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10 CHAPTER THE COST OF CAPITAL
(Difficulty Levels: Easy, Easy/Medium, Medium, Medium/Hard, and Hard)
PART I New and Revised Carryover Problems and Questions
Multiple Choice: Problems
Component cost of preferred stock
1
EASY
.
Klieman Companys perpetual preferred stock sells for $90 per share and pays a $7.50 annual dividend per share. If the company were to sell a new preferred issue, it would incur a flotation cost of 5.00% of the price paid by investors. What is the company's cost of preferred stock? a. b. c. d. e. 7.50% 7.79% 8.21% 8.57% 8.77% EASY
Component cost of preferred stock
2
.
A companys perpetual preferred stock currently trades at $80 per share and pays a $6.00 annual dividend per share. If the company were to sell a new preferred issue, it would incur a flotation cost of 4%. What would the cost of that capital be? a. b. c. d. e. 7.51% 7.81% 7.99% 8.36% 8.62% EASY
Component cost of retained earnings: CAPM
3
.
Assume that you are a consultant to Thornton Inc., and you have been provided with the following data: rRF = 5.5%; RPM = 6.0%; and b = 0.8. What is the cost of equity from retained earnings based on the CAPM approach? a. 9.65% b. 9.91% c. 10.08% d. 10.30% e. 10.49%
Chapter 10: The Cost of Capital
Page 55
Component cost of retained earnings: CAPM
4
EASY
.
Heino Inc. hired you as a consultant to help them estimate their cost of capital. You have been provided with the following data: rRF = 5.0%; RPM = 5.0%; and b = 1.1. Based on the CAPM approach, what is the cost of equity from retained earnings? a. b. c. d. e. 10.50% 10.71% 10.88% 11.03% 11.14% EASY
Component cost of retained earnings: DCF, D1
5
.
Assume that you are a consultant to Morton Inc., and you have been provided with the following data: D1 = $1.00; P0 = $25.00; and g = 6% (constant). What is the cost of equity from retained earnings based on the DCF approach? a. 9.79% b. 9.86% c. 10.00% d. 10.20% e. 10.33%
Component cost of retained earnings: DCF, D1
6
EASY
.
Rhino Inc. hired you as a consultant to help them estimate their cost of capital. You have been provided with the following data: D1 = $1.30; P0 = $40.00; and g = 7% (constant). Based on the DCF approach, what is the cost of equity from retained earnings? a. 9.66% b. 9.84% c. 9.97% d. 10.08% e. 10.25%
Cost of retained earnings: bond-yield-plus-risk premium
7
EASY
.
P. Daves Inc. hired you as a consultant to help them estimate their cost of equity. The yield on the firms bonds is 6.5%, and Daves' investment bankers believe that the cost of equity can be estimated using a risk premium of 4.0%. What is an estimate of Daves' cost of equity from retained earnings? a. b. c. d. e. 9.77% 10.02% 10.19% 10.33% 10.50%
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Chapter 10: The Cost of Capital
WACC
8
EASY
.
You were hired as a consultant to Keys Company, and you were provided with the following data: Target capital structure: 40% debt, 10% preferred, and 50% common equity. The after-tax cost of debt is 4.00%, the cost of preferred is 7.50%, and the cost of retained earnings is 11.50%. The firm will not be issuing any new stock. What is the firms WACC? a. b. c. d. e. 7.55% 7.73% 7.94% 8.10% 8.32% MEDIUM
Component cost of debt
9
.
Several years ago the Haverford Company sold a $1,000 par value bond that now has 25 years to maturity and an 8.00% annual coupon that is paid quarterly. The bond currently sells for $900.90, and the companys tax rate is 40%. What is the component cost of debt for use in the WACC calculation? a. b. c. d. e. 5.40% 5.73% 5.98% 6.09% 6.24% MEDIUM
Component cost of debt
10
.
To help finance a major expansion, Dimkoff Development Company sold a bond several years ago that now has 20 years to maturity. This bond has a 7% annual coupon, paid quarterly, and it now sells at a price of $1,103.58. The bond cannot be called and has a par value of $1,000. If Dimkoffs tax rate is 40%, what component cost of debt should be used in the WACC calculation? a. b. c. d. e. 3.03% 3.28% 3.66% 3.85% 4.04%
Chapter 10: The Cost of Capital
Page 57
Component cost of retained earnings: DCF, D0
11
MEDIUM
.
Assume that Mary Brown Inc. hired you as a consultant to help it estimate the cost of capital. You have been provided with the following data: D0 = $1.20; P0 = $40.00; and g = 7% (constant). Based on the DCF approach, what is Brown's cost of equity from retained earnings? a. b. c. d. e. 10.06% 10.21% 10.37% 10.54% 10.68% MEDIUM
Component cost of retained earnings: DCF, D0
12
.
Angell Inc. hired you as a consultant to help them estimate their cost of capital. You have been provided with the following data: D0 = $1.20; P0 = $50.00; and g = 6% (constant). Based on the DCF approach, what is the cost of equity from retained earnings? a. b. c. d. e. 8.07% 8.26% 8.41% 8.54% 8.70% MEDIUM
Component cost of new common stock, based on DCF, D1
13
.
Wagner Lumber Company hired you to help them estimate their cost of capital. You were provided with the following data: D1 = $1.25; P0 = $40; g = 6% (constant); and F = 5%. The firm must issue new stock; what is the cost of equity raised by selling new common stock? a. b. c. d. e. 9.29% 9.40% 9.62% 9.85% 9.99% MEDIUM
Component cost of new common stock, based on DCF, D1
14
.
You were recently hired by Hemmings Media, Inc., to estimate their cost of capital. You were provided with the following data: D1 = $2.50; P0 = $60; g = 7% (constant); and F = 5%. What is the cost of equity raised by selling new common stock? a. b. c. d. e. 11.02% 11.20% 11.39% 11.58% 11.74%
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Chapter 10: The Cost of Capital
WACC
15
MEDIUM
.
You were hired as a consultant to Locke Company, and you were provided with the following data: Target capital structure: 40% debt, 10% preferred, and 50% common equity. The interest rate on new debt is 7.5%, the yield on the preferred is 7.0%, the cost of retained earnings is 11.50%, and the tax rate is 40%. The firm will not be issuing any new stock. What is the firms WACC? a. b. c. d. e. 8.25% 8.38% 8.49% 8.61% 8.76% MEDIUM
Retained earnings breakpoint
16
.
Crum International's target capital structure calls for 80% debt and 20% equity. The company expects to have $3 million of net income this year, and 60% of the net income will be paid out in dividends. How large can the firms capital budget be this year before it will have to issue new common stock? a. b. c. d. e. $5.5 $6.0 $6.3 $6.8 $7.1 million million million million million MEDIUM/HARD
Cost of new common stock: DCF and payout ratio
17
.
Browning Co. expects to earn $3.50 per share during the current year, its expected payout ratio is 40%, its expected constant dividend growth rate is 4.0%, and its common stock currently sells for $40.00 per share. New stock can be sold to the public at the current price, but a flotation cost of 10% would be incurred. What would the cost of equity from new common stock be? a. b. c. d. e. 7.56% 7.70% 7.89% 7.99% 8.12%
Chapter 10: The Cost of Capital
Page 59
WACC
18
MEDIUM/HARD
.
Reingaart Systems is expected to pay a $3.00 dividend at year end (D1 = $3.00), the dividend is expected to grow at a constant rate of 7% a year, and the common stock currently sells for $60 a share. The before-tax cost of debt is 8%, and the tax rate is 40%. The target capital structure consists of 60% debt and 40% common equity. What is the companys WACC if all equity is from retained earnings? a. b. c. d. e. 7.17% 7.31% 7.45% 7.68% 7.84% HARD
Cost of retained earnings: risk premium, CAPM, and DCF
19
.
Malko Inc. hired you as a consultant to help them estimate their cost of capital. You have been provided with the following data. (1): rd = yield on the firms bonds = 6.5% and risk premium over own debt cost = 4%. (2) rRF = 5.5%, RPM = 5.5%, and b = 1.0. (3) D1 = $1.20; P0 = $40.00 and g = 7% (constant). You were asked to estimate the cost of equity based on the three most commonly used methods and then to indicate the difference between the highest and lowest of these estimates. What is this difference? a. b. c. d. e. 0.90% 1.00% 1.10% 1.20% 1.30% HARD
Cost of retained earnings vs. cost of new common stock
20
.
Shilling Co.s common stock currently sells for $40.00 per share, the company expects to earn $3.50 per share during the current year, its expected payout ratio is 40%, and its expected constant growth rate is 4.0%. New stock can be sold to the public at the current price, but a flotation cost of 10% would be incurred. By how much would the cost of new stock exceed the cost of retained earnings? a. b. c. d. e. 0.26% 0.39% 0.51% 0.60% 0.72%
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Chapter 10: The Cost of Capital
WACC, equity from retained earnings, must find YTM
21
HARD
.
