CHAPTER 13

THE COST OF CAPITAL

FOCUS The cost of capital was introduced in Chapter 10 as an underpinning for capital budgeting, so the student is already familiar with the basic concept. Here we focus on the practical intricacies of the calculation and the importance of using market values.

PEDAGOGY The cost of capital is a "big" calculation. Many students have trouble wrapping their arms around it. It's therefore important to develop an overview of the whole idea before getting lost in the calculations. In other words, it’s a good idea to spend some time talking about the cost of capital as an “average rate” the company pays for the use of its long-term money, and why knowing the cost of capital is important.

TEACHING OBJECTIVES After studying this chapter, the student should appreciate the details of the weighted average cost of capital concept, be able to calculate component capital costs, and develop the WACC as well as an MCC schedule.

OUTLINE

I. THE PURPOSE OF THE COST OF CAPITAL The cost of capital as a benchmark for evaluating capital budgeting projects and as the firm's required rate of return.

II. COST OF CAPITAL CONCEPTS A. Capital Components

Debt, Equity, and Preferred Stock.B. Capital Structure

Structure as a mix of components. The target structure and the proportions in which money is raised.

C. Returns on Investments and the Costs of Capital ComponentsThe conceptual relationship between the return an investor receives and the cost of a component.

D. The Weighted Average Calculation - the WACC A preview of the weighted average idea and how it works.

E. Capital Structure and Cost - Book Versus Market Values The idea that structure and cost can be based on either book or market values and an explanation of why market values are preferred.

III. CALCULATING THE WACC A. Developing Market-Value-Based Capital Structures

How to develop a structure based on the current prices of the underlying securities.B. Calculating Component Costs of Capital

Adjusting returns for taxes and flotation cost to arrive at component costs.C. Putting the Weights and Costs Together

IV. THE MARGINAL COST OF CAPITAL (MCC) A. The Break in MCC When Retained Earnings Run Out

Defining the breakpoint and calculating its position.

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B. The MCC ScheduleDefining the MCC schedule and its use

V. THE COST OF CAPITAL - A COMPREHENSIVE EXAMPLE A detailed example illustrating the calculation of the WACC and MCC.

VI. A POTENTIAL MISTAKE - HANDLING SEPARATELY FUNDED PROJECTS The fallacy of evaluating a project that comes with its own debt financing on the basis of the cost of that financing rather than the WACC.

QUESTIONS

1. Compare the cost of capital concept with the idea of the required return on a stock investment made by an individual. Relate both ideas to the risk of the investment. How would a very risky investment/ project be handled in the capital budgeting/cost of capital context?

ANSWER: An individual won't invest in a stock unless its expected return exceeds his or her required return. Similarly, a company won't invest in a project unless its expected return, traditionally called the IRR, exceeds the firm's cost of capital. Hence the cost of capital functions exactly like a required return with respect to business investments. In fact, the terms can be used interchangeably. Investors’ required returns increase with the risk of the investment being considered (remember the SML). The cost of capital, however, is the same regardless of the investment being evaluated. In this regard the concepts are different. Therefore it doesn't make sense to evaluate high-risk projects with the cost of capital. A rate adjusted upward for risk is more appropriate.

2. Define the idea of capital structure and capital components. Why is capital structure important to the cost of capital concept? In many capital structure discussions, preferred stock is lumped in with either debt or common equity. With respect to the cost of capital, however, it's treated separately. Why?

ANSWER: Capital components are the sources of capital, generally debt, equity and preferred stock. Capital structure is the mix in which capital components are used. It is important to the cost of capital, because it provides the proportions in which we mix component costs to arrive at an overall cost of capital. Preferred is treated separately because it generally has a cost that's different from either the cost of debt or the cost of equity.

3. You are a new financial analyst working for a company that's more than 100 years old. The CFO has asked you and a young member of the accounting staff to work together in reviewing the firm's capital structure for the purpose of recalculating its cost of capital. As you both leave the CFO's office, your accounting colleague says that this job is really going to be easy, because he already has the information. In preparing the latest annual report, he worked on the capital section of the balance sheet, and has the values of debt, preferred stock, and equity at his fingertips. He says that the two of you can summarize these into a report in five minutes, and then go out for a beer. How do you react and why? Is the fact that the firm is quite old relevant? Why?

ANSWER: You should politely tell your colleague that using book values of debt and equity will result in a cost of capital that reflects past conditions. Since the cost of capital will be used to evaluate new projects, a figure that reflects current capital markets is more appropriate. This is obtainable by using market values for capital structure. The fact that the firm is old makes it likely that book values will be very different from market values. Hence, it makes a book approach even more undesirable.

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4. The investor's return and the company's cost are opposite sides of the same coin—almost, but not quite. Explain.

ANSWER: The money paid to investors is the company's cost. However, certain third parties are involved that make the amounts paid and received different. Flotation costs are paid to investment bankers, so companies receive less than investors pay for securities. That makes the companies' costs higher than the investors' returns. Interest is tax deductible, so the government essentially contributes part of a company's interest payment to lenders. That makes the cost of debt lower than the investor's return.

5. There's an issue of historical versus market value with respect to both the cost of capital components and the amounts of those components used in developing weights. We're willing to accept an approximation for the weights, but not for the cost/returns. Why?

ANSWER: We never raise money in the exact proportions of the capital structure, so any set of weights is an approximation of what's likely to happen when the firm actually issues securities. Component costs, however, are close estimates of what will actually be encountered in the market. Since those costs can vary considerably, it pays to use the latest estimates of market conditions. There is, however, an inconsistency in all this. The cost of capital is not a precise calculation, so expending a great deal of effort on excessive accuracy in any one part is futile.

