mba711 - chapter11 - answers to all homework problems

Chapter 11, Solutions Cornett, Adair, and Nofsinger

CHAPTER 11 – CALCULATING THE COST OF CAPITAL

Questions

LG1 11-1 How would you handle calculating the cost of capital if a firm were planning two issue two different classes of common stock?

Solution: As the two different classes of common stock are likely to have different component costs, calculate the cost and weight for each separately.

LG2 11-2 Why don’t we multiply the cost of preferred stock by 1 minus the tax rate, as we do for debt?

Solution: Because dividends on preferred stock, unlike interest on debt, are paid out of after-tax income.

LG2 11-3 Expressing WACC in terms of iE, iP, and iD, what is the theoretical minimum for the WACC?

Solution: The theoretical minimum WACC would be that for an all-debt firm: iD × (1-TC)

LG3 11-4 Under what situations would you want to use the CAPM approach for estimating the component cost of equity? The Constant-Growth model?

Solution: You would want to use the CAPM when you can estimate the firm’s beta with a good deal of certainty: you would only want to use the constant-growth model if the firm’s stock is expected to experience constant dividend growth.

LG3 11-5 Could you calculate the component cost of equity for a stock with nonconstant expected growth rate in dividends if you didn’t have the information necessary to compute the component cost using the CAPM? Why or why not?

Solution: You could try and adjust the constant growth model for initial periods of nonconstant growth, but doing so would require estimating the growth rate for all of the nonconstant growth periods.

LG4 11-6 Why do we use market-based weights instead of book-value-based weights when computing the WACC?

Solution: Because we’re interested in determining what the cost of financing the firm’s assets would be given today’s market situation and the component costs the firm currently faces, not what the historic prices would have been.

LG5 11-7 Suppose your firm wanted to expand into a new line of business quickly, and that management anticipated that the new line of business would constitute over 80

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percent of your firm’s operations within 3 years. If the expansion was going to be financed partially with debt, would it still make sense to use the firm’s existing cost of debt, or should you compute a new rate of return for debt based on the new line of business?

Solution: Given that the new line of business will comprise so much of the firm’s operations, it probably isn’t appropriate to count on the current, existing operations to pay off the debt. Therefore, the fir should probably compute a new required rate of return for this firm’s debt.

LG6 11-8 Explain why the divisional cost of capital approach may cause problems if new projects are assigned to the wrong division.

Solution: If projects are assigned to the wrong division, the risk of that division may be significantly different than the risk of the project, implying that the project will be evaluated with a divisional cost of capital that is much different from what a project-specific cost of capital would be.

LG7 11-9 When will the subjective approach to forming divisional WACCs be better than using the firm-wide WACC to evaluate all projects?

Solution: As long as the subjective approaches manages to use divisional costs of capital that are, on average, closer to what the project-specific costs of capital would be than the firm-wide cost of capital is, the subjective approach will improve the firm’s accept/reject decisions.

LG8 11-10 Suppose a new project was going to be financed partially with retained earnings. What flotation costs should you use for retained earnings?

Solution: Retained earnings do not carry any flotation cost, so you should use a cost of zero.

Problems

Basic Problems

LG3 11-1 Diddy Corp stock has a beta of 1.2, the current risk-free rate is 5 percent, and the expected return on the market is 13.5 percent. What is Diddy’s cost of equity?

Solution: Using equation 11-2:

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LG3 11-2 JaiLai Cos. stock has a beta of 1.1, the current risk-free rate is 6.2 percent, and the expected return on the market is 12 percent. What is JaiLai’s cost of equity?


LG3 11-3 Oberon Inc. has a $20 million (face value) bond issue selling for 97 percent of par that pays an annual coupon of 8.25 percent. What would be Oberon’s before-tax component cost of debt?

Solution: Solving equation 11-5 for iD:

Yields iD = .087115, or 8.7115%

LG3 11-4 KatyDid Clothes has a $150 million (face value) bond issue selling for 104 percent of par that carries a coupon rate of 11 percent, paid semiannually. What would be Katydid’s before-tax component cost of debt?

