Chapter 12. Risk, Cost of Capital, and Valuation

AnthroPort has a beta of 1.1 and its RWACC is 13.6 percent. The market risk premium is 7.2 percent and the risk-free rate is 2.3 percent. The firm's cash flow at Time 4 is $28,800 with a growth rate of 2.1 percent. What is the value of the firm at Time 4?

$255,693.91 TV4 = [$28,800 × (1 + .021)]/(.136 − .021) = $255,693.91

A firm has net income of $21,350, depreciation of $2,780, interest of $640, and taxes of $10,990. The EBITDA multiple is 10.2. What is the value of the firm?

$364,752 EV = ($21,350 + $2,780 + $640 + $10,990)(10.2) = $364,752

Builder's Supply has a beta of 1.47 and its RWACC is 11.8 percent. The market risk premium is 7.4 percent and the risk-free rate is 3.6 percent. The firm's cash flow at Time 3 is $73,900 with a growth rate of 2.2 percent. What is the terminal value of the firm at Time 3?

$786,727.08 TV3 = [$73,900(1 + .022)]/(.118 − .022) = $786,727.08

The cost of equity for Rosenthal Corporation is 13.61 percent. The expected return on the market is 12.5 percent, the risk-free rate is 1.4 percent, and the expected inflation rate is 3.3 percent. What is the company's equity beta?

.1361 = .014 + β(.125 − .014) β = 1.10

A levered firm has a debt-to-equity ratio of .38 and an equity beta of 1.42. What would be the beta of the firm if it switched to an all-equity financial structure?

1.029 βAsset = [1/(.38 + 1)] × 1.42 = 1.029

A stock portfolio consists of 9.36 percent Stock A, 61.05 percent Stock B, and the remainder is invested in Stock C. The security betas are .40, .97, and 1.80 for Stocks A, B, and C, respectively. What is the portfolio beta?

1.16 βP = .0936(.40) + .6105(.97) + (1 − .0936 − .6105)(1.80) = 1.16

An all-equity firm has a beta of 1.27. What will be the equity beta if the firm adopts a debt-to-equity ratio of .42?

1.803 βEquity = 1.27[1 + (0.42 / 1)] = 1.803

Cosmic Corp. has a proposed investment with an initial cost of $84 million. Debt represents 44 percent of the capital structure. The cost of equity is 14.5 percent, the pretax cost of debt is 5.45 percent, and the tax rate is 21 percent. What is the company's WACC?

10.01% WACC = (1 − .44)(.145) + .44(.0545)(1 − .21) = .1001, or 10.01%

Assume the overall market has a risk premium of 7.5 percent and the risk-free rate is 3.5 percent. What is the total risk premium for a stock that has a beta of 1.43 and a standard deviation of 12.7 percent?

10.7% Risk premiumS = 1.43(.075) = .107, or 10.7%

Green Roof Foods currently has a debt-to-equity ratio of .53, its cost of equity is 14.2 percent, and its pretax cost of debt is 6.8 percent. The tax rate is 35 percent and the risk-free rate is 3.1 percent. The firm's preferred capital structure consists of 35 percent debt. What discount rate should be assigned to a new project the firm is considering if the project is equally as risky as the overall firm and will be financed solely with equity?

10.78% Discount rate = (1 − .35)(.142) + .35(.068)(1 − .35) = .1078, or 10.78%

An all-equity firm has a beta of 1.2. The firm is evaluating a project that will increase the output of the firm's existing products. The market risk premium is 6.5 percent and the risk-free rate is 3.5 percent. What discount rate should be assigned to this expansion project?

11.3% RS = .035 + 1.2(.065) = .113, or 11.3%

Goliath Corp. just paid an annual dividend of $5.40 per share. The dividend growth rate is 5.5 percent, the tax rate is 21 percent, and the common stock sells for $58.50 per share. What is the cost of equity?