Tapley Inc. recently hired you as a consultant to estimate the companys WACC. You have obtained the following information. (1) Tapley's bonds mature in 25 years, have a 7.5% annual coupon, a par value of $1,000, and a market price of $936.49. (2) The companys tax rate is 40%. (3) The risk-free rate is 6.0%, the market risk premium is 5.0%, and the stocks beta is 1.5. (4) The target capital structure consists of 30% debt and 70% equity. Tapley uses the CAPM to estimate the cost of equity, and it does not expect to have to issue any new common stock. What is its WACC? a. b. c. d. e. 9.89% 10.01% 10.35% 10.64% 10.91% HARD
WACC, equity from new stock, uses DCF
22
.
Assume that you are on the financial staff of Christopher Inc., and you have collected the following data: (1) The yield on the companys outstanding bonds is 7.0%, and its tax rate is 40%. (2) The expected year-end dividend is $0.80 a share, the dividend is expected to grow at a constant rate of 6% a year, the price of Christopher's stock is $25 per share, and the flotation cost for selling new shares is 10%. (3) The target capital structure is 40% debt and 60% equity. What is Christopher's WACC assuming that it must issue new stock to finance its capital budget? a. b. c. d. e. 7.11% 7.26% 7.41% 7.67% 7.89% HARD
Risk adjustments to the WACC
23
.
Moussawi Enterprises, which finances only with equity from retained earnings, is considering two large capital budgeting projects, and its CFO hired you to assist in deciding whether one, both, or neither of the projects should be accepted. You have the following information: (1) rRF = 5.5%; RPM = 6%; and b = 0.8. (2) The company adds 3% to the corporate WACC when it evaluates relatively risky projects, and it deducts 1% from the WACC when evaluating relatively safe projects. (3) Project S is relatively safe, it costs $10,000, and its expected rate of return is 8%, while Project R is relatively risky, it costs $15,000, and its expected rate of return is 12%. If these are the only two projects under consideration, how large should the capital budget be? a. b. c. d. e. $ 5,000 $10,000 $15,000 $20,000 $25,000 Page 61
Chapter 10: The Cost of Capital
Multiple Choice: Conceptual Note to Professors: We designated most of these questions as being MEDIUM. However, their difficulty as seen by students will depend on (1) what was discussed in class and (2) how long students have to answer the questions. If time is not an issue, then many of the questions should be classified as EASY, but under exam conditions with time pressure, they might be regarded as being HARD. So, consider the amount of time students have when selecting questions for an exam.
Capital components
24
EASY
.
Which of the following is not a capital component when calculating the weighted average cost of capital (WACC)? a. b. c. d. e. Long-term debt. Common stock. Retained earnings. Accounts payable. Preferred stock. EASY
Capital components
25
.
For a typical firm, which of the following is correct? All rates are after taxes, and assume the firm operates at its target capital structure. a. b. c. d. e. rd > rs > WACC re > WACC re re > rs > > > re > rd rs > rd > > rs WACC > rs WACC. WACC. > rd. > rd. > re. MEDIUM
Capital components
26
.
Which of the following statements is CORRECT? a. If a companys tax rate increases but the YTM of its noncallable bonds remains the same, the after-tax cost of its debt will fall. b. All else equal, an increase in a companys stock price will increase its marginal cost of retained earnings, rs. c. All else equal, an increase in a companys stock price will increase its marginal cost of new common equity, re. d. Since the money is readily available, the after-tax cost of retained earnings is usually much lower than the after-tax cost of debt. e. When calculating the cost of preferred stock, a company needs to adjust for taxes, because preferred stock dividends are tax deductible.
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Chapter 10: The Cost of Capital
Capital components
27
MEDIUM
.
Which of the following statements is CORRECT? a. Because of tax effects, an increase in the risk-free rate will have a greater effect on the after-tax cost of debt than on the cost of common stock. b. When calculating the cost of preferred stock, companies must adjust for taxes, because dividends paid on preferred stock are deductible by the paying corporation. c. When calculating the cost of debt, a company needs to adjust for taxes, because interest payments are deductible by the paying corporation. d. If a companys beta increases, this will increase the cost of equity used to calculate the WACC, but only if the company does not have enough retained earnings to take care of its equity financing and hence needs to issue new stock. e. Higher flotation costs reduce investor returns, and that leads to a reduction in a companys WACC.
WACC
28
Which of the following statements is CORRECT?
MEDIUM
.
a. The WACC as used in capital budgeting is an estimate of a companys before-tax cost of capital. b. There is an opportunity cost associated with using retained earnings they are not free. c. The WACC as used in capital budgeting is an estimate of the cost of all the capital a company has raised to acquire its assets. d. The percentage flotation costs associated with issuing new common equity are typically smaller than the flotation costs for new debt. e. The WACC as used in capital budgeting will be the after-tax cost of debt if the firm plans to use only debt to finance its capital budget during the coming year. WACC
29
MEDIUM
.
Which of the following statements about the cost of capital is CORRECT? a. A change in a companys target capital structure cannot affect its WACC. b. WACC calculations should be based on the before-tax costs of all the individual capital components. c. If a companys tax rate increases, then, all else equal, its weighted average cost of capital will decrease. d. Flotation costs associated with issuing new common stock normally lead to a decrease in the WACC. e. An increase in the risk-free rate will normally lower the marginal costs of both debt and equity financing.
Chapter 10: The Cost of Capital
Page 63
WACC and capital components
30
MEDIUM
.
Which of the following statements is CORRECT? a. The WACC is calculated using before-tax costs for all components. b. The after-tax cost of debt usually exceeds the after-tax cost of equity. c. The WACC that should be used in capital budgeting is the firms marginal, after-tax cost of capital. d. Retained earnings that were generated in the past and are reflected on the firms balance sheet are generally available to finance the firms capital budget during the coming year. e. The after-tax cost of debt is generally more expensive than the aftertax cost of preferred stock.
WACC and capital components
31
MEDIUM
.
For a company whose target capital structure calls for 50% debt and 50% common equity, which of the following statements is CORRECT? a. The cost of equity is usually greater than or equal to the cost of debt. b. The WACC exceeds the cost of equity. c. The WACC is calculated on a before-tax basis. d. The interest rate used to calculate the WACC is the average cost of all the debt the company has outstanding and shown on its balance sheet. e. The cost of retained earnings typically exceeds the cost of new common stock.
Factors influencing WACC
32
MEDIUM
.
Maese Sisters Inc has been paying out all of its earnings as dividends, and hence has no retained earnings. This same situation is expected to persist in the future. The company uses the CAPM to calculate its cost of equity. Its target capital structure consists of common stock, preferred stock, and debt. Which of the following events would reduce the WACC? a. b. c. d. e. The flotation costs associated with issuing new common stock increase. The market risk premium declines. The companys beta increases. Expected inflation increases. The flotation costs associated with issuing preferred stock increase. MEDIUM
Risk and project selection
33
.
Wagner Inc estimates that its average-risk projects have a WACC of 10%, its below-average risk projects have a WACC of 8%, and its above-average risk projects have a WACC of 12%. Which of the following projects (A, B, and C) should the company accept? a. b. c. d. e. Project A is of average risk and has a return of 9%. Project B is of below-average risk and has a return of 8.5%. Project C is of above-average risk and has a return of 11%. None of the projects should be accepted. All of the projects should be accepted. Chapter 10: The Cost of Capital
Page 64
Divisional risk
34
MEDIUM
.
Basu Inc. uses only equity capital, and it has two equally-sized divisions. Division As cost of capital is 10.0%, Division Bs cost is 14.0%, and the composite WACC is 12.0%. All of Division As projects have the same risk, and all Division B projects are also equally risky. However, the projects in Division A do not have the same risk as those in Division B. Which of the following projects should Basu accept? a. b. c. d. e. A A A A A Division Division Division Division Division A B B A B project project project project project with with with with with an 11% return. a 12% return. a 13% return. a 9% return. an 11% return. MEDIUM
Miscellaneous cost of capital concepts
35
.
Which of the following statements is CORRECT? a. Since debt capital is riskier than equity capital, the after-tax cost of debt is always greater than the WACC. b. Because of the risk of bankruptcy, the cost of debt capital is always higher than the cost of equity capital. c. If a company assigns the same cost of capital to all of its projects regardless of the projects risk, then it follows that the company will tend to reject some safe projects that it actually should accept and accept some risky projects that it should reject. d. Because companies flotation costs are not required to obtain capital as retained earnings, the cost of retained earnings is generally lower than the after-tax cost of debt. e. Higher flotation costs tend to reduce the cost of equity capital.
Capital components
36
MEDIUM
.
Which of the following statements is CORRECT? a. In the WACC calculation, we must adjust the cost of preferred stock (the market yield) because 70% of the dividends received by corporate investors are excluded from their taxable income. b. We should use historical measures of the component costs from prior financings when estimating a companys WACC for capital budgeting purposes. c. The cost of new equity (re) could possibly be lower than the cost of retained earnings (rs) if the market risk premium, risk-free rate, and the companys beta all decline by a sufficiently large amount. d. The component cost of preferred stock is expressed as rp(1 - T), because preferred stock dividends are treated as fixed charges, similar to the treatment of debt interest. e. The cost of retained earnings is the rate of return stockholders require on a firms common stock.
Chapter 10: The Cost of Capital
Page 65
CAPM cost of equity estimation
37
MEDIUM
.