6. A number of investment projects are under consideration at your company. You've calculated the cost of capital based on market values and rates, and analyzed the projects using IRR and NPV. Several projects are marginally acceptable. While watching the news last night you learned that most economists predict a rise in interest rates over the next year. Should you modify your analysis in light of this information? Why?

ANSWER: Yes. Since rates are expected to rise, capital over the next year will probably be more expensive than capital raised today would be. That means your cost of capital is probably understated. If some projects are marginal, they would probably be unacceptable at the coming rates. You should recalculate your cost of capital based on expected rates and rework your analysis. Then show the decision makers both sets of figures explaining your reasoning. They may or may not agree with the economists.

7. Establishing the cost of equity is the most arbitrary and difficult part of developing a firm's cost of capital. Outline the reasons behind this problem and the approaches available to making the best of it.

ANSWER: The cost of equity is related to the return on an investment in the firm's stock. That return depends on dividends and price movements which can only be estimated. The return on bonds and preferred stock is exact, because interest and principal payments and preferred dividends are specified in the contracts with investors. Because of this inaccuracy, we estimate the cost of equity based on projected growth rates and risk. The growth rate approach uses the Gordon model. There are two risk approaches. One uses the CAPM while the other adds a risk premium to the return the firm pays on its debt.

8. Retained earnings are generated by the firm's internal operations and are immediately reinvested to earn more money for the company and its shareholders. Therefore, such funds have zero cost to the company. Is that statement true or false? Explain.

ANSWER: False. Retained earnings belong to stockholders and have been reinvested for them without their explicit permission. Stockholders are therefore entitled to the same return on those equity funds

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that they receive on the price paid for stock. The cost of retained earnings, therefore, is the same as the cost of equity received from the sale of stock except for the absence of flotation costs.

9. Define the marginal cost of capital (MCC) and explain in words why it predictably undergoes a step function increase (breaks) as more capital is raised during a budget period.

ANSWER: The marginal cost of capital is the cost of the next dollar raised. As more money is raised during a single period, investors become concerned about risk and demand higher returns. As required returns increase, so does the cost of capital components and the WACC. The first increase generally occurs before risk is a factor. When the firm exhausts currently retained earnings, it must obtain new equity by selling stock. But selling stock involves flotation cost, which makes it more expensive than retained earnings.

10. After the break in the MCC caused by using up retained earnings, the schedule can be expected to remain flat indefinitely. Is this statement right or wrong? If wrong, explain what can be expected to happen to the MCC and why.

ANSWER: The statement is incorrect. As more money is raised during a single period, investors become concerned about risk and demand higher returns. As required returns increase, so does the cost of capital components and the WACC. This implies that the MCC will experience step function increases as more money is raised.

11. Why is it appropriate to define the WACC as the highest step on the MCC under the IOS? Is anything lost by using this definition?

ANSWER: If the WACC is defined as the highest step on the MCC under the IOS, we don't have to worry about changing it as more money is raised. Since projects are generally considered in descending order of IRR, using the highest WACC will not reject anything to the left of the intersection, so nothing is lost by using that one rate throughout.

BUSINESS ANALYSIS

1. You're the newly hired CFO of a small construction company. The privately held firm is capitalized with $2 million in owner's equity and $3 million in variable rate bank loans. The construction business is quite risky, so returns of 20% to 25% are normally demanded on equity investments. The bank is currently charging 14% on the firm's loans, but interest rates are expected to rise in the near future. Your boss, the owner, started his career as a carpenter and has an excellent grasp of day-to-day operations. However, he knows little about finance. Business has been good lately, and several expansion projects are under consideration. A cash flow projection has been made for each. You're satisfied that these estimates are reasonable. The owner has called you in and confessed to being confused about the projects. He instinctively feels that some are financially marginal and may not be beneficial to the company, but he doesn't know how to demonstrate this or to choose among the projects that are financially viable. Assuming the owner understands the concept of return on investment, write a brief memo explaining the ideas of IRR and cost of capital and how they can solve his problem. Don't get into the detailed mechanics of the calculations, but do use the figures given above to make a rough estimate of the company's cost of capital, and use the result in your memo.

ANSWER: Every business has to pay for the funds it uses. We call that payment the cost of the funds and generally express it as a percentage like an interest rate. Long-term money, comes from debt and equity, and the cost of each is closely related to the returns the firm pays those investors.

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When a firm considers projects that use long-term money, it's appropriate to estimate its cost in a pooled sense. When we do that we call the money capital and develop a single cost figure for it. Under this logic, the overall cost of capital, is an average of the costs of debt and equity where the average is weighted by the amounts of debt and equity in use. In our case, the company is financed with a mix that's about 40% equity and 60% debt. The cost of equity is about 20% while the after tax cost of debt is in the neighborhood of 9%. That means our overall cost of capital is between 13% and 14%. Once we know what our money costs, it's apparent that we should never use it in a venture that returns less than that cost. Now let's turn to projects for a moment. They earn returns on invested funds called "Internal Rates of Return (IRRs)". For example, the IRR on just putting money in the bank is the interest rate the bank pays. Choosing among projects is conceptually simple. If risks are about the same, we choose projects with the highest IRRs. But it never makes sense to undertake a project that doesn't earn at least as much as the cost of funds put into it. To do that would be to plan to lose money! For example, it wouldn't make much sense to put company money in a savings account paying 5%, because the money costs us 14%. Now put the ideas of cost of capital and IRR together. The projects we're considering all have calculated IRRs. Anything with an IRR below 14% isn't a good idea, because that's less than what we pay for the money we'll put into it. Projects with IRRs between 14% and about 16% are pretty marginal. Those with higher IRRs may be ok if the cash projections are reasonable and the risks aren't out of line.