15.24% RS = ($5.40 × 1.055)/$58.50 + .055 = .1524, or 15.24%

Tangential is an all-equity financed firm. The beta is .90, the market risk premium is 5.7 percent, and the tax rate is 21 percent. The firm just issued its annual dividend of $5.50 per share and announced that future dividends will increase by 4.5 percent annually. The stock sells for $53.25 per share. What is the cost of equity?

15.29% RS = ($5.50 × 1.045)/$53.25 + .045 = .1529, or 15.29%

Although a definitive value cannot be determined, which one of the following values is considered to be the best estimate of the market's historical risk premium according to your textbook authors?

7%

The price of Ravelle Events stock is $38.00 per share. The stock's beta is 1.30. At the end of one year, the firm will pay its annual dividend of $1.05 per share. Dividends are expected to grow 4.5 percent per year for the foreseeable future. What is the cost of equity capital?

7.26% RS = ($1.05/$38.00) + .045 = .0726 or 7.26%

Assume the S&P 500 has a dividend yield of 2.8 percent. Analysts expect overall dividends to grow at 4.4 percent annually. Treasury bills yield 1.9 percent. The expected market rate of return is __________ percent, and the market risk premium is __________ percent.

7.2; 5.3 RM = 2.8% + 4.4% = 7.2% RM − RF = 7.2% − 1.9% = 5.3%

Finally There! has 1,500 bonds outstanding with a $1,000 par value, a yield to maturity of 6.4 percent, and a market price of $989 each. The firm also has 74,000 shares of common stock outstanding at a price per share of $35 and a beta of 1.08. The risk-free rate is 2 percent, the market risk premium is 7 percent, and the tax rate is 34 percent. What is the company's WACC?

7.62% MVDebt = 1,500 × $989 = $1,483,500 MVEquity = 74,000 × $35 = $2,590,000 MVD + E = $1,483,500 + $2,590,000 = $4,073,500 RS = .02 + 1.08(.07) = .0956, or 9.56% RB = 6.4% (given) WACC = ($2,590,000/$4,073,500)(.0956) + ($1,483,500/$4,073,500)(.064)(1 − .34) = .0762, or 7.62%

Falk Delivery is an unlevered firm that is equally as risky as the market. U.S. Treasury bills are yielding 3.1 percent and the market rate of return is 7.7 percent. What discount rate should be assigned to a project that has the same risks as Falk Delivery?

7.7%

Golden Eagle has 1,250 bonds outstanding with a market value of $980 each. The pretax cost of debt is 7.2 percent. The firm also has 46,000 shares of common stock outstanding at a price per share of $32 and a beta of 1.21. The risk-free rate is 2.4 percent, the market risk premium is 7.3 percent, and the tax rate is 34 percent. What is the company's WACC?

8.29% MVDebt = 1,250 × $980 = $1,225,000 MVEquity = 46,000 × $32 = $1,472,000 MVD + E = $1,225,000 + $1,472,000 = $2,697,000 RS = .024 + 1.21(.073) = .11233, or 11.233% WACC = ($1,472,000/$2,697,000)(.11233) + ($1,225,000/$2,697,000)(.072)(1 − .34) = .0829, or 8.29%

The Flying Dove has 1,600 bonds outstanding with a $1,000 par value, a coupon rate of 5.5 percent, 12 years to maturity, annual interest payments, and a market price equal to par. The firm also has 52,000 shares of common stock outstanding at a price per share of $43 and a beta of 1.3. The risk-free rate is 3 percent, the market risk premium is 7 percent, and the tax rate is 35 percent. What is the company's WACC?

8.54% MVDebt = 1,600 × $1,000 × 1 = $1,600,000 MVEquity = 52,000 × $43 = $2,236,000 MVD + E = $1,600,000 + $2,236,000 = $3,836,000 RS = .03 + 1.3(.07) = .121, or 12.1% Since the bonds are selling at par, the yield to maturity equals the coupon rate, so: RB = 5.5 WACC = ($2,236,000/$3,836,000)(.121) + ($1,600,000/$3,836,000)(.055)(1 − .35) = .0854, or 8.54%

The UpTowner has a beta of 1.18, a debt-to-equity ratio of .36, and a cost of equity of 11.74 percent. The market rate of return is 10.4 percent and the tax rate is 35 percent. If the pretax cost of debt is 6.9 percent, what is the company's WACC?