When applying the CAPM, which of the following factors can be determined with the most precision? a. b. c. d. e. The expected rate of return on the market, rM. The beta coefficient, bi, of a relatively safe company. The risk-free rate, rRF. The market risk premium (RPM). The beta coefficient of either the market or a stock that is known with certainty to be of average risk. MEDIUM
Internal vs. external common equity
38
.
Nachman Corporation forecasts that if all of its existing financial policies are adhered to, its proposed capital budget would be so large that it would have to issue new common stock. Since new stock has a higher cost than of retained earnings, Nachman would like to avoid issuing new stock. Which of the following actions would REDUCE its need to issue new common stock? a. b. c. d. Increase the dividend payout ratio for the upcoming year. Increase the percentage of debt in the target capital structure. Increase the proposed capital budget. Reduce the amount of short term bank debt in order to increase the current ratio. e. Reduce the percentage of debt in the target capital structure.
Risk and project selection
39
MEDIUM
.
Boe Enterprises, an all-equity firm, has a beta of 2.0. Boes chief financial officer is evaluating a project with an expected return of 21%, before any risk adjustment. The risk-free rate is 7%, and the market risk premium is 6%. The project being evaluated is riskier than Boes average project, in terms of both its beta risk and its total risk. Which of the following statements is CORRECT? a. The project should definitely be accepted because its expected return (before any risk adjustments) is greater than its required return. b. The project should definitely be rejected because its expected return (before risk adjustment) is less than its required return. c. The accept/reject decision depends on the risk-adjustment policy of the firm. If the firms policy is to reduce a riskier-than-average projects expected return by 1%, to 20%, then it should be accepted. d. Riskier-than-average projects should have their expected returns increased to reflect their higher risk. Clearly, this would make the project acceptable regardless of the amount of the adjustment. e. Capital budgeting projects should be evaluated solely on the basis of their total risk. Thus, insufficient information has been provided to make the accept/reject decision.
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Chapter 10: The Cost of Capital
Risk-adjusted cost of capital
40
MEDIUM
.
The Nunnally Company has equal amounts of low-risk, average-risk, and high-risk projects. Nunnally estimates that its overall WACC is 12%. The CFO believes that this is the correct WACC for the companys average-risk projects, but that a lower rate should be used for lower risk projects and a higher rate for higher risk projects. However, the CEO argues that, even though the companys projects have different risks, the WACC used to evaluate each project should be the same because the company obtains capital for all projects from the same sources. If the CEOs opinion is followed, what is likely to happen over time? a. The company will take on too many low-risk projects and reject too many high-risk projects. b. The company will take on too many high-risk projects and reject too many low-risk projects. c. Things will generally even out over time, and, therefore, the firms risk should remain constant over time. d. The companys overall WACC should decrease over time because its stock price should be increasing. e. The CEOs recommendation would maximize the firms intrinsic value.
Risk-adjusted cost of capital
41
MEDIUM
.
If a typical U.S. company uses the same cost of capital to evaluate all projects, the firm will most likely become a. b. c. d. e. Riskier over time, and its intrinsic value will not be maximized. Riskier over time, but its intrinsic value will be maximized. Less risky over time, and its intrinsic value will not be maximized. Less risky over time, and its intrinsic value will be maximized. There is no reason to expect its risk position or value to change over time as a result of its use of a single discount rate. HARD
Retained earnings break point
42
.
Assume that a firms total dollar capital budget is fixed and will not be changed. Which of the following will increase the retained earnings break point, i.e., increase the dollar amount of total capital at which the WACC will increase due to having to issue new common stock? a. The firms net income increases. b. The firm increases its dividend payout ratio. c. The firm increases the percentage of equity in its target capital structure. d. The risk of the average capital budgeting project increases. e. The risk of the average capital budgeting project decreases.
Chapter 10: The Cost of Capital
Page 67
Retained earnings break point
43
HARD
.
Assume that a firms total dollar capital budget is fixed and will not be changed. Which of the following will decrease the retained earnings break point, i.e., decrease the dollar amount of total capital at which the WACC will increase due to having to issue new common stock? a. The firm decides to pay out a lower percentage of its income as dividends. b. The firm increases the amount of debt in its target capital structure. c. The average risk of projects in the capital budget decreases. d. The firms net income increases. e. The firm has been using preferred stock in its capital structure, but it now decides to stop financing with preferred stock and to replace the preferred with common equity.
Cost of capital estimation
44
HARD
.
Which of the following statements is CORRECT? a. The cost of capital used to evaluate a project should be the cost of the specific type of financing used to fund that project, i.e., it is the after-tax cost of debt if debt is to be used to finance the project or the cost of equity if the project will be financed with equity. b. The after-tax cost of debt that is used as the component cost when calculating the WACC is the average after-tax cost of the firms outstanding debt. c. Suppose some of a publicly-traded firms stockholders are not diversified; they hold only the one firms stock. In this case, the CAPM approach will result in an estimated cost of equity that is too low in the sense that if it is used in capital budgeting, projects will be accepted that will not maximize the firms intrinsic values. d. The bond-yield-plus-risk-premium approach is the most sophisticated and objective method for estimating a firms cost of equity capital. e. The cost of equity is generally harder to measure than the cost of debt because there is no stated, contractual cost number on which to base the cost of equity.
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Chapter 10: The Cost of Capital
Cost of equity estimation
45
HARD
.
Which of the following statements is CORRECT? a. Although some methods used to estimate the cost of equity are subject to severe difficulties, the CAPM is a simple, straightforward, and reliable model that consistently produces accurate cost of equity estimates. In particular, academics and corporate finance people generally agreed that its key inputsbeta, the risk-free rate, and the market risk premiumcan be estimated with very little error. b. The DCF model is generally preferred by academics and financial executives over other models for estimating the cost of equity. This is because of the DCF models logical appeal and also because accurate estimates for its key input, the growth rate, are easy to obtain. c. The bond-yield-plus-risk-premium approach to estimating the cost of equity may not always be accurate, but it has the advantage that its two key inputs, the firms own cost of debt and the firms risk premium, can be found by using standardized and objective procedures. d. The CAPM is probably the most widely used method for estimating the cost of equity. However, other methods are also used because CAPM estimates may be subject to error, and people like to use different methods as checks on one another. If all of the methods produce similar results, then decision makers can have more confidence in the estimated cost of equity. e. The DCF model is preferred by academics and finance people over other cost of capital models because it correctly recognizes that the expected return on a stock consists of a dividend yield plus an expected capital gains yield.
CAPM and DCF estimation
46
HARD
.
Which of the following statements is CORRECT? a. Beta measures market risk, which is the most relevant risk measure for a publicly-owned firm that seeks to maximize its intrinsic value. This is true even if not all of the firms stockholders are well diversified. b. If the calculated beta underestimates the firms true investment risk (i.e., the forward-looking beta that investors think exists), then the CAPM method will produce an estimate of rs and thus WACC that is too high. c. The discounted cash flow method of estimating the cost of equity cannot be used unless the growth rate, g, is expected to be constant forever. d. An advantage shared by both the DCF and CAPM methods is that little or no judgment is required when they are used to estimate the cost of equity. e. The specific risk premium used in the CAPM is the same as the risk premium used in the bond-yield-plus-risk-premium approach.
Chapter 10: The Cost of Capital
Page 69
WACC
47
Which of the following statements is CORRECT?
HARD
.
a. The WACC can change depending on the amount of funds a firm raises during a given year. Moreover, the WACC at each level of funds raised is a weighted average of the marginal costs of each capital component, with the weights based on the firms target capital structure. b. The WACC is calculated using a before-tax cost for debt equal to the interest rate that must be paid on new debt, along with the after-tax cost for common stock and for preferred stock if it is used. c. An increase in the risk-free rate is likely to reduce the marginal costs of both debt and equity. d. The bond-yield-plus-risk-premium approach to estimating the cost of common equity involves adding a risk premium to the interest rate on the companys own long-term bonds. The size of the risk premium for bonds with different ratings is published daily in the Wall Street Journal. e. Beta measures market risk, which is generally the most relevant risk measure for a publicly-owned firm that seeks to maximize its intrinsic value. However, this is not true unless all of the firms stockholders are well diversified. WACC
48
Which of the following statements is CORRECT?
HARD
.
a. An increase in the flotation cost required to sell a new issue of stock will increase the cost of retained earnings. b. When the WACC is calculated, it should reflect the cost of new common stock, retained earnings, preferred stock, long-term debt, short-term bank loans if the firm normally finances with bank debt, and accounts payable if the firm normally has accounts payable on its balance sheet. c. An increase in a firms tax rate will increase the component cost of debt, provided the YTM on the firms bonds is not affected. d. Since its stockholders are not directly responsible for paying a corporations income taxes, corporations should focus on before-tax cash flows when calculating the WACC. e. If a firm has been suffering accounting losses and is expected to continue suffering such losses in the foreseeable future, and therefore its tax rate is zero, then it is possible for the after-tax cost of preferred stock to be less than the after-tax cost of debt.
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Chapter 10: The Cost of Capital
Risk-adjusted cost of capital
49
HARD
.