Solution: Solving equation 11-5 for iD:

Yields iD = .052586, or 5.2586% on a semiannual basis. Since the cost of debt is normally quoted on a nominal annual basis, we should multiple this semiannual rate by two to get a quoted component cost of 5.2586% × 2 = 10.5172%

LG3 11-5 ILK has preferred stock selling for 97 percent of par that pays an 8 percent annual coupon. What would be ILK’s component cost of preferred stock?


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LG3 11-6 Marme Inc. has preferred stock selling for 137 percent of par that pays an 11 percent annual coupon. What would be Marme’s component cost of preferred stock?


LG4 11-7 FarCry Industries, a maker of telecommunications equipment, has 2 million shares of common stock outstanding, 1 million shares of preferred stock outstanding, and 10 thousand bonds. If the common shares are selling for $27 per share, the preferred share are selling for $14.50 per share, and the bonds are selling for 98 percent of par, what would be the weight used for equity in the computation of FarCry’s WACC?

Solution: Using the computation for equity weight given in equation 11-1:

LG4 11-8 OMG Inc. has 4 million shares of common stock outstanding, 3 million shares of preferred stock outstanding, and 5 thousand bonds. If the common shares are selling for $17 per share, the preferred share are selling for $26 per share, and the bonds are selling for 108 percent of par, what would be the weight used for equity in the computation of OMG’s WACC?


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LG4 11-9 FarCry Industries, a maker of telecommunications equipment, has 2 million shares of common stock outstanding, 1 million shares of preferred stock outstanding, and 10 thousand bonds. If the common shares are selling for $27 per share, the preferred share are selling for $14.50 per share, and the bonds are selling for 98 percent of par, what weight should you use for debt in the computation of FarCry’s WACC?


LG4 11-10 OMG Inc. has 4 million shares of common stock outstanding, 3 million shares of preferred stock outstanding, and 5 thousand bonds. If the common shares are selling for $17 per share, the preferred share are selling for $26 per share, and the bonds are selling for 108 percent of par, what weight should you use for debt in the computation of OMG’s WACC?


LG4 11-11 FarCry Industries, a maker of telecommunications equipment, has 2 million shares of common stock outstanding, 1 million shares of preferred stock outstanding, and 10 thousand bonds. If the common shares sell for $27 per share, the preferred shares sell for $14.50 per share, and the bonds sell for 98 percent of par, what weight should you use for preferred stock in the computation of FarCry’s WACC?


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LG4 11-12 OMG Inc. has 4 million shares of common stock outstanding, 3 million shares of preferred stock outstanding, and 5 thousand bonds. If the common shares sell for $17 per share, the preferred share sell for $26 per share, and the bonds sell for 108 percent of par, what weight should you use for preferred stock in the computation of OMG’s WACC?


Intermediate Problems

LG2 11-13 Suppose that TapDance, Inc.’s capital structure features 65 percent equity, 35 percent debt, and that its before-tax cost of debt is 8 percent, while its cost of equity is 13 percent. If the appropriate weighted average tax rate is 34 percent, what will be TapDance’s WACC?


LG2 11-14 JLP Industries has 6.5 million shares of common stock outstanding with a market price of $14.00 per share. The company also has outstanding preferred stock with a market value of $10 million, and 25,000 bonds outstanding, each with face value $1,000 and selling at 90% of par value. The cost of equity is 14%, the cost of preferred is 10%, and the cost of debt is 7.25%. If JLP's tax rate is 34%, what is the WACC?


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LG2 11-15 Suppose that JB Cos. has a capital structure of 78 percent equity, 22 percent debt, and that its before-tax cost of debt is 11 percent while its cost of equity is 17 percent. If the appropriate weighted average tax rate is 25 percent, what will be JB’s WACC?


LG2 11-16 Suppose that B2B, Inc. has a capital structure of 37 percent equity, 17 percent preferred stock, and 46 percent debt. If the before-tax component costs of equity, preferred stock and debt are 14.5 percent, 11 percent and 9.5 percent, respectively, what is B2B’s WACC if the firm faces an average tax rate of 30%?