9.82% RWACC = (1/1.36)(.1174) + (.36/1.36)(.069)(1 − .35) = .0982, or 9.82%

Which one of the following statements is true?

A U.S. Treasury bill has a beta of zero.

What value should you assign as the flotation cost of internally generated equity financing?

A cost of zero

How does the valuation of a company vary from the valuation of a project using WACC?

A terminal value is included in the valuation process for a company but generally not for a project.

Mojave Corp. issued 10-year bonds six years ago. The bonds have an annual coupon rate of 3 percent and are now yielding 7.5 percent. Coupons are paid semiannually. Mojave's income tax rate is 21 percent. What is the annual aftertax cost of the firm's debt?

Aftertax cost = .075(1 − .21) = .0593 or 5.93%

Which one of the following statements related to beta is correct?

Beta measures the risk of a single security if held in a large, diversified portfolio.

The Red Hen currently has a debt-to-equity ratio of .45, its cost of equity is 13.3 percent, and its beta is 1.49. The pretax cost of debt is 7.2 percent, the tax rate is 35 percent, and the risk-free rate is 3.1 percent. The firm's target debt-to-equity ratio is .4. What discount rate should be assigned to a new project the firm is considering if the project is equally as risky as the overall firm and will be financed solely with debt?

Discount rate = (1/1.4)(.133) + (.4/1.4)(.072)(1 − .35) = .1084, or 10.84%

Which one of the following measures will produce an acceptable estimate of the value of the market risk premium?

Dividend yield of the S&P 500 plus Consensus forecast of future dividend growth minus U.S. Treasury bill rate

Which one of the following is a commonly used multiple for overall company valuation?

EV/EBITDA

Which one of these statements is correct?

Financial leverage refers to a firm's use of debt and its related fixed costs of finance.

Which of the following outcomes may occur if a company uses its overall cost of capital as the discount rate for all projects? I. Profitable low-risk projects may be incorrectly rejected. II. Only projects with risks similar to the current company will be accepted. III. Too many high-risk projects may be accepted. IV. Only low-risk projects will be accepted.

I and III only

Which of the following are determinants of beta? I. Financial leverage II. Cyclicality of revenues III. State of the economy IV. Operating leverage

I, II, and IV only

If you assume beta is greater than one, which of the following will increase the cost of equity capital according to CAPM? I. Increase in the risk-free rate II. Decrease in the risk-free rate III. Increase in the market rate of return IV. Decrease in the market rate of return

II and III only

Which of the following are the two primary advantages of CAPM? I. Simplicity II. Absence of estimation error III. Applicability to both dividend and non-dividend paying firms IV. Explicit adjustment for risk

III and IV

A project has an internal rate of return of 11.76 percent. The company beta is 1.22 and the pure play beta is 1.14. The market rate of return is 11.8 percent, the tax rate is 35 percent, and the risk-free rate is 3.3 percent. Should this project be accepted according to the CAPM if the firm is all-equity financed? Why or why not?

No, the CAPM rate is 12.99 percent. RS = .033 + 1.14(.118 − .033) = .1299, or 12.99% The project should be rejected because the IRR < CAPM.

Taylor's has a beta of .97 and a debt-to-equity ratio of .46. The market rate of return is 11.3 percent, the tax rate is 34 percent, and the risk-free rate is 2.2 percent. The pretax cost of debt is 6.4 percent. What is the firm's WACC?

RS = .022 + .97(.113 − .022) = .11027 RWACC = [1/(1 + .46)](.11027) + [.46/(1 + .46)](.064)(1 − .34) = .0888, or 8.88%

Eventide, Inc., has 10-year bonds with a total market value of $15,000,000 and 15-year bonds with a total market value of $55,000,000. The pretax costs are 11 percent and 4 percent, respectively. The firm also has common stock with a total market value of $75,000,000 and a pretax cost of 13%. The tax rate is 21 percent. What is the firm's WACC?