Kish Consolidated has two divisions of equal size: a computer division and a restaurant division. Its CFO believes that stand-alone restaurant companies typically have a WACC of 8%, while stand-alone computer companies typically have a 12% WACC. She also believes that Kishs restaurant and computer divisions have the same risk as their typical peers. Consequently, Kish estimates that its composite, or corporate, WACC is 10%. A consultant has suggested using an 8% hurdle rate for the restaurant division and a 12% hurdle rate for the computer division. However, Kish has ignored its consultant and assigned a 10% WACC to all projects in both divisions. Which of the following statements is CORRECT? a. While Kishs decision not to use risk-adjusted WACCs will result in its accepting more projects in the computer division and fewer projects in its restaurant division than if it followed the consultants recommendation, this should not affect the firms intrinsic value. b. Kishs decision not to adjust for risk means, in effect, that it is favoring the restaurant division. Therefore, that division is likely to become a larger part of the consolidated company over time. c. Kishs decision not to adjust for risk means that the company will accept too many projects in the computer business and too few projects in the restaurant business. This will lead to a reduction in the firms intrinsic value over time. d. Kishs decision not to risk adjust means that the company will accept too many projects in the computer business and too few projects in the restaurant business. This may affect the firms capital structure but it will not affect the intrinsic value. e. Kishs decision to not risk adjust means that the company will accept too many projects in the restaurant business and too few projects in the computer business. This will lead to a reduction in the intrinsic value.
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Divisional risk and project selection
50
HARD
.
Safeco Company and Risco Inc are identical in size and capital structure. However, the riskiness of their assets and cash flows are somewhat different, resulting in Safeco having a WACC of 10% and Risco a 12% WACC. Safeco is considering Project X, which has an IRR of 10.5% and is of the same risk as a typical Safeco project. Risco is considering Project Y, which has an IRR of 11.5% and is of the same risk as a typical Risco project. Now assume that the two companies merge and form a new company, Safeco/Risco Inc. Moreover, the new companys market risk is an average of the pre-merger companies market risks, and the merger has no impact on either the cash flows or the risks of projects X and Y. Which of the following statements is CORRECT? a. Safeco/Riscos WACC, as a result of the merger, would be 10%. b. If evaluated using the correct post-merger WACC, Project X would have a negative NPV. c. After the merger, Safeco/Risco would have a corporate WACC of 11%. Therefore, it should reject Project X but accept Project Y. d. If the firm evaluates these projects and all other projects at the new overall corporate WACC, it will become riskier over time. e. After the merger, Safeco/Risco should select Project Y but reject Project X.
Miscellaneous concepts
51
HARD
.
Which of the following statements is CORRECT? a. Suppose a firm has been losing money and thus is not paying taxes, and this situation is expected to persist into the foreseeable future. In this case, the firms before-tax and after-tax costs of debt will both be equal to the interest rate on the firms currently outstanding debt, which was issued during the past 5 years. b. The component cost of preferred stock is expressed as rp(1 - T). This follows because preferred stock dividends are treated as fixed charges, and as such they can be deducted by the issuer for tax purposes. c. No cost should be assigned to retained earnings because the firm does not have to pay anything to raise themthey are generated as cash flows by operating assets that were raised in the past, hence they are free. d. A cost should be assigned to retained earnings due to the opportunity cost principle, which refers to the fact that the firms stockholders could themselves earn a return on earnings if they were paid out rather than retained and reinvested. e. If a firm has enough retained earnings to fund its capital budget, then there is no need to estimate a cost of equity when determining the WACC.
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Beta and project risk
52
HARD
.
Which of the following statements is CORRECT? publicly-owned corporation.
Assume that the firm is a
a. If a firm has a beta that is less than 1.0, say 0.9, this would suggest that the expected returns on its assets are negatively correlated with the returns on most other firms assets. b. If a firms managers want to maximize the value of the stock, they should, in theory, concentrate on project risk as measured by the standard deviation of the projects expected future cash flows. c. If a firm evaluates all projects using the same cost of capital, then its risk will probably decline over time. d. Project A has a standard deviation of expected returns of 20%, while Project Bs standard deviation is only 10%. As returns are negatively correlated with the firms other assets and with returns on most stocks in the economy, while Bs returns are positively correlated. Therefore, Project A is less risky to a firm and should be evaluated with a lower cost of capital. e. Projects with more than average risk typically have higher than average expected returns. Therefore, to maximize a firms intrinsic value, its managers should favor high beta projects over low beta projects.
PART II Questions and Problems from Prior Test Bank not used in Part I
Multiple Choice: Problems
MEDIUM (#53 through #59) Component cost of debt
53
.
Hamilton Company has 20-year, 8% quarterly coupon bonds that currently sell for $686.86. The companys tax rate is 40%. What is the firms nominal component cost of debt? a. 3.05% b. 7.32% c. 7.36% d. 12.20% e. 12.26%
Cost of retained earnings
54
.
The common stock of Anthony Steel has a beta of 1.20. The risk-free rate is 5% and the market risk premium is 6%. Assume the firm will be able to use retained earnings to fund the equity portion of its capital budget. What is the companys cost of retained earnings, rs? a. 7.0% b. 7.2% c. 11.0% d. 12.2%
Chapter The 10: Cost of Capital
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e. 12.4% Cost of retained earnings
55
.
Allison Engines Corporation has established a target capital structure of 40% debt and 60% common equity. The current market price of the firms stock is P0 = $28; its last dividend was D0 = $2.20, and its expected dividend growth rate is 6%. What will Allisons marginal cost of retained earnings, rs, be? a. 15.8% b. 13.9% c. 7.9% d. 14.3% e. 9.7%
Cost of external equity
56
.
A company just paid a $2.00 per share dividend (D0 = $2.00). The dividend is expected to grow at a constant rate of 7% per year. The stock currently sells for $42 a share. If the company issues additional stock, it must pay its investment banker a flotation cost of $1.00 per share. What is the cost of external equity, re? a. b. c. d. e. 11.76% 11.88% 11.98% 12.22% 12.30%
Cost of new equity
57
.
Blair Brothers stock currently has a price of $50 per share and is expected to pay a year-end dividend of $2.50 per share (D1 = $2.50). The dividend is expected to grow at a constant rate of 4% per year. The company has insufficient retained earnings to fund capital projects and must, therefore, issue new common stock. The new stock has an estimated flotation cost of $3 per share. What is the companys cost of new equity capital? a. 10.14% b. 9.21% c. 9.45% d. 9.32% e. 9.00%
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Divisional risk
58
.
Dandy Products overall corporate WACC is 10%. Its yogurt division is riskier than average, its fresh produce division has average risk, and its institutional foods division has below-average risk. Dandy adjusts for both divisional and project risk by adding or subtracting 2%. Thus, the maximum adjustment is 4%. What is the risk-adjusted cost of capital for a low-risk project in the yogurt division? a. 6% b. 8% c. 10% d. 12% e. 14%
Retained earnings break point
59
.
Stephenson & Sons has a capital structure that consists of 20% equity and 80% debt. The company expects to report $3 million in net income this year, and 60% of the net income will be paid out as dividends. How large can the firms capital budget be this year without it having to issue any new common stock? a. b. c. d. e. $ 1.20 $13.00 $ 1.50 $ 0.24 $ 6.00 million million million million million
MEDIUM/HARD (#60 through #72) WACC
60
An analyst has collected the following information regarding Christopher Co.: The companys capital structure is 70% equity and 30% debt. The YTM on the companys bonds is 9%. The companys year-end dividend is forecasted to be $0.80 a share. The company expects a constant dividend growth rate of 9% a year. The companys stock price is $25. The companys tax rate is 40%. The company anticipates that it will need to raise new common stock this year, and flotation costs will equal 10% of the amount issued.
.
Assume the company accounts for flotation costs by adjusting the cost of capital. Given this information, calculate the companys WACC. a. b. c. d. e. 10.41% 12.56% 10.78% 13.55% 9.29%
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WACC
61
Trojan Services CFO is interested in estimating the companys WACC and has collected the following information: The company has 26-year, 7.5% annual coupon bonds that have a face value of $1,000 and sell for $920. The risk-free rate is 6%. The market risk premium is 5. The stocks beta is 1.2. The companys tax rate is 40%. The companys target capital structure consists of 70% equity and 30% debt. The company uses the CAPM to estimate the cost of equity and does not include flotation costs as part of its cost of capital.
.
What is Trojans WACC? a. 9.75% b. 9.39% c. 10.87% d. 9.30% e. 9.89% WACC
62
A company has determined that its optimal capital structure consists of 40% debt and 60% equity. Assume the firm will not have enough retained earnings to fund the equity portion of its capital budget, and the cost of capital is adjusted to account for flotation costs. Given the following information, calculate the firms WACC. rd = 8%. Net income = $40,000. Payout ratio = 50%. Tax rate = 40%. P0 = $25. Growth = 0%. Shares outstanding = 10,000. Flotation cost on additional equity = 15%.
.
a. 7.60% b. 8.05% c. 11.81% d. 13.69% e. 14.28%
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WACC
63
Johnson Industries finances its projects with 40% debt, 10% preferred stock, and 50% common stock. The company can issue bonds at a YTM of 8.4%. The cost of preferred stock is 9%. The risk-free rate is 6.57%. The market risk premium is 5%. Johnson Industries beta is equal to 1.3. Assume that the firm will be able to use retained earnings to fund the equity portion of its capital budget. The companys tax rate is 30%.