2. You're the CFO of a small company that is considering a new venture. The president and several other members of management are very excited about the idea for reasons related to engineering and marketing rather than profitability. You've analyzed the proposal by using capital budgeting techniques, and found that it fails both IRR and NPV tests using a cost of capital based on market returns. The problem is that interest rates have risen steeply in the last year, so the cost of capital seems unusually high. You've presented your results to the management team, who are very disappointed. In fact, they'd like to find a way to discredit your analysis, so they can justify going ahead with the project. You've explained your analysis, and everything seems well understood except for one point. The group insists that the use of returns currently available to investors as a basis for the cost of capital components doesn't make sense. The vice president of marketing put his objection as follows. "Two years ago we borrowed $1 million at 10%. We haven't paid it back, and we're still making interest payments of $100,000 every year. Clearly, our cost of debt is 10% and not the 14% you want to use. If you'd use our "real" cost of debt, as well as of equity and preferred stock, the project would easily qualify financially." How do you respond? (The appropriate response is relatively short. It's worth noting that this kind of thing happens all the time in corporations. Marketing and engineering people often get carried away with "neat" projects that don't make sense financially. The CFO has to watch the bottom line and it's not unusual to be seen as a wet blanket who wants to spoil the others' fun!)

ANSWER: We can't use the money we raised two years ago on this project, because it's already been spent. We have to raise new capital for the new project. You're right in that the cost of our existing capital is a much lower figure than the one I'm using. But that fact is irrelevant. What's important is the cost of the money we'll be raising in the near future to fund this project. That cost is reflected by current market rates, which are much higher than our old rates.

3. The engineering department at Digitech Inc. wants to buy a new, state-of-the-art computer. The proposed machine is faster than the one now being used, but whether the extra speed is worth the expense is questionable, given the nature of the firm's applications. The Chief Engineer (who has an MBA and a reasonable understanding of financial principles) has put together an enormously detailed

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capital budgeting proposal for the acquisition of the new machine. The proposal concludes that it's a great deal. You're a financial analyst for the firm, and have been assigned to review the engineering proposal. Your review has highlighted two problems. First, the cost savings projected as a result of using the new machine seem rather optimistic. Second, the analysis uses an unrealistically low cost of capital. With respect to the second point, the engineering proposal contains the following exhibit documenting the development of the cost of capital used:

Digitech's capital structure is 60% debt and 40% equity

The manufacturer is offering financing at 8% as a sales incentive

Cost of capital = 8% .6 = 4.8%

After tax this is 4.8% (1T) = 4.8%(.6) = 2.9%

You've checked the market and found that Digitech's bonds are currently selling to yield 14% and the stock is returning about 20%. How would you proceed? That is, explain the chief engineer's error(s) and indicate the correct calculations.

ANSWER: The chief engineer has really forgotten his finance! The first mistake is using the cost of dedicated financing to evaluate a project instead of the cost of capital. This is an incorrect procedure that leads to bad decisions in the long run although it will virtually assure acceptance of the current project. (See "A Potential Mistake - Handling Separately Funded Projects.") On top of that, the proposal uses part of a weighted average calculation to further decrease the interest rate used to evaluate the project. This coupled with the optimistic cash flow estimates makes one think that the computer may be something the engineers want but can't really support financially. That means it's likely to be an emotional issue. It's probably best if you don't go to the chief engineer yourself to challenge his proposal. Take your findings to the CFO and let her approach the chief engineer in private and work the matter out. This situation illustrates something that's fairly common. A proposal is presented with so much supporting information that it's difficult to find the errors and unrealistic assumptions buried in the details.

4. Whitefish Inc. operates a fleet of 15 fishing boats in the North Atlantic Ocean. Fishing has been good in the last few years, as has the market for product, so the firm can sell all the fish it can catch. Charlie Bass, the vice president for operations, has worked up a capital budgeting proposal for the acquisition of new boats. Each boat is viewed as an individual project identical to the others, and shows an IRR of 22%. The firm's cost of capital has been correctly calculated at 14% before the retained earnings break and 15% after that point. Charlie argues that the capital budgeting figures show that the firm should acquire as many new boats as it possibly can, financing them with whatever means it finds available. You are Whitefish's CFO. Support or criticize Charlie's position. How should the appropriate number of new boats be determined? Does acquiring a large number of new boats present any problems or risks that aren’t immediately apparent from the financial figures?

ANSWER: Although the WACC is 15% after the retained earnings break, it won't remain at that level indefinitely. As more boats are acquired with new financing, the cost of capital will rise and eventually exceed 22%. The appropriate level of investment in new boats should be determined by investigating how the MCC will behave, and estimating where it will exceed 22%.

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Charlie's estimate is based on current fishing and market conditions. If those conditions aren't stable, buying a large number of new boats could increase the firm's risk substantially.

PROBLEMS

WACC Calculations: Example 13-1 (page 561)1. Blazingame Inc.'s capital components have the following market values:

Debt $35,180,000 Preferred Stock $17,500,000 Common Equity $48,350,000Calculate the firm's capital structure and show the weights that would be used for a weighted average cost of capital (WACC) computation.

SOLUTION:Values Weights

Debt $35,180 .348 Preferred Stock $17,500 .173 Common Equity $48,350 .479 $101,030 1.000

2. The Aztec Corporation has the following capital components and costs. Calculate Aztec's WACC.

Component Value CostDebt $23,625 12.0%Preferred Stock $ 4,350 13.5%Common Equity $52,275 19.2%

SOLUTION:Component Value Weights Cost FactorsDebt $23,625 .294 12.0% 3.53Preferred Stock $ 4,350 .054 13.5% .73Common Equity $52,275 .652* 19.2% 12.52

$80,250 1.000 16.78 Use WACC = 16.8%

*Rounding sometimes causes the weights to sum to a figure slightly different from 1.000. When that happens we generally round one figure the wrong way to show weights that add to exactly 1.000.

