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# Introduction to Corporate Finance

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Introduction to Corporate Finance

Chapter 20: Cost of Capital

Multiple Choice Questions

1. Which of the following statements is false?

A. Financing total assets is called the financial structure decision. B Capital structure is how invested capital is financed. C. The financial structure is \$34,000 if the total assets are \$34,000. D. The invested capital is \$50,000 if the total assets are \$50,000. Level of difficulty: Medium

Solution: D

Invested capital = all interest-bearing liabilities + total equity The invested capital is \$50,000 if the invested capital (all interest-bearing liabilities + total

equity) is \$50,000, not necessarily total assets.

2. If an all-equity firm is expected to earn and pay out a \$5.50 dividend forever (in perpetuity),

what is the value of the firm’s stock given a cost of equity is 15 percent? A. \$37

B. \$36

C. \$38

D. \$40

Level of difficulty: Medium

Solution: A

X5.50V\$37 K0.15e

3. What is the earnings yield given a \$40,000 earnings figure, a \$10 market price per share, and

10,000 shares outstanding?

A. 0.5

B. 0.4

C. 0.3

D. 4,000

Level of difficulty: Medium

Solution: B

40,000EPS\$410,000

EPS4EarningsYield0.4P10

4. What does a firm have to earn given the following? MV of debt = \$40,000; MV of equity =

\$69,000; k = 12.5%; k = 7% ed

A. \$11,425

B. \$2,800

C. \$8,625

D. \$10,099

Level of difficulty: Medium

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Solution: A

To satisfy bond holders, 40,000 (7%) = 2,800 To satisfy equity holders, 69,000 (12.5%) = 8,625 Total minimum earnings = 2,800 + 8,625 = \$11,425

5. Which of the following statements is true?

, management is adding value to the firm. A. When ROE < ke

B. When ROE > k , management is destroying the firm’s value. e

C. When ROE > k, the market price goes above the book value of the investment. e

D. When ROE = k, the market price goes above the book value of the investment. e

Level of difficulty: Medium

Solution: C

When ROE > k, the management is adding value to the firm and the market price goes e

above the book value of the investment. When ROE = k, the management is neither increasing nor destroying firm’s value. e

When ROE < k, the management is destroying firm’s value. e

6. Which of the following is not an input in the calculation of WACC? A. Book values of equity and debt

B. Market values of equity and debt

C. Cost of equity

D. Corporate tax rate

Level of difficulty: Medium

Solution: A

Market values are used to calculate the weights of equity and debt, not book values.

7. To increase the stock price of a firm that is assumed to grow at a constant rate g,

A. increase the cost of equity.

B. increase the constant growth rate. C. decrease the dividend payout ratio. D. increase the retention ratio.

Level of difficulty: Medium

Solution: B

DEPS(Payout)EPS(1b)1PRecall kgkgkgeee

To increase P, increase payout, or decrease retention ratio, or decrease cost of equity, or

increase g.

8. Star Inc. just paid a \$9.50 dividend, which is expected to grow at a constant rate. Recent EPS

is \$10.50 and net income is \$550,000. Total equity is \$1,100,000 and the cost of equity is 12

percent. What is the share market price? A. \$142.50

B. \$135.70

C. \$130.90

D. \$129.90

Level of difficulty: Difficult

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Solution: A

10.59.5550,000gbROE0.10.50.0510.51,100,000 D9.5(1.05)1P142.5kbROE0.120.05e

9. Which of the following firms is a growth firm?

A. ROE > k e

B. ROE < k e

C. ROE = k e

D. Net income ? k e

Level of difficulty: Medium

Solution: A

A growth firm is the one that adds values to the firm and has growth opportunities: ROE > k. e

10. Which of the following statements is false?

A. Star firms have both higher PVGO and PVEO.

B. Google and Yahoo are examples of turnarounds.

C. Cash cows could be called growth stocks as well.

D. Utility firms are examples of cash cows.

Level of difficulty: Medium

Solution: C

Cash cows do not have significant growth opportunities.

Practice Problems

Use the information below to answer Problems 11 to 13.

BALANCE SHEET

Cash \$140,000 Accounts pa yable \$200,000

Marketable securities 200,000 Wage payable 100,000

Accounts receivable 40,000 Short-term debt 250,000

Inventory 1,000,000 Long-term debt 690,000

Total liabilities \$1,240,000

Fixed assets 900,000 Common stock 950,000

Retained earnings 90,000

Total assets \$2,280,000 Total Equity & Liabilities \$2,280,000

INCOME STATEMENT

Sales \$1,200,000

CGS 400,000

Amortization 90,000

Interest 56,400

EBT \$653,600

Taxes \$261,440

NI \$392,160

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Shares outstanding 300,000

) given RF = 5%, beta (β)= 1.2, expected market return (ER) 11. What is the cost of equity (keM

= 10%?