.
What is the companys WACC? a. 8.33% b. 8.95% c. 9.79% d. 10.92% e. 13.15% WACC
64
Helms Aircraft has a capital structure that consists of 60% debt and 40% common stock. The firm will be able to use retained earnings to fund the equity portion of its capital budget. The company recently issued bonds with a yield to maturity of 9%. The risk-free rate is 6%, the market risk premium is 6%, and Helms beta is equal to 1.5. If the companys tax rate is 35%, what is the companys WACC? a. 8.33% b. 9.51% c. 9.95% d. 10.98% e. 11.84%
.
Chapter 10: The Cost of Capital
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WACC
65
Dobson Dairies has a capital structure consisting of 60% debt and 40% common stock. The companys CFO has obtained the following information: The before-tax YTM on the companys bonds is 8%. The companys common stock is expected to pay a $3.00 dividend at year end (D1 = $3.00), and the dividend is expected to grow at a constant rate of 7% a year. The common stock currently sells for $60 a share. Assume the firm will be able to use retained earnings to fund the equity portion of its capital budget. The companys tax rate is 40%.
.
What is the companys WACC? a. 12.00% b. 8.03% c. 9.34% d. 8.00% e. 7.68% WACC
66
A stock analyst has obtained the following information about J-Mart: The company has 20-year, 12% annual coupon bonds that have a $1,000 face value and sell at a price of $1,273.8564. Over the past four years, the returns on the market and on J-Mart were: Year 2002 2003 2004 2005 Market 12.0% 17.2 -3.8 20.0 J-Mart 14.5% 22.2 -7.5 24.0
.
The current risk-free rate is 6.35%, and the expected market risk premium is 5%. The companys tax rate is 35%. The company anticipates that its proposed investment projects will be financed with 70% debt and 30% equity.
What is the companys WACC? a. 8.04% b. 9.00% c. 10.25% d. 12.33% e. 13.14%
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Chapter 10: The Cost of Capital
WACC
67
Clark Communications has a capital structure that consists of 70% common stock and 30% long-term debt. In order to calculate Clarks WACC, an analyst has accumulated the following information: The company currently has 15-year, 8% annual coupon bonds that have a face value of $1,000 and sell for $1,075. The risk-free rate is 5%. The market risk premium is 4%. The beta on Clarks common stock is 1.1. The companys retained earnings are sufficient so that they do not have to issue any new common stock to fund capital projects. The companys tax rate is 38%.
.
Given this information, what is Clarks WACC? a. b. c. d. e. 5.93% 7.40% 7.91% 8.07% 8.73%
WACC and dividend growth rate
68
.
Grateway Inc. has a WACC of 11.5%. Its target capital structure is 55% equity and 45% debt. The company has sufficient retained earnings to fund the equity portion of its capital budget. The before-tax cost of debt is 9%, and the companys tax rate is 30%. If the expected dividend next period (D1) is $5 and the current stock price is $45, what is the companys growth rate? a. b. c. d. e. 2.68% 3.44% 4.64% 6.75% 8.16%
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WACC and optimal capital budget
69
.
Kenforest Grocers managers are determining the companys optimal capital budget for the next year. Kenforest is considering the following projects: Project A B C D E F G Size $200,000 500,000 400,000 300,000 100,000 200,000 400,000 Rate of Return 16% 14 12 11 10 10 7 Risk High Average Low High Average Low Low
The company estimates that its WACC is 11%. All projects are independent. The company adjusts for risk by adding 2% to the WACC for high-risk projects and subtracting 2% from the WACC for low-risk projects. Which of the projects will the company accept? a. b. c. d, e. A, B, A, A, A, B, D, B, B, B, C, F, C, C, C, E, F G E D, E F
CAPM, beta, and WACC
70
.
Bradshaw Steel has a capital structure with 30% debt and 70% common equity. The YTM on the companys long-term bonds is 8%, and the firm estimates that its overall composite WACC is 10%. The firm uses the CAPM to determine its cost of equity. The risk-free rate is 5.5%, the market risk premium is 5%, and the companys tax rate is 40%. What is the beta on Bradshaws stock? a. b. c. d. e. 1.07 1.48 1.31 0.10 1.35
Required rate of return
71
.
Arizona Rock, an all-equity firm, currently has a beta of 1.25. The riskfree rate, rRF, is 7% and the market risk premium, RPM, is 7%. Suppose the firm sells 10% of its assets with beta equal to 1.25 and purchases the same proportion of new assets with a beta of 1.1. What will be the firms new overall WACC, and what rate of return must the new assets produce in order to leave the stock price unchanged? a. b. c. d. e. 15.645%; 15.750%; 15.645%; 15.750%; 14.750%; 15.645% 14.700% 14.700% 15.645% 15.750% Chapter 10: The Cost of Capital
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Beta risk
72
.
Sun State Mining Inc., an all-equity firm, is considering forming a new division that will increase the firms assets by 50%. Sun State currently has a required return of 18%, U.S. Treasury bonds yield 7%, and the market risk premium is 5%. If Sun State wants to reduce its required return to 16%, what is the maximum beta coefficient the new division could have? a. b. c. d. e. 2.2 1.0 1.8 1.6 2.0
HARD (#73 through #74) WACC
73
Heavy Metal Corp. is a steel manufacturer that finances its operations with 40% debt, 10% preferred stock, and 50% equity. The interest rate on the companys debt is 11%. The preferred stock pays an annual dividend of $2 and sells for $20 a share. The companys common stock trades at $30 a share, and its current dividend (D0) of $2 a share is expected to grow at a constant rate of 8% per year. The flotation cost of external equity is 15% of the dollar amount issued, while the flotation cost on preferred stock is 10%. The company estimates that its WACC is 12.30%. Assume that the firm will not have enough retained earnings to fund the equity portion of its capital budget. What is the companys tax rate? a. b. c. d. e. 30.33% 32.86% 35.75% 38.12% 40.98%
.
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Chapter 10: The Cost of Capital
WACC and cost of preferred stock
74
.
Anderson Company has four investment opportunities with the following costs (paid at t = 0) and expected returns: Project A B C D Cost $2,000 3,000 5,000 3,000 Expected Return 16.0% 14.5 11.5 9.5
The company has a target capital structure that consists of 40% common equity, 40% debt, and 20% preferred stock. The company has $1,000 in retained earnings. The company expects its year-end dividend to be $3.00 per share (D1 = $3.00). The dividend is expected to grow at a constant rate of 5% a year. The companys stock price is currently $42.75. If the company issues new common stock, the company will pay its investment bankers a 10% flotation cost. The company can issue corporate bonds with a YTM of 10%. The company has a 35% tax rate. How large can the cost of preferred stock be (including flotation costs) and it still be profitable for the company to invest in all four projects? a. 7.75% b. 8.90% c. 10.46% d. 11.54% e. 12.68%
Multiple Part:
(The following information applies to the next three problems.) The Global Advertising Co. has a tax rate of 40%. The company can raise debt at a 12% interest rate. Globals stock price is $8.59 per share and it recently issued a dividend of $0.90, which is expected to grow at a constant rate of 5%. If Global issues new common stock, the flotation cost incurred will be 10%. Global plans to finance all capital expenditures with 30% debt and 70% equity. Cost of retained earnings
75
.
What is Globals cost of retained earnings if it can use retained earnings rather than issue new common stock? a. b. c. d. e. 12.22% 17.22% 10.33% 9.66% 16.00%
Chapter 10: The Cost of Capital
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Cost of external equity
76
.
What is the cost of common equity raised by selling new stock? a. b. c. d. e. 12.22% 17.22% 10.33% 9.66% 16.00% What is the firms WACC if the firm has sufficient retained earnings to fund the equity portion of its capital budget? a. b. c. d. e. 11.95% 12.22% 12.88% 13.36% 14.21% (The following information applies to the next two problems.)
WACC
77
.
Byron Corporations target capital structure consists of 40% debt and 60% common equity. Assume that the firm has no retained earnings. The companys last dividend (D0) was $2.00, which is expected to grow at a constant rate of 5%; and the current equilibrium stock price is $21.88. Byron can raise all the debt financing it needs at 14%. If Byron issues new common stock, a 20% flotation cost will be incurred. The firms tax rate is 40%. Cost of external equity
78
.
What is the component cost of the equity raised by selling new common stock? a. b. c. d. e. 17.0% 16.4% 15.0% 14.6% 12.0% What is the firms WACC? a. b. c. d. e. 10.8% 13.6% 14.2% 16.4% 18.0%
WACC
79
.
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Chapter 10: The Cost of Capital
(The following information applies to the next six problems.) Rollins Corporation has a target capital structure consisting of 20% debt, 20% preferred stock, and 60% common equity. Assume the firm has insufficient retained earnings to fund the equity portion of its capital budget. It has 20year, 12% semiannual coupon bonds that sell at their par value of $1,000. The firm could sell, at par, $100 preferred stock that pays a 12% annual dividend, but flotation costs of 5% would be incurred. Rollins beta is 1.2, the riskfree rate is 10%, and the market risk premium is 5%. Rollins is a constant growth firm that just paid a dividend of $2.00, sells for $27.00 per share, and has a growth rate of 8%. The firms policy is to use a risk premium of 4% when using the bond-yield-plus-risk-premium method to find rs. Flotation costs on new common stock total 10%, and the firms marginal tax rate is 40%. Cost of debt
80
.