3. Willerton Industries Inc. has the following balances in its capital accounts as of 12/31/x3:

Long Term Debt $65,000,000Preferred Stock $15,000,000Common Stock $40,000,000Paid in Excess $15,000,000Retained Earnings $37,500,000

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Calculate Willerton’s capital structure based on book values.

SOLUTION ($M)%

Debt $65.0 37.7Preferred Stock 15.0 8.7Equity 92 .5 53 .6 Total $172.5 100.0

Market Value Based Capital Structure: Example 13-2 (page 564)4. Referring to Willerton Industries of the previous problem, the company’s long term debt is

comprised of 20-year $1,000 face value bonds issued seven years ago at an 8% coupon rate. The bonds are now selling to yield 6%. Willerton’s preferred is from a single issue of $100 par value, 9% preferred stock that is now selling to yield 8%. Willerton has four million shares of common stock outstanding at a current market price of $31. Calculate Willerton’s market value based capital structure.

SOLUTION:a. Market value of debt:

n = 13 x 2 = 26FV = 1,000I/Y = 6/2 = 3PMT = 1,000 x 8%/2 = 40PV = ? = 1,178.77

Market value of preferred stockNumber of preferred shares from previous problem$15M/$100 = 150,000$9/.08 = $112.50

Total market values Market Value %

Debt $1,178.77 x 65,000 $76,620,050 35.2Preferred stock $112.50 x 150,000 16,875,000 7.8Equity $31 x 4,000,000 124,000,000 57 .0

$217,495,050 100.0

5. Again referring to Willerton of the two previous problems, assume the firm’s cost of retained earnings is 11% and its marginal tax rate is 40%, calculate its WACC using its book value based capital structure ignoring floatation costs. Make the same calculation using the market value based capital structure. How significant is the difference?

SOLUTION:

Book ValueDebt .377 x 6.0% x (1 - .4) 1.36Preferred .087 x 8% .70Equity .536 x 11% 5 .90 WACC 7.96%

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Market ValueDebt .352 x 6.0% x (1 - .4) 1.27Preferred .078 x 8% .62Equity .57 x 11% 6 .27 WACC 8.16%

In this case, WACCs based on book and market values are only 0.2% apart, a relatively insignificant difference.

6. A relatively young firm has capital components valued at book and market and market component costs as follows. No new securities have been issued since the firm was originally capitalized.

Values MarketComponent Market Book CostDebt $42,830 $40,000 8.5%Preferred Stock $10,650 $10,000 10.6%Common Equity $65,740 $32,000 25.3%

a. Calculate the firm's capital structures and WACCs based on both book and market values, and compare the two. b. What appears to have happened to interest rates since the company was started? c. Does the firm seem to be successful? Why? d. What would be the implication of using a WACC based on book as opposed to market values? In other words, what kinds of mistakes might management make by using the book values?

SOLUTION:a. Factors

Market Weights Book Weights Costs Market BookDebt $42,830 .359 $40,000 .488 8.5% 3.05 4.15Preferred Stock $10,650 .090 $10,000 .122 10.6% .95 1.29Common Equity $65,740 .551 $32,000 .390 25.3% 13.94 9.87

$119,220 1.000 $82,000 1.000 17.94 15.31 Use WACCs = 17.9% 15.3%

Comparison: The overall cost of capital has risen due to the net impact of a large increase in the value of the firm's equity. This throws more of equity's high cost into the WACC.

b. Interest rates appear to have fallen, since the market values of debt and preferred exceed their original values.

c. The firm seems to be successful because of the substantial increase in the value of equity. This could be due to an increase in stock price or a rapid accumulation of retained earnings or a combination of both.

d. Using the book based WACC might lead to accepting projects that wouldn't achieve the expectations investors have for the company's return.

7. Five years ago Hemingway Inc. issued 6,000 thirty-year bonds with par values of $1,000 at a coupon rate of 8%. The bonds are now selling to yield 5%. The company also has 15,000 shares of preferred stock outstanding that pay a dividend of $6.50 per share. These are currently selling to yield

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10%. Its common stock is selling at $21, and 200,000 shares are outstanding. Calculate Hemingway’s market value based capital structure.

SOLUTION:The current price of the bonds is

PB = PMT[PVFAk,n] + FV[PVFk,n]PB = $40[PVFA2.5,50] + $1,000[PVF2.5,50]PB = $40[28.3623] + $1,000[.2909]PB = $1,134.49 + $290.90PB = $1,425.39

The market value of 6,000 bonds is $1,425.39 6,000 = $8,552,340

The preferred stock shares are each worthPP = $6.50 / .10 = $65.00

In total they’re worth $65.00 15,000 = $975,000

The market value of the stock is simply $21.00 200,000 = $4,200,000

Total capital is the sum of these figures and capital structure is each component divided by the total stated as a percent.

Component Value Capital Structure Debt $ 8,552,340 62.3% Preferred 975,000 7.1% Equity 4,200,000 30.6% Total Capital $13,727,340 100.0%

8. The Wall Company has 142,500 shares of common stock outstanding that are currently selling at $28.63. It has 4,530 bonds outstanding that won’t mature for 20 years. They were issued at a par value of $1,000 paying a coupon rate of 6%. Comparable bonds now yield 9%. Wall’s $100 par value preferred stock was issued at 8% and is now yielding 11%; 7,500 shares are outstanding. Develop Wall’s market value based capital structure.