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LG2 11-17 Suppose that MNINK Industries’ capital structure features 63 percent equity, 7 percent preferred stock, and 30 percent debt. If the before-tax component costs of equity, preferred stock and debt are 11.60 percent, 9.5 percent and 7 percent, respectively, what is MNINK’s WACC if the firm faces an average tax rate of 34%?


LG3 11-18 TAFKAP Industries has 3 million shares of stock outstanding selling at $17 per share and an issue of $20 million in 7.5 percent, annual coupon bonds with a maturity of 15 years, selling at 106 percent of par. If TAFKAP’s weighted average tax rate is 34 percent and its cost of equity is 14.5 percent, what is TAFKAP’s WACC?

Solution: First, solve equation 11-5 for iD:

Then, using equation 11-1:

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LG3 11-19 Johnny Cake Ltd. has 10 million shares of stock outstanding selling at $23 per share and an issue of $50 million in 9 percent, annual coupon bonds with a maturity of 17 years, selling at 93.5 percent of par. If Johnny Cake’s weighted average tax rate is 34 percent, its next dividend is expected to be $3.00 per share, and all future dividends are expected to grow at 6 percent per year, indefinitely, what is its WACC?


Next, use equation 11-3 to solve for iE:

Then, using equation 11-1, solve for WACC:

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LG4 11-20 BetterPie Industries has 3 million shares of common stock outstanding, 2 million shares of preferred stock outstanding, and 10 thousand bonds. If the common shares are selling for $47 per share, the preferred shares are selling for $24.50 per share, and the bonds are selling for 99 percent of par, what would be the weights used in the calculation of BetterPie’s WACC?

Solution: Using the computations for component weights given in equation 11-1:

LG8 11-21 Suppose that Brown-Murphies’ common shares sell for $19.50 per share, are expected to set their next annual dividend at $.57 per share, and that all future dividends are expected to grow by 4 percent per year, indefinitely. If Brown-Murphies faces a flotation cost of 13% on new equity issues, what will be the flotation-adjusted cost of equity?


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Advanced Problems

LG2 11-22 A firm is considering a project that will generate perpetual after-tax cash flows of $15,000 per year beginning next year. The project has the same risk as the firm's overall operations and must be financed externally. Equity flotation costs 14% and debt issues cost 4% on an after-tax basis. The firm's D/E ratio is 0.8. What is the most the firm can pay for the project and still earn its required return?

Solution: If the D/E ratio is 0.8, then D/(D+E) will be 0.8/1.8 = .4444 and E/(D+E) will be 1.0/1.8 = .5556.

Then, using equation 11-1, solve for WACC:

LG2 11-23 A firm has 5,000,000 shares of common stock outstanding, each with a market price of $8.00 per share. It has 25,000 bonds outstanding, each selling for $800. The bonds mature in 10 years, have a coupon rate of 8%, and pay coupons semi-annually. The firm’s equity has a beta of 1.4, and the expected market return is 15%. The tax rate is 35% and the WACC is 15%. Calculate the risk free rate.


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Then solve equation 11-1 for iE:

Finally, putting this into equation 11-6 and solving for the risk-free rate:

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LG6 11-24 An all-equity firm is considering the projects shown below. The T-bill rate is 4 percent and the market risk premium is 7 percent. If the firm uses its current WACC of 12 percent to evaluate these projects, which project(s), if any, will be incorrectly rejected?

Project Expected Return BetaA 8.0% 0.5B 19.0% 1.2C 13.0% 1.4D 17.0% 1.6

Solution: Using the firm’s WACC of 12 percent as the IRR benchmark, project A would be rejected. Using equation 11-2, the project-specific benchmarks for each project should be:

If Project A’s expected return of 8% had been compared to the project-specific required return of 7.5%, it would have been accepted. Therefore, Project A would have been incorrectly rejected if the firm-wide WACC had been used as its benchmark.

LG6 11-25 An all-equity firm is considering the projects shown below. The T-bill rate is 4 percent and the market risk premium is 7 percent. If the firm uses its current WACC of 12 percent to evaluate these projects, which project(s), if any, will be incorrectly accepted?