What is Rollins component cost of debt? a. 10.0% b. 9.1% c. 8.6% d. 8.0% e. 7.2%
Cost of preferred stock
81
.
What is Rollins cost of preferred stock? a. b. c. d. e. 10.0% 11.0% 12.0% 12.6% 13.2%
Cost of equity: CAPM
82
.
What is Rollins cost of retained earnings using the CAPM approach? a. b. c. d. e. 13.6% 14.1% 16.0% 16.6% 16.9%
Cost of equity: DCF
83
.
What is the firms cost of retained earnings using the DCF approach? a. b. c. d. e. 13.6% 14.1% 16.0% 16.6% 16.9%
Chapter 10: The Cost of Capital
Page 85
Cost of equity: risk premium
84
.
What is Rollins cost of retained earnings using the bond-yield-plus-riskpremium approach? a. b. c. d. e. 13.6% 14.1% 16.0% 16.6% 16.9% What is Rollins WACC, if the firm has insufficient retained earnings to fund the equity portion of its capital budget? a. b. c. d. e. 13.6% 14.1% 16.0% 16.6% 16.9% (The following information applies to the next two problems.)
WACC
85
.
The Jackson Company has just paid a dividend of $3.00 per share on its common stock, and it expects this dividend to grow by 10% per year, indefinitely. The firm has a beta of 2.00; the risk-free rate is 6%; and the market risk premium is 5%. The firms investment bankers believe that new issues of common stock would have a flotation cost equal to 5% of the current market price. Stock price--constant growth
86
.
How much should an investor be willing to pay for this stock today? a. b. c. d. e. $62.81 $70.00 $43.75 $55.00 $30.00
Cost of external equity
87
.
What will be Jacksons cost of new common stock if it issues new stock in the marketplace today? a. b. c. d. e. 15.25% 16.32% 17.00% 12.47% 9.85%
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Chapter 10: The Cost of Capital
(The following information applies to the next three problems.) The following information applies to the Coetzer Company: Coetzer has a target capital structure of 40% debt and 60% common equity. Coetzer has 15-year, 12% annual coupon bonds that have a face value of $1,000 and sell for $1,150. The risk-free rate is 5%. The market risk premium (RPM) is also 5%. Coetzers common stock has a beta of 1.4. Coetzers tax rate is 40%.
Cost of debt
88
.
What is the companys after-tax cost of debt? a. 3.6% b. 6.0% c. 7.2% d. 10.0% e. 12.0%
Cost of common equity:
89
CAPM
.
What is the companys after-tax cost of common equity? a. 6.0% b. 8.4% c. 9.6% d. 10.0% e. 12.0%
WACC
90
What is the companys WACC? a. 6.0% b. 7.4% c. 9.6% d. 10.8% e. 12.2%
.
Chapter 10: The Cost of Capital
Page 87
(The following information applies to the next four problems.) Viduka Constructions CFO has collected the following information to estimate the companys WACC: The company currently has 20-year, 8.5% annual coupon bonds that have a face value of $1,000 and sell for $945. The companys stock has a beta = 1.20. The market risk premium, RP , equals 5%. The risk-free rate is 6%. The company has outstanding preferred stock that pays a $2.00 annual dividend. The preferred stock sells for $25 a share. The companys tax rate is 40%. The companys capital structure consists of 40% long-term debt, 40% common stock, and 20% preferred stock.
M
Cost of debt
91
.
What is the companys after-tax cost of debt? a. b. c. d. e. 5.10% 5.46% 6.46% 8.50% 9.11%
Cost of preferred stock
92
.
What is the companys after-tax cost of preferred stock? a. b. c. d. e. 4.80% 5.60% 7.10% 8.00% 8.40% CAPM
Cost of common equity:
93
.
What is the companys after-tax cost of common equity? a. 7.20% b. 7.32% c. 7.94% d. 12.00% e. 12.20%
WACC
94
What is the companys WACC? a. 7.95% b. 8.12% c. 8.59% d. 8.67% e. 10.04%
.
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Chapter 10: The Cost of Capital
Chapter 10: The Cost of Capital
Page 89
(The following information applies to the next three problems.) Burlees Inc.s CFO has collected the following information to calculate its WACC: The companys capital structure consists of 40% debt and 60% common stock. The company has 25-year, 12% annual coupon bonds that have a face value of $1,000 and sell for $1,252. The company uses the CAPM to calculate the cost of common stock. Currently, the risk-free rate is 5% and the market risk premium is 6%. The companys common stock has a beta of 1.6. The companys tax rate is 40%.
After-tax cost of debt
95
.
What is the companys after-tax cost of debt? a. b. c. d. e. 3.74% 4.80% 5.62% 7.20% 8.33% CAPM
Cost of common equity:
96
.
What is the companys cost of common equity? a. b. c. d. e. 9.65% 14.00% 14.60% 17.60% 18.91% What is the companys weighted average cost of capital (WACC)? a. b. c. d. e. 10.5% 11.0% 11.5% 12.0% 12.5%
WACC
97
.
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Chapter 10: The Cost of Capital
CHAPTER 10 ANSWERS AND SOLUTIONS
1.
Component cost of preferred stock
Preferred stock price Preferred dividend Flotation cost rp $90.00 $7.50 5.00% 8.77%
EASY
2.
Component cost of preferred stock
Preferred stock price Preferred dividend Flotation cost rp $80.00 $6.00 4.00% 7.81%
EASY
3.
Component cost of retained earnings: CAPM
rRF RPM b rs 5.50% 6.00% 0.80 10.30%
EASY
4.
Component cost of retained earnings: CAPM
rRF RPM b rs 5.00% 5.00% 1.10 10.50%
EASY
5.
Component cost of retained earnings: DCF, D1
D1 P0 g rs $1.00 $25.00 6.00% 10.00%
EASY
6
.
Component cost of retained earnings: DCF, D1
D1 P0 g rs $1.30 $40.00 7.00% 10.25%
EASY
7.
Cost of retained earnings: bond-yield-plus-risk premium
Bond yield Risk premium re 6.50% 4.00% 10.50%
EASY
8.
WACC
Weights 40% 10% 50% 8.10% Costs 4.00% 7.50% 11.50%
EASY
Debt Preferred Common WACC
9.
Component cost of debt Coupon rate Periods/year Maturity (yr) Bond price Par value Tax rate 8.00% 4 25 $900.90 $1,000 40%
MEDIUM
Calculator inputs: N 100 PV -$900.90 PMT $20 FV $1,000 I/YR 2.25% times 4 = 9.0% = Before-tax cost of debt 5.40% = After-tax cost of debt (A-T rd) for use in WACC 10
.
Component cost of debt
MEDIUM
Coupon rate Periods/year Maturity (yr) Bond price Par value Tax rate
7.00% 4 20 $1,103.58 $1,000 40%
Calculator inputs: N 80 PV -$1,103.58 PMT $17.50 FV $1,000 I/YR 1.52% times 4 = 6.1% = Before-tax cost of debt 3.66% = After-tax cost of debt (A-T rd) for use in WACC 11. Component cost of retained earnings: DCF, D0
D0 P0 g D1 rs $1.20 $40.00 7.00% $1.28 10.21%
MEDIUM
12.
Component cost of retained earnings: DCF, D0
D0 P0 g D1 rs $1.20 $50.00 6.00% $1.27 8.54%
MEDIUM
13.
Component cost of new common stock, based on DCF, D1
D1 P0 g F re $1.25 $40.00 6.00% 5.00% 9.29%
MEDIUM
14
.
Component cost of new common stock, based on DCF, D1
MEDIUM
D1 P0 g F re
$2.50 $60.00 7.00% 5.00% 11.39%
15.
WACC
Weights 40% 10% 50% 40% 8.25% Rate 7.50% AT Costs 4.50% 7.00% 11.50%
MEDIUM
Debt Preferred Common Tax rate WACC
16.
Retained earnings breakpoint
Weight of debt Weight of equity Expected Income Dividend payout ratio Retained earnings Retained earnings breakpoint 80% 20% $3,000,000 60% $1,200,000 $6,000,000
MEDIUM
17.
Cost of new common stock: DCF and payout ratio
Expected EPS1 Payout ratio Current stock price g F D1 re $3.50 40% $40.00 4.00% 10.00% $1.40 7.89%
MEDIUM/HARD
18
.
WACC
MEDIUM/HARD
D1 P0 g rd Tax rate Weight debt Weight equity rd(1-t) rs WACC 19.
$3.00 $60.00 7.00% 8.00% 40% 60% 40% 4.80% 12.0% 7.68% HARD
Cost of retained earnings: risk premium, CAPM, and DCF Bond yield Risk premium re rRF RPM b rs D1 P0 g re Max Min Difference 6.50% 4.00% 10.50% 5.50% 5.50% 1.00 11.00% $1.20 $40.00 7.00% 10.00% 11.00% 10.00% 1.00%
20.