SOLUTION:The current price of the bonds is

PB = PMT[PVFAk,n] + FV[PVFk,n]PB = $30[PVFA4.5,40] + $1,000[PVF4.5,40]PB = $30[18.4016] + $1,000[.1719]PB = $552.05 + $171.90PB = $723.95

The market value of 4,530 bonds is $723.95 4,530 = $3,279,494

The preferred stock shares pay a dividend of ($100x.08=) $8.00, and are each worthPP = $8.00 / .11 = $72.73

In total they’re worth $72.73 7,500 = $545,475

The market value of the common stock is $28.63 142,500 = $4,079,775

Total capital is the sum of these figures and capital structure is each component divided by the total stated as a percent.

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Component Value Capital Structure Debt $3,279,494 41.5% Preferred 545,475 6.9% Equity 4,079,775 51.6% Total Capital $7,904,744 100.0%

9. The market price of Albertson Ltd.’s common stock is $5.50, and 100,000 shares are outstanding. The firm's books show common equity accounts totaling $400,000. There are 5,000 preferred shares outstanding that originally sold for their par value of $50, pay an annual dividend of $3, and are currently selling to yield an 8% return. Also, 200 bonds outstanding that were issued five years ago at their $1,000 face values for 30-year terms pay a coupon rate of 7%, and are currently selling to yield 10%. Develop Albertson's capital structure based on both book and market values.

SOLUTION:Debt: Book: 200 $1,000 = $200,000

Market: PB = PMT[PVFA5,50] + F[PVF5,50] = $35(18.2559) + $1,000(.0872) = $726.16

Market Value = 200 $726.16 = $145,232

Preferred: Book $50 5,000 = $250,000 Market ($3/.08) 5,000 = $187,500

Equity: Book = $400,000 Market = $5.50 100,000 = $550,000

Book Weights Market Weights Debt $200,000 .235 $145,232 .165 Preferred $250,000 .294 $187,500 .212 Equity $400,000 .471 $550,000 .623 $850,000 1.000 $882,732 1.000

Cost of Debt: Example 13-3 (page 567)10. Asbury Corp. issued 30-year bonds 11 years ago with a coupon rate of 9.5%. Those bonds are

now selling to yield 7%. The firm also issued some 20-year bonds two years ago with an 8% coupon rate. The two bond issues are rated equally by Standard and Poors and Moody’s. Asbury’s marginal tax rate is 38%.

a. What is Asbury’s after-tax cost of debt? b. What is the current selling price of the 20-year bonds?

SOLUTION:

a. 7.0% x (1 - .38) = 4.34%

b. N = 18 x 2 = 36FV = 1,000I/Y = 7.0/2 = 3.5PMT = (1,000 x 8%)/2 = 40PV = ? = $1,101.45

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11. The Dentite Corporation’s bonds are currently selling to yield new buyers a 12% return on their investment. Dentite’s marginal tax rate including both federal and state taxes is 38%. What is the firm’s cost of debt?

SOLUTION:The cost of debt is the return received by investors reduced by the company’s tax savings due to

the fact that interest is tax deductible. Cost of debt = Investor’s return (1 – T)

= 12(1 .38)= 12(.62)= 7.44%

12. Kleig Inc.'s bonds are selling to yield 9%. The firm plans to sell new bonds to the general public and will therefore incur flotation costs of 6%. The company's marginal tax rate is 42%. a. What is Kleig's cost of debt with respect to the new bonds? (Hint: Adjust the cost of debt formula to include flotation costs.) b. Suppose Kleig also borrows directly from a bank at 12%. 1. What is its cost of debt with respect to such bank loans? (Hint: Would bank loans be subject to flotation costs?) 2. If total borrowing is 60% through bonds and 40% from the bank, what is Kleig's overall cost of debt? (Hint: Think weighted average.)

SOLUTION:

a.

b.1.) Cost of Bank Loans = kd(1T) = 12% (.58) = 6.96%

2.) .6 5.55% = 3.33% .4 6.96% = 2.78%

6.11%

Cost of Preferred Stock: Example 13-4 (page 568)13. Harris Inc.’s preferred stock was issued five years ago to yield 9%. Investors buying those shares on the secondary market today are getting a 14% return. Harris generally pays flotation costs of 12% on new securities issues. What is Harris’s cost of preferred financing?

SOLUTION:The cost of preferred is the current investor’s return adjusted for flotation costs.Cost of preferred = Investor’s return / (1 f)

= 14% / (1 .12)= 14% / .88= 15.91%

14. Fuller, Inc. issued $100, 8% preferred stock five years ago. It is currently selling for $84.50. Assuming Fuller has to pay floatation costs of 10%, what is Fuller’s cost of preferred stock?

SOLUTION:

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Cost of Preferred Stock = $8.00/($84.50)(1 - .1) = 10.52%

15. A few years ago Hendersen Corp issued preferred stock paying 8% of its par value of $50. The issue is currently selling for $38. Preferred stock flotation costs are 15% of the proceeds of the sale. What is Hendersen's cost of preferred stock?

SOLUTION:Dp = $50 .08 = $4kp = $4/$38 = 10.53%

Cost of preferred = kp/(1f) = 10.53% /.85 = 12.39%

16. New buyers of Simmonds Inc. stock expect a return of about 22%. The firm pays flotation costs of 9% when it issues new securities. What is Simmonds’ cost of equity (Hint: This problem is very simple since we don’t have to estimate the investors’ return.)

a. From retained earnings?b. From new stock?

SOLUTION:a. New equity from retained earnings is not subject to flotation costs nor is it tax deductible, so there are no adjustments to the investors’ returns to get cost. Hence the firm’s cost of retained earnings is 22%.

b. New stock is subject to flotation costs so the return must be grossed up to allow for their payment. Cost of new equity = Investor’s return / (1 f)

= 22% / (1 .09)= 22% / .91= 24.18%

Cost of Retained Earnings – Constant Growth (Gordon) Model: Example 13-6 (page 570)17. Klints Inc. paid an annual dividend of $1.45 last year. The firm’s stock sells for $29.50 per share, and the company is expected to grow at about 4% per year into the foreseeable future. Estimate Klints’ cost of retained earnings.