Level of difficulty: Easy

Solution:

kRF;(ERRF)5;1.2(105)11% eM

12. What is the market price and market-to-book ratio assuming the firm’s stock is a perpetuity

and retention ratio (b) = 0?

Level of difficulty: Medium

Solution:

DEPSbEPSNI(1)(10)/#392,160111P11.88kkkk300,0000.11eeee

gbROE(0%)

PROENIE/392,1603.43BVPSkk(950,000;90,000)(0.11)ee

13. Calculate invested capital and ROI.

Level of difficulty: Medium

Solution:

Invested Capital = short-term debt + long-term debt + total equity

= 250,000 + 690,000 + 950,000 + 90,000 = 1,980,000

ROI=NI/Invested capital = 392,160/1,980,000 = 19.8%

14. Provide two reasons why the cost of a security to a company differs from its required return in capital markets.

Level of difficulty: Medium

Solution:

i) Flotation costs: Issuing expenses on new securities have to be paid from the gross proceeds

of an issue so that the firm’s initial cash inflow doesn’t match the funds provided by

investors.

ii) Taxes: The tax deductibility of interest payments made by the firm separates the cost of

debt from the corresponding market yield.

15. A firm is going to finance a new project 100 percent with debt, through a new bond issue. Since the firm is only using debt to finance the project, the NPV of the project should be calculated using the cost of debt as the discount rate. Is this statement true, false, or uncertain? Explain.

Level of difficulty: Medium

Solution:

The statement is false. The cost of capital for a new project depends on the use of funds, not the source. Even if this particular project will be funded with debt, it is probably only one of

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many projects that the firm undertakes. The firm, over time, will raise financing through a number of sources, including internal funds, new equity, new preferred shares, and new debt. The source of funding for this project is from the pool of available funds. Therefore the cost of capital for the project should be the WACC, appropriately adjusted for the risk of this particular project.

16. Calculate the WACC (Weighted Average Cost of Capital). The market values of equity and debt are \$500,000 and \$600,000, respectively. The before-tax cost of debt = 6%; RF = 4%; beta (β) = 1.5; the market risk premium = 10%; and the tax rate = 40%.

Level of difficulty: Medium

Solution:

kRF;(ERRF)4;1.5(10)19%eM

500,000600,000WACC19%;6%(10.4)10.6%500,000;600,000500,000;600,000

17. What is V given the expected earnings per share on the S&P500 is \$10 and the long-term Fed

U.S. bond rate is 5 percent?

Level of difficulty: Medium

Solution:

ExpEPS()10V\$250 fedk1%5%1%Tbond

18. AB Inc. just announced its EPS of \$3. Retention ratio (b) = 0.7. The earnings are expected to grow at 10 percent for one year and then grow at 4 percent indefinitely. Given that k = 15%. e

What is the market price?

Level of difficulty: Medium

Solution:

D = D (1 + g) = EPS (1 b)(1 + g) = (3)(1 0.7)(1.1) = 0.99 10101

D = D (1 + g) = 0.99 (1.04) = 1.03 212

D1.032P9.361kg0.150.04e2

0.99;9.36P\$901.15

19. Calculate the cost of issuing new equity for a firm assuming: issue costs are 5 percent of share price after taxes; market price per share = \$20; current dividend = \$3.50; and the constant growth rate in dividends is 5 percent.

Level of difficulty: Medium

Solution:

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D1k;geP(1F)

3.5(1.05) ;0.0520(10.05)

24%

20. A small brokerage firm and a software development company are both separately considering developing and marketing a new software package. Neither party is aware that the other is considering this project and it is NOT at any point going to become a joint venture. These new software packages will organize mutual fund data into a new type of database and then run a series of complicated algorithms on that new database. The beta of the brokerage firm is 0.8 and the beta of the software firm is 1.4. The risk-free rate is 5 percent and the market risk premium is 10 percent. The NPV of the project, using a 13 percent discount rate, is +\$1 million. However, using a 19 percent discount rate, the project has a \$500,000 NPV. Should

either or both parties go ahead with the project?

Level of difficulty: Medium

Solution:

The appropriate discount rate should be based on the risk of the project, not on the risk of the individual companies undertaking the project. In this case, the development of a software package would be more closely associated with the risk of the software development firm. Therefore the appropriate discount rate would be 5 + 1.4 × 10 = 19%. At this discount rate, the NPV of the project is negative and neither party should proceed with the project.