Cost of retained earnings vs. cost of new common stock Expected EPS1 Payout ratio Current stock price g F D1 rS re Difference = higher cost of re $3.50 40% $40.00 4.00% 10.00% $1.40 7.50% 7.89% 0.39%
HARD
21.
WACC, equity from retained earnings, must find YTM
HARD
Coupon rate Maturity Bond price Par value Tax rate rRF RPM b Weight debt Weight equity Bond yield A-T cost of debt Cost of equity, rs WACC 22.
7.5% 25 $936.49 $1,000 40% 6.0% 5.0% 1.5 30% 70% 8.10% 4.86% 13.50% 10.91% HARD
WACC, equity from new stock, uses DCF YTM Tax rate D1 g P0 F Weight debt Weight equity A-T cost of debt Cost of retained earnings, rs Cost of new stock, re WACC 7.0% 40% $0.80 6.0% $25.00 10.0% 40% 60% 4.20% 9.20% 9.56% 7.41%
23
.
Risk adjustments to the WACC
HARD
rRF RPM b rs Return on S Return on R Cost of investing in S Cost of investing in R Investment in S Investment in R Total capital budget 24. 25. 26. Capital components Capital components Capital components
5.50% 6.00% 0.80 10.30% 8.00% 12.00% $10,000 $15,000 $0 $15,000 $15,000 EASY EASY
MEDIUM
Statement a is true, because the after-tax cost of debt is rd(1 - T). So, if rd remains constant but T increases, rd(1 - T) decreases. The other statements are all false. 27. Capital components MEDIUM
Statement c is true, because interest payments on debt are tax deductible. The other statements are false. 28. 29. WACC WACC MEDIUM MEDIUM
Statement c is true, because if the tax rate increases the tax deductibility benefits of debt financing increase, resulting in a lower WACC. The other statements are false. 30. 31. WACC and capital components WACC and capital components MEDIUM MEDIUM
Statement a is true, because equity is more risky than debt and hence investors require a higher return on equity. Also, interest on debt is deductible, and this further reduces the cost of debt. The others are false. 32. 33. Factors influencing WACC Risk and project selection MEDIUM MEDIUM
The project whose return is greater than its risk-adjusted cost of capital should be selected. Only Project B meets this criterion. 34. Divisional risk MEDIUM
The correct answer is statement a. Division A should accept only projects with a return greater than 10.0%, and Division B should accept only projects with a return greater than 14%. Only statement a meets this criterion. 35. 36. 37. Miscellaneous cost of capital concepts Capital components CAPM cost of equity estimation MEDIUM MEDIUM MEDIUM
By definition, both the market and an average stock have betas of 1.0. Since we know this to be the case, we can obviously determine beta for the market or an average stock with precision. 38. Internal vs. external common equity MEDIUM
Statement b is correct, because if more debt is used, then less equity will be needed to fund the capital budget, so the need of a stock issue would be reduced. 39. Risk and project selection MEDIUM
Statement c is correct. Here is the proof: rs = 7% + 6%(2.0) = 7% + 12% = 19%. Expected return = 21%. 21% - 1% = 20%. Risk-adjusted return = 20% > rs = 19%. Thus, the project should be selected. 40. Risk-adjusted cost of capital MEDIUM
By not adjusting the cost of capital for project risk, the firm will tend to reject low-risk projects since their returns will be lower than the average cost of capital, and it will take on high-risk projects since their returns will be higher than the average cost of capital. For this reason, statement b is true, while all remaining statements are false. 41. 42. Risk-adjusted cost of capital Retained earnings break point MEDIUM HARD
Statement a is true, because more net income means that more equity capital will be available without requiring new equity to be issued. 43 . Retained earnings break point HARD
Statements a, b, c, and d are all false, but e is true because under e the firm will be using a higher percentage of common equity, which will lower the break point. 44. 45. 46. 47. Cost of capital estimation Cost of equity estimation CAPM and DCF estimation WACC HARD HARD HARD HARD
Statement a is truethe WACC will increase if the firm raises more funds than can be supported by retained earnings. 48. WACC HARD
Statement e true. The firm would get no tax saving on interest, but corporate investors would get to deduct 70% of the preferred dividends they receive. Therefore, corporate investors will accept a lower before-tax yield on preferred stock than on bonds. 49. Risk-adjusted cost of capital HARD
By not making the risk adjustment, Kish will accept too many projects in the computer division and too few in the restaurant division. As a result, the company will become riskier overall, raising its cost of capital. Investors will discount their cash flows at a higher rate, and the firms value will fall. Therefore, statement c is true and all other statements are false. 50. 51. 52. Divisional risk and project selection Miscellaneous concepts Beta and project risk HARD
HARD HARD
The fact that As returns are negatively correlated means that it serves as a sort of insurance policy to the firm. The fact that its SD is high does not matterthe negative correlation will cause the projects beta versus the market and also with the firms other assets to be relatively low, denoting a low risk and thus justifying a relatively low cost of capital. 53. Component cost of debt
Calculate the nominal YTM of bond: Inputs: N = 80; PV = -686.86; PMT = 20; FV = 1000. Output: I/YR = 3.05% periodic rate. Nominal annual rate = 3.05% 4 = 12.20%. Calculate rd after-tax: rd,AT = 12.20(1 - T) = 12.20(1 - 0.4) = 7.32%. 54. Cost of retained earnings The rs = = = 55. cost of retained earnings as calculated from the CAPM is rRF + RPM(b) 5% + (6%)1.2 12.2%.
Cost of retained earnings Use the dividend growth model to calculate rs: D (1 + g) $2.20(1.06) rs = 0 +g= + 0.06 P0 $28 = 0.0833 + 0.06 = 0.1433 14.3%.
56 .
Cost of external equity D0 = $2; D1 = $2(1.07) = $2.14.
re = D1/[P0(1 - F)] + g = $2.14/($42 - $1) + 7% = 12.22%. 57. Cost of new equity Find the cost of new equity capital, re: re = D1/(P0 - F) + g = $2.50/($50 - $3) + 4% = $2.50/$47 + 4% = 5.32% + 4% = 9.32%. 58. Divisional risk rYD = 10% + 2% = 12%. However, for a low-risk project, Dandy Product subtracts 2%. required rate of return is 10%. rYD,Low-risk project = 10% + 2% - 2% = 10%. Retained earnings break point Therefore, the
59 .
Additions to retained earnings will be: $3.0 million 0.4 = $1.2 million. The retained earnings breakpoint is $1.2 million/0.2 = $6 million. 60. WACC WACC = wdrd(1 - T) + wcre. rd is given = 9%. re = D1/[P0(1 - F)] + g = $0.8/[$25(1 - 0.1)] + 0.09 = 0.125556. Find re:
Now you can calculate WACC: WACC = (0.3)(0.09)(0.6) + (0.7)(0.125556) = 10.41%. 61. WACC Data given: rRF = 6%; RPM = 5%; b = 1.2; T = 40%; wd = 0.3; wc = 0.7. WACC = wdrd(1 - T) + wcrs. Step 1: Determine the firms costs of debt and equity: Enter the following data as inputs in your calculator: N = 26; PV = -920; PMT = 75; FV = 1000; and then solve for I/YR = r d = 8.2567%. rs = rRF + (RPM)b = 6% + (5%)1.2 = 12%. Step 2: Calculate the firms WACC: WACC = wdrd(1 - T) + wcrs = 0.3(8.2567%)(1 - 0.4) + 0.7(12%) = 1.4862% + 8.4% = 9.8862% 9.89%.
62.
WACC
Find the dividend, D1 = [(0.5)$40,000]/# of Shares = $20,000/10,000 = $2.00. Since the firm will not have enough retained earnings to fund the equity portion of its capital budget, the firm will have to issue new common stock. Find the cost of new common stock: re = D1/[P0(1 - F)] + g = $2.00/[$25(1 - 0.15)] + 0% = 0.0941 = 9.41%. Finally, calculate WACC, using re = 0.0941, and rd = 0.08, so WACC = wd(1 - T)rd + were = 0.4(0.08)(1 - 0.4) + 0.6(0.0941) = 0.0757 7.6%. 63. WACC Cost Cost Cost WACC 64. WACC Cost of debt = 0.09(1 - 0.35) = 0.0585 = 5.85%. Cost of retained earnings = rRF + (RPM)b = 6% + 6%(1.5) = 15%. WACC = 0.60(0.0585) + 0.40(0.1500) = 0.0951 = 9.51%. of debt = 0.084(1 - 0.30) = 0.0588 = 5.88%. of preferred stock = 0.09 = 9%. of retained earnings = rRF + (RPM)b = 6.57% + (5%)1.3 = 13.07%. = 0.4(0.0588) + 0.10(0.09) + 0.50(0.1307) = 9.79%.
65.
WACC rs = D1/P0 + g = $3.00/$60.00 + 0.07 = 0.12 = 12%. WACC = wdrd(1 - T) + wcrs = (0.6)(0.08)(1 - 0.4) + (0.4)(0.12) = 0.0768 = 7.68%.
66 .
WACC WACC = [(0.7)(rd)(1 - T)] + [(0.3)(rs)].