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Project Expected Return BetaA 8.0% 0.5B 19.0% 1.2C 13.0% 1.4D 17.0% 1.6

Solution: Using the firm’s WACC of 12 percent as the IRR benchmark, projects B, C and D would be accepted. Using equation 11-2, the project-specific benchmarks for each project should be:

If Project C’s expected return of 13% had been compared to the project-specific required return of 13.8%, it would have been rejected. Therefore, Project C would have been incorrectly accepted if the firm-wide WACC had been used as its benchmark.

LG7 11-26 Suppose your firm has decided to use a divisional WACC approach to analyze projects. The firm currently has 4 divisions, A through D, with average betas for each division of 0.6, 1.0, 1.3 and 1.6, respectively. If all current and future projects will be financed with half debt and half equity, and if the current cost of equity (based on an average firm beta of 1.0 and a current risk-free rate of 7 percent) is 13 percent and the after-tax yield on the company’s bonds is 8 percent, what will the WACCs be for each division?

Solution: Using equation 11-2, we can solve for the expected rate of return on the market:

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Reusing equation 11-2, we can solve for the divisional costs of equity using the average divisional betas:

Finally, we can solve for the divisional WACCs using equation 11-1:

Research It! (Web-Exercises): Finding the Before-Tax Cost of Debt, iDFor component debt costs, we’d like to use the yield to maturity on bonds that resemble the maturity of our potential debt as possible. Let’s assume that we want to find a bond issue with approximately 10 years until maturity (as of January, 2007) for Bear Stearns. Luckily, Bear Stearns has quite a few outstanding bond issues to choose from, and we can access the information on these issues on the Yahoo! Finance page. Go to http://finance.yahoo.com/ and start by clicking on “Investing” and then “Bonds” as shown to the right:

Then enter Bear Stearns in the “Bond Lookup” box and click on “Search” as shown below: You’ll be presented with a list of Bear Stearns’ outstanding bonds sorted in order of decreasing maturity: Once you’ve identified the bond with the maturity closest to the maturity you want, click on the “Issue” entry and look up the Yield to Maturity.

Your turn: go to the Yahoo! Finance web site and find the YTM on the bond with a maturity that’s as close as possible to 10 years from today’s date.

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http://finance.yahoo.com/


Integrated Minicase: WACC for a New ProjectLilyMac Studios, a national chain of photography studios, is considering opening up a chain of coffee shop/art galleries. While the existing operations of the firm have a beta of 1.17, the new chain is expected to have a beta of 0.8.

LilyMac currently has 500,000 shares of common stock outstanding, which are selling for $63.72 per share, and a $10 million dollar bond issue, selling at 104 percent of par. The expected market risk premium is 6 percent, and the current risk-free rate is 5.5%. The bonds pay an 8 percent semiannual coupon and mature in 20 years.

LilyMac’s next expected dividend is $4.00 per share, and future dividends are expected to grow at 4% per year.

The current operations of the firm produce EBIT of $18 million per year, and the chain’s operations are expected to add only $25 million per year to that. The new chain will be funded with 65% percent equity and 35% debt, and estimated flotation costs are expected to be 12 percent and 5 percent, respectively.

What should be the WACC for the new chain of coffee shops?

Solution: Using the constant growth formula along with the flotation cost of equity, 12 percent of $63.72 will be $7.64, so the cost of equity will be equal to:

Notice that, without the flotation cost, this would be:

Which is an increase of 11.13% - 10.28% = .86% due to the flotation cost, so if we use the CAPM approach, the cost of equity will be equal to:

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Which would be similarly adjusted to 10.3% + .86% = 11.16%. Taking an average of the two costs of equity, we will use (11.13% + 11.16%)/2 = 11.145%.

The YTM on the new bonds issued to finance this project will be:

Which gives us an annual iD of 8.1224%.

Finally, the current EBIT puts the firm in the 38% tax bracket, so the additional EBIT generated by the project will be taxed at an average marginal tax rate of:

Which gives us an after-tax cost of debt of 8.1224%×(1-.3504)=5.2763%

Using these component costs for equity and debt, and taking the capital structure of the new chain, we get a WACC of:

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mba711 - chapter11 - answers to all homework problems

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