21. Suppose a firm uses a constant WACC to calculate the NPV of all of its capital budgeting projects, rather than adjusting for risk of the individual projects. What errors will the firm make in its capital budgeting decisions?

Level of difficulty: Medium

Solution:

The firm will make both type 1 and type 2 errors. In the first case, it will tend to accept high-risk projects that it should have rejected. Since the project has high risk, using the WACC (which is too low a discount rate given the risk of the project) will overestimate the NPV and will lead management to accept projects it should well have rejected. In the second case, the firm may reject low-risk projects that it should have accepted. Again, using the WACC (in this case a discount rate that is too high given the risk) will underestimate the NPV and lead management to reject projects it should have accepted.

22. A firm has common shares outstanding with a market capitalization rate of 12 percent. The current market price is \$13.80, and dividend payments for this year are expected to be \$0.28. What is the per share implied growth rate?

Level of difficulty: Medium

Solution:

P0=D1/(r-g)=D0*(1+g)/(r-g)

13.8=0.28*(1+g)/(0.12-g)

g=0.098

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23. A firm’s earnings and dividends are expected to grow at a constant rate indefinitely, and it is

expected to pay a dividend of \$9.20 next year. Expected EPS and BVPS next year are \$10.50 and \$30, respectively. The cost of equity is 12 percent and there are 10,000 shares outstanding. Calculate the firm’s value assuming that the retention ratio stays the same and

the market value of debt is \$500,000.

Level of difficulty: Difficult

Solution:

NIEPS10.5 ROE35%EBVPS30

10.59.2gbROE0.350.0410.5

D9.21P\$115kg0.120.04e

V11510,000;500,000\$1,650,000

24. Calculate the cost of equity using constant growth DDM given the following: current dividend = \$2.50; payout ratio = 0.7 (assuming it is not changing); ROE = 15%; and the current market price of the stock = \$11.50. Is the current management adding to or reducing the shareholders’ value?

Level of difficulty: Difficult

Solution:

gbROE(1payout)ROE(10.7)15%4.5%

D2.5(1.045)1k;g;0.04527% eP11.5

ROE15%k27%e

Therefore, management is reducing the shareholders’ value.

25. Calculate PVGO and PVEO given the following information: ROE = 20%; ROE= 25%; 12

further investment (Inv) = \$50; BVPS = \$10; and k = 15%. Is this firm a star? If not, what is e

it according to Boston Consulting Group?

Level of difficulty: Difficult

Solution:

ROEkROEBVPSInv2e1;()Pk(1;k)keee

0.2010500.250.15 ;0.151.150.15

13;29

\$42

PVGO = \$29, PVEO = \$13

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and ROE are both greater than cost of equity, therefore this firm has both high PVGO ROE1 2

and PVEO. It is a star.

26. A firm has the following capital structure based on market values: equity 65 percent and debt 35 percent.

The current yield on government T-bills is 10 percent, the expected return on the market portfolio is 15 percent, and the firm’s beta is approximated at 0.85. The firm’s common shares are trading at \$25, and the current dividend level of \$3 per share is expected to grow at an annual rate of 3.5 percent. The firm can issue debt at a 2 percent premium over the current risk-free rate. The firm’s tax rate is 40 percent, and the firm is considering a project to be funded out of internally generated funds that will not alter the firm’s overall risk. This project requires an initial investment of \$11.5 million and promises to generate net annual after tax cash flows of \$1.4 million perpetually. Should this project be undertaken? Level of difficulty: Difficult

Solution:

We must first determine the firm’s cost of equity. We have enough information to estimate k e

using either the CAPM or the constant dividend growth model.

CAPM

k = RF + B(ER RF) eM

= 0.1 + 0.85 (0.15 0.10) = 14.25%

Dividend Growth

k = D ? P + g e10

= 3(1.035)/25 + 0.035 = 15.92%

We can now estimate the cost of debt from the information given.

I = \$1,000[r + 2%] = 120 f

k = (1 T) × I ? NP= (1 0.4) × 120 ? 1,000 = 7.2% bb

From the ranges of costs we have derived, we can now solve for the firm’s weighted

average cost of capital.

k = B × K ? V + E × K ? V ie

k = 0.35 × 0.072 + 0.65 × 0.1425 = 11.8%

OR

k = 0.35 × 0.072 + 0.65 × 0.1592= 12.9%

We can now perform a net present value calculation.