Use bond information to solve for rd: N = 20; PV = -1273.8564; PMT = 120; FV = 1000; and solve for I/YR = rd = 9%. To solve for rs, we can use the SML equation, but we need to find beta. Using Market and J-Mart return information and a calculators regression feature we find b = 1.3585. rs = 0.0635 + (0.05)(1.3585) = 0.1314 = 13.14%. Plug these values into the WACC equation and solve: WACC = [(0.7)(0.09)(1 - 0.35)] + [(0.3)(0.1314)] = 0.0804 = 8.04%. 67. WACC Step 1: Find the cost of debt: N = 15; PV = -1075; PMT = 80; FV = 1000; and then solve for I/YR = r d =
7.1678%. Step 2: Find the cost of equity: rs = rRF + RPM (b) = 5% + 4%(1.1) = 5% + 4.4% = 9.4%. Calculate the firms WACC: WACC = wdrd(1 - T) + wcrs = (0.3)(7.1678%)(1 - 0.38) + (0.7)(9.4%) = 1.3332% + 6.58% = 7.9132% 7.91%.
Step 3:
68.
WACC and dividend growth rate Solve for rs: WACC = wdrd(1 - T) + wcrs 11.5% = 0.45(0.09)(0.70) + 0.55rs rs = 15.75%.
Solve for g: 69.
15.75% = D1/P0 + g 15.75% = $5/$45 + g g = 4.64%. WACC and optimal capital budget Project A B C D E F G Rate of Return 16% 14 12 11 10 10 7 Risk-Adjusted Cost of Capital 13% 11 9 13 11 9 9
Projects A, B, and C are profitable because their returns surpass their riskadjusted costs of capital. D is not profitable because its return (11%) is less than its risk-adjusted cost of capital (13%). E is not acceptable for the same reason: Its return (10%) is less than its risk-adjusted cost of capital (11%). F is accepted since it is low risk and its return (10%) surpasses the risk-adjusted cost of capital of 9%. G is rejected because its return (7%) is less than the risk-adjusted cost of capital (9%). 70. CAPM, beta, and WACC Data given: RPM = 5%. Step 1:
wd = 0.3; wc = 0.7; rd = 8%; WACC = 10%; T = 40%; rRF = 5.5%,
Determine the firms cost of equity using the WACC equation: WACC = wdrd(1 - T) + wcrs 10% = (0.3)(8%)(1 - 0.4) + (0.7)rs 8.56% = (0.7)rs rs = 12.2286%. Calculate the firms beta using the CAPM equation: rs = rRF + RPM(b) 12.2286% = 5.5% + 5%(b) 6.7286% = 5%(b) b = 1.3457 1.35.
Step 2:
71.
Required rate of return bOld, firm = 1.25. rOld, firm = 0.07 + (0.07)1.25 = 15.75%. bNew, firm = 0.9(1.25) + 0.1(1.1) = 1.235. rNew, firm = 0.07 + 1.235(0.07) = 15.645%. rNew, assets = 0.07 + 1.1(0.07) = 14.7%.
72
.
Beta risk Old assets = 1.0. Old required rate: 18% = 7% + (5%)b beta = 2.2. New assets = 0.5. Total assets = 1.5. New required rate: 16% = 7% + (5%)b beta = 1.8.
New b must not be greater than 1.8, therefore 1 0.5 (2.2) + (b) = 1.8 1.5 1.5 0.3333(b) = 0.3333 b = 1.0. Therefore, beta of the new division cannot exceed 1.0. 73. WACC Capital structure: 40% D, 10% P, 50% E. WACC = 12.30% (given). rd = 11% (given). WACC = 0.4(rd)(1 - T) + 0.1(rp) + 0.5(re). Because the firm has insufficient retained earnings to fund the equity portion of the firms capital budget, use re in the WACC calculation. a. Calculate re: $2(1.08) re = + 8% = 8.47% + 8% = 16.47%. $30(0.85) b. Calculate rp: Dp $2 rp = = = 11.11%. Pp $20(0.9) c. Find T by substituting values for rd, rp, and re in the WACC equation: 0.1230 = 0.4(0.11)(1 - T) + 0.1(0.1111) + 0.5(0.1647) 0.1230 = 0.044(1 - T) + 0.0111 + 0.08235 0.02954 = 0.044(1 - T) 0.671364 = 1 - T 0.328636 = T.
74
.
WACC and cost of preferred stock
We need to find rp at the point where all 4 projects are accepted. In other words, the capital budget = $2,000 + $3,000 + $5,000 + $3,000 = $13,000. The WACC at that point is equal to IRRD = 9.5%. Step 1: Find the retained earnings break point to determine whether r s or re is used in the WACC calculation: $1,000 BPRE = = $2,500. 0.4 Since the capital budget > the retained earnings break point, re is used in the WACC calculation. Calculate re: $3.00 re = + 5% = 12.80%. $42.75(0.9) Find rp: 9.5% = 0.4(10%)(0.65) + 0.2(rp) + 0.4(12.80%) 9.5% = 2.60% + 0.2(rp) + 5.12% 1.78% = 0.2rp 8.90% = rp.
Step 2:
Step 3:
75.
Cost of retained earnings rs = $0.90(1.05) + 0.05 = 0.1600 = 16.00%. $8.59
76 .
Cost of external equity re = $0.90(1.05) + 0.05 = 0.1722 = 17.22%. $8.59(1 - 0.10)
77 .
WACC
Since the firm can fund the equity portion of its capital budget with retained earnings, use rs in WACC. WACC = = = = wdrd(1 - T) + wcrs 0.3(0.12)(1 - 0.4) + 0.7(0.16) 0.0216 + 0.112 0.1336 = 13.36%.
78 .
Cost of external equity
re = 79 . 80. WACC
$2.00(1.05) + 0.05 = 17%. $21.88(1 - 0.2)
WACC = 0.4(0.14)(1 - 0.4) + 0.6(0.17) = 0.1356 = 13.56% 13.6%. Cost of debt Since the bond sells at par of $1,000, its YTM and coupon rate (12%) are equal. Thus, the before-tax cost of debt to Rollins is 12.0%. The after-tax cost of debt equals: rd,After-tax = 12.0%(1 - 0.40) = 7.2%. Financial calculator solution: Inputs: N = 40; PV = -1000; PMT = 60; FV = 1000; Output: I/YR = 6.0% = rd/2. rd = 6.0% 2 = 12%. rd(1 - T) = 12.0%(0.6) = 7.2%.
81. 82 .
Cost of preferred stock Cost of preferred stock: Cost of equity: CAPM Cost of retained earnings (CAPM approach): rs = 10% + (5%)1.2 = 16.0%. rp = $12/$100(0.95) = 12.6%.
83.
Cost of equity: DCF Cost of retained earnings (DCF approach): $2.00(1.08) rs = + 8% = 16.0%. $27
84 .
Cost of equity: risk premium
85 .
Cost of retained earnings (bond yield-plus-risk-premium approach): rs = 12.0% + 4.0% = 16.0%. WACC Calculate re: re = $2.00(1.08) + 8% = 16.89%. $27(1 0.1)
86 .
WACC = wdrd(1 - T) + wprp + wcre = 0.2(12.0%)(0.6) + 0.2(12.6%) + 0.6(16.89%) = 14.09 14.1%. Stock price--constant growth rs = 6% + (5%)2.0 = 16%. $3.00(1.10) P0 = = $55.00. 0.16 - 0.10
87
.
Cost of external equity Cost of new common equity: $3.30 re = + 0.10 = 16.32%. $55.00(0.95)
88
.
Cost of debt
Using a financial calculator: N = 15; PV = -1150; PMT = 120; FV = 1000; solve for I/YR = r d = 10.03%. after-tax cost of debt is 10.03%(1 - T) = 10.03%(0.6) = 6.02% 6%. 89 . Cost of common equity: CAPM
The
Using the CAPM equation: rs = rRF + (RPM)b rs = 5% + (5%)1.4 rs = 12%.
Since equity costs are not tax-deductible, this is also the after-tax cost of equity. 90. WACC
Use the target debt and equity ratios and the WACC equation as follows: WACC = wdrd(1 T) + wcrs = (0.40)(0.06) + (0.60)(0.12) = 0.096, or 9.6%. 91. Cost of debt
Using a financial calculator: N = 20; PV = -945; PMT = 85; FV = 1000; and solve for rd = I/YR = 9.11%. A-T rd = 9.11%(1 - 0.4) = 5.46%. 92. Cost of preferred stock rp = Dp
Pp rp = $2/$25 rp = 8.0%. 93. Cost of common equity: rs = rRF + RPM(b) rs = 6% + 5%(1.2) rs = 12.0%. CAPM
94.
WACC WACC = wdrd(1 T) + wprp + wcrs WACC = 0.4(9.11%)(1 - 0.4) + 0.2(8%)+ 0.4(12%) WACC = 8.59%.
95.
After-tax cost of debt
Using a financial calculator: N = 25; PV = -1252; PMT = 120; FV = 1000; solve for I/YR = rd = 9.3594%. To calculate the after-tax cost of debt, multiply by (1 T) as follows: (1 - 0.40) 9.3594% = 5.6156% 5.62%. 96. Cost of common equity: CAPM
rs = 5% + (6%)1.6 = 14.6%. 97. WACC WACC = (0.40)(5.6156%) + (0.60)(14.6%) = 11.0062% 11.0%.

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