: Basic Solution: Some basic principles of IFRS 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: Basic Solution: Total Assets = Total Liabilities + Shareholders’ Equity Shareholders’ Equity = $529,500 – $379,000 = $150,500 18. Section: 3.3 Preparing Accounting Statements Learning Objective: 3.3 Level of difficulty: Basic Solution: Retained Earnings (Ending) = Retained Earnings (Beginning) + Net Income – Dividends = 15,000 + 7,500 – 4,000 = $18,500 19. Section: 3.3 Preparing Accounting Statements Learning Objective: Level of Difficulty: Basic Solution: Total liabilities = total assets – common equity – retained earnings = 525,600 – 136,000 – 75,000 = $314,600 20. Section: 3.3 Preparing Accounting Statements Learning Objective: 3.3 Level of Difficulty: Basic Solution: Additional retained earnings = net income × (1 – dividend payout ratio) = 14,300 × (1 – 0.30) = $10,010.

Ending retained earnings = beginning retained earnings + additional retained earnings = 18,000 + 10,010 = $28,010

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21. Section: 3.3 Preparing Accounting Statements Learning Objective: 3.3 Level of Difficulty: Basic Solution: EPS = earnings/number of shares outstanding = $85 million / 60 million = $1.42 22. Section: 3.3 Preparing Accounting Statements Learning Objective: 3.3 Level of Difficulty: Basic Solution: Cash flow from financing = debt – interest – dividends = $3 million – ($3 million × 10%) – ($1 × 0.5 million) = $2.2 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 $3 million – $500,000 = $2.5 million is perfectly acceptable.

23. Section: 3.5 The Canadian Tax System Learning Objective: 3.5 Level of difficulty: Basic Solution: Marginal tax = Federal rate + Ontario rate from Table 3-5 = 29% + 13.16% = 42.16%. The top personal tax rate in Ontario is 42.16 percent.

24. Section: 3.5 The Canadian Tax System Learning Objective: 3.5 Level of difficulty: Basic Solution: Year 1:

Year 2:

½ Capital Cost CCA = $2,000 x 45% UCC (end of year 1) Add ½ Net Additions UCC (start of year 2) CCA = $3,100 x 45% UCC (end of year 2)

$2,000 900 1,100 2,000 3,100 1,395 1,705

25. Section: 3.3 Preparing Accounting Statements Learning Objective: 3.3 Level of difficulty: Basic Solution: a. With a four-year life and straight-line amortization (based on “equal value each year”), the annual charge to amortization will be $2,400 / 4 = $600 (total for all six boats).

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b.

Year

Amortization

0 1 2 3 4

– 600 600 600 600

Book Value (net) 2,400 1,800 1,200 600 0

c. With a four-year life and straight-line amortization (based on “equal value each year”), the annual charge to amortization will be ($2,400 – $400) / 4 = $500 (total for all six boats).

Intermediate 26. Section: 3.5 The Canadian Tax System Learning Objective: 3.5 Level of difficulty: Intermediate Solution: Year 1: ½ Capital Cost CCA = $1,200x15% UCC (end of Year 1) Year 2: Add ½ Capital Cost UCC (start of Year 2) CCA = $2,220.00x15% UCC Year 3: CCA = $1,887.00x15% UCC Year 4: CCA = $1,603.95x15% 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

27. Section: 3.2 Organizing a Firm’s Transactions Learning Objective: 3.2 Level of difficulty: Intermediate Solution: The correct entries are as follows: Debit accounts receivable by $80,000 Credit sales revenue by $80,000 Debit cost of goods sold (COGS) by $50,000 Credit inventories by $50,000 28. Section: 3.3 Learning Objective: 3.3 Level of difficulty: Intermediate Solution: Total Shareholders’ Equity ($150,500) = Capital Stock + Retained Earnings ($18,500).

Therefore, Capital Stock = $132,000

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29. Section: 3.3 Preparing Accounting Statements Learning Objective: 3.3 Level of difficulty: Intermediate Solution: Statement of Financial Position for Finns’ Fridges Assets Liabilities and Owners’ Equity Current assets 2,000 Interest payable 200 Property and equipment 4,000 Other current liabilities 800 (net) Long-term liabilities 3,200 Owners’ equity 1,800 Total assets Total liabilities and owners’ 6,000 6,000 equity Statement of Comprehensive Income for Finns’ Fridges Revenues 2,000 Less: expenses Amortization expense (1,000) Interest expense ( 200) Net income

$800

30. Section: 3.3 Preparing Accounting Statements Learning Objective: 3.3 Level of difficulty: Intermediate Solution: Working Capital = Current Assets – Current Liabilities = $2,000 – ($200 + $800) = $1,000 31. Section: 3.3 Preparing Accounting Statements Learning Objective: 3.3 Level of difficulty: Intermediate Solution: From question 29, net income (before tax) is $800. At a tax rate of 40 percent, the income tax payable is 0.40 x $800 = $320. Net income (after tax) = $ 800 – $320 = $480.

32. Section: 3.3 Preparing Accounting Statements Learning Objective: 3.3 Level of difficulty: Intermediate Solution: There are 100 shares outstanding at the moment. Based on the net income from question 29, EPS = Net income / Shares outstanding = $800 / 100 = $8 per share.

33. Section: 3.3 Preparing Accounting Statements Learning Objective: 3.3 Level of difficulty: Intermediate

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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 2015 = $1.4 million – $1 million = $0.4 million. That is, financing activities generated cash of $400,000.

34. Section: 3.3 Preparing Accounting Statements Learning Objective: 3.3 Level of difficulty: Intermediate Solution: a.

Revenue 100,000 Cost of sales 40,000 Rent 15,000 Depreciation 3,000 Interest 2,000 Income before tax 40,000 Taxes paid 14,000 Net income 26,000 b. Dividends = net income × dividend payout ratio = 26,000 × 20% = $5,200 Retained earnings = net income – dividends = 26,000 – 5,200 = $20,800.

35. Section: 3.3 Preparing Accounting Statements Learning Objective: 3.3 Level of Difficulty: Intermediate Solution: Current assets in year 1 = cash and equivalents + accounts receivable + inventory = 150,000 + 35,000 + 23,000 = $208,000 Current assets in year 2 = 80,000 + 20,000 + 15,000 = 115,000 The change in dollar amount = 115,000 – 208,000 = –$93,000 The change in percentage = –93,000 / 208,000 = –44.71% 36. Section: 3.3 Preparing Accounting Statements Learning Objective: Level of difficulty: Intermediate Solution: Net working capital in year 2 = current assets – current liabilities = 781 – 720 = $61 37. Section: 3.3 Preparing Accounting Statements Learning Objective: Level of difficulty: Intermediate Solution: Net working capital in year 1 = current assets – current liabilities = 840 – 790 = 50 Changes in net working capital = 61 – 50 = $11

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38. Section: 3.3 Preparing Accounting Statements Learning Objective: Level of difficulty: Intermediate Solution: Additions in retained earnings = 800 – 556 = 244 Net income = additions in retained earnings / (1 – dividend payout ratio) = 244 / (1 – 0.30) = $349 39. Section: 3.3 Preparing Accounting Statements Learning Objective: Level of difficulty: Intermediate Solution: EPS = net income / number of shares outstanding = $349 / 200 = $1.75 40. Section: 3.4 CP’s Accounting Statements Learning Objective: 3.4 Level of difficulty: Intermediate Solution: The earnings (net income) figure is $1,476 million, and the earnings per common share (EPS) is reported as $8.54. Therefore, there must have been $1,476 million / $8.54 = 172,833,724 shares outstanding at the end of 2014.

41. Section: 3.4 CP’s. Accounting Statements Learning Objective: 3.4 Level of difficulty: Intermediate Solution: In $millions Dec 31, 2014 Cash and cash equivalents 226 Restricted cash and cash -equivalents Account receivable, net 702 Materials and supplies 177 Deferred income taxes 56 Other current assets 116 Total current assets 1,277

Dec 31, 2013 Change ($) Change (%) 476 –250 –52.52% 411 580 165 344 53 2,029

–411 122 12 –288 63 –752

–100.00% 21.03% 7.27% –83.72% 118.87% –37.06%

Cash and cash equivalents, restricted cash, and deferred income taxes decreased. Accounts receivable net, materials and supplies, and other current assets increased. Restricted cash changed (decreased) the most in dollar value. However, other current assets changed (increased) the most in terms of percent.

42. Section: 3.4 CP’s Accounting Statements Learning Objective: 3.4 Level of difficulty: Intermediate Solution:

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Dividend per common share = dividends paid / # shares = $244 million / 172,833,724 = $1.41 43. Section: 3.4 CP’s Accounting Statements Learning Objective: 3.4 Level of difficulty: Intermediate Solution: average tax rate is $562 million / $2,038 million = 27.58% 44. Section: 3.4 CP’s Accounting Statements Learning Objective: 3.4 Level of difficulty: Intermediate Solution: The sales growth rate in 2014 is ($6,464 million / $5,982 million) – 1 = 8.06%.

The sales growth rate in 2013 is ($5,982 million / $5,550 million) – 1 = 7.78%.

The sales growth rate increased only a small amount from 2013 to 2014.

45. Section: 3.5 The Canadian Tax System Learning Objective: 3.5 Level of difficulty: Intermediate Solution: a. The sale price is greater than the original capital cost (purchase price), so there is a capital gain of $35,000 – $25,000 = $10,000.

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 $15,000 proceeds from the sale would leave $0. There is no CCA recapture. 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.

46. Section: 3.5 The Canadian Tax System Learning Objective: 3.5 Level of difficulty: Intermediate 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 – $250,000 (CCA) = $750,000. At a tax rate of 30 percent, it will pay $225,000 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.

47. Section: 3.5 The Canadian Tax System

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Learning Objective: 3.5 Level of difficulty: Intermediate Solution: Net income (before tax) will be $1 million – $250,000 (amortization) = $750,000 for both firms (on their public financial statements).

Firm A, having paid $225,000 in taxes (see Practice Problem 46) appears to have paid $225,000 / $750,000 = 30%.

Firm B appears to have paid $180,000 / $750,000 = 24%. This lower apparent tax rate is the direct result of the higher CCA claim.

48. Section: 3.5 The Canadian Tax System Learning Objective: 3.5 Level of difficulty: Intermediate Solution: Year 1:

Year 2:

Year 3:

½ Capital Cost of 1st plane CCA = $45,000 x 25% UCC (end of Year 1) Add ½ Capital Cost of 1st plane Add ½ Capital Cost of 2nd plane UCC (start of Year 2) CCA = $128,750 x 25% UCC (end of Year 2) Add ½ Capital Cost of 2nd plane UCC (start of Year 3) CCA = $146,562.50 x 25% UCC (end of Year 3)

$45,000 11,250 33,750 45,000 50,000 128,750 32,187.50 96,562.50 50,000 146,562.50 36,640.63 109,921.87

49. Section: 3.5 The Canadian Tax System Learning Objective: 3.5 Level of difficulty: Intermediate Solution: In Year 2, the value of “Net additions” to the asset pool will be $100,000 – 50,000 = $50,000.

Year 1:

Year 2:

Year 3:

½ Capital Cost of 1st plane CCA = $45,000 x 25% UCC (end of Year 1) Add ½ Net Additions UCC (start of Year 2) CCA = $58,750 x 25% UCC (end of Year 2) Add ½ Net Additions UCC (start of Year 3) CCA = $69,062.50 x 25% UCC (end of Year 3)

$45,000 11,250 33,750 25,000 58,750 14,687.50 44,062.50 25,000 69,062.50 17,265.63 51,796.87

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

Capital gain = selling price – original cost = 45,000 – 25,000 = $20,000.

CCA recapture (terminal loss) = lower of selling price and original cost – UCC = 25,000 – 5,000 = $20,000.

The number is positive, so it represents a CCA recapture of $20,000.

Challenging 51. Section: 3.2 Organizing a Firm’s Transactions Learning Objective: 3.2 Level of difficulty: Challenging Solution: Canadian GAAP uses historical 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. If Finns’ Fridges was a public company reporting under IFRS, it could report market value less amortization = (25 x $210) - $1,000 = 5,250 – 1,000 = $4,250 52. Section: 3.3 Preparing Accounting Statements Learning Objective: 3.3 Level of difficulty: Challenging Solution: The lost rental income will reduce the company’s revenues Reduction = 5 students x $10 = $50.

Statement of Comprehensive Income for Finns’ Fridges (Revised) Revenues 2,000 Bad debt expense 50 Amortization expense 1,000 Interest expense 200 Loss on disposal (160) Net income 590 The stolen refrigerator “impairs” (reduces) the value of property and equipment. The value of one fridge is $4,000 / 25 = $160. Current assets (accounts receivable) 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.

Statement of Financial Position for Finns’ Fridges (Revised) Assets Liabilities and Owners’ Equity

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Current assets Property and equipment (net)

1,950 Interest payable 3,840 Other current liabilities Long-term liabilities

200 800 3,200

Total assets

Owners’ equity 5,790 Total liabilities equity

1,590 5,790

and owners’

53. Section: 3.3 Preparing Accounting Statements Learning Objective: 3.3 Level of difficulty: Challenging 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

54. Section: 3.3 Preparing Accounting Statements Learning Objective: 3.3 Level of difficulty: Challenging 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).

55. Section: 3.5 The Canadian Tax System Learning Objective: 3.5

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Level of difficulty: Challenging Solution: GG Inc. Statement of Comprehensive Income for Year 2015 Revenue $100,000 Cost of sales 30,000 Rent 10,000 Depreciation 1,500 Interest 2,800 Salary 6,000 Taxable income 49,700 Taxes paid (26.5%) 13,171 Net income 36,529 56. Section: 3.5 The Canadian Tax System Learning Objective: 3.5 Level of difficulty: Challenging Solution: a. Yes. Firms apply IFRS when reporting public financial statements, but have to use CCA when reporting to CRA. b. Firm A pays higher taxes. 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, taxable income 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 taxable income of $10 million – $2 million = $8 million. It will therefore pay $8 million x 30% = $2.4 million in taxes. It will also record future income taxes of 30% x $1,000,000 or $300,000 because of the excess CCA charge over the depreciation. d. Firm A: net income = earnings before tax – tax = $9 million – $2.7 million = $6.3 million.

Firm B: net income = earnings before tax – tax = $9 million – $2.4 million – $0.3 million = $6.3 million.

Having different CCA deductions does not impact net income because of future income taxes that result from increased CCA over depreciation expense.

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

Year 1:

Year 2:

½ Capital Cost of 1st machine CCA = $500,000 x 20% UCC (end of Year 1) Add ½ Net Additions UCC (start of Year 2) CCA = $900,000 x 20% UCC (end of Year 2)

$500,000 100,000 400,000 500,000 900,000 180,000 720,000

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Year 3: UCC (start of Year 3) CCA = $720,000 x 20% UCC (end of Year 3)

720,000 144,000 576,000

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

Year 2: Add ½ Capital Cost of 2nd machine $250,000 CCA = $250,000 x 20% 50,000 UCC (end of Year 2) 200,000 Year 3: Add ½ Net Additions 250,000 UCC (start of Year 3) 450,000 CCA = $450,000 x 20% 90,000 UCC (end of Year 3) 360,000 c. In the third year the total ending UCC = 576,000 + 360,000 = $$936,000 58. Section: 3.5 The Canadian Tax System Learning Objective: 3.5 Level of Difficulty: Challenging Solution: a. The EPS before tax = $1, but the EPS after tax = $1(1– 0.25) = $0.75, which is the DPS paid to shareholders. For a shareholder, for each $0.75 dividend received, the dividend gross up = $0.75(1.38) = $1.0350. The taxes are calculated as the marginal taxes less the dividend tax credit: Combined marginal taxes = $1.0350(0.42) = $0.4347 Less: dividend tax credit = $1.0350(0.2142) = $0.2217 Net tax paid = $0.2130 So a shareholder would receive a $0.75 dividend, pay $0.2130 in taxes, and would be left with $0.75 – $0.2130 = $0.5370. This is 53.70% of the original $1 EPS (0.5370 / 1), or 71.60% of the $0.75 dividend received (0.5370 / 0.7500) b. If you received $0.75 in interest income: Interest received = $0.7500 Less: combined marginal taxes = $0.75(0.42) = $0.3150 Net interest after tax = $0.4350 So you would receive $0.75 in interest, pay $0.3150 in taxes, and would be left with $0.75 – $0.3150 = $0.4350. This is 58% of the original interest as you pay taxes at a 42% rate. c. If you received $1.00 in interest income: Interest received = $1.0000 Less: combined marginal taxes = $1.00(0.42) = $0.4200 Net interest after tax = $0.5800 So you would receive $1.00 in interest, pay $0.42 in taxes, and would be left with $1.00 – $0.42 = $0.58. This is 58% of the original interest as you pay taxes at a 42% rate.

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d. The average tax rate = taxes paid / income received (a) $0.75 dividend Average tax rate = 0.2130 / 0.7500 = 28.40% (b) $0.75 interest Average tax rate = 0.3150 / 0.7500 = 42% (marginal rate) (c) $1.00 interest Average tax rate = 0.4200 / 1.000 = 42% (marginal rate) Remember, interest is a tax deductible expense for a firm, while dividends are paid out of aftertax income. For individuals, dividends receive preferential treatment, in the form of a dividend tax credit, as a way of mitigating the double taxation effect. For individuals, interest income is taxed as ordinary income.

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Answers to Concept Review Questions 3.1 Accounting Principles Concept review questions 1. What does IFRS stand for? What types of Canadian companies must prepare their financial statements in accordance with IFRS (or U.S. GAAP)?

International financial reporting standards (IFRS) set out the basic conventions for preparing financial statements in Canada and in many countries around the world. They are intended to ensure that a firm’s financial position is fairly represented to those who use the firm’s financial statements (e.g., shareholders and creditors) and that these users are able to understand the firm’s transactions. IFRS has been the primary accounting standard for publically accountable enterprises in Canada since January 2011, replacing our previous standard, which we refer to as our “former” Canadian generally accepted accounting principles (GAAP). Publically accountable enterprises include any company that has issued debt or equity that is or will be traded in a public market or any organization that holds assets in a fiduciary capacity for a broad group of outsiders as one of its primary businesses, such as a bank or a mutual fund. Private companies or not-for-profit organizations have the option but are not required to report their financial results under IFRS. 2. Who prescribes GAAP for U.S. companies?

GAAP consists of the principles of the Financial Accounting Standards Board (FASB) 3. What are the major provisions of SOX? The main provisions of this act were: i) The establishment of a Public Company Accounting Oversight Board that would register and inspect the accounting audit firms and establish audit standards; ii) The separation of audit functions from other services provided by the big accounting firms, such as consulting, with the auditor rotating every five years so that they do not get too cosy with the company they are auditing; iii) The implementation of much stricter governance standards including internal controls with the auditor reporting to the company’s audit committee, which is to be composed of independent members of the BOD with the power to engage independent consultants; iv) The company’s annual report is required to contain an internal control report which indicates the state of the firm’s internal controls and assess their effectiveness; and, v) Finally, both the CEO and CFO shall “certify” that the firm’s financial statements “fairly present, in all material respects, the operations and financial condition of the issuer.”

3.2 Organizing a Firm’s Transactions Concept review questions 1. Differentiate between debits and credits with respect to assets and liabilities.

By convention we record increases in assets like cash as “debits” and record them on the left side of a balance sheet. In contrast, an increase in liabilities, like the capital owed to Jim, is recorded as a “credit” on the right hand side of the balance sheet.

2. What is the primary objective of financial reporting under IFRS?

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They are intended to ensure that a firm’s financial position is fairly represented to those who use the firm’s financial statements (e.g., potential investors, lenders, and other creditors making decisions about providing resources to the entity) and that these users are able to understand the firm’s transactions. IFRS has been the primary accounting standard for publically accountable enterprises in Canada since January 2011, replacing our previous standard, which we refer to as our “former” Canadian generally accepted accounting principles (GAAP).

3. Explain what is meant by the matching principle. How is this principle related to the use of accrual accounting?

The matching principle is that the revenues must be matched against the costs that generated those revenues. The most powerful principle is then the matching principle, which leads to accrual accounting. This means that costs and revenues have to match the time period, even if the cash components of the transactions occur in other periods.

3.3 Preparing Accounting Statements Concept review questions 1. How is the balance sheet related to the income statement?

Balance sheet is simply a snapshot of the financial position of the firm. Income statement is a firm’s financial statement showing the sales, expenses and net profit for a given period. When an accountant is adding transactions to the balance sheet account, he is actually making up the income statement.

2. What happens to the net income figure when a firm’s accountants make more aggressive accounting assumptions? Briefly explain.

The net income figure will increase under more aggressive accounting assumptions. For example, the revenue will increase when promised sales are included, depreciation can decrease when less depreciation is assumed, and salary expense can decrease when the salary is used for development.

3. How do cash flow statements alleviate the impact of most major accounting assumptions?

Cash flow statements undo the effects of judgment as much as possible and track the actual flow of hard cash through a firm since cash flows does not vary with the accounting assumptions.

4. Why do income statements differ from tax statements? What is the major difference?

In particular firms are allowed to present one set of accounts to Revenue Canada (the tax authorities) and then another to the investing public. The major differences result from what the company recognizes as an expense and what Revenue Canada allows. Some of the differences are temporary and some of the differences are permanent. In the Canadian tax system, the membership at the golf course may be an expense for reporting to the public; but, is not an allowable expense for tax purposes. The same can be said for one half of business meals. These are permanent differences. On the other hand, some differences may be temporary. Expenses such as depreciation/amortization or warranty expenses may or accounting for inventory will eventually be the same over time. Revenue Canada will only accept Capital Cost Allowance (declining balance) for tax purposes while the company may report using straight line. Over the long run, the same amount of expense may be recognized; but, they are differences every year.

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There are limits as to how different they can be, but Canada is not like Northern European countries, where there is one set of statements so that the accounts to the tax authorities are the same as those presented to the general public.

3.4 Canadian Pacific Accounting Statements Concept Review Questions 1. Who is responsible for the preparation of a company’s financial statements?

Management prepares the financial statements in accordance with IFRS or U.S. GAAP, not the auditors. IFRS (International financial reporting standards) has been the primary accounting standard for publically accountable enterprises in Canada since January 2011, replacing the previous standard, Canadian generally accepted accounting principles (GAAP). If a firm is listed on a U.S. stock exchange it must prepare its statements under U.S. GAAP. 2. What are the scope and purpose of the auditor’s opinion?

First, they indicate that they carry out some tests to make sure that things are as the management says. It used to be that the auditor checked up on everything, which is now infeasible, so they do spot checks. Second, they check on the judgment that management uses. Auditors check that the judgment uses in choosing a depreciation rate, recognizing revenue, and so on, is reasonable.

Finally, they assess the overall financial statement presentation.

3. Identify the main components of a firm’s balance sheet and income statement.

A firm’s balance sheet has assets on the left hand side and liabilities and shareholder’s equity on the right hand side. Total assets must equal the sum of the total liabilities and total shareholder’s equity. On each side, items are listed according to the liquidity with the most liquid item on the top. A firm’s income statement has the following components from the top to bottom: revenue, costs, earnings before income taxes and minority interest, income taxes, earnings before minority interest, minority interest, earnings for the year, retained earnings, dividend paid, and finally the balance at end of year.

3.5 The Canadian Tax System Concept Review Questions 1. Explain how to calculate the CCA expense for an asset class in a given year.

CCA is usually the beginning-of-year UCC multiplied by the CCA rate. In year 1, the beginningof-year UCC is half the assets. The beginning-of-year UCC is the end-of-prior-year UCC. 2. Explain why a firm cannot claim CCA recapture and a terminal loss for the same asset class in the same year.

When an asset is terminated, the salvage value is greater than, equal to, or less than the UCC. If the salvage value is higher, then there is a CCA recapture. If the salvage value equals the remaining UCC, there is no CCA recapture or terminal loss. If the salvage value is lesser, then there is a terminal loss.

3. Why would firms prefer to receive dividend income and make interest payments rather than make dividend payments and receive interest payments?

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The reason is that interest payments are made before the taxes paid and dividend are paid after taxes are paid.

4. What form of investment income has the highest tax rate in Canada?

Interest from debt has the highest tax rate because it is taxed as ordinary income.

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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: Basic 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: Intermediate Solution: D Sales Assets NI NI  = (Net Profit Margin)(Asset Turnover)(Leverage) =  E Sales Assets Equity NI NI Assets =  = ROA* Leverage E Assets Equity 3. Section: 4.2 A Framework for Financial Analysis Learning Objective: 4.2 Level of difficulty: Intermediate Solution: C Net profit margin = NI/Sales = (3,090)(1 – 0.40) / (6,500) = 1,854 / 6,500 = 28.52% Asset Turnover = Sales/Assets = 6,500 / (30,900 + 18,500) = 6,500 / 49,400 = 13.16% Leverage = Assets/Equity = 49,400 / 18,500 = 2.67 4. Section: 4.2 A Framework for Financial Analysis Learning Objective: 4.2 Level of difficulty: Basic 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: Intermediate Solution: D

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Debt Ratio =

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Liabilities 600,000 + 190,000 + 250,000 + 2,000,000 3,040,000 = = = 0.51 TA 5,930,000 5,930,000

6. Section: 4.3 Leverage Ratios Learning Objective: 4.3 Level of difficulty: Intermediate Solution: D D 2,000,000 Debt-Equity Ratio = = = 0.69 SE 2,800,000 + 90,000 Times Interest Earned Ratio =

EBIT I

=

560,000 + 150,000 150,000

=

710,000

= 4.73

150,000

7. Section: 4.4 Efficiency Ratios Learning Objective: 4.4 Level of difficulty: Intermediate Solution: A Gross Profit Margin = Sales − COGS = 1,290,000 − 380,000 = 910,000 = 70.54% Sales 1,290,000 1,290,000 Operating Margin = EBIT = 1,290,000 − 380,000 − 200,000 = 710,000 = 55.04% Sales 1,290,000 1,290,000 8. Section: 4.5 Productivity Ratios Learning Objective: 4.5 Level of difficulty: Intermediate Solution: D Days Sales in Inventory =

350,000 INV = = 99days ADS 1,290,000/ 365

9. Section: 4.6 Liquidity Ratios Learning Objective: 4.6 Level of difficulty: Intermediate Solution: A Working Capital Ratio = CA = 500,000 + 600,000 + 350,000 = 1,450,000 = 24.45% TA 5,930,000 5,930,000 10. Section: 4.3 Leverage Ratios Learning Objective: 4.3 Level of difficulty: Intermediate

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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: Basic Solution: D Times interest earned is measured as EBIT divided by interest expense.

12. Section: 4.6 Liquidity Ratios Learning Objective: 4.6 Level of difficulty: Basic 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: Basic 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: Basic 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: Basic Solution: A Dividend yield is the only financial ratio that relates dividend policy to external stock market performance.

Practice Problems Basic 16. Section: 4.2 A Framework for Financial Analysis Learning Objective: 4.2 Level of difficulty: Basic 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.

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17. Section: 4.2 A Framework for Financial Analysis Learning Objective: 4.2 Level of difficulty: Basic 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: Basic Solution: ROA = NI / TA 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: Basic Solution: From the year 2 statement of financial position, Debt Ratio = TL / TA = 3,210 / 4,700 = 0.683 and the Debt-Equity Ratio = D / SE = 2,600 / 1,490 = 1.745. Using either ratio, Finns’ Fridges is much more highly leveraged than its competitor.

20. Section: 4.2 A Framework for Financial Analysis Learning Objective: 4.2 Level of difficulty: Basic 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% Intermediate 21. Section: 4.4 Efficiency Ratios Learning Objective: 4.4 Level of difficulty: Intermediate 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.

22. Section: 4.2 A Framework for Financial Analysis Learning Objective: 4.2 Level of difficulty: Intermediate Solution: Year 1

Year 2

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

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413 / 1,950 = 21.2%

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).

23. Section: 4.3 Leverage Ratios Learning Objective: 4.3 Level of difficulty: Intermediate 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.

24. Section: 4.4 Efficiency Ratios Learning Objective: 4.4 Level of difficulty: Intermediate Solution: 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.

25. Section: 4.5 Productivity Ratios Learning Objective: 4.5 Level of difficulty: Intermediate 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).

26. Section: 4.6 Learning Objective: 4.6 Liquidity Ratios Level of difficulty: Intermediate Solution:

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

Year 1 1,150 / 4,990 = 23.0% 1,150 / (200+177+200) = 1.993 = 199.3%

Year 2 493 / 4,381 = 11.3% 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.

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27. Section: 4.8 Financial Forecasting Learning Objective: 4.8 Level of difficulty: Intermediate Solution: Percentage of Sales Balance Sheet for Finns’ Fridges % of Sales

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

2,200 493 3,888 4,381

22.4% 176.7% 199.1%

160 182 210 2,400 2,952 1,000 429 1,429 4,381

7.3% 8.3% 9.5% 109.1% 134.2% 45.5% 19.5% 65.0% 199.1%

28. Section: 4.8 Financial Forecasting Learning Objective: 4.8 Level of difficulty: Intermediate 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

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

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

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-

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.

29. Section: 4.8 Financial Forecasting Learning Objective: 4.8 Level of difficulty: Intermediate 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 Revenues (net of bad debts) Selling & admin expenses EBITDA Amortization expense EBIT Interest expense Earnings before tax Tax (30%) Net income

Year 3 2,600 260 2,340 1,422 918 120 798 239 559

30. Section: 4.8 Financial Forecasting Learning Objective: 4.8 Level of difficulty: Intermediate 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.

31. Section: 4.8 Financial Forecasting Learning Objective: 4.8 Level of Difficulty: Intermediate Solution: Retained earnings (year 3) = Retained earnings (year 2) + Net income – Dividends =

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429 + 559 – 270= 718 32. Section: 4.8 Financial Forecasting Learning Objective: 4.8 Level of Difficulty: Intermediate Solution: The external financing requirement is now $5,177 – $4,770 = $407.

33. Section: 4.4 Efficiency Ratios Learning Objective: 4.4 Level of difficulty: Intermediate 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.

34. Section: 4.7 Valuation Ratios Learning Objective: 4.7 Level of difficulty: Intermediate 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 35. Section: 4.7 Valuation Ratios Learning Objective: 4.7 Level of difficulty: Intermediate Solution: Re-arranging the P/E ratio equation, we find EPS = P/(P/E ratio). To find the expected EPS (EEPS) for 2017 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 2017.

36. Section: 4.7 Valuation Ratios Learning Objective: 4.7 Level of difficulty: Intermediate Solution: We know (see Problem 34) 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.

37. Section: 4.4 Efficiency Ratios Learning Objective: 4.4 Level of difficulty: Intermediate Solution:

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EBT  (1 − T ) = NI 685,750 NI = 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 = Break-Even Point = = $3,314,063 CM (5,050,000 −1,850,000) / 5,050,000 38. Section: 4.4 Efficiency Ratios Learning Objective: 4.4 Level of difficulty: Intermediate Solution: EBT  (1 − T ) = NI 180,000 NI = EBT = = $300,000 1 − T (1 − 0.40) CM Sales − VC 400,000 − 130,000 DTL = = = = 0.90 EBT EBT 300,000 80,000 FC = Break-Even Point = = $118,519 CM (400,000 −130,000) / 400,000 39. Section: 4.7 Valuation Ratios Learning Objective: 4.7 Level of difficulty: Intermediate Solution: BVPS =

SE #

=

945,000

= $1.89

500,000

Dividend yield =

DPS

=

150,000 / 500,000

= 3.2% 9.5 150,000 / 500,000 Dividend payout = = = 34.6% EPS 433,000 / 500,000 P 9.5 = Market-to-book ratio = = 5.03 BVPS 1.89 Earnings per share = NI/# = 433,000/500,000 = $0.866 PE ratio = P/EPS = 9.5/0.866 = 10.97 P DPS

40. Section: 4.2 A Framework for Financial Analysis Learning Objective: 4.2 Level of Difficulty: Intermediate Solution:

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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 41 Section: 4.2 A Framework for Financial Analysis Learning Objective: 4.2 Level of Difficulty: Intermediate 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 42 Section: 4.3 Leverage Ratios Learning Objective: 4.3 Level of Difficulty: Intermediate 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.

43. Section: 4.3 Leverage Ratios Learning Objective: 4.3 Level of Difficulty: Intermediate Solution: TIE = EBIT/I = 1,065/80 = 13.31 44. Section: 4.4 Efficiency Ratios Learning Objective: 4.4 Level of Difficulty: Intermediate 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% Gross profit margin excludes the impact of depreciation, while operating margin includes it.

45. Section: 4.5 Productivity Ratios Learning Objective: 4.5 Level of Difficulty: Intermediate Solution: Receivable turnover = S/AR = 1,850/234 = 7.91 Average collection period = 365/receivable turnover = 365/7.91 = 46.1 days

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46. Section: 4.5 Productivity Ratios Learning Objective: 4.5 Level of Difficulty: Intermediate Solution: Inventory turnover = COGS/inventory = 605/435 = 1.39 Average days of sales in inventory = 365/inventory turnover = 262.6 days 47. Section: 4.5 Productivity Ratios Learning Objective: 4.5 Level of Difficulty: Intermediate Solution: Net fixed asset turnover = S/NFA = 1,850/1,888 = 0.98 48. Section: 4.6 Liquidity Ratios Learning Objective: 4.6 Level of Difficulty: Intermediate 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.

49. Section: 4.7 Valuation Ratios Learning Objective: 4.7 Level of Difficulty: Intermediate 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 50. Section: 4.9 Formula Forecasting Learning Objective: 4.9 Level of Difficulty: Intermediate Solution: Expected total dividends = current dividends × (1 + g) = 585 × (1 + 5 percent) = $614.25 51. Section: 4.7 Valuation Ratios Learning Objective: 4.7 Level of Difficulty: Intermediate Solution: Earnings per share = NI/# = 829/100 = 8.29

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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 52. Section: 4.9 Formula Forecasting Learning Objective: 4.9 Level of Difficulty: Intermediate 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% 53. Section: 4.9 Formula Forecasting Learning Objective: 4.9 Level of Difficulty: Intermediate Solution: EFR = [–b × PM + (a – b × PM) × g] × S = [–0.29 × 0.448 + (1.0535 – 0.29 × 0.448) × 0.05] × 1,850 = –154.92 This corporation has a cash surplus of $154.92.

Challenging 54. Section: 4.9 Formula Forecasting Learning Objective: 4.9 Level of difficulty: Challenging 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.

Forecast Balance Sheet for Finns’ Fridges (Revised) Year 3 Assets Cash Property and equipment (net) Total assets Liabilities and Owners’ Equity

431 3,516 3,947

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Interest payable Tax payable Dividends payable Long-term debt Total liabilities Common shares Retained earnings Total owners’ equity Total liabilities and owners’ equity

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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.

55. Section: 4.9 Formula Forecasting Learning Objective: 4.9 Level of Difficulty: Challenging 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 = (2,600 + 1,490) / 2,400 = 1.7042 (170.42%) ii) Retention Ratio, b = (Net Income – Dividends) / Net Income = (462 – 220) / 462 = 0.5238 (52.38%) iii) Net Profit Margin, PM = Net Income / Revenues = 462 / 2,400 = 0.1925 (19.25%) g* =

(0.5238)(0.1925) b  PM = = 0.0629 = 6.29% (a − b  PM ) 1.7042 − (0.5238)(0.1925))

56. Section: 4.9 Formula Forecasting Learning Objective: 4.9 Level of difficulty: Challenging Solution: InvestedCapital 900,000 + 2,500,000 a= = = 0.67 Sales 5,050,000 NI 685,750 = PM = = 0.1358 Sales 5,050,000 dividend 200,000 b = 1 − payout = 1 − = 1− = 0.71 NI 685,750

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EFR S = −b  PM ) + (a − b  PM )g = −(0.71)  (0.1358) + (0.67 − 0.71 0.1358)  0.05 = −0.068 We can re-write the above formula as follows: EFR = −b  PM + (a − b  PM )g = −b(1 + g)  PM + ag S

Dividend payout is positively related to EFR; the higher the dividend payout, the lower the “b”, and the higher the EFR. Profit margin ratio is negatively related to EFR, i.e., the higher the profit margin, the lower the EFR. Sustainable growth rate is g = (b x PM)/(a-b x PM) = (0.71 x 0.1358)/(0.67 - 0.71 x 0.1358) = 16.81% 57. Section: 4.9 Formula Forecasting Learning Objective: 4.9 Level of difficulty: Challenging Solution: Use Equation 4-32 from the text. The parameter values were computed in Practice Problem 56: a = 0.67; profit margin = 0.1358; b = 0.71. With the growth rate specified as 25 percent, we have: EFR = a  S  g − b  PM  (1 + g)  S = 0.67  $5,050,000  0.25 − 0.71 0.1358 (1 + 0.25)  $5,050,000 = 845,875 − 608,639 = $237,236 G.G. Co. will need an additional $237,236 to finance its growth.

58. Section: 4.5 Productivity Ratios Learning Objective: 4.5 Level of difficulty: Challenging Solution: Receivable Turnover = Sales = 950,000 = 1.58 times AR 600,000 Inventory Turnover = COGS = Sales − GrossProfit = 950,000 − 550,000 = 0.73 times INV INV 550,000

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Collection Period =

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600,000 AR = = 231 days ADS 950,000 / 365

Interpretation of receivable turnover: on average, the corporation collects all receivables 1.58 times a year.

Interpretation of inventory turnover: on average, the corporation turns over all inventories 0.73 times a year. Note that 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 / 550,000 = 1.73 times.

Interpretation of average collection period: On average, it takes 231 days for the customers to pay their bills after purchase, an unusually high number.

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Chapter 5: Time Value of Money Multiple Choice Questions 1. Section: 5.2 Simple Interest; 5.3 Compound Interest Learning Objective: 5.2; 5.3 Level of difficulty: Basic Solution: C. Simple interest rate: $1,000 + ($1,000)(8%)(6) = $1,480 Compound interest rate: $1,000(1+.08)6 = $1,586.87 2. Section: 5.2 Simple Interest; 5.3 Compound Interest Learning Objective: 5.2; 5.3 Level of difficulty: Intermediate Solution: C Simple interest: Total interest paid over three years: $6,200 - $5,000 = $1,200 Annual interest = $1,200/3 = $400 $400/$5,000 = 8% Compound interest:

3. Section: 5.2 Simple Interest; 5.3 Compound Interest Learning Objective: 5.2; 5.3 Level of difficulty: Intermediate Solution: B 4. Section: 5.2 Simple Interest; 5.3 Compound Interest Learning Objective: 5.2; 5.3 Level of difficulty: Basic Solution: D. 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)10 = $1,967 Therefore, D is the largest.

5. Section: 5.3 Compound Interest Learning Objective: 5.3 Level of difficulty: Intermediate Solution: B.

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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, FV=15,000,000, PMT = 0, CPT PV= –4,429,541.58 6. Section: 5.2 Simple Interest; 5.3 Compound Interest Learning Objective: 5.2; 5.3 Level of difficulty: Intermediate 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: Intermediate Solution: D. FV=PV(1+k)n 16,000=10,000(1+ k)8 8ln(1+k)=ln(1.6), therefore k=6.05% Or using a financial calculator (TI BAII Plus), N=8, PV= –10,000, FV=16,000, PMT = 0, CPT I/Y=6.05% 8. Section: 5.3 Compound Interest Learning Objective: 5.3 Level of difficulty: Intermediate 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, FV=3, PMT = 0, CPT N=12.7 9. Section: 5.4 Annuities and Perpetuities Learning objective: 5.4 Level of difficulty: Intermediate 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: Challenging

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Solution: C. (1 + k)20 −1 (1 + .15)20 −1 FV20 = PMT  .15  = 2,000(102.4436) = $204,887  =$ 2,000 k     Or using a financial calculator (TI BAII Plus), N=20, I/Y=15, PMT= -2,000, PV = 0, CPT FV=204,887 11. Section: 5.4 Annuities and Perpetuities Learning Objective: 5.4 Level of difficulty: Intermediate Solution: B. 1  1  1 − 1−  (1 + k )n   (1.15)20  PV0 = PMT   = $2,000   = 2,000(6.25933 ) = $12,519 .15 k            Or using a financial calculator (TI BAII Plus), N=20, I/Y=15, PMT= –2,000, FV = 0, CPT PV=12,519 12. Section: 5.4 Annuities and Perpetuities Learning Objective: 5.4 Level of difficulty: Basic Solution: D. PV0=PMT/k=$1,500/.12=$12,500 13. Section: 5.4 Annuities and Perpetuities Learning Objective: 5.4 Level of difficulty: Basic Solution: A. PV0=PMT/k=$1,500/.12 + $1,500 =$14,000 14. Section: 5.7 Loan or Mortgage Arrangements Learning Objective: 5.7 Level of difficulty: Intermediate Solution: B PV of annuity of 120 remaining payments at 1% per month.

1  1 1 − 1−   (1 + k )n   (1.01)120  PV0 = PMT   = $3,303.26  = 3,303.26(69.7005) = $230,238.95 .01 k           

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Using a financial calculator (TI BAII Plus), N = 120, I/Y = 1, PMT = -3,303.26, FV = 0, CPT PV = 230,238.95 15. Section: 5.4 Annuities and Perpetuities Learning Objective: 5.4 Level of difficulty: Challenging Solution: A. The future value of a perpetuity cannot be computed as it is infinite.

Practice Problems Basic 16. Section: 5.2 Simple Interest Learning Objective: 5.2 Level of difficulty: Basic 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 17. Section: 5.2 Simple Interest Learning Objective: 5.2 Level of difficulty: Basic 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.

18. Section: 5.2 Simple Interest Learning Objective: 5.2 Level of difficulty: Basic 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.

19. Section: 5.2 Simple Interest Learning Objective: 5.2 Level of difficulty: Basic Solution:

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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.

20. Section: 5.3 Compound Interest Learning Objective: 5.3 Level of difficulty: Basic 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.

21. Section: 5.2 Simple Interest; 5.3 Compound Interest Learning outcome: 5.2; 5.3 Level of difficulty: Basic Solution: A. Value = P + (n x P x k) = $24 + (389 x $24 x 5%) = $491 B. FV389 years = $24  (1 + 0.05)389 = $4,196,126,573 22. Section: 5.3 Compound Interest Learning outcome: 5.3 Level of difficulty: Basic Solution: The future value of the loan (the amount to be repaid) is $5,000. The amount that can be borrowed is the present value amount, calculated as: PV0 = FV1 

1 1 = $5,000 = $4,716.98 1 (1+ k) (1+ .06)1

Or using a financial calculator (TI BAII Plus), N=1, I/Y=6, FV= -5,000, PMT = 0, CPT PV=4,716.98 23. Section: 5.3 Compound Interest Learning Objective: 5.3 Level of difficulty: Basic Solution: a. FV1 year = $20,000  (1 + 0.10)1 = $22,000.00 b. FV5 years = $20,000  (1 + 0.10)5 = $32,210.20

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c. FV10 years = $20,000  (1 + 0.10)10 = $51,874.85 24. Section: 5.3 Compound Interest Learning Objectives: 5.3 Level of difficulty: Basic 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, FV= -800, PMT = 0, CPT PV=691.07 25. Section: 5.4 Annuities and Perpetuities Learning outcome: 5.4 Level of difficulty: Basic Solution: Present value of the perpetual scholarship payment: 1  1  PV = PMT = $5000 = $166, 667 0 k   0.03  26. Section: 5.6 Quoted versus Effective Rates Learning Objective: 5.6 Level of difficulty: Basic Solution: 2 .

07 0  25 = 1 +2 − 1 = 7 .

3  For Bank A, k   4

For Bank B,

.

07 0  20 k = 1 + 1 = 7 .

4  − 4  12

For Bank C,

.

07 0  15 k = 1 + 1 = 7 .

3  − 12  

Bank B pays the highest effective annual rate.

27. Section: 5.6 Quoted versus Effective Rates Learning Objective: 5.6 Level of difficulty: Basic

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Solution: a. For annual compounding, the effective annual rate will be the same as the quoted rate. To check this:  QR   9.5%  k = 1 +  −1 = 1+  −1 = 9.5% m 1     m

1

b. With quarterly compounding, set m=4,  9.5%  k = 1 +  −1 = 9.84% 4   4

c. With monthly compounding, set m=12,  9.5%  k = 1 +  −1 = 9.92% 12   12

28. Section: 5.6 Quoted versus Effective Rates Learning Objective: 5.6 Level of difficulty: Basic Solution: a. k = Quoted Rate = 6%  FV1year = PV0 (1 + k) = $50,000  (1.06) = $53,000 12

 QR  b. k = 1 + 12  −1 = 6.16778%  FV1year = $50,000  (1.0616778) = $53,083.89   365

 QR  c. k = 1 + 365   

−1 = 6.18313%  FV1year = $50,000  (1.0618313) = $53,091.57

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

30. Section: 5.4 Annuities and Perpetuities Learning Objective: 5.4 Level of difficulty: Basic Solution:

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

1  1 − 3  (1 + 0.06)   (1 + 0.06) = $18,417.05 PV0 = $6,500   0.06     Or using a financial calculator (TI BAII Plus), Hit [2nd] [BGN] [2nd] [Set] N=3, I/Y=6, PMT= -6,500, FV = 0, CPT PV=18,417.05 31. Section: 5.4 Annuities and Perpetuities Learning Objective: 5.4 Level of difficulty: Basic Solution: 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 32. Section: 5.5 Growing Annuities and Perpetuities Learning Objective: 5.5 Level of difficulty: Basic 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 =

33. Section: 5.8 Comprehensive Examples Learning Objective: 5.7 Level of difficulty: Basic 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  

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(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 34. Section: 5.8 Comprehensive Examples Learning Objective: 5.8 Level of difficulty: Basic 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.

Intermediate 35. Section: 5.1 Opportunity Cost Learning Objective: 5.1 Level of difficulty: Intermediate Solution: Cost = tuition + textbook + loss of income = $800+$300+$900 = $2,000 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.

36. Section: 5.4 Annuities and Perpetuities Learning outcome: 5.4 Level of difficulty: Intermediate Solution: Present value of the perpetual scholarship payment at the end of 4 years: 1  1  PV = PMT = $5000  = $166, 667 4 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.

37. Section: 5.4 Annuities and Perpetuities

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Learning outcome: 5.4 Level of difficulty: Intermediate Solution: Find the present value of the four-year annuity at year 3: 1  1 1− 1−   (1+ k )n   (1+ 0.05)4  PV3 = PMT   = $6,000    = $21,275.70 0.05 k            Or using a financial calculator (TI BAII Plus), N=4, I/Y=5, PMT= -6,000, FV = 0, CPT PV= 21,275.70 Now, find the present value of this amount today:  1   1  PV0 = FV (1+ k) 3  = $21,275.70 (1.05)3  = $18,378.75 







Or using a financial calculator (TI BAII Plus), N=3, I/Y=5, PMT = 0, FV= 21,275.70, CPT PV= 18,378.75 38. Section: 5.4 Annuities and Perpetuities Learning outcome: 5.4 Level of difficulty: Intermediate 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, FV = 0, 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 because 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.

39. Section: 5.6 Quoted versus Effective Rates Learning Objective: 5.6 Level of difficulty: Intermediate Solution: Step 1: determine monthly effective rate

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1 / 12

 .09 4  kmonthly = 1 +   4   

− 1 = 0.7444 %

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

QR monthly = 12 x 0.7444 = 8.9333% Therefore, 9% compounded quarterly is equivalent to 8.9333% compounded monthly.

40. Section: 5.6 Quoted versus Effective Rates Learning Objective: 5.6 Level of difficulty: Intermediate.

Solution: a. m = 365: k = (1 + b. m = 4: c. m = 3: d. m = 2:

.24

)365 − 1 = 27.11%.

365 .24 4 ) − 1 = 26.25%.

4 .24 3 k = (1 + ) − 1 = 25.97%.

3 .24 2 k = (1 + ) − 1 = 25.44%.

2 k = (1 +

k = e.24 − 1 = 27.12%.

e. Continuous compounding:

f. The effective monthly rates for a. to d. are: m

i. m=365, f=12

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

ii. m=4, f=12.

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

iii. m=3, f=12.

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

iv. m=2, f=12.

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

m

41. Section: 5.4 Annuities and Perpetuities

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Learning Objective: 5.4 Level of difficulty: Intermediate 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   42. Section: 5.4 Annuities and Perpetuities Learning Objective: 5.4 Level of difficulty: Intermediate Solution: Find the present value of the four-year annuity due: 1  1  1 − 1 − n  4  (1 + k ) (1 + 0.05) (1 + k ) = $5,000     (1 + 0.05) = $18,616.24 PV5 = PMT  0.05 k            Or using a financial calculator (TI BAII Plus), Hit [2nd] [BGN] [2nd] [Set] N=4, I/Y=5, PMT= -5,000, FV = 0, CPT PV=18,616.24 Now, discount this amount back five years:  1   1  PV0 = FV (1 + k) 5  = $18,616.24  (1.05)5  = $14,586.31     Or using a financial calculator (TI BAII Plus), N=5, I/Y=5, PMT =0, FV= 18,616.24, CPT PV=-14,586.31 43. Section: 5.4 Annuities and Perpetuities Learning Objective: 5.4 Level of difficulty: Intermediate Solution: 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):

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1 4   1 − (1 + 0.07)  = $33,872.11 PV = $10,000   8   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   44. Section: 5.5 Growing Annuities and Perpetuities Learning Objective: 5.5 Level of difficulty: Intermediate 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.

45. Section: 5.5 Growing Annuities and Perpetuities Learning Objective: 5.5 Level of difficulty: Intermediate Solution:

= $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 46. Section: 5.5 Growing Annuities and Perpetuities Learning Objective: 5.5

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Level of difficulty: Intermediate 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.

47. Section: 5.4 Annuities and Perpetuities 5.6; Quoted versus Effective Rates Learning Objective: 5.4; 5.6 Level of difficulty: Intermediate Solution: Solve the annuity equation to find k, the interest rate: 1  1 − 5  $25,000.00 = $6,935.24   (1 + k )  k = ?  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.

48. Section: 5.4 Annuities and Perpetuities; 5.6 Quoted versus Effective Rates Learning Objective: 5.4; 5.6 Level of difficulty: Intermediate 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.

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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.

49. Section: 5.6 Quoted versus Effective Rates Learning Objective: 5.6 Level of difficulty: Intermediate 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% 50. Section: 5.7 Loan or Mortgage Arrangements Learning Objective: 5.7 Level of difficulty: Intermediate Solution: a. In Canada, fixed-rate mortgages use semi-annual compounding of interest, so m=2. The effective annual rate is therefore:  QR   0.064  k = 1 +  −1 = 1 +  −1 = 6.5024% m 2     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 − 240  = $1,322.69 $180,000 = PMT  (1 + 0.005264 )   PMT 0.005264      Or using a financial calculator (TI BAII Plus), N=240, I/Y=.5264, PV=180,000, FV = 0, CPT PMT = -1,322.69 d. With monthly compounding and payments, the effective monthly interest rate is:

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12  QR  m = 1+ 1 + 0.0636  12 −1 = 0.530% f −1 =   monthly   m   12 

The monthly payments can be computed using a financial calculator (TI BAII Plus), N=240, I/Y=.53, PV=180,000, FV = 0, CPT PMT = -1,327.24 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.

51. Section: 5.7 Loan or Mortgage Arrangements Learning Objective: 5.7 Level of difficulty: Intermediate Solution: With semi-annual compounding (the norm in Canada) and monthly payments, m=2 and f=12.The effective monthly rate is:  QR  m  0.039 2 12 k = 1+ −1 = 0.3224% f −1 = 1 +     monthly 2  m    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     Or using a financial calculator (TI BAII Plus), N=300, I/Y=.3224, PMT=-1,950, FV = 0, CPT PV = $374,553.72 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.

52. Section: 5.8 Comprehensive Examples Learning Objective: 5.8 Level of difficulty: Intermediate Solution: a. This is an annuity due. Timmy makes his first payment on his 21st birthday and the last payment on his 60th birthday. When Timmy turns 61, the value of these 40 annuity payments is: (1 + 0.10)40 −1 FV40 = $3,000     (1.10) = $1,460,555.43 0.10  

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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, PV = 0, CPT N = 37.1.

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

53. Section: 5.8 Comprehensive Examples Learning Objective: 5.8 Level of difficulty: Intermediate 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 1 1 −   30  7,353,535 = PMT  (1 + .1) (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=709,143 Challenging 54. Section: 5.1 Opportunity Cost; 5.3 Compound Interest Learning Objective: 5.1; 5.3 Level of difficulty: Challenging Solution:

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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.

55. Section: 5.4 Annuities and Perpetuities Learning Objective: 5.4 Level of difficulty: Challenging 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:  1 5   1 −   1 (1 + 0.12)  +  $2.00  PV = $3.00 5   = $10.81+ $16.67  0.5674 = $20.27 0  0.12    0.12  (1 + 0.12)        

56. Section: 5.4 Annuities and Perpetuities Learning Objective: 5.4 Level of difficulty: Challenging Solution: 0.045 = 0.375% kmonthly = 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 $550 because it will be paid today.

1 1−   (1+ 0.00375 )35  PV0 = $550     (1+ 0.00375 ) + $550 = $18,626.17 0.00375    

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57. Section: 5.4 Annuities and Perpetuities Learning Objective: 5.4 Level of difficulty: Challenging 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 be a better deal.

58. Section: 5.4 Annuities and Perpetuities Learning outcome: 5.4 Level of difficulty: Challenging Solution: Step 1: determine Betty’s annual deposits: (1 + 0.05)40 −1 $1,000,000 = PMT    PMT = $8,278.16 0.05   Or using a financial calculator (TI BAII Plus), N=40, I/Y=5, FV= -1,000,000, PV = 0, CPT PMT= 8,278.16 Betty will have to make annual deposits of $8,278.16 per year for 40 years at 5% in order to have $1 million.

Step 2: Abe will be making deposits of 2*8,278.16 = $16,556.32. 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: 28.52

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1,000,000 .05 1 ln  16,556.32 +   = 28.52 n= ln(1.05) 

(1 + 0.05)n − 1

$1,000,000 = 16,556.32 0.05  Or using a financial calculator (TI BAII Plus), I/Y=5, PMT= 16,556.32, FV= -1,000,000, PV = 0, CPT N=28.52 Therefore, Abe can afford to wait 11 years before he has to start making his large deposits.

59. Section: 5.1 Opportunity Cost; 5.2 Simple Interest; 5.3 Compound Interest; 5.4 Annuities and Perpetuities Learning outcome: 5.1; 5.2; 5.3; 5.4 Level of difficulty: Challenging 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.

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.

60. Section: 5.4 Annuities and Perpetuities; 5.6 Quoted versus Effective Rates Learning Objective: 5.4; 5.6 Level of difficulty: Challenging 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

 .06 12  14 = 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.

61. Section: 5.4 Annuities and Perpetuities; 5.6 Quoted versus Effective Rates Learning Objective: 5.4; 5.6 Level of difficulty: Challenging Solution: Step 1: make the payment frequency match the compounding frequency. We need to convert the 6% compounded quarterly to a monthly effective rate.

4

 .06  1 + kannual = 1 + 4  

1

1 + kmonthly = (1 + kannual ) 12  .06 4  112 = 1 +  4     4 12  .06  = 1 + 4   kmonthly = 0.4975% Step 2: Now we have an annuity of 10*12 = 120 monthly payments, a present value of $250,000 and an effective monthly rate of 0.4975%. Solving for the payments we get $2,771.75.

1  1 − 120  = $2,771.75 $250,000 = PMT   (1 + 0.004975 )   PMT 0.004975      Or using a financial calculator (TI BAII Plus),

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N=120, I/Y=.4975, PV= -250,000, FV = 0, CPT PMT= 2,771.75 62. Section: 5.3 Compound Interest; 5.4 Annuities and Perpetuities Learning Objective: 5.3; 5.4 Level of difficulty: Challenging 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, PMT = 0, 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 63. Section: 5.3 Compound Interest; 5.6 Quoted versus Effective Rates Learning Objective: 5.3; 5.6 Level of difficulty: Challenging 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, PMT =0, CPT N = 8.04 So the investment will double in just over 8 years. b. Quarterly: With quarterly compounding, the effective annual rate is,  0.09  k = 1+  −1 = 9.3083% , and a financial calculator allows us to find: 4   4

PV = -1, FV = 2, I/Y = 9.3083, PMT = 0, CPT N = 7.79 The higher effective rate means that only 7.79 years are needed to double the value of the investment.

64. Section: 5.4 Annuities and Perpetuities Learning Objectives: 5.4 Level of difficulty: Challenging

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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.