Solution: Write equation 13.7 and substitute.

D0 (1+g) $1.45 (1.04)ke = ———— + g = —————— + .04 = .051 + .040 = 9.1%

P0 $29.50

Cost of RE and New Stock: Examples 13-6 and 13-8 (pages 570 and 572)18. The Pepperpot Company's stock is selling for $52. Its last dividend was $4.50, and the firm is expected to grow at 7% indefinitely. Flotation costs associated with the sale of common stock are 10% of the proceeds raised. Estimate Pepperpot's cost of equity from retained earnings and from the sale of new stock.

SOLUTION:

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For retained earnings:

For new equity:

Cost of Retained Earnings – SML: Example 13-5 (page 570)19. The Longlife Insurance Company has a beta of .8. The average stock currently returns 15% and short-term treasury bills are offering 6%. Estimate Longlife's cost of retained earnings.

SOLUTION: ke = kRF + (kM kRF) b = 6% + (15% 6%).8 = 13.2%

Cost of Retained Earnings – Risk Premium: Example 13-7 (page 571)20. The Longlife Insurance Company of the preceding problem has several bonds outstanding that are currently selling to yield 9%. What does this imply about the cost of the firm's equity?

SOLUTION: The risk premium approach says the cost of equity should be 3-5% higher than the return on the same company's debt. In this case that's 12-14% which is consistent with the results of the preceding problem.

21. Hammell Industries has been using 10% as its cost of retained earnings for a number of years. Management has decided to revisit this decision based on recent changes in financial markets. An average stock is currently earning 8%, treasury bills yield 3.5%, and shares of Hammell’s stock are selling for $29.44. The firm just paid a dividend of $1.50, and anticipates growing at 5% for the foreseeable future. Hammell’s CFO recently asked an investment banker about issuing bonds and was told the market was demanding a 6.5% coupon rate on similar issues. Hammell stock has a beta of 1.4. Recommend a cost of retained earnings for Hammell.

SOLUTION:Estimate the cost of retained earnings in three ways and reconcile the results.CAPM

k = kRF + (kM – kRF)bH

= 3.5% + (8.0% - 3.5%) x 1.4 = 9.8%

Risk Premiumk = kd + rpe

= 6.5% + 4% = 10.5%

Gordon Modelk = [D0(1+g)/P0] + g = [$1.50(1.05)/$29.44] + .05 = 10.35%

The three approaches give results that are fairly close to one another and average 10.2%, a figure that’s slightly higher than the one the firm has been using. A change to 10.2% is appropriate but probably isn’t necessary.

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22. Suppose Hammell of the previous problem needs to issue new stock to raise additional equity capital. What is its cost of new equity if and flotation costs are 12%?

SOLUTION:k = [D0(1+g)/P0(1-f)] + g = [$1.50(1.05)/$29.44(1-.12)] + .05 = 11.08%

MCC: Example 13-9 (page 573)23. Whitley Motors Inc. has the following capital.

Debt: The firm issued 900, 25 year bonds five years ago which were sold at a par value of $1,000. The bonds carry a coupon rate of 7%, but are currently selling to yield new buyers 10%.

Preferred Stock:3,500 shares of 8% preferred were sold 12 years ago at a par value of $50. They’re now priced to yield 11%.

Equity: The firm got started with the sale of 10,000 shares of common stock at $100 per share. Since that time earnings of $800,000 have been retained. The stock is now selling for $89. Whitley’s business plan for next year projects net income of $300,000, half of which will be retained.

The firm’s marginal tax rate is 38% including federal and state obligations. It pays flotation costs of 8% on all new stock issues. Whitely is expected to grow at a rate of 3.5% indefinitely and recently paid an annual dividend of $4.00.

Develop Whitley’s WACC before and after the retained earnings break and indicate how much capital will have been raised when the break occurs.

SOLUTION:First develop the market based capital structure by valuing the capital components.

Debt: Use a financial calculator to value Whitley’s bonds as follows: n=40, I/Y=5, PMT=35, FV=1000: PV = $742.61

multiply by the number of bonds outstanding for the market value of debt$742.61 x 900 = $668,349

Preferred: Each preferred share pays a dividend of $50 x .08 = $4.00

And is valued at$4.00 / .11 = $36.36

Multiply by the number of preferred shares outstanding for the market value of preferred stock$36.36 x 3,500 = $127,260

Equity: Simply multiply the number of shares outstanding by the stock’s market price for the market value of equity

10,000 x $89.00 = $890,000

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The market value based capital structure is thenDebt $ 668,349 39.7%Preferred 127,260 7.5%Equity 890,000 52.8%

$1,685,609 100.0%

Next develop the capital component costs.

Debt: Cost of debt = kd(1-T) = 10(1-.38) = 6.2%

Preferred: Cost of preferred = kp / (1-f) = 11 / (1-.08) = 12.0%

Equity from RE:

ke = [D0(1+g) / P0] + g = [4.00(1.035) / 89] +.035 = .047 +.035 = 8.2%

Equity from new stock:

ke = [D0(1+g) / P0(1-f)] + g = [4.00(1.035) / 89(1-.08)] +.035 = .051 +.035 = 8.6%

WACC calculations: Before the break

Mix Cost FactorDebt .397 6.2 2.5Preferred .075 12.0 .9Equity .528 8.2 4.3

1.000 7.7

After the break Mix Cost Factor

Debt .397 6.2 2.5Preferred .075 12.0 .9Equity .528 8.6 4.5

1.000 7.9

Calculate the break point Planned RE = $300,000 x .5 = $150,000$150,000 / .528 = $284,091

24. The Longenes Company uses a target capital structure when calculating the cost of capital. The target structure and current component costs based on market conditions follow.