RWACC = {($15,000,000/$145,000,000) × [.11 × (1 − .21)]} + {($55,000,000/$145,000,000) × [.04 × (1 − .21)]} + [($75,000,000/$145,000,000) × .13] = .882 or 8.82%

Which one of these formulas will provide an estimate of the growth rate of a security's dividends?

Retention ratio × Return on equity

Which one of the following statements is correct?

The DDM seems to have more estimation error than the CAPM.

Assume each firm within an industry has similar operations and financial structures as the industry as a whole. Which one of the following statements related to beta is correct given this assumption?

The error in beta estimation for a single security exceeds the error for a portfolio of securities.

Why is an accurate WACC so important when evaluating a new project? Assume a negative cash outflow at Time 0 and positive project cash flows thereafter.

The project's accept/reject decision will be based on the NPV calculated using that WACC.

When computing the weights to be used in a project's WACC equation, you should use the:

average market weights of debt and equity that are expected over the project's life.

The beta of a security provides an estimate of the:

characteristic line for the security.

Assume an all-equity company is considering expanding its current operations by increasing the size of its warehouse. The discount rate used for this project should be the:

company's cost of equity capital.

Beta values are highly dependent on the:

covariance of a security with the market.

To calculate beta, you divide the __________ of the stock with the market portfolio by the __________ of the market portfolio.

covariance; variance

The discount rate for a project should equal the:

expected return on a financial asset of comparable risk.

The use of debt is called:

financial leverage.

Companies A and B are identical except for their capital structures. Company A is an all-equity company while Company B is levered. Given this, you can assume that Company B's equity beta is ___ Company A's beta and its debt beta is assumed to be ___.

greater than; equal to zero

A firm with high operating leverage is best defined as a firm that has:

high fixed costs relative to variable costs.

In project analysis, flotation costs are generally:

included in the amount raised.

The cost of preferred stock:

is equal to the annual dividend divided by the present value of all the future dividend payments.

In a changing interest rate environment, the cost of new debt:

is equal to the cost of borrowing.

The use of WACC as the discount rate when evaluating a project is acceptable when the:

risk of the project is equal to the company's overall level of risk.

Which one of the following is represented by the slope of the characteristic line?

security beta

Assume a company's cost of equity exceeds its pretax cost of debt. Given this assumption and assuming all else is held constant, the company's WACC must increase if the:

tax rate decreases.

A company's cost of debt will decrease when:

tax rates increase.

The asset beta is defined as the beta of:

the common stock of an unlevered firm.

The weights used in the computation of a project's flotation costs should be based on the:

the company's target debt-to-equity ratio.

When the CAPM is used to estimate the cost of equity capital, the expected excess market return is equal to:

the difference between the return on the market and the risk-free rate.

Tires and More is a levered company providing automobile supplies through its retail outlets. The company is considering expanding into electric scooter sales. Since this is an entirely new venture, the company should:

use the pure play approach to assign a discount rate to the project.

Gutters by Gunther has an equity beta of 1.47, a capital structure with three parts of debt for every five parts of equity, and a zero tax rate. What is its asset beta?

βAsset = [5/(3 + 5)](1.47) = .919

Alaskan Markets has a target capital structure of 40 percent debt and 60 percent equity. The pretax cost of debt is 6.3 percent, the tax rate is 35 percent, and the cost of equity is 14.6 percent. The firm is considering a project that is equally as risky as the overall firm. The project has an initial cash outflow of $1.92 million and annual cash inflows of $562,000 at the end of each year for 4 years. What is the NPV of the project?

−$153,776.15 RWACC = .60(.146) + .40(.063)(1 − .35) = .10398 NPV = −$1,920,000 + $562,000({1 − [1/(1 + .10398)4]}/.10398) = −$153,776.15