65. Section: 5.5 Growing Annuities and Perpetuities Learning Objective: 5.5 Level of difficulty: Challenging Solution: n PMT1   1 + g    PV = 1−    0 k − g   1 + k   n PMT1   1 + g   n  FV = PV (1 + k ) = 1−   (1 + k ) n n 0 k − g   1 + k   25 PMT1   1 + .04   )25 ( )25 PMT1 ( $1,000,000 = 1−  (1 + .06)25 = 1 + .06 − 1 + .04   .06 − .04   1 + .06   .02

(

=

PMT1

)

*1.62603439

.02 The initial deposit is $12,299.86 (1 + 0.06)25 −1 $1,000,000 = PMT    PMT = $18,226.72 0.06   If Xiang made constant deposits (i.e., no growth), he would have to deposit $18,226.72 per year for the next 25 years.

66. Section: 5.7 Loan or Mortgage Arrangements Learning Objective: 5.7 Level of difficulty: Challenging Solution: a. The effective monthly interest rate is,

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k

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 0.051 212 = 1+ −1 = 0.4206%   monthly 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, FV = 0, 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, FV = 0, 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: 5.6 Quoted versus Effective Rates; 5.7 Loan or Mortgage Arrangements Learning Objective: 5.6; 5.7 Level of difficulty: Challenging Solution: a. First, find the effective interest corresponding to the frequency of Jimmie’s car payments (f =12); with monthly compounding, set m=12, 12  QR  m k = 1+ f −1 = 1+ 8.5%  12 −1 = 0.70833%  monthly    m   12  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

(2) Payment

(3) Interest =k*(1)

1 2 3 4 5

29,000.00 28,610.44 28,218.12 27,823.01 27,425.11

594.98 594.98 594.98 594.98 594.98

205.42 202.66 199.88 197.08 194.26

(4) Principal Repayment = (2)-(3) 389.56 392.32 395.10 397.90 400.72

Ending Principal = (1)-(4) 28,610.44 28,218.12 27,823.01 27,425.11 27,024.40

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6 7 8 9 10 11 12 13 ...

35 36 37 ...

59 60

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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

191.42 188.56 185.69 182.79 179.87 176.93 173.97 170.98

403.56 406.42 409.29 412.19 415.11 418.05 421.01 424.00

26,620.84 26,214.42 25,805.13 25,392.94 24,977.82 24,559.77 24,138.76 23,714.76

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

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 PV0 = $13,089.22    = $10,152.19 36  (1 + 0.0070833)    68. Section: 5.6 Quoted versus Effective Rates; 5.7 Loan or Mortgage Arrangements Learning Objective: 5.6, 5.7 Level of difficulty: Challenging Solution: The 60 monthly payments form an annuity whose present value is $30,000. Finding the interest rate is most easily done with a financial calculator (TI BAII Plus): N=60, PMT=622.75, PV= -30,000, FV =0, CPT I/Y = 0.75% Note that we used N=60 months, so the solution is a monthly interest rate, however, the problem asks for the effective annual rate. k = (1 + k monthly )12 − 1 = (1 + 0.0075)12 −1 = 9.38% The quoted rate would be: 1

1

QR = m [(1 + k) 12 −1] = 12 [(1 + 0.0938) 12 −1] = 9.00%

Or simply:

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QR = m  kmonthly = 12  0.0075 = 9.00%

69. Section: 5.7 Loan or Mortgage Arrangements Learning Objective: 5.7 Level of difficulty: Challenging 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:  .06  112 2 kmonthly = 1+   −1 = 0.00493862 2    Step 2: determine the monthly payments:

1  1 − $250,000 = PMT   (1 + 0.00493862)300   0.00493862    PMT = $1,599.5162 Or using a financial calculator (TI BAII Plus), N=300, I/Y=.493862, PV=250,000, FV =0, CPT PMT = -1,599.5162 Step 3: determine Present Value of remaining (300 – 60) payments of $1,599.5162 1  1 − (1 + 0.00493862 )300−60  PV = $1,599.5162    = $224,591.7542 0.00493862      Or using a financial calculator (TI BAII Plus), N=240, I/Y=.493862, PMT=-1,599.5162, FV = 0, CPT PV = $224,591.7542 Part 2: determine new payments Step 1: determine new effective monthly rate  .08  112 2 kmonthly = 1+   −1 = 0.00655820 2   

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Step 2: determine the new monthly payment 1  1 − $224,591.7542 = PMT   (1 + 0.00655820)300−60   0.00655820    PMT = $1,860.4231 Or using a financial calculator (TI BAII Plus), N=240, I/Y=.65582, PV=224,591.7542, FV = 0, CPT PMT = 1,860.4231 Franklin’s new payment is $1,860.4231, an increase of $260.91.

70. Section: 5.7 Loan or Mortgage Arrangements Learning Objective: 5.7 Level of difficulty: Challenging Solution: a. PV=$200,000, monthly rate=12%/12=1%, N = (10)(12)=120 months 1 1 −   120  200,000 = PMT  (1 + .01)  .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 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, CPT PV=182,920

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2

c. kmonthly= (1 +

.12 12 ) −1=.9759% 2

1 1 −   120 200,000 = PMT  (1 + .009759)   .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 71. Section: 5.8 Comprehensive Examples Learning Objective: 5.8 Level of difficulty: Challenging 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)  =$23,749.19 PV25 = $5,500   .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 2nd, discount this amount for five years back to today when she is 20.

PV0 = FV5 

1 1 = $23,749.19  = $11,218.3231 5 (1 + k) (1.16183424)5

Or, N=5, I/Y=16.183424, PMT = 0, FV=- 23,749.19, CPT PV=11,218.3231 Investor B:

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.16 4 ) −1=16.985856% 4 1 1 −    (1 + .16985856)10 (1.16985856) $11,218.3231 = PMT    .16985856    

k= (1 +

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.

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Answers to Concept Review Questions 5.1 Opportunity Cost Concept review questions 1. Why does money have a “time value”?

An investor can simply store a dollar (tuck them under the bed!) and spend them in the future, in this sense a dollar is always worth at least a dollar in the future. However this ignores the fact that the saver has other uses for that dollar, which in economics we call an “opportunity cost” or simply an “alternative use.” This results in a “time value” of money.

2. What is an “opportunity cost”?

The opportunity cost of money is the interest rate you can earn by investing the dollar today.

5.2 Simple Interest Concept review questions 1. Explain how simple interest payments are determined.

Simple interest payments are n × p × k, where n is number of periods in years, p is principal and k is the simple annual interest rate.

2. Why does simple interest take into account the time value of money?

Simple interest can be used to calculate the future value of money assuming that only the principal in reinvested.

5.3 Compound Interest Concept review questions 1. Explain how to compute future values and present values when using compound interest.

FVn = PV0 (1 + k)n, where PV0 is the present value, k is the compound value interest factor, n is the number of periods and FVn is the future value in year n.

2. What is the relationship between FVIFs and PVIFs? Why does this make sense?

FVIF=1/PVIF. This relationship make sense because by definition, FVIF = (1+ k )n and PVIF = 1/(1 + k)n.

3. Why does compound interest result in higher future values than simple interest?

Compound interest refers to a process whereby interest is earned on the invested principal amount and on any accrued interest. However, simple interest is only earned on the principal amount.

5.4 Annuities and Perpetuities Concept review questions

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1. Explain how to calculate the present value and future value of an ordinary annuity and an annuity due. (1 + k)n −1 FVn = PMT   gives the future value of an ordinary annuity. Since each flow gets one k   extra period of compounding in an annuity due, the FV (annuity due) = [FV (ordinary annuity)](1 + k). The present value of both an annuity and an annuity due is PV0 = FVn (1 + k)n.

2. Define “perpetuity”.

Perpetuities are special annuities in that they go on forever so n goes to infinity in the annuity equation.

3. Why is the present value of $1 million in 50 years’ time worth very little today?

If the required return is 12% a year, the present value of $1 million in 50 years’ time is $3,460.

The small present value is caused by the discounting process.

5.5 Growing Perpetuities and Annuities Concept review questions 1. Explain how to evaluate a growing perpetuity.

Estimate the payment (PMT), the required rate of return (k), and the expected growth rate to infinity (g), and apply Equation 5A-2.

2. Explain how to calculate the present value of a growing annuity.

Estimate the payment (PMT), the required rate of return (k), the number of years for the annuity (n), the expected growth rate to infinity (g), and apply Equation 5A-4.

5.6 Quoted versus Effective Rates Concept review questions 1. Why can effective rates often be very different from quoted rates?

If the quoted rates are not annually compounded, the effective rates are different from the quoted rates because of the different number of compounding periods.

2. Explain how to calculate the effective rate for any period.  QR  The effective annual rate for any given compounding interval: k = 1 +  −1 , where k = m   m

effective annual rate, QR = quoted rate, and m = the number of compounding intervals per year.

Rates for payments that are other than annual payments require an effective period rate. The  QR  m f −1 , where k = effective period rate for payments other than annual is given as k = 1 +   m   effective period rate, QR is the nominal quoted rate, m = the number of compounding period per year and f = the frequency of payments per year.

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5.7 Loan or Mortgage Arrangements Concept review questions 1. Explain how loan and mortgage payments can be determined using annuity concepts.

Since these loans involve equal payments, at regular intervals based on one fixed interest rate specified when the loan is taken out, the payments can be viewed as annuities.

2. What complications arise when dealing with mortgage loans in Canada?

In Canada, the interest rates are quoted semi-annually and the payments are made monthly.

Mortgages are amortized over long periods of time; but, the rates are set for terms or periods that may be shorter than the amortization period. When the term is expired, a new rate of interest need to be negotiated and interest rates may have increased.

3. Why is a 6 percent U.S. mortgage not the same as a 6 percent Canadian mortgage?

Interest rates are compounded semi-annually in Canada and compounded monthly in U.S. 5.8 Comprehensive Examples Concept review questions 1. Explain how timelines can be used to break a complicated time value of money problem into manageable components.

You can visualize the problem and break complicated cash flows into its three constituent parts since you should develop an understanding of what is approximately the right answer.

2. Demonstrate how to solve a typical retirement problem.

There are three steps. First, calculate the present value of retirement funds in the year of retirement. Second, calculate the cash you need to raise through investment in the year of retirement. Third, determine the required year-end payments to give you the future value of the amount that is calculated in the second step.

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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: Intermediate 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: Intermediate Solution: B Debentures are generally unsecured.

3. Section: 6.2 Bond Valuation Learning Objective: 6.2 Level of difficulty: Intermediate Solution: A 1  1 − 1 10  =58.8807+55.8395=$114.72 B = 8   (1 + .06) + 100   10 .06 (1 + .06)     Or, by financial calculator: N = 10; I/Y= 6; PMT = 8; FV = 100; CPT PV = –114.72 4. Section: 6.2 Bond Valuation Learning Objective: 6.2 Difficulty: Intermediate 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: Intermediate 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% 6. Section: 6.3 Bond Yields

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Learning Objective: 6.3 Difficulty: Intermediate 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 less than YTM. 7. Section: 6.4 Interest Rate Determinants Learning Objective: 6.4 Difficulty: Intermediate 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: Intermediate Solution: D. P =

10,000 10,000 = = $9,852.62 182 (1 + 0.03  ) 1.014958904 365

Because it is quoted on a basis of $100, the quoted price is $98.5262.

9. Section: 6.5 Other Types of Bonds/Debt Instruments Learning Objective: 6.5 Difficulty: Intermediate 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: 6.6 Difficulty: Intermediate 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 Basic 11. Section: 6.1 The Basic Structure of Bonds Learning Objective: 6.1 Difficulty: Basic

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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: Basic 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: Basic Solution: Coupon = ($1,000) (6%) /2=$30, n=10×2=20, k=5%/2=2.5% By financial calculator: N = 20; I/Y= 2.5; PMT = 30; FV = 1,000; CPT PV = - 1,077.95 14. Section: 6.2 Bond Valuation Learning Objective: 6.2 Difficulty: Basic 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.

15. Section: 6.2 Bond Valuation Learning Objective: 6.2 Difficulty: Basic 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.

16. Section: 6.2 Bond Valuation Learning Objective: 6.2 Difficulty: Basic Solution: N = 30; I/Y = 6; PV = –841.7; FV = 1,000; CPT PMT = 48.5 Semi-annual coupon =$48.5 Annual =$48.5×2 =$97 Coupon rate =97/1000 = 9.7% 17. Section: 6.4 Interest Rate Determinants

Introduction to Corporate Finance, Fourth Edition

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Learning Objective: 6.4 Difficulty: Basic 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%) 18. Section: 6.4 Interest Rate Determinants Learning Objective: 6.4 Difficulty: Basic Solution: The Fisher relationship uses expected inflation figures, not the actual rate of inflation experienced in the past. Therefore, RF = 2.50% +3.2% = 5.70% (Using the exact relationship, RF = (1+0.025) × (1.032)–1= 5.78% 19. Section: 6.4 Interest Rate Determinants Learning Objective: 6.4 Level of difficulty: Basic 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% 20. Section: 6.4 Interest Rate Determinants Learning Objective: 6.4 Level of difficulty: Basic Solution: Exact equation: (1 + RF) = (1 + real rate) (1 + expected inflation rate) Real rate = (1 + RF) / (1 + expected inflation rate) – 1 = (1.08) / (1.036)–1 = 4.25% Approximate equation: RF = real rate + expected inflation rate Real rate = RF – expected inflation rate =8% – 3.6% = 4.4% 21. Section: 6.5 Other Types of Bonds/Debt Instruments Learning Objective: 6.5 Difficulty: Basic Solution: As a holder of a retractable bond, you will exercise your right if you expect a rise in interest rates.

22. Section: 6.4 Interest Rate Determinants Learning Objective: 6.4

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Difficulty: Basic Solution: Downgrading implies more risk, which in turn implies more return is required. Therefore the price of the bond is expected to fall.

Intermediate 23. Section: 6.2 Bond Valuation Learning Objective: 6.2 Difficulty: Intermediate 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.

24. Section: 6.2 Bond Valuation Learning Objective: 6.2 Difficulty: Intermediate Solution: a. by financial calculator: N = 5; I/Y= 5.5; PMT = 100; FV = 1,000; CPT PV = –1,192.16 b. By financial calculator: N = 10; I/Y= 2.75; PMT = 50; FV = 1,000; CPT PV = –1,194.40 c. By financial calculator: N = 60; I/Y= 0.458333; PMT = 8.3333; FV = 1,000; CPT PV = - 1,196.32 Notice that the value of the bond increases with more frequent coupon payments.

25. Section: 6.2 Bond Valuation Learning Objective: 6.2 Difficulty: Intermediate 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.

26. Section: 6.2 Bond Valuation

Introduction to Corporate Finance, Fourth Edition

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Learning Objective: 6.2 Difficulty: Intermediate 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.

27. Section: 6.2 Bond Valuation Learning Objective: 6.2 Difficulty: Intermediate 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 four months have elapsed since the last coupon payment, so we count 4 x 30 = 120 days out of 360 in the year.

Accrued interest = $1,000 × 6% × (120/360) = $20.00 Cash Price = 938.63 + 20.00 = 958.63 Peter would actually pay $958.63 for this bond. b. The day count convention in Canada is “Actual/365.” From January 1 to May 1, 2015, there are 31 + 28 + 31 + 30 = 120 days. Accrued interest = $1,000 × 6% × (120/365) = $19.73. You would have to pay 938.63 + 19.73 = $958.36 for this bond.

28. Section: 6.2 Bond Valuation Learning Objective: 6.2 Difficulty: Intermediate 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 29. Section: 6.2 Bond Valuation Learning Objective: 6.2 Difficulty: Intermediate 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.

30. Section: 6.3 Bond Yields

Introduction to Corporate Finance, Fourth Edition

Learning Objective: 6.3 Difficulty: Intermediate Solution: Using a financial calculator: N = 12; PMT = 80; FV = 1,000; PV = -928; CPT I/Y = 9.01 The YTM of the bond is 9.01% 31. Section: 6.3 Bond Yields Learning Objective: 6.3 Difficulty: Intermediate Solution: The price of the bond = $1,000×106.2% = $1,062 Using a financial calculator: N = 18; PMT = 32.5; FV = 1,000; PV = -1,062; CPT I/Y = 2.8065 The market yield = 2.8065×2 = 5.613% 32. Section: 6.3 Bond Yields Learning Objective: 6.3 Difficulty: Intermediate 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.

33. Section: 6.3 Bond Yields Learning Objective: 6.3 Difficulty: Intermediate Solution: a. N = 20; I/Y = 2; PMT = 25; FV = 1,000; CPT PV = –1,081.76 CY = 50/1,081.76 = 4.62% So, Coupon Rate > CY > YTM when the bond trades at a premium. b. PV = –1,000.00 (because YTM = coupon rate) CY = 50/1000 = 5.0% So, Coupon Rate = CY = YTM when the bond trades at par. c. N = 20; I/Y = 3; PMT = 25; FV = 1,000; CPT PV = –925.61 CY = 50/925.61= 5.40%

Booth, Cleary, Rakita

Introduction to Corporate Finance, Fourth Edition

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So, Coupon Rate < CY < YTM when the bond trades at a discount.

34. Section: 6.3 Bond Yields Learning Objective: 6.3 Difficulty: Intermediate Solution: Using a financial calculator: N = 30; PMT = 27.5; FV = 1,000; PV = -936; CPT I/Y = 3.08 The YTM of the current bond = 3.08×2=6.16% The company should set the coupon rate on its new bonds at the current YTM of 6.16%.

35. Section: 6.5 Other Types of Bonds/Debt Instruments Learning Objective: 6.5 Difficulty: Intermediate 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 C. N = 30; I/Y = 6; PMT = 0; FV = 1,000; CPT PV = $174.11 36. Section: 6.5 Other Types of Bonds/Debt Instruments Learning Objective: 6.5 Difficulty: Intermediate Solution: 100 − 97.75 360 k BDY =  100 100 92 =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.

100 − 97.75 365 k BEY =  100 97.75 92 =9.13% 37. Section: 6.5 Other Types of Bonds/Debt Instruments Learning Objective: 6.5 Difficulty: Intermediate 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%.

38. Section: 6.5 Other Types of Bonds/Debt Instruments Learning Objective: 6.5 Difficulty: Intermediate

Introduction to Corporate Finance, Fourth Edition

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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): = 4.673% =

k BDY

100 − P 100



360

100  P = 98.83175

90

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

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

39.39.

Section: 6.5 Other Types of Bonds/Debt Instruments Learning Objective: 6.5 Difficulty: Intermediate Solution: Price of bond =$950 Cost per share through conversion = $950/25 =$38.00 Discount = $40-$38 =$2 Percentage discount = 2/40= 5% 40. Section: 6.3 Bond Yields Learning Objective: 6.3 Difficulty: Intermediate 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.

41. Section: 6.3 Bond Yields Learning Objective: 6.3 Difficulty: Intermediate Solution: We can calculate yield to maturity using the formula below, where r1, r2, ... rn are the spot rates 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= C/(1+ytm)+C/(1+ytm)2+C/(1+ytm)3…+(C+F/)(1+ytm)n 42. Section: 6.3 Bond Yields Learning Objective: 6.3 Difficulty: Intermediate Solution: Bond price = $70×0.927644 + $1,070 ×0.854172 =$978.90

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N = 2; PMT = 70; PV = –978.90; FV = 1,000; CPT I/Y = 8.19 Yield to maturity = 8.19% 43. Section: 6.5 Other Types of Bonds/Debt Instruments Learning Objective: 6.5 Difficulty: Intermediate 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.

44. Section: Appendix 6A: Interest Rate Parity Learning Objective: 6.6 Difficulty: Intermediate 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.

Challenging 45. Section: 6.2 Bond Valuation Learning Objective: 6.2 Difficulty: Challenging 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 = 40; I/Y= 2.75; PMT = 30; FV = 1,000; CPT PV = –1,060.20 This is an increase in price of $60.20 or 6.02%.

An increase of 50bp results in a market yield of 6.5% N = 40; I/Y= 3.25; PMT = 30; FV = 1,000; CPT PV = –944.48 This is a price decrease of $55.52 or 5.55% Falling market yields cause larger price impacts than increasing market yields.

46. Section: 6.2 Bond Valuation Learning Objective: 6.2 Difficulty: Challenging

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Solution: Using a financial calculator: a.and b. 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% 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.

47. Section: 6.2 Bond Valuation Learning Objective: 6.2 Difficulty: Challenging Solution: Using a financial calculator: a. and b. 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% 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.

48. Section: 6.3 Bond Yields Learning Objective: 6.3 Difficulty: Challenging 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%.

1 1 −   (1 + .04)2 

B = 50    

.04

1

= $1,018.86

 + 1,000  (1 + .04)2 

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:

Introduction to Corporate Finance, Fourth Edition

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10% − YTM $1,000 − $1,010 = 10% − 8% $1,000 − $1,018.86 YTM = 10% − (10% − 8%) 

$1,000 − $1,010 $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.

49. Section: 6.4 Interest Rate Determinants Learning Objective: 6.4 Difficulty: Challenging 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.

50. Section: 6.2 Bond Valuation, 6.3 Bond Yields, and 6.5 Other Types of Bonds/Debt Instruments Learning Objective: 6.2; 6.3; 6.5 Difficulty: Challenging 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 3 2 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

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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).

51. Section: Appendix 6A: Interest Rate Parity Learning Objective: 6.6 Difficulty: Challenging Solution: According to IRP, (1 + kdomestic ) (1.03) F = S = ($1.4768)  = $1.4350 / Euro (1 + k foreign ) (1.06) Since $1.4350/Euro ≠$1.4090/Euro, there is an arbitrage opportunity.

Forward rate calculated from IRP ($1.4350/Euro) > the market one-year forward rate ($1.4090/Euro). This means the Euro forward contract is under-priced.

Bower should buy Euros through the forward contract and sell Euros (underlying asset) today and apply the following transactions: 1st: Borrow 677.14 Euros at 6%, which is the equivalent of $1,000 at the spot rate ($1.4768/Euro) (i.e., $1,000/($1.4768/Euro) = 677.14 Euros). He needs to repay 677.14 Euros × 1.06 = 717.77 Euros after one year. Long (buy) Euros through the forward contract.

2nd: Invest $1,000 in one-year Canadian T-bill at 3%. After one year he will receive $1,030. (i.e., $1,000 × (1.03) = $1,030) 3rd: After one year, convert $1,011.34 into Euros at the contract forward rate $1.4090/Euro and get 717.77 Euros. (i.e., $1,011.34/($1.4090/Euro) = 717.77 Euros).

Repay 717.77 Euros and keep the remainder as his profit.

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Arbitrage profit of investing $1,000=$1,030 – $1,011.34 = $18.66 Explanation: If other investors seize the same arbitrage opportunity as Bower, the forward price would quickly rise to $1.4350/Euro so that IRP holds.

52. Section: Appendix 6B: The Yield for Callable Bonds Learning Objective: 6.7 Difficulty: Challenging 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 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.

53. Section: Appendix 6B: The Yield for Callable Bonds Learning Objective: 6.7 Difficulty: Challenging Solution: Using a financial calculator: YTM of the bond: N = 24; PMT = 37.5; FV = 1,000; PV = -1,038; CPT I/Y = 3.513 YTM = 3.513 × 2 = 7.03% YTC of the bond: N = 8; PMT = 37.5; FV = 1,045; PV = -1,038; CPT I/Y = 3.687 YTC = 3.687 × 2 = 7.37% The call price is greater than the bond price. It is unlikely that the bond will be called.

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Answers to Concept Review Questions 6.1 The Basic Structure of Bonds Concept Review Questions 1. In what ways are bonds different from mortgages?

The structure of the payments differs from that of the loan or mortgage discussed in Chapter 5, since those involved “blended” payments that included both interest and principal components.

In contrast a typical bond has interest payments throughout its life and the balloon principal payment at maturity.

2. How is a traditional bond structured?

A bond can be viewed as these two separate components: an annuity consisting of the identical and regular interest payments, plus a lump-sum principal payment at maturity.

3. What is a bond indenture?

It is a legal document that specifies the payment requirements, and all other salient matters relating to the issue, such as any assets that might serve as security or collateral for the bond; any protective provisions, and other additional features.

4. What is the difference between a positive and a negative covenant provision?

Negative covenants prohibit certain actions, for example, a company may be restricted from making a dividend payment larger than certain amount or prevented from pledging its assets to another lender. Positive covenants specify actions that the firm agrees to undertake, for example, to provide quarterly financial statements or maintain certain working capital levels.

5. How do callable bonds differ from retractable and extendable bonds?

Callable bonds give the issuer the option to “call,” or repurchase, outstanding bonds at predetermined prices at specified times. Retractable bonds allow the bondholder to sell back to the issuer at predetermined prices at specified times earlier than the maturity date. Unlike callable bonds, a necessary condition for holders of retractable bonds to exercise their option is that market interest rates have gone up. Extendible bonds allow the bondholder to extend the maturity date of the bond. “Extendibles” and “retractables” give bondholders the flexibility to change the maturity of the bonds to their advantage.

6. How do sinking funds work?

There are two ways in which this is done. In the first way the firm repurchases a certain amount of debt each year so that the amount of debt actually goes down. In the second way the firm pays money into the sinking fund to buy other bonds, usually government bonds, so that money is available at maturity to pay off the debt, although the amount due at maturity is unchanged.

6.2 Bond Valuation Concept Review Questions 1. What time-value-of-money formula do we need to value a bond?

Introduction to Corporate Finance, Fourth Edition

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The interest payments are annuities and the principal repayment is a one-time payment. Thus the present value formula for an annuity and a single cash payment are needed.

2. When market interest rates are above the coupon rate on a bond, is it a premium or discount bond?

It is a discount bond. This is because the coupon rate is less than the market interest (discount) rate, which means that investors require a return greater than 6% on equivalent bonds under current market conditions. Since the future payments are fixed, the only way to get a return higher than the coupon rate on this bond is to pay less than the par value for it.

3. If market interest rates go up, what happens to bond prices?

Bond prices will go down.

4. Which types of bonds have more interest rate risk: short-term or long-term bonds?

Long term bonds have more interest rate risk.

5. What is the day count convention in Canada and the United States?

The day count convention in U.S. is “30/360”. The day count convention in Canada is “Actual/365.”

6.3 Bond Yields Concept Review Questions 1. Why is there no simple analytical formula for the yield to maturity?

Various powers are used in the formula, and so logarithms are needed to solve the pricing function.

2. When bonds sell above their par value, is the yield to maturity greater or less than the coupon rate?

The yield to maturity is less than the coupon rate.

6.4 Interest Rate Determinants Concept Review Questions 1. How does the expected rate of inflation affect nominal interest rates?

Nominal interest rate = real interest rate + expected inflation.

2. Why do interest rates differ between Canada and the United States?

Interest rates are heavily influenced by inflation and other domestic macroeconomic variables, global factors such as foreign exchange rates and inflation differentials also play an important role in the level of interest rates at any given point in time.

3. Why do interest rates on different-maturity Canada bonds differ?

This is called the term structure of interest rate. It is explained by three theories including the liquidity preference theory, expectation theory and the market segmentations theory.

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4. What is a corporate spread?

Corporate spread is the required rate of return of a corporate bond minus risk free rate and maturity yield differential. It compensates the investor for the assumption of additional risks, which may include some or all of the following: (1) default or credit risk; (2) liquidity; and, (3) issue-specific features. We discuss each of these in turn.

6.5 Other Types of Bonds/Debt Instruments Concept Review Questions 1. How does the formula for determining the price of a T-bill resemble the formula for determining the price of a zero coupon bond? Why is this so?

T-bill is a short-term zero coupon bond that is issued by the government. Thus its pricing formula resembles the formula of a zero-coupon bond.

2. How do U.S. bank discount yields differ from bond equivalent yields?

Face − P 360 =  100 individually.

The formulas are k F − P 365 and k =  BDY BEY Face n P n 3. How do floaters and real return bonds provide protection against inflation?

Floating rate bonds (floaters) have “adjustable” coupons that are usually tied to some variable short-term rate such as T-bill rates; although many variations exist. They differ significantly from traditional “fixed income” bonds since the coupons increase as interest rates increase and vice-versa. Therefore, they provide protection against rising interest rates and tend to trade near their par value. Government of Canada Real Return Bonds provide investors with protection against inflation by providing a real yield of about 4.25 percent. This is achieved by pegging the face value to the rate of inflation (as measured by the Consumer Price Index), and having the coupon rate of 4.25 percent apply to the inflation-adjusted face value.

Appendix 6B The Yield for Callable Bonds Concept Review Questions 1. Is the yield to call always greater than the yield to maturity?

Generally speaking, the yield to call will be greater than the yield to maturity when a callable bond is trading at market price that is below its call price. When the reverse is true, the yield to call will usually be less than the yield to maturity.

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Chapter 7: Equity Valuation Multiple Choice Questions 1. Section: 7.1 Equity Securities Learning Objective: 7.1 Level of difficulty: Basic Solution: A Jason’s ownership=46,000/2,000,000 = 2.3% 2. Section: 7.1 Equity Securities Learning Objective: 7.1 Level of difficulty: Intermediate Solution: D Total return = ((2,250 + 250) – 2000)/2000 = 25% 3. Section: 7.1 Equity Securities Learning Objective: 7.1 Level of difficulty: Basic 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: Basic Solution: A Required rate of return (k) = RF + Risk Premium = 3% + 5.5% = 8.5% 5. Section: 7.3 Common Share Valuation: The Dividend Discount Model (DDM) Learning Objective: 7.3 Level of difficulty: Intermediate 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: Intermediate Solution: A D0 = $2.00. D1 = $2.00 × (1 + 0.065) = $2.13 k = RF + Risk Premium = 4% + 7.5% = 11.5% P0 = $2.13/(0.115 – .065) = $42.60 7. Section: 7.3 Common Share Valuation: The Dividend Discount Model (DDM) Learning Objective: 7.3 Level of difficulty: Intermediate

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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: Intermediate Solution: C Capital Gain = (37.5 – 34) × 200 = $700 9. Section: 7.1 Equity Securities Learning Objective: 7.1 Level of difficulty: Intermediate 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: Intermediate Solution: C Payout ratio = D0/EPS0 = $1.5/$3 = 1/2 = 50% ROE = NI/E = EPS/BVPS = $3/$36 = 1/12 = 8.33% g = (1– payout ratio) × ROE = (retention ratio) × ROE = (1 – 1/2) × 8.33% = 4.17% 11. Section: 7.3 Common Share Valuation: The Dividend Discount Model (DDM) Learning Objective: 7.3 Level of difficulty: Intermediate 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: Intermediate 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: Intermediate 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: Basic

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

B

$60

$50

3%

$1.80 = 3.6% $50.00

C

$5.00 0.08 = $62.50

$70

$75

$70 =

$8.00 kp

$5.00

D

$60 =

$8.00

0.03 D = $1.80 $8.00

14%

D = .14*50

=10.67% $75.00

k p = 11.43% D

$50

$50

$50 =

$7.00

= $7.00

kp k p = 14% E

F

G

H

$150

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

$30

7%

$10.50 = 35% $30.00

$150 =

D

0.07 D = $10.50 $9.50

$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 =

D

0.05 D = $0.90

20. Section: 7.1 Equity Securities Learning Objective: 7.1 Level of difficulty: Basic 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: $105 = DP/kP = .08*100/kP kP = 7.62% Step 2: the risk premium = 7.62% – 2.5% = 5.12% 21. Section: 7.3 Common Share Valuation: The Dividend Discount Model (DDM) Learning Objective: 7.3 Level of difficulty: Basic Solution:

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a.

Assuming the dividend is paid annually: 4 + 65 𝐷1 + 𝑃1 𝐷1 + 𝑃1 − 1 = 43.75% 𝑃0 = 𝑘𝑐 = −1= 1 + 𝑘𝑐 𝑃0 48 b. 𝑘𝑐 =

4 + 38 𝐷1 + 𝑃1 − 1 = −12.5% −1= 𝑃0 48

c. 𝐷1 + 𝑃1 1 + 𝑘𝑐 𝑃1 = 𝑃0(1 + 𝑘𝑐) − 𝐷1 = 48(1 + (−.05)) − 4 = 48 ∗ .95 − 4 = $41.60 𝑃0 =

d.

P1 = 48(1+.18) – 4 = $52.64 22. Section: 7.3 Common Share Valuation: The Dividend Discount Model (DDM) Learning Objective: 7.3 Level of difficulty: Basic Solution: Solving these requires algebraic manipulation of the dividend discount formula.

Co.

Price

A

5.00 .15 −.1111 = $128.57 $600

B

C

P0 =

$70

Common Shares in Canada Required Dividend Current return growth dividend 5.00 15% $4.50 g= −1 4.50 = 11.1111% 3% 1% 12 D0 = 1.01 = $11.88 70 = kc =

8 kc −.05 8 + 3.50

70 = 16.43%

5%

D1 1+ g 8 = 1.05 = $7.62

D0 =

Dividend expected in 1 year $5.00

$600 =

D1

.03 −.01 D1 = 600*(.03 −.01) = $12 $8.00

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D

$55

55 = kc =

E

P0 =

(

D0 1 + g

)

11

Booth, Cleary, Rakita

10%

$10.00

$11.00

6%

$9.50

D1 = D0 (1+ g )

kc −.10 11+ 5.50

55 = 30% 14%

k−g

= 9.50*1.06

c

9.50 *1.06 .14 − .06 = $125.88 18 P0 = .15 −.0 = $120.00 $40

= $10.07

=

F

G

15%

0%

$18.00

5%

-2%

D = 0

=

$18.00

D1

P =

1+ g 2.80

(

1 + −.02 = $2.86

0

)

40 =

D1 kc − g D1 .05 − (−.02)

D1 = $2.80

23. Section: 7.3 Common Share Valuation: The Dividend Discount Model (DDM) Learning Objective: 7.3 Level of difficulty: Basic Solution: a. The total earnings of ToolWerks is $12 million. The EPS is $12,000,000/4,000,000 shares which equals $3. b. The expected dividends are determined by the dividend payout ratio multiplied by the earnings. The total dividends are 30% of $12 million or $3.6 million. On a per share basis, the expected dividends per share are $.90. c. The dividend growth rate expected for ToolWerks is: 𝑃0 =

𝐷1 𝑘𝑐 − 𝑔

45 =

. 90 . 10 − 𝑔

𝑔 = 8%

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 $3/.10 = $30. PVGO = $45 – $30 = $15 24. Section: 7.3 Common Share Valuation: The Dividend Discount Model (DDM) Learning Objective: 7.3 Level of difficulty: Basic Solution: Value of firm, assuming no growth opportunities, is 1.85/.08 = $23.13

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PVGO = $50 – $23.13 = $26.87 25. Section: 7.3 Common Share Valuation: The Dividend Discount Model (DDM) Learning Objective: 7.3 Level of difficulty: Basic 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 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% 26. Section: 7.4 Using Multiples to Value Shares Learning Objective: 7.4 Level of difficulty: Basic Solution: All else being equal, the 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.

Intermediate 27. Section: 7.3 Common Share Valuation: The Dividend Discount Model (DDM) Learning Objective: 7.3 Level of difficulty: Intermediate Solution: a. D1 = D2 = $1.50 D + P2 D1 + 2 (1+ kc ) (1+ kc )2 1.50 + 75 1.50 + 50 = 2 (1 + kc ) (1 + kc )

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+

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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%.

Expected annual return = –13.05% 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 28. Section: 7.3 Common Share Valuation: The Dividend Discount Model (DDM) Learning Objective: 7.3 Level of difficulty: Intermediate D (1+ g) D1 Solution: As indicated by equation P = 0 , market share price is positively = 0 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.

29. Section: 7.2 Preferred Share Valuation Learning Objective: 7.2 Level of difficulty: Intermediate Solution: Annual dividend = $100 × 6.75% = $6.75 Pps = Dp/kp = 6.75/.115 = $58.70 30. Section: 7.4 Using Multiples to Value Shares Learning Objective: 7.4 Level of difficulty: Intermediate Solution: Payout = 1 – Retention ratio = 1 – 0.4 = 0.6 Leading P/E = payout ratio/(kc – g) = 0.6/(.10 – 0.06) = 15 31. Section: 7.3 Common Share Valuation: The Dividend Discount Model (DDM) Learning Objective: 7.3 Level of difficulty: Intermediate 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.

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32. Section: 7.3 Common Share Valuation: The Dividend Discount Model (DDM) Learning Objective: 7.3 Level of difficulty: Intermediate Solution: a. P = D1 = 1.50 = $37.50 0 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: P= 1

D2 kc − g

=

1.50(1.03) = $38.63 .07 − .03

ii) The one-year holding period return = (1.50 + 38.63)/37.5 – 1 = 7% 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: Intermediate 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.

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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(1.04 x $40). The expected earnings will be 4 × 2.08 = $8.32.

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:

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.

The expected price today is:

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

2.00(1+.08) .09−.08

=$216 and the expected earnings are 4 ×

(2 × 1.08) = $8.64. The leading P/E ratio is 25. 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

Introduction to Corporate Finance, Fourth Edition

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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: Intermediate Solution: The first dividend occurs at the end of year 5. The price of the stock at the end of year 4 is 𝑃4 = 𝐷5 1.80 = $30 = 𝑘𝑐−𝑔

.105−.045

To obtain the price today, we discount the price back 4 years to time 0. The discount rate is 10.5 percent (the required rate of return for the stock).

The current price of the stock is: 30 4 = $20.12 1.105 35. Section: 7.3 Common Share Valuation: The Dividend Discount Model (DDM) Learning Objective: 7.3 Level of difficulty: Intermediate 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: Intermediate 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 = D 5(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 = $63.75 P= = 5 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 63.75 Note: the first 5 payments are present value of the stock price in year 5. P t=1 (1.10) + ( = 0  t 1.10)5 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.

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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: Intermediate Solution: a. The expected dividend at the end of year 5 D5 = D0(1 + g1)5 = 4(1.1)5 = $6.44 b. The expected dividend at the end of year 6 D6 = D5 (1 + g2) = D0 (1 + g1)5(1 + g2) = 4(1.1)5(1.03) = $6.6353 c. The expected price of the stock at the end of year 5 (immediately after the year 5 dividend) 6.6353 𝐷6 = = $69.85 𝑃5 = 𝑘𝑐 − 𝑔2 . 125 − .03 d. The price of the stock today: We will use Excel to calculate this.

Year Dividend 4 1 4.4 2 4.84 3 5.324 4 5.8564 5 6.442

Stock price at end of year 5

Present value

69.85

3.9111 3.8242 3.7392 3.6561 42.3340

Price of stock in year 0

57.4646

The price of the stock today is $57.46 The formulas used in Excel are given below: A B C D 1 Year Dividend Stock price at end of year 5 Present value 20 4 31 =1.1*B2 =B3/(1+0.125)^A3 42 =1.1*B3 =B4/(1+0.125)^A4 53 =1.1*B4 =B5/(1+0.125)^A5 64 =1.1*B5 =B6/(1+0.125)^A6 75 =1.1*B6 =(B7*1.03/(0.125-0.03)) =B7/(1+0.125)^A7+C7/1.125^A7 8

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9 Price of stock in year 0: 10

Booth, Cleary, Rakita

=SUM(D3:D7)

38. Section: 7.3 Common Share Valuation: The Dividend Discount Model (DDM) Learning Objective: 7.3 Level of difficulty: Intermediate Solution: The easiest way to solve this problem is to use Excel.

Year 0 1 2 3 4 5 6 7 8

Growth rate

Dividend

9% 9% 9% 6% 6% 6% 6% 2%

3.6000 3.9240 4.2772 4.6621 4.9418 5.2383 5.5526 5.8858 6.0035

Discount rate:

12%

Price of stock in year 0:

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

60.0352

3.5036 3.4097 3.3184 3.1406 2.9724 2.8131 29.8193

$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

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

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14 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: Intermediate 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: D = D (1 + g )3 = 4.00(1 + .25)3 = 7.8125 3

0

1

The expected value of the stock at the end of year 3: P3 =

D3(1 + g2 ) kc − g 2

=

7.8125 *1.10 = $171.875 .15 − .10

Step 2: Using the Cash Flow Worksheet in the BAII + CF0 = 0 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

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: Intermediate Solution: a. Implied growth rate D1 D 1 P =  g = k − 1 = 0.15 − = 0.1 = 10% c 0 P0 20 kc − g b. Share price in recession D1 1 P = = = $6.67 0 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

Introduction to Corporate Finance, Fourth Edition

P =

D1

1

=

Booth, Cleary, Rakita

=



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: 0

𝐷1

𝐷1(1 + 𝑔) 𝐷1(1 + 𝑔)2 𝐷1(1 + 𝑔)3 𝐷1(1 + 𝑔)𝑛−1 𝑃0 = + 1 + 𝑘𝑐 (1 + 𝑘𝑐 )2 + (1 + 𝑘𝑐 )3 + (1 + 𝑘𝑐 )4 + ⋯ + (1 + 𝑘𝑐 )𝑛 + ⋯ ∞ For kc = g: 𝐷1 𝐷1 𝐷1 𝐷1 𝐷1 + + + + ⋯+ 𝑃0 = + ⋯∞ 1 + 𝑘𝑐 1 + 𝑘𝑐 1 + 𝑘𝑐 1 + 𝑘𝑐 1 + 𝑘𝑐 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 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: Intermediate Solution:

1 + 𝑔1 5 𝑃5 𝐷1 × (1 − ( ) )+ 𝑃0 = (1 + 𝑘𝑐 )5 𝑘𝑐 − 𝑔1 1 + 𝑘𝑐 𝑊ℎ𝑒𝑟𝑒: 𝑃 = 𝐷6 , 𝐷 = 𝐷 × (1 + 𝑔 )5 × (1 + 𝑔 ) 5 0 1 2 𝑘𝑐 − 𝑔2 6 𝐷6 = 4 × 1.095 × 0.99 = $6.093 4 × 1.09

1 + .09 5 6.093 ) ) + = $45.04 ∴ 𝑃0 = × (1 − ( . 12 − .09 1 + .12 (.12 + .01) × (1 + .12) 5 42. Section: 7.3 Common Share Valuation: The Dividend Discount Model (DDM) Learning Objective: 7.3

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Level of difficulty: Intermediate Solution: a. Current share price of Dillon Mechanical: 𝐷5

=

1.5

=

1.5

= $15 𝑘𝑐 − 𝑔 . 15 − .05 .1 𝑃4 15 ∴ 𝑃0 = = (1 + 𝑘𝑐 )4 1.154 = $8.58 𝑃4 =

b. Current share price of Sterling: 𝑃0 =

𝐷1 𝑘𝑐 − 𝑔

=

𝐷0 × 1.02 𝑘𝑐 − 𝑔

=

6 × 1.02 . 15 − .02

=

6.12 . 13

= $47.08

c. PVGO of Dillon Mechanical: 𝐸𝑃𝑆1 𝑃0 = + 𝑃𝑉𝐺𝑂 𝑘𝑐 4 ∴ 8.58 = . 15 + 𝑃𝑉𝐺𝑂  𝑃𝑉𝐺𝑂𝐷𝑖𝑙𝑙𝑜𝑛 = −18.09

 The negative PVGO suggests that Dillon’s growth is destroying value d. PVGO of Sterling: 𝐸𝑃𝑆1 + 𝑃𝑉𝐺𝑂6 𝑘𝑐 ∴ 47.08 = . 15 + 𝑃𝑉𝐺𝑂 𝑃𝑉𝐺𝑂𝑆𝑡𝑒𝑟𝑙𝑖𝑛𝑔 = 7.08 The positive PVGO suggests that Sterling’s growth opportunities are creating value.

𝑃0 =

43. Section: 7.3 Common Share Valuation: The Dividend Discount Model (DDM) Learning Objective: 7.3 Level of difficulty: Intermediate 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%

Sustainable growth rate 9.50% 9.00% 8.50% 8.00% 7.50% 7.00% 6.50% 6.00% 5.50%

Percentage change in stock price 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%

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50% 55% 60% 65% 70% 75%

5.00% 4.50% 4.00% 3.50% 3.00% 2.50%

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–5.45% –5.22% –5.00% –4.81% –4.63% –4.47%

$10.5000 $9.9524 $9.4545 $9.0000 $8.5833 $8.2000

Challenging 44. 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: Challenging Solution: a. No growth g = 0, D0 = $2.40, kc = 10.5% D23 = D0 = $2.40

𝐷23 𝑃22 =

𝑘𝑐 − 𝑔

=

2.40 . 105

= $22.86

b. Growth: 𝑔 = 4%, 𝐷0 = $2.40, 𝑘𝑐 = 10.5% 𝐷23 = 𝐷0 × (1 + 𝑔)23 = $2.40 × (1 + 0.04)23 = $5.9153 𝐷23 5.9153 = = $91.00 𝑃22 = 𝑘𝑐 − 𝑔 . 105 − .04 𝐷19 𝐷0 × (1 + 𝑔)19 5.0564 = = = $77.79 𝑃18 = 𝑘𝑐 − 𝑔 𝑘𝑐 − 𝑔 . 105 − .04 𝐷29 𝐷0 × (1 + 𝑔)29 7.4848 = = = $115.15 𝑃28 = 𝑘𝑐 − 𝑔 𝑘𝑐 − 𝑔 . 105 − .04 45. Section: 7.3 Common Share Valuation: The Dividend Discount Model (DDM) Learning Objective: 7.3 Level of difficulty: Challenging 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.

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Step 1: Calculating the present value of the growing annuity: Present value of a growing annuity is given by: t PMT1   1 + g   PV =  1 −     0 k−g  1+ k  (11− 5) 6    1 + g1  D 6 2  PV =  1 −  1 −  1 + 0.1  = $9.36 = 5  1 + k   1 + 0.15   kc − g1  c  0.15 − 0.1  Step 2: Calculating the present value of the growing perpetuity: PMT1 PV0 = k−g D 2  1.15  1.05  PV = 12 = 33.82 = 11 kc − g2 0.15 − 0.05 Step 3: Calculate the price of the stock: PV11 PV5 9.36 33.82 + + P0 = = 11.92 11 = (1 + k) 5 5 (1 + k) (1 + 0.15) (1 + 0.15)11 Excel Solution:

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

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a. Calculating g2 P4 =

D  (1 + g )  (1 + g ) 4

D 5

kc − g2

=

0

1

2

kc − g2

0.5  (1 + 0.05 )  (1 + g 2 ) 4

10 =

0.15 − g2

=

0.6078  (1 + g2 ) 0.15 − g2

 1.5 − 10  g2 = 0.6078 + 0.6078  g2 0.8922 = 0.0841 = 8.41% or : g2 = 10.6078 b. Calculating price of TelTec 5 years from now:

P5 = P4  (1 + g2 )= 10  1.0841 = $10.841  $10.84 Alternatively : You can also use the following formula to get the same answer 4 2 D  (1 + g )  (1 + g ) D 1 2 6 P5 = = 0 kc − g 2 0.15 − 0.0841

c. Current price of TelTec 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: 4 D1  1 −  1 + g1   P4  +  0 4 kc − g1   1 + kc   (1 + k4 c ) 0.5  1.05   1 + 0.05   10 + = $7.32  P0 =  1 −   0.15 − 0.05   1 + 0.15   (1 + 0.15 )4 Excel Solution:

P =

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47. Section: 7.3 Common Share Valuation: The Dividend Discount Model (DDM) Learning Objective: 7.3 Level of difficulty: Challenging Solution: Notation: t = 0 is December 31, 2015 t = 5 is December 31, 2020 t = 10 is December 31, 2025 t = 11 is December 31, 2026 (January 1, 2016 is the beginning of “year 1” so it is considered t = 0 just like December 31, 2015.)

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 P = PVGA+ PVGP= 0

6 D5  1 + g 2   D 1 1 − 1    + 11  4 r − g3 (1+ r )1 0 r − g2   1+ r   (1+ r ) 

6 $ 5 . 0 2 8 39 31.0 6  1 $ 1 1 . 4 1 2 5 9 41  P0 = 0.1−   = $7 2.1 1 1 −  4 + 10 0.1 − 0.02 (1.1) 0.06   1.1   (1.1)

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48. Section: 7.3 Common Share Valuation: The Dividend Discount Model (DDM) Learning Objective: 7.3 Level of difficulty: Challenging 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 + .11)1 (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 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: Appendix 7B Additional Multiples or Relative Value Ratios Learning Objective: 7.7 Level of difficulty: Challenging Solution: Payout=D0/EPS0 = $4/$6 = 0.6667, Retention ratio (b) = 1 – Payout ratio = 1 – 0.6667 = 0.3333 D/E=0.6, leverage ratio A/E=(D+E)/E=(0.6+1)/1=1.6 ROE = Net profit margin × Asset turnover × leverage ratio = 15% × 1.25 × 1.6 = 30% g = b × ROE = 0.3333 × 30% = 10% EPS1 = EPS0 (1 + g) = $6 × 1.1 = $6.60 k = 3.5% + 10% = 13.5% Leading P/E = payout/(k – g) = 0.6667/(0.135 – 0.10) = 19.05 P0 = leading P/E × EPS1 = 19.05 × $6.60 = $125.73

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50. Section: 7.2 Preferred Share Valuation Learning Objective: 7.2 Level of difficulty: Challenging Solution: The required rates of return for the two stocks: D 0.07 * 50 Dillon: $70 = p = k = 5.00% p kp kp D 0.04 * 60 Sherwood: $45 = p = k = 5.33% p kp kp As the risk-free rate is the same for both firms, the only way Sherwood can have a higher required return is if the risk premium is higher. A higher risk premium reflects a higher level of risk; therefore, Sherwood is the riskier preferred stock.

51. Section: 7.3 Common Share Valuation: The Dividend Discount Model (DDM) Learning Objective: 7.3 Level of difficulty: Challenging Solution: 𝐷0(1 + 𝑔) 𝑘𝑐 − 𝑔 5(1 + 𝑔) 120 = . 10 − 𝑔 12 − 120𝑔 = 5 + 5𝑔 7 = 125𝑔 𝑔 = 5.6%

𝑃0 =

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

P = 0

(

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, Apex should buy the stock. b. The stock price can be expected to increase for two reasons: first, as Apex starts buying shares, that will increase demand for the stock and the price will rise. Secondly, Apex is not the only smart organization examining this company and if anyone else comes to the same

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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: Challenging Solution: There are two problems with Prime’s 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 WX 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. Section: 7.3 Common Share Valuation: The Dividend Discount Model (DDM) Learning Objective: 7.3 Level of difficulty: Challenging 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 Selkirk is $58.72 ($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: Challenging Solution: Year Growth rate 0 1 2 3 4

-4% -4% -4% 0%

Discount rate: Price of stock in year 0:

Dividend 5.0000 4.8000 4.6080 4.42368 4.42368

Stock price at Present value of end of year 3 each cash flow

36.864

4.2857 3.6735 29.3878

12% $37.347

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56. Section: 7.3 Common Share Valuation: The Dividend Discount Model (DDM) Learning Objective: 7.3 Level of difficulty: Challenging 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 = 5% × 1.4 × 1.0 × (1 – 0.50) = 3.50% 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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Answers to Concept Review Questions 7.1 Equity Securities Concept Review Questions 1. How do equity shareholders exert their influence over a company?

Shareholders exert their influence through their right to vote on key corporate issues and to elect the Board of Directors.

2. What are the two main components of the required rate of return on equity securities?

The risk-free rate (commonly measured using the return on riskless government debt instruments) and the risk premium (which is a function of the riskiness associated with the security).

7.2 Preferred Share Valuation Concept Review Questions 1. In what ways are preferred shares different from bonds?

The main difference between the preferred share and a bond is that the Board of Directors has to declare a dividend and until then, and unlike an interest payment, it is not a legal obligation of the firm.

2. How is a traditional preferred share valued?

A traditional preferred share is valued as a preferred share dividend divided by its discount rate.

3. How can we estimate the investor’s required rate of return for a traditional preferred share?

It is the dividend of a preferred share divided by its price.

7.3 Common Share Valuation: The Dividend Discount Model (DDM) Concept Review Questions 1. Why is share value based on the present value of expected future dividends?

Unlike bonds or even preferred shares this is not a trivial issue because there is no requirement that common shares pay dividends at all. In addition, the level of dividend payments is also discretionary, which implies we must make estimates regarding the amount and timing of any dividend payments.

2. What is the “bigger fool theorem” of valuation?

Suppose, for example, your broker calls and says “buy XYZ at $30.” You say no it’s only worth $25 to which he says “I know but there is momentum behind it and I am seeing a lot of interest I think it will go to $40 by next year.” You are a fool if you pay $30 for something you think is worth $25, but it is not known as the fool theorem but the bigger fool theorem. The reason is that if you do buy it you are a fool, but you are also assuming that there is an even bigger fool than you who you are going to sell it to in a year’s time.

3. Why does an increase in the expected dividend growth rate increase share prices?

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Simply because a share price is the present value of future dividends, thus an increase of the expected dividend growth rate will increase the share price.

4. Why can’t the expected growth rate exceed the investor’s required return in the constant growth model?

To have a positive price, the expected dividend growth rate must be less than the required return.

5. How can we estimate future growth rates?

One approach is to determine the company’s sustainable growth rage, which equals the retention ration multiplied by the return on common equity. Another approach is to examine historic rates of growth in dividends and earnings levels, including long-term trends in these growth rates for the company, the industry, and the economy as a whole.

7.4 Using Multiples to Value Shares Concept Review Questions 1. Why can the P/E ratio be viewed as a type of payback period?

P/E ratio means that if this level of earnings stays constant it will take (P/E) years to earn back the price of the shares. In this sense the multiple is an example of a payback period. The higher the multiple the longer the payback period and the more the investor is expecting earnings to increase.

2. What drives P/E ratios?

The expected dividend payout ratio (D1/EPS1), the required rate of return (kc), and the expected growth rate of dividends (g) drives the price, and hence the P/E ratio.

3. Why do P/E ratios differ even between comparable firms?

There are differences in the expected dividend payout ratio (D1/EPS1), the required rate of return (kc), and the expected growth rate of dividends (g), causing the difference even across comparable firms.

4. How are multiples linked to a discounted cash flow valuation?

P/E ratio can be rewritten as (D1/EPS1)/(k-g) by using the simplest DDM model. Thus the P/E ratio is linked to a DCF valuation.

7.5 A Simple Valuation Example Concept Review Questions 1. What are some of the key assumptions that must be made when applying the valuation concepts discussed in this chapter to an actual valuation situation?

The analyst must make judgments regarding: which models will work best for a given company; what companies to use as comparables; estimates regarding future growth in earnings, cash flows and dividends; and, the appropriate discount rate to use.

Appendix 7B Additional Multiples or Relative Value Ratios 1. What other relative valuation multiples are useful in valuation?

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Additional multiples are: the market-to-book ratio, the price-to-sales ratio, the price-to-cash-flow ratio, the market value to EBITDA ratio, and etc.

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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: Basic Solution: B. Capital gain return = (34 – 32)/32 = 0.0625 = 6.25% 2. Section: 8.1 Measuring Returns Learning Objective: 8.1 Difficulty: Basic Solution: D. Total return = [(4 × 1.50) + (34 – 32)] / 32 = 0.25 = 25% 3. Section: 8.1 Measuring Returns Learning Objective: 8.2 Difficulty: Intermediate Solution: B. The arithmetic mean is greater than the geometric mean.

4. Section: 8.1 Measuring Returns Learning Objective: 8.2 Difficulty: Basic Solution: A. Expected return = 0.25(30%) + 0.4(40%) + 0.35(15%) = 28.75% 5. Section: 8.2 Measuring Risk Learning Objective: 8.3 Difficulty: Basic Solution: D

 = .25(30 − 28.75)2 + .40(40 − 28.75)2 + .35(15 − 28.75)2 =

0.390625 + 50.625 + 66.171875 = 117.1875 = 10.825%

6. Section: 8.2 Measuring Risk Learning Objective: 8.3 Difficulty: Intermediate 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: Intermediate 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: Intermediate 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: Intermediate Solution: C. Portfolios A, B, and C are attainable, but D is not.

10. Section: 8.5 Diversification Learning Objective: 8.6 Difficulty: Intermediate 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 Basic 11. Section: 8.1 Measuring Returns Learning Objective: 8.2 Difficulty: Basic Solution: We use arithmetic mean 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).

12. Section: 8.4 The Efficient Frontier Learning Objective: 8.5 Difficulty: Basic 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.