Component Mix Cost* Debt 25% 8% Preferred Stock 10% 12% Common Equity 65% 20%

* The costs of debt and preferred stock are already adjusted for taxes and/or flotation costs. The cost of equity is unadjusted.

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The firm expects to earn $20 million next year, and plans to invest $18 million in new capital projects. It generally pays dividends equal to 60% of earnings. Flotation costs are 10% for common and preferred stock. a. What is Longenes’ initial WACC? b. Where is the retained earnings breakpoint in the MCC? (Round to the nearest $.1M.) c. What is the new WACC after the break? (Adjust the entire cost of retained earnings for flotation costs.) d. Longenes can borrow up to $4 million at a net cost of 8% as shown. After that the net cost of debt rises to 12%. What is the new WACC after the increase in the cost of debt? e. Where is the second break in the MCC? That is, how much total capital has been raised when the second increase in WACC occurs? f. Sketch Longenes’ MCC.

SOLUTION:a. Component Mix Cost Factors

Debt 25% 8.0% 2.0 Preferred Stock 10% 12.0% 1.2 Common Equity 65% 20.0% 13.0

WACC = 16.2%b. Available retained earnings = $20M .4 = $8M Breakpoint = $8M /.65 = $12.3M

c. Cost of new equity = ke/.9 = 20%/.9 = 22.2%

Component Mix Cost Factors Debt 25% 8.0% 2.0 Preferred Stock 10% 12.0% 1.2 Common Equity 65% 22.2% 14.4 WACC = 17.6%

d. Component Mix Cost Factors Debt 25% 12.0% 3.0 Preferred Stock 10% 12.0% 1.2 Common Equity 65% 22.2% 14.4 WACC = 18.6%

e. $4M/.25 = $16M

f.

18.6%

17.6%

16.2% / / /

$12.3M $16.0M

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Cost of Capital Comprehensive Problem and IOS: Example 13-10 (page 576) and Combining the MCC and the IOS (page 575)25. Taunton Construction Inc.'s capital situation is described as follows: Debt: The firm issued 10,000 25-year bonds10 years ago at their par value of $1,000. The bonds carry a coupon rate of 14% and are now selling to yield 10%. Preferred Stock: 30,000 shares of preferred stock were sold six years ago at a par value of $50. The shares pay a dividend of $6 per year. Similar preferred issues are now yielding 9%. Equity: Taunton was initially financed by selling 2 million shares of common stock at $12. Accumulated retained earnings are now $5 million. The stock is currently selling at $13.25. Taunton's Target Capital Structure is as follows:

Debt 30.0%Preferred Stock 5.0%Common Equity 65.0% 100.0%

Other information: Taunton's marginal tax rate (state and federal) is 40%. Flotation costs average 12% for common and preferred stock. Short-term treasury bills currently yield 7.5%. The market is returning 12.5%. Taunton's beta is 1.2. The firm is expected to grow at 6% indefinitely. The last annual dividend paid was $1.00 per share. Taunton expects to earn $5 million next year. The firm can borrow an additional $2 million at rates similar to the market return on its old

debt. Beyond that lenders are expected to demand returns in the neighborhood of 14%. Taunton has the following capital budgeting projects under consideration in the coming year.

These represent its investment opportunity schedule (IOS).

Capital CumulativeProject IRR Required Cap. Req.A 15.0% $3M $3MB 14.0% $2M $5MC 13.0% $2M $7MD 12.0% $2M $9ME 11.0% $2M $11M

a. Calculate the firm's capital structure based on book and market values and compare with the target capital structure. Is the target structure a reasonable approximation of the market value based structure? Is the book structure very far off? b. Calculate the cost of debt based on the market return on the company's existing bonds. c. Calculate the cost of preferred stock based on the market return on the company's existing preferred stock. d. Calculate the cost of retained earnings using three approaches, CAPM, dividend growth, and risk premium. Reconcile the results into a single estimate. e. Estimate the cost of equity raised through the sale of new stock using the dividend growth approach. f. Calculate the WACC using equity from retained earnings based on your component cost estimates and the target capital structure. g. Where is the first breakpoint in the MCC (the point where retained earnings runs out)? Calculate to the nearest $.1M. h. Calculate the WACC after the first breakpoint.

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i. Where is the second breakpoint in the MCC (the point at which the cost of debt increases.) Why does this second break exist? Calculate to the nearest $.1M. j. Calculate the WACC after the second break. k. Plot Taunton's MCC. l. Plot Taunton's IOS on the same axes as the MCC. Which projects should be accepted and which should be rejected? Do any of those rejected have IRRs above the initial WACC? If so, explain in words why they're being rejected. m. What is the WACC for the planning period? n. Suppose project E is self-funding in that it comes with a source of its own debt financing. A loan is offered through an equipment manufacturer at 9%. The cost of the loan is 9% (1T) = 5.4%.Should project E be accepted under such conditions?

