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Chapter12: Cost of Capital

Questions and problems

BASIC QUESTIONS (1–25)

1.  
Calculating Cost of Equity. Bommer Ltd has just paid a dividend of $2.40 per share on its ordinary shares. The company is expected to maintain a constant 6% growth rate in its dividends indefinitely. If the share price is $48, what is the company's cost of equity? <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/premium/0071010319/student/pg111_4.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (K)</a>

  <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/premium/0071010319/student/pg112_1a.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (K)</a>

Selected problems are available in McGraw-Hill Connect Plus.

2.  
Calculating Cost of Equity. Star Jet Ltd's ordinary shares have a beta of 1.3. If the risk-free rate is 5% and the expected return on the market is 13%, what is Star Jet's cost of equity capital? <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/premium/0071010319/student/pg111_4.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (K)</a>

3.  
Calculating Cost of Equity. Shares in Kelpie Industries have a beta of 0.9. The market risk premium is 8%, and short-term government bonds are currently yielding 4.5%. Kelpie's most recent dividend was $2.60 per share, and dividends are expected to grow at a 5% annual rate indefinitely. If the share price is $48, what is your best estimate of Kelpie's cost of equity? <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/premium/0071010319/student/pg111_4.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (K)</a>

4.  
Estimating the DCF Growth Rate. Suppose Cactus Ltd just paid a dividend of $1.89 per share on its ordinary shares. The company paid dividends of $1.47, $1.62, $1.67 and $1.78 per share in the last four years. If the share price is $65, what is your best estimate of the company's cost of equity capital using arithmetic and geometric growth rates? <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/premium/0071010319/student/pg111_4.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (K)</a>

5.  
p. 392

6.

  
Calculating Cost of Debt. ICU Window Ltd is trying to determine its cost of debt. The firm has a debt issue outstanding with seven years to maturity that is quoted at 93% of face value. The issue makes half-yearly payments and has an embedded cost of 5.6% annually. What is ICU's pre-tax cost of debt? If the tax rate is 30%, what is the after-tax cost of debt? <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/premium/0071010319/student/pg113_3.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (K)</a>

7.  

Calculating Cost of Debt. Jimmy's Cricket Farm issued a thirty-year, 8% half-yearly bond seven years ago. The bond currently sells for 108% of its face value. The company's tax rate is 30%.

a.

 

What is the pre-tax cost of debt?

b.

 

What is the after-tax cost of debt?

c. 
8.  
Calculating Cost of Debt. For the firm in Problem 7, suppose the book value of the debt issue is $60 million. In addition, the company has a second debt issue, a zero coupon bond with twenty years left to maturity; the book value of this issue is $70 million, and it sells for 26.5% of par. What is the total book value of debt? The total market value? What is the after-tax cost of debt now? <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/premium/0071010319/student/pg113_3.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (K)</a>

9.  

Calculating WACC. Cobber Farm Ltd has a target capital structure of 70% ordinary shares, 5% preference shares and 25% debt. Its cost of equity is 14%, the cost of preference shares is 6% and the cost of debt is 7.5%. The relevant tax rate is 30%.

a.

 

What is Cobber Farm Ltd's WACC under a classical tax system and an imputation system?

b.

 

The company CEO has approached you about Cobber Farm's capital structure. He wants to know why the company does not use more preference-share financing, since it costs less than debt.


  <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/premium/0071010319/student/pg112_5.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (K)</a>
10.  
Taxes and WACC. Jorgenson Manufacturing has a target debt–equity ratio of 0.8. Its cost of equity is 14%, and its cost of debt is 8%. If the tax rate is 30%, what is Jorgenson's WACC, given Jorgenson is operating under a classical tax system? What happens to WACC if Jorgenson's was under an imputation system? <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/premium/0071010319/student/pg113_2.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (K)</a>

11.  
Finding the Target Capital Structure. Fama's Llamas has a WACC of 10.5%. The company's cost of equity is 14% and its cost of debt is 8%. The tax rate is 30%. What is Fama's target debt–equity ratio? (Assume a classical tax system.) <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/premium/0071010319/student/pg112_1.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (K)</a>

12.  