13. Section: 8.1 Measuring Returns Learning Objective: 8.2 Difficulty: Basic Solution: Calculate the expected price: .30 × $60 + .45 × $110 + .25 × $85 = $88.75

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Expected return = (88.75 / 83) –1 = 6.93% 14. Section: 8.1 Measuring Returns Learning Objective: 8.1 Level of difficulty: Basic Solution: Value at the end of 6 days = $182 × (1–.08)(1+.18)(1–.3)(1+.06)(1+.07)(1−.05) = $149.02 15. Section: 8.3 Expected Return and Risk for Portfolios Learning Objective: 8.4 Difficulty: Basic Solution: w A

=

B

 A +B

=

32.27 = 0.6 21.51 + 32.27

wB = 1–wA = 1–0.6 = 0.4 Intermediate 16. Section: 8.1 Measuring Returns Learning Objective: 8.1 Difficulty: Intermediate Solution: Capital gain = ($87–$84)×300 = $900 Total dollar return = $900 + $780 = $1,680 Percentage return = $1,680/($84×300) = 6.67% 17. Section: 8.1 Measuring Returns Learning Objective: 8.1 Difficulty: Intermediate Solution: P0 = $24,000/1,500 =$16.00 Total dollar return = ($15–$16) ×1,500 + $3,750 = $2,250 Capital gain/(loss) = ($15–$16) ×1,500 = ($1,500) Percentage return = $2,250/$24,000 = 9.375% Dividend yield = $3,750/$24,000 = 15.625% 18. Sections: 8.1 Measuring Returns and 8.2 Measuring Risk Learning Objective: 8.2 and 8.3 Difficulty: Intermediate 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%

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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.

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: Intermediate 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)(0.96)(1.15)(0.97)(1.06) = $1.1919 So if $1 grows to $1.1919 in five days the cumulative return is $1.1919 − 1 = 19.19% $1.00 An easy way to calculate this is: DEF: 0.96 × 1.18 × 0.94 × 1.12 × 1.05 – 1 = 25.22%

Introduction to Corporate Finance, Fourth Edition

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ii) Geometric average daily return ABC: (1 + cumulative return)1/5 –1 = (1 +.1919)1/5 – 1 = 3.57% DEF: 4.60% 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 Y03 X04 Y04 X05 Y05

Your response 5 –4 –4 18 15 -6 –3 12 6 5

<ENTER> ↓ <ENTER> ↓ <ENTER> ↓ <ENTER> ↓ <ENTER> ↓ <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 = 3.8 sx = 7.7266 σx = 6.9109 Ӯ=5 sy = 10.247 σy = 9.1652 a = 9.5034 b = –1.1851

Interpretation

Additional action

Sample size is 5 Arithmetic mean daily return of ABC is 3.8% (remember we entered the data in percent) Sample standard deviation of ABC is 7.7266% Population standard deviation of ABC is 6.9109% Arithmetic mean daily return of DEF is 5%

<STO> 1

Sample standard deviation of DEF is 10.247% Population standard deviation of DEF is 9.1652% Coefficients of a regression of ABC and DEF. We don’t need this information for this question.

<STO> 2

Introduction to Corporate Finance, Fourth Edition

↓

r = –0.8936

Booth, Cleary, Rakita

The sample correlation between ABC and DEF

<STO> 3

The covariance between ABC and DEF is therefore: Cov = rsxsy = –0.8936 × 7.7266 × 10.247 = –70.8 20. Section: 8.3 Expected Return and Risk for Portfolios Learning Objective: 8.4 Difficulty: Intermediate Solution: 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%

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%

$ invested in stock 1 $ invested in stock 2 Total $ invested Weight in stock 1 Weight in stock 2 Expected return of stock 1

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%

Introduction to Corporate Finance, Fourth Edition

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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% (same as portfolio) 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: Intermediate Solution: a. w2 = 1– w1= 1 – .55 = .45 σ2p = w12σ12+ w22σ 22 +2w1w2ρ σ1 σ2 = (.55)2(.06)2 + (.45)2(.2)2 + 2 × .55 × .45 × .8 × .06 × .2 = .001089 + .0081 +.004752 = .013941 σp = 0.1181 The portfolio standard deviation is 11.81% when the correlation is 0.8. b.

σ2p = w21σ 12+ w22σ 22 +2w1w2ρ σ1 σ2 = (.55)2(.06)2 + (.45)2(.2)2 + 2 × .55 × .45 × (–0.8) × .06 × .2 = .001089 + .0081 –0.004752 = 0.004437 σp = 0.0666

The portfolio standard deviation is 6.66% when the correlation is –0.8.

22. Sections: 8.3 Expected Return and Risk for Portfolios Learning Objective: 8.4 Difficulty: Intermediate Solution:

Weight in stock 1 Weight in stock 2 Standard deviation of stock 1 Standard deviation of

Case 1 75% 25%

Case 2 15% 85%

15%

2%

3%

10%

Introduction to Corporate Finance, Fourth Edition

Booth, Cleary, Rakita

stock 2 Covariance between stocks 1 and 2 Correlation between stocks 1 and 2 Portfolio variance Portfolio standard deviation

–0.2*.15*.03 = –.0009

.40*.02*.10 = 0.0008

–.20

.40

0.012375

0.007438

11.1243%

8.624%

Case 1: portfolio variance σ2p = w12σ12+ w22σ 22 +2w1w2ρ σ1 σ2 = (.75)2(.15)2 + (.25)2(.03)2 + 2 × .75 × .25 × (–0.20) × .15 × .03 = 0.012375 Portfolio standard deviation is the square root of 0.012375 or 11.1243% Case 2: portfolio variance σ2p = w12σ12+ w22σ 22 +2w1w2ρ σ1 σ2 = (.15)2(.02)2 + (.85)2(.1)2 + 2 × .15 × .85 × (0.40) × .02 × .1 = 0.007438 Portfolio standard deviation is the square root of 0.007438 or 8.624% 23. Section: 8.3 Expected Return and Risk for Portfolios Learning Objective: 8.4 Difficulty: Intermediate Solution: a.

Daily returns 0% 0%

1%

2%

3%

Returns

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

4%

5%

6%

Introduction to Corporate Finance, Fourth Edition

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Daily returns

Returns

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

1%

2%

3%

4%

5%

6%

4%

5%

6%

4%

5%

6%

XYZ returns DEF

Returns

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

1%

2%

3%

XYZ returns GHI

Returns

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

1%

2%

3% XYZ returns JKL

Introduction to Corporate Finance, Fourth Edition

Booth, Cleary, Rakita

Returns

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

1%

2%

3%

4%

5%

6%

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 Difficulty: Intermediate 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: Intermediate Solution: k = (50%+ 30%+ 20%+ 35%+ 55%)/5 = 38%

Introduction to Corporate Finance, Fourth Edition

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(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: Intermediate Solution: Stock B = 60,000 – 15,000 – 20,000 = $25,000 w1 = 15,000/60,000 = 1/4 = 25% w2 = 20,000/60,000 = 1/3 = 33.33% w3 = 25,000/60,000 = 5/12 = 41.67% ERp = w1ER1+ w2ER2+ w3ER3 =.25(12%) +.3333(8%) +.4167(20%) = 14.00% 27. Sections: 8.1 Measuring Returns and 8.2 Measuring Risk Learning Objective: 8.2 and 8.3 Difficulty: Intermediate Solution: a. Expected return = .20 × (–3%) + .50 × 5% + .30 × 8% = 4.3% b.

2 2 2  2 = .2 ( −0.03 − .043) + .5 (.05 − .043) + .3 (.08 − .043) = 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 the square root of 0.001501 or 0.038743 = 3.87% 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>

Introduction to Corporate Finance, Fourth Edition

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↓ 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 Learning Objective: 8.2 Difficulty: Intermediate Solution: January 1: the expected price of GTS in one year is .25 × 150 + .75 × 200 = $187.50 If the market agrees with FinCorp Inc.’s analysis, then we would expect the stock price to be $187.50 discounted back to January 1. As the discount rate is zero, the expected price on January 1 is $187.50.

July 1: the expectations about GTS have changed so we need to determine the new expected price in six months: .40 × 150 + .60 × 200 = $180 If the market agrees with FinCorp Inc., then the expected price on July 1 will be $180 The expected change in the stock price is a decrease of 4% or $7.50.

29. Section: 8.1 Measuring Returns Learning Objective: 8.2 Difficulty: Intermediate

Introduction to Corporate Finance, Fourth Edition

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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: Intermediate Solution: .06 = [(1+.16)(1+.19)(1–.23)(1+.14)(1–.08)(1+X)]1/6 – 1 (1.06)6 = 1.114778(1+X) X = 27.2468% 31. Section: 8.3 Expected Return and Risk for Portfolios Learning Objective: 8.4 Difficulty: Intermediate Solution: a. Set w = weight in Encor 16% = w* 2% + (1− w)* 25% 16% − 25% 2% − 25% = 39.1304%

w=

b.

2 2 2 2  P2 = (.391304 ) (.01) + (.608696 ) (.10 ) + 2 *.4 * (.391304 )(.608696 )(.01)(.10 ) = 0.00391097  P = 0.062538 = 6.2538% 32. Section: 8.3 Expected Return and Risk for Portfolios Learning Objective: 8.4 Difficulty: Intermediate 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

Introduction to Corporate Finance, Fourth Edition

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0 = 0.0093w2 – 0.0192w + 0.0064 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% 33. Section: 8.3 Expected Return and Risk for Portfolios Learning Objective: 8.4 Difficulty: Intermediate Solution:

 p = (w X )2 ( X )2 + (wY )2 (Y )2 + 2(wX )(wY )(COVX ,Y ) 6 = (0.6)2 (12)2 + (0.4)2 (15)2 + 2(0.6)(0.4)(COV X ,Y ) 36 = 51.84+36+0.48 COVX,Y COVX,Y = –108 %2 COVX ,Y − 108 = –0.6  XY = =  X Y (12)(15) 34. Section: 8.3 Expected Return and Risk for Portfolios Learning Objective: 8.4 Difficulty: Intermediate Solution 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% 35. Section: 8.3 Expected Return and Risk for Portfolios Learning Objective: 8.4 Difficulty: Intermediate 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% 36. Section: 8.3 Expected Return and Risk for Portfolios Learning Objective: 8.4 Difficulty: Intermediate Solution ERp = .4(16)+.6(27) = 22.60%

Introduction to Corporate Finance, Fourth Edition

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Standard deviation of portfolio = [0.42(10)2 + 0.62(23)2 + 2 × .4 × .6 × .45 × 10 × 23]1/2 = 16% Standard deviation of portfolio = [0.42(10)2 + 0.62(23)2 + 2 × .4 × .6 × (–.45) × 10 × 23]1/2 = 12.52% Challenging 37. Section: 8.1 Measuring Returns Learning Objective: 8.1 Difficulty: Challenging Solution:

M

Opening price $100

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

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

−1

100 = 22%

Tu

$115

$2 7% =

−1 115 X = $123.05

W

Tr

F

$123.05 = closing price on Tuesday $127.36 = closing price on Wednesday $131.18 = closing price on Thursday

$8 10% =

X +8

−1 123.05 X = $127.36

4% =

X

127.36 X = $5.09

$0

7%

123.05 + 2 −1 115 = 8.74%

6.50% = 8/123.05

3.50%=(127.36– 123.05)/123.05

10%

4%

3%

7% = 4% +3%

0% (no dividend)

15% = total daily return – dividend return

15%

2

X

3% =

X

127.36 X = $131.18

−1

$150.86 = (1+15%)*131.18

115 = 1.7391%

38. Section: 8.3 Expected Return and Risk for Portfolios Learning Objective: 8.4 Level of difficulty: Challenging Solution: a.

Introduction to Corporate Finance, Fourth Edition

Booth, Cleary, Rakita

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.

Introduction to Corporate Finance, Fourth Edition

Booth, Cleary, Rakita

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.

39. Section: 8.3 Expected Return and Risk for Portfolios Learning Objective: 8.4 Difficulty: Challenging 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 =

B =

462.75 = 21.51%

.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 =+1 4th:  AB = =  A B (21.51)(32.27)

40. Section: 8.3 Expected Return and Risk for Portfolios Learning Objective: 8.4 Difficulty: Challenging Solution: R(A) = [(600)(32) – (600)(23)+(600)(1)(4)]/(600)(23) = 56.52% R(B) = [(1,000)(32)–(1,000)(34)+(1,000)(1.5)(4)]/(1,000)(34) = 11.76% wA = (600)(23)/[(600)(23)+(1,000)(34)] = 0.2887

Introduction to Corporate Finance, Fourth Edition

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wB = (1,000)(34)/[(600)(23)+(1,000)(34)] = 0.7113 Total return of the portfolio = wAR(A)+wBR(B) = 0.2887(56.52%)+0.7113(11.76%) = 24.68% 41. Section: 8.3 Expected Return and Risk for Portfolios Learning Objective: 8.4 Difficulty: Basic Solution:

 p = (w A ) 2 ( A ) 2 + (w B ) 2 ( B ) 2 + 2(w A )(w B )( A,B )( A )(B ) P = =

(.2887)2 (28)2 + (.7113)2 (15)2 + 2(.2887)(.7113)(.4)(28)(15)

65.3446 +113.8382 + 68.9984 =

248.18 = 15.75%

42. Section: 8.3 Expected Return and Risk for Portfolios Learning Objective: 8.4 Difficulty: Challenging 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 Correlation between stocks 1 and 2 Portfolio variance Portfolio standard deviation

Case 1 35% 65%

Case 2 40% 60%

3%

51.6236%

25%

20%

.141685*.03*.25 = 0.001063

.022

0.027

.022/(.516236*.20) = 0.21308 0.0676

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 1 : Portfolio standard deviation is square root of 0.027 or 16.4317% Case 2: Portfolio variance is Portfolio standard deviation squared or 0.0676

Introduction to Corporate Finance, Fourth Edition

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Case 2: standard deviation of stock 1 .0676 = (.4 ) (1 ) + (.6 ) (.2 ) + 2 *.022 *.4 *.6 2

2

2

2

= .161 2 +.0144 +.01056 .0676 −.0144 −.01056  12 = .16 = .2665 1 = 51.6236% 43. Section: 8.3 Expected Return and Risk for Portfolios Learning Objective: 8.4 Difficulty: Challenging 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% 44. Section: 8.3 Expected Return and Risk for Portfolios Learning Objective: 8.4 Difficulty: Challenging 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: Challenging Solution: ERABC = 0.1 (-5) + 0.20(-2) + 0.40(5) + 0.3(10)

Introduction to Corporate Finance, Fourth Edition

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= -0.5 - 0.4 + 2 + 3 = 4.1% ERDEF= 0.1(-7) + 0.20(2) + 0.40(6) + 0.3(15) = -0.7 + 0.4 + 2.4 + 4.5 = 6.6% ERp = 0.5(4.1) + 0.5(6.6) = 5.35% Standard deviation of ABC = [ 0.1 (–5 – 4.1)2 + 0.20(–2 – 4.1)2 + 0.40(5 – 4.1)2 + 0.3(10 – 4.1)2]1/2 = 5.15% Standard deviation of DEF = [ 0.1 (–7 – 6.6)2 + 0.20(2 – 6.6)2 + 0.40(6 – 6.6)2 + 0.3(15 –6.6)2]1/2 = 6.64% Covariance = 0.1 (-5-4.1) × (–7 – 6.6) + 0.20(–2 – 4.1) × (2-6.6) + 0.40(5-4.1) × (6 – 6.6) + 0.3 (10 – 4.1) × (15 – 6.6) = 32.64 Standard deviation of portfolio = [ (0.5)2(5.15)2 + (0.5)2(6.64)2 +2 × 0.5 × 0.5 × 32.64]1/2 = 5.83% In the second part we are investing 80 percent in the above portfolio and 20 percent in T-bills.

Thus ER on the new portfolio = 0.8 × 5.35 + 0.2 × 23.5 = 4.98% 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 = [(0.8)2(5.83)2]1/2 = 4.66% 46. Section: 8.4 The Efficient Frontier Learning Objective: 8.5 Level of difficulty: Challenging 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 the2portfolio by choice of weight.  2 = w2 2 + (1− w )  2 + 2  w (1− w )   P

1

2

1

2

d 2

P 2w 12 − 2(1− w) 22 + (1− 2w ) 2   1 2 dw = 2 2 2 = 2w  +  − 2  − 2 + 2 

(

w* =

(

1

2

2 − 2 1 2 2 2

)

1

2

)

2 12 +  22 − 2 1 2

= 63.7931%

2

1

2

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Computation is (2 x 25 + 1.6 x 3 x 5)/ 2(9 + 25 + 1.6 x 3 x 5) 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: Challenging 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− 2w + 2  w − 2  w2  

=  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: Challenging 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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Booth, Cleary, Rakita

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: Challenging 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% Weight in ABC

80%

100%

120%

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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

1 -0.70389

DEF 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%

–0.70389

Correlation

Weight in ABC 0 0.1 0.2 0.3 0.4

DEF 3.26%

Weight in DEF 1 0.9 0.8 0.7 0.6

Portfolio standard deviation 3.26% 2.70% 2.18% 1.72% 1.39%

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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. Section: 8.4 The Efficient frontier Learning Objective: 8.5 Difficulty: Challenging 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 BB.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

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 BlackBerry -

BB.TO

RY.TO

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%

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%

^GSPTSE -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%

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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 BlackBerry 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 BB/RY frontier. e.

Compared to a portfolio of just BlackBerry and the Royal Bank, the S&P/TSX is an efficient portfolio. With just BlackBerry 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: 8.5 Diversification Learning Objective: 8.6 Difficulty: Challenging 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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Answers to Concept Review Questions 8.1 Measuring Returns Concept Review Questions 1. What is the difference between ex ante and ex post returns?

Ex post simply means after the fact, so ex post returns are past or historical return. Ex ante means before the fact, so ex ante returns are expected returns.

2. Why do the income and capital gains component of the total return differ between common shares and bonds?

The yield on bonds is the return earned by buying the bond and holding it to maturity, so in this sense it is also an expected return over that very long investment horizon. In contrast the dividend yield on stocks is simply the cash that investors can expect to earn if the dividend payments over the next year are the same as they were over the previous period. This is because it is the current dividend payments divided by the current value of the index not the forecast dividends.

3. Why is the GM return a better estimate of long run investment performance than the AM return?

Since GM is the rate of return used to find the future return, it is a better estimate of long run investment performance than AM. 4. Why might a scenario-based estimate be more accurate for a short-run expected return estimate than a historical AM estimate?

There are pros and cons of each method for determining expected rate of return. For short term forecasts the scenario based approach makes more sense, since where we are today has a huge bearing on what is likely to happen over a short period of time.

8.2 Measuring Risk Concept Review Questions 1. Why is the range sometimes a poor measure of risk?

Since range only uses two observations, the maximum and minimum, it ignores all other observations. Thus, it is a poor measure of risk.

2. What is the difference between estimating a scenario-based (probability) estimate of risk versus a historic data-based estimate of risk?

The scenario based standard deviation is ex ante since we are explicitly taking into account updated probabilities of events happening. The historic data based estimate of risk is the standard deviation for a series of historic or ex-post returns.

3. Why would we sometimes want to use scenario based risk measures rather than the standard deviation of actual returns over a long time period?

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The standard deviation of actual returns only reflects the economic circumstances of the period over which it is estimated. Thus the standard deviation fluctuates a lot over time. That is why we want to use scenario based measure.

8.3 Expected Return and Risk for Portfolios Concept Review Questions 1. Why is the expected return on a portfolio a weighted average of the expected returns of the underlying securities?

A portfolio return is a weighted average of the returns of the underlying securities, thus the expected value of a portfolio return is the weighted average of the expected value of the underlying securities’ returns.

2. Why is portfolio standard deviation not a weighted average of the standard deviations of the underlying securities?

A portfolio’s standard deviation depends on weights, standard deviations, and correlations between the individual securities. If the correlation between the underlying securities is not exactly equal to 1, the standard deviation is less than a weighted average of the standard deviations of the underlying securities.

3. What is the difference between the covariance and the correlation coefficient?

While covariance provides us with a useful measure of the relationship of the co-movements of returns on individual securities, it is difficult to interpret intuitively since as was the case with the variance, the unit is percent squared (%2). Fortunately, covariance is related to another statistical measure, the correlation coefficient (ρAB), which may be interpreted in a more intuitive manner.

The correlation coefficient is covariance divided by the product of individual standard deviations.

4. Why is all risk removed in a two-security portfolio if the securities are perfectly negatively correlated? B If weight of security A is w =  A +  B , then the standard deviation of the whole portfolio is 0 if security A and B are perfectly negatively correlated.

5. Is the zero-risk portfolio described in Question 4 generally equally weighted in both securities? Explain.

The weight depends on the standard deviation of each security. As long as the standard deviation is not the same for both securities, the weight is different.

8.4 The Efficient Frontier Concept Review Questions 1. How do you form the minimum variance frontier in the two-security case?

We can vary the weights in each security and determine the resulting portfolio expected returns and standard deviations for various weights invested in each security. If we plot these expected return-standard deviation combinations with expected return on the vertical axis and standard

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deviation on the horizontal axis, we get the efficient frontier, which represents all possible portfolio combinations that can be constructed by varying the weights in our two securities A and B. 2. What assumptions about investors underlie Markowitz’s theories regarding efficient portfolios?

• Investors are rational decision-makers.

• Investors are risk averse (which means that they like expected returns and dislike risk, and therefore, they require compensation to assume additional risk); and, • Investor preferences are based on a portfolio’s expected return and risk (as measured by variance or standard deviation).

3. Why is the efficient frontier bowed?

If the correlation between assets is 1, then the efficient frontier is a straight line. If the correlation between assets is -1, then the efficient frontier is two straight lines which cross the vertical axis.

If the correlation is between -1 and 1, then the efficient frontier is bowed because there is a diversification effect, but the risk cannot be totally diversified away. In reality, the average correlation between assets is between -1 and 1, so the efficient frontier is bowed.

4. What is an unattainable portfolio, and what is a dominated portfolio?

Portfolios which lie below the efficient frontier are not attainable and dominated. It is unattainable because it can only be attained by deliberately wasting money – i.e., by simply not investing some portion of their wealth and “leaving money under the mattress” earning zero return. It is also dominated because it offers a lower expected rate of return for the same risk as another portfolio on the upper half of the minimum variance frontier.

8.5 Diversification Concept Review Questions 1. What is naïve diversification?

Random or naive diversification refers to the act of randomly diversifying without regard to relevant investment characteristics such as company size, industry classification, etc.

2. What is the difference between diversifiable and non-diversifiable risk?

The part of the total risk that is eliminated by diversification is the company-specific unique (or non-systematic) or diversifiable risk. The part that is not eliminated by diversification is the market (or systematic) or non-diversifiable risk.

3. Why is it logical to believe that international diversification will provide benefits to investors?

This is logical, since we would expect the returns among stock returns on different global markets to have lower correlation coefficients than those in the same market.

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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: Intermediate Solution: A wRF = 7,500/(2,500+7,500) = 0.75 ERP = (wRF)(RF) + (1 – wRF) (ERA) = (0.75)(8%)+(1 – 0.75)(20%) = 11%  p = (1 − wRF )( A ) = (1 – 0.75)(25%) = 6.25% 2. Section: 9.1 The New Efficient FrontierLearning Objective: 9.1 Difficulty: Intermediate 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: Intermediate Solution: C. ERM − RF  k = RF +  P P    M  10 − 4  16 = 4 + ( ) p  30  Therefore σp = 60% 4. Section: 9.3 The CAPM and Market Risk Learning Objective: 9.3 Difficulty: Intermediate 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: Intermediate 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.

6. Section: 9.3 The CAPM and Market Risk

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Learning Objective: 9.3 Difficulty: Intermediate 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 ERM − RF  ), respectively. CML only applies to the efficient and CML are (ER − RF ) and ( M    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: Basic 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: Intermediate 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: Intermediate 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.

Practice Problems Basic 10. Section: 9.1 The New Efficient Frontier Learning Objective: 9.1 Difficulty: Basic 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?).

11. Section: 9.1 The New Efficient Frontier Learning Objective: 9.1

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Difficulty: Basic 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.

12. Section: 9.2 The Capital Asset Pricing Model (CAPM) Learning Objective: 9.2 Difficulty: Basic 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.

13. Section: 9.2 The Capital Asset Pricing Model (CAPM) Learning Objective: 9.2 Difficulty: Basic 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, 3 and 4 Overvalued: Portfolios 2 and 5 14. Section: 9.3 The CAPM and Market Risk Learning Objective: 9.3 Difficulty: Basic 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.

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15. Section: 9.3 The CAPM and Market Risk Learning Objective: 9.3 Difficulty: Basic 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.

16. Section: 9.2 The Capital Asset Pricing Model (CAPM) Learning Objective: 9.2 Difficulty: Basic Solution: Determine which line consisting of the security and the RF produces the greatest slope.  ER − RF   20 − 5 = slope =  A =3  A   5   ER − RF   25 − 5 = slope =  B =2  B   10   ER − RF   30 − 5 slope =  C = 1.67 =  C   15  Therefore, choose A. 17. Section: 9.3 The CAPM and Market Risk Learning Objective: 9.3 Difficulty: Basic Solution: Expected return = [(P1 – P0)+D]/P0 = [(22 -20)+1]/20 = 15% Required return = RF + (ERM − RF ) = 4% + (1.6)(10%—4%) = 13.6% Expected return (15%) > Required return (13.6%), so the stock lies above the SML. It is under-valued.

18. Section: 9.3 The CAPM and Market Risk Learning Objective: 9.3 Difficulty: Basic Solution: By having a portfolio of stocks, we can potentially eliminate diversifiable risk.

19. Section: 9.3 The CAPM and Market Risk Learning Objective: 9.3 Difficulty: Basic Solution: 15.5 = 5+6 ×   = (15.5-5)/6 = 1.75 20. Section: 9.4 Alternative Asset Pricing Models Learning Objective: 9.4

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Difficulty: Basic Solution: Roll argued that the 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.

Intermediate 21. Section: 9.1 The New Efficient Frontier Learning Objective: 9.1 Difficulty: Intermediate Solution: wRF = -1,000/2,500 = -0.40; (1 – wRF) = 1 – (-0.40) = +1.40 Therefore, ERP = (-0.4)(6%) + (1.4)(15%) = 18.60%  = (1.4) (25%) = 35% p

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

Expected return 14%

Standard deviation 9%

=

Sharpe Ratio ERp − Rf

p

= 1.333

Portfolio 2 Portfolio 3 Portfolio 4 Portfolio 5

10% 12% 9% 6%

7% 8% 5% 4%

1.143 1.250 1.400 1.000

Required rate of return  ERm − Rf  E (R ) = R +  p f    p  m  8% − 2%   = 2% +   9%  5%  = 12.80% 10.40% 11.60% 8.00% 6.80%

23. Section: 9.3 The CAPM and Market Risk Learning Objective: 9.3 Difficulty: Intermediate Solution: Security 1 beta Case .50

Security 2 beta 1.50

Weight in Security 1 .40

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

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1 Case 2 Case 3

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=.1.10 1.95

0.65

.50

1.30

2.1 = w*1.1

1.10

+ (1− w)*1.9

1.90

2.10

2.1 = −.8w +1.90 w = −.25

Case 4 Case 5

1.25

0.80

.75

1.1375

1.30

3.425

.20

3.00

24. Section: 9.3 The CAPM and Market Risk Learning Objective: 9.3 Difficulty: Intermediate Solution: a. ρ σ (0.7)(.28) β FM = FM,M FM = = 1.225 σM (.16) b. kFM = RF + (ERM − RF )FM = 4.5%+1.225(13.5% — 4.5%) = 15.525% c. Stock FM has a required rate of return (15.525%), which is higher than the market return (13.5%) because its beta is higher than the market beta of 1.

25. Section: 9.3 The CAPM and Market Risk Learning Objective: 9.3 Difficulty: Intermediate 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 26. Section: 9.3 The CAPM and Market Risk Learning Objective: 9.3 Difficulty: Intermediate Solution: Expected Standard Security Beta Recommendation return deviation ABC

15%

19%

1.6

Buy (I require 14.2%, but I

Required return 14.20%

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RTS

10%

13%

1.15

DKF OPL WEQ

8% 9% 12%

10% 14% 16%

0.65 0.8 1.35

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expect to get 15%) Sell (I require 11.05%, but I only expect the security to 11.05% get 10%) Buy 7.55% Buy 8.60% Sell 12.45%

27. Section: 9.3 The CAPM and Market Risk Learning Objective: 9.3 Difficulty: Intermediate Solution: a) 𝑅 = 𝑅𝑓 + (𝑅𝑚 − 𝑅𝑓) = 3% + 1.28 ∗ 8% = 13.24% b) Here we will need to use the dividend discount model: 1.5∗(1+.05)

𝑃0 = .1324−.05 = $19.11 28. Section: 9.3 The CAPM and Market Risk Learning Objective: 9.3 Difficulty: Intermediate Solution: Market or systematic risk: (a), (c), and (e) Unique or unsystematic risk: (b), (d), and (f) 29. Section: 9.3 The CAPM and Market Risk Learning Objective: 9.3 Difficulty: Intermediate Solution: βM = 1. βRF = 0 βP = wAβA + wBβB + ... + wnβn WA = 100/(100+400+300+200) = 0.1 WB = 400/(100+400+300+200) = 0.4 WRF = 300/(100+400+300+200) = 0.3 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.

30. Section: 9.3 The CAPM and Market Risk Learning Objective: 9.3

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Difficulty: Intermediate Solution: kA = RF + (ERM − RF )  A = 3%+.82(6%) = 3% + 4.92% = 7.92% < 8.5% kB = RF + (ERM − RF )B = 3%+1.05(6%) = 3% + 6.3% = 9.3% > 8.5% Therefore Portfolio A lies above the SML and is under-valued, while Portfolio B lies below the SML and is over-valued. If the market is efficient, Portfolios 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 rise and Portfolio B’s price will fall. Thus, you should buy the under-valued Portfolio A and sell the over-valued Portfolio B. 31. Section: 9.3 The CAPM and Market Risk Learning Objective: 9.3 Difficulty: Intermediate 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(1 + .04) 32 = 𝑅 − .04  32𝑅 − 1.28 = 4.16  𝑅 = 17% . 17 = .03 + (. 09 − .03) = .03 +  ∗ .06   = 2.3333 32. Section: 9.3 The CAPM and Market Risk Learning Objective: 9.3 Difficulty: Intermediate Solution: 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.

33. Section: 9.3 The CAPM and Market Risk Learning Objective: 9.3 Difficulty: Intermediate 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%

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34. Section: 9.3 The CAPM and Market Risk Learning Objective: 9.3 Difficulty: Intermediate Solution: 15= RF +  A × risk premium(i) 9= RF +  B × risk premium (ii) (i)-(ii): 6= 0.4×risk premium Risk premium = 6/0.4 = 15% 35. Section: 9.3 The CAPM and Market Risk Learning Objective: 9.3 Difficulty: Intermediate Solution:  =cov//σ2M= 0.09504/.0576= 1.65 ERABC = 5+1.65 × 8 = 18.2% 36. Section: 9.3 The CAPM and Market Risk Learning Objective: 9.3 Difficulty: Intermediate Solution: Beta of the portfolio= .2 × 0.8+.3 × 1.2+.15 × 1.35+.35 × 1.15 = 0.16+0.36+0.2025+0.4025 =1.125 ER = 5+1.125 × 8 =14% 37. Section: 9.4 Alternative Asset Pricing Models Learning Objective: 9.4 Difficulty: Intermediate Solution: ERi =4% + (0.4)(12%) + (0.7)(6%) + (.8)(10%)+ (1.2)(8%) = 4%+4.8%+4.2%+8%+9.6% = 30.6% Challenging 38. Section: 9.1 The New Efficient Frontier Learning Objective: 9.1 Difficulty: Challenging 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

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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 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 39. Section: 9.1 The New Efficient Frontier Learning Objective: 9.1 Difficulty: Challenging Solution:

Investor

Weight in risk-free asset

$ amount invested in risk-free asset

Expected portfolio return

Portfolio standard deviation = (1 − wRf ) M

Charles

25%

.25*2,500=$625

=0.25*4+0.75*12 =10%

Sonja

-1,000/2,500 = -40% wRf *.04+(1- wR f )*.12=.09

Borrowed $1,000

15.2%

= .75*.16 = 12% 22.4%

Fritz

0.12-.08 wRf =.09

$937.50

9%

10%

Borrowed $4,062.50

25%

42%

$1,562.50

7%

6%

wRf = 37.5% Eddy Nellie

-162.5% 𝑃 = (1 − 𝑤𝑅𝑓)𝑀 . 06 = (1 − 𝑤𝑅𝑓). 16 𝑤𝑅𝑓 = 62.5%

40. Section: 9.1 The New Efficient Frontier Learning Objective: 9.1 Difficulty: Challenging Solution:

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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%

Geeta Amir

8.00%

Amanda

6.00% 4.00%

Xiang Rina

2.00% 0.00% 0.20%

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.

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

41. Section: 9.1 The New Efficient Frontier

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Learning Objective: 9.1 Difficulty: Challenging 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)

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

0.02

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Rf = 2% Standard deviation 0 =0.01+A10 =0.01+A11

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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

Standard Expected Portfolio deviation return A 5.00% 8.00% B 7.00% 13.00% C 11.00% 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. 42. Section: 9.3 The CAPM and Market Risk Learning Objective: 9.3 Difficulty: Challenging Solution: a. The data is already downloaded in Chapter 8 Question 50. One would expect BlackBerry 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 BlackBerry. The Royal Bank is a very large firm and therefore a more substantial component of the S&P/TSX than BlackBerry and, therefore, the correlation between the Royal Bank and the market should be closer to 1. BlackBerry, 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: BB returns

RY returns

TSX returns

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BB returns RY returns TSX returns

0.028990553 0.000873019 0.002774488

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0.0023217 0.0007303 0.001226981

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

Beta=COV(r, rm)/VARm Beta: BB 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.

43. 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: Challenging 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.

44. Section: 9.3 The CAPM and Market Risk Learning Objective: 9.3 Difficulty: Challenging 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.

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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

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Answers to Concept Review Questions 9.1 The New Efficient Frontier Concept Review Questions 1. What is risk aversion and how do we know investors are risk averse?

Risk aversion means that investors will not willingly undertake fair gambles. If someone turns down a fair gamble, he or she is defined as risk averse.

2. What is the risk of a portfolio consisting of a risk-free asset and a risky security?

The risk of such a portfolio is the weight of the risky security times its standard deviation.

3. Why is the tangent portfolio so important?

Portfolios composed of the risk free rate and the tangent portfolio offer the highest expected rate of return for any given level of risk and represent the new efficient frontier. Thus the tangent portfolio is so important.

4. How do we generate a portfolio with a higher expected rate of return than that on the tangent portfolio?

Getting to such a portfolio involves more than 100% invested in the tangent portfolio (w > 100%) and thus a negative or short position in the risk free asset.

9.2 The Capital Asset Pricing Model (CAPM) Concept Review Questions 1. What is the slope of the CML, and why can it be reviewed as the market price of risk for efficient portfolios according to the CML? The slope of the capital market line is the incremental expected return divided by the incremental risk. However, this is a special trade-off of risk and return called the market price of risk for efficient portfolios or the equilibrium price of risk in the capital market. It indicates the additional expected return that the market demands for an increase in a portfolio’s risk.

2. Assuming the CAPM holds, if the expected return on a diversified portfolio lies above the CML, should an investor buy or sell the portfolio?

If a portfolio has a high expected rate of return, relatively low risk and lays above the CML. The expected rate of return exceeds the required rate of return according to the CML. Investors would bid up its price and cause its expected rate of return to fall until the expected return lies on the CML. Since the investor is expecting a price increase in the market, they should buy more.

3. When is the expected return equal to the required return?

When the expected rate of return is the same as the required rate of return, so the portfolio is “fairly priced” and the portfolio will lie on the CML. 4. Why is the Sharpe ratio frequently referred to as a ‘risk-adjusted’ measure of performance?

The Sharpe ratio provides a measure of the amount of return generated per unit of risk undertaken by the investor.

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9.3 The CAPM and Market Risk Concept Review Questions 1. Why is beta a measure of market risk for a security?

Consider a security with a beta of 0. This means that its return is unrelated to the return on the market as whole. As a result, all of the variability in this security’s return is diversifiable to any investor holding a well-diversified portfolio. Further if this security is added to a diversified portfolio it has no impact on the portfolio’s risk since all of its risk is diversifiable. In contrast a security with a beta of say 2.0 increases by twice the return on the market portfolio on average.

Adding a “high beta security” to the portfolio thus increases the risk of the portfolio and makes it more sensitive to market movements.

2. If a security’s correlation with the market return increases, will its beta get larger or smaller?

If a security’s correlation with the market return increases, its beta will get larger.

3. What is a characteristic line, and why is it useful?

A characteristic line is typically estimated by first plotting the returns on an individual security on the vertical axis relative to the returns for the market, which are plotted along the horizontal axis, and then fitting a line through the observations. It displays how the expected return on securities moves with the change on the market return. For example, if the slope coefficient is 0.85, which indicates that if the market return goes up or down by 1.0% we would expect the return on this security to go up or down by 0.85%; that is, it changes by 0.85 of the return on the market.

4. If the market risk premium increases will securities become over or under valued?

If the market risk premium increases, the required return will increase, then the expected return will be less than the required returns, so the securities become overvalued.

9.4 Alternative Asset Pricing Models Concept Review Questions 1. Why is the CAPM called a single-factor model?

The CAPM is what is commonly referred to as a “single-factor” model, since it suggests that the required return on equities is determined by only one risk factor – market risk.

2. Describe some of the criticisms of the CAPM, including Roll’s critique.

It is often criticized since it is developed based on several assumptions, many of which are called into question in the real world. In addition, a substantial amount of empirical evidence has been produced that finds that the CAPM does not holds extremely well in practice. In particular, while empirical estimates of the ex-post SML suggest that it is indeed an upward-sloping straight line, the ex-post y-intercept has been found to be higher than RF, and the slope of the SML is less than that predicted by theory - that is, it is “flatter” than it should have been. Although this research remains very controversial, a 1992 study of U.S. stock returns by Fama and French (1992) concluded that beta, the sole risk factor in the CAPM, possessed no explanatory power for predicting stock returns.

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An important theoretical problem associated with tests of the CAPM was identified by Richard Roll in 1976, and is commonly referred to as Roll’s Critique. He argued that the CAPM cannot be tested empirically since the market portfolio, which consists of all risky assets, is unobservable. Therefore researchers are forced to use market proxies, which may or may not be the optimal mean-variance efficient portfolio. In effect, Roll 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. As a result the empirical tests have no power.

3. Briefly describe the strengths and weaknesses of the Fama-French model and the APT. Strengths of Fama-French model: Fama and French (1992) find that their model does a much better job of explaining common stock returns.

Weaknesses of Fama-French model: It is not based on sound economic fundamentals as is the CAPM. Further, many believe that it is simply an example of data mining, where the data has been examined so many times that eventually some variables are bounds to be discovered that explain returns better than the CAPM. Strengths of APT: The APT holds under very few assumptions, unlike the CAPM. In particular, the APT does not depend on the existence of an underlying market portfolio, and it allows for the possibility that several types of risk may affect security returns. In fact, APT is based simply on the no-arbitrage principle, which states that two otherwise identical assets cannot sell at different prices.

Weaknesses of APT: the factors are not specified ahead of time. In fact, it does not even pre-specify the number of risk factors that exist, or state which factors will be the most important. As a result, these factors, as well as their relative importance must be identified empirically.

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Chapter 10: Market Efficiency Multiple Choice Questions 1. Section: 10.1 Defining Market Efficiency Learning Objective: 10.1 Level of difficulty: Basic Solution: C 2. Section: 10.1 Defining Market Efficiency Learning Objective: 10.1 Level of difficulty: Basic Solution: A 3. Section: 10.1 Defining Market Efficiency Learning Objective: 10.1 Level of difficulty: Basic Solution: C 4. Section: 10.2 The Efficient Market Hypothesis (EMH) Learning Objective: 10.2 Level of difficulty: Basic Solution: C. The three forms of EMH are weak, semi-strong (not semi-weak), and strong.

5. Section: 10.2 The Efficient Market Hypothesis (EMH) Learning Objective: 10.2 Level of difficulty: Medium Solution: C 6. Section: 10.5 Implications of Market Efficiency Learning Objective: 10.5 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 already 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.

7. Section: 10.2 The Efficient Market Hypothesis (EMH) Learning Objective: 10.2 Level of difficulty: Basic Solution: C 8. Section: 10.2 The Efficient Market Hypothesis (EMH) Learning Objective: 10.2 Level of difficulty: Medium

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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. 9. Section: 10.3 Empirical Evidence Regarding Market Efficiency Learning Objective: 10.3 Step 1: Concept of market efficiency Level of difficulty: Medium Solution: C 10. Section: 10.3 Empirical Evidence Regarding Market Efficiency Learning Objective: 10.3 Level of difficulty: Medium Solution: C 11. Section: 10.1 Defining Market Efficiency Learning Objective: 10.1 Level of difficulty: Medium Solution: D 12. Section 10.2 The Efficient Market Hypothesis (EMH) Learning Objective: 10.2 Level of difficulty: Medium Solution: B 13. Section: 10.3 Empirical Evidence Regarding Market Efficiency Learning Objective: 10.3 Level of difficulty: Medium Solution: D 14. Section: 10.3 Empirical Evidence Regarding Market Efficiency Learning Objective: 10.3 Level of difficulty: Medium Solution: D 15. Section: 10.3 Empirical Evidence Regarding Market Efficiency Learning Objective: 10.3 Level of difficulty: Medium Solution: D 16. Section: 10.5 Implications of Market Efficiency Learning Objective: 10.5 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.

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17. Section: 10.3 Empirical Evidence Regarding Market Efficiency Learning Objective: 10.3 Level of difficulty: Difficult Solution: B. Stock returns tend to produce statistically higher returns in January than in the other 11 months of the year. Value stocks have consistently outperformed growth stocks. Small cap stocks tend to outperform large cap stocks.

18. Section: 10.3 Empirical Evidence Regarding Market Efficiency Learning Objective: 10.3 Level of difficulty: Difficult Solution: D. 19. Section: 10.3 Empirical Evidence Regarding Market Efficiency Learning Objective: 10.3 Level of difficulty: Basic 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.

20. Section: 10.4 Behavioural Finance Learning Objective: 10.4 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.

21. Section: 10.4 Behavioural Finance Learning Objective: 10.4 Level of difficulty: Medium Solution: C 22. Section: 10.3 Empirical Evidence Regarding Market Efficiency Learning Objective: 10.3 Level of difficulty: Medium Solution: C Practice Problems Basic 23. Section: 10.1 Defining Market Efficiency Learning Objective: 10.1 Level of difficulty: Basic 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).

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c. This market is likely to suffer from informational inefficiency as the stock prices cannot quickly respond to news due to trading limitations.

24. Section: 10.1 Defining Market Efficiency Learning Objective: 10.1 Level of difficulty: Basic 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.

25. Section: 10.3 Empirical Evidence Regarding Market Efficiency Learning Objective: 10.3 Level of difficulty: Basic 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.

26. Section: 10.1 Defining Market Efficiency Learning Objective: 10.1 Level of difficulty: Basic 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.

27. Section: 10.3 Empirical Evidence Regarding Market Efficiency Learning Objective: 10.3 Level of difficulty: Basic 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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28. Section: 10.5 Implications of Market Efficiency Learning Objective: 10.5 Level of difficulty: Basic 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.

Intermediate 29. Section: 10.3 Empirical Evidence Regarding Market Efficiency Learning Objective: 10.3 Level of difficulty: Intermediate 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.

30. Section: 10.1 Defining Market Efficiency Learning Objective: 10.1 Level of difficulty: Intermediate 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.

31. Section: 10.3 Empirical Evidence Regarding Market Efficiency Learning Objective: 10.3 Level of difficulty: Intermediate Solution: The momentum effect refers to the fact that stocks that have experienced high returns in previous 3- to 12-month periods tend to outperform in the subsequent 3- to 12-month periods.

It contradicts weak form efficiency.

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32. Section: 10.5 Implications of Market Efficiency Learning Objective: 10.5 Level of difficulty: Intermediate 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?

33. Section: 10.5 Implications of Market Efficiency Learning Objective: 10.5 Level of difficulty: Intermediate 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.

34. Section: 10.5 Implications of Market Efficiency Learning Objective: 10.5 Level of difficulty: Intermediate 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.

35. Section: 10.5 Implications of Market Efficiency Learning Objective: 10.5 Level of difficulty: Intermediate 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.

36. Section: 10.4 Behavioural Finance Learning Objective: 10.4 Level of difficulty: Intermediate Loss aversion refers to investors’ unwillingness to place “fair bets.” It implies that investors may engage in suboptimal investing decisions to avoid losses, which they dislike more than they like comparable gains.

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Risk aversion is an underlying assumption of traditional finance. It implies that investors dislike risk but are willing to assume risk if they are adequately compensated in the form of higher expected returns.

Challenging 37. Section: 10.5 Implications of Market Efficiency Learning Objective: 10.5 Level of difficulty: Challenging 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.

38. Section: 10.5 Implications of Market Efficiency Learning Objective: 10.5 Level of difficulty: Challenging 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.

39. Section: 10.5 Implications of Market Efficiency Learning Objective: 10.5 Level of difficulty: Challenging 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.

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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.

40. Section: 10.4 Behavioural Finance Learning Objective: 10.4 Level of difficulty: Challenging 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.

41. Section: 10.4 Behavioural Finance Learning Objective: 10.4 Level of difficulty: Challenging 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.

42. Section: 10.4 Behavioural Finance Learning Objective: 10.4 Level of difficulty: Challenging 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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Answers to Concept Review Questions 10.1 The Defining Market Efficiency Concept Review Questions 1. Define market efficiency in terms of information.

2. Discuss the reasonableness of the assumptions underlying market efficiency.

3. Distinguish from among operational efficiency, informational efficiency, and allocation efficiency.

10.2 The Efficient Market Hypothesis (EMH) Concept Review Questions 1. Explain the efficient market hypothesis (EMH).

The efficient market hypothesis (EMH) asserts that markets are efficient and, therefore, that prices accurately reflect all available information at any given time.

2. Describe the various forms of EMH. Weak form EMH: the theory that security prices fully reflect all market data, which refers to all past price and volume trading information.

Semi-strong form EMH: the theory that all publicly known and available information, including market data, is reflected in security prices.

Strong form EMH: the theory that stock prices fully reflect all information, which includes both public and private information.

10.3 Empirical Evidence Regarding Market Efficiency Concept Review Questions 1. Is the weak form EMH well supported by empirical evidence? Discuss any exceptions.

The weak form EMH is well supported by empirical evidence. Statistics tests, like serial correlation test and runs test, in general supported the return independence. Further, most of the evidence suggests that technical trading rules, on average, have not been able to outperform a simple buy-and-hold strategy, after accounting for risk and trading costs.

Exceptions include over-reaction, momentum, seasonal patterns like January effect, Friday defect, and end-of-month effect.

2. Is the semi-strong form EMH well supported by empirical evidence? Discuss any exceptions.

Most studies support the semi-strong EMH; however, some do not. One approach to test it is event studies, which supports it with the exception of post-earnings-announcement drift. A second general approach to testing semi-strong market efficiency is to examine the performance of investors and see if they are able to use publicly available information to consistently generate abnormal risk-adjusted returns over sustained periods of time. A variety of active strategies have been tested, with most of the results suggesting that such strategies do not outperform a simple buy-and-hold strategy. Perhaps the strongest evidence of semi-strong market efficiency is the

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fact that professional fund managers, with all of their training, expertise, technological capability, and access to data, do not outperform the market on a risk-adjusted basis, on average.

The exception includes some style investments. One of the most important of these exceptions is that “value” stocks have consistently outperformed “growth” stocks. Others include size effect and Value Line rankings.

3. Is the strong form EMH well supported by empirical evidence? Discuss any exceptions.

No. Several studies have found that insiders have consistently earned abnormal returns on their stock transactions, which refutes strong form efficiency. However, some studies have found that insiders perform only slightly better than average. It should be noted that the trading activity of insiders is restricted in order to protect the general investing public. Therefore, their potential to exploit this insider knowledge is quite restricted.

10.4 Behavioural Finance Concept Review Questions 1. Contrast behavioural finance with the traditional view.

Many of the theories and activities in finance are based on what is sometimes called “the traditional view of finance.” This view suggests that investors: i. Consider all available information; ii. Act rationally and do not make systematic errors, either in processing information or in implementing investment decisions; and, iii. Adhere to the basic tenets of modern portfolio theory (MPT), which implies they are risk averse, they diversify, and they consider risk in the context of a well-diversified portfolio.

Contrary to the traditional view of finance, the evidence “reveals repeated patterns of irrationality, inconsistency, and incompetence in the ways human beings arrive at decisions and choices when faced with uncertainty.” Behavioural finance suggests that investors are motivated by numerous “irrational” forces, such as overconfidence and extreme loss aversion. Recognizing these consistent errors in judgement provides us with the opportunity to avoid making such common errors ourselves, and/or to exploit market inefficiencies that present themselves due to the mistakes made by other market participants.

2. Explain why behavioural flaws could result in investors holding portfolios that are not as predicted by modern portfolio theory.

Traditional finance suggests that investors should make their decisions based on their perceived investing needs and their beliefs regarding the appropriateness of market prices. Traditional finance also suggests that investors consider all available information and place the appropriate rational weight on each item, regardless of when information was received. The role of human behaviour usually comes into play at some point during the process. Our list of behavioural investing flaws is far from exhaustive, but it does provide an overview of how psychological elements can affect the implementation of the investment decision. This can lead investors to hold poorly diversified portfolios, either because they hold too many risky securities or because they don’t hold a sufficient number of securities. Clearly, this does not represent rational behaviour.

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3. Explain why behavioural traits can cause asset price bubbles.

Herding Effect: it is indeed difficult to sit and watch as others make fantastic gains on their investments, without feeling you are missing out on a “sure thing.”

Snake Bitten Effect: loss-averse investors are reluctant to invest in anything but the safest investments and are slow to re-enter stock markets.

Investor Over Confidence Effect: Investors tend to weight recent information more heavily than more distant information. Investors tend to focus on information that they consider important, and downplay other pertinent information. They also tend to attribute their investing successes to their ability rather than to market factors they tend to attribute investing failure to factors beyond their control. Overconfidence can lead investors to hold overly risky securities that might produce huge payoffs, which they take credit for, or huge losses, which they can blame on matters beyond their control. It can also lead them to hold poorly diversified portfolios, either because they hold too many risky securities or because they don’t hold a sufficient number of securities.

Anchoring Effect: Investors have a tendency to become emotionally tied to some initial price or perception. Investors are often reluctant to sell investments below their original purchase price, or below some historically higher price (i.e., the price they could have sold it for a month ago).

Mental Accounting Effect: Investors have a process of accounting for individual investments separately. This can cause employ different investing approaches to manage their investments, depending on the source of the money. “Winnings” more aggressively invested than monies earned (this is known as the “house money effect”). This causes them to maintain separate mental accounts—i.e., “speculative” accounts, conservative accounts, and so on. This can lead to poorly diversified portfolios that may not be consistent with investor objectives.

10.5 Implications of Market Efficiency Concept Review Question 1. What are the main implications of the EMH for investors? For corporate officers?

Some of the implications for investors include the following: i) Technical analysis is not likely to be rewarded by substantial abnormal returns, because markets appear to be weak form efficient. ii) Fundamental analysis based on various forms of publicly available information is likely to be unsuccessful at generating abnormal profits, although some opportunities appear to be available. iii) In light of items 1 and 2 above, active trading strategies are unlikely to outperform “passive” portfolio management strategies on a consistent basis. iv) Whether investors decide to pursue a passive or active strategy, it is critical that they focus on the basics of good investing by defining their objectives in terms of expected return and acceptable risk levels, and by maintaining an adequately diversified portfolio.

Two of the most important implications for corporate officers are the following: i) The timing of security issues or repurchases is unimportant in an efficient market because prices will be correct, on average.

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ii) Management should monitor the price of the company’s securities and determine whether price changes reflect new information or short-run momentum and/or overreaction.

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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: Intermediate 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. Choices A, C, and D are true.

2. Section: 11.1 Forward Contracts Learning Objective: 11.1 Level of difficulty: Intermediate Solution: A (1 + kdomestic ) (1 + 0.05) F= 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: Intermediate 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: 11.1 Level of difficulty: Intermediate Solution: C Cost of carry = 1.05/1.04 – 1= 0.96% 5. Section: 11.1 Forward Contracts Learning Objective: 11.1 Level of difficulty: Intermediate 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: Intermediate Solution: D. Short means investors owe something.

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7. Section: 11.1 Forward Contracts Learning Objective: 11.1 Level of difficulty: Intermediate Solution: A. Profit from a long position is positively affected by the spot price.

8. Section: 11.2 Futures Contracts Learning Objective: 11.2 Level of difficulty: Intermediate 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: 11.2 Level of difficulty: Intermediate 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: 11.2 Level of difficulty: Intermediate 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: 11.2 Level of difficulty: Intermediate Solution: A In practice, most of the futures contracts are closed out with an offsetting transaction before the final day of trading.

12. Section: 11.2 Futures Contracts Learning Objective: 11.2 Level of difficulty: Intermediate

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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: 11.2 Level of difficulty: Intermediate 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: 11.2 Level of difficulty: Intermediate 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: 11.2 Level of difficulty: Intermediate Solution: D. Futures on the S&P 500 Index are traded on the Chicago Mercantile Exchange.

16. Section: 11.2 Futures Contracts Learning Objective: 11.2 Level of difficulty: Intermediate 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: 11.3 Level of difficulty: Intermediate Solution: B Net interest rate (ABC) = LIBOR + 9.5% – 9.5% = LIBOR 18. Section 11.3 Swaps Learning Objective: 11.3 Level of difficulty: Challenging Solution: A

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Net interest rate (ABC) = LIBOR (as calculated in Question 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: 11.3 Level of difficulty: Intermediate Solution: C Net cash settlement actually decreases the credit risk of the interest rate swap.

20. Section 11.3 Swaps Learning Objective: 11.3 Level of difficulty: Intermediate Solution: B 21. Section 11.3 Swaps Learning Objective: 11.3 Level of difficulty: Intermediate 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 11.4 Level of difficulty: Intermediate Solution: D. Credit default swaps are traded over the counter.

23. Section 11.5 Forward Interest Rates and Forward Rate Agreements (FRAs) 11.5 Learning Objective 11.5 Level of difficulty: Intermediate Solution: B FRAs are designed to hedge against exposure to interest rates.

Practice Problems Basic 24. Section 11.2 Futures Contracts Learning Objective: 11.2 Level of difficulty: Basic Solution:

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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.

25. Section 11.2 Futures Contracts Learning Objective: 11.2 Level of difficulty: Basic 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.

26. Section 11.3 Swaps Learning Objective: 11.3 Level of difficulty: Basic 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. They can both gain by entering into an interest rate swap.

27. Section 11.4 The Financial Crisis and the Credit Default Swap Market Learning Objective: 11.4 Level of difficulty: Basic 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.

28. Section 11.2 Future Contracts Learning Objective: 11.2 Level of difficulty: Basic Solution: Not necessarily. Although the number of contracts that have been traded have been increasing, the trading activity can consist of a few new contracts and the closing of a larger number of existing contracts. Therefore the number of outstanding contracts at any given time can actually decrease even though the trading volume has increased.

Intermediate 29. Section 11.1 Forward Contracts

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Learning Objective: 11.1 Level of difficulty: Intermediate 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 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, he 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.

30. Section 11.1 Forward Contracts Learning Objective: 11.1 Level of difficulty: Intermediate 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:

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= (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.

Be careful about how the foreign exchange rates are quoted. For example, in the above example, 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 31. Section 11.1 Forward Contracts Learning Objective: 11.1 Level of difficulty: Intermediate Solution:

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A

B

Spot

Cost of carry

$200

(.08* 200 ) + .04 * 200  200 = 12%

$235

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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 $285

19.2766%

2% of spot

.07+.03=10%

$300

7%

3% of spot

400

$400

4%

F = (1+ c)S 285 = (1+ c)* 235 c = 21.2766%

C

S=

F

(1 + c) 300 S= 1.10 S = $272.73

D

$350

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

−1 = 14.2857%

350

(F) To determine the spot price: .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 c=

Cost of carry is ((286.41 x .03) + 5)/ 286.41 = 4.75% (G) To determine interest rate:

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285 = 250 + 250i + 15 i = .08 32. Section 11.1 Forward Contracts Learning Objective: 11.1 Level of difficulty: Intermediate Solution: Compare the costs and benefits of using the spot and forward markets: 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.