SOLUTION:a.Debt: Book = 10,000 $1,000 = $10,000,000Market : PB = PMT[PVFA5,30] + F[PVF5,30] = $70(15.3725) + $1,000(.2314) = $1,307.48Market Value = 10,000 $1,307.48 = $13,074,800

Preferred Book = $50 30,000 = $1,500,000 Market = ($6/.09) 30,000 = $2,000,000 Equity: Book = 2,000,000 $12 + $5,000,000 = $29,000,000 Market = 2,000,000 $13.25 = $26,500,000

Book Market Target

Value Weights Value Weights Weights Debt $10,000,000 24.7% $13,074,800 31.4% 30.0% Preferred $ 1,500,000 3.7% $ 2,000,000 4.8% 5.0% Equity $29,000,000 71.6% $26,500,000 63.8% 65.0% $40,500,000 100.0% $41,574,800 100.0% 100.0%

The target structure is very close to the market structure. The book structure is off, but not by a great deal.

b. Cost of Debt = kd(1T) = 10%(1.4) = 6%

c. Cost of Preferred = kp/(1f) = 9%/(1.12) = 10.2%

d. Cost of Retained Earnings: CAPM: ke = kRF+(kMkRF)b = 7.5 + (12.57.5)1.2 = 13.5%

Dividend Growth:

Risk Premium: ke = kd + 3-5% = 10% + 3-5% = 13%-15% Reconciliation: 14% is a reasonable, round number.

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e. Cost of new equity:

f. Component Target Weights Cost Factors Debt .30 6.0% 1.80 Preferred Stock .05 10.2% 0.51 Common Equity .65 14.0% 9.10 1.00 WACC = 11.41

Use WACC = 11.4%

g. Next year's dividend and retained earnings: Dividends

Common: $1.06/share 2,000,000 shares = $2,120,000Preferred: $6/share 30,000 shares = 180,000

$2,300,000 RE = Earnings Dividends = $5.0M $2.3M = $2.7M Breakpoint = $2.7M/.65 = $4.2M

h. Component Target Weights Cost Factors Debt .30 6.0% 1.80 Preferred Stock .05 10.2% 0.51 Common Equity .65 15.1% 9.82 1.00 WACC = 12.13

Use WACC = 12.1%

i. $2M/.30 = $6.7M. This break exists because the cost of debt, a capital component, has increased. That impacts the WACC in the same way that the earlier rise in the cost of equity does.

j. Component Target Weights Cost Factors Debt .30 8.4%* 2.52 Preferred Stock .05 10.2% 0.51 Common Equity .65 15.1% 9.82 1.00 WACC = 12.85*14% .6 = 8.4% Use WACC = 12.9%

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The Cost of Capital

k and l. k%

15%

14%IOS

13% 12.9%

11.4%

11% / / /

$2M $4M $6M $8M $10M

$4.2M $6.7M

Accept A, B, and CReject D, EYes, project DBy the time D is undertaken, the WACC has risen higher than its IRR.

m. For the planning period, WACC = 12.9%.n. No. See the Potential Mistake discussion.

26. Newrock Manufacturing Inc. has the following target capital structure Debt 25%, preferred 20% equity 55%

Investment bankers have advised the CFO that the company could raise up to $5 million in new debt financing by issuing bonds at a 6.0% coupon rate, beyond that amount new debt would require a 7% coupon. Newrock’s 8.5% preferred stock, issued at a par value of $100, currently sells for $112.50. There are 3,000,000 shares of common stock outstanding on which the firm paid an annual dividend of $2.00 recently. The stock currently trades at $36 per share. Next year’s net income is projected at $14,000,000 and management expects 6% growth in the foreseeable future. Floatation costs are 6% on debt and 11% on common and preferred stock. The marginal tax rate is 40%.

a. Calculate the WACC using the target capital structure and the cost of retained earnings for the equity component.

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12.1% 12%

$11ME

WACCD $9M

C $7M

B $5M

A $3M

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Chapter 13

b. Plot Newrock’s MCC identifying the levels of funding at which the first two breaks occur, and calculate the WACCs after each break.c. Newrock has identified the following capital projects for next year:

Project Investment IRRA $ 4.0 million 11.0%B $ 3.6 million 10.5%C $ 8.6 million 13.2%D $ 2.0 million 8.7%E $ 5.5 million 9.5%F $ 5.0 million 7.2%G $ 4.1 million 10.5%H $ 6.4 million 8.0%

Projects A and B are mutually exclusive, as are Projects C and H. Plot the IOS and the MCC and determine the ideal size of next year’s capital program.

SOLUTION:a. Cost of Capital Components

Cost of debt = kd(1-T)/(1-f) (flotation costs on debt are unusual) = [6.0% x (1 - .4)]/(1 - .06) = 3.83%

Cost of Preferred = Dp/Pp(1-f) = $8.50/($112.50)(1 - .11) = 8.49%

Cost of Equity = [D0(1+g)/P0(1-f)] + g = [$2(1.06)/$36] + .06 = 11.89%

WACC CalculationDebt 3.83 x .25 = .957Preferred 8.49% x .20 = 1.698Equity 11.89 x .55 = .540WACC 9.195% use 9.2%

b. Breakpoint for new equity = (Net Income – Dividends)/% Equity = [$14 million – 3 million ($2.12)]/.55 = $13.89 million

Cost of new Equity = $2.12/[$36.00 x (1 - .11)] + .06 = 12.62%

Breakpoint for debt = $5 million/.25 = $20 millionCost of New Debt = 7% x (1 - .4)/(1 - .06) = 4.47%

WACC after the first break point (new equity)Debt 3.83% x .25 = .957Preferred 8.49% x .20 = 1.698Equity 12.62% x .55 = 6.941

WACC 9.596% use 9.6%

WACC after the second break point (debt)Debt 4.47% x .25 = 1.118Preferred 8.49% x .20 = 1.698Equity 12.62% x .55 = 6.941

WACC 9.757% use 9.8%

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c. Between Projects A and B, pick A; between C and H, pick C. Therefore of the remaining projects the order should be C, A, G, E, D and F.

Projects C, A, and G should be accepted which will result in a capital program totaling $16.7 million. The next eligible project E has an expected return of 9.5%, but the marginal cost of capital is 9.6% at this point, so Project E should be rejected.

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9

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$10 $20 $29

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A

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