Eugene F. Brigham, Michael C. Ehrhardt
Chapter 9
The cost of Capital - all with Video Answers
Educators
Chapter Questions
Calculate the after-tax cost of debt under each of the following conditions:
a. Interest rate of $13 \%,$ tax rate of $0 \%$
b. Interest rate of $13 \%$, tax rate of $