33. Section 11.1 Forward Contracts Learning Objective: 11.1 Level of difficulty: Intermediate 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 34. Section 11.1 Forward Contracts Learning Objective: 11.1 Level of difficulty: Intermediate 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) 35. Section 11.1 Forward Contracts Learning Objective: 11.1 Level of difficulty: Intermediate Solution: a. Because the firm has a short position (i.e., short exposure) 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

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Notice that the cost is the same regardless of what the six-month spot rate is— thus, the position is hedged.

36. Section 11.1 Forward Contracts Learning Objective: 11.1 Level of difficulty: Intermediate Solution: a. Because the firm has a long position (i.e., long exposure) 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.

37. Section 11.1 Forward Contracts Learning Objective: 11.1 Level of difficulty: Intermediate Solution: I will receive R3.5 million in one year, so: Borrow the PV of R3.5 million (3.5/ 1.07 = 3.2710) in South Africa (this gives me Rands today) 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.

38. Section 11.2 Futures Contracts Learning Objective: 11.2 Level of difficulty: Intermediate Solution: Forwards Contracts Customized Trading Dealer or OTC Markets Default (credit) risk Important

Futures Standardized Exchanges Unimportant—guaranteed by clearinghouse

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Initial deposit

Not required

Settlement

On maturity date

Initial margin and maintenance margin required Marked to market daily

39. Section 11.2 Futures Contracts Learning Objective: 11.2 Level of difficulty: Intermediate 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.

40. Section 11.2 Futures Contracts Learning Objective: 11.2 Level of difficulty: Intermediate 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

41. Section 11.2 Futures Contracts Learning Objective: 11.2 Level of difficulty: Intermediate Solution: Day 0 1

Spot price 20.00 20.50

Daily profit 0 25,000

Equity position (margin balance) 50,000 75,000

Equity position (margin balance) $30,000 $55,000 $80,000 $50,000 $0 $30,000

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2 3 4 5

20.75 21.00 19.75 19.25

12,500 12,500 -62,500 -25,000

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87,500 100,000 37,500 12,500

42. Section 11.2 Futures Contracts Learning Objective: 11.2 Level of difficulty: Intermediate 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 25,000 12,500 0 62,500 87,500

43. Section 11.2 Future Contracts Learning Objective: 11.2 Level of difficulty: Intermediate Solution:

Day

Spot price

Daily profit (loss)

0 1 2 3 4 5

$100 $92 $95 $103 $90 $100

0 −$8,000 3,000 8,000 -13,000 10,000

44. Section 11.3 Swaps Learning Objective: 11.3 Level of difficulty: Intermediate Solution:

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 2,000 0

Equity position (margin balance) $30,000 $22,500 $25,500 $33,500 $22,500 $32,500

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Start of Period 1 2 3 4

LIBOR % 4% 5% 3% 1%

Floating pay % 3% 3.5% 2.5% 1.5%

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Fixed pay % –3% –3% –3% –3%

Net pay % 0% .5% –.5% –1.5%

Net pay $ $0 $5,000 –$5,000 –$15,000

45. Section 11.4 The Financial Crisis and the Credit Default Swap Market Learning Objective: 11.4 Level of difficulty: Intermediate Solution: There are two big differences between a credit default swap (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.

46. Appendix 11A Learning Objective 11.5 Level of difficulty: Intermediate Solution: 1 year forward rate expected in 1 year

2 years

Implied 1-year forward rate % F2 = F3 =

(1.05)

2

1.03

(1.07 ) (1.05 )

−1 = 7.0388%

3

2

−1 = 11.1150%

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(1.06 )

4

3 years

F4 =

3

−1 = 3.0557%

4 years

F5 =

4

−1 = 1.0935%

5 years

Cannot be determined

(1.07 ) 5 (1.05 ) (1.06 )

47. Appendix 11A Learning Objective 11.5 Level of difficulty: Intermediate Solution: (1 + 2.65%)2 = (1 + 2.10%)  (1 + F1)

F1 = 3.20% (1 + 3.25%)3 = (1 + 2.65%)2 (1 + F 2)

F2 = 4.46% (1 + 3.75%)4 = (1 + 3.25%)3  (1 + F3 )

F3 = 5.26% 48. Section 11.2 Future Contracts Learning Objective: 11.2 Level of difficulty: Intermediate Solution: In the table below, a buy is recorded as a positive number and a sell is recorded as a negative number.

Investor V Investor W Investor X Investor Y Investor Z

Set 1 +10, + 5

Set 2

Set 3

+8, +3

-7 +7, + 1 -1

-10 -5

-8 -3

Set 4 -2

+2, +6 -6

Net +13 +4 -2 -1 -14 +17 - 17

We can see from the net result in the last column that there are a total of 17 contracts long (+13+4 = 17) and 17 contracts short (-2-1-14 = -17). Therefore the open interest at the end of the day is 17 contracts.

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49. Section 11.2 Future Contracts Learning Objective: 11.2 Level of difficulty: Intermediate Solution: Open interest will decrease. These futures traders will want to close out their positions prior to maturity to avoid delivery of, or taking delivery of, the underlying asset. As the question indicates, these traders are only interested in the financial exposure of the underlying asset during the duration of taking a position. There is no interest in actually taking physical delivery of the underlying asset (e.g., speculating on commodity prices without investing the entire capital outlay).

Challenging 50. Section 11.1 Forward Contracts Learning Objective: 11.1 Level of difficulty: Challenging 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 could 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 1.5 million = 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

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would be, then there would be no currency risk (by definition) and hedging is unnecessary.

Hedging decisions are made ex-ante to remove risk.

51. Section 11.1 Forward Contracts Learning Objective: 11.1 Level of difficulty: Challenging 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.

52. Section 11.3 Swaps Learning Objective: 11.3 Level of difficulty: Challenging 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.

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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 swap

Cash flows on floating mortgage

1 2

-$6,000 -$8,000

$0 $2,000

Cash flows if Total cash flows obtained desired (floating + fixed mortgage swap) (no swap) -$6,000 -$7,000 -$6,000 -$7,000

Gain from swap $1,000 $1,000

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$1,000 -$1,000

-$7,000 -$5,000

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-$6,000 -$6,000

-$7,000 -$7,000

$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 creditworthiness) than directly obtaining the desired type of mortgage. Basically, Anthony gave part of his benefits of creditworthiness to Joyce in return for obtaining his desired pattern of cash flows.

53. Section 11.3 Swaps Learning Objective: 11.3 Level of difficulty: Challenging 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 in 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%.

54. Section 11.3 Swaps Learning Objective: 11.3 Level of difficulty: Challenging

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Solution: To deal with this question, CanGold needs to determine its exposures. In one year they will be: Short (owe) €103.5 million Long 1 million ounces of gold Long US$ (after selling gold) To determine the best way of hedging the two risks, we will consider two strategies and see which gives CanGold 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.

55. Section 11.3 Swaps Learning Objective: 11.3 Level of difficulty: Challenging 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 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

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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.

56. Appendix 11A Learning Objective 11.5 Level of difficulty: Challenging 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: 3 (1.10 ) F3 = 2 −1 = 16.2547% (1.07) 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 = .07PA + .07PB +1.07PC  1000   1000  1000  = .07  + .07 +1.07   1.07 2   (1.10 )3   1.05  )    ( = 66.6667 + 61.1407 + 803.9068 = $931.7142 57. Section 11.2 Future Contracts Learning Objective: 11.2 Level of difficulty: Challenging Solution: Longs: 2,000 (new positions) and 8,000 (closing out short positions)

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Shorts: 9,000 (new positions) and 1,000 (closing out long positions) Net new long positions: 2000 - 1,000 = 1,000 Net new short positions: 9,000 - 8,000 = 1,000 The open interest went up by 1,000.

(Note: The buyer or seller does not need to know if the other is entering a new position or closing out an existing position.)

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Answers to Concept Review Questions 11.1 Forward Contracts Concept review questions 1. Why do forward contracts involve credit risk for banks?

The party in a forward contract whose position incurs a loss from a changing spot price may decide to renege on the contract. Credit risk is this risk that a borrower will not repay what is owed or does not have the required payment to fulfil the obligation under the forward contract.

2. When would a speculator assume a long position in a forward contract on an underlying asset?

When would a speculator assume a short position?

In a currency forward contract, if for example, the Canadian dollar is expected to depreciate; a speculator would take a long position on the U.S. dollar so that when the Canadian dollar depreciated, the long position on the U.S. dollar would gain. The speculator would take a short position on the U.S. dollar if the Canadian dollar is expected to appreciate.

3. When would a hedger assume a long position in a forward contract on an underlying asset?

When would a hedger assume a short position?

A Canadian importer of U.S. goods who needs to pay the seller in U.S. dollars has an exposure on the U.S. currency. Being the short in the underlying transaction the importer would hedge this exposure by taking a long position in a forward contract to buy U.S. dollars. That is taking an opposite position so that a loss on the underlying transaction is offset by a gain on the forward contract and vice versa. The hedger would assume the short position in the forward contract if they were exporting to the U.S. and expecting payment in U.S. dollars.

4. What is the relationship among spot rates, forward rates, and the cost of carry?

The spot rate is the current price for immediate delivery while the forward rate is the price set today for future delivery. The cost of carry is the total cost of buying a commodity spot and then carrying it or effecting physical delivery when the forward contract expires.

11.2 Futures Contracts Concept review questions 1. Define initial margin, maintenance margin, margin call, open interest, and notional amount.

Initial margin is a small deposit in a futures contract made by the long and the short positions with the clearinghouse. It is between 2 and 10 percent of the value of the contract.

Maintenance margin is a minimum amount that must be maintained in a margin account, and usually it is 75 percent of the initial margin.

Margin call is a requirement to add money and increase a falling equity position (equivalent to the initial margin) restore the equity to the required minimum level.

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Open interest is the number of futures contracts that are outstanding. The open interest reflects the true amount of futures market activity.

Notional amount is the dollar value of the underlying futures contract.

2. Explain what is meant by “marked to market”.

All futures contracts are marked to market at the end of each trading day and this means all profits and losses on a futures contract are credited to investors’ accounts every day to calculate their equity position in the underlying contracts. Losses reduce a party’s equity position and margin calls are made for the party to pay more money to restore the required minimum equity position.

3. What is basis risk? Why is it important for hedgers?

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. Basis risk is important for hedgers in that if it is considerable in a futures contract, the hedger may have to consider using a forward contract instead of a futures contract to hedge risk because forward contracts can be tailor-made to eliminate this risk, unlike futures contracts which are standardized.

4. Compare and contrast forwards and futures.

Though they are conceptually similar, forwards are customized and therefore offer more flexibility than futures contracts which are standardized. Forwards trade over-the- counter while futures trade on formal exchanges. While forwards involve credit risk, the margin requirement and marking to market eliminate credit risk from futures. There is no margin requirement for forwards. Last, the counter-party in a future is a clearinghouse while in the case of forwards two parties contract with each other and there is no clearinghouse.

11.3 Swaps Concept Review Questions 1. Explain how plain vanilla interest rate swaps are structured and what purpose they serve.

Plain vanilla interest rate swaps serve to convert fixed rate debt into floating rate debt and vice-versa to suit different needs. A borrower who is eligible for a low fixed rate loan but who prefers a floating rate can borrow at the low fixed rate and enter into an interest rate swap as a floating rate payer and that way effectively converts to a floating rate payer.

2. Explain how currency swaps are structured and how they can be used for hedging purposes.

Currency swaps are used to hedge foreign currency risk. A Canadian company owing US $1 million to a bank in the USA faces currency exposure if the Canadian dollar depreciates. To hedge this risk, the company can enter into a currency swap to pay Canadian dollars for US dollars. If the depreciation occurs, the company makes a loss on its US bank payment but gains on the swap.

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3. Why does it make sense that interest rate swaps involve an exchange of net payments, while currency swaps exchange all cash flows?

In an interest rate swap, the payoff or loss is the difference between the fixed rate and the floating rate multiplied by the notional principal. It would be cumbersome if whole amounts had to change hands. On the other hand, in currency swaps, the counter-party is usually not the same party to the transaction that gives rise to currency risk exposure. It follows that all the amounts involved in a currency swap should change hands.

11.4 The Financial Crisis and the Credit Default Swap Market Concept Review Questions 1. Explain the difference between an insurance contract and a credit default swap.

First, the risk attached to regular insurance is essentially random risk depends on factors unique to an individual. In contrast, for a CDS the underlying risk depends on the economy and 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.

2. How and why did AIG fail?

Many CDSs were sold as insurance to cover those exotic financial instruments that created and spread the sub-prime housing crisis. As those mortgage- backed securities and collateralized debt obligations became nearly worthless, suddenly that seemingly low-risk event—an actual bond default—was happening on a daily basis. The banks and hedge funds selling CDSs were no longer taking in free cash; they were having to pay out big money. Most banks, though, were not all that bad off, because they were simultaneously on both sides of the CDS trade. Most banks and hedge funds would buy CDS protection on the one hand and then sell CDS protection to someone else at the same time. When a bond defaulted, the banks might have to pay some money out, but they’d also be getting money back in. They netted out. Everyone that is, except for AIG. AIG was on one side of these trades only: They sold CDSs. They never bought. Once bonds started defaulting, they had to pay out and nobody was paying them. And AIG did not have the cash available to pay out 3. Why would making CDSs an exchange-listed product have avoided the collapse of AIG and averted the 2008–9 financial crisis?

To normalize the risk, there is a push to convert the CDS OTC market into an exchange-listed market, where the protection writers have to post margin—just like a futures contract—to ensure that they can fulfill the contract.

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11A Appendix Forward Interest Rates and Forward Rate Agreements (FRAs) Concept Review Questions 1. Discuss three different strategies you can follow to invest in Canadian securities to obtain a return over a three-year period.

There are many different ways of investing in fixed income securities for a three-year time horizon. Assuming discount bonds so there are no coupons to reinvest, the simplest ways are a) buy a three-year bond, b) buy a short dated bond such as two year bond and then reinvest the proceeds in one year bond, or 3) buy a long dated bond such as a five year bond and sell it after three years.

2. If the yield curve is upward (downward/inverted) where is the market expecting short-term interest rates to go?

Assuming that the unbiased expectations theorem holds such that the forward rate is equal to the expected rate for that period, then an upward (downward) sloping yield curve implies that future interest rates are expected to increase (decrease).

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Chapter 12: Options Multiple Choice Questions 1. Section: 12.1 Call Options Learning Objective: 12.1 Level of Difficulty: Basic 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: Intermediate 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: Intermediate 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: Intermediate 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: Intermediate Solution: D According to put-call parity: C +

X (1 + r)t

= P+S

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We can rewrite it as

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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: Intermediate 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: Intermediate 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 The Black-Scholes Option Pricing Model Learning Objective: 12.4 Level of Difficulty: Intermediate 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: Intermediate 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 Learning Objective: 12.6 Level of Difficulty: Intermediate Solution: C. PU − PD 52 − 45 h= = = 1.75 PU − S 52 − 48 11. Section: Appendix 12A Binomial Option Pricing and Risk-Neutral Probabilities Learning Objective: 12.6 Level of Difficulty: Intermediate 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 Learning Objective: 12.6 Level of Difficulty: Intermediate Solution: B The actual probability of an asset price going up and down is not the risk-neutral probability.

Practice Problems Basic 13. Section: 12.4 The Black-Scholes Option Pricing Model Learning Objective: 12.4 Level of Difficulty: Basic 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.

14. Section: 12.3 Put-Call Parity Learning Objective: 12.3 Level of Difficulty: Basic Solution: Using put-call parity, S = C + PV(X) –P = 10 +50/1.05 – 2 = $55.62 Intermediate

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15. Sections: 12.1 Call Options and 12.2 Put Options Learning Objective: 12.1 and 12.2 Level of Difficulty: Intermediate 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

16. Sections: 12.1 Call Options and 12.2 Put Options Learning Objective: 12.1, and 12.2 Level of Difficulty: Intermediate Solution:

Long or Short Long Short Long Short Long Short Long Short

At expiration Value of Value of Payoff Call or Strike Profit option underlying (intrinsic Put price (loss) today asset value) Call 130 5 155 25 20 Call 130 5 155 -25 (20) Put 130 5 100 30 25 Put 130 5 100 -30 (25) Call 155 5 130 0 (5) Call 155 5 130 0 5 Put 155 5 175 0 (5) Put 155 5 175 0 5

17. Sections: 12.1 Call Options and 12.2 Put Options Learning Objective: 12.1 and 12.2 Level of Difficulty: Intermediate Solution:

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18. Sections: 12.1 Call Options and 12.2 Put Options Learning Objective: 12.1 and 12.2 Level of Difficulty: Intermediate 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.

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19. Section: 12.1 Call Options Learning Objective: 12.1 Level of Difficulty: Intermediate Solution: 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.

20. Sections: 12.1 Call Options and 12.2 Put Options Learning Objective: 12.1 and 12.2 Level of Difficulty: Intermediate Solution: a. The individual securities:

The portfolio:

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b. The individual securities:

The portfolio:

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c. The individual securities:

The portfolio:

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Note: the value of the portfolio is the same as being long a share. d. The individual securities:

The portfolio:

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e. The individual securities and the portfolio:

Note: the portfolio payoff diagram is the same as a put. f. The individual securities and the portfolio:

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Note: the portfolio graph is the same as the payoff diagram for a call.

21. Sections: 12.1 Call Options and 12.2 Put Options Learning Objective: 12.1 and 12.2 Level of Difficulty: Intermediate Solution: 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

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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.

22. Sections: 12.1 Call Options and 12.2 Put Options Learning Objective: 12.1 and 12.2 Level of Difficulty: Intermediate 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.

strategy 1. Buy C1 2. Buy C2 3. Buy C3 4. Buy C4

S*≤40 0 0 0 0

Cash flows at expiration 40<S*≤50 50<S*≤70 70<S*≤80 0 0 S*-70 0 0 0 0 S*-50 S*-50 S*-40 S*-40 S*-40

S*>80 S*-70 S*-80 S*-50 S*-40

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*≤50 S*>50 -60 S* S* C3 0 S*-50 -60-C3

Action Cash flow today Short sell stock 60 Buy 2 calls -2C2 Total cash flow 60-2C2 Profit d.

S* S*-60-C3

2S*-50 2S*-110-C3

Cash flow at expiration S*≤80 S*>80 -S* 0

-S* 2(S*-80)

-S* -S*+60-2C2

S*-160 S*-90-2C2

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Action Buy stock Write 2 calls Total cash flow Profit

Cash today

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flow Cash flow at expiration S*≤40 S*>40 -60 S* S* 2C4 0 2(40-S*)

-60+2C4

S* S*-60+2C4

80-S* 20-S*+2C4

23. Section: 12.1 Call Options Learning Objective: 12.1 Level of Difficulty: Intermediate 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 S*≤X S*>X Cash flow today -S S* S* -C 0 S*-X

24. Section: 12.3 Put-Call Parity Learning Objective: 12.3 Level of Difficulty: Intermediate Solution:

A B C D E F

XCT stock Price of call price 100 25.048 130 30 16.0943 3 22.73 5 95 25 140 25

Price of put 6 4.762 2 5 30 20

Strike price 85 110 16 25 100 141.75

Riskfree rate 5% 5% 6% 10% 0.00% 5%

(A) Solving for the price of the call: C = P +S – PV(X) = 6+100-85/1.05 = 106 – 80.9524 = $25.0476

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(B) Solving for the price of the put: P = C – S + PV(X) = 30 – 130 + (110/1.05) = -100 + 104.762 = $4.762 (C) Solving for the stock price: 16 S = C − P + PV ( X ) = 3 − 2 + = $16.0943 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: 95 = 25 – 30 + 100/(1+r) 100 = 100/(1+r) 1 + r = 100/100 = 1 r = 0% (F) Solving for the strike price: 140 = 25 − 20 + PV ( X ) = 25 − 20 +

X 1.05

X 1.05 X = $141.75

135 =

25. Section: 12.4 The Black-Scholes Option Pricing Model Learning Objective: 12.4 Level of Difficulty: Intermediate Solution: Using Excel to compute N(d1) and N(d2): Call S

X

r

σ

A

100

98

0.02

0.03

B

100

98

0.02

C

100

98

D

100

E

100

d1

N(d1)

d2

N(d2)

Xe-rt

value

1

1.35509

0.912306

1.32509

0.9074294

96.05947

4.063373

0.04

1

1.025068

0.847334

0.985068

0.8377046

96.05947

4.263979

0.03

0.03

1

1.688424

0.954335

1.658424

0.951384

95.103662

4.9534

99

0.02

0.03

1

1.016678

0.845347

0.986678

0.8380997

97.039669

3.205747

98

0.02

0.03

0.3

1.602862

0.945517

1.58643

0.9436791

97.41376

2.62441

t

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F

99

98

0.02

0.03

1

1.020079

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0.846155

0.990079

0.8389323

96.05947

26. Section: 12.3 Put-Call Parity Learning Objective: 12.3 Level of Difficulty: Intermediate Solution: X C+ = P+S (1 + r)T P=C+

X 33 − S; 10 + − 30 = 7.15 T (1.05)4 (1 + r)

7.15≠13, therefore put-call parity does not hold.

According to put-call parity, P = $7.15 27. Section: 12.4 The Black-Scholes Option Pricing Model Learning Objective: 12.4 Level of Difficulty: Intermediate Solution: Using Excel to compute N(d1) and N(d2): LN (S / X ) + (r +  2 / 2)t d1 =

 t

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 28. Section: 12.1 Call Options Learning Objective: 12.1 Level of Difficulty: Intermediate Solution Using Excel premium: Intrinsic value = Premium – Time value = 8.20 – 5.00 = $3.20 29. Section: 12.3 Put-Call Parity Learning Objective: 12.3 Level of Difficulty: Intermediate Solution using the Excel call price: Using put-call parity:

3.181909

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P=C+

X rt

32

− S;8.20 +

e

0.052

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− 36 = $1.1548

e

Note that the risk-free rate used in the Black-Scholes model is continuously compounded.

30. Section: 12.3 Put-Call Parity and 12.4 The Black-Scholes Option Pricing Model Learning Objective: 12.3 and 12.4 Level of Difficulty: Intermediate Solution: Using the Black-Scholes option pricing model: LN (S / X ) + (r +  2 / 2)t LN (45 / 50) + [0.05 + (.5 / 2)].5 = 0.0893 d1 = = 0.7071 .5  t 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 50 𝑃 = 𝐶 − 𝑆 + 𝑃𝑉(𝑋) = 7.49 − 45 +

1.050.5

= 11.29

31. Section: 12.3 Put-Call Parity Learning Objective: 12.3 Level of Difficulty: Intermediate 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.

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Cash flow today

Action Desired cash flows from synthetic call Buy 1/5 stock Borrow 1/5 PV(85) Stock + loan

-20.00 16.19 -3.81

Future value of stock $85 $135 0 $10 17 -17 0

27 -17 10

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).

32. Section: 12.3 Put-Call Parity Learning Objective: 12.3 Level of Difficulty: Intermediate 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.

33. Section: Appendix 12.A Binomial Option Pricing and Risk-Neutral Probabilities Learning Objective: 12.3 and 12.6 Level of Difficulty: Intermediate Solution: a. First we need to determine the hedge ratio:

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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 = $17.50 34. Section: Appendix 12A Binomial Option Pricing and Risk-Neutral Probabilities Learning Objective: 12.6 Level of Difficulty: Intermediate 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

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in the down state.

35. Section: Appendix 12A Binomial Option Pricing and Risk-Neutral Probabilities Learning Objective: 12.6 Level of Difficulty: Intermediate 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.

36. Section: Appendix 12A Binomial Option Pricing and Risk-Neutral Probabilities Learning Objective: 12.6 Level of Difficulty: Intermediate Solution: X = PU −

PU − PD h

= 50 −

50 − 42

= 46

2

37. Section: Appendix 12A Binomial Option Pricing and Risk-Neutral Probabilities Learning Objective: 12.3 and 12.6 Level of Difficulty: Intermediate 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 1 PD  1  55  C = S − = 98 −  = $24.33 h  (1 + r ) 1.875 1.05  h=

And use put-call parity to get the value of the put option

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𝑃 = 𝐶 − 𝑆 + 𝑃𝑉(𝑋) = 24.33 − 98 +

90 = $12.04 1.05

Challenging 38. Sections: 12.1 Call Options and 12.2 Put Options Learning Objective: 12.1 and 12.2 Level of Difficulty: Challenging Solution:

Long or Short A B C D E F G H I J K L M N

Long Long Short Short Long Short Long Long Long Short Short Long Short Short

Value Call Value of Strike of or underlying price option Put asset today Put 90 .05 90 Call 90 2.00 91 Put 90 .05 89 Call 90 .05 91 Call 109 1.00 135 Put 134 2.00 135 Put 35 2.00 105 Call 35 2.00 105 Call 85 13.00 100 Put 85 2.00 100 Call 85 5.00 100 Put 85 2.00 100 Call 110 2.00 110 Put 80 3.00 55

In/Out of the money At In In In In Out Out In In Out In Out At/Out In

Payoff (intrinsic value of option) 0 1 -1 -1 26 0 0 70 15 0 -15 0 0 -25

Profit (loss) -.05 -1 -.95 -.95 25 2 -2 68 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).

39. Sections: 12.1 Call Options and 12.2 Put Options Learning Objective: 12.1 and 12.2 Level of Difficulty: Challenging Solution:

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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.

40. Sections: 12.1 Call Options and 12.2 Put Options Learning Objective: 12.1 and 12.2 Level of Difficulty: Challenging Solution: Since you don’t expect the price to go above $115, you should write a call option with an exercise price of $115 or more and since you don’t expect the price to fall below $105, you should write a put option of $105 or less and earn the premiums.

41. Section: 12.3 Put-Call Parity and 12.4 The Black-Scholes Option Pricing Model Learning Objective: 12.3 and 12.4 Level of Difficulty: Challenging 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 calls. 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.

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b. To determine the value of the call (strike=1,200) 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 (d2 )

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 = 3.789 e. 3x1

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.

42. Section: 12.3 Put-Call Parity Learning Objective: 12.3 Level of Difficulty: Challenging 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

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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 $22.80, which is the maximum I would be willing to pay.

43. Section: 12.3 Put-Call Parity Learning Objective: 12.3 Level of Difficulty: Challenging 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.

44. Section: Appendix 12A Binomial Option Pricing and Risk-Neutral Probabilities Learning Objective: 12.6 Level of Difficulty: Challenging 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

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If we buy the stock, borrow $77.27 and sell 5.25 ($105/$20) 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 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 riskfree portfolio’s price must equal a risk-free asset, independent of risk aversion so we need to use the risk-neutral probabilities.

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Answers to Concept Review Questions 12.1 Call Options Concept Review Questions 1. Explain why the payoff from a call option is non-linear.

The payoff of a call option is max(S-X, 0), where S is the stock price at maturity and X is the strike price. Thus this payoff function is 0 when S<X and S-X when S>=X, which is non-linear.

2. Explain how to estimate the intrinsic value and time value for a call option.

Intrinsic value is a call option’s payoff function at maturity, i.e., max(S-X, 0). The time value of money is the difference between the option premium and the intrinsic value.

3. Briefly describe the main factors that affect a call option’s value, and how they affect the value.

Option prices • Approach their intrinsic value for deep in and deep out of the money calls; • Increase with the price of the underlying asset; • Decrease with a higher strike price; • Increase if the underlying asset is riskier; • Increase as the time to expiration increases; • Decrease as the dividend payments of the underlying asset increase; • Increase as interest rates increase.

12.2 Put Options Concept Review Questions 1. Contrast the payoff from a put option with that from a call option.

A call option’s payoff function is max(S-X, 0) while a put option’s payoff function is max (X-S, 0). Thus call option holders benefit from stock price increases and are protected against stock price decreases. In contrast, put option holder’s benefit from stock price decreases and are protected against stock price increases.

2. Explain how to estimate the intrinsic value and time value for a put option.

The intrinsic value of a put option is max (X-S, 0), which is X-S when S<=X and 0 when S>X. The time value of a put option is the difference between the option premium and the intrinsic value.

3. Briefly describe the main factors that affect a put or a call option’s value, and explain how they affect the value of each.

Asset price, strike price, term to maturity, volatility, interest rates, and dividends affect both call

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options and put options. As shown in Table 12-1, call prices increases with asset price, term to maturity, volatility, and interest rates, and decreases with strike price and dividends. Put prices increases with strike price, term to maturity, volatility, and dividends, and decreases with asset price and interest rates.

12.3 Put-Call Parity Concept Review Questions 1. Illustrate how to combine the four basic option positions to create a variety of net payoff positions.

For one example, a long underlying asset, a long call position, and a short put position have the same payoff as a long forward position. For another example, a long put position and a long underlying asset have the same payoff as a long call position and a deposit of the present value of the strike price.

2. Explain why the put-call parity relationship should hold if markets are efficient.

The put-call parity holds only when the security prices are known to all investors, and they can quickly long and short without transaction cost to explore any arbitrage opportunities. This requires market efficiency.

3. Explain how to synthetically create long and short positions in calls, puts, and the underlying assets using put-call parity.

A long put position and a long underlying asset have the same payoff as a long call position and a deposit of the present value of the strike price.

12.4 The Black Scholes Option Pricing Model Concept Review Questions 1. How can the Black-Scholes equation be used to price options?

The Black-Scholes equation is a simple “plug-in” formula for option pricing, which only needs the input variables of current asset price, strike price, term to maturity, risk-free interest rate, and volatility.

2. What is measured by each of the five Greeks discussed in this section?

Delta is the change in the price of the option for a given change in the price of the underlying asset. Theta is the change in the option value with time. Gamma is the change in delta with respect to a change in the underlying asset. Vega is the change in the option value with respect to a change in the volatility of the underlying asset. Rho is the change in the option value with respect to a change in the interest rate.

12.5 Options Markets

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Concept Review Questions 1. Where are options traded?

Options are either traded over the counter, mainly with the major banks, or on organized exchanges.

2. How are implied volatilities calculated? What information do they provide?

Implied volatilise are calculated using the option pricing model and the market option prices. The implied volatility provides the forward-looking volatilities, which is useful for asset pricing.

3. What real options have you been given over the past year and how valuable were they? What factors do you think influenced your valuation of them?

All the factors that have been presented will have an effect on the value of any option. How the value is affected depends on how the option reacts to the changes in the risk factor.

Appendix 12A Binomial Option Pricing and Risk-Neutral Probabilities Concept Review Questions 1. Explain how to create a risk-free portfolio from the stock and the option’s payoff.

With the binomial model for a call option you determine the payoff from the long position when the stock price falls, since the call is then worthless. For a risk-free payoff this payoff has to be the same as when the stock price rises. So this payoff is set equal to the value of the stock minus the hedge ratio, times the value of the call.

2. What is a hedge ratio?

The hedge ratio is the number of calls that have to be sold to hedge a long position in the stock, such that the portfolio’s payoff is independent of the stock price.

3. Why don’t the probabilities of going up and down affect the options value?

This is because with only two possibilities (up or down) we can create a risk-free hedge and value the option indirectly from the value of the risk-free portfolio and the value of the stock.

4. What are risk-neutral probabilities?

Since we don’t need the probability of the stock going up or down to value it, we can use any probabilities. The best choice, consistent with rational valuation, is to assume the investor is risk neutral so the expected return on the stock is the risk-free rate. The risk neutral probabilities are the probabilities that generate this risk-free return on the stock.

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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: Intermediate 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: Basic 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: Intermediate Solution: B Using a financial calculator (TI BA II Plus): [CF][2nd][CLR WORK] –22,000 [Enter][] 0 [Enter][] 2 [Enter][] 10,200 [Enter][] 5 [Enter][] [NPV][16][Enter] [] [CPT] gives $2,820.00 4. Section: 13.2 Evaluating Investment Alternatives Learning Objective: 13.2 Difficulty: Challenging 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: Challenging Solution: A. Using a financial calculator (TI BA II Plus): Project A: Project B: [CF][2nd][CLR WORK] [CF][2nd][CLR WORK] –5,000 [Enter][] –5,000 [Enter][] 1,500 [Enter][] [] 1,500 [Enter][] [] 4,000 [Enter][] [] 1,500 [Enter][] []

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2,000 [Enter][] [] 4,500 [Enter][] [] [NPV][12][Enter] [] [NPV][12][Enter] [] [CPT] gives $951.62 [CPT] gives $738.09 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 A. 6. Section: 13.2 Evaluating Investment Alternatives Learning Objective: 13.2 Difficulty: Intermediate Solution: C Using a financial calculator (TI BA II Plus): [CF][2nd][CLR WORK] –8,000 [Enter][] 2,000[Enter][] [] 3,000[Enter][] [] 4,000[Enter][] [] 5,000[Enter][] [] [IRR][CPT] gives 22.66% Since 22.66% > 18%, we should accept the project.

7. Section: 13.2 Evaluating Investment Alternatives Learning Objective: 13.2 Difficulty: Intermediate 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: Intermediate 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: Challenging 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: Intermediate Solution: B.

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11. Section 13.5 International Considerations Learning Objective: 13.5 Difficulty: Intermediate 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: Intermediate 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: Intermediate 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: Intermediate Solution: C. MIRR is greater than IRR only when cash flows are reinvested at a higher rate than IRR. Practice Problems Basic 15. Section: 13.2 Evaluating Investment Alternatives Learning Objective: 13.2 Difficulty: Basic 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 13-1) are NPV, IRR, and payback period.

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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.

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: 13.2 Evaluating Investment Alternatives Learning Objective: 13.2 Difficulty: Basic 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.

17. Section: 13.2 Evaluating Investment Alternatives Learning Objective: 13.2 Difficulty: Basic 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.

18. Section: 13.4 Capital Rationing Learning Objective: 13.4 Difficulty: Basic 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.

19. Section: 13.4 Capital Rationing Learning Objective: 13.4 Difficulty: Basic 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 A +C+ D +E → NPV = 5+8+7+3=$23 million Recommendation: invest in projects: A, C, D, and E (maximizes the NPV).

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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.

Intermediate 20. Section: 13.1 Capital Expenditures Learning Objective: 13.1 Difficulty: Intermediate 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 21. Section: 13.2 Evaluating Investment Alternatives Learning Objective: 13.2 Difficulty: Intermediate Solution:

Year 0 1 2 3 4 5

Project A –1,200.00 454.55 826.45 901.58 1,707.53 1,862.76

NPV IRR Payback period Discounted payback period Profitability index

Discounted cash flows Project B Project C Project D Project E Project F Project G –2,400.00 –8,500.00 –5,100.00 –5,300.00 –11,000.00 –3,200.00 1,363.64 1,818.18 4,363.64 2,272.73 2,727.27 1,363.64 991.74 1,652.89 826.45 2,479.34 1,652.89 991.74 225.39 6,010.52 4,507.89 3,756.57 751.31 375.66 341.51 1,366.03 –2,049.04 683.01 1,366.03 0.00 124.18 1,552.30 –2,483.69 1,862.76 1,862.76 0.00

Project A Project B Project C Project D Project E Project F Project G $4,552.87 $646.46 $3,899.92 $65.25 $5,754.42 –$2,639.73 –$468.97 0% 79.40% 24.77% 25.61% 6.34% 47.17% 0% 1.70

1.75

2.56

1.30

1.93

5.00

3.00

1.90

2.20

2.84

1.89

2.15

N/A

N/A

4.79

1.27

1.46

1.01

2.09

0.76

0.85

22. Section: 13.2 Evaluating Investment Alternatives Learning Objective: 13.2 Difficulty: Intermediate Solution:

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a. i. NPV: accept all positive NPV projects → A, B, C, D, and E ii. IRR: accept all projects with IRR > 10% → A, B, C, and E (notice that we should exclude D from the IRR consideration due to the change in signs) iii. Payback period: Accept all projects with payback less than or equal to 2 years → A, B, D, and E iv. Discounted payback period: Accept all projects with discounted payback less than or equal to 2.5 years → A, B, D, and E b. 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.

23. Section: 13.2 Evaluating Investment Alternatives Learning Objective: 13.2 Difficulty: Intermediate Solution: a. i. Take the project with the greatest NPV → E ii. Take the project with the greatest IRR that is greater than 10% (the firm’s cost of capital) and excluding D (due to the change in signs) → A iii. Take the project with the shortest payback period that is less than 2 years (Note: this criteria is arbitrary) → Project D iv. Take the project with the shortest discounted payback period that is less than 2.5 years (Note: this criteria is arbitrary) → Project D v. Take the project with the highest profitability index → Project A b. 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.

24. Section: 13.4 Capital Rationing Learning Objective: 13.4 Difficulty: Intermediate 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

Project D

Project E

Initial investment

-$1,200

-$2,400

-$8,500

-$5,100

-$5,300

IRR NPV

79.40% $4,552.87

24.77% $646.46

25.61% $3,899.92

6.34% $65.25

47.17% $5,754.42

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The investment opportunities available for the $9,000 budget are: C: total NPV = $3,899.92 A+B+D: total NPV = $4,552.87 + $646.46 + $65.25 = $5,264.58 A+B+E: total NPV = $4,552.87 + $646.46 + $5,754.42 = $10,953.75 Recommendation: BigCo should invest in projects A, B, and E as this results in the greatest increase in wealth for the firm (maximizes the NPV).

25. Section: 13.2 Evaluating Investment Alternatives Learning Objective: 13.2 Difficulty: Intermediate 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.

26. Section: 13.2 Evaluating Investment Alternatives Learning Objective: 13.2 Difficulty: Intermediate

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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

Project B

Project C

Incremental cash flows: C–B

-$2,400 1,500 1,200 300 500 200

-$8,500 2,000 2,000 8,000 2,000 2,500

-$6,100 $500 $800 $7,700 $1,500 $2,300

The IRR of the incremental cash flows is: 25.80% To check your result, plot the NPV profiles of the two projects and we can see that the two profiles cross at approximately 25.80% (hard to see exactly on the graph—hence we need the calculation)

27. Section: 13.4 Capital Rationing Learning Objective: 13.4

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Difficulty: Intermediate 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 10% 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.

28. Section: 13.2 Evaluating Investment Alternatives Learning Objective: 13.2 Difficulty: Intermediate 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:

29. Section: 13.2 Evaluating Investment Alternatives Learning Objective: 13.2 Difficulty: Intermediate Solution:

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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. 30. Section: 13.2 Evaluating Investment Alternatives Learning Objective: 13.2 Difficulty: Intermediate 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 = $140 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.

31. Section: 13.2 Evaluating Investment Alternatives Learning Objective: 13.2 Difficulty: Intermediate 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 Daria’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.

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32. Section: 13.2 Evaluating Investment Alternatives Learning Objective: 13.2 Difficulty: Intermediate Solution: The crossover rate is the discount rate that makes the NPVs of both projects the same.

7,800 16,500 6,600 10,200 19,800 5,400 + + + + − 25,000 = − 20,000 2 3 2 1 1 (1 + k) (1 + k ) (1 + k) (1 + k)3 (1 + k) (1 + k)

We can write it in this way to mirror a single project’s cash flows: 2,400 3,300 1,200 + + − 5,000 = 0 2 1 (1 + k) (1 + k)3 (1 + k)

Using a financial calculator (TI BA II Plus): [CF][2nd][CLR WORK] –5,000 [Enter][] 1,200 [Enter][] [] 2,400 [Enter][] [] 3,300 [Enter][] [] [IRR] [CPT] gives 15.2895%.

If you use 15.2895% to calculate NPVs of both projects, you will get the same NPV of $1,319.69.

33. Section: 13.2 Evaluating Investment Alternatives Learning Objective: 13.2 Difficulty: Intermediate Solution: PI = PV (cash inflows)/ PV (cash outflows) NPV = - 12,050 + PV (cash inflows) → PV (cash inflows) = NPV + 12,050 = 5,360 + 12,050 = $17,410 → PI = 17,410/12,050 = 1.44 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.

34. Section: 13.2 Evaluating Investment Alternatives Learning Objective: 13.2 Difficulty: Intermediate Solution: Project A: 2,500 – (800 + 1,200) = 500 500 ÷ 900 = 0.56 Payback period = 2 + 0.56 = 2.56 years.

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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.

35. Section: 13.2 Evaluating Investment Alternatives Learning Objective: 13.2 Difficulty: Intermediate Solution: Projects

Initial CF CF1

CF2

CF3

CF4

A 2,500 discounted CF

800 1,200 714.2857 956.6327

900 2,000 640.6022 1,271.0362

B

750

1,000

discounted CF

3,000

1,500

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.

36. Section: 13.2 Evaluating Investment Alternatives Learning Objective: 13.2 Difficulty: Intermediate 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.

37. Section: 13.2 Evaluating Investment Alternatives Learning Objective: 13.2 Difficulty: Intermediate Solution: Project discount rate (k) = WACC + risk premium = 16.6% + 3.8% = 20.4%

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Using a financial calculator (TI BA II Plus): [CF][2nd][CLR WORK] –60,000 [Enter][] 20,000 [Enter][] [] 22,000 [Enter][] [] –8,000 [Enter][] [] 38,050 [Enter][] [] 55,000 [Enter][] [] 16,000 [Enter][] [] [NPV][20.4][Enter] [] [CPT] gives $12,302.15 Since NPV > 0, SK Inc. should accept the project.

38. Section: 13.2 Evaluating Investment Alternatives Learning Objective: 13.2 Difficulty: Intermediate 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.

39. Section: 13.2 Evaluating Investment Alternatives Learning Objective: 13.2 Difficulty: Intermediate 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

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Since the NPV is higher when selling to your cousin, you should sell the truck to your cousin.

40. Section: 13.2 Evaluating Investment Alternatives Learning Objective: 13.2 Difficulty: Intermediate Solution: NPV = PV of cash inflows – initial cash outflow = 11,400/(.12–.04) – 118,000 = $142,500 – $118,000 = $24,500 41. Section: 13.2 Evaluating Investment Alternatives Learning Objective: 13.2 Difficulty: Intermediate Solution: When the discount rate is zero, the discounted payback period will be equal to the payback period.

42. Section: 13.2 Evaluating Investment Alternatives Learning Objective: 13.2 Difficulty: Intermediate Solution: Discounted Cash Flow Discounted Cash Flow Year (A) (B) 0 -160,000 -110,000 1 27,273 54,545 2 41,322 37,190 3 52,592 22,539 4 61,471 13,660 Project A Payback = 3 + ($160,000-$30,000-$50,000-$70,000)/$90,000 = 3.11 years.

Discounted payback = 3 + ($150,000 – $27,273 – $41,322 – $52,592)/$61,471 = 3.63 years.

Project B Payback = 2.17 years.

Discounted payback = 2 + ($110,000-$54,545-$37,190)/$22,539 = 2.81 years.

Both methods favour project B. 43. Section: 13.2 Evaluating Investment Alternatives Learning Objective: 13.2 Difficulty: Intermediate Solution: Payback = N I0=R*N R= I0/N 44. Section: 13.2 Evaluating Investment Alternatives

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Learning Objective: 13.2 Difficulty: Intermediate Solution: Present value of cash inflows = 1,600/(.1-.03) = $22,857.14 NPV = -24,000 + 22,857.14 = –1,142.86 Since NPV is negative, you should not invest in the project 45. Section: 13.2 Evaluating Investment Alternatives Learning Objective: 13.2 Difficulty: Intermediate 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.

46. Section: 13.3 Independent and Interdependent Projects Learning Objective: 13.3 Difficulty: Intermediate 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.

47. Section: 13.3 Independent and Interdependent Projects Learning Objective: 13.3 Difficulty: Intermediate 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.

48: Section: 13.5 International Considerations Learning Objective: 13.5

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Difficulty: Intermediate 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?

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?

Challenging 49. Section: 13.3 Independent and Interdependent Projects Learning Objective: 13.3 Difficulty: Challenging Solution: a. Project D’s life = 5 years, NPV (using discount rate of 10% given earlier) = $65.25. Project H’s life = 3 years, NPV = $44.70 Annual cash flows Project D Project H Initial investment -$5,100 -3,500 Year 1 4,800 1,800 Year 2 1,000 1,400 Year 3 6,000 1,000 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:

Project H:

The NPV of project H is greater than D, so we would choose H. b.

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Project D’s life = 5 years, NPV (using discount rate of 10% given earlier) = $65.25. Project H’s life = 3 years, NPV = $44.70 Project D: find the annuity of 5 years that has the same PV as the project.

N= 5, PV = 65.25, I=10%, solve for PMT. Annuity = $17.21 Project H: N=3, PV = 44.70, I=10%, solve for PMT. Annuity = $17.97 Choose project H as it has the higher equivalent annual NPV. 50. Section: 13.2 Evaluating Investment Alternatives Learning Objective: 13.2 Difficulty: Challenging 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%.

51. Section: 13.2 Evaluating Investment Alternatives Learning Objective: 13.2 Difficulty: Challenging 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% 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.

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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%.

52. Section: 13.2 Evaluating Investment Alternatives Learning Objective: 13.2 Difficulty: Challenging Solution: a. Required return on the entire company is determined using the beta of the firm: 3.5% + 1.35*6% = 11.60%. 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 MLS and therefore we need to determine the required rate of return for MLS’s assets. Using the comparable firm’s beta of 0.75, we find the required return is 3.5% + 0.75*6% = 8%. As the expected return on the project is 8.80% (=880/10,000), the company should 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.

53. Section: 13.2 Evaluating Investment Alternatives Learning Objective: 13.2 Difficulty: Challenging Solution: re = 3% + 1.6(7%) = 14.2% WACC = 10% (0.6)(1 -.35) + (14.2%) (0.4) = 9.58% Cost of capital (project) = 9.58% (WACC) Using a financial calculator (TI BA II Plus): [CF][2nd][CLR WORK] –125,000 [Enter][] 36,000 [Enter][] 5 [Enter][] [IRR][CPT] gives 13.53% Since 13.53% is greater than 9.58%, the cost of capital of the project, accept the project.

54. Section: 13.2 Evaluating Investment Alternatives Learning Objective: 13.2

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Difficulty: Challenging Solution: CF CF CF1 + (1 + k2)2 + (1 + k3)3 + ... − CF0 NPV = 1 (1 + k ) CF2 CF3 CF1 + 2 + 0= (1 + k ) (1 + k )3 + ... − CF0 − NPV (1 + k )1 Using a financial calculator (TI BA II Plus) to calculate k by using the same method of calculating IRR: –CF0 – NPV= –55,000 – 200,000 = –255,000 and use 255,000 as an” initial investment” [CF][2nd][CLR WORK] –255,000 [Enter][] 40,000 [Enter][] 60,000 [Enter][] [] 80,000 [Enter][] [] 70,000 [Enter][] [] 60,000 [Enter][] [] 50,000 [Enter][] [] [IRR][CPT] gives 10.5612% Therefore, for this project, 10.5612% is actually the cost of capital, k.

To test 10.5612%: CF1 + CF2 + CF3 2 (1 + k )3 + ... − CF0 (1 + k )1 (1 + k ) 40,000 60,000 80,000 70,000 60,000 50,000 = + + + + + − 200,000 3 4 5 1.105612 (1.105612)2 (1.105612) (1.105612) (1.105612) (1.105612)6 = 36,179.06 + 49,084.66 + 59,194.55 + 46,847.57 + 36,319.31 + 27,374.96 − 200,000 = 55,000.11 NPV =

55. Section: 13.2 Evaluating Investment Alternatives Learning Objective: 13.2 Difficulty: Challenging Solution: PVCashInflows PI = PVCashOutflow 20,000 40,000 100,000 = + + = 17,391 + 30,246 + 57,175 = 104,812 PV CashInflows 1.15 1.152 1.154 15,000 + 90,000 = 99,863 PVCahOutflows = 3 1.15 104,812 PI = = 1.05  1 99,863 Accept the project.

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56. Section: 13.2 Evaluating Investment Alternatives Learning Objective: 13.2 Difficulty: Challenging 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.

57. Section: 13.2 Evaluating Investment Alternatives Learning Objective: 13.2 Difficulty: Challenging Solution:

Time 0 1 2 3 4 5 Cash Inflows 5,750 5,750 5,750 5,750 5,750 Initial cost -15,000 Maintenance cost -1,200 -1,200 -1,200 -1,200 -1,200 Net Cash Flows -16,200 4,550 4,550 4,550 4,550 5,750 Discount Factor 1.00 1.10 1.21 1.331 1.4641 1.61051 Present Value -16,200 4,136.36 3,760.33 3,418.48 3,107.71 3,570.30 NPV 1,793.18 58. Section: 13.3 Independent and Interdependent Projects

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Learning Objective: 13.3 Difficulty: Challenging 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: = -400,000 + PV of 5 year annuity of -10,000 at 8% + PV of 10 year annuity of -15,000 at 8 % discounted back another 5 years at 8% = –400,000 – 39,927.10 – 68,501.53 = –$508,428.63 BAII+: using the CF worksheet: CF0 = –400,000 C01 = –10,000 F01 = 5 C02 = –15,000 F02 = 10 NPV → I=8, solve for NPV = –$508,428.63 NPV of PDW581: BAII+: using the CF worksheet: CF0 = –100,000 C01 = –30,000 F01 = 10 NPV → I=8, solve for NPV = –$301,302.44 Approach 1: The Chain Approach: PDX (repeats twice): =–$508,428.63 –$508,428.63/1.0815 =–508,428.63 –160,277.91 =–$668,706.54 PDW (repeats three times): = –$301,302.44 – $301,302.44/1.0810 – $301,302.44/1.0820 = – 301,302.44 – 139,561.33 – 64,643.90 = – $505,507.67

Based on this analysis, we would prefer PDW as its cost is lower.

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Approach 2: Using the EANPV approach: Using the BAII+ for the PDX project: N= 15, I/Y= 8, PV = –$508,428.63solve for PMT. PMT = -$59,399.49 (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= 8, PV = –301,302.44 solve for PMT. PMT = -$44,902.95 (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).

59. Section: 13.3 Independent and Interdependent Projects Learning Objective: 13.3 Difficulty: Challenging Solution: Cost of capital (r) = 4% + 1.25*8% = 14% 9,500   5,500 6,000 −12,095 = 15,853.60 −12,095 = +3,758.60 + + NPV1 =  1 3 2 (1.14) (1.14) (1.14)   3,000   3,450 − 3,080 = 5,334.72 − 3,080 = +2,254.72 NPV2 =  1 + 2 (1.14) (1.14)   Only one of the projects can be chosen.

3,758.60 NPV = 3,758.60 + 1 = 3,758.60 + 2,536.95 = $6,295.55  (1.14)3   2,254.72 2,254.72 NPV = 2,254.72 + + = 2,254.72 + 1,734.93 + 1,334.97 = $5,324.62   (1.14)2 (1.14)4  Using the chain replication approach, project 1 should be chosen.

2

60. Section: 13.3 Independent and Interdependent Projects Learning Objective: 13.3 Difficulty: Challenging Solution: Cost of capital = 4% + 1.25(8%) = 14% 9,500   5,500 6,000 −12,095 = 15,853.60 −12,095 = +3,758.60 + + NPV1 =  1 3 2 (1.14) (1.14) (1.14)   3,000   3,450 − 3,080 = 5,334.72 − 3,080 = +2,254.72 NPV2 =  1 + 2 (1.14) (1.14)   Solving the problem by financial calculator (TI BA II Plus): Project 1: PV = 3,758.6; n = 3; I/Y = 14; Compute PMT = -1,618.95 or, $1,618.95.

Project 2: PV = 2,254.72; n = 2; I/Y = 14; Compute PMT = -1,369.27 or, $1,369.27.

Using EANPV, project 1 should be chosen, which is the same result as Problem 59.

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61. Section: 13.3 Independent and Interdependent Projects Learning Objective: 13.3 Difficulty: Challenging 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: 236.29 236.29  + = 236.29 + 178.67 + 135.10 = $550.06 NPV = 236.29 +   A (1.15)2 (1.15)4   Replicate Project B290.46 twice: NPV = 290.46 + = 290.46 + 190.98 = $481.44  B (1.15)3   NPVA > NPVB, therefore choose Project A. 62. Section: 13.3 Independent and Interdependent Projects Learning Objective: 13.3 Difficulty: Challenging Solution: From Problem 61, we get NPVA = $236.29; NPVB = $290.46 Using a financial calculator (TI BA II Plus): Project A: N = 2, I/Y = 15, PV = -236.29, FV = 0, CPT PMT = 145.35 Project B: N = 3, I/Y = 15, PV = -290.46, FV = 0, CPT PMT = 127.21 PMTA > PMTB, therefore choose Project A. 63. Section: 13.4 Capital Rationing

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Learning Objective: 13.4 Difficulty: Challenging Solution: First calculate each project’s NPV: Project A: [CF][2nd][CLR WORK] –120,000 [Enter][] 90,000 [Enter][][] 90,000 [Enter][][] [NPV][15][Enter][] [CPT] gives $26,313.80 Project B: [CF][2nd][CLR WORK] –100,000 [Enter][] 50,000 [Enter][][] 60,000 [Enter][][] 70,000 [Enter][][] [NPV][15][Enter][] [CPT] gives $34,873.02 Project C: [CF][2nd][CLR WORK] –130,000 [Enter][] 45,000 [Enter][][] 90,000 [Enter][][] 80,000 [Enter][][] [NPV][15][Enter][] [CPT] gives $29,784.66 Combinations A& B A& C B&C

Total budget Total NPV 220,000 61,186.82 250,000 56,098.46 230,000 64,657.68

Within the budget?

Yes Yes Yes

Therefore, SK should choose Projects B and C because the total NPV is the greatest and the total budget is within $250,000.

64: Section: Appendix 13A Modified Internal Rate of Return Learning Objective: 13.6 Difficulty: Challenging 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):

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[CF][2nd][CLR WORK] –20,000 [Enter][] 8,500 [Enter][] [] 6,400 [Enter][] [] 11,200 [Enter][] [] [IRR][CPT] gives 13.8305% IRR assumes that cash flows are reinvested at IRR. b. At an annual interest rate of 4%: cf FV of cf 0 –20,000 1 8,500 9,193.60 2 6,400 6,656.00 3 11,200 11,200 sum of FV 27,049.60 PV = $20,000 FV = $27,049.60 N=3 Solve for I/Y → I/Y = 10.5886 percent So MIRR= 10.5886%. c. At an annual interest rate of 10%: cf FV of cf 0 –20,000 1 8,500 10,285.00 2 6,400 7,040.00 3 11,200 11,200 sum of FV 28,525.00 PV = $20,000 FV = $28,525 N=3 Solve for I/Y → I/Y = 12.5637 percent So MIRR=12.5637%. d. At an annual interest rate of 13.83%: cf FV of cf 0 –20,000 1 8,500 11,013.68 2 6,400 7,285.12 3 11,200 11,200 sum of FV 29,498.80

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PV = $20,000 FV = $29,498.80 N=3 Solve for I/Y → I/Y = 13.8304 percent So MIRR=13.8304%.

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Answers to Concept Review Questions 13.1 Capital Expenditures Concept Review Questions 1. What is the difference between a tangible asset and an intangible asset?

Tangible assets include property, plant and equipment; intangible assets include research and development, copyrights, brand names and franchise agreements. The difference between tangible and intangible assets is simply that tangible represents hard physical assets. DCF capex analysis is similar to valuing common shares is that we need to estimate the timing and size of future cash flows and the appropriate discount rate.

2. What are irrevocable investment decisions? Why are they important for capital budgeting?

A firm’s capital expenditures (capex) usually involve large amounts of money and the decisions are frequently irrevocable. It is therefore important that the decision to make these investments is made on sound financial and economic grounds.

3. Contrast top down and bottom up analysis.

Bottom up analysis is based on the idea that a firm is simply a set of capex decisions.

In contrast, top down analysis focuses on the strategic decisions of which industries or products the firm should be involved in.

4. In what ways is DCF capex analysis similar to valuing common shares, and in what ways is it different?

DCF capex analysis is similar to valuing common shares is that we need to estimate the timing and size of future cash flows and the appropriate discount rate. The only practical difference is that whereas the cash flows are fixed in valuing bonds and shares in the sense that the analyst cannot change them, in making capex decisions the analyst can change the underling cash flows by changing the structure of the project.

13.2 Evaluating Investment Alternatives Concept Review Questions 1. Why is the payback period a poor evaluation technique?

The payback period has some important drawbacks. It disregards the time and risk value of money. In addition, the payback period does not account for the cash flows received after the cutoff date, which could be substantial for some long-lived projects. Finally, the choice of the cutoff date is somewhat arbitrary and may vary from one firm to the next.

2. What discount rate do we use to determine the NPV of a project and why?

We can use the risk-adjusted discount rate (RADR), which is set based on the overall riskiness of the project. The reason is that the required return is based on the assessment of the project risk.

3. Why do we sometimes get multiple IRRs for a project?

If the sign of cash flow changes, we can get multiple IRRs.