NPV = 11.5 + 1.4 ? 0.118 = \$.364 million

NPV = 11.5 + 1.4 ? 0.129 = \$0.647 million

The net present value calculations indicate that the project should be undertaken at a

discount rate of 11.8 percent but should not be undertaken at a discount rate of 12.9

percent.

27. A firm has the following balance sheet items:

Common stock: 300,000 shares at \$8 each \$2,400,000

Retained earnings 900,000

Debt: 15% coupon, 15 years to maturity 1,800,000

Preferred shares: 12% dividend 1,200,000

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The before-tax interest cost on new 15-year debt would be 10 percent, and each \$1,000 bond would net the firm \$975 after issuing costs. Common shares could be sold to net the firm \$8 per share, a 12 percent discount from the current market price. Current shareholders expect a 15 percent return on their investment. Preferred shares could be sold at par to provide a yield of 9 percent, with after-tax issuing and underwriting expenses amounting to 5 percent of par value. The firm’s tax rate is 45 percent, and internally generated funds are insufficient to

finance anticipated new capital projects. Compute the firm’s marginal cost of capital.

Level of difficulty: Difficult

Solution:

We first compute the costs of each source of funds:

Debt:

NP = \$975; Assuming annual coupons I = (.10)(\$1,000) = \$100; n = 15

So we have:

1115((1;K)1i(975100(1.45);1,000 15K(1;K)(ii(

Solving for K, as shown in Chapter 6, we get: i

By financial calculator:

PMT = 100(1 - .45) = \$55; PV = -975; FV = 1,000; N = 15.

Then compute I/Y will give 5.75%, which is the firm’s annual after-tax cost of debt.

Preferred: k = D ? NP= 0.09 ? 0.95 = 9.47% ppp

Equity: k = k × P ? NP = (0.15) *(8 × 1.12) / ( 8) = 16.80% neneee

We next compute the market value of each component:

Debt: The market value of debt outstanding is:

1115(1(1;.10)(B =× 1,800 = \$2,484,547 150;1,000\$1,380.30150.10(1;.10)(

(

Preferred: The market value is the total dividend payments divided by the market capitalization rate.

P = 0.12 × (\$1,200,000) ? 0.09 = \$1,600,000

Equity: Shares are currently trading at (8 × 1.12) = \$8.96

E = 300,000 (\$8.96) = \$2,688,000

Note the value of retained earnings is incorporated into the current market price of equity. Total market value = V = B + P + E

= \$2,484,547 + \$1,600,000 + \$2,688,000

= \$6,772,547

Finally we can compute the weighted average cost of capital:

k = B ? V × k + P ? V × k + E ? V × k bpe

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k = [2,484,547 ?6,772,547 × 0.0575] + [1,600,000 ?6,772,547 × 0.0947]

+ [2,688,000 ?6,772,547 × 0.1680]

=11.01%

28. A company can issue new 20-year bonds at par that pay 10 percent annual coupons. The net proceeds to the firm (after-taxes) will be 95 percent of par value. They estimate that new preferred shares providing a \$2 annual dividend could be issued to investors at \$25 per share to “net” the firm \$22 per share issued (after taxes). The company has a beta of 1.20, and present market conditions are such that the risk-free rate is 6 percent, while the expected return on the market index is 12 percent. The firm’s common shares presently trade for \$30,

and they estimate the net proceeds from a new common share issue would be \$26 per share (after tax considerations). The firm’s tax rate is 40 percent.

A. Determine the firm’s cost of long-term debt, preferred shares, and common equity

financing (internal and external sources) under the conditions above.

B. What is the firm’s weighted average cost of capital assuming that they have a “target”

capital structure consisting of 30 percent debt, 10 percent preferred equity, and 60%

common equity. Assume that they have \$2 million in internal funds available for

reinvestment and require \$3 million in total financing.

C. Suppose everything remains as above, except that the company decides it needs \$5 million

in total financing. Calculate the firm’s marginal cost of capital.

Level of difficulty: Difficult

Solution:

A. Cost of Debt:

NP = \$950; Assuming annual coupons I = (.10)(\$1,000) = \$100; n = 20

So we have:

1120((1;K)1i(950100(1.40);1,000 20K(1;K)(ii(

Solving for K, as shown in Chapter 6, we get: i

By financial calculator:

PMT = 100(1 - .40) = \$60; PV = -950; FV = 1,000; N = 20.

Then compute I/Y will give 6.45%, which is the firm’s annual after-tax cost of debt.

Cost of Preferred shares:

K= 2/22 = 9.09%

Cost of Common Shares:

K= 6+1.20(12-6) = 13.2%

13.2% *(30/26)= 15.23%

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