Book Value versus Market Value. Fruit Loop Ltd has 10 million ordinary shares outstanding. The current share price is $53, and the book value per share is $1. Fruit Loop also has two bond issues outstanding. The first bond issue has a face value of $75 million, has a 7.5% coupon and sells for 97% of par. The second issue has a face value of $40 million, has a 7% coupon and sells for 96% of par. The first issue matures in twenty years, the second in twelve years.

a.

 

What are Fruit Loop's capital structure weights on a book-value basis?

b.

 

What are Fruit Loop's capital structure weights on a market-value basis?

c.

 
13.  
Calculating the WACC. In Problem 12, suppose the most recent dividend is $2.60 and the dividend growth rate is 7%. Assume that the overall cost of debt is the weighted average of that implied by the two outstanding debt issues. Both bonds make half-yearly payments. The tax rate is 30%. What is the company's WACC, assuming a classical tax system? <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/premium/0071010319/student/pg112_1.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (K)</a>

14.

  

WACC. Koala Ltd has a target debt–equity ratio of 0.55. Its WACC under a classical tax system is 10.5% and the tax rate is 30%.

a.

 

If Koala's cost of equity is 14%, what is its pre-tax cost of debt?

b.

 
15.  

Finding the WACC. Given the following information for Jackaroo Construction Ltd, find the WACC under both a classical and an imputation system. Assume the company's tax rate is 30%.

Debt: 6500 bonds, outstanding at 8.5% coupon, $1000 par value, twenty-five years to maturity, selling for 104% of par; the bonds make half-yearly payments.

Ordinary shares: 150 000 shares outstanding, selling for $78 per share; beta is 1.15.

Preference shares: 6.25% preference shares, 10 000 outstanding, currently selling for $80 per share.


  <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/premium/0071010319/student/pg112_5.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (K)</a>
p. 393

16.

  

Finding the WACC. Gabby Mining Corporation has 9 million ordinary shares outstanding; 500 000 6% preference shares outstanding, and 200 000 9.4% half-yearly bonds outstanding, par value $1000 each. The ordinary shares currently sell for $64 and have a beta of 1.10; the preference shares sell for $83; and the bonds have fifteen years to maturity and sell for 108% of par. The market risk premium is 8%; government bonds are yielding 5.5%; and Gabby Mining's tax rate is 30%.

a.

 

What is the firm's market-value capital structure?

b.

 
If Gabby Mining is evaluating a new investment project that has the same risk as the firm's typical project, what rate should the firm use to discount the project's cash flows under a classical tax system? <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/premium/0071010319/student/pg112_1.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (K)</a>

  <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/premium/0071010319/student/pg112_5.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (K)</a>
17.  

SML and WACC. An all-equity firm is considering the following projects:

<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/premium/0071010319/student/pg393_1.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (K)</a>

The risk-free rate is 5%, and the expected return on the market is 13%.

a.

 

Which projects have a higher expected return than the firm's 13% cost of capital?

b.

 

Which projects should be accepted?

c.

 
18.  

Calculating the WACC. Calculate the WACC for Widgets Ltd under a classical tax system and imputation system:

Debt: 7000 bonds with a 7.5% coupon rate, $1000 face value and a quoted price of $1080. The bonds have twenty years to maturity.

Ordinary shares: 180 000 ordinary shares. The dividends have a growth rate of 6% indefinitely; the current price is $60; and the dividend next year will be $2.80. The beta of the share is 0.9.

Preference share: 8000 5.50% preference shares with a current price of $94.


19.  

Calculating the WACC. You are given the following information concerning Cocky Enterprises:

Debt: two thousand 7% coupon bonds outstanding, at $1000 face value, with twenty years to maturity and a quoted price of $93. These bonds pay interest half-yearly.

Ordinary shares: 80 000 ordinary shares selling for $45 per share. The share has a beta of 1.2 and will pay a dividend of $3.25 next year. The dividend is expected to grow by 7% per year indefinitely.

Preference shares: seven thousand 6% preference shares selling at $93 per share.

Market: 12% expected return, a 4% risk-free rate and a 30% tax rate.


20.  
Calculating the WACC. In the previous problem, suppose that Cocky Enterprises thinks that it should have a capital structure of 25% debt, 5% preference shares and 70% equity. Assuming that the cost of each form of financing remains the same, what is Cocky's new cost of capital? <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/premium/0071010319/student/pg112_1.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (K)</a>

p. 394

21.

  

Calculating the WACC. Calculate the cost of capital for the following firm under an imputation system:

Debt: 8000 9% coupon bonds outstanding, at $1000 face value, twenty-five years to maturity and a quoted price of $104. These bonds pay interest half-yearly.

Ordinary shares: 200 000 ordinary shares selling for $75. The shares have a beta of 1.1 and will pay a dividend of $3.40 next year. The dividend is expected to grow by 7% per year indefinitely.


22.  
Calculating Capital Structure Weights. Kanga Industrial Machines issued 90 000 zero coupon bonds four years ago. The bonds originally had thirty years to maturity with a 8.2% yield to maturity. Interest rates have recently decreased, and the bonds now have a 7.3% yield to maturity. If Kanga has a $40 million market value of equity, what weight should it use for debt when calculating the cost of capital? <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/premium/0071010319/student/pg112_1.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (K)</a>

23.  
Calculating the Cost of Equity. Over the past five years, Alpine Clothing has paid dividends of $1.80, $1.93, $2.02, $2.09 and $2.21. The most recent share price is $51. What is your best estimate of the cost of equity for Alpine Clothing? <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/premium/0071010319/student/pg111_4.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (K)</a>

24.  
Calculating the WACC. Your company has 4 million ordinary shares outstanding with a current market price of $30. The market risk premium is 7.75%, and Treasury bills are yielding 5.5%. There are also sixty thousand $1000 bonds outstanding with a 7.5% half-yearly coupon, eighteen years to maturity and a current price of $960. If the share has a beta of 0.9, what is the WACC for your company under a classical tax system? The tax rate is 30%. <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/premium/0071010319/student/pg112_1.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (K)</a>

25.  
Calculating the WACC. Gnomes ‘R’ Us is considering a new project. The company has a debt–equity ratio of 0.40. The company's cost of equity is 13.5%, and the after-tax cost of debt is 6.25%. The firm believes that the project is riskier than the company as a whole and that it should use an adjustment factor of +3%. What is the WACC it should use for the project under a classical tax system? <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/premium/0071010319/student/pg112_1.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (K)</a>

INTERMEDIATE QUESTIONS (26–29)

26.  
WACC and NPV. Southern Sails Ltd is considering a project that will result in initial after-tax cash savings of $4.5 million at the end of the first year, and these savings will grow at a rate of 4% per year indefinitely. The firm has a target debt–equity ratio of 0.5, a cost of equity of 14% and an after-tax cost of debt of 7%. The cost-saving proposal is somewhat riskier than the usual project the firm undertakes; management uses the subjective approach and applies an adjustment factor of +2% to the cost of capital for such risky projects (assume a classical tax system). Under what circumstances should Southern Sails Ltd take on the project? <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/premium/0071010319/student/pg113_2.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (K)</a>

27.  
WACC and NPV. Margaret River Wines (MRW) has a project available that will provide after-tax cash flows of $215 000 for the next eight years. The project has more risk than the company, so the general manager has told you to use an adjustment factor of +3% in your calculations. The company uses 60% equity and 40% debt in its capital structure. The cost of equity is 14%, and the after-tax cost of debt is 8%. What is the most MRW can afford to pay for the new project? <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/premium/0071010319/student/pg113_2.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (K)</a>

28.  
Calculating the Cost of Debt. Ying Import has several bond issues outstanding, each making half-yearly interest payments. The bonds are listed in the table below. If the corporate tax rate is 30%, what is the after-tax cost of Ying's debt? (Assume the bonds' face value is $100.) <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/premium/0071010319/student/pg113_3.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (K)</a>

<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/premium/0071010319/student/pg394_1.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (K)</a>

p. 395

29.

  

Calculating the Cost of Equity. Fiji Light Industries shares have a beta of 1.2. The company has just paid a dividend of $0.80, and the dividends are expected to grow at 6%. The expected return of the market is 12.5% and the risk-free rate is 5%. The most recent share price for Fiji Light's ordinary shares is $72.

a.

 

Calculate the cost of equity using the dividend growth model method.

b.

 

Calculate the cost of equity using the SML method.

c.

 

CHALLENGE QUESTIONS (30–31)

30.  

Flotation Costs and NPV. Photo Corporation (PC) manufactures time-series photographic equipment. It is currently at its target debt–equity ratio of 0.8. It is considering building a new $80 million manufacturing facility. This new plant is expected to generate after-tax cash flows of $10.9 million in perpetuity. The company raises all equity from outside financing. There are three financing options:

a.

 

A new issue of ordinary shares: The required return on the company's new equity is 17%.

b.

 

A new issue of twenty-year bonds: If the company issues these new bonds at an annual coupon rate of 9%, they will sell at par.

c.

 

Increased use of accounts payable financing: Because this financing is part of the company's ongoing daily business, the company assigns it a cost that is the same as the overall firm WACC. Management has a target ratio of accounts payable to long-term debt of 0.20. (Assume there is no difference between the pre-tax and after-tax accounts payable cost.)


31.  

Project Evaluation. This is a comprehensive project evaluation problem, bringing together much of what you have learned in this and previous chapters. Suppose you have been hired as a financial consultant to Defence Electronics Ltd (DEL), a large, publicly traded firm that is the market-share leader in radar detection systems (RDSs). The company is considering setting up a manufacturing plant overseas to produce a new line of RDSs. This will be a five-year project. The company bought some land three years ago for $6 million in anticipation of using it as a toxic dump site for waste chemicals, but it built a piping system to safely discard the chemicals instead. If the land were sold today, the net proceeds would be $6.4 million after taxes. In five years, the land will be worth $7 million after taxes. The company wants to build its new manufacturing plant on this land; the plant will cost $9.8 million to build. The following market data on DEL's securities are current:

Debt: twenty-five thousand 6.5% coupon bonds outstanding, twenty years to maturity, selling for 96% of par; the bonds have a $1000 par value each and make half-yearly payments.

Ordinary shares: 400 000 ordinary shares outstanding, selling for $89 per share; the beta is 1.2.

Preference shares: thirty-five thousand 6.5% preference shares outstanding, selling for $99 per share.

Market: 8% expected market risk premium; 5.2% risk-free rate.

DEL's tax rate is 30%. The project requires $825 000 in initial net working capital investment to get operational.

a.

 

Calculate the project's Time 0 cash flow, taking into account all side effects.

b.

 

The new RDS project is somewhat riskier than a typical project for DEL, primarily because the plant is being located overseas. Management has told you to use an adjustment factor of +2% to account for this increased riskiness. Calculate the appropriate discount rate to use under a classical tax system when evaluating DEL's project.

c.

 

The manufacturing plant has an eight-year tax life, and DEL uses straight-line depreciation. At the end of the project (i.e. the end of Year 5), the plant can be scrapped for $1.25 million. What is the after-tax salvage value of this manufacturing plant?

d.

 

The company will incur $2 100 000 in annual fixed costs. The plan is to manufacture 11 000 RDSs per year and sell them at $10 000 per machine; the variable production costs are $9300 per RDS. What is the annual operating cash flow (OCF) from this project?

e. 
Finally, DEL's management wants you to throw all your calculations, all your assumptions and everything else into a report for the chief financial officer: all he wants to know are the RDS project's internal rate of return, IRR and net present value (NPV). What will you report? <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/premium/0071010319/student/pg112_1.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (K)</a>

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