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4. What are the reinvestment rate assumptions underlying NPV and IRR? They assume that all cash flows can be reinvested at the same discount rate.

5. What is the crossover rate?

The crossover rate is the discount rate that makes two projects to have the same NPV. 6. Is the PI rule consistent with the NPV rule?

Yes. If PI>1, then NPV>0, and a project will be accepted. If PI<0, then NPV<0, and a project will be rejected.

13.3 Independent and Interdependent Projects Concept Review Questions 1. What is the difference between independent and mutually exclusive projects?

Two or more independent projects are those that have no relationship with one another. This implies that a firm’s decision to accept one project has no impact on a firm’s decision to accept another project that is independent of it. Among mutually exclusive projects, the decision to accept one project excludes other projects.

2. How can we compare two choices, one involving a wooden bridge lasting 10 years and another involving a steel bridge lasting 25 years that costs more?

We can use either the chain replication approach or the equivalent annual NPV approach.

13.4 Capital Rationing Concept Review Questions 1. What complications arise when firms are rationed in terms of their available capital budget?

Theoretically, firms should accept all independent projects that generate positive NPVs, which will enhance firm value. However, in practice, firms often face capital budget constraints, which may force them to turn down attractive projects.

2. Explain how firms should decide which projects to accept and which to reject when capital rationing exists.

First, it only chooses feasible projects under the budget. Second, it chooses projects with positive and the highest NPV. 3. How and why do we adjust the discount rate for multi-divisional firms?

If a project is a typical investment, and will not substantially change the asset mix of the company, then we can use WACC. However, if a company is considering a project that is “atypical” in the sense that it is either more or less risky than the average investment for that company, this fact should be reflected in the discount rate used to evaluate that project.

4. What mistakes can occur if firms do not make the appropriate adjustments?

The firm may accept a project with negative NPV, or reject a project with positive NPV. By using too high of a discount rate, firms will reject projects that should be accepted; thus, will over-allocate capital to risky projects or divisions and under-allocate capital to less risky projects

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and divisions. On the other hand, using too low of a discount rate, the firm will accept projects that should be rejected and the firm will over-allocate capital to low risk projects or divisions and under-allocate capital to riskier projects or divisions.

13.5 International Considerations Concept Review Questions 1. What is so different about evaluating FDI compared to domestic projects?

Some practical difficulties arise when attempting to apply the NPV evaluation process to foreign investments. For example: • • • • •

How do we account for the political risk of expropriation or an insurrection or the imposition of foreign exchange controls so the firm can’t get its investment back?

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 the foreign exchange risk since the 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 they are paid back to Canada they may be taxed again?

How do we finance a foreign project if the local markets are poorly developed?

2. Name some unique risks that may arise when evaluating FDI. • Breach of contract risk • Conversion risk • Expropriation risk (including gradual or creeping expropriation) • Non-payment by a sovereign obligor • Political violence risk • Repossession risk • Transfer risk Appendix 13A The Modified Internal Rate of Return (MIRR) Concept Review Questions 1. What improvement does MIRR represent over traditional IRR? The IRR assumes that all cash flows are invested at the IRR. The problem with this assumption is that the IRR may not be attainable for the reinvestment of the funds. Thus, the MIRR modifies this assumption by calculating the return on the project with a more realistic assumption of reinvesting the cash flows at the required rate of return which is more obtainable and more realistic.

2. When will a calculated MIRR be greater than a calculated IRR? The calculated MIRR will be greater than the calculated IRR if the IRR is less than required rate of return or the risk adjusted required rate of return

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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: Intermediate 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: Intermediate 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: Basic 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: Basic 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: Intermediate Solution: B. R&D costs associated with the project are sunk costs, which should not be considered.

CF0 = C0 + NWC0 + OC = 435,050 – 12,000 + 81,000 + 6,000 = $510,050 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: Basic 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: Intermediate Solution: A CF2 = CFBT2(1 – T) + CCA2(T) = (48,000 – 29,000)(1 – 0.40) + (42,000)(0.40)

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=11,400 + 16,800 = 28,200 8. Section: 14.2 Estimating and Discounting Cash Flows Learning Objective: 14.2 Level of difficulty: Intermediate Solution: C. CFBT1 (1 − T ) CFBT16 (1 − T ) 1 PV (Operating CFs) = −  , 15 k−g k−g (1 + k ) (50,000 − 20,400)(1 − 0.40) (50,000 − 20,400)(1 − 0.40)(1.05)15 1 −  0.15 − 0.05 0.15 − 0.05 (1 + .15)15 17,760 (17,760)(2.078928) = −  (0.122894) = $177,600 − $45,375 = $132,225 0.10 0.10 =

9. Section: 14.2 Estimating and Discounting Cash Flows Learning Objective: 14.2 Level of difficulty: Intermediate Solution: D. An increase in the discount rate, a decrease in the corporate tax rate and 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.

10. Section: 14.2 Estimating and Discounting Cash Flows Learning Objective: 14.2 Level of difficulty: Intermediate Solution: D. A terminal loss occurs when the salvage value is less than the ending UCC for the asset or asset class.

11. Section: 14.2 Estimating and Discounting Cash Flows Learning Objective: 14.2 Level of difficulty: Intermediate Solution: D. ECFn = SVn + NWC n = 11,500 + 2,500 = 14,000 12. Section: 14.2 Estimating and Discounting Cash Flows Learning Objective: 14.2 Level of difficulty: Intermediate Solution: B. ECFn = SVn + NWCn – (SVn – UCCn) × T = 12,000 + 10,000 – (12,000 – 20,408) × 0.35 = $24,942.80 PV(ECFn) = 24,942.80 × 1/(1.12)5 = $14,153.21 13. Section: 14.2 Estimating and Discounting Cash Flows Learning Objective: 14.2 Level of difficulty: Intermediate

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Solution: C. ECFn = SVn + NWCn – (SVn – UCCn) × T = 22,000 + 10,000 – (22,000 – 20,408) × 0.35 = $31,442.80 PV(ECFn) = 31,442.80 × 1/(1.12)5 = $17,841.49 14. Section: 14.4 Sensitivity to Inputs Learning Objective: 14.4 Level of difficulty: Basic 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.

15. Section: 14.3 Replacement Decisions Learning Objective: 14.3 Level of difficulty: Intermediate Solution: B. C 0 = C0New − C0Old = 250,000 − 50,000 = $200,000 CCA1 = d × (1/2)△C0 = 0.30 × (1/2)(200,000) = 30,000 UCC (beginning of year 2) = UCC (beginning of year 1) – CCA1 = 200,000 – 30,000 = 170,000 CCA2 = 170,000×0.30 = 51,000 16. Section: 14.3 Replacement Decisions Learning Objective: 14.3 Level of difficulty: Intermediate 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.

17. Section: 14.5 Inflation and Capital Budgeting Decisions Learning Objective: 14.5 Level of difficulty: Intermediate Solution: B. We need to discount the nominal cash flow by the nominal discount rate, which is $1,050/(1+0.0815) = $970.87 Practice Problems Basic 18. Section: 14.1 General Guidelines for Capital Expenditure Analysis Learning Objective: 14.1 Level of difficulty: Basic 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.

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19. Section: 14.1 General Guidelines for Capital Expenditure Analysis Learning Objective: 14.1 Level of difficulty: Basic 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.

20. Section: 14.1 General Guidelines for Capital Expenditure Analysis Learning Objective: 14.1 Level of difficulty: Basic 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.

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.

21. Section: 14.2 Estimating and Discounting Cash Flows Learning Objective: 14.2 Level of difficulty: Basic Solution: CF0A = C0 + ΔNWC0 + OC = 195,000 + 4,500 + 30,500 + 18,000 = $248,000 CF0B = C0 + ΔNWC0 + OC = 220,500 + 10,000 – 12,000 + 31,500 = $250,000 CF0B > CF0A →project B requires more initial cash flows.

22. Section: 14.2 Estimating and Discounting Cash Flows Learning Objective: 14.2 Level of difficulty: Basic 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.

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23. Section: 14.4 Sensitivity to Inputs Learning Objective: 14.4 Level of difficulty: Basic 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.

24. Section: 14.4 Sensitivity to Inputs Learning Objective: 14.4 Level of difficulty: Basic 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.

Intermediate 25. Section: 14.1 General Guidelines for Capital Expenditure Analysis Learning Objective: 14.1 Level of difficulty: Intermediate 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 expense is a little different from other cash expenses in that it reflects 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

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Total required: $1,350 to satisfy all the providers of capital 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%.)

26. Section: 14.1 General Guidelines for Capital Expenditure Analysis Learning Objective: 14.1 Level of difficulty: Intermediate 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) 27. Section: 14.2 Estimating and Discounting Cash Flows Learning Objective: 14.2 Level of difficulty: Intermediate Solution: For Project A: CFt = CFBTt(1 – T) = $5,000(1 – 24%) = $3,800 1 −1/(1.05)5  PV(Future CFs) = $3,800 *   = $16,452.01 .05   Using a financial calculator (TI BAII Plus) N=5, I/Y=5,PMT=3,800, CPT PV= –16,452.01

A B C D E

Tax rate 24% 43% 36% 50% 15%

Annual CFBT $5,000 $3,000 $8,000 $15,000 $9,000

Discount rate 5% 10% 8% 15% 36%

Project life 5 6 3 4 2

PV(Future CFs) $16,452.01 $7,447.50 $13,194.74 $21,412.34 $9,761.03

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30%

$20,000

Booth, Cleary, Rakita

12%

7

28. Section: 14.2 Estimating and Discounting Cash Flows Learning Objective: 14.2 Level of difficulty: Intermediate Solution: End of year Opening UCC CCA balance 1 $80,000 $12,000 2 $68,000 $20,400 3 $47,600 $14,280 4 $33,320 $9,996

$63,892.59

Closing UCC balance $68,000 $47,600 $33,320 $23,324

29. Section: 14.2 Estimating and Discounting Cash Flows Learning Objective: 14.2 Level of difficulty: Intermediate Solution: Components PV(CCA Tax shields) A B C D E F G

$3,112.44 $2,527.95 $13,830.08 $9,660.53 $14,839.00 $2,770.24 $14,546.42

C0dT d +k 3,360.0000 2,823.5294 14,583.3333 10,384.6154 15,789.4737 3,000.0000 15,187.5000

1+.5k 1+ k

SV0dT d +k

1 (1 + k ) n

0.954545 0.938596 0.976190 0.946429 0.962963 0.934783 0.971698

168.0000 235.2941 729.1667 415.3846 789.4737 120.0000 506.2500

0.564474 0.519369 0.556837 0.403883 0.463193 0.284262 0.417265

30. Section: 14.2 Estimating and Discounting Cash Flows Learning Objective: 14.2 Level of difficulty: Intermediate Solution:

A B C D E F

C0 CCA Tax k Project NWC SV % % % $ $ $ Life 15 35 10 6 16,000 1,000 800 20 40 14 5 12,000 800 1,000 25 35 5 12 50,000 2,000 2,500 20 45 12 8 30,000 1,500 1,200 30 50 8 10 40,000 1,800 2,000 20 35 15 9 15,000 500 600

UCC $ 6,567 4,424 1,848 5,662 1,372 2,265

Asset Class Open Closed Closed Open Closed Open

ECFn $ PV(ECFn) $ 1,800.0 1,016.05 3,169.6 1,646.19 4,271.8 2,378.70 2,700.0 1,090.48 3,486.0 1,614.69 1,100.0 312.69

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10

27

6

15

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90,000 2,500 3,000 19,560 Closed 9,971.2

4,160.63

31. Section: 14.2 Estimating and Discounting Cash Flows Learning Objective: 14.2 Level of difficulty: Intermediate 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.

32. Section: 14.2 Estimating and Discounting Cash Flows Learning Objective: 14.2 Level of difficulty: Intermediate 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) (C0 )(d )(T ) (1+ .5k) (UCCn )(d )(T ) 1 =  −  d +k (1+ k) (d + k) (1+ k) n (SVn −UCCn )(T ) − (1+ k) n =

300,000 0.3 0.4 (1+ 0.5 0.165) 55,000 0.3 0.4 1  −  (35,000 − 55,000)(0.4) − 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 33. Section: 14.2 Estimating and Discounting Cash Flows Learning Objective: 14.2 Level of difficulty: Intermediate

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Solution: a. WACC = (40%)(6%)(1 – 0.4) + (40%)(12%) + (20%)(8%) = 7.84% b. k = 7.84% + 2.5% = 10.34% c.

1  1    1− (1+ k) n  1− (1.1034)8  PV (Operatingcash flows) = CFBT(1− T )    = [215,000(1−.40)]   k   .1034         = (129,000) (5.269529) = $679,769.20

34. Section: 14.2 Estimating and Discounting Cash Flows Learning Objective: 14.2 Level of difficulty: Intermediate Solution: k = rf + β(market risk premium) = 8% + 0.8(5.5%) = 12.4% PV (Operating Re venues) =

Re v1 (1 − T ) k−g

−

Re v9 (1 − T ) k−g

1



(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 ) k−g

−

Cost9 (1 − T )



k−g

1

,

(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 35. Section: 14.2 Estimating and Discounting Cash Flows Learning Objective: 14.2 Level of difficulty: Intermediate Solution: a. Year 1 CCA expense is lower than year 2 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

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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 Challenging 36. Section: 14.2 Estimating and Discounting Cash Flows Learning Objective: 14.2 Level of difficulty: Challenging 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 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.

37. Section: 14.2 Estimating and Discounting Cash Flows Learning Objective: 14.2 Level of difficulty: Challenging Solution: Step 1: initial cash flow = –CF0 = –$48,000 Step 2: PV of after-tax operating cash flow Discount rate = 0.08, payment = $8,500 * (1 – tax rate) = $8,500 * (1 – 0.4), N = 10, and PV = $34,221.42 Step 3: PV of CCA tax shield.

There is no capital gain, capital recapture, or terminal loss.

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Using Equation [14-7], C0dT/(d + k) = 15,157.89, (1 + 0.5k)/(1 + k) = 0.962963, SVdT/(d + k) = 789.47, 1/(1 + k)n = 0.463913, and PV of CCA tax shield = $14,230.81 Step 4: PV of ECF Discount rate = 0.08, future value = salvage value = 2,500 N = 10, and PV = $1,157.98 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 = $1,610.21 This project has a positive NPV. The company should take it.

38. Section: 14.2 Estimating and Discounting Cash Flows Learning Objective: 14.2 Level of difficulty: Challenging 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: Approach 1: (long way) Example (Project A): UCC beg CCA 1 $40,000.00 $2,000.00 2 $38,000.00 $3,800.00 3 $34,200.00 $3,420.00

UCC end $38,000.00 $34,200.00 $30,780.00

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

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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.

39. Section: 14.2 Estimating and Discounting Cash Flows Learning Objective: 14.2 Level of difficulty: Challenging 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

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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.

40. Section: 14.2 Estimating and Discounting Cash Flows Learning Objective: 14.2 Level of difficulty: Challenging 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 = –$120,000.

Step 2: PV of after-tax operating cash flow Discount rate = 0.12, payment = $27,500 * (1 – tax rate) = $27,500 * (1 – 0.40), N = 10, and PV = $93,228.68 Step 3: PV of CCA tax shield.

Using the ending UCC formula above, the ending UCC = $4,116.07 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) = 34,285.71, (1 + 0.5k)/(1 + k) = 0.946429, UCC*dT/(d + k) = 1,176.02, 1/(1 + k)n = 0.321973, (SVn–UCCn)(T)/(1 + k)n = 2,689.63, and PV of CCA tax shield = $29,380.70

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Step 4: PV of ECF Discount rate = 0.12, future value = salvage value = 25,000 N = 10, and PV = $8,049.33 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 = $10,658.71 This project has a positive NPV. The company should take it.

41. Section: 14.2 Estimating and Discounting Cash Flows Learning Objective: 14.2 Level of difficulty: Challenging 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 = –$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

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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.

42. Section: 14.2 Estimating and Discounting Cash Flows Learning Objective: 14.2 Level of difficulty: Challenging 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 = –$16,500 Step 2: PV of after-tax operating cash flow Discount rate = 0.15, payment = $5,000 * (1 – tax rate) = $5,000 * (1 – 0.40), N = 6, and PV = $11,353.45 Step 3: PV of CCA tax shield.

Using the ending UCC formula above, the ending UCC = $4,866.05 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) = 3,771.43, (1 + 0.5k)/(1 + k) = 0.934783, UCC*dT/(d + k) = 1,112.24, 1/(1 + k)n = 0.432328, (SVn – UCCn)(T) /(1 + k)n = –582.09, and PV of CCA tax shield = $3,626.71 Step 4: PV of ECF Discount rate = 0.15, future value = salvage value = 1,500 N = 6, and PV = $648.49 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 = –$871.35

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This project has a negative NPV. The company should not take it.

43. Section: 14.2 Estimating and Discounting Cash Flows Learning Objective: 14.2 Level of difficulty: Challenging 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.

Salary (ugrad Year only) 1 40000 =1+A2 =+(1.05)*B2 =1+A3 =+(1.05)*B3 =1+A4 =+(1.05)*B4 =1+A5 =+(1.05)*B5 =1+A6 =+(1.05)*B6 =1+A7 =+(1.05)*B7 =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

CF (grad school) -8000 -8000 -8000 -8000 100 =+(1.07)*C6 =+(1.07)*C7 =+(1.07)*C8 =+(1.07)*C9 =+(1.07)*C10 =+(1.07)*C11 =+(1.07)*C12 =+(1.07)*C13 =+(1.07)*C14

PV of ugrad option: PV grad option:

=NPV(0.04,B2:B41) =NPV(0.04,C2:C41)

Difference:

=E2-E3

Use solver to determine the starting salary at which you are indifferent between the undergraduate and graduate option:

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You will need to have a starting salary after graduate school of $37,275.73 to be indifferent between grad school or not.

44. Section: 14.2 Estimating and Discounting Cash Flows Learning Objective: 14.2 Level of difficulty: Challenging 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

Net value of owning home:

108458.844 25000 $132,278.21 –$48,819.36

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:

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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

Interest

Mortgage Mortgage balance interest rate per Payment at end of month month

250000

=+D2*G2

=+D2–(C2–E2)

=0.07/12

=C2 =C3

=F2 =F3

=+D3*G3 =+D4*G4

=+D3–(C3–E3) =+D4–(C4–E4)

=G2 =G3

700

=C10

=F10

=1+A11

700

=C11

=F11

=1+A12

700

=C12

=F12

=1+A13

=1.01* B2

=C13

=F13

Month

Rent

1

700

=H2

=1+A2 =1+A3 …….

700 700

=1+A10

…….

=+D11*G1 =+D11–(C11–E11) 1 =+D12*G1 =+D12–(C12–E12) 2 =+D13*G1 =+D13–(C13–E13) 3 =+D14*G1 =+D14–(C14–E14) 4

=G10 =G11 =G12 =G13

Annuity factor

=(1– =D2/I2 1/(1+G2)^(241– A2))/G2

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=1+A60

=1.01* B49

=C60

Booth, Cleary, Rakita

=F60

=+D61*G6 =+D61–(C61–E61) 1

=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 =(1– =0.07/12+((A62 – =D62/I62 1/(1+G62)^(241– A62))/G62 1)/60*0.005)/12 =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.

45. Section: 14.2 Estimating and Discounting Cash Flows Learning Objective: 14.2 Level of difficulty: Challenging Solution: Capital Cost = C0 = $1,800,000 Initial Cash Outlay = CF0 = C0 + ΔNWC0 + OC = 1,800,000 + 150,000 + 0 = $1,950,000 k = rf + β(rm – rf) = 4.5% + 1.25(9.5 – 4.5) = 10.75%  1 5  (1,800,000)(.30)(.40)  .30 +.1075  1+.5(.1075) 1+.1075 − (200,000)(.30)(.40) .30 +.1075   (1.1075)  PV (CCATax Shield) =    = 504,336.03 − 35,348.01 = $468,988.02 ECFn = SVn + NWC n = 200,000 +150,000 = 350,000 ECFn 350,000 = = 210,062.91 PV (ECFn ) = n (1+ k) (1.1075)5

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5 Rev1(1− T )   1+ g    , PV (OperatingRevenues) = 1−  k−g   1+ k   5   = (400,000)(1− 0.40) 1−  1.05  0.1075 − 0.05 1.1075  = $976,702.64     5 Cost1 (1− T )   1+ g    , PV (OperatingCosts) = 1−  k − g   1+ k   = (125,000)(1− 0.40) 1−  1.04 5  0.1075 − 0.04 1.1075  = $299,766.21    

PV(Operating CFs) = $976,702.64 – $299,766.21 = $676,936.43 NPV = PV (Operating CFs) + PV (CCA Tax Shield) + PV (ECFn ) − CF0 = 676,936.43 + 468,988.02 + 210,062.91 − $1,950,000 = −$594,012.64  0 Therefore, Brigid Co. should not accept this project.

46. Section: 14.4 Sensitivity to Inputs Learning Objective: 14.4 Level of difficulty: Challenging Solution: Capital Cost =C = $1,800,000 0 Initial Cash Outlay = CF0 = C0 + ΔNWC0 + OC = 1,800,000 + 150,000 + 0 = $1,950,000 k = rf + β(rm - rf) = 4.5% + 0.8(9.5 – 4.5) = 8.5% 1 10  (1,800,000)(.30)(.40)   (1.085) .30 + .085  1 +1.5(.085) + .085 − (100,000)(.30)(.40) .30 + .085 PV (CCATax Shield) =   = 539,062.78 − 13,785.52 = $525,277.26 ECFn = SVn + NWC n = 100,000 + 150,000 = 250,000 ECFn 250,000 = = 110,571.35 PV (ECFn ) = n (1 + k) (1.085)10 10 Re v1(1 − T )   1 + g    , PV (Operating Re venues) = 1 −  k−g   1 + k   10   (500,000)(1 − 0.40)  1.05  =   = $2,396,259.98 1 −  0.085 − 0.05   1.085  

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10 Cost 1(1 − T )  1 + g    , PV (OperatingCosts) = 1 −  k−g   1 + k   10   (125,000)(1 − 0.40)  1.04  =   = $575,515.90 1 −  0.085 − 0.04 1.085    

PV(Operating CFs) = $2,396,259.98 – $575,515.90 = $1,820,744.08 NPV = PV (Operating CFs) + PV (CCA Tax Shield) + PV (ECFn ) − CF0 = 1,820,744.08 + 525,277.26 + 110,571.35 −1,950,000 = $506,592.69  0 Therefore, Brigid Co. should accept this project.

47. Section: 14.2 Estimating and Discounting Cash Flows Learning Objective: 14.2 Level of difficulty: Challenging 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%.

Year

UCC begin

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)

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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 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 Invest.

X-ray Glasses Lost Saved revenues Prod. costs –220000 –220000 –220000 –220000 –220000

20000 20000 20000 20000 20000

Determining after-tax cash flows:

Year

NonTaxable taxable CCA tax cash cash effects flows 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.

48. Section: 14.2 Estimating and Discounting Cash Flows Learning Objective: 14.2 Level of difficulty: Challenging Solution: Capital Cost = C0 = 60,000 + 1,800 = $61,800 Initial Cash Outlay = CF0 = C0 + NWC 0 + OC = 61,800 + 3,000 + 0 = $64,800.

1 1 −   6  (1 + .12) PV(Future CFt’s) = 9,000   = (9,000)(4.111407) = $37,002.67 .12    

Introduction to Corporate Finance, Fourth Edition

PV (CCA Tax Shield) = =

Booth, Cleary, Rakita

(C0 )(d )(T ) (1 + .5k ) (UCCn )(d )(T ) (SVn − UCCn )(T ) 1  −  − n d+k (1 + k) (d + k) (1 + k ) (1 + k) n (61,800)(.30)(.40) (1 + 0.5  0.12) (10,469)(.30)(.40) 1  −  .30 + .12 .30 + .12 (1.12) (1.12)6

(5,000 −10,469)(.40) (1.12)6 = 16,711.22 − 1,515.41 + 1,108.31 = $16,304.12 ECFn = SVn + NWCn = 5,000 + 3,000 = $8,000 −

−

Note: Capital gains are not possible because SV < C0.

NPV = PV (Operating CFs) + PV (CCA Tax Shield) + PV (ECFn ) PV (CapitalGainsTaxes Paid) − CF0 8,000 = 37,002.67 + 16,304.12 + + 0 – 64,800 (1 + .12)6 = – $7,440.16 Since NPV < 0, GG Inc. should reject the project.

49. Section: 14.2 Estimating and Discounting Cash Flows Learning Objective: 14.2 Level of difficulty: Challenging Solution: Capital Cost = C0 = 60,000 + 1,800 = $61,800 Initial Cash Outlay = CF0 = C0 + NWC 0 + OC = 61,800 + 3,000 + 0 = $64,800.

PV (Operatingcash flows) 1  1 − = CFBT(1 − T )   (1 + k ) n   k   

1  1 − = [(70,000 − 40,000)(1 − .40)]  (1.12)6   .12     = (18,000)  (4.111407) = $74,005.33 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:

Introduction to Corporate Finance, Fourth Edition

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(C0 )(d )(T ) (1 + .5k) (SVn )(d )(T ) 1  −  d +k (1 + k ) (d + k ) (1 + k) n (61,800)(.30)(.40) (1 + .5 .12) (5,000)(.30)(.40) 1 =  −  .30 + .12 1 + .12 .30 + .12 (1.12)6

PV (CCA Tax Shield) =

= 16,711.22 − 723.76 = $15,987.46 ECFn = SVn + NWCn = 5,000 + 3,000 = $8,000 8,000 = $4,053.05 PV (ECFn ) = (1.12)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 = 74,005.33 + 15,987.46 + 4,053.05 − 64,800 = $29,245.84 Therefore, GG Inc. should go ahead with this project.

50. Section: 14.2 Estimating and Discounting Cash Flows Learning Objective: 14.2 Level of difficulty: Challenging Solution: C0 = $61,800; CF0 = $64,800; (as in Problem 48) PV (Operatingcash flows) 1  1 − = CFBT(1 − T )   (1 + k ) n   k   

1  1 − = [(70,000 − 40,000)(1 − .40)]  (1.12)6   .12     = (18,000)  (4.111407) = $74,005.33 Since the asset class is closed, we use Equation 14-8 to estimate the present value of the CCA tax shield:

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(C0 )(d )(T ) (1 + .5k ) (UCCn )(d )(T ) 1  −  d+k (1 + k ) (d + k ) (1 + k )n (SVn − UCCn )(T ) − (1 + k )n (61,800)(.30)(.40) (1 + 0.5  0.12) (10,469)(.30)(.40) 1 (5,000 − 10,469)(.40) =  −  − .30 + .12 .30 + .12 (1.12) (1.12)6 (1.12)6

PV (CCA Tax Shield) =



= 16,711.22 − 1,515.41 + 1,108.31 = $16,304.12 ECFn = SVn + NWCn = 5,000 + 3,000 = $8,000 8,000 PV (ECFn ) = = $4,053.05 (1.12)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 = 74,005.33 + 16,304.12 + 4,053.05 − 64,800 = $29,562.50 Therefore, GG Inc. should go ahead with this project.

51. Section: 14.2 Estimating and Discounting Cash Flows Learning Objective: 14.2 Level of difficulty: Challenging Solution: k = rf + β(market risk premium) = 3.4% + 1.2 (5.5%) = 10% Capital Cost = C0 = 60,000 + 1,800 = $61,800 Initial Cash Outlay = CF0 = C0 + NWC 0 + OC = 61,800 + 3,000 + 0 = $64,800.

PV (Operatingcash flows) 1  1−  = CFBT(1− T )   (1+ k) n   k    1− 1   6 = [(70,000 − 40,000)(1− .40)]  (1.10)  .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:

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(C0 )(d )(T ) (1 + .5k) (SVn )(d )(T ) 1  −  d +k (1 + k ) (d + k ) (1 + k) n (61,800)(.30)(.40) (1 + .5 .10) (5,000)(.30)(.40) 1 =  −  .30 + .10 1 + .10 .30 + .10 (1.10)6

PV (CCA Tax Shield) =

= 17,697.27 − 846.71 = $16,850.56 ECFn = SVn + NWCn = 5,000 + 3,000 = $8,000 8,000 = $4,515.79 PV (ECFn ) = (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 + 16,850.56 + 4,515.79 − 64,800 = $34,961.35 Therefore, GG Inc. should go ahead with this project. Δ%NPV =

34,961.05

−1 = 19.54% (Δk = 10% - 12% = -2%)

29,245.85

52. Section: 14.4 Sensitivity to Inputs Learning Objective: 14.4 Level of difficulty: Challenging Solution: Initial Cash Outlay = CF0 = $64,800. 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) = =

(C0 )(d )(T ) (1 + .5k ) (UCCn )(d )(T ) (SVn − UCCn )(T ) 1  −  − n d+k (1 + k) (d + k) (1 + k ) (1 + k) n (61,800)(.30)(.40) (1 + 0.5  0.12) (10,469)(.30)(.40) 1  −  .30 + .12 .30 + .12 (1.12) (1.12)6

(5,000 −10,469)(.40) (1.12)6 = 16,711.22 − 1,515.41 + 1,108.31 = $16,304.12 ECFn = SVn + NWCn = 5,000 + 3,000 = $8,000 8,000 PV (ECFn ) = = $4,053.05 (1.12)6 −

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0 = NPV = PV (Operating CFs) + PV (CCA Tax Shield) + PV (ECFn ) − CF0 = PV (Operating CFs) + 16,304.12 + 4,053.05 − 64,800 PV (Operating CFs) = 44,442.83

1  1 − PV (Operatingcash flows) = [Break − even Operating CF ]   (1.12)6   .12    44,442.83= (Break − even Operating CF )  (4.111407) Break − even Operating CF = $10,809.64 53. Section: 14.4 Sensitivity to Inputs Learning Objective: 14.4 Level of difficulty: Challenging Solution: a.

Year 0 1 2 3 4

Cash flow

UCC (open)

-$2,500.00 $700.00 2,500 $735.00 2,375 $771.75 2,137.50 $810.34 1,923.75

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

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

–2,500

–2,500

–2,500

–2,500

–2,500

–2,500

–2,500

–2,500

–2,500

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1 2 3 4

300.00 306.00 312.12 318.36

256.25 288.88 287.53 286.87

NPV

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239.49 700.00 252.32 735.00 234.71 771.75 218.85 810.34 – $1,554.63

556.25 610.63 632.25 655.85

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

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

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

D

Year

CCA

Cash flow

Growth 48 rate 49 50 51 52 53 54 55

Year 1 cash flow 0 1 125 2 237.5 3 213.75 4 192.375 NPV

E 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)

54. Section: 14.4 Sensitivity to Inputs Learning Objective: 14.4 Level of difficulty: Challenging

–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)

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Solution: a. The NPV of the terrestrial alternative: NPV = $155.7798 million NPV (Terrestrial)

1  1 − = CFBT(1 − T )   (1 + k ) n   k    1   1 −  (1.18)12  = [(50,000,000)(1 − .35)]    = $155,779,808 .18     b. Expected NPV of the satellite alternative: Forecasted cash flows if satellite successful: 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

400.000 340.000 238.000 166.600 116.620 81.634 57.144 40.001 28.000 19.600 13.720 9.604

UCC end

60.000 102.000 71.4000 49.980 34.986 24.490 17.143 12.000 8.400 5.880 4.116 2.881

340.000 238.000 166.600 116.620 81.634 57.144 40.001 28.000 19.600 13.720 9.604 6.723

Investment Revenue: -400 -5

After tax -400 21.000 30.7000 -25 8.740 -25 1.243 -25 -4.005 150 106.072 150 103.500 150 101.700 150 100.440 150 99.558 150 98.941 150 98.508

NPV = -185.90 using 18% discount rate.

CCA terminal loss is $6.723 million.

PV of CCA terminal loss = $6.723(35%)*1/(1.18)12 = 0.32288 million.

The NPV of the successful launch: PV of after-tax cash flow + PV of CCA terminal loss = –$185.90 million +$0.32288 million = –$185.58 million c. If the satellite explodes: Satellite explodes

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Year

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UCC beg 0 1 2

CCA UCC end Investment Revenue: After tax –400 –400 400 60 340 21 340 102 238 –5 30.7

CCA terminal loss is UCC end at year 2, which is $238 million.

PV of CCA terminal loss = 238(35%)*1/(1.18)2 = $59.825million NPV = PV of after tax cash flow + PV of CCA terminal loss = –360.155 + 59.825 = –$300.33 million d. The expected NPV for the satellite = .3*(–300.33) + .7*(–185.58) = –$220 million Based on the above analysis, I do not recommend that AK 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.

55. Section: 14.4 Sensitivity to Inputs Learning Objective: 14.4 Level of difficulty: Challenging 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.iii.

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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

Portfolio 2: Action

Buy .9231m oz gold Borrowing pv 184.6154

Cash flow today

Cash flow in future

–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.

56. Section: 14.3 Replacement Decisions Learning Objective: 14.3 Level of difficulty: Challenging

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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 57. Section: 14.3 Replacement Decisions Learning Objective: 14.3 Level of difficulty: Challenging 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).

New machine CCA schedule UCC Year CCA begin 0 1 2 3 4 5

25000 2500 22500 4500 18000 3600 14400 2880 11520 2304

Old machine

New machine

Incremental after-tax CF

UCC Rev. Maint. Invest/Rev. Maint. New - Old end 22500 1500 18000 1500 14400 1500 11520 1500 9216 1500

3000 3500 4000 4500 5000

–25000 6,000 6,000 6,000 6,000 6,000

500 500 500 500 500

–25000 4620 4950 5280 5610 5940

CCA Tax shield 850 1530 1224 979.2 783.36

Total –25000 5470 6480 6504 6589.20 6723.36

The cash flows are given as nominal values so we need to use the appropriate nominal discount rate: the approximation is 5% + 3% = 8%. The more exact value for the nominal rate would be 1.05 * 1.03 – 1 = 8.15%

PV of incremental cash flows + PV of salvage value of new machine + PV of CCA terminal loss

k=8.15% 25,100.18 3,379.38 968.83

k=8% 25,202.52 3,402.92 975.58

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– Cost of the new machine NPV of replacing old machine

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25,000.00 $4,448.39

25,000.00 $4,581.01

Based on the analysis above, the old machine should be replaced.

58. Section: 14.3 Replacement Decisions Learning Objective: 14.3 Level of difficulty: Challenging Solution:New C = C − COld = 100,000 − 50,000 = $50,000 0

0

0

CF0 = C0 + NWC0 + OC = 50,000 + 4,000 + 0 = $54,000 Δ CFBT =10,000 – 6,000 = $4,000 1  1 − PV (Operating CFs) = (CFBT)(1 − T ) (1 + k ) n   k    1  1 − 5 = (4,000)(1 − .40) (1.15) = (4,000)(.60)(3.352155) = $8,045  .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 (C0 )(d )(T ) (1 + .5k) (SVn )(d )(T ) 1 PV (CCA Tax Shield) =  −  d +k (1 + k) (d + k) (1 + k)n (50,000)(.30)(.40) 1 5    (1.15) .30 + .15  1 +1.5(.15) + .15  − (20,000)(.30)(.40) .30 + .15 =    = 12,464 − 2,652 = $9,812 ECFn = SVn + NWCn = 20,000 + 4,000 = 24,000 ECFn 24,000 PV (ECF ) = = = $11,932 n n 5 (1+ k) (1.15) NPV = PV ( Operating CFs) + PV (CCA Tax Shield ) + PV (ECFn ) − CF0 . = 8,045 + 9,812 + 11,932 – 54,000 = –$24,211 Therefore, GG Inc. should not go ahead with this replacement project.

59. Section: 14.5 Inflation and Capital budgeting Decisions Learning Objective: 14.5 Level of difficulty: Challenging a.

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NPV = −15, 000 +

10, 000*3*(1− .30) .08 −.05

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= $685, 000

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) .08 − (.05 +.02)

= $2, 085, 000

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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Answers to Concept Review Questions 14.1 General Guidelines for Capital Expenditure Analysis Concept review questions 1. How should we treat taxes and inflation when determining the present value of future cash flows?

We should use after-tax items only. We should treat inflation consistently: discount nominal cash flows with nominal discount rates, and real cash flows with real discount rates.

2. What do we mean by incremental cash flows?

Incremental cash flows are the changes in the cash flows that result from the investment in the capital project. The NPV analysis considers the additional investment the firm is making and the resulting changes (both increases and decrease) in the cash flows for the duration of the project.

3. What are externalities and opportunity costs?

Externalities are the consequences that often result from an investment that may benefit or harm unrelated third parties. The new product line may create health problems for local residents; however, the cost of their health problems is not a consideration for the project.

Opportunity costs represent cash flows that must be forgone as a result of an investment decision.

For example, a new production line will require a building that could be sold. As a result of using the building, the firm has foregone the opportunity to sell the property. The current market value of the property must be considered in the investment decision.

4. Why do we not deduct interest costs from the cash flows to be discounted?

We do not deduct associated interest and dividend payments in estimated project cash flows, because they should already be accounted for in the discount rate (i.e., the appropriate cost of capital). This is why we discount with the weighted average cost of capital (WACC), where all the financing costs are captured in the discount rate.

14.2 Estimating and Discounting Cash Flows Concept review questions 1. Why does the initial cash outlay often exceed the purchase price of an asset?

Initial cash outlay includes the purchase price of an asset, the change in net working capital requirements, and the opportunity costs associated with the project.

2. How do taxes affect the annual cash flows and terminal cash flows of an investment project?

The annual cash flows are those that are estimated to occur as a result of the investment decision.

These cash flows comprise the associated expected incremental increase in after-tax operating cash flow, as well as any incremental tax savings (or additional taxes paid) that result from the initial investment outlay. The terminal cash flow is the total cash flow that is expected to be generated in the terminal year of a project, aside from that year’s expected after-tax cash flow.

Capital gain is taxable, but capital loss is not tax deductible. CCA recapture is taxable, and terminal loss is tax deductible.

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3. Explain why the valuation by components approach can save computational time and still lead to the correct answer.

The components approach considers all the cash flows from CCA: the annual CCA tax and the CCA adjustment when an asset class is terminated. Thus it leads to the correct answer. Once the input variables are known, one single formula can give the valuation. Thus computational time is saved.

14.3 Replacement Decisions Concept review questions 1. Discuss any differences in the evaluation of a replacement decision versus the evaluation of an expansion decision.

The incremental cash flows are different. For expansion decisions, the new cash flows arise from the investment decision. For replacement projects, the incremental cash flow is the difference between the new and old projects.

14.4 Sensitivity to Inputs Concept review questions 1. What insights can be gained by using sensitivity analysis, scenario analysis, and NPV breakeven analysis?

Sensitivity analysis shows the sensitivity of NPV to one input variable, scenario analysis shows the change of NPV with respect to the changes of several variables, and NPV break-even analysis gives the level of input that makes NPV 0.

2. What limitations of scenario analysis does the real option valuation approach address?

Scenario analysis assumes that a firm’s action is fixed in a scenario. However, in practice, firms respond to changing circumstances. Real option valuation (ROV), takes into account that the firm responds to different circumstances and changes its operating characteristics.

14.5 Inflation and Capital Budgeting Decisions Concept review questions 1. Why is it usually more precise to use nominal cash flows and nominal discount rates when evaluating projects?

One difficulty with real items is that the CCA tax savings estimates represent the actual amount of CCA that can be charged in a given year. Thus it is more precise to work with nominal items.

2. Why might inflation affect cash inflows differently from the way it would affect cash outflows?

The reason is that inflation affects sales, expenses, and discount rate differently. Much depends on the industry they are in and on the products they sell.

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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: Intermediate 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: Intermediate 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: Intermediate 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: Intermediate 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: Intermediate 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: Intermediate 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: Intermediate 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: Basic 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: Intermediate 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: Intermediate 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: Intermediate 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: Intermediate Solution: A Market value of the equity = P/E0 × E0 = P/E0 × E1/(1 + g) = 14.5 × 550,000/(1.05) = $7,595,238.10 13. Section: 15.5 Valuation Issues Learning Objective: 15.5 Level of difficulty: Basic Solution: B

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The cash flows used in the DCF valuation approach will be the company’s free cash flow.

According to the discount rate you use, you could use free cash flow to the firm (use WACC) or free cash flow to equity holders (use cost of the equity).

14. Section: 15.5 Valuation Issues Learning Objective: 15.5 Level of difficulty: Intermediate Solution: B Liquidation value equals liquidation value of current assets plus market value of tangible assets minus the value of liabilities.

Practice Problems Basic 15. Section: 15.1 Types of Takeovers Learning Objective: 15.1 Level of difficulty: Basic 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: 15.3 Friendly versus Hostile Takeovers Learning Objective: 15.3 Level of difficulty: Basic Solution: Total shares Mr. tendered by VanDuun’s Vendall tendered shareholders shares 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

17. Section: 15.3 Friendly versus Hostile Takeovers Learning Objective: 15.3 Level of difficulty: Basic Solution: Friendly acquisition: 1) At first, the acquirer can approach the target, or the target can post an offering memorandum if it decides to sell itself.

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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.

18. Section: 15.3 Friendly versus Hostile Takeovers Learning Objective: 15.3 Level of difficulty: Basic 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 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 the 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.

19. Section: 15.3 Friendly versus Hostile Takeovers Learning Objective: 15.3 Level of difficulty: Basic 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.

20. Section: 15.4 Motivations for Mergers and Acquisitions Learning Objective: 15.4 Level of difficulty: Basic 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

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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.

21. Section: 15.4 Motivations for Mergers and Acquisitions Learning Objective: 15.4 Level of difficulty: Basic 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.

22. Section: 15.4 Motivations for Mergers and Acquisitions Learning Objective: 15.4 Level of difficulty: Basic Solution: Financing synergies of M&A: 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.

23. Section: 15.4 Motivations for Mergers and Acquisitions Learning Objective: 15.4 Level of difficulty: Basic 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

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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.

24. Section: 15.6 Accounting for Acquisitions Learning Objective: 15.6 Level of difficulty: Basic 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 at the acquisition date.

Goodwill will result if the purchase price exceeds the FMV of the target firm’s equity.

Intermediate 25. Section: 15.2 Securities Legislation Learning Objective: 15.2 Level of difficulty: Intermediate 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% 26. Sections: 15.2 Securities Legislation and 15.4 Motivations for Mergers and Acquisitions Learning Objective: 15.2 and 15.4 Level of difficulty: Intermediate 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.

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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.

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.

27. Section: 15.6 Accounting for Acquisitions Learning Objective: 15.6 Level of difficulty: Intermediate Solution: Goodwill = Price paid – MV of Target’s equity = Price paid – (MV of target’s assets –MV of target’s liabilities) = 1,500– (2,000– 1,250) = 1,500 – 750 = 750 Challenging 28. Section: 15.4 Motivations for Mergers and Acquisitions Learning Objective: 15.4 Level of difficulty: Challenging Solution: a. i) The current price of the target is $22 per share.

The bidder is offering 2 shares valued at $16 for a total of $32.

The offer premium is $32/$22 – 1 = 1.45 – 1 = 0.45 or 45% 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

$16

$32

$32 – $22 = $10

2(16 – 16) = $0

$10

$32

$64

$64 – $22 = $42

2(16 – 32) = –$32

$10

$5

$10

$10 – $22 = –$12

2(16 – 5) = $22

$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.

29. 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

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Level of difficulty: Challenging 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 • 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.

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Use the following information to answer practice problems 30 to 34.

Sales Cost of goods sold Depreciation Interest Income tax Dividends Common shares outstanding P/EBITDA

$1,750,000 450,000 400,000 150,000 275,000 300,000 500,000 10x

30. Section: 15.5 Valuation Issues Learning Objective: 15.5 Level of difficulty: Challenging Solution: EBITDA = 1,750,000 – 350,000 = 1,400,000 P = 10 × (1,400,000)/500,000) = $28.00 31. Section: 15.5 Valuation Issues Learning Objective: 15.5 Level of difficulty: Challenging Solution: Assume g = 6% NI = 1,750,000 – 450,000 – 400,000 – 150,000 – 275,000 = 475,000 EPS0 = 475,000/500,000 = 0.95 Trailing P/E: P/E0 = 28/0.95 = 29.5 times EPS1 = 0.95 × 1.06 = 1.007 Forward P/E: P/E1 = 28/1.007 = 27.8 times 32. Section: 15.5 Valuation Issues Learning Objective: 15.5 Level of difficulty: Challenging Solution: k = RF +β (market risk premium) = 3.5 + 1.12 (5) = 9.1% payout = dividends/NI = 300,000/475,000 = 0.6316 P/E1 = payout / (k – g) = 0.6316/(9.1% – 6%) = 20.37X P/E0 = P/E1 (1 + g) = 20.37(1.06) = 21.6X 33. Section: 15.5 Valuation Issues Learning Objective: 15.5 Level of difficulty: Challenging Solution: Free cash flow to equity (FCFE0) = NI + Depreciation – Δ CA + Δ CL – Capital Expenditures 475,000 + 400,000 – 400,000 + 300,000 –100,000 = 675,000

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Equity = E = FCFE1 = 675,000(1.06) = 715,500 = $23,080,645 0 k−g .091− .06 0.031 Value of the firm = Market value of (equity + debt) = 23,080,645 + 1,000,000 = $24,080,645 34. Section: 15.5 Valuation IssuesLearning Objective: 15.5 Level of difficulty: Challenging Solution: k = 8%; FCFE1 = $675,000(1.08) = 729,000; FCFE2 = $729,000(1.08) = 787,320; FCFE3 = $787320 (1.05) = 826,686 CF3 = (826,686) = $27,556,200 V2 = k−g .08 − .05 k=9.1% (from cost of equity in Q32) 729,000 787,320 27,556,200 V0 = + + (1.091) (1.091)2 (1.091)2 = 668,194 + 661,457 + 23,151,004 = $24,480,655 Value of the firm = Market value of (equity + debt) = 24,480,655 + 1,000,000 = $25,480,655 35. Section: 15.5 Valuation Issues Learning Objective: 15.5 Level of difficulty: Challenging Solution: (i) Cash: The cost is $24 × 500,000 = $12,000,000 Purchasing DEF by cash would generate an NPV of $25,875,000 – $12,000,000 = +$13,875,000. (ii) Post-merger value of ABC-DEF = Value of ABC + Value of DEF to ABC = (600,000)($23) + $25,875,000 = $13,800,000 + $25,875,000 = $39,675,000 Since there will be 600,000 + 500,000(2) = 1,600,000 shares outstanding in the new firm, each share will be worth $39,675,000/1,600,000 = $24.797 So, the actual cost of giving DEF’s shareholders 1,000,000 shares equals: Cost = (1,000,000 shares)($24.297 per share) = $24,797,000 Thus, the NPV under this scenario would be $25,875,000 – $24,797,000 = +$1,078,000 Therefore, firm ABC should use cash to purchase DEF, since this method generates the higher NPV. 36. Section: 15.5 Valuation Issues Learning Objective: 15.5 Level of difficulty: Challenging Solution: Total Earnings = $25,000 + $8,000 = $33,000 Total Shares outstanding = 8,000 (i.e., the number of shares Bidder had outstanding) Post-merger EPS = $33,000/8,000 = $4.125 (well above Bidder’s pre-merger EPS of $3.13).

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Notice that if the market was inefficient and the P/E ratio for the Bidder remained at 9.44, the value of B-T would = EPS  P/E ratio = $4.125  9.44 = $38.94.

Therefore, the market value of B-T would equal $38.94  8,000 = $311,520 However, according to the fact that no synergies arise, the market value of B-T should equal 236,000 + 48,000 = $284,000 Therefore, P/E = 284,000/33,000 = 8.606 Post-merger share price = 4.125  8.606 = $35.50 In conclusion, the post-merger EPS = $4.125; market value of B-T = $284,000; new P/E = 8.606; post-merger share price = $35.50.

37. Section: 15.6 Accounting for Acquisitions Learning Objective: 15.6 Level of difficulty: Challenging 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 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: Challenging Solution: Bidder Current assets

25,000

Target (book value) 4,500

Long-term assets

10,000

2,000

Target (FMV) 4,900

B-T(post-merger)

2,300

12,300

21,900

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Goodwill Total assets

35,000

6,500

7,200

Current liabilities Long-term debt Common stock Retained earnings Total

11,000 5,000 15,000 4,000 35,000

1,500 1,200 2,400 1,400 6,500

1,500 1,200 4,500 7,200

3,500* 37,700 12,500 6,200 15,000 4,000 37,700

*Goodwill = 8,000 (Price paid) – MV (Target’s equity) = 8,000 - [7,200 MV (Target’s assets) – 2,700 MV(Target’s liabilities)] = 8,000 – 4,500 = $3,500 Note that Cash of $8,000 was paid out to the target’s shareholders (from Current Assets)

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Answers to Concept Review Questions 15.1 Types of Takeovers Concept review questions 1. What is the difference between an acquisition and a merger?

An acquisition occurs when one firm (the acquiring firm or bidder) completely absorbs another firm (the target firm). In contrast, a merger is usually the combination of two firms into a new legal entity.

2. What is an amalgamation?

In an amalgamation, a new company is created and both sets of shareholders have to agree to exchange their existing shares for shares in the new company. This means that, in a genuine merger, both sets of shareholders are required to approve the transaction. In Canada, this process is called an amalgamation (the two companies approve an amalgamation agreement, and a special meeting of the shareholders is called to vote on the agreement. Under the Canada Business Corporations Act (CBCA), 21 days’ notice is given for this special meeting, and since the shareholders have to vote, all the normal rules for proxy statements and other information are invoked. The basic rule is that two-thirds of the shareholders of both amalgamating firms have to approve the special resolution to amalgamate.

3. What is the majority of the minority rule?

When a controlling shareholder seeks approval for an amalgamation, special rules kick in. The reason for this is the presumption that the controlling shareholder knows much more accurately what the true value of the shares really is and will abuse this position unless safeguards are in place. The critical safeguards are that a “majority of the minority” shareholder has to approve the special resolution to amalgamate the two companies and that there be a fairness opinion.

15.2 Securities Legislation and Takeovers Concept review questions 1. What is a tender?

Shareholders tender is the acceptance of the offer by signing the authorizations sent to them; in the event of a competing offer, they can withdraw their acceptance. A competing bid automatically increases the takeover window by 10 days.

2. What is a takeover circular?

A takeover circular, describing the bid, financing, and all relevant information, similar to a prospectus, must be sent to all shareholders for review.

3. What is a creeping takeover?

Creeping takeovers refer that a company acquires a target over a long period of time by slowly accumulating shares.

15.3 Friendly versus Hostile Takeovers

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Concept review questions 1. What goes into a confidentiality agreement and why do people sign them?

The target firm can disclose more information by setting up a data room where it can keep confidential information. When serious acquirers express interest, they can access the data room by signing a confidentiality agreement. Some acquirers sign them to get better information to value the target.

2. What is due diligence?

This process of evaluating the target is called due diligence and is an important part of the acquisition process.

3. What is a shareholder rights plan?

A shareholder rights plan, also known as a poison pill, is a plan passed by a vote of the board of directors that indicates that in the event of a takeover, the non-acquiring company shareholders get the right to buy 50 percent more shares at a discount price. Clearly this increase in the number of shares makes it much more expensive to make the acquisition and, all else constant, forces the acquirer to negotiate with the target company and make a friendly offer, since the BOD can then remove the poison pill through a vote.

4. What are some standard takeover defences?

Some standard takeover defences are a poison pill, selling the crown jewels, and using a white knight.

5. When is it best to mount a hostile bid?

It is best to mount a hostile bid when the following conditions are satisfied. First, the business is straightforward and known to the acquirer, so little due diligence is needed; that is, there is no great uncertainty about the value of the target. Second, there is no other strategic buyer that could generate similar value by acquiring the target. Finally, the acquirer could afford a long, drawnout takeover battle, since the value of the target is unaffected by the struggle.

15.4 Motivations for Mergers and Acquisitions Concept review questions 1. What is the difference between vertical and horizontal mergers?

A horizontal merger occurs when two firms in the same industry combine. In a vertical merger, 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”).

2. What is an extension M&A, an overcapacity M&A, and a geographic roll-up M&A? Extension M&A extends a firm’s expertise. An overcapacity M&A occurs when too many firms operate in an industry. A geographic roll-up M&A occurs when a national firm is created out of a series of regional firms.

3. What financial synergies are possible in an M&A transaction?

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Financial synergies in a M&A transaction include reduced cash flow variability, increase in debt capacity, reduction in average issuing costs, and fewer information problems.

4. What tax benefits can occur in an M&A? Tax benefits occur when one firm has substantial operating loss credit that it cannot take advantage of because it is not operating profitably. These losses are valuable since they can be carried forward and used against future profits to reduce taxes. Yet if the firm is unlikely to become profitable in the near term, these losses may expire worthless. On the other hand, if the firm combines with another profitable one in the same basic line of business, these losses can be used to offset the other firm’s profits to reduce taxes. Tax benefits may also arise due to the depreciation of capital assets (current cost accounting tax shields) that can be charged by the combined entity, and the increased use of debt financing with more interest tax shields, as discussed above.

5. What is the empirical record on the success of M&As in the 1990s?

In the 1990s, many international M&A such as Chrysler and Daimler-Benz, Seagram and Martel occurred. Strategic motives were advanced although the jury was still out on whether this was truly achieved.

6. What is SVAR and why do managers prefer to finance with shares than cash?

SVAR is the shareholder value at risk. When using cash, the acquirer bears all the risk, whereas when using share swaps, the risk is borne by the shareholders in both companies.

15.5 Valuation Issues Concept review questions 1. What is the difference between value and price?

Value generically means a willingness to sell or to buy; that is, we are talking about supply and demand curves. The price, on the other hand, is the value at which a deal is consummated. In an illiquid market such as M&A, there may be a wide range of possible deal price.

2. What is fair market value?

Fair market value is the highest price obtainable in an open and unrestricted market between knowledgeable, informed and prudent parties acting at arm’s length, with neither party being under any compulsion to transact.

3. What key multiples are used in valuing companies?

The key multiples include price-earnings (P/E), market-to-book (M/B), price-to-sales (P/S), and price-to-cash flow (P/CF).

4. Why do differing capital structures cause problems with using P/E multiples?

Because of the tax shield of debt, firms with different capital structure and the same earnings and profitability have different P/E ratios.

5. What is free cash flow?

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Free cash flow is used in the DCF approach. It is the free cash flow to equity holders, since it represents the cash flows left over after all obligations, including interest payments, have been paid. It equals net income minus non-cash items, changes in net working capital, and net capital expenditures.

6. When does EPS increase when using a share swap?

An acquiring firm can increase its EPS if it acquires a firm that has a P/E ratio lower than its own P/E ratio, even if no synergies arise from the merger.

15.6 Accounting for Acquisitions Concept review questions 1. Explain how the purchase method gives rise to goodwill.

The purchase method is an accounting method for business combinations where one firm assumes the fair market value of all of the assets and liabilities of the other (target) firm and all operating results included from the date of acquisition going forward. If the purchase price exceeds the FMV of the target firm’s equity, the excess amount is referred to as goodwill.

2. How is goodwill treated for accounting purposes in Canada and the United States?

Goodwill is the access amount of a target firm’s purchase price over fair market value of its equity. It is reported on the asset side of the balance sheet for the new entity. Goodwill is no longer amortized for the firm. Instead, the market value of goodwill must be assessed annually, and it will be written down and charged directly to earnings per share if the value is deemed to have been permanently “impaired.” As a result of this new treatment of goodwill, its fair value will be subject to an annual impairment test.

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Chapter 16: Leasing Multiple Choice Questions 1. Section: 16.1 Leasing Arrangements Learning Objective: 16.1 Level of Difficulty: Intermediate 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: Intermediate 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: Intermediate Solution: B The lender receives interest payments from the lessor, not lessee. The other statements are correct.

4. Section: 16.2 Accounting for Leases Learning Objectives: 16.2 Level of Difficulty: Challenging 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.

5. Section: 16.2 Accounting for Leases Learning Objectives: 16.2 Level of Difficulty: Basic 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.

6. Section: 16.2 Accounting for Leases Learning Objectives: 16.2 Level of Difficulty: Intermediate

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Solution: A Asset/Liability = PVMLP =

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1   1 − (1 + k ) n  PMT   

k

1   1 − 1.055 

(1 + k ) = 15,000  (1.05) = 68,189.26   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 7. Section: 16.2 Accounting for Leases Learning Objectives: 16.2 Level of Difficulty: Intermediate 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.

8. Section: 16.2 Accounting for Leases Learning Objectives: 16.2 Level of Difficulty: Intermediate 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.

9. Section: 16.2 Accounting for Leases Learning Objectives: 16.2 Level of Difficulty: Intermediate 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.

Practice Problems Basic 10. Section: 16.4 Motivation for Leasing Learning Objectives: 16.4 Level of Difficulty: Basic 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

Introduction to or Corporate Finance, Fourth Edition restrictions, better-looking financial statements by using an operating lease. Booth, Cleary, Rakita

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11. Section: 16.4 Motivation for Leasing Learning Objectives: 16.4 Level of Difficulty: Basic 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.

Intermediate 12. Section: 16.1 Leasing Arrangements Learning Objective: 16.1 Level of Difficulty: Intermediate Solution: a. Air Canada: Long-term debt and capital leases in 2014: $4,732. Long-term capital leases = $283. Fraction = 5.98% b. TELUS: Total long-term debt in 2011:$9,310. Capital leases: 0. Fraction: 0%.

Notice the dramatic difference. These two industries are, in general, characterized by very different usage of capital leases.

13. Section: 16.2 Accounting for Leases Learning Objectives: 16.2 Level of Difficulty: Intermediate Solution: Expected Annual lease Purchase economic payments Length price at PV of lease payments life of the (End of of lease end of asset year) 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

Percentage of acquisition price 93.36% (Financial) 19.96% (Operating) 11.37% (Operating)

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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

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.

14. Section: 16.2 Accounting for Leases Learning Objectives: 16.2 Level of Difficulty: Intermediate 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 Kitchen Widgets (KW) and Kitchen Thingies (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: 16.3 Evaluating the Lease Decision Learning Objectives: 16.3 Level of Difficulty: Intermediate Solution: University does not pay taxes.

NPV(leasing) = CF0 (i.e., purchase price savings) − PV(lease payments) CF0 = $2,000,000 1   1 − (1.06)5  PV(lease payments) = $450,000×    (1.06) = $2,009,298 .06       NPV(leasing) = $2,000,000 – $2,009,298 = -$9,298

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Since the NPV is negative it is better to buy the shuttle buses.

Challenging 16. Section: 16.2 Accounting for Leases Learning Objectives: 16.2 Level of Difficulty: Challenging Solution: First, we decide the type of lease.

Lease term ÷ economic life = 5 ÷ 6 = 83.33% > 75% Therefore, it is a capital lease.

Or, using financial calculator: [2nd][BGN][2nd][SET] N = 5; I/Y = 7%; PMT = $12,000; FV = 0; CPT PV = -$52,646.54 Annual depreciation expense = 52,646.54 ÷ 5 = $10,529.31 Interest expense = 52,646.54 × 0.07 = 3,685.26 Principal repayment = 12,000 – 3,685.26 = 8,314.74 Total expense = 10,529.31+ 3,685.26 = 14,214.57 (notice it’s greater than 12,000) Change in Net Income = –$14,214.57 Change in Cash Flow from Operations = –$3,685.26 Change in Cash Flow from Financing = –$8,314.74 17. Section: 16.2 Accounting for Leases Learning Objectives: 16.2 Level of Difficulty: Challenging Solution: Now the lease term ÷ economic life = 5 ÷ 7 = 71.43% < 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 = $12,000 Change in Net Income=–$12,000 Change in Cash Flow from Operations=–$12,000 Change in Cash Flow from Financing=0 Compared with the NI under financial lease, NI is increased by $2,214.57 (14,214.57– 12,000).

The whole lease payment is deducted from cash flow from operations (CFO) and there is no deduction from cash flow from financing (CFF).

Compared with the NI under a financial lease, CFO is decreased by $8,314.74 (actually the principal repayment deducted from CFF under financial lease is now deducted from CFO).

Compared with the NI under a financial lease, CFF is increased by $8,314.74.

18. Section: 16.2 Accounting for Leases

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Learning Objectives: 16.2 Level of Difficulty: Challenging 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 = + $52,646.54 Change in the current liability = + $8,314.74 Change in the long-term liability = + (52,646.54– 8,314.74) = +$44,331.80 19. Section: 16.3 Evaluating the Lease Decision Learning Objectives: 16.3 Level of Difficulty: Challenging Solution: a.

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. Ignoring walking away at 10 years, 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

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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 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: Challenging Solution: a.

Firm buys asset

Cash flow from asset Interest payments Lease payments CCA on asset Earnings before taxes Tax payment After-tax cash flows

Year 1

Year 2

Year 3

Year 4

Year 5

800,000

800,000

800,000

800,000

800,000

-157,500

-157,500

-157,500

-157,500

-157,500

0

0

0

0

0

350,000

350,000

350,000

350,000

350,000

292,500

292,500

292,500

292,500

292,500

117,000

117,000

117,000

117,000

117,000

$525,500

$525,500

$525,500

$525,500

$525,500

Principal repayment

-1,750,000

-1,750,000

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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 0 500,000 350,000 (20,000)

800,000 0 500,000 350,000 (20,000)

800,000 0 500,000 350,000 (20,000)

800,000 0 500,000 350,000 (20,000)

800,000 0 500,000 350,000 (20,000)

After-tax cash flows

$320,000 $320,000 $320,000 $320,000 $320,000

Principal repayment 0

c.

Lessor in financial lease

Cash flow from asset Interest payments Lease payments CCA on asset Earnings before taxes Tax payment After-tax cash flows

Year 1

Year 2

Year 3

Year 4

Year 5

0 -157,500 500,000 0 342,500 137,000 205,500

0 -157,500 500,000 0 342,500 137,000 205,500

0 0 -157,500 -157,500 500,000 500,000 0 0 342,500 342,500 137,000 137,000 205,500 205,500

0 -157,500 500,000 0 342,500 137,000 205,500

Principal repayment -1,750,000

-1,750,000

d. No; Ms.. 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 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. The lessee is assumed to be able to apply its loss against other income.

Lessee Lessor Total

Year 1 (20,000) 137,000 117,000

Year 2 (20,000) 137,000 117,000

Annual tax payments Year 3 (20,000) 137,000 117,000

Year 4 (20,000) 137,000 117,000

Year 5 (20,000) 137,000 117,000

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 iii) 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.

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21. Section: 16.3 Evaluating the Lease Decision Learning Objectives: 16.3 Level of Difficulty: Challenging Solution: NPV (leasing) = CF0 (purchase price savings) – PV(foregone depreciation tax savings) – PV(foregone salvage value) – PV(after-tax lease payments) CF0 = $900,000; Depreciation tax savings = 0.40 × $90,000 = $36,000 per year at year end.

After-tax cost of borrowing = 9% × (1 – .40) = 5.4%.

1  1 − (1.05)9  PV(Depreciation tax savings) = 36,000 ×   = $251,385  .054    Or, using financial calculator: N = 9; I/Y = 5.4%; PMT = $36,000; FV = 0; CPT PV = $251,385

Or, using financial calculator: N = 9; I/Y = 5.4%; PMT = 0; FV = 90,000; CPT PV = $56,063

PV(after-tax lease payments) 1   1 − 9 (1.054) = 45,000(1 – 0.4) ×    (1.054) = $198,719 .054     Or, using financial calculator: [2nd][END][2nd][SET] N = 9; I/Y = 5.4%; PMT = $27,000; FV = 0; CPT PV = -$198,719 NPV(leasing) = CF0 – PV(foregone depreciation tax savings) – PV(foregone salvage value) – PV(after-tax lease payments) = 900,000 – 251,385 – 56,063 – 198,719 = +$393,833 > 0 The firm should lease the equipment instead of purchasing it.

22. Section: 16.3 Evaluating the Lease Decision

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Learning Objectives: 16.3 Level of Difficulty: Challenging 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 = $300,000; After-tax borrowing cost = 9%  (1 – 0.40) = 5.4%

Or, using financial calculator: N = 4; I/Y = 5.4%; PMT = $15,000; FV = 0; CPT PV = -$52,699 Since the salvage value is the ending UCC at the end of four years.

Year Value (beginning year) CCA (20%) Value (year end)

1 (half-year rule) 2 $300,000 30,000 $270,000

3

4

$270,000

$216,000

$172,800

54,000 $216,000

43,200 $172,800

34,560 $138,240

= =(94,488.19)(0.9744) – (43,540.16)(0.8103) =$56,789 𝑃(𝑆𝑎𝑙𝑣𝑎𝑔𝑒 𝑣𝑎𝑙𝑢𝑒)=138,240×1/(1.054)4=$112,014 Or, using financial calculator: N = 4; I/Y = 5.4%; PMT = 0; FV = 138,240; CPT PV = -$112,014

Or, using financial calculator: [2nd][BGN][2nd][SET]

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N = 4; I/Y = 5.4%; PMT = $21,000; FV = 0; CPT PV = $77,762 NPV(leasing) = CF0 + PV(maintenance savings) – PV(foregone depreciation tax savings) – PV(foregone salvage value) – PV(after-tax lease payments) =300,000 + 52,699 - 56,789 - 112,014 – 77,762=$106,134>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: Challenging 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 = 9% ÷ 12 = 0.75%; Number of monthly payments = 6 years × 12 months = 72 25,000 = $447.28 Monthly lease payments = 1  1 −   (1.0075)72   (1.0075) .0075       Loan: (N.B. Loan payments are usually at the end of the month.)

Monthly loan rate = 8% ÷ 12 = 0.67%; 25,000 = $438.82 1 Monthly loan payments =  1 −  (1.0067)72    .0067      Estimate the PV of the beginning-of-month 1 lease payments using the loan rate. 1 − (1.0067 )72  PV(lease payments) = 447.28 ×  (1.0067 ) = $25,653 .0067     This implies that the firm should enter into the loan arrangement, since the effective cost of the asset would be greater than $25,000, which is the cost under the loan arrangement 24. Section: 16.3 Evaluating the Lease Decision Learning Objectives: 16.3 Level of Difficulty: Challenging Solution: NPV(leasing) = CF0 (i.e., purchase price savings) − PV(forgone depreciation tax savings)

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−PV(forgone salvage value) − PV(after-tax lease payments) CF0 = $1,500,000 Depreciation tax savings = 0.35 × $160,000 = $56,000 per year After-tax cost borrowing cost = 9% x (1–.35) = 5.85% 1 1 −   5  (1.0585 ) PV (Depreciation tax savings) = $56,000 ×   = $236,858  0.0585    PV (Salvage value) = $800,000 × (1/(1.0585)5) = $602,054 PV (after-tax lease payments) 1  1 − (1.0585)5  = $538,364 = $185,000(1-0.35) ×   × (1.0585) .0585      NPV(leasing) = $1,500,000 – $236,858 – $602,054 – $538,264 = +$122,824 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: Challenging 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 – $236,858 – $602,054= $661.088 Using the annuity due formula with PV = 661.088, FV = 0, I/Y = 5.85 and N = 5, we get payment as $147,662 Before-tax lease payment = $147,662/0.65 = $227,172 26. Section: 16.3 Evaluating the Lease Decision Learning Objectives: 16.3 Level of Difficulty: Challenging Solution: NPV(leasing) = CF0 (i.e., purchase price savings) − PV(forgone depreciation tax savings) − PV(after-tax lease payments)

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CF0 = $2,000,000 After-tax cost of borrowing is 6% (1–0.4) = 3.6%.

(C )(d )(T ) (1 + .5k ) PV (CCA Tax Shield ) = 0  d +k (1 + k ) (2,000,000)(.25)(.40) (1 + .5 .03) =  .25 + .03 (1 + .03) = $714,285.71 x 0.9854369 = $703,884 PV(lease payments) =

NPV(leasing) = $2,000,000 – $703,884 – $1,259,382 =$36,734 Since the NPV is positive it is now better to lease the shuttle buses.

27. Section: 16.3 Evaluating the Lease Decision Learning Objectives: 16.3 Level of Difficulty: Challenging Solution: Monthly lease rate = 7.5% ÷12 = 0.625% Number of monthly payments = 12 years × 12 months = 144 2,500,000 = $26,216.80 Monthly lease payments = 1  1 −  (1.00625)144   (1.00625) .00625     Monthly loan rate = 7.5% ÷12 = .625% 2,500,000 = $26,380.66 1 Monthly loan payments =  1 −  (1.00625)144    .00625     1 1 −   144  (1.00625 ) PV(lease payments) = $26,216.80×   (1.00625 ) =$2,500,000.00 .00625       Since the lease payment is equal to $2,500,000, the firm could take the loan or the lease.

28. Section: 16.3 Evaluating the Lease Decision

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Learning Objectives: 16.3 Level of Difficulty: Challenging Cost of the car =$25,000 Monthly discount rate = 6% ÷ 12 = 0.5% 1 1 −   (1.005)48  PV of lease = $650×   = $27,677 .005      1 1 −   (1.005)48    1 PV of loan from father = ($25,000–$8,000) ×  +$300×   .005 (1.005)48        = 13,381 + 12,774 = 26,155 The present value of the loan is lower, implying the loan is cheaper; therefore, you should take the loan.

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Answers to Concept Review Questions 16.1 Leasing Arrangements Concept review questions 1. What is the difference between an operating and a financial lease?

Operating lease is a lease where some of the benefits of ownership do not transfer to the lessee and remain with the lessor. Financial lease is a lease where essentially all the benefits of ownership transfer to the lessee; also known as a capital or full payout lease.

2. What type of leases do chartered banks normally make?

Chartered banks normally make financial leases, which are also commonly referred as capital leases. They are restricted from leasing consumer householder property, vehicles, and real property. They also cannot write leases where they have significant exposure to the residual value of the asset.

3. What is a sale and leaseback agreement (SLB)?

In an SLB, the owner of an asset sells an asset (usually to an insurance company or pension fund) and then signs an agreement to lease the asset back. Thus, the lessee retains the use of the asset and receives a large, one-time cash inflow at the time of the sale. This type of arrangement was particularly popular for organizations in very low tax brackets.

16.2 Accounting for Leases Concept review questions 1. What are the cash flow from operations and the free cash flow implications of an operating versus a financial lease?

The differences are as follows. First, the asset. The lease is on the balance sheets of lessors in operating leases, but on those of lessee in capital leases. Second, the expenses. The lease is classified as rental in operating leases. In financing leases, the expense for lessee is decomposed to interest and principal repayment. Interest is an expense. Principal is not an expense, but is reflected in the declining value of the liability in balance sheets. Third, the depreciation.

Depreciation is claimed by the lessee in operating leases, but claimed by the lesser in financing leases.

2. Which type of lease, operating or financial, gives a higher asset turnover ratio?

Operating leases give a higher asset turnover ratio for lessees. Asset turnover ratio is sales divided by total assets. Operating leases have lower total assets while the sales are the same.

16.3 Evaluating the Lease Decision Concept review questions 1. Explain how to calculate comparisons in the lease-versus-buy decision when the lease in question is an operating lease.

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NPV (leasing) = CF0 (i.e., purchase price savings) – PV (foregone depreciation tax savings) –PV (foregone salvage value) – PV (after-tax lease payments). The after-tax cost of borrowing is used in the discount.

2. How does the analysis change when the lease is a financial lease?

We can calculate the PV of the financial lease and compare it with the PV of the loan, which is the notional of the loan.

16.4 Motivation for Leasing Concept review questions 1. Why are leases often more flexible than a borrow-purchase option?

Leases often offer more flexibility. For example, they often include the option to cancel a lease, which may be important where obsolescence is a possibility. Also the lease payment can be seasonal according to the income of the lessee. Canadian Finance and Leasing Association (CFLA) offers the example of a ski-lift operator that financed the lifts with a lease where payments were seasonal to coincide with the winter months for obvious reasons.

2. Why do you think that the major market for leasing is often SMEs, rather than large corporations?

Leasing provides flexibility and convenience especially for SME, instead of large corporations.

The benefits include cheaper financing, lower the risks of asset ownership because the lessees do not need to sell the asset, implicit fixed interest rates, no maintenance, convenience because the lessees can lease for a relatively short period and/or if it is a very specialized or illiquid asset that may be hard to sell in the future, flexibility with the option to cancel a lease or a seasonal payment, low capital budgeting restrictions because leases requires only a very limited initial capital outlay, and better financial statement effects.

3. If you were opening a copy centre, do you think you would lease or borrow to buy the equipment and why?

The equipment should be leased for the following reasons: • Low initial capital outlay – Copy machines are too expensive for a small business like a copy center.

• Technical services – Lessors usually provide installation, service, and insurance, which are essential because of the technical difficulties associated with copy machines.

• Flexibility in monthly payment – The monthly payment can be tailored to the copy centre’s anticipated revenues.

• Flexibility in replacing machines – Lessors generally negotiate the replacement of the old technology with the new one, rolling the costs into a new lease with a new payment schedule.

• Better financial ratios because of the off-balance-sheet feature • Absence of resale

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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: Basic 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: Intermediate 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: Intermediate 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: Intermediate 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: Basic 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: Intermediate 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: Basic 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: Intermediate 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: Intermediate.

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: Intermediate 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: Basic 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: Intermediate 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 Basic 13. Section: 17.3 IPOs and Investment Banking Learning Objective: 17.4 Level of difficulty: Basic Solution: A lock-up period prevents the founders of the company from selling their shares for a given time.

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14. Section: 17.3 IPOs and Investment Banking Learning Objective: 17.4 Level of Difficulty: Basic 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.

15. Section: 17.3 IPOs and Investment Banking Learning Objective: 17.4 Level of difficulty: Basic Solution: The net proceeds were $25 million × (1 – 0.028) – $150,000 = $24,150,000.

Winnipeg Water & Gas paid a total of $25 million – $24.15 million = $850,000 in fees (gross proceeds less the net figure above), which is $850,000 / $25,000,000 = 3.40% of the total issue amount.

Intermediate 16. Section: 17.1 Conflicts between Issuers and Investors Learning Objective: 17.1 Level of difficulty: Intermediate Solution: a. Arthur pays $0.85 x 100,000 = $85,000 for the stamps. He sells them for $0.86 × 100,000 = $86,000, so his profit is $1,000. b. Arthur sells the stamps for $0.8525 × 100,000 = $85,250 and pays shipping and insurance, leaving $85,250 – $249 = $85,001. Therefore, his profit is exactly $85,001 – $85,000 = $1. A “quick buck” indeed! c. He makes $86,000 – $85,000 – $249 = $751.

17. Section: 17.2 A Primer on Securities Legislation in Canada Learning Objective: 17.2 Level of difficulty: Intermediate 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.

18. Section: 17.2 A Primer on Securities Legislation in Canada Learning Objective: 17.2 Level of difficulty: Intermediate 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.

19. Section: 17.2 A Primer on Securities Legislation in Canada Learning Objective: 17.3 Level of difficulty: Intermediate Solution:

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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.

20. Section: 17.3 IPOs and Investment Banking Learning Objective: 17.4 Level of difficulty: Intermediate 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.

21. Section: 17.3 IPOs and Investment Banking Learning Objective: 17.4 Level of difficulty: Intermediate 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.

22. Section: 17.3 IPOs and Investment Banking Learning Objective: 17.4 Level of difficulty: Intermediate 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.

23. Section: 17.3 IPOs and Investment Banking Learning Objective: 17.4 Level of difficulty: Intermediate 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.

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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.

24. Section: 17.3 IPOs and Investment Banking Learning Objective: 17.4 Level of difficulty: Intermediate Solution: 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.

25. Section: 17.3 IPOs and Investment Banking Learning Objective: 17.4 Level of difficulty: Intermediate 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.

26. Section: 17.3 IPOs and Investment Banking Learning Objective: 17.4 Level of difficulty: Intermediate 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: 17.4 Post-IPO Regulation and Seasoned Offerings Learning Objective: 17.5 Level of difficulty: Intermediate 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.

28. Section: 17.3 IPOs and Investment Banking Learning Objective: 17.4 Level of difficulty: Intermediate Solution: There are 500,000 shares outstanding before the IPO, and 250,000 new shares are being issued, bringing the total to 750,000. Of these, the brothers will retain 250,000 (half of their original holdings). Therefore, they will own (250,000 / 750,000) = 33.33% of the shares (and of the company).

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29. Section: 17.3 IPOs and Investment Banking Learning Objective: 17.4 Level of difficulty: Intermediate Solution: The IPO is intended to sell 250,000 + 250,000 = 500,000 shares. When investor demand is strong, the “green-shoe” standard overallotment clause means that 500,000 × 15% = 75,000 additional shares will have to be issued by the company. This would raise the total outstanding shares to 750,000 + 75,000 = 825,000. The Finn brothers will still own 250,000 shares, which would then represent (250,000 / 825,000) = 30.30% of the company.

30. Section: 17.3 IPOs and Investment Banking Learning Objective: 17.4 Level of difficulty: Intermediate Solution: a. To raise $4 million, the equity offering, before fees, will have to be $4,000,000 / (1 – 0.06) = $4,255,319.15. The flotation costs will be this gross figure less the net $4 million, or $255,319.15. b. To raise $4 million, the equity offering, before fees, will have to be $4,000,000 / (1 – 0.05) = $4,210,526.32. The flotation costs will be this gross figure less the net $4 million, or $210,526.32. It saves $255,319.15 – $210,526.32 = $44,792.83 on flotation costs.

Challenging 31. Section: 17.1 Conflicts between Issuers and Investors Learning Objective: 17.1 Level of difficulty: Challenging Solution: The probability of a fraudulent bond is 1/8 = 0.125, and the probability of a nonfraudulent bond is 1 – 0.125 = 0.875. 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+0.08 one year later.

Option 2: invest $1 on an investment. One year later, there is 0.125 chance of default when investors get $0, and 0.0875 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: (0.125 x 0) + [0.875 x (1+k)] = 1.08 Solving the equation above: k = 23.43%.

32: Section: 17.3 IPOs and Investment Banking Learning Objective: 17.4 Level of difficulty: Challenging Solution: There is too little competition for business in Canada, and Canadian firms do not need to tolerate high underpricing, because they want the best price for their shares.

A large number of reasons have been given for the underpricing 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

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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 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 rationale 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.

33. Section: 17.3 IPOs and Investment Banking Learning Objective: 17.4 Level of Difficulty: Challenging Solution: With fees of 4 percent, Lansdowne Ltd. will receive 96 percent of the offer price for each share, or $50 × 0.96 = $48. To raise $20 million, the company must issue $20,000,000 / $48 = 416,667 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.

34. Section: 17.3 IPOs and Investment Banking Learning Objective: 17.4 Level of Difficulty: Challenging Solution: Under Plan I, you will gross $11 × 1 million shares = $11 million and will pay $11 million × 0.07 = $770,000 in fees. The net proceeds are therefore $11,000,000 – $770,000 = $10,230,000.

Under Plan II, only 95 percent, or 950,000 shares are expected to be sold, so the gross proceeds will be $12 × 950,000 = $11,400,000. After the dealer’s fees, net proceeds will be $11,400,000 – $850,000 = $10,550,000. The investment dealer charges $850,000.

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).

35. Section: 17.3 IPOs and Investment Banking Learning Objective: 17.4 Level of Difficulty: Challenging Solution: a. On the undervalued shares, your profit will be 1,000 shares × $3 = $3,000. On the overvalued shares, you will lose 1,000 × $2 = $2,000. Your net gain is $1,000. b. You will only receive 500 shares of the undervalued issue, so your profit will be 500 × $3 = $1,500. On the overvalued shares, you will still lose $2,000. In this situation, you will have a net loss of $500. c. You will only receive 200 shares or one fifth of the undervalued issue, so your profit will be 200 x $3 = $600. On the overvalued shares, you will still lose $2,000. In this situation, you will have a net loss of $1,400.

36. Section: 17.3 IPOs and Investment Banking

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Learning Objective: 17.4 Level of Difficulty: Challenging Solution: a. Working down from the top of the list (highest limit price), selling 800,000 shares means that investors A, B, C, D, and E would buy the shares (with a partial allotment of 100,000 shares for investor E.) For all these investors to buy the shares, the price can be no higher than $19.00 (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 H (with a partial allotment of 150,000 shares for investor H), and the lowest limit price for this group is $18.00. c. According to Table 17-1 in the text, the historical underpricing in Canada has been 6.5%.

Therefore, you would expect the stock to rise to $18.00 × 1.065 = $19.17 on the first day of trading. In the U.S., the first-day return has averaged 16.9%, so you might expect the price to rise to $18.00 × 1.169 = $21.04.

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Answers to Concept Review Questions 17.1 Conflicts between Issuers and Investors Concept review questions 1. How does the existence of asymmetric information lead to market inefficiencies?

Information asymmetry means that people frequently have different information about the same future stream of cash flows, and thus they value the securities differently. In fact, they can disagree so much that a market may not exist and a firm cannot find anyone to buy its securities and experiences a “financing gap”.

2. Why can increases in interest rates not be used to solve the “lemons problem” in markets?

Let us take a typical example of “lemons problem”. Suppose bad money drives out good. If the interest rates increase, people are lured to circulate more bad money. Thus increases in interest rates make “lemons problem” even worse.

3. Why are securities legislation and corporate laws essential for markets to perform properly?

Asymmetric information causes market inefficiencies, which may cost investors big money.

Securities legislation and corporate laws aim to reduce the information asymmetry.

17.2 A Primer on Securities Legislation in Canada Concept review questions 1. What are some of the more important issues arising from the fact that securities regulation is a provincial and territorial, but not a federal, responsibility in Canada?

Securities regulation is designed to protect investors in that jurisdiction, so the provincial and territorial authorities exert authority whenever its citizens are involved. In contrast, a security is national in scope. A federal regulation will foster more responsive policy-making, improve market efficiency, eliminate duplication, provide common standards of investor protection, and strengthen Canada’s voice in international discussions on regulatory standards.

2. Why are prospectuses so important for public market issues?

The assumption here is that the issuer, controlling shareholders, or the restricted shareholders know more about the true value of the securities than the investors do. Hence, the prospectus is designed to remedy this information asymmetry.

3. Explain how offering memorandums differ from prospectuses and how exempt markets differ from public markets.

First, they differ in content. Memorandums are short, have much less information, and have lower cost of preparation. Second, they are used in different situations. Memorandums may have more sophisticated investors such as offerings to institutional investors. They have less risk, for example, government debts. They may be part of takeovers and corporate reorganizations. So they are covered by corporate law requirements to provide proxy circulars and similar documents. They may be offerings of some types of private firms. The market for non-registered securities is called the exempt market while the public market a prospectus is required for most distributions of securities, and in the process the securities are registered, which means that

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trades in the securities can be affected by a securities firm that is registered with the appropriate securities commission.

4. What is a reverse takeover and a backdoor listing?

A reverse takeover occurs when a takeover firm is acquired that has reduced its operating activities to bypass the IPO process and thereby avoid the long form prospectus. If the acquisition is by a private firm and acquired firm is an actively traded firm, the private firm has acquired a backdoor listing on the exchange.

17.3 IPOs and Investment Banking Concept review questions 1. Briefly discuss the possible motivation for firms to enter into IPOs, and relate these motivations to the five stages of firm development discussed by Myers (1999).

The motivations are “cash out” and access to more diversified set of financing options. Myers (1999) points out five stages of firm development: 1. technological experimentation; 2. pilot studies and sales; 3. improvement in production and scaling up manufacturing; 4. full-scale marketing and production; 5. expansion into other lines. In Myers’ view, the entrepreneur is essential at stages 1 and 2, valuable at stage 3, useful but replaceable at stage 4, and not needed at all at stage 5. The entrepreneur, as well as the partner, then needs a commitment to go public at stage 3 and certainly by stage 4, as the proportion of intellectual or human capital versus real capital in the value of the firm goes down. That is when the entrepreneur cashes out.

2. List and briefly describe the four basic stages of the IPO process.

The four basis stages are as follows: i. Discussion triggers IPO ii. The firm issues preliminary prospectus which takes 3 to 5 months iii. Waiting period and road shows take another 1 to 2 months iv. Pricing, distribution, and after-market stabilization, which takes another 1 month.

3. List and briefly describe some possible reasons for the existence of IPO underpricing.

First, it lowers the risk of the underwriter losing money on the issue. Second, the underpricing in US is the litigious nation of the US economy. If the share price falls, then the risk is high that someone will mount a class action suit against the underwriter for misleading the purchasers.

Third, a well-received public offering paves the way for subsequent offerings by the firm and builds momentum into the share price. Fourth, the underwriter allocates IPOs to favoured clients, knowing that they will make a large profit on the first day and making some people very wealthy.

17.4 Post-IPO Regulation and Seasoned Offerings Concept review questions 1. Explain why the lock-up period is an important consideration for investors, especially for issues that are still largely held by insiders.

Large issuer insiders want to cash out their shares. Without the lock-up period, stock prices may drop sharply right after IPO because of the selling from large shareholders. The lock-up period requirement prevents investors from this loss.

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2. How do continuous disclosure requirements protect investors?

The prospectus is out of date after IPO. Continuous disclosures reduce information asymmetry and then protect investors.

3. Briefly explain why short-form prospectuses are permitted by regulators for a large percentage of seasoned issues, and explain why they have led to the growth in popularity of bought deals.

Essentially, any reporting issuer with an outstanding Annual Information Form can issue securities under a short-form prospectus, which indicates the nature and pricing of the securities, omits all corporate information, and incorporates existing documents by reference. As long as the securities are not “novel” they can be cleared by the OSC in a matter of days, so that issues can be brought to market very quickly.

Short-term prospectuses led to the growth of the bought deal, in which the underwriting contract is signed even before the drafting of the preliminary prospectus. The OSC allows this because it knows that the prospectus now only includes details of the offering, rather than of the issuer, and that the prospectus will follow within two days. This allows the investment dealer to market the issue to major institutions and close the transaction usually within two to three days from the initial discussions with the issuer.

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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: Intermediate Solution: B 2. Section: 18.1 What Is Debt?

Learning Objective: 18.1 Level of difficulty: Basic Solution: B After-tax cost of debt = 6% (1 – 0.4) = 3.6% 3. Section: 18.2 Short-Term Debt and the Money Market Learning Objective: 18.2 Level of difficulty: Intermediate Solution: D 1 + kTB 1.01 R= −1 = −1 = 3.06% P 0.98 4. Section: 18.2 Short-Term Debt and the Money Market Learning Objective: 18.2 Level of difficulty: Intermediate Solution: C Use the equivalent maturity T-bill yield: 5% – 1% = 4% 5. Section: 18.2 Short-Term Debt and the Money Market Learning Objective: 18.2 Level of difficulty: Intermediate 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: Intermediate 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: Intermediate Solution: A

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8. Section: 18.3 Bank Financing Learning Objective: 18.3 Level of difficulty: Intermediate Solution: D 9. Section: 18.3 Bank Financing Learning Objective: 18.3 Level of difficulty: Intermediate Solution: D 10. Section: 18.3 Bank Financing Learning Objective: 18.3 Level of difficulty: Intermediate 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: Basic Solution: B Practice Problems Basic 12. Section: 18.1 What Is Debt?

Learning Objective: 18.1 Level of difficulty: Basic 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: Basic Solution: 1,000 1,000 = Price = = $997.05 (1 + K ) (1 + .012  90 / 365) 14. Section: 18.2 Short-Term Debt and the Money Market Learning Objective: 18.2 Level of difficulty: Basic Solution: The yield spread is the difference between the promised yield (not the expected yield) and the Tbill rate: Yield spread = 10% – 1% = 9%.

15. Section: 18.2 Short-Term Debt and the Money Market

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Learning Objective: 18.2 Level of difficulty: Basic Solution: The total cost of issuing the commercial paper is 10% + 0.125% + 0.125% = 10.25%. For the BAs, the total cost is 9.75% + 0.325% = 10.075%. The bankers’ acceptances are the better choice as they are slightly less costly overall.

16. Section: 18.3 Bank Financing Learning Objective: 18.3 Level of difficulty: Basic Solution: The annual interest payment, at the current rate, is 10.75% x $25 million = $2,687,500. To stay on-side with the covenant, Collingwood must earn at least: EBIT = 2 x $2,687,500 = $5,375,000 this year.

Intermediate 17. Section: 18.2 Short-Term Debt and the Money Market Learning Objective: 18.2 Level of difficulty: Intermediate The borrower receives a net amount of $10,000 – $75 = $9,925. A year later, he must repay $10,000 plus interest of $10,000 (0.08) = $800. Therefore, the effective interest paid by the borrower is: 10,800 − 9,925 = 8.82% 9,925 Thus, service fees and other costs increase the effective interest rate of a loan.

18. Section: 18.2 Short-Term Debt and the Money Market Learning Objective: 18.2 Level of difficulty: Intermediate Solution: k = 3.8(91)/365 = 0.9474% (0.009474) P=

1,000,000 = $990,615 1.009474

19. Section: 18.2 Short-Term Debt and the Money Market Learning Objective: 18.2 Level of difficulty: Intermediate Solution: Using equation 18.2 2,000,000(1.04)(0.97) + 0(1 − 0.97) 𝑃= = $1,769,825 1.14 20. Section: 18.2 Short-Term Debt and the Money Market Learning Objective: 18.2

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Level of difficulty: Intermediate Money market debt instruments 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.

21. Section: 18.2 Short-Term Debt and the Money Market Learning Objective: 18.1, 18.2 Level of difficulty: Intermediate Solution: Interest on loan = $125,000(0.06) = $7,500

EBIT Interest Taxable Income Tax (30%) Net Income

No Debt $143,500 0 143,500 43,050 $100,450

$125,000 loan at 6% $143,500 7,500 136,000 40,800 $95,200

The net income for Jackie’s company will fall by ($100,450 – $95,200) = $5,250, as shown in the table above. Although the company will pay $7,500 in interest on the loan, these payments are tax deductible. The result is that the company really pays only (1 – Tax Rate) = (1 – 30%) = 70% of the interest cost ($7,500 x 70% = $5,250), with the remainder being offset by lower taxes.

22. Section: 18.2 Short-Term Debt and the Money Market Learning Objective: 18.2 Level of difficulty: Intermediate 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) = (6%)(1 – 0.30) = 4.2% We could also obtain this result by noting that the impact of the interest payment on net income was $5,250. For a $125,000 loan, this amounts to an interest rate of 5,250 / 125,000 = 4.2% 23. Section: 18.3 Bank Financing Learning Objective: 18.3 Level of difficulty: Intermediate Solution: Collingwood can borrow up to: 75% x Accounts Receivable + 50% x Inventory = 0.75 x $8,536,000 + 0.50 x $80,196,000 = $46.5 million.

24. Section: 18.4 Long-Term Debt and the Money Market Learning Objective: 18.4 Level of difficulty: Intermediate

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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.

25. Section: 18.2 Long-Term Debt and the Money Market Learning Objective: 18.4 Level of difficulty: Intermediate Solution: The “bullet” payment pays off the entire principal amount of the loan so the annual payments consist of interest only: $2.65 million / $25 million = 10.6% per year.

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 15). 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.

26. Section: 18.5 Bond Ratings Learning Objective: 18.5 Level of difficulty: Intermediate 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 are 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.

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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.

Challenging 27. Section: 18.2 Short-Term Debt and the Money Market Learning Objective: 18.2 Level of difficulty: Challenging 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 (10% / 6) = 1.67%, and Michael requires a (14% / 6) = 2.33% return. Thus, his expected value is: Par (1 + R)  P + Recover (1 − P) $1,000  (1.0167)  0.99 + $750  0.01 = = $990.88 (1.0233) (1 + K ) 28. Section: 18.2 Short-Term Debt and the Money Market Learning Objective: 18.2 Level of difficulty: Challenging Solution: At 10% per year, the promised return is 1.67% (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 $750. Using Equation 18-2, we find: 1,000  (1.0167 )  P + 750  (1 − P) (1.01) 1,000  (1.01) − 750 260 P= = = 0.9749 1,000  (1.0167 ) − 750 266.70

$1,000 =

This is the probability of NOT defaulting. Therefore, the probability of a default is (1 – 0.9749) = 0.0251, or 2.51% 29. Section: 18.2 Short-Term Debt and the Money Market Learning Objective: 18.2 Level of difficulty: Challenging Solution:

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A 1 percent chance of default means that the probability of not defaulting is, P = 99%. As in Problem 28, the promised yield is 1.67 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 using equation 18.2 is: 1,000  (1.0167 )  0.99 + Recover  (1 − 0.99) $1,000 = (1.01) 1,000  (1.01) − 1,000  (1.0167 )  0.99 3.4670 = $346.70 Recover = = 0.01 (1 − 0.99) Thus, investors expect to recover $346.70 for every $1,000 invested, or 34.67% if Collingwood were to default on the commercial paper.

30. Section: 18.5 Bond Ratings Learning Objective: 18.5 Level of difficulty: Challenging Solution: a. Table 18-5 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  (1.09)  0.9101+ 0 V= = $935.86 (1.06) So Collingwood’s bonds are worth $935.86 per $1,000 of face value, or 0.93586 x $25 million = $23,396,500 in total.

31. Section: 18.5 Bond Ratings Learning Objective: 18.5 Level of difficulty: Challenging Solution: From Table 18-6, the default recovery rate on senior unsecured bonds has averaged 40.6%.

Using this in conjunction with the solution to Problem 30 and equation 18.2, V=

$1,000  (1.09)  0.9101+ 0.406 1,000  0.0899 = $970.29 (1.06)

The bonds are worth $970.29 per $1,000 of face value, or 0.97029 x $25 million = $24,257,250 in total.

32. Section: 18.5 Bond Ratings Learning Objective: 18.5 Level of difficulty: Challenging Solution: This is 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

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Answers to Concept Review Questions 18.1 What Is Debt?

Concept review questions 1. Distinguish debt from equity.

First, debt is a fixed contractual commitment, but shareholders can only claim residuals. Second, interest payments from debt are paid before taxes, but dividends of equity are paid after taxes.

2. Explain how to estimate the after-tax cost of debt.

The after-tax cost of debt is the before-tax interest cost of debt multiplied by one minus the tax rate.

3. What three characteristics does the CRA look for to determine whether interest payments are tax deductible?

The three characteristics are the following: i. Interest is compensation for the use or retention of money owed to another ii. interest must be referable to a principal sum iii. interest accrues from day to day 18.2 Short-Term Debt and the Money Market Concept review questions 1. Explain how interest is received on most money market instruments.

There are three major money market instruments: T-bills, commercial papers, and Banker’s acceptances. T-bills are sold at discounts. CRA regards the increase from the purchase price to the par value as interest and not capital gains. Most money market issues are traded on a discount basis but some commercial paper is issued in interest-bearing form. The actual yields on commercial papers is less than then quoted interest rate because of its credit risk. If an issuer does not have a good enough credit rating to access the CP market, it can have its bank guarantee or “accept” its commercial paper by selling the CP to the bank, which then accepts it by stamping “accepted” on it and selling it from its own money market desk. Thus the yield on banker’s acceptances is lower than commercial papers.

2. Contrast treasury bills, commercial paper, and BAs in terms of who issues them, their basic structure and default risk, and the yields they provide.

They differ in the following ways. First, who issues them? T-bills are issued by the government, but commercial papers and BAs are issued by corporations. Second, basic structure and default risk. T-bills are risk free, commercial papers are unsecured and risky, and BAs are backed up by major banks. Third, yields. T-bill has the lowest yields, BAs have medium yields, and commercial papers have the highest yields.

3. Define yield spreads and explain how they arise.

Yield spreads are the difference between yield of a corporate debt security and the T-bill. The spreads rise mainly because of firms’ default risk. T-bills are risk-free.

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18.3 Banking Financing Concept review questions 1. Briefly describe operating LCs, revolving LCs, and term loans.

Bank Financing includes line of credit (LCs) and term loans. LCs fall into two types: operating LCs and revolving LCs. Operating LCs lending facilities that are made available by the bank for the firm’s operating purposes and that generally cannot be used to back up a CP program; these demand loans can be cancelled at any time.

Term or revolving LC is usually at least 364 days and is often out to five years, renewable every six months. Often a five-year “revolver” is renewed at the end of each year, making it an “evergreen” five-year line of credit. Because the revolver is a commitment of credit, the bank has to provide capital against these commitments to ensure the liquidity of the bank. The common 364-day LC occurs because more capital is required against a one-year or 365-day LC. Term loans differ from lines of credit because they have a fixed maturity, require repayment to be made on a fixed schedule, and are made to finance longer-term requirements such as equipment purchases.

2. Why do banks typically impose debt covenants on their borrowing customers?

The covenants allow the bank to pull the loan (i.e., demand payment) and prevent the firm from drawing it down beyond a certain amount as its credit quality deteriorates.

3. Why is it reasonable to assume that most firms will have a banking relationship?

For large-amount financing, CPs require the line-of-credit backups from a bank, and BAs require the credit support from a bank. For smaller, irregular-sized financing requirements, firms rely more on traditional bank financing. Thus regardless of firm size, most firms have a banking relationship.

18.4 Long-Term Financing Debt and the Money Market Concept review questions 1. Define mortgage bonds, secured debentures, unsecured debentures, and subordinated debt.

Mortgage bonds are similar to residential mortgage arrangements, in which the lender has registered a claim on the underlying real property that is financed. Secured debentures mean that the investor has underlying assets to seize in the event of a default. Unsecured debentures mean that the investor has no underlying assets to seize in the event of a default. Subordinated debts are paid after other senior debts in the event of a default.

2. Discuss the rationale for including debt covenants in a public issue.

Unlike a bank who can monitor the operation and financing of a firm, the investors in a public issue are diversified and do not have the capability to monitor a firm. Thus a covenant is necessary to ensure that a firm cannot hurt the investors’ right to claim the principle and interest rate.

3. Briefly describe the negative pledge and cross-default clauses.

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Negative pledge is a clause that stipulates that a borrower may not create higher-priority debt without giving the other debt holders the same security. Cross-default clause means that default on one obligation also constitutes default on another.

18.5 Bond Ratings Concept review questions 1. Differentiate investment-grade debt from junk debt.

The lowest investment-grade bond rating is BBB (low), and below this the bonds are commonly referred to as junk bonds, although they are more politely referred to as high-yield bonds.

2. Briefly describe the main factors DBRS considers in determining its debt ratings.

In determining its rating, DBRS looks at six basic factors: core profitability, asset quality, strategy and management strength, balance sheet strength, business strength, miscellaneous issues.

3. Briefly summarize the evidence regarding how well debt ratings work.

DBRS tracked the default probability after 5, 10, 20 years after the original rating. The most noteworthy evidence is that the default rates clearly increases as the DBRS rating goes down, so their ratings provide a good indicator of credit risk.

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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: Basic 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: Intermediate 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: Basic Solution: C 4. Section: 19.3 Warrants and Convertible Securities Learning Objective: 19.4 Level of difficulty: Intermediate 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: Intermediate Solution: D 6. Section: 19.3 Warrants and Convertible Securities Learning Objective: 19.4 Level of difficulty: Intermediate Solution: A (Number of shares)(Price – Exercise) = 2*(30 – 20) = $20 7. Section: 19.3 Warrants and Convertible Securities Learning Objective: 19.4 Level of difficulty: Intermediate Solution: B CV = (CP)(Price) = 20($55) = $1,100 > market price, so convert 8. Section: 19.3 Warrants and Convertible Securities Learning Objective: 19.4

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9. Section: 19.4 Other Hybrids Learning Objective: 19.5 Level of difficulty: Basic Solution: D Permanence, subordination, legal, and subjective are the four factors.

10. Section: 19.4 Other Hybrids Learning Objective: 19.5 Level of difficulty: Intermediate 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: Intermediate Solution: D See Figure 19-4.

Practice Problems Basic 12. Section: 19.1 Shareholders’ Equity Learning Objective: 19.1 Level of difficulty: Basic 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: 19.2 Preferred Shares, 19.3 Warrants and Convertible Securities Learning Objective: 19.3, 19.4 Level of Difficulty: Basic Solution: From Equation 19-3, Conversion Price (CP) = Par / Conversion Ratio (CR), therefore CR = Par / CP =$100 / $20 = 5. This means that each preferred share will be converted into 5 common shares.

14. Section: 19.2 Preferred Shares, 19.3 Warrants and Convertible Securities Learning Objective: 19.2, 19.4 Level of Difficulty: Basic Solution: The conversion price of the common stock is$10. A 20 percent premium means the price would have to be 0.20 x $10 = $2 higher, or $12 per share before the firm would call (and force conversion of) the preferred shares.

Intermediate 15. Section: 19.2 Preferred Shares

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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.

16. Section: 19.1 Shareholders’ Equity Learning Objective: 19.1 Level of Difficulty: Intermediate Solution: a. i. The equity holders will receive the “equity”: $1.7 million less $1.5 million owed to creditors, or $200,000. a. 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.

17. Section: 19.1 Shareholders’ Equity Learning Objective: 19.1 Level of Difficulty: Intermediate Solution: a. You own 500 out of 1 million shares, or 500 / 1,000,000 = 0.05% b. You will purchase 500 / 5 =100 extra shares, giving you 600. In total, the company will sell an additional 1,000,000 / 5 = 200,000 shares, so there are 1.2 million 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 1.2 million outstanding. Your percentage share of the firm’s equity has fallen to 500 / 1,200,000 = 0.04167% 18. Section: 19.1 Shareholders’ Equity Learning Objective: 19.1 Level of Difficulty: Intermediate 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.

19. Section: 19.1 Shareholders’ Equity, 19.2 Preferred Shares Learning Objective: 19.1, 19.3 Level of Difficulty: Intermediate 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 $50 (par) x 2

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for the common shareholders. Therefore, a dividend of $3 million / 50,000,000 shares = $0.06 per share will be paid on each common share.

20. Section: 19.1 Shareholders’ Equity Learning Objective: 19.2 Level of Difficulty: Intermediate Solution: Collingwood Corp. will receive 4.5% x $10 million = $450,000 in dividends, before paying tax.

However, corporations receive dividends from other companies tax-free, so the net income aftertax is still $450,000.

21. Section: 19.2 Preferred Shares, 19.3 Warrants and Convertible Securities Learning Objective: 19.3, 19.4 Level of Difficulty: Intermediate Solution: The conversion value, CV = CR x P (where P = the price of the common stock). From Problem 13, CR =5, therefore CV = 5 x $15 = $75.

The conversion premium uses the price of the preferred shares and the conversion value: Premium = (P – CV) / CV = ($100 – $75) / $75 = 33.33%.

This figure may be interpreted to mean that the value of the preferred shares is 33.33% more than what they would be without the conversion privilege, or that the common shares must increase in value by 33.33% before conversion would make sense.

22. Section: 19.3 Warrants and Convertible Securities Learning Objective: 19.4 Level of difficulty: Intermediate 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: Intermediate Solution: Conversion Price = $100 / 5 = $20.

Conversion value = $18(5) = $90.

Because $90 < $102 or$18 < $20, the convertible bonds should not be converted.

24. Section: 19.4 Other Hybrids Learning Objective: 19.5 Level of Difficulty: Intermediate Solution: The interest payable is 8% × $30 million (par value) = $2.4 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.

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Challenging 25. Section: 19.3 Warrants and Convertible Securities Learning Objective: 19.4 Level of Difficulty: Challenging Solution: Conversion price: CP = Par / CR = $1,000 / 25.32 = $39.49 Conversion Value: CV = CR*P = 25.32 x $34 = $860.88 Value as a straight bond: 1 1 − (1 + 𝑘𝑏)𝑛 𝑆𝐵𝑉 = 𝐼 𝑥 [

𝑘𝑏

]+

𝐹

1 1 − (1.09)10

(1 + 𝑘𝑏 )𝑛 = 57.50 𝑥 [

0.09

]+

1,000 (1.09)10

= $791.43

Floor Value: FV = Max(SBV, CV) = $860.88 Thus, these bonds cannot trade at a price lower than $860.88 Conversion premium = (MV – CV) / CV = (1,051 – 860.88) / 860.88 = 22.08% 26. Section: 19.3 Warrants and Convertible Securities Learning Objective: 19.4 Level of difficulty: Challenging Solution: m Payoff = (V + mX ) − mX m+n 150,000 = (10,000,000 + 150,000x$10) − 150,000x$10 150,000 + 950,000 = $68,181.82 𝐷𝑖𝑙𝑢𝑡𝑖𝑜𝑛𝐹𝑎𝑐𝑡𝑜𝑟 =

150,000 𝑚 = = 0.1364 𝑚 + 𝑛 150,000 + 950,000

27. Section: 19.3 Warrants and Convertible Securities Learning Objective: 19.4 Level of Difficulty: Challenging Solution: a. The market value of Orion’s equity is: V = nP = 12,000,000 (shares) x $5 = $60 million b. The warrant holders will pay the strike price, X = $4.25, for each new share. In total, they will pay mX = 2,000,000 x $4.25 = $8.5 million c. The new shares will be purchased from the company, so its value will increase to (V + mX) = ($60 million + $8.5 million) = $68.5 million. The warrant holders will own [m / (m+n)] = 2 million / 14 million = 14.29% of the shares. Therefore, in total they will own shares worth 0.1429 x $68.5 million = $9,788,650. d. The payoff to the warrant holders is their total value less their cost: $9,788,650 – 8,500,000 = $1,288,650. On a per share basis this is $1,288,650 / 2 million = $0.64. Thus, the fair value (the amount you should be willing to pay) for each warrant is $0.64.

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Level of Difficulty: Challenging 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: Challenging Solution: With a 4 percent yield, the convertible preferred shares are paying 0.04 x $25 = $1.00 per year in dividends. The price of a straight preferred share paying this same amount of dividends would be: SPV = Div / k = $1 / 0.08 = $12.50. We know that the conversion value for these preferred shares is $15. Thus, the Floor Value = Max (SPV, CV) = Max ($12.50, $15) = $15. These convertible preferred shares will not sell for less than $15.

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Answers to Concept Review Questions 19.1 Shareholders’ Equity Concept review questions 1. What are the basic rights associated with equity securities? How do these differ across different categories or classes of equities?

There are three basic rights associated with equity securities: the right to vote, the right to receive dividend, and the right to receive the remaining property of the corporation on dissolution.

Different classes may have different voting rights, fixed or variable dividends, or different seniorities in receiving residual value of the firm.

2. Why do voting rights affect the prices of some common shares and not others?

The value of these voting rights very much depends on who has control of the company and whether it is good or bad for shareholder value creation. Empirical studies reveal that differential voting rights may not affect value when the founder runs the company, but they do when that founder ceases to be involved. Regardless, the limited or non-voting shares usually have a slight premium in terms of the right to a dividend to offset the lost value of control.

3. Why is dividend income preferred by both corporations and individual investors?

Dividends are very attractive in Canada for tax reasons, both for corporations and for individuals.

Dividends received by one Canadian corporation from another Canadian corporation are not taxed to avoid double taxation of income at the corporate level. In contrast, interest income is taxable between corporations because, as we discussed before, interest expense is tax deductible.

Dividend income is also attractive for individuals, because of the dividend tax credit system in Canada. Traditionally, this system was structured so that the effective tax rate paid was the same for owners of a small private corporation whether they withdrew their compensation as dividends or as salary. However, in the May 2006 budget, the federal government reformed the tax rates to reduce the overall tax rate on dividend income from public corporations, and since then most of the provinces have also reformed their taxation of dividend income.

19.2 Preferred Shares Concept review questions 1. Briefly describe the following types of preferred shares: straight, retractable, and floating rate.

Straight preferred shares do not have maturity date and pay a fixed dividend at regular intervals.

Retractable preferred shares give investors the right to sell them back to the issuer, thus creating an early maturity date. Floating rate preferred share generally have a long maturity date, but every three or six months their dividend is reset by an auction mechanism so that the dividend yield will be in line with current market interest rates. Alternatively, many of the floating rate preferred shares issued by the major banks have their dividend rate float with 75 percent of the prime rate, usually to some maximum rate. The result is that they always sell very close to their par value, because their dividend rate is always very close to the current market rate.

2. Briefly describe the following features that may be associated with preferred shares: cumulative provision, callable feature, and purchase funds.

Cumulative provision which means that no dividends can be paid on common shares until

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means that at the company’s option, it can call the preferred shares away from their owners by paying the fixed price. Purchase funds require the company to buy back a certain number of shares each year, which produces a “two-edged” sword: in the short run, it increases the number of purchasers and ensures a ready market for the shares, but in the long run, as the number of shares goes down, it has the opposite effect.

3. Why are preferred shares sometimes called hybrid securities?

Preferred share many characteristics with debt, for example, they usually have fixed dividend payments, and rated by the rating agencies. They are commonly regarded as a hybrid security: part debt and part equity.

4. Why would you want a cumulative feature when purchasing preferred shares?

The payoff on shares is not a fixed contractual commitment similar to interest on a bond, so the firm can omit a dividend without any direct legal consequences. Without the cumulative feature it would be legally possible to omit the preferred share dividend for years and then simply pay it when the common shareholders are paid a dividend. Such a policy would be challenged by the preferred shareholders but the cumulative feature makes it clear that the unpaid dividends to the preferred shareholders need to be paid prior to any future dividend to the common shareholders.

19.3 Warrants and Convertible Securities Concept review questions 1. Explain why issuing debt or preferred shares with warrants attached or issuing convertible bonds or convertible preferred shares, may represent attractive sources of financing for higherrisk firms.

When the warrants are exercised, the warrant holder pays the exercise price to the company in return for shares. Warrants thus provide primary financing because the issuing company raises capital from their sale. Convertible bonds or preferred shares can be converted to common shares, resulting is a reduced debt ratio.

2. Define and explain how to determine the following for a convertible: conversion price, conversion value, straight bond value, floor value, and convertible premium.

Convertible price is the strike price at which a convertible security can be converted into common shares based on its conversion ratio. Conversion value is the value of a convertible security if it is immediately converted into common shares. Straight bond value is the price that the convertible bonds would sell for if they could not be converted into common stock. Floor value is the lowest price a convertible bond will sell for, which is equal to the larger of its straight bond value and its conversion value. Convertible premium is the market price minus the conversion value, divided by the conversion value.

19.4 Other Hybrids Concept review questions 1. Name and discuss the four criteria used by DBRS to classify a security as debt versus equity.

DBRS looks at four major factors to determine whether a security is debt or equity: (1) the permanence factor, (2) the subordination factor, (3) the legal factor, and (4) the subjective factor.

The permanence factor relates to whether or not the security will be outstanding for a long

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subordination factor refers to the priority of the claim on the firm’s assets and income stream.

Again, common shares are the gold standard and BAs are obvious debt because they have an absolute claim to be paid off in 30 or 60 days. The legal factor means the legal rights of the investors—that is, whether they have a contractual right to receive income or whether it is in some way discretionary, such as the declaration of a dividend by the BOD. Finally, the major subjective factor is the intention of the company when it issues the securities.

2. Define the following types of hybrids: income bonds, commodity bonds, real return bonds, original issue discount bonds, LYONs, ARCs, preferred securities, and COINS. Income bonds are generally issued after a re-organization, so that the “interest” is tied to some cash flow level for the firm. Commodity bond is a bond whose interest or principal is tied to the price of an underlying commodity, such as gold. Original issue discount bonds (OIDs) or lowyield notes are bonds that sell at a discount from par value when issued by firms. Liquid Yield Option Notes (LYONs) are low-yield notes that are combined with a convertible feature and are accretive convertibles, because the principal accretes or increases over time. Adjustable Rate Convertible Subordinated Securities (ARCS) have fixed principal and maturity, and the interest normally comprises two parts: a fixed interest rate, and some function of the dividend paid in the prior six months. These securities are almost all convertible into common shares, so the dividend is expressed as a percentage of the conversion price. Preferred securities are not preferred shares.

They are generated by a company by creating a 100 percent owned subsidiary that issues the shares and then loans the proceeds to the parent company, for whom the interest is tax deductible; interest flows to the subsidiary, where it is not taxed, and is used to make dividend payments. Canadian optional interest notes (COINS) or prepaid bonds 99-year are bonds that are sold at their par values of $100, on which the firm immediately prepays the interest from years 11 to 99 on issue, leaving it with a net inflow and allowing it to continue to deduct annual interest payments of $100, even though it has effectively borrowed less.

3. Relate the costs of various financing options to their equity-like characteristics.

The costs of financing options differ according to how much equity weight they have. The more the weight is, the higher the cost is.

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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: Intermediate 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: Basic Solution: D X 2.25 V= = = $22.50 Ke 0.10 3. Section: 20.1 Financing Sources Learning Objective: 20.1 Level of difficulty: Intermediate Solution: D 55,000 EPS = = $5.50 10,000 EPS EarningsYield = = 5.50 = 0.275 20.00 P 4. Section: 20.1 Financing Sources Learning Objective: 20.1 Level of difficulty: Intermediate Solution: C To satisfy bond holders, 50,000 (5%) = 2,500 To satisfy equity holders, 115,000 (10%) = 11,500 Total minimum earnings = 2,500 + 11,500 = $14,000 5. Section: 20.1 Financing Sources Learning Objective: 20.1 Level of difficulty: Intermediate 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.

6. Section: The Cost of Capital

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Learning Objective: 20.2 Level of difficulty: Intermediate 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: Intermediate 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: Challenging Solution: C 6 − 3.6 450,000 g = b  ROE =  = 0.4  0.25 = 0.1 1,800,000 6 D1 3.6(1.1) P= = = $198.00 ke − 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: Intermediate 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: Intermediate Solution: C Cash cows do not have significant growth opportunities.

Practice Problems Intermediate 11. Section: 20.6 Risk-Based Models and the Cost of Common Equity Learning Objective: 20.6 Level of difficulty: Intermediate Solution: ke = RF +  (ERM − RF ) = 0.03 +1.4(0.10 − 0.03) = 12.8% 12. Section: 20.5 Growth Models and the Cost of Common Equity Level of difficulty: Intermediate

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Learning Objective: 20.5 Solution: P=

D1 EPS1 (1− b) EPS1 (1− 0) NI /# 1,056,020 = $16.50 = = = = 500,000 0.128 ke ke ke ke 





(g = b  ROE = 0%) P 

BVPS

=

ROE 

ke

=

NI / E ke

=

1,056,020

= 6.76

(1,040,000 +180,000)(0.128)

13. Section: 20.1 Financing Sources Learning Objective: 20.1 Level of difficulty: Intermediate Solution: Invested Capital = short-term debt + long-term debt + total equity = 210,000 + 780,000 + 1,040,000 + 180,000 = 2,210,000 EBIT = EBT + Interest = 1,508,600 + 66,400 = 1,575,000 Before-tax ROI=EBIT/Invested capital = 1,575,000/2,210,000 = 71.27% 14. Section: 20.3 Estimating the Non-Equity Component Costs Learning Objective: 20.3 Level of difficulty: Intermediate 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: Intermediate Solution: ke = RF +  (ERM − RF) = 0.03 +1.08(0.08) = 11.64% 750,000 250,000 WACC = 11.64% + 6%(1− 0.25) = 9.86% 750,000 + 250,000 750,000 + 250,000 16. Section: 20.5 Growth Models and the Cost of Common Equity Level of difficulty: Intermediate Learning Objective: 20.5 Solution: Exp(EPS) 23.50 = $626.67 V fed = = k Tbond −1% 4.75% −1% 17. Section: 20.5 Growth Models and the Cost of Common Equity Learning Objective: 20.5

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Level of difficulty: Intermediate Solution: D1 = D0 (1 + g1) = EPS0 (1 – b)(1 + g1) = ($5)(1 – 0.4)(1.1) = $3.30 P0 =

3.3 = $30 .16 − .05

18. Section: 20.5 Growth Models and the Cost of Common Equity Learning Objective: 20.5 Level of difficulty: Intermediate Solution: D1 ke = +g P(1 − F ) 3.75(1.04) = + 0.04 50(1 − 0.06) = 12.3% 19. Section: 20.5 Growth Models and the Cost of Common Equity Learning Objective: 20.5 Level of difficulty: Intermediate 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) = (25*0.105 – 1.2)/(1.2 + 25) g = 5.44% 20. Section: 20.5 Growth Models and the Cost of Common Equity Learning Objective: 20.5 Level of difficulty: Intermediate Topic: Growth Models and the Cost of Common Equity Solution: EPS = 12 = 0.24 BVPS 50 E 12 − 9 g = b  ROE =  0.24 = 0.06 12 D1 9 P= = = $120 ke − g 0.135 − 0.06 ROE =

NI

=

V = 120 15,000 + 600,000 = $2,400,000

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21. Section: 20.5 Growth Models and the Cost of Common Equity Learning Objective: 20.5 Level of difficulty: Intermediate Solution: g = b  ROE = (1 − payout)  ROE = (1 − 0.5)12% = 0.06 D 3(1.06) k = 1 +g= + 0.06 = 19.25% e P 24 ROE = 12%  ke = 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: Intermediate Solution: P =

ROE1  BVPS ke

o

=

0.15 25

+

+

Inv  ROE2 − ke 

(1+ k e )  200  0.2 − 0.12

ke



0.12 1.12  0.12  = 31.25 +119.05 = $150.30 PVGO = $119.05, PVEO = $31.25 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: Intermediate 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: Intermediate 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

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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.

25. Section: 20.7 The Cost of Capital and Investment Learning Objective: 20.7 Level of difficulty: Intermediate 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.

Challenging 26. Section: 20.7 The Cost of Capital and Investment Learning Objective: 20.5, 20.6 and 20.7 Level of difficulty: Challenging 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) = 0.03 + 2.15(0.1 – 0.03) = 18.05% Dividend Growth ke= D1 ÷ P0 + g = 4(1.05)/30 + 0.05 = 19.00% We can now estimate the after-tax cost of debt from the information given. kb = (1 – T) × (RF + 3%) = (1 – 0.3)*(3% + 3%) = 4.2% 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 = 0.4 × 0.042 + 0.6 × 0.1805 = 12.51% OR k = 0.4 × 0.042 + 0.6 × 0.19 = 13.08% We can now perform a net present value calculation: NPV = –15 + 2.25/0.1251 = $2,985,612 NPV = –15 + 2.25/0.1308 = $2,201,835 The net present value calculations indicate that the project should be undertaken at both discount rates.

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27. Section: 20.7 The Cost of Capital and Investment Learning Objective: 20.5, 20.6 and 20.7 Level of difficulty: Challenging Solution: We first compute the costs of each source of funds: Debt: NP = $972; Assuming annual coupons I = (0.07)($1,000) = $70; n = 15 So we have: 1  1 − (1 + K i )15  1  + 1,000  972 = 70  (1 − .3) Ki   (1 + K i )15     Solving for Ki, as shown in Chapter 6, we get: By financial calculator: PMT = 70(1 –0.3) = $49; PV = -972; FV = 1,000; N = 15.

Then compute I/Y will give 5.17%, which is the firm’s annual after-tax cost of debt.

Preferred: kp = Dp/NPp = 0.055/0.95 = 5.79% Equity: kne = ke × P0/NP0 = (0.16) *10/(1 – 0.12)/(10) = 18.18% We next compute the market value of each component: Debt: The market1 value of debt outstanding is:  1 − 15  1 = $1,091.08  2,000 = $2,182,160 B = 80 (1 + 0.07)  + 1,000  15 0.07 (1 + 0.07)     Preferred: The market value is the total dividend payments divided by the market capitalization rate.

P = 0.06 × ($1,500,000)/0.055 = $1,636,364 Equity: Shares are currently trading at 10/(1 – 0.12)= $11.36 E = 400,000 ($11.36) = $4,544,000 Note the value of retained earnings is incorporated into the current market price of equity.

Total market value =V=B+P+E = $2,182,160 + 1,636,364 + $4,544,000 = $8,362,524 Finally we can compute the weighted average cost of capital: B P E WACC = K K K V B +V P +V E 2,182,160 1,636,364 4,544,000 WACC = (0.0517) + (0.0579) + (0.1818) = 12.36% 8,362,524 8,362,524 8,362,524 28. Section: 20.7 The Cost of Capital and Investment Learning Objective: 20.5, 20.6 and 20.7

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Level of difficulty: Challenging Solution: a.

Cost of Debt: NP = $960; Assuming annual coupons I = (0.06)($1,000) = $60; n = 20 So we have: 1  1 − 20  (1 + K i ) 1  + 1,000  960 = 60  (1 − .30) Ki   (1 + K i )20     Solving for Ki, as shown in Chapter 6, we get: By financial calculator: PMT = 60(1 – .30) = $42; PV = –960; FV = 1,000; N = 20.

Then compute I/Y will give 4.51%, which is the firm’s annual after-tax cost of debt.

Cost of Preferred shares: K= 2/23.50 = 8.51% Cost of Common Shares: K= 0.03 + 1.18(0.10 – 0.03) = 11.26% Ke= 0.1126(30/27) = 12.51% b.

Since they need $5m in total financing, all of the common equity financing ($5m*0.5 = $2.5m) can be raised from internal funds. So, we should use the cost of common equity using internal funds.

WACC= 0.3(0.0451) + 0.2(0.0851) + 0.5(0.1126) = 8.69% c. Since they need $8m in total financing, the common equity financing needed ($8m*0.5 = $4m) exceeds the $3m internal funds, and the MCC would be computed using the cost of new equity, or 12.51%: MCC = 0.3(0.0451) + 0.2(0.0851) + 0.5(0.1251) = 9.31% 29. Section: 20.7 The Cost of Capital and Investment Learning Objective: 20.5, 20.6 and 20.7 Level of difficulty: Challenging Solution: a. Cost of LT debt: NP = $965; Semi-annual coupons I = (0.07/2)($1,000) = $35; n = 25*2 = 50 So we have: 1   1− (1+ K )50  1 i  +1,000  965 = 35  (1−.30) Ki (1+ K i )50    

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Solving for Ki, as shown in Chapter 6, we get: By financial calculator: PMT = 35(1 – .30) = $24.50; PV = –965; FV = 1,000; N = 50.

Then compute I/Y will give 2.58%, which is the firm’s semi-annual after-tax cost of debt.

So, their annual after-tax cost of debt = (1.0258)2 – 1 = 5.23% b. Cost of Preferred Shares: D 4 k = p = = 8.42%. p NPp 47.5 c. and d.

Cost of Common Equity Financing: (i) Dividend Growth Model Approach: 2 D D 2 + 0.04 = 10.25%, and k = 1 + g = k = 1 +g= + 0.04 = 10.90%. ne e 32 NP 29 P0 (ii) CAPM Approach: ke = RF +[ERM − RF]i = 0.04 + 0.95(0.12 − 0.04) = 11.6%  P0   32  k = k = (0.116) = 12.8%. ne  NP  e 29   30. Section: 20.7 The Cost of Capital and Investment Learning Objective: 20.7 Level of difficulty: Challenging Solution: a. Using ke, we get: B P CE WACC = ki + k p + ke V V V = (0.2)(0.0586) + (0.2)(0.0612) + (0.6)(0.15) = 11.40% b.

Break InternalFundsAvailable $4m = = = $6.67m.

CE Point 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 k k + CE k = (0.2)(0.0586) + (0.2)(0.0612) + (0.6)(0.2) = 14.40% ne i + p V V V

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Answers to Concept Review Questions 20.1 Financing Sources Concept review questions 1. Why is the earnings yield not usually an adequate measure of the investor’s required return on equity?

Since most firms have some expectation for growth, so the stock price reflects these growth opportunities as well as the current earnings. The earnings yield cannot capture the growth opportunities.

2. How are the ROE and Ke related to a firm’s growth opportunities and its M/B ratio?

If ROE exceeds Ke, then the price goes above the book value of the investment, so M/B is more than 1. The increase of price is positively related to the growth opportunities.

20.2 The Cost of Capital Concept review questions 1. Why is the weighted average cost of capital (WACC) so important?

The cost of capital is a way of calculating the overall required rate of return needed to meet investor expectations. Thus it is important.

2. What are the steps involved in estimating a firm’s WACC? There are three steps involved in estimating the WACC: i. Estimate market values for the sources of capital, since our focus is on how to increase the market value of the funds invested in the firm and we need these to estimate the weights of the different sources of capital in the total firm value. ii. Estimate the current required rates of return for the various sources of capital invested in the firm. iii. Put them all on the same corporate tax basis to recognize that interest on debt is tax deductible, whereas the return to the equity holders is not.

3. How can we estimate the market value of common equity, preferred equity, and long-term debt?

The market value of common equity is simply price per share multiplied by the number of shares outstanding. The market value of preferred equity is the dividend divided by the required return on preferred shares. The market value of bond equals the present value of all future cash payments.

20.3 Estimating the Non-Equity Component Costs Concept review questions 1. How do flotation costs affect the cost of capital sources for a firm?

One complication that arises with respect to all sources of capital, except for internally generated funds, is that the firm incurs issuing or flotation costs when new securities are issued. These include any fees paid to the investment dealer and/or any discounts provided to investors to

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entice them to purchase the securities. As a result, the cost of issuing new securities will be higher than the return required by investors, since the net proceeds to the firm from any security issue will be lower than that security’s market price.

2. Explain how to estimate the cost of debt and preferred equity for a firm.

The cost of debt is obtained by using Equation 20-13. The left-hand side is the after-tax afterflotation proceeds of debt. The right-hand side is the present value of the after tax interest payments and the present value of the principle. The cost of preferred equity is dividend divided by the after-flotation net proceeds.

20.4 The Effects of Operating and Financial Leverage Concept review questions 1. Distinguish between operating and financial leverage.

Operating leverage measures the increased volatility in operating income caused by fixed operating costs. Financial leverage measures the increased volatility in earnings caused by bearing debt (a fixed interest cost) resulting in increased risk.

2. Why do we say that equity holders bear the brunt of the effects of leverage?

Common shareholders claim the residual in the income statement. As the firm’s sales drop, everyone has a higher priority claim than that of the common shareholders, so they see much greater volatility in their return than either the debt holders or others with a stake in the firm’s operations.

20.5 Growth Models and the Cost of Common Equity Concept review questions 1. Explain how we can use the constant growth DDM to estimate the cost of firms’ internal common equity, as well as the cost of new common share issues.

The cost of firms’ internal common equity is the dividend yield plus the growth rate of dividends. The cost of new common share issues is dividend divided by after-flotation net proceeds plus the growth rate of dividends.

2. Explain the relationship among ROE, retention rates, and firm growth.

Firm growth rate equals ROE multiplied by retention rates.

3. How can we relate the existence of multiple growth stages to four commonly used firm classifications?

Assume that a firm earns current earnings in the first stage and starts to grow with a constant rate in the second stage. Then a firm’s value has two components with one for the present value of the existing opportunity (PVEO), and another for the present value of the growth opportunities (PVGO). If we classify these four cases as types of firms, we have the following: A, High PVEO and high PVGO; B, High PVEO and low PVGO; C, Low PVEO and high PVGO; D, Low PVEO and low PVGO.

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4. Describe the Fed model and how it may be used to estimate the required rate of return of the market as a whole.

The Fed model was used to estimate whether the stock market was over- or undervalued and whether the U.S. Fed should “talk down” market values that might be excessive and cause problems if they collapsed. The exact equation used is the actual price divided by the Fed price, and the Fed price is the expected earnings per share on the Standard and Poor’s 500 Index as reported by security market analysts (Exp(EPS)), divided by the yield on the long-term U.S. Treasury Bond (KTBond) minus 1.0 percent.

20.6 Risk-Based Models and the Cost of Common Equity Concept review questions 1. Explain how we can use the CAPM to estimate the cost of common equity.

DCF performs poorly when applied to growth stocks, which pay low dividends and/or display high growth rates. In these situations, it makes sense to rely more heavily on risk-based models.

The most important risk-based model is the capital asset pricing model (CAPM). The risk-free rate used in corporate applications of the CAPM is usually the yield on 30-year Government of Canada bond. The market premium can be obtained by using a long term of the historical data.

The beta estimation is period specific.

2. Explain why beta estimates are “period specific” and outline the potential problems that may arise. Allude to problems with recent beta estimates.

The beta estimation is time varying. In the past ten years, one sub index shows rapidly increasing beta coefficients (the IT sub index), whereas most of the other beta coefficients show a constant or decreasing trend. In fact, Consumer Staples and Utilities actually had negative beta estimates, indicating that they moved in the opposite manner to the stock market as a whole, and reduced the risk of a diversified portfolio. Beta estimation using an inappropriate period causes mistakes in calculating WACC. 20.7 The Cost of Capital and Investment Concept review questions 1. Explain the importance of using the WACC as a hurdle rate for making investment decisions.

If investors want an overall WACC, this suggests that this firm should not reinvest funds within its operations that earn a rate of return less than this hurdle rate. Consequently the WACC is not just a valuation tool—it is also used going forward as a tool to evaluate investments.

2. Why does the MCC suddenly jump up and become expensive?

When the common equity portion of financing comes entirely from reinvested earnings, the firm’s cost of equity will equal the return required by its shareholders, as discussed previously.

However, when the firm is forced into issuing new common shares, it must pay flotation costs for issuing these shares, so the cost to the firm is higher than the cost of using internally generated funds. It is clear the most common cause of this increase in the MCC occurs when the firm cannot supply all of its required common equity financing from reinvested earnings (i.e., internal funds). Therefore, it must issue new common shares and bear the brunt of issuing costs,

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in addition to providing common shareholders with their required rate of return. This causes the cost of common equity to increase, meaning the MCC increases at this point.

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Chapter 21: Capital Structure Decisions Multiple Choice Questions 1. Section: 21.1 Financial Leverage Learning Objective: 21.1 Level of difficulty: Intermediate Solution: B Invested capital = short-term debt + long-term debt + shareholders’ equity = 90,000 + 200,000 + 450,000 = 740,000 2. Section: 21.1 Financial Leverage Learning Objective: 21.1 Level of difficulty: Basic Solution: D ROE represents financial risk and business risk.

3. Section: 21.1 Financial Leverage Learning Objective: 21.1 Level of difficulty: Intermediate Solution: B ROE = ROI if a firm is 100 percent financed by equity, not debt; i.e., B = 0. ROE = ROI. 4. Section: 21.1 Financial Leverage Learning Objective: 21.1 Level of difficulty: Intermediate Solution: A The use of debt increases the expected ROE. 5. Section: 21.1 Financial Leverage Learning Objective: 21.1 Level of difficulty: Intermediate Solution: D − RDB(1 − T ) EBIT(1 − T ) EPS = + # # The EPS-EBIT line is steeper if there are fewer shares outstanding. Its slope = (1 – T)/#. Its intercept = –RD B (1 – T)/#. Only D is true.

6. Section: 21.1 Financial Leverage Learning Objective: 21.1 Level of difficulty: Basic Solution: C There are no transaction costs.

7. Section: 21.2 Determining Capital Structure Learning Objective: 21.2

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Level of difficulty: Intermediate Solution: D Recall WACC = were + wdrd (1 - Tc) A decrease in the tax rate, an increase in the cost of debt, and an increase in the cost of equity will increase WACC. However, since the cost of equity is usually higher than the cost of debt, WACC decreases when the weight of equity decreases.

8. Section: 21.4 The Impact of Taxes on Capital Structure Learning Objective: 21.4 Level of difficulty: Intermediate Solution: D WACC stays the same regardless of the debt-equity ratio in the M&M irrelevance world.

9. Section: 21.4 The Impact of Taxes on Capital Structure Learning Objective: 21.4 Level of difficulty: Intermediate Solution: A ke = ku + (ku − kd )(1 − T )D / S L = 10% + (10% − 6%)(1 − 0.25)0.5 = 11.5% 10. Section: 21.7 Capital Structure in Practice Learning Objective: 21.7 Level of difficulty: Intermediate Solution: B Profitability, riskiness of the underlying business, firm size, and stock price performance affect the firm’s ability to raise debt from creditors. A large firm with stable earnings and cash flows would be the most creditworthy and able to raise debt in the capital market without paying a substantial risk premium.

Practice Problems Basic 11. Section: 21.1 Financial Leverage Learning Objective: 21.1 Level of difficulty: Basic Solution: Rule #1: For value-maximizing firms, the use of debt increases the expected ROE so shareholders expect to be better off by using debt financing, rather than equity financing.

Rule #2: Financing with debt increases the variability of the firm’s ROE, which usually increases the risk to the common shareholders.

Additional rule: Financing with debt increases the likelihood of the firm running into financial distress and possibly even bankruptcy.

12. Section: 21.3 The Modigliani and Miller (M&M) Irrelevance Theorem Learning Objective: 21.3 Level of difficulty: Basic

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Solution: M&M’s key assumptions are as follows: i) There exist two firms in the same “risk class” with different levels of debt. ii) The earnings of both firms are perpetuities. iii) Markets are perfect in the sense that there are no transaction costs or asymmetric information problems. iv) There are no taxes. v) There is no risk of costly bankruptcy or associated financial distress.

13. Section: 21.5 Financial Distress, Bankruptcy, and Agency Costs Learning Objective: 21.5 Level of difficulty: Basic Solution: The static trade-off model balances the benefit of lower WACC through the use of less-costly debt with the increased risk of financial distress and bankruptcy caused by taking on more leverage. Although the cost of equity increases as a firm adds more debt, initially the WACC will decline as long as the cost of debt is lower than the cost of equity. However, at some point, as more debt is added, the trend in WACC will reverse and it will begin to increase as the financial distress and bankruptcy risk of the incremental change in debt begins to outweigh any capital cost advantage. The point where the WACC stops decreasing and begins to increase is the optimal capital structure.

14. Section: 21.6 Other Factors Affecting Capital Structure Learning Objective: 21.6 Level of difficulty: Basic Solution: Firms usually finance by internal cash flow, then debt, and finally common equity. Myers’ argument is based on divulging information. Issuing common shares involves revealing privileged information to the public, while issuing debt only involves revealing privileged information to the lender. Using internal cash flow does not involve divulging information.

15. Section: 21.7 Capital Structure in Practice Learning Objective: 21.7 Level of difficulty: Basic Solution: The first question you should ask yourself is whether or not the firm is profitable. If it is, you could take advantage of the tax shield from issuing debt. If not, the firm has to be financed by all equity. The second question you should ask is whether or not the firm has the ability to issue debt. This will depend on the type of assets the firm holds, i.e., are they tangible to be used as the collateral for secured loans? You should also assess the firm’s underlying business risk, i.e., the ability to generate consistent cash flows to pay interest. If your firm has significant business risk, you should not consider a large debt portion in the capital structure.

Moreover, you should consider the size of your firm. The larger the firm size, normally, the more diversified it is (this implies smaller business risk). The smaller the business risk, the larger the financial risk tolerance the firm could take. Finally, you should balance all the above factors with the growth rate and profitability of your firm. Growing firms need cash, whereas profitable firms generally spin off cash. You need to take into consideration the current equity market if the firm

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currently has common stock outstanding. If you observe that the firm’s stock is over-valued by the market, you probably want to take advantage of equity financing.

These are some of the basic factors you should consider. You must also ensure that the WACC is at the lowest possible level to maximize shareholders’ wealth.

Intermediate 16. Section: 21.1 Financial Leverage Learning Objective: 21.1 Level of difficulty: Intermediate Solution: EBIT = 480,000 – 100,000 – 55,000 – 60,000 = 265,000 I = 0.09* (500,000) = 45,000 Tc =66,000/(265,000 – 45,000) = 30% (EBIT − RD B)(1 − T ) (265,000 − 0.09  500,000)(1 − 0.3) = = 19.25% SE 800,000 (EBIT)(1 − T ) 265,000(1 − 0.3) ROI = = = 14.27% SE + B 800,000 + 500,000 ROE =

17. Section: 21.1 Financial Leverage Learning Objective: 21.1 Level of difficulty: Intermediate Solution: ROE = ROI + [ROI − RD (1 − T )] = 15% + [15% − 10%(1 − 0.3)]

B

SE 300,000

500,000 = 15% + 4.8% = 19.8% ROI represents business risk, which is 15 percent, while the second part of the equation represents financial risk, which is 4.8 percent.

18. Section: 21.1 Financial Leverage Learning Objective: 21.1 Level of difficulty: Intermediate Solution: B B ROE = ROI (1 + ) − R D (1 − T ) SE SE 300,000 300,000 = ROI (1 + ) − (0.10)(1 − 0.3) 500,000 500,000 = −0.042 + 1.6ROI Intercept: –4.20% Slope: 1.6

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The higher the debt-equity ratio, the steeper (the higher the slope of) the financial leverage line.

If ROI increases/decreases by 1 percent, ROE increases/decreases by 1.6 percent.

19. Section: 21.1 Financial Leverage Learning Objective: 21.1 Level of difficulty: Intermediate Solution: B B ROE1 = ROI (1 + 1 ) − RD (1 − T ) 1 SE1 SE1 B B ROE2 = ROI (1 + 2 ) − RD (1 − T ) 2 SE2 SE2 ROE1 = ROE2 ROI(1+ 0.6) − 8%(1− 0.25)(0.6) = ROI (1+1.5) − 8%(1− 0.25)(1.5) ROI = 6% When ROI is 6 percent, the ROEs of the two strategies are the same, regardless of how the firm finances.

20. Section: 21.1 Financial Leverage Learning Objective: 21.1 Level of difficulty: Intermediate Solution: Method 1 EBIT = Sales − COGS = 400,000 − 120,000 = 280,000 IC = SE + B = B / 25% = 250,000 / 0.25 = 1,000,000 EBIT (1 − T ) 280,000  (1 − 0.25) ROI = = = 21% SE + B 1,000,000 Method 2 IC = SE + B = B/25% = 250,000/0.25 = 1,000,000 SE = IC − B = 1,000,000 − 250,000 = 750,000 (Sales − COGS − I )(1 − TC ) (400,000 − 120,000 − 20,000)(1 − 0.25) ROE = = = 26% 750,000 SE B ROE = ROI + (ROI − RD (1 − T )) SE 26% = ROI + (ROI − 6%)(250,000 / 750,000) ROI = 21% 21. Section 21.2 Determining Capital Structure

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Learning Objective: 21.2 Level of difficulty: Intermediate Solution: EBITDA = EBIT + D + A = 680,000 + 66,000 = 746,000 Fixed Burden Coverage =

CFTD =

746,000 EBITDA = = 9.49 I + (Pr ef . Div. + SF) /(1 − T ) 0 + (40,000 + 15,000) /(1 − 0.3)

EBITDA 746,000 = = 3.39 Debt 220,000

Analysts use EBITDA more often because it adds back the non-cash deductions for depreciation and amortization to EBIT and is therefore a “better” estimate of the firm’s cash flow.

22. Section: 21.2 Determining Capital Structure Learning Objective: 21.2 Level of difficulty: Intermediate Solution: Z = 1.2X1 + 1.4X2 + 3.3X3 + 0.6X4 + 0.999X5 WC RE EBIT MVTE S = 1.2 + 1.4 + 3.3 + 0.6 + 0.999 TA TA TA BL TA = 4.3 Compared with the Moody’s rating list, we get 4.3 > 2.17, therefore this company is an IG firm.

23. Section: 21.2 Determining Capital Structure Learning Objective: 21.2 Level of difficulty: Intermediate Solution: Higher working capital: more receivables and inventory Retained earnings: the firm earned money in the past EBIT: measures operating profitability MVTE/BL: market-valued debt ratio Sales/TA: the extent of the productivity of the firm using the assets 24. Section: 21.2 Determining Capital Structure Learning Objective: 21.2 Level of difficulty: Intermediate Solution: (EBIT − RD B)(1 − T ) (EBIT) − (0.1)(675,000))(1 − 0.2) 0.8EBIT − 54,000 EPS = = 75% D / E = # 30,000 30,000 (EBIT) − (0.06)(420,000))(1 − 0.2) 0.8EBIT − 20,160 EPS = 30% D / E = 65,000 65,000

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0.8EBIT * −54,000 0.8EBIT * −20,160 = 30,000 65,000 EBIT * = $103,757.14 This point is where the two EPS-EBIT lines intersect. When EBIT > EBIT*, the 75 percent D/E option is preferred since it produces a higher EPS. When EBIT < EBIT*, the 30 percent D/E option is preferred. At an EBIT level of $125,000, which is above EBIT*, the 75 percent D/E option is preferred because it produces a higher EPS. 25. Section: 21.3 The Modigliani and Miller (M&M) Irrelevance Theorem Learning Objective: 21.3 Level of difficulty: Intermediate Solution: VL = VU = EBIT/KU = (480,000 + 0.08*500,000)/0.16 = 3,250,000 SL = VL – D = 3,250,000 – 500,000 = 2,750,000 D 500,000 = 16% + (16% − 8%) = 17.45% Ke = Ku (Ku − K D ) + SL 2,750,000 26. Section: 21.3 The Modigliani and Miller (M&M) Irrelevance Theorem Learning Objective: 21.3 Level of difficulty: Intermediate Solution: V =

EBIT

=

2,100,000

= $14 million

U

KU 0.15 VL = VU = $14 million.

SL= VL – D = 14 – 5 = $9 million 27. Section: 21.4 The Impact of Taxes on Capital Structure Learning Objective: 21.4 Level of difficulty: Intermediate Solution: VU = EBIT(1 – T)/KU = (480,000 + 0.08 * 500,000)(1 – 0.30)/0.16 = 2,275,000 VL = VU + DT = 2,275,000 + 500,000 (0.30) = $2,425,000 SL = VL – D = 2,425,000 – 500,000 = 1,925,000 D

500,000 = 17.45% 1,925,000 SL D 500,000 ] = 17.45% Ke = RF MRPU [1+ (1− T ) ] = 3% + MRP(1.2)[1+ (1− 0.3) + 1,925,000 SL MRP = 10.19% Ke = Ku

+

(Ku − KD )(1− T )

= 16% + (16% − 8%)(1− 0.3)

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28. Section: 21.4 The Impact of Taxes Learning Objective: 21.4 Level of difficulty: Intermediate Solution: VU =

EBIT(1− T ) $3(1− 0.3) = = $13.125million KU 0.16

VL = VU + DT = $13.125 + (5)(0.3) = $14.625 million.

SL= VL – D = 14.625 – 5 = $9.625 million.

Ke = KU + (KU − K D )(1− T ) D = 0.16 + (0.16 − 0.08)(1− 0.3)(5 / 9.625) = 18.91% SL WACCL = (9.625/14.625)(18.91%) + (5/14.625)(8%)(1 – 0.3) = 14.36% 29. Section: 21.5 Financial Distress, Bankruptcy, and Agency Costs Learning Objective: 21.5 Level of difficulty: Intermediate Solution: The static trade-off model ignores two important issues: information asymmetry problems and agency problems. Information asymmetry problems arise when shareholders, creditors, and management have access to and base their decisions on different information, while agency problems can arise when management's incentives are not well aligned with shareholder interests.

30. Section 21.5 Financial Distress, Bankruptcy, and Agency Costs Learning Objective: 21.5 Level of difficulty: Intermediate Solution: Profitability, the type of assets a firm has, the risk of the firm's underlying business, the size of the firm, and the firm's growth rate are important practical considerations. Generally, larger, more profitable firms with tangible assets that can be pledged as security and stable, reliable cash flows are able to borrow more funds at lower capital costs. Firms with these characteristics that do not need large infusions of capital for growth can borrow on even more generous terms. Conversely, smaller, less profitable firms with intangible assets, hard-to-predict cash flows, and a need for capital infusions for growth will be able to borrow less and must pay higher borrowing costs.

31. Section: 21.5 Financial Distress, Bankruptcy, and Agency Costs Learning Objective: 21.5 Level of difficulty: Intermediate Solution: There are two ways bankruptcy occurs. The first way is when the firm commits an act of bankruptcy, such as the non-payment of interest, and creditors enforce their legal rights as a result. This form of bankruptcy is involuntary. The other way is when the firm voluntarily declares itself unable to meet its financial obligations.

Under CCAA, the court will appoint a monitor, who is normally a trustee in bankruptcy working for one of the larger accounting firms. The monitor reports back to the court. The

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monitor has considerable flexibility in preventing creditors from exercising their claims against the firm, in restructuring contracts, and in allowing the management of the firm to develop a plan to reorganize in the hope of continuing operations.

The main differences between bankruptcy under CCAA and BIA are the size of the scope for preventing creditors from seizing assets, the ability to raise DIP financing, and the possibility of a settlement on all creditors given a majority agreement. BIA is more rigid, but more predictable and simpler. It has much less scope for preventing creditors from seizing assets than CCAA. Under BIA the firm cannot raise DIP financing and has no provision for imposing a settlement on all creditors. BIA is used mainly by smaller companies, while CCAA is used mainly by larger companies.

32. Section: 21.5 Financial Distress, Bankruptcy, and Agency Costs Learning Objective: 21.5 Level of difficulty: Intermediate Solution: As Figure 21-8 indicates, under the bankruptcy world, distress costs rise as the firm increases its debt ratio. Firm value is the sum of unlevered firm value and financial distress costs. It increases with the increasing debt ratio.

However, agency costs tend to rise when a firm is approaching bankruptcy when the interests of the debt holders and shareholders diverge. Shareholders are actually holding a call option on the underlying firm. If the firm value exceeds the debt outstanding, they pay off the debt and keep the residuals. However, shareholders are also protected by their limited liability against the downside risk if the firm value falls below the debt outstanding. Furthermore, shareholders tend to gamble in the event of bankruptcy by accepting poor and more risky projects. In either case, the resulting agency costs may be huge. Creditors can choose not to lend long term to risky firms by using short-term debt or including sinking fund payments that create a continuous cash payment to the creditors.

33. Section: 21.7 Capital Structure in Practice Learning Objective: 21.7 Level of difficulty: Intermediate Solution: In an efficient market (semi-strong form) the price of the stock reflects all publicly available information. The problem here is the information asymmetry between the firm and the investors.

Gus knows that the project is a positive NPV and if he could credibly convince investors of that fact, the share price would rise. However, investors have no way of knowing whether the new issue is to invest in a positive NPV project or because Gus thinks his stock is overvalued and is trying to sell new stock at inflated prices. Investors take these two possibilities into account when determining the price of the new stock.

34. Section: Appendix 21A: Personal Taxes and Capital Structure Learning Objective: 21.8 Level of difficulty: Intermediate Solution: Your cousin is mixing corporate and personal taxes. If the investor does not pay taxes, then, with corporate taxes, we want the firm to maximize the tax shield earned from debt.

However, with personal taxes there is a trade-off between the tax shield earned by the

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corporation and the tax paid by the investor on the interest income. If the investor pays more tax than the shield earned, then the investor would prefer the firm to pay dividends or create capital gains rather than use debt. In this way, if there are personal and corporate taxes, an investor may prefer the firm to use no debt.

Example: corporate tax = 35%, personal taxes: dividends and capital gains = 10%, interest income 60%. Compare two firms (both earn $1,000 before interest and taxes, and interest is $ 250):

(350.00) $650.00

Levered $1,000.00 (250.00) (262.50) $487.50

Before-tax distributions Debt holders Equity holders Total before-tax distributions

$650.00 $650.00

$250.00 $487.50 $737.50

After personal taxes Debt holders Equity holders Total after-tax distributions

$585.00 $585.00

$100.00 $438.75 $538.75

Operating income Interest Corporate taxes Net corporate income

Unlevered $1,000.00

We can see in the above example that when there are no personal taxes, the total cash flows to investors (equity and debt) is greater with debt (“total before-tax distributions”) which is expected given the value of the tax shield. However, we also see that with this set of personal taxes, the total cash flows to investors is greater when the firm is unlevered (“total after-tax distributions”) due to the high personal tax rate on interest.

Challenging 35. Section: 21.3 The Modigliani and Miller (M&M) Irrelevance Theorem Learning Objective: 21.3 Level of difficulty: Challenging Solution:

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480,000 = $4,000,000 U 0.12 4,000,000 P= = $20 200,000 480,000 + 0.18 3,000,000 − 0.08 3,000,000 = $3.90 b) EPSnew = 200,000 0.18 3,000,000 c) NewVL = VU + = $4,000,000 + $4,500,000 = $8,500,000 0.12 SL = VL − D = NewVL − D = $8,500,000 − $3,000,000 = $5,500,000 3,000,000 = 14.1818% d) ) = 12% + (12% − 8%) 5,500,000 Ke a) V =

e) NewP =

$3.90 = $27.50 0.141818

36. Section: 21.4 The Impact of Taxes on Capital Structure Learning Objective: 21.4 Level of difficulty: Challenging Solution: OPI: value of debt = 100,000/0.1 = $1.0 million –> value of equity is $2 million (using D/E = 0.5) and therefore, value of the firm is $3 million.

Obtaining the value of the debt from the D/E ratio: x = D / E then E = D / x V = D+E =D+D/x Vx = D(1+ x) Vx =D (1+ x) Step 1: Determine what the cash flows from OPI would be if the firm had the desired D/E ratio: Desired by Susan

Desired by Celia

Value of firm

OPI with D/E = .5 $3,000,000

OPI with D/E = .2 $3,000,000

OPI with D/E = 1.1 $3,000,000

Value of debt Value of equity

$1,000,000 $2,000,000

$500,000 $2,500,000

$1,571,429 $1,428,571

EBIT

$750,000

$750,000

$750,000

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Interest Cash flows to equity

$100,000 $650,000

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$50,000 $700,000

$157,143 $592,857

Step 2: Use the arbitrage approach of the M&M proof to determine how much each sister has to borrow/lend to end up with the desired cash flows.

Assume each sister buys 50% of the equity of OPI. Each will invest $1 million and will receive cash flows of $325,000 from OPI. However, Susan wants a cash flow from the investment of $350,000 (50% of the cash flows to equity from OPI if it had a D/E ratio of .2) for an investment of $1,250,000 (50% of the value of the equity of OPI if it had a D/E ratio of .2); Celia is also not happy; if OPI had the desired D/E ratio of 1.1, her cash flows would only be $296,429 and her investment would be $714,286.

Susan: Would like OPI to have less debt; therefore, to undo the leverage decision of OPI Susan will need to lend Susan will lend $250,000.

She will receive interest income of $25,000 per year.

Celia: Would like OPI to have more debt; therefore, to increase the leverage of OPI Celia will need to borrow Celia will borrow $285,714.

She will pay $28,571 interest on her loan Check that each has the desired cash flows (50% of the cash flows to equity from the desired OPI) and that each has invested the desired amount (50% of the value of the equity of the desired OPI).

Investment in 50% of equity of OPI Lend Borrow Net investment Cash flow from OPI investment Interest from lending/borrow Net cash flows

Susan $1,000,000 250,000

Celia $1,000,000

$1,250,000

285,714 $714,286

$325,000 25,000 $350,000

$325,000 (28,571) $296,429

37. Section: 21.4 The Impact of Taxes on Capital Structure Learning Objective: 21.4 Level of difficulty: Challenging Solution: a. To value Saskatchewan Botanicals we need the cash flows that are available to the shareholders (the cash flows after paying all other claimants and capital expenditures). Note: If given EBIT, deduct taxes to obtain the free cash flow (assuming CAPEX = 0).

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Value of Saskatchewan Botanicals with zero debt = $1,080,000 / 0.18 = $6 million b. Firm value adjusts upon announcement of stock repurchase financed by debt even before the debt is issued. The value of equity before repurchase is equal to the value of the firm.

SL = VL = VU + DT = 6 + 3(0.3) = $6.9 million Stock price before repurchase = value of equity before repurchase / number of shares = $6.90 Proceeds of $3 million from debt issue will repurchase $3 million/$6.90 = 434,783 shares.

Shares outstanding after repurchase = 1,000,000 – 434,783 = 565,217 shares.

Value of equity after repurchase = $6.90 × 565,217 = $3.9 million Or, value of the equity after repurchase = $6.9 million – $3 million = $3.9 million Price per share after repurchase = $3.9 million / 565,217 = $6.90 c.

Ke = KU

+

(KU − KD )(1− T )

D

= 0.18 + (0.18 − 0.08)(1− 0.3)

SL

3 = 23.38% 3.9

d. We know from part (a) that EBIT(1 – T) = $1,080,000 per year. To obtain the cash flows available to equity, we need to deduct the after-tax cost of debt (1 – T)*8%*$3 million = $168,000. Therefore, cash flows available for equity holders = $1,080,000 – $168,000 = $912,000.

Value of the equity is then $912,000 / 0.2338 = $3.9 million 38. Section: 21.4 The Impact of Taxes on Capital Structure Learning Objective: 21.4 Level of difficulty: Challenging Solution: a. Assuming that all cash flows are permanent, then the new value of Athabascan Drilling is $11.2 million.

VL = VU + DT = 10 + 4(0.3) = $11.2 million

b. To calculate the WACC, calculate: • The value of equity: ➢ value of firm = $11.2 million, value of debt = $4 million ➢ value of equity = $7.2 million • Cost of debt: given as 12% • Cost of equity = 23.11% Ke = KU The WACC is then:

+

(KU − KD )(1 − T )

D SL

= 0.2 + (0.2 − 0.12)(1 − 0.3)

4 = 23.11% 7.2

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WACC =

SL VL

+

K VL

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7.2

K (1 − T ) =

4 11.2

e

(0.2311) D

+ 11.2

(0.12)(1 − 0.3) = 17.86%

39. Section: 21.4 The Impact of Taxes on Capital Structure Learning Objective: 21.4 Level of difficulty: Challenging Solution: a.

As the number of shares is unspecified assume there are N shares (as we are examining the change in EPS, the number of shares is not critical).

Value of the firm = EBIT(1 – T)/WACC = $8.4 million. D/E = 2/3 so the value of debt = $3.36 million. Interest is therefore, 0.05*3.36 million = $168,000 before tax. Earnings or net income after tax is (EBIT – I)*(1–T) = (1,200,000 – 168,000)*(1 – 0.3) = $722,400.

EPS(before) = $722,400 / N Price per share is $5.04 million / N To determine the new value of debt after the change in D/E ratio: Value of the firm with no leverage: VL = VU + DT 8.4 = VU + 3.36(0.3) VU = $7,392,000 Value of the firm with a D/E of 1/3 D = V*(1/3) / (1+1/3) = V/4 VL = VU

+

DT = VU +

V = 7.392 +

VL

VL

T

4

(0.3) 4 VL = $7,991,351 L

D = V/4 = 7,991,351 / 4 = $1,997,838 Value of the debt is $1,997,838 resulting in interest of $99,892 per year. New value of equity is $5,993,513.

Value of debt has changed from $3.36 million to $1,997,838 million—stock worth $1,362,162 must be issued to retire this debt. Therefore, it is necessary to issue 1,1,362,162/ (5.04 million/N) = 0.27027 * N shares

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Earnings after the restructuring is $(1,200,000 – 99,892)*(1-0.3) = $770,076

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770,076 1.27027N 722,400 EPSOLD = N EPSNEW 770,076 1 = * = 0.8392 EPSOLD 722,400 1.27027 EPS NEW =

We can see from above that the EPS declined by 16.08% and that this change was caused by a combination of an increase in income and an increase in the number of shares outstanding. b.

To determine the cost of equity of Straightforward Theatre Company, obtain the cost of unlevered equity (remember this does not change as the capital structure changes): VU = 7,392,000 =

EBIT(1 − T ) KU 1,200,000(1 − 0.3) KU

KU = 11.36% Then, using the cost of levered equity formula, obtain the old cost of equity (before the change in capital structure): D 2 = 0.1136 + (0.1136 − 0.05)(1 − 0.3) = 14.33% Ke = KU (KU − KD )(1 − T ) + 3 S L

Double check using WACC = (5.04/8.4)* 14.33% + (3.36/8.4)*5%*(1–0.3) = 10% Calculate the cost of equity with the new D/E ratio of 1/3: D 1 = 0.1136 + (0.1136 − 0.05)(1 − 0.3) = 12.84% Ke = KU (KU − KD )(1 − T ) + 3 S L

Summary: Cost of equity with D/E of 2/3 is 14.33% Cost of equity with D/E of 1/3 is 12.84% As expected, decreasing the level of leverage (D/E) has resulted in a decrease in the cost of equity.

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Answers to Concept Review Questions 21.1 Financial Leverage Concept review questions 1. Define business risk and financial risk.

Business risk is the variability of a firm’s operating income caused by operational risk. Financial risk the variability in a firm’s net income caused by the use of financial leverage 2. How does financial leverage affect the relationship between ROI and ROE? ROE = ROI (1+ B/SE ) – Rd(1-T))B/SE. ROE linearly increases with ROI. 3. What are the three rules of leverage?

First, for value-maximizing firms, the use of debt increases the expected ROE so shareholders expect to be better off by using debt financing, rather than equity financing. Second, financing with debt increases the variability of the firm’s ROE, which usually increases the risk to the common shareholders. Third, financing with debt increases the likelihood of the firm running into financial distress and possibly even bankruptcy.

4. Describe how we determine the ROE and EPS indifference points for a firm based on various financing alternatives, and explain why this analysis provides the firm with useful information.

EPS indifference point is the EBIT level at which two financing alternatives generate the same EPS. We can solve for this indifference point in terms of EBIT by setting the EPS equal for two alternative financing plans under consideration. Then we merely solve for this indifference EBIT level, which we denote as EBIT*. This will provide the firm with some useful direction in choosing between financing alternatives since firms will generally want to maximize their “bottom line” as measured by EPS, and they will usually have an estimate of their expected EBIT. The ROE indifference point works the same way as EPS indifference point.

21.2 Determining Capital Structure Concept review questions 1. What are the main determinants of capital structure?

The main determinants are analysis of cash flows, consultations, risk considerations, impact on profits, and industry comparisons.

2. Explain how ratios may be used to assess a company’s ability to assume more debt.

First, interest ratio is EBIT divided by interests. EBIT is not cash flow. Also this ratio cannot measure a firm’s ability to cover other commitments. Second, fixed burden coverage ratio uses EBITDA in the denominator. EBITDA is a better estimate of the firm’s cash flow. The denominator includes after tax preferred share dividends and sinking funds. This ratio measures a company’s ability to pay other commitments. Third, cash-flow-to-debt ratio (CFTD) a direct measure of the cash flow over a period that is available to cover a firm’s stock of outstanding debt. CFTD combines capital and stock variables.

3. What is Altman’s Z score and what does it measure?

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Altman’s Z-score is due to the work of Professor Ed Altman, and is a weighted average of several key ratios that he found were useful for predicting a firm’s probability of bankruptcy. His prediction equation is as follows: Z = 1.2X1 + 1.4X2 + 3.3X3 + 0.6X4 + 0.999X5. Where, X1 = working capital divided by total assets, X2 = retained earnings divided by total assets, X3 = EBIT divided by total assets, X4 = market values of total equity divided by non-equity book liabilities, and X5 = sales divided by total assets.

21.3 The Modigliani and Miller (M&M) Irrelevance Theorem Concept review questions 1. State the assumptions underlying the M&M irrelevance theory.

M&M’s key assumptions are as follows. (1) There exist two firms in the same “risk class” with different levels of debt. (2) The earnings of both firms are perpetuities. (3) Markets are perfect in the sense that there are no transaction costs or asymmetric information problems. (4) There are no taxes. (5) There is no risk of costly bankruptcy or associated financial distress.

2. Explain the importance of this theory.

Unfortunately, the “M&M results” are only as good as their assumptions, and most of them have been shown to poorly reflect the “real” world. However, in looking at how their assumptions affect their result, their research has pointed the way for many of the significant developments in corporate finance theory and practice over the last 50 years.

3. What is the basic argument that M&M use to arrive at the irrelevancy result?

M&M proved their proposition by means of an arbitrage argument that there is no such thing as “free money” and that investors prefer more money to less. So let’s think about what this means to two firms with the same business risk, but different levels of debt. There are two strategies.

One is to buy a percentage share of the un-levered firm, the payoff is αEBIT. The other is to buy a percentage share of the levered firm, and a percentage of its debt. The payoff is α(EBIT – KDD) + αKDD = αEBIT. By no arbitrage argument, since two strategies have the same payoff and the same risk, the value of the two firms at present must be the same. Thus VL=VU. 4. In this ideal M&M world, what will affect firm value?

In this ideal M&M world, only EBIT and un-levered equity cost affect firm value.

21.4 The Impact of Taxes on Capital Structure Concept review questions 1. How do taxes affect the M&M argument?

VL = VU + DT. Leverage increases firm value. The difference between VL and VU is the tax shield of debt.

2. What are the practical difficulties associated with the implications of M&M’s corporate tax model?

This model contains a crucial flaw, which is that the adjustment is based on the M&M equation, which implies that 100 percent debt financing is optimal: since there is always more tax shield value to using more debt, why stop? While it seems obvious on an intuitive level that firms

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should not finance with 100 percent debt, we can address the issue more formally by relaxing M&M’s assumptions that there are no costs related to the risk of financial distress or bankruptcy.

21.5 Financial Distress, Bankruptcy, and Agency Costs Concept review questions 1. Explain the impact of financial distress and agency costs on M&M’s conclusions regarding capital structure.

The probability of financial distress increases with debts. Financial distress brings both direct and indirect costs to a firm. When a firm is in distress, the equity holders (who get to vote) may undertake measures to try to get something for themselves, at the expense of the debt holders, for example, a large dividend. Because of the cost with financial distress and agency problem, firms do not take 100 percent debt.

2. Why can the firm’s debt be viewed as the exercise price to the shareholders’ option to purchase the firm?

If a firm’s value is greater than debt, shareholders can the difference between the firm value and debt. Otherwise, shareholders get nothing. The payoff function for the shareholders are max[0, V-D], which is exactly the payoff function of a call option with debt being the exercise price.

3. Explain the static trade-off theory.

Static trade-off model states that the firm uses debt to maximize its tax advantages up to the point where these benefits are outweighed by the associated estimated costs of financial distress and bankruptcy.

21.6 Other Factors Affecting Capital Structure Concept review question 1. Explain how the existence of informational asymmetries and agency problems may lead firms to follow a pecking order to financing.

Myers’ argument that firms follow a pecking order is based on divulging information. If the firms use internal cash flow then they do not need anyone’s permission. For example, even the shareholders can’t force the firm to pay a dividend. Similarly the firm can talk to a bank and divulge privileged information to secure a loan. However, when it issues new common shares, However, when it issues new common shares, as we have seen, the firm has to file a prospectus and reveal all material facts that affect the share price. In the process, the firm has to be careful not to reveal facts to a competitor that may give it a jump start and allow it to compete away the NPV benefits of the project.

The pecking order was also discussed in a different context by Gordon Donaldson.

Donaldson justified the pecking order through what we would now call agency arguments. He showed that managers’ commitment to the firm was through their human capital, versus the “short-term” financial commitment of shareholders. As a result, they were more concerned about the long-term survival of the firm and less inclined to take risks. For these agency reasons, he also argued that managers had a preference for internal cash flow (retained earnings), then debt, and finally issuing new common equity. In an agency model, this financing hierarchy imposes the least risk on the firm and requires the least justification by managers.

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21.7 Capital Structure in Practice Concept review question 1. Explain four of the most important factors influencing capital structure decisions as indicated in the survey results and how they relate to the conceptual discussion of an optimal capital structure.

The four most important factors in the Deutsche Bank survey were: 1) Credit rating 2) Tax shield 3) The ability to continue making investments 4) The ability to maintain dividends The credit rating reflects the ability of the firm to maintain its credit and raise capital. The tax shield value reflects the tax advantage to using debt financing. It is the firm’s underlying business risk that might restrict the firm’s ability to pay dividends or make investments if it has “too much” debt. The latter two concerns reflect the fact that the underlying M&M assumption that capital is always available, does not in reality hold.

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Chapter 22: Dividend Policy Multiple Choice Questions 1. Section: 22.3 Modigliani and Miller’s Dividend Irrelevance Theorem Learning objective: 22.3 Level of difficulty: Basic Solution: B 2. Section: 22.1 Forms of Dividend Payments Learning objective: 22.1 Level of difficulty: Intermediate Solution: C Retained earnings remain unchanged.

3. Section: 22.1 Forms of Dividend Payments Learning objective: 22.1 Level of difficulty: Intermediate Solution: B Ex-dividend date is the second business date before the holder of record date.

4. Section: 22.1 Forms of Dividend Payments Learning objective: 22.1 Level of difficulty: Intermediate Solution: A 5. Section: 22.2 Historical Dividend Data Learning objective: 22.2 Level of difficulty: Intermediate Solution: C 6. Section: 22.3 Modigliani and Miller’s Dividend Irrelevance Theorem Learning objective: 22.3 Level of difficulty: Intermediate Solution: B 7. Section: 22.3 Modigliani and Miller’s Dividend Irrelevance Theorem Learning objective: 22.3 Level of difficulty: Intermediate Solution: C P=

X1 − I1 +V1 400,000 − 200,000 +1,200,000 = = 1,217,391 1+ k 1+ 0.15

8. Section: 22.5 Dividend Policy in Practice Learning objective: 22.5 Level of difficulty: Intermediate

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Solution: C β=1 means that the firm adjusts immediately to the target dividend. ΔD = 1(4.5 – 3.75) = $0.75 9. Section: 22.5 Dividend Policy in Practice Learning objective: 22.5 Level of difficulty: Intermediate Solution: A The stock with the lower dividend yield will have higher capital gains (given that the pre-tax returns of the two stocks are the same).

10. Section: 22.6 Relaxing the M&M Assumptions: Welcome to the Real World!

Learning objective: 22.6 Level of difficulty: Intermediate Solution: D 11. Section: 22.7 Share Repurchases Learning objective: 22.7 Level of difficulty: Intermediate Solution: D 12. Section: 22.7 Share Repurchases Learning objective: 22.7 Level of difficulty: Intermediate Solution: C Practice Problems Basic 13. Section: 22.1 Forms of Dividend Payments Learning objective: 22.1 Level of difficulty: Basic Solution: A cash dividend plus a DRIP gives the investor a choice to decide whether to buy more shares with the cash distributed, while a stock dividend does not distribute cash to investors at all. A stock dividend is fully taxable, despite the fact that no cash is received.

14. Section: 22.3 Modigliani and Miller’s Dividend Irrelevance Theorem Learning objective: 22.3 Level of difficulty: Basic Solution: Given the M&M assumptions (no taxes, perfect market, all firms maximize value, and no debt), investors can buy or sell shares in an underlying company to meet their own cash flow needs.

The underlying company’s dividend policy is irrelevant. Investors willing to receive no dividends could use dividends to buy shares or participate in a DRIP while investors willing to receive more cash flows could simply sell a portion of their holdings.

15. Section: 22.4 The “Bird in the Hand” Argument

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Learning objective: 22.4 Level of difficulty: Basic Solution: Investors consider current (in hand) dividends more valuable than future capital gains.

16. Section: 22.5 Dividend Policy in Practice Learning objective: 22.5 Level of difficulty: Basic Solution: According to Lintner, the adjustment factor β measures how quickly a firm’s actual dividend moves towards its target dividend in a given period, with a value of 1 indicating immediate and full adjustment, and 0 representing no adjustment. An adjustment factor of 0.50 indicates that a firm only moves 50% of the way towards its target dividend in each period.

17. Section: 22.6 Relaxing the M&M Assumptions: Welcome to the Real World!

Learning objective: 22.6 Level of difficulty: Basic Solution: Investors in a lower tax bracket tend to hold high-dividend yielding stocks, while investors with longer horizons tend to hold low-dividend yielding stocks.

18. Section: 22.6 Relaxing the M&M Assumptions: Welcome to the Real World!

Learning objective: 22.6 Level of difficulty: Basic Solution: With transaction costs, the firm may have no cash or decreased cash available for dividend payout and consequently decrease its value. The payment of transaction costs also decreases the firm’s ability to accept positive NPV projects.

Intermediate 19. Section: 22.2 Historical Dividend Data Learning objective: 22.2 Level of difficulty: Intermediate Solution: D Payout Ratio = Earnings D = Payout Ratio * Earnings = 36% × $22,000,000 = $7,920,000 Div $7,920,000 Dividends per share = = = $1.32 6,000,000 nheld We use the dividend yield formula at this point to find the price per share: Div Per Share Div Yield = P Therefore: P =Div per share/Div Yield=$1.32/3.8%=$34.74

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20. Section 22.3 Modigliani and Miller’s Dividend Irrelevance Theorem Learning objective: 22.3 Level of difficulty: Intermediate Solution: P0 =

d1 + P1 1+k

=

2.50 + 30 = $28.02 1.16

21. Section: 22.3 Modigliani and Miller’s Dividend Irrelevance Theorem Learning objective: 22.3 Level of difficulty: Intermediate Solution: mP = V = m(D1 + P1 ) 0 0 (1 + K e) 150,000(1.80 + 1,800,000 =

1,800,000  (1.06)) 150,000

(1 + K e )

K e = 21% 22. Section: 22.3 Modigliani and Miller’s Dividend Irrelevance Theorem Learning objective: 22.3 Level of difficulty: Intermediate Solution: a. New proceeds required: nP1 = mD1 − ( X 1 − I1 ) = 5  5 − (42 − 30) = $13million b. Current equity market value = $64 × 5m = $320 million As the firm equity market value is not changed: 5P1 + nP1 = $320 5P1 = $320 - $13 = $307 P1 = $307/5 = $61.40 c. This implies the firm will need to issue the following number (n) of new shares: n = $13m/$61.4 = 211,726 new shares 23 Section: 22.5 Dividend Policy in Practice Learning objective: 22.5 Level of difficulty: Intermediate Solution: Number of shares outstanding = 5,600,000/32 = 175,000 Residuals this year = 800,000 – 600,000 = 200,000 Dividend per share = 200,000/175,000 = $1.14 per share The biggest shortcoming is the volatility of the dividend payout. With the residual dividend policy, dividend payout fluctuates with profits, especially for cyclical stocks. A stable dividend payout is optimal.

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24. Section: 22.5 Dividend Policy in Practice Learning objective: 22.5 Level of difficulty: Intermediate Solution: Setting dividend payout as a portion of profits increases the volatility of the dividend payments, which is taken as a negative signal by the market and consequently decreases firm value.

Particularly for firms in cyclical industries, dividend payout volatility could place significant downward pressure on the equity price. In practice, firms do not increase dividends until they are certain the new level could be maintained or could be increased to another new level, rather than having dividend payout fluctuate with profits.

25. Section: 22.6 Relaxing the M&M Assumptions: Welcome to the Real World!

Learning objective: 22.6 Level of difficulty: Intermediate Solution: We can calculate the after-tax dividend amount by multiplying the dividend by (1-T) where T is the personal tax rate.

Investor A’s after-tax dividend amount: D*(1-T) = nheld*(Div per share)*(1-T) = 1,000*$1.75*(1-0.30) = $1,225 Investor B’s after-tax dividend amount: D*(1-T) = nheld*(Div per share)*(1-T) = 1,000*$1.60*(1-0.22) = $1,248 Investor B receives the larger after-tax dividend amount.

26. Section: 22.6 Relaxing the M&M Assumptions: Welcome to the Real World!

Learning objective: 22.6 Level of difficulty: Intermediate Solution: Dividend initiation is usually a positive signal to the market, and pushes the equity price up. A dividend increase could be viewed as a positive signal or a negative signal depending on the perspective of the market. If the firm increases the dividend payout due to the lack of available investment and/or has no growth prospects, the equity value will decrease. If the firm is profitable, and is confident about keeping the increased dividend payout at the new level, then its equity value increases. A decrease of dividend is normally viewed negatively by the market.

27. Section: 22.6 Relaxing the M&M Assumptions: Welcome to the Real World!

Learning objective: 22.6 Level of difficulty: Intermediate Solution: The amount of the per share dividend increase is: Div per share increase = Div per share new – Div per share original = $0.42 – $0.30 = $0.12 Therefore the annual amount by which the dividend payment to the investor would increase is: Div = nheld*Div. per share increase = 1,500*$0.12 = $180.

Finally, calculating the increase in taxes: Tax Effect = Div*t = $180*25% = $45

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28. Section: 22.7 Share Repurchases Learning objective: 22.7 Level of difficulty: Intermediate Solution: Firms repurchase shares to: • Offset the exercise of executive stock options (ESOs).

• Return the firm to its optimal capital structure after debt is raised.

• Send a signal; management often indicates that it repurchased shares to signal to the market that it thinks the stock is undervalued.

• Repurchase dissident shares; when there is substantial disagreement among shareholders about the future of the firm, a share repurchase program gives the dissidents an opportunity to sell their shares without depressing the market price, thereby removing an “overhang” of shares.

• Remove cash without generating expectations for future distributions.

• Take the firm private.

Challenging 29. Section: 22.3 Modigliani and Miller’s Dividend Irrelevance Theorem Learning objective: 22.3 Level of difficulty: Challenging Solution: a. Currently the firm has free cash flows of $2 million a year which could be paid in dividends and has a value of $50*2 million shares = $100 million. This valuation implies a discount rate of 2%. This discount rate is not expected to change as George buys or sells stock—the business itself does not change. To receive $20 million, George will need to sell 400,000 shares at $50.

The result of this transaction is that George will now own 1.2 million – 400,000 = 800,000 shares or 40% of the company. The impact on CGC is minimal unless George is a critical participant in the management of the firm and his decision signals that he may be planning on leaving the firm. The impact on George’s control of the firm may be important—he is going from owning 60% of the firm to owning 40%. For most firms this is still sufficient to maintain effective control of the firm, but he will no longer have absolute control. This may be a major issue for George. b. From the Modigliani-Miller dividend irrelevance theorem, we know that the value of the firm will not be changed. For George to receive a dividend of $20 million, the firm will need to pay a total dividend of $33.33 million (remember George only owns 60% of the firm). CGC will need to issue $33.33 million / $50 = 666,667 shares. If they issue more stock, The dividend will need to go higher than $33.33 million because of George’s reduced ownership (see next part). ii) The total value of CGC will remain at $100 million as the operating cash flows and capital expenditure needs have not changed. To see this: $2 million of continuing free cash flows divided by 2% = $100 million. We are assuming that the $33.3 million is a one-time special dividend.

The impact of the firm issuing stock is that George will now own 1.2 million shares but there are now 2.67 million shares outstanding. He will own 45% of the firm after the new issue. Once again, George’s level of control of the firm will be diluted.

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30. Section: 22.3 Modigliani and Miller’s Dividend Irrelevance Theorem Learning objective: 22.3 Level of difficulty: Challenging Solution: D 8 = = $53.33 a. Price = ke 0.15 b. If the firm undertakes the project, there will be no dividend in the current year. Starting next year, the dividend will be $8.80 (if return is 10%), or $9.20 (if return is 15%), or $9.60 (if return is 20%).

Therefore: 8.80 1  10% return would imply: Share Price = = $51.01 0.15 1.15 9.20 1  15% return would imply: Share Price = = $53.33 0.15 1.15 9.60 1  20% return would imply: Share Price = = $55.65 0.15 1.15 Given a 15% return on the new investment, shareholders are indifferent between receiving a dividend this year or receiving increased dividends from next year. At 20%, they prefer the new investment. At 10% the new investment should not be undertaken. c. If investments for the kind of business the firm is in typically provide a rate of return of 15% (as required by the shareholders), it is not reasonable to assume that the firm can continually find enough positive NPV opportunities yielding at least 20 percent.

31. Section: 22.3 Modigliani and Miller’s Dividend Irrelevance Theorem Learning objective: 22.3 Level of difficulty: Challenging Solution: a. If the firm pays out all earnings in dividends, D 10 10 (1 – 0.3) Price = = or = $66.67 ke 0.15 0.105 b. If the firm retains the current dividend for reinvesting at 15%, then the dividends from next year will be $11.5, which after tax will be (1-0.3)*11.5=$8.05 To provide an expected after-tax return of 10.5% at the end of the current year, the shares should 8.05 trade at: = = $76.67 0.105 which provides a $10 capital gain over the current share price of $66.67. Thus, if earnings are reinvested in new projects that provide a 15% rate of return, then the current shareholder trades off a $10 dividend against a $10 capital gain. The desirability of this new project will now depend on the relative tax rate levied on dividends vs. capital gains. Investors will prefer the investment if capital gains are taxed at a lower rate than dividends. If dividends are taxed at a lower rate than capital gains, the project should not be undertaken.

32. Section: 22.3 Modigliani and Miller’s Dividend Irrelevance Theorem

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Learning objective: 22.3 Level of difficulty: Challenging Solution: a. Paying cash dividends: P0 = (P1+ D1)/ (1+K) = (30+6)/ (1+0.12) = $32.14 b. Share buyback: Number of shares outstanding after buyback = 100,000 – (600,000 / 36) = 100,000 – 16,666.67 = 83,333.33 c. Po = [3,000,000 / (83,333.33)] / (1.12) = $32.14 The price would be the same either way.

33. Section: 22.3 Modigliani and Miller’s Dividend Irrelevance Theorem Learning objective: 22.3 Level of difficulty: Challenging Solution: Each share pays a dividend of $2,000 a year. The value of a share is $2,000/.05 = $40,000. Note that because the dividends are a perpetuity, the value of the shares will not change over time.

Each person (Marie, Charlie, and Frank) owns 10% of the company or 100 shares. Assume that they all sell their shares at the end of year two, although that is not a necessary scenario.

Marie: wants $400,000 at the end of year 1.

• At the end of year one, she will receive 100*2,000 = $200,000 of dividends.

• She will need to sell (400,000 – 200,000)/40,000 = 5 shares • Net effect: receive $400,000 at the end of year 1, which she consumes and now owns 95 shares • At the end of year 2: receives $190,000 of dividends and sells the remaining 95 shares at $40,000 for $3,800,000 • Value at the end of year 2: $190,000+$3.8 million = $3.99 million.

Value at time 2 = $3.99 million. PV at 5% = $3.62 million. Note: this is less than the value of the shares at time zero because her consumption of the dividends at time 1 was a negative NPV project. The value of the stock was based on the assumption that the dividends would be reinvested at 5%.

Charlie: • Receives $200,000 dividend and sells 5 shares • Invests $400,000 at 15% for one year ▪ At the end of year 2: value of this investment = $460,000 • At the end of year 2, receives $190,000 dividends and sells the remaining 95 shares at $40,000 for a total of $3.99 million • Value at the end of year 2: $460,000 + $190,000 + 3.99 million = $4.64 million.

PV at 5% of $4.64 million at the end of year 2 = $4.21 million. Note: this is greater than the value of the shares because Charlie reinvested the dividend at a rate that was greater than 5%.

Radha:

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Receives $200,000 dividend and buys 5 more shares At the end of year 2, receives 105*$2,000 = $210,000 dividends and sells the remaining 105 shares at $40,000 for a total of $4,410,000 Value at the end of year 2 = $4.410 million.

PV at 5% of $4.410 million at the end of year 2 = $4 million. Note: this is equal to the value of the shares at time zero because Radha reinvested the dividend at 5%.

34. Section: 22.4 The “Bird in the Hand” Argument Learning objective: 22.4 Level of difficulty: Challenging Solution: a. The “bird in the hand” argument is consistent with Client A. She prefers to have the “sure thing,” the dividend, rather than the potential capital gain. b. Essentially these two investors are interested in different aspects of the stock: Client A wants the dividends while Client B wants the capital gains. If Alice were to buy the stock and then sell Client A a claim to the dividends and sell Client B a claim to whatever is left over (i.e., the capital gain) then Alice would be able to satisfy the needs of both investors. Client A would get her desired pattern of steady cash flows and Client B would not have to pay taxes on the dividends as he would only have the capital gains.

35. Section: 22.6 Relaxing the M&M Assumptions: Welcome to the Real World!

Learning objective: 22.6 Level of difficulty: Challenging Solution: a. If the change in dividends was unexpected, then I would expect the price of Abacus to increase on July 26. The amount of the increase should be more than $1 if I expect the increased dividend to continue in the future. If the change in the dividends was expected, then I would not expect the price of Abacus to change on July 26. The price would already have incorporated the change in dividends, so it would not be news when the announcement was made. b. If the shareholders do not pay taxes, I would expect the stock price to decline by the amount of the dividend. On the day before the ex-dividend date, the stock’s value = X + dividend. On the ex-dividend date, the stock’s value no longer includes the dividend, so as long as there was not information released on the ex-dividend date, the stock price should change from X + dividend to X, a decline equal to the value of the dividend. c. The stock price reaction will be less than the value of the dividend. Investors buying the stock prior to the ex-dividend date will only be willing to pay X + the after-tax value of the dividend.

On the ex-dividend date, the stock will drop to X and the decline will be equal to the after-tax value of the dividend. As long as tax rates are greater than 0, the decline should be less than the before-tax value of the dividend. Consider an extreme example: tax rate on dividends = 100%.

There should be no stock price reaction on the ex-dividend date. There is no change in the cash flows to the investors as the government will take the entire dividend so the investor would not have paid “extra” for the stock prior to the ex-dividend date.

36. Section: 22.6 Relaxing the M&M Assumptions: Welcome to the Real World!

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Learning objective: 22.6 Level of difficulty: Challenging Solution: Kumar has not considered the impact of the information asymmetry between investors (the market) and management (the firm). Kumar knows he has a good project and that this project will increase shareholder wealth; however, investors do not know this. Kumar could tell investors this news, but why should they believe him? If Kumar could credibly signal the value of the project, then the dividend cut would be positively received by the market. However, as he cannot do so, the investors form an expectation about what type of firm it is—good or bad.

Based on this expectation, the investor reacts.

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Answers to Concept Review Questions 22.1 Forms of Dividend Payments Concept review questions 1. Define four important dates that arise with respect to dividend payments.

The four dates are the declaration dates, ex-dividend date, holder of record date, and pay date in the time order.

2. Explain the similarities and differences of DRIPs, stock dividends, and stock splits.

A cash dividend along with a DRIP is similar to a stock dividend because investors receive shares rather than cash payments. However, there is one very significant difference between them. With the cash dividend plus DRIP, the cash is distributed first and it is up to the investor to decide whether they want to buy more shares. Regardless of the investors’ decisions, the firm has to have the cash to make the distribution. With the stock dividend, on the other hand, firms often do not have the cash and simply issue a stock dividend to give the investor “something.”

An extreme version of a stock dividend is a stock split. In this case, there is a greater than 25 percent increase in the number of shares outstanding. Both stock dividends and stock splits simply divide the value of the common shares among more shares and all else constant, reduce the price per share. There are some accounting advantages to this since the retained earnings account is not altered, but the number of shares outstanding is simply increased. In addition, unlike stock dividends, investors face no tax implications arising from a stock split, except that the average purchase price will be adjusted downward to reflect the split.

22.2 Historical Dividend Data Concept review questions 1. What obvious question arises when we examine historical patterns in aggregate dividend payouts?

This naturally raises an important question (1): Why are dividends smoothed and not matched to profits? Or another way of saying this is: why don’t firms just pay a constant proportion of profits out as dividends and cut them when their profits and cash flows drop as they do during recessions?

2. What obvious question arises when we examine cross-sectional patterns in the dividend payouts of individual companies?

This raises another important question (2): Why is there such a substantial difference in dividend yields (and payouts) across major Canadian companies? Why do some firms have very high dividends and some very low or non-existent?

22.3 Modigliani and Miller’s Dividend Irrelevance Theorem Concept review questions 1. Explain how and under what assumptions M&M show that dividends are irrelevant.

The assumptions are as follows: (1) There are no taxes; (2) Markets are perfect; (3) All firms maximize value; (4) There is no debt. Without any debt, the sources and uses of funds identity (i.e., sources = uses) can be expressed as: X1+nP1=I1+nD1. Substituting this identity into

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mP0=V0=m (D1+P1)/(1+Ke), the price becomes the sum of the discounted future (X-I). Dividend does not enter the pricing formula.

2. Explain the relationship between M&M’s argument and the use of a residual dividend policy.

According to M&M’s argument, stock value equals the present value of future (X-I). According to discount dividend model, stock value equals the present value of future dividends. These two arguments should give the same price. Obviously these two approaches must give exactly the same value, which implies that the dividend is equal to the free cash flow each period. In this way the dividend is the residual that remains after the firm has taken care of all of its investment requirements, so we call this the residual theory of dividends.

3. Briefly describe the notion of homemade dividends as it relates to M&M’s irrelevancy argument.

The example above illustrates that investors can buy or sell shares in an underlying company to create their own cash flow patterns, or simulated dividend streams. Investors who don’t like dividends can sign up for a DRIP and undo the effects of a firm’s dividend policy. Conversely, investors who like dividends can create a cash flow from the firm simply by selling part or all of their shares. What the example illustrates is that under the M&M assumptions, the investor is indifferent as to a firm’s dividend policy.

22.4 The “Bird in the Hand” Argument Concept review questions 1. Explain the “bird in the hand” argument about dividends.

“Bird in the hand” argument is a notion that a cash dividend is worth more than an equivalent capital gain. The intuition is that firms that pay cash dividends are less risky than ones where the investors’ return comes by way of a capital gain. It then seems to follow that firms that do not pay a cash dividend will be seen as riskier, causing the cost of equity capital to increase and the stock price to fall. This idea is called the bird in the hand argument on the basis that a “bird in the hand” (cash dividend) is worth more than “two in the bush” (twice as much in capital gains).

2. Reconcile the predictions of M&M with Gordon’s arguments about dividend policy.

Gordon is right in arguing that the dividend yield does indicate the risk of the firm and firms that pay large amounts of dividends are less risky than non-dividend-paying firms. However, M&M are also right because changing the dividend cannot change the underlying risk of the firm; this comes from its underlying operations. In this sense, the dividend should reflect the firm’s operations through the residual value of dividends and the firm cannot change these underlying operational characteristics by merely changing the dividend.

22.5 Dividend Policy in Practice Concept review question 1. What does real-world evidence imply about how firms manage their dividend payments?

M&M suggests that a firm can cut the dividend if it is short of cash and increase it when it has surplus in cash. However, the real work evidence implies that firms smooth dividends and are reluctant to cut dividends.

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22.6 Relaxing the M&M Assumptions: Welcome to the Real World!

Concept review questions 1. Explain why dividend policy will be relevant in the presence of transactions costs, informational asymmetry and agency problems, and taxes.

(1) Transactions costs are important because in the M&M model, it is assumed that the firm can pay a dividend and then issue shares to raise the money needed to make the required level of investment. Let’s take an extreme situation where transactions costs are very high and the firm cannot raise new capital. In this case the payment of the cash dividend reduces the amount of money available to invest and causes the firm to forgo positive NPV projects. The value of the firm would go down since it is not creating value by accepting positive NPV projects. Thus growth firms do not pay dividends and dividend paying firms smooth dividends.

(2) Information asymmetry. M&M assumes perfect markets where all market participants have access to the same information. In practice, management usually knows more than external investors. Investors tend to view firms’ information releases with a great deal of skepticism. One way of signaling is to only increase the dividend when the firm believes that it will not have to cut it in the future. The fact that paying the cash dividend reduces the funds available to the firm means that they will only do so when they think that their internal funds are increasing and are enough to support the dividend payment. Otherwise, it will impose more transactions costs on the firm in having to raise more funds in the future. This signaling model explains why share prices tend to increase on unexpected dividend initiations or increases. In both cases the dividend increase indicates good news because it suggests that management believes it can support the dividend out of future earnings.

(3) Agency costs. Investors are worried that senior management may waste corporate resources in over-investing in poor (negative NPV) projects, since it is not “their” money but the shareowners’. Paying a large dividend and forcing the firm to justify future expenditures creates value by controlling management. However, while an agency perspective justifies the stock market’s reaction to dividends, it cannot explain the dividend smoothing phenomena.

(4) Tax. Investors with low tax rate on dividends buy high dividend stocks, but investors with high tax rate on dividends buy low-dividend stocks. So although the payment of a dividend may not have an impact on the general level of share prices, it will be an important influence on the type of investors that a firm attracts.

2. Describe split shares, and explain what their popularity implies about investor preferences for dividends in the real world.

The popularity of split shares has two major implications. First, there are investor dividend clienteles and dividends do matter to some investors. This emphasizes the need for companies to consider dramatic dividend changes as a serious event not to be taken lightly. Second, the capital shares are marketed as a leveraged investment and can be considered an application of the “homemade” leverage theorem advanced by M&M. 22.7 Share Repurchases

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Concept review questions 1. Why can share repurchases be viewed as an alternative to paying a cash dividend?

Share repurchase is simply another form of payout policy. It is an alternative to a cash dividend where the objective is to increase the price per share rather than paying a dividend and forcing the shareholders to immediately pay tax on the dividend.

2. What factors may influence a firm’s decision to enter into share repurchases?

Several other reasons may motivate share repurchases, including: offsetting the exercise of executive stock options (ESOs); leveraged recapitalizations; Information or signaling effects; repurchase dissident shares; removing cash without generating expectations for future distributions; and take the firm private.

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Chapter 23: Working Capital Management – General Issues Multiple Choice Questions 1. Section: 23.1 The Importance of Working Capital Management Learning Objective: 23.1 Level of difficulty: Intermediate Solution: C 2. Section: 23.2 An Integrated Approach to Net Working Capital (NWC) Management Learning Objective: 23.2 Level of difficulty: Intermediate Solution: C 3. Section: 23.2 An Integrated Approach to Net Working Capital (NWC) Management Learning Objective: 23.2 Level of difficulty: Intermediate Solution: D As sales increase, cash, inventory, accounts receivable, and trade credit normally increase. Shortterm debt does not necessarily increase as sales increase.

4. Section: 23.4 Working Capital Management Learning Objective: 23.4 Level of difficulty: Intermediate Solution: C Current Ratio =

CA 500,000 + 800,500 + 700,000 + 1,003,000 = = 3.34 CL 100,000 + 800,000

500,000 + 800,500 + 700,000 = 2.22 100,000 + 800,000 5. Section: 23.4 Working Capital Management Learning Objective: 23.4 Level of difficulty: Intermediate Solution: D ACP = 365 / (Rev/AR) = 365 / (1,287,555/700,000) = 198 days Quick Ratio =

6. Section: 23.4 Working Capital Management Learning Objective: 23.4 Level of difficulty: Intermediate Solution: C Operating cycle = ACP + ADRI = ACP + [365 / (CGS/Invent)] = 198 + 365/(550,000/1,003,000)= 198 + 666 = 864 days.

7. Section: 23.4 Working Capital Management Learning Objective: 23.4

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Level of difficulty: Intermediate Solution: C 8. Section: 23.4 Working Capital Management Learning Objective: 23.4 Level of difficulty: Intermediate Solution: B 9. Section: 23.4 Working Capital Management Learning Objective: 23.4 Level of difficulty: Intermediate Solution: A 10. Sections: 23.3 Analyzing Cash Inflows and Outflows and 23.4 Working Capital Management Learning Objectives: 23.3 and 23.4 Level of difficulty: Intermediate Solution: B 11. Section: 23.3 Analyzing Cash Inflows and Outflows and 23.4 Working Capital Management Learning Objectives: 23.3 and 23.4 Level of difficulty: Intermediate Solution: D 12. Section: 23.3 Analyzing Cash Inflows and Outflows and 23.4 Working Capital Management Learning Objectives: 23.3 and 23.4 Level of difficulty: Intermediate Solution: A Practice Problems Basic 13. Section: 23.1 The Importance of Working Capital Management Learning Objective: 23.1 Level of difficulty: Basic Solution: Characteristics of sound net working capital management include: • Maintenance of optimal cash balances • Investment of any excess liquid funds in marketable securities that provide the best return possible, considering any liquidity and/or default risk constraints • Proper management of accounts receivable • An efficient inventory management system • Obtaining an appropriate level of short-term financing, in the least expensive and most flexible manner possible 14. Section: 23.1 The Importance of Working Capital Management Learning Objective: 23.1 Level of difficulty: Basic

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Solution: Net working capital is current assets – current liabilities. Both items are taken from the firm’s balance sheet.

15. Section: 23.4 Working Capital Management Learning Objective: 23.4 Level of difficulty: Basic Solution: CCC = Operating cycle (OC) – Average days of revenues in payables (ADRP) = OC – [365 / (Rev/AP)] = 864 – [365 / (1,287,555/800,000)] = 864 – 227 = 637 days Intermediate 16. Section: 23.1 The Importance of Working Capital Management Learning Objective: 23.1 Level of difficulty: Intermediate Solution: Businesses that allow a customer long periods of time to pay their bills are, in effect, providing short-term financing to their customers by allowing them to use the cash necessary to pay its invoices for other purposes in the short-term. For example, if a customer is allowed 60 days to pay an invoice instead of 30, it can use the cash amount of the invoice for alternative purposes during the extra 30 days.

17. Section: 23.1 The Importance of Working Capital Management Learning Objective: 23.1 Level of difficulty: Intermediate Solution: Net working capital (NWC) is defined as the difference between current assets and current liabilities. Both current assets and current liabilities represent a significant component of the balance sheet in an absolute and relative sense for the majority of firms. Therefore efficient management of NWC is vital for the overall success of most firms.

18. Section: 23.2 An Integrated Approach to Net Working Capital (NWC) Management Learning Objective: 23.2 Level of difficulty: Intermediate Solution: Cash inflows come primarily from cash sales and collections of accounts receivable.

Cash outflows come from expenses that are paid in cash and the payment of accounts payable.

19. Section: 23.2 An Integrated Approach to Net Working Capital (NWC) Management Learning Objective: 23.2 Level of difficulty: Intermediate Solution: Cash budgets are in effect detailed (i.e., constructed monthly, weekly, or daily) pro forma cash flow statements and can be used to construct longer term aggregate pro forma cash flow statements, as well as income statements and balance sheets.

20. Section: 23.2 An Integrated Approach to Net Working Capital (NWC) Management Learning Objective: 23.2

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Level of difficulty: Intermediate Solution: a. Sources of funds using the indirect method described in chapter 2: Net operating income Depreciation Sale of land Total sources of funds

$60,000 10,000 25,000 $95,000

Purchase of equipment Retirement of long-term debt Dividends paid Purchase of long-term investments Total uses of funds

$15,000 30,000 15,000 10,000

b. Uses of funds:

$70,000

c. Increase in cash: $95,000 – $70,000 = $25,000 21. Section: 23.2 An Integrated Approach to Net Working Capital (NWC) Management Learning Objective: 23.2 Level of difficulty: Intermediate Solution: Cash inflows: 50,000 + 100,000 + 70,000 = 220,000 Cash outflows: 35,000 + 20,000 + 80,000 + 35,000 = 170,000 Ending cash = 20,000 + 220,000 – 170,000 = $70,000 22. Section: 23.3 Analyzing Cash Inflows and Outflows Learning Objective: 23.3 Level of difficulty: Intermediate Solution: a. Decrease b. Decrease c. Increase d. Increase e. Increase f. Decrease 23. Section: 23.3 Analyzing Cash Inflows and Outflows Learning Objective: 23.3 Level of difficulty: Intermediate Solution: a. If a firm’s planned sales growth exceeds its break-even sales growth rate, then the firm will require an infusion of cash from external sources in order to achieve its planned sales growth.

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b. If, on the other hand, a firm’s planned sales growth rate is less than its break-even sales growth rate, then the firm is not growing as fast as it potentially could. There may be economic reasons that the firm is not making substantial reinvestments in its business, such as mature products, substantial market penetration, and decreasing returns to scale from further growth.

24. Section: 23.4 Working Capital Management Learning Objective: 23.4 Level of difficulty: Intermediate Solution: The receivables turnover ratio and the average collection period both measure the efficiency of a firm’s credit policy. The receivables turnover ratio indicates the number of times the average dollar of receivables is collected during a year. The average collection period measures the average number of days it takes for the average dollar of receivables to be collected from customers.

25. Section: 23.3 Analyzing Cash Inflows and Outflows Learning Objective: 23.3 Level of difficulty: Intermediate Solution: Measures to improve working capital management include: • Scenario analysis to show the potential impact on cash flow of unforeseen events, such as market cycles, loss of a prime customer, or actions by competitors • Contingency planning and risk-management procedures to keep the company solvent when unexpected events occur • Addressing the issue of working capital on a corporate-wide basis, so that cash generated at one location or by one business unit can be utilized by another. Integrated financial reporting and decision making are essential for this to succeed.

• An innovative approach to management that combines operational and financial skills to identify and implement strategies that generate short-term cash • Effective dispute management procedures and improved customer service that result in reduced operating costs • Integrated planning with customers and suppliers, particularly where it involves matching production with their inventory requirements to reduce inventory levels 26. Section: 23.3 Analyzing Cash Inflows and Outflows Learning Objective: 23.4 Level of difficulty: Intermediate Solution: The operating cycle is the average time required to acquire inventory, sell it, and collect the proceeds. The cash conversion cycle is an estimate of the average time between when a firm pays cash for its inventory purchases and when it receives cash for its sales (the average number of days of revenues a firm must finance outside the use of trade credit). The operating cycle and the cash conversion cycle are related: to determine the cash conversion cycle, we subtract the average number of days it takes to discharge payables from the operating cycle.

27. Section: 23.4 Working Capital Management Learning Objective: 23.4 Level of difficulty: Intermediate

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Solution: The current ratio compares current assets to current liabilities, while the quick ratio compares only cash and near-cash current assets to current liabilities. Generally, this means that while the current ratio includes inventories, the quick ratio excludes inventories. While marketable securities and receivables can usually be collected quickly without a loss of value, it is often necessary to discount (sometimes heavily) inventories in order to sell them quickly.

28. Section: 23.4 Working Capital Management Learning Objective: 23.4 Level of difficulty: Intermediate Solution: ACP = AR/(Annual Sales/365), so originally AR = ACP × (Annual Sales/365) = 32 × (125,000/365) = $10,958.90 New AR = 30 × (140,000/365) = $11,506.85 So the change in NWC = $11,506.85 - $10,958.90= $547.95 29. Section: 23.4 Working Capital Management Learning Objective: 23.4 Level of difficulty: Intermediate Solution:

Before: OC = ADRI + ACP = 98 + 90 = 188 CCC = OC – ADRP = 188 – 58 = 130 After: OC = 82 + 90 = 172 CCC = 172 – 48 = 124 The operating cycle will decrease by 16 days and the cash cycle will decrease by 6 days.

30. Section: 23.4 Working Capital Management Learning Objective: 23.4 Level of difficulty: Intermediate Solution:

ADRI = 365/IT = 365/6.25 = 58.4 days ACP = 365/RT = 365/8 = 45.6 days.

OC = ADRI + ACP = 58.4 + 45.6 = 104.0 days CCC = OC – ADRP = 104.0 – 40.0 = 64.0 days So, on average this firm must finance 64.0 days of purchases.

31. Section: 23.4 Working Capital Management Learning Objective: 23.4 Level of difficulty: Intermediate Solution: a. CR = CA / CL = (250+150+300) / (250+100) = 700/350 = 2.00

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QR = (CA – Invent) / CL = (700–300) / 350 = 400/350 = 1.14 NWC = CA – CL = 700 – 350 = $350 b. IT = Rev / Invent = 2,000/300 = 6.67 RT = Rev / AR = 2,000/150 = 13.33 PT = Rev / AP = 2,000/250 = 8.00 c. ADRI = 365 / IT = 365/6.67 = 54.7 days ACP = 365 / RT = 365/13.33 = 27.4 days ADRP = 365 / PT = 365/8.00 = 45.6 days d. OC = ADRI + ACP = 54.7 + 27.4 = 82.1 days CCC = OC – ADRP = 82.1 – 45.6 = 36.5 days Challenging 32. Section: 23.2 An Integrated Approach to Net Working Capital (NWC) Management Learning Objective: 23.2 Level of difficulty: Challenging Solution:

Opening cash balance Total cash receipts Cash on hand Less: Operating expenses – fixed – variable Closing cash balance Line of credit

October $43,000 20,000 63,000

November $15,000 30,000 45,000

December $ 0 85,000 85,000

40,000

40,000

40,000

8,000 15,000

12,000 – 7,000

34,000 11,000

0

7,000

– 7,000

0

$4,000

7,000

(7,000)

New opening cash balance

$15,000

Line of credit used (paid)

0

$

33. Section: 23.2 An Integrated Approach to Net Working Capital (NWC) Management Learning Objective: 23.2 Level of difficulty: Challenging Solution: Cash Inflows: Sales Current month sales

January

February

March

April

50,000

51,000

52,500

55,000

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Previous month’s sales Sales from two months ago Total cash inflows

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25,000

25,000

25,500

26,250

25,000

25,000

25,000

25,500

100,000

101,000

103,000

106,750

60,000 60,000

60,000 60,000

60,000 60,000

70,000 70,000

20,000

30,000

35,000

25,000

*40,000 120,000 –20,000

0 90,000 11,000

**20,000 115,000 –12,000

0 95,000 11,750

30,000 10,000 0

10,000 21,000 11,000

21,000 9,000 –1,000

9,000 20,750 10,750

Cash Outflows: Purchases Two months ago Total purchase outflows Wages and miscellaneous Other cash outflows Total cash outflows Net cash flow Beginning cash Ending cash Surplus/deficit *Dividend Payment **Equipment Purchase

34. Section: 23.3 Analyzing Cash Inflows and Outflows Learning Objective: 23.3 Level of difficulty: Challenging Solution: a. With the data α = 0.60; b = 0.80; β = 0.4 and γ = 2.0.

Plugging these values into Equation 23-4 we get: 1−b 1 − 0.80 g= = = 0.1515 = 15.15% b( +  ) −  0.80(0.4 + 2) − 0.60 b. With the new policy, γ = 3 and α = 0.4, so the growth rate decreases to: 1 − 0.80 g= = 0.0862 = 8.62% 0.80(0.4 + 3.0) − 0.4 35. Section: 23.3 Analyzing Cash Inflows and Outflows Learning Objective: 23.3 Level of difficulty: Challenging Solution: a. With the data α = 0.75; b = 0.60; β = 0.5 and γ = 4.0.

Plugging these values into Equation 23-4 we get:

g=

1 − 0.6 1−b = = 0.2051 = 20.51% b( +  ) −  0.6(0.5 + 4) − 0.75

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b. With the new policy, γ = 3 and b = 0.55, so the growth rate increases to: g=

1 − 0.55 = 0.3830 = 38.30% 0.55(0.5 + 3) − 0.75

36. Section: 23.4 Working Capital Management Learning Objective: 23.4 Level of difficulty: Challenging Solution: CCC = OC – ADRP = ADRI + ACP – ADRP CCC = 365/15 + 365/10 – 365/5 = 24.3 + 36.5 – 73 = 60.8 – 73 = –12.2 days A negative cash conversion cycle can be achieved, for example, when a company has an efficient inventory policy and collects from customers before it pays its suppliers. These are extremely advantageous business conditions, and usually require some sort of market power over either customers or suppliers or both in order to sustain them in the long run. Notice that, in this case, MB Corporation turns its receivables over twice as fast as it turns its payables over.

37. Section: 23.4 Working Capital Management Learning Objective: 23.4 Level of difficulty: Challenging Solution: The firm could have CA=$80,000 and CL=$100,000, which gives us: CR = CA / CL = 80,000 / 100,000 = 0.80, which is less than one as specified in the question.

Suppose the firm pays an existing $10,000 account payable, so now we have: CR = CA / CL = (80,000 – 10,000) / (100,000 – 10,000) = 0.7778 We can see that if the CR < 1, then the CR decreases with the cash payment.

We can also show that if the CR > 1, the CR would increase; and if the CR = 1, the CR would not change with the cash payment.

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Answers to Concept Review Questions 23.1 The Importance of Working Capital Management Concept review questions 1. What is the difference between profit and cash flow from operations?

The basic difference is that profits are not cash and a firm can only pay its bills with cash.

In accounting items, depreciation and amortizations are non-cash charges and need to be added to net income to get cash flow. Moreover, sales on credit are income, but not cash. Also unsold goods are inventories in accounting, but it is a cash outflow. The increase in receivables and inventory, net of payables, are the most important net working capital items.

2. Why should all firms prepare a cash budget?

The important thing about the cash budget is that it forecasts cash inflows and outflows over a forecast horizon and their cumulative impact on the firm’s cash balances. Typically, firms prepare a cash budget for at least the upcoming year, on at least a monthly (and sometimes even a weekly or daily) basis. These cash budgets are important planning tools for the firm. For example, they indicate when and for how long a firm can expect to have excess cash balances that can be invested in marketable securities. Cash budgets also show when and for how long a firm may require some additional borrowing to cover any cash shortfalls, so it can arrange for some short-term borrowing.

23.3 Analyzing Cash Inflows and Outflows Concept review questions 1. What is the relationship between the break-even sales growth rate and a firm’s collection policy, payables policy, and inventory policy?

The relationship is given in Equation 23-4. g = (1–b)/((b*(beta + gamma) – alpha), where g is the break-even sales growth rate, b is the percentage of cost of goods sold, alpha is the percentage of sales collected this month, beta is the proportion of this month’s production costs that are paid this month, gamma is the percentage of the firm’s monthly sales tied up in inventory, and 1/gamma is the monthly inventory turnover ratio.

2. Why does cash flow from operations increase if the firm speeds up the collection of receivables, delays paying its bills, or increases its inventory turnover ratio?

The cash change formula is given in Equation 23-3. That is change in cash/previous sales = (1 – b) + [alpha–b(beta + gama)]*g, where g is the sales growth rate, b is the percentage of cost of goods sold, alpha is the percentage of sales collected this month, beta is the proportion of this month’s production costs that are paid this month, gamma is the percentage of the firm’s monthly sales tied up in inventory, and 1/gamma is the monthly inventory turnover ratio. As seen in this equation, cash increases with the percentage of sales collected this month (alpha), decreases in the percentage of this month’s production cost that is paid this month (beta), and increases in the inventory turnover ratio (1/gamma).

23.4 Working Capital Management in Practice

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Concept review questions 1. What are the limitations of the current ratio and the quick ratio as measures of working capital management?

A high current ratio or a high quick ratio does not necessarily mean that the firm is practicing effective W/C management. In fact, it could indicate quite the opposite—that is, perhaps the firm is being too conservative and maintaining excessive liquidity, or perhaps it has high ratios because its credit policy is too lenient, which has left it with high levels of receivables outstanding.

2. What are the operating cycle and the cash conversion cycle, and how are they related to working capital policy?

The operating cycle (OC) measures the average number of days a firm holds items in inventory before they are sold, plus the average time it takes to collect on sales. Large OC figures indicate that a firm has a long operating cycle that requires large average investments in receivables or inventory. The cash conversion cycle (CCC) represents the average number of days of sales that a firm must finance outside the use of trade credit. As such, it is an important ratio that firms and their creditors consider when arranging financing.

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Chapter 24: Working Capital Management – Current Assets and Current Liabilities Multiple Choice Questions 1. Section: 24.1 Cash and Marketable Securities Learning Objective: 24.1 Level of difficulty: Basic Solution: D 2. Section: 24.1 Cash and Marketable Securities Learning Objective: 24.1 Level of difficulty: Intermediate Solution: D Near-cash is virtually default free, i.e., little credit risk.

3. Section: 24.2 Accounts Receivable Learning Objective: 24.2 Level of difficulty: Intermediate Solution: A Historically, mailing time is the longest.

4. Section: 24.2 Accounts Receivable Learning Objective: 24.2 Level of difficulty: Intermediate Solution: A 365 20  365 45−30   n − day financing cost  n k = 1 + − 1 = 63.49%  − 1 = 1 + 980  Purchase price     5. Section: 24.2 Accounts Receivable Learning Objective: 24.2 Level of difficulty: Basic Solution: D Sometimes a factor will purchase a firm’s receivables.

6. Section: 24.3 Inventory Learning Objective: 24.3 Level of difficulty: Basic Solution: D 7. Section: 24.4 Short-Term Financing Considerations Learning Objective: 24.4 Level of difficulty: Basic Solution: D The cost of operating loans is relatively low.

8. Section: 24.4 Short-Term Financing Considerations

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Learning Objective: 24.4 Level of difficulty: Intermediate Solution: C K= (1+0.06/12)12 –1 = 6.17% 9. Section: 24.4 Short-Term Financing Considerations Learning Objective: 24.4 Level of difficulty: Basic Solution: D Only large firms with top-notch credit ratings can issue CP. Practice Problems Basic 10. Section: 24.2 Accounts Receivable Learning Objective: 24.2 Level of difficulty: Basic Solution: Three major sources of float are: • The time it takes the cheque to reach the firm after it is mailed by the customer (longest).

• The time it takes the receiving firm to process the cheque and deposit it in their account after the cheque is received.

• The time it takes the cheque to clear through the banking system so that the funds are available to the firm.

Common methods include post-dated cheques, debit cards, pre-authorized payment, electronic funds transfer (EFT) and electronic data interchange (EDI), and concentrated banking arrangement.

11. Section: 24.2 Accounts Receivable Learning Objective: 24.2 Level of difficulty: Basic Solution: A factor acts as an independent credit department outside of a firm by checking credit of new customers, authorizing credit, handling collections, and bookkeeping. A factor may also purchase accounts receivable from its clients at a discount. However, we should always evaluate the cost and benefits of hiring a factor. A similar example is a pension buyout in the UK, where insurance firms purchase pension liabilities from various pension plans.

12. Section: 24.2 Accounts Receivable Learning Objective: 24.2 Level of difficulty: Basic Solution: The purpose of credit analysis is to assess the creditworthiness of potential customers and the corresponding risk of late payments or default. Credit analysis consists of: • Gathering information about the potential customer.

• Analysis of this information to derive a credit decision that establishes the terms of payment and the maximum amount of trade credit to be granted.

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13. Section: 24.2 Accounts Receivable Learning Objective: 24.2 Level of difficulty: Basic Solution: 1. The applicant’s liquidity to determine the ability to meet short-term obligations.

2. The applicant’s attitude and character to determine the willingness to pay.

14. Section: 24.4 Short-Term Financing Considerations Learning Objective: 24.4 Level of difficulty: Basic Solution: Discount = $25 million – $24.5 million = $0.5 million or $500,000 Market price = $24.5 million Discount 365 500,000  365 = 4.14%  = Market price Days to maturity 24,500,000 180 Intermediate 15. Section: 24.1 Cash and Marketable Securities Learning Objective: 24.1 Level of difficulty: Intermediate Solution: Transactions motive refers to the cash required for a firm’s normal operations. Manufacturing firms keep cash to pay invoices. Pension plans keep cash on hand to pay monthly pensions and refunds. Retailers keep actual cash to run their business.

16. Section: 24.1 Cash and Marketable Securities Learning Objective: 24.1 Level of difficulty: Intermediate Solution: Optimal cash balance means a balance between the risks of illiquidity and expected return that is associated with maintaining cash. It differs across firms. Firms that do not need a large amount of cash on hand have lower risks of not meeting their liquidity needs and those firms keep a lower level of cash compared to the firms that need a large amount of cash on hand to handle normal business.

17. Section: 24.1 Cash and Marketable Securities Learning Objective: 24.1 Level of difficulty: Intermediate Solution: Four main motives for firms to hold cash are: Transaction motives – to support normal operations Precautionary motives – to support unexpected cash outlays Finance motives – to support any major outlays Speculative motives – to take advantage of “bargains”

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18. Section: 24.2 Accounts Receivable Learning Objective: 24.2 Level of difficulty: Intermediate Solution: Firms that sell or manufacture high-cost equipment occasionally establish wholly owned financing subsidiaries known as captive finance companies. The purpose of captive finance companies is to provide customers with term financing in the purchase of the company’s products.

19. Section: 24.3 Inventory Learning Objective: 24.3 Level of difficulty: Intermediate Solution: Advantages of carrying inventories include: • Larger purchases of inventory allow for bulk purchases at lower prices.

• Higher in-process inventory can permit more efficient production.

• Larger finished goods inventory result in lower stock-outs and improved customer service.

• Firms that face seasonal demands often carry seasonal inventories in order to level out production, utilizing fixed assets and labour more efficiently.

20. Section: 24.3 Inventory Learning Objective: 24.3 Level of difficulty: Intermediate Solution: Disadvantages of carrying inventories include: • Expense of warehousing and handling • Insurance costs • Obsolescence • Spoilage • Financing costs 21. Section: 24.3 Inventory Learning Objective: 24.3 Level of difficulty: Intermediate Solution: The four inventory management approaches are: 1. The ABC Approach: inventory is divided into several categories. The higher the priority of the inventory item, the more time and effort are devoted to its management.

2. The Economic Order Quantity (EOQ) Model: an optimal inventory level is assumed when total shortage costs = carrying costs.

3. Materials Requirement Planning (MRP): a detailed computerized system that orders inventory in conjunction with production schedules.

4. Just-in-Time (JIT) Inventory Systems: It fine tunes the receipt of raw materials so that they arrive exactly when they are required in the production process.

22. Section: 24.4 Short-Term Financing Considerations

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Learning Objective: 24.4 Level of difficulty: Intermediate Solution: Unlike commercial paper, bankers’ acceptances are “stamped” by a bank as accepted in return for a fee that is usually 0.25 to 1.00 percent of the face value of the bankers’ acceptance. The fee paid to the bank obtains its guarantee that the payments associated with the stamped security will be made to the holder. In this way, bankers’ acceptances have the credit risk of the financial institution that stamped them instead of the credit risk of the company that is borrowing funds.

Commercial paper, by contrast, carries the credit risk of the issuing company.

23. Section: 24.4 Short-Term Financing Considerations Learning Objective: 24.4 Level of difficulty: Intermediate Solution: Discount = $100 million – $99 million = $1 million Standby fee = 0.0015 × $100 million = $150,000 Total financing cost = $1 million + $150,000 = $1,150,000  n − day financing cost  365 n  1,150,000  365 90 k = 1 + − 1 = 4.80%  − 1 = 1 + 99,000,000  Purchase price    

24. Section: 24.4 Short-Term Financing Considerations Learning Objective: 24.4 Level of difficulty: Intermediate Solution: a.

ForgoingDiscount = 800  2% = $16 True Price = 800 −16 = $784 16 365 /(60−15) ) −1 = 17.81% k = (1 + 784 b. Forgoing discount of another supplier = 820 – 784 = $36 36 365 /(90−15) ) −1 = 24.42% k = (1 + 784 You should take advantage of credit terms of 2/15 net 40 and finance your purchase by using loans at 10%.

25. Section: 24.4 Short-Term Financing Considerations Learning Objective: 24.4 Level of difficulty: Intermediate Solution:

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Special purpose vehicles (SPVs) are conduits for packaging portfolios of receivables and selling them to investors in the money market. The advantage of using SPVs is the credit risk of the seller of receivables or loans is not directly involved. Over-collateralization, issuing subordinated debt to absorb further defaults on termination of SPVs, and issuing different classes of securities to let the prepayment risks be allocated to different securities are all forms of credit enhancement.

26. Section: 24.4 Short-Term Financing Considerations Learning Objective: 24.4 Level of difficulty: Intermediate Solution: Loan amount = 900,000×90% = $810,000 Commission = 0.005×900,000 = $4,500 Interest = 810,000×0.06×(45/365) = $5,991.78 Net cost = 4,500 + 5,991.78 – 8,000 = $2,491.78 2,491.78 365/ 45 The effective annual cost = k = (1 + ) −1 = 2.52% 810,000

27. Section: 24.4 Short-Term Financing Considerations Learning Objective: 24.4 Level of difficulty: Intermediate Solution: Discount = 5,000,000 – 4,850,000 = $150,000 Standby fee = 0.001 × 5,000,000 = $5,000 Total financing cost = 150,000 + 5,000 = $155,000 365 155,000 90 k = (1 + ) −1 = 13.61% 4,850,000

28. Sections: 24.2 Accounts Receivable and 24.4 Short-Term Financing Considerations Learning Objectives: 24.2 and 24.4 Level of difficulty: Intermediate Solution: 1,000  0.01 30−10 A: k = (1 + ) −1 = 20.13% 1,000  (1 − 0.01) 365

1,100  0.03 60−10 ) −1 = 24.90% 1,100  (1 − 0.03) 365

B: k = (1 +

Supplier A has a lower effective annual cost.

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Challenging 29. Section: 24.1 Cash and Marketable Securities Learning Objective: 24.1 Level of difficulty: Challenging Solution: Receivables decrease by 2 days * $100,000 = $200,000 Savings = annual cost of financing $200,000 in receivables = $200,000 * 0.02 = $4,000 Cost = $100 * 12 =$1,200 Therefore, the company should adopt it since it will save $4,000 – $1,200 = $2,800 per year.

30. Section: 24.2 Accounts Receivable Learning Objective: 24.2 Level of difficulty: Challenging Solution: CF0 = 30 days × sales per day = 30 × [($50 + 2) × (10,000 + 1,000) /365 days] = 30 days × $1,567.12 /day = $47,013.70 Future CFs = (1,000) × ($52 – $25) + (10,000) × ($2) – ($3,000) = $27,000 + $20,000 – $3,000 = $44,000 k = 5% (1 – 0.20) = 4% PV (Future CFs) = [$44,000 × (1 – 0.20)] / 0.04 = $880,000 NPV = PV (Future CFs) – CF0 = $880,000 – $ 47,013.70 = +$832,986.30 Since the NPV of the cash flow is positive, the firm should begin extending credit under the terms described above.

31. Section: 24.2 Accounts Receivable Learning Objective: 24.2 Level of difficulty: Challenging Solution: The new average collection period (ACP) = [0.80 × 10 days + 0.20 × 30 days] = 14 days The old ACP = 30 days Change in receivables = (14 × $53 × 11,000/365) – (30 × $52 × 11,000/365) = 22,361.64 – 47,013.70 = –$24,652.06 PV(Future CFs) = [11,000 × ($53 – $52) – (0.80 × 11,000) × (0.03 × $53 per unit)] × (1 – 0.40) / [0.05 (1 – 0.4)] = –$59,840 NPV = PV(Future CFs) – CF0 = –$59,840+ $24,652.06 = –$35,187.94

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Since the NPV of the cash flow is negative, the firm should not offer the discount under consideration.

32. Section: 24.2 Accounts Receivable Learning Objective: 24.2 Level of difficulty: Challenging Solution: A/R = ACP ×daily credit sales = 60 × $75,000 = $4,500,000 Loan amount = 0.9 × $4,500,000 = $4,050,000 Commission = 0.015 × $4,500,000 = $67,500 Interest = 0.10 × 60/365 × $4,050,000 = $66,575.34 Savings = 3,000 + 0.01 × $500,000 = $8,000 Net cost = Interest – Savings + Commission = $66,575.34 – $8,000 + $67,500 = $126,075.34 365 126,075.34 60 k = (1 + ) −1 = 20.50% 4,050,000 33. Section: 24.2 Accounts Receivable Learning Objective: 24.2 Level of difficulty: Challenging Solution: CF0 = A/R(new) – A/R(old) = [20 days × ($45 × 10,000)/365] – [25 days × ($45 × 12,000)/365] = –$12,328.77 Incremental before-tax CFs = (–$2,000)(45 – 37) + $1,000 = –$15,000 PV (future CFs) = –$15,000(1 – 0.3)/0.05 = –$210,000 NPV = PV(future CFs) – CF0 = –$210,000 + $12,329 = –$197,671.23 < 0 Therefore the firm should not switch to the new policy.

34. Section: 24.4 Short-Term Financing Considerations Learning Objective: 24.4 Level of difficulty: Challenging Solution: F − P 365  P 270 10M − P 270 = 5%  P 365 P = $9,643,328.93

5% =

Discount = 10,000,000 – 9,643,328.93 = $356,671.07 Stamping fee = 10,000,000×0.006 = $60,000 Total financing cost = 356,671.07 + 60,000 = $416,671.07 365 416,671.07 270 k = (1 + ) −1 = 5.89% 9,643,328.93

Introduction to Corporate Finance, Fourth Edition

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35. Section: 24.4 Short-Term Financing Considerations Learning Objective: 24.4 Level of difficulty: Challenging Solution: Effective monthly rate = 0.09/12 = 0.0075 Interest (months 1 to 6) = 100,000 × 75% × 0.0075 × 6 = $3,375 Interest (months 7 to 12) = 100,000 × 60% × 0.0075 × 6 = $2,700 Total interest = 3,375 + 2,700 = $6,075 Commitment fee (months 1 to 6) = 100,000 × 25% × 0.0025 × 6 = $375 Commitment fee (months 1 to 6) = 100,000 × 40% × 0.0025 ×6 = $600 Total commitment = 375 + 600 = $975 Total cost = 6,075 + 975 = $7,050 Avg. net financing = [(1/2) 75,000 + (1/2) 60,000] = $67,500 7,050 1 ) −1 = 10.44% k = (1 + 67,500

36. Section: 24.4 Short-Term Financing Considerations Learning Objective: 24.4 Level of difficulty: Challenging Solution: Effective monthly rate = 0.06/12 = 0.0050 or 0.50% Total interest = $1,200,000×0.0050×4 + $500,000×0.0050×8 = 24,000 + 20,000 = $44,000 Total commitment fees = (2,000,000–1,200,000)×0.008×4 + (2,000,000–500,000)×0.008×8 = $121,600 Avg. net financing = (4/12)×1,200,000 + (8/12)×500,000 = $733,333.33 Effective annual cost = (44,000 + 121,600) / 733,333.33 = 22.58% 37. Section: 24.4 Short-Term Financing Considerations Learning Objective: 24.4 Level of difficulty: Challenging Solution: For bankers’ acceptances:

Introduction to Corporate Finance, Fourth Edition

10,000,000 − P 365  P 180 P = $9,735,929.58 discount = 10,000,000 − 9,735,929.58 = $264,070.42

5.5% =

Stamping Fee = 0.004 10,000,000 = $40,000 (264,070.42 + 40,000) k =[ + 1]365 / 180 − 1 = 6.43% 9,735,929.58 For commercial paper: discount = 10,000,000 − 9,748,000 = $252,000

Standby Fee = 0.004 10,000,000 = $40,000 (252,000 + 40,000) k =[ + 1]365 / 180 − 1 = 6.17% 9,748,000 The 180-day bankers’ acceptance has a higher effective annual cost.

Booth, Cleary, Rakita

Introduction to Corporate Finance, Fourth Edition

Booth, Cleary, Rakita

Answers to Concept Review Questions 24.1 Cash and Marketable Securities Concept review questions 1. Why do firms hold cash?

The reasons include transaction motive, precautionary motive, finance motive, and speculative motive.

2. What is float and why is it important to the firm?

Float is the time that elapses between the time the paying firm initiates payment, for example, mails the cheque, and when the funds are available for use by the receiving firm. During this float period, the receiving firm does not have the funds available for use.

24.2 Accounts Receivable Concept review questions 1. Why is trade credit different from bank credit?

First, the firm’s cost is the cost of goods sold, rather than the amount that it charges for the widgets, because it has to factor a profit margin into the calculation. If the customer does not pay, the firm loses the cost of goods sold. If the customer does pay, it becomes an established customer that may make further purchases, generating further profit margins for the firm. The fact that the firm thinks in terms of future profit margins from developing a good customer and loses only its production cost in the case of default means that trade credit is granted to customers who could not secure credit from a bank on the same terms.

2. What are the four C’s of credit?

The four C’s include capacity, character, collateral, and conditions. All four are interrelated.

3. What does 2/10 net 30 mean, and what is the implicit interest cost?

Credit terms of 2/10 net 30 offer customers a 2 percent discount if they pay the full amount due by day 10, with the full amount being due by day 30. The implicit interest cost is k=(1+2/98)365/20-1=44.59% annually.

4. What is an aged accounts receivable report?

An aged accounts receivable report categorizes the balances in receivables according to how long they have been outstanding.

24.3 Inventory Concept review questions 1. Identify the costs and benefits of holding inventory.

One reason firms hold large amounts of inventory is that they may have received discounts on large-volume purchases. However, the more important benefits of holding inventory are that holding sufficient levels of raw materials minimizes disruptions in the production process, while

Introduction to Corporate Finance, Fourth Edition

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maintaining adequate levels of finished goods on hand helps minimize lost sales (and lost customer goodwill) because of shortages.

The benefits of holding inventory do not come without significant costs. Aside from the obvious cost of financing the funds tied up in inventory, a number of other costs are important, including storage, handling, insurance, spoilage, and the risk of obsolescence.

2. What are the drawbacks to using the turnover ratio to measure inventory policy?

First, it does not measure shortage costs or explicitly measure financing costs, and so on. Second, turnover ratios cannot be compared across companies that use different methods of accounting for inventory (i.e., LIFO, FIFO, average cost), because the reported inventory levels will differ substantially. Finally, inventory turnover says nothing about the breakdown of inventory in terms of raw materials, work-in-process inventory, and finished goods, which can make a big difference in establishing the market value of inventory.

24.4 Short-Term Financing Considerations Concept review questions 1. What is the cost of 3/15 net 60 trade credit?

The cost is k=(1+3/97)365/45-1=28.03% annually.

2. What is the difference between a bank operating line of credit and a traditional loan?

The difference is that operating line of credit is generally set up so that the firm makes “interest only” payments. The amount of borrowing can be reduced at the firm’s discretion, and many companies will have the bank automatically “revolve” the loan for them (for a fee). This involves paying down the amount of the loan whenever there is sufficient cash in the current account, or increasing the borrowing level when there is insufficient cash. Having the bank revolve the loan therefore reduces unnecessary interest costs, because the loan will be paid down whenever the firm has sufficient funds available.

3. What additional services does a factor provide over a bank?

It checks the credit of new customers, authorizes credit, handles collections and bookkeeping, and sometimes will purchase a firm’s receivables (at a discount). In practice, various arrangements are possible, with factors providing various combinations of the services listed above. Factors provide the ultimate in convenience; however, as with most things, there is a cost, and the costs are typically quite high.

4. What is the difference between a BA and commercial paper?

BAs differ from CP because they are “stamped” by a bank as accepted in return for a fee that is usually 0.25 percent to 1 percent of the face value of the BAs. In return, the bank guarantees the payments associated with these instruments. Therefore, BAs carry the credit risk of the bank that stamps them and not the company that borrows by using them. Most of the firms that issue BAs are large, well-known firms with excellent credit ratings. However, because of the bank guarantee, some firms that are not able to issue CP may be able to borrow by using BAs— provided they can find a bank that is willing to guarantee their payments.

5. Why do securitizations require credit enhancements?

Introduction to Corporate Finance, Fourth Edition

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If a portfolio of receivables or loans is simply sold to investors, in all likelihood the credit quality would not be high enough to get an investment-grade rating. As a result credit enhancements have to be made, such as requiring collateral, insurance, or other agreements, to reduce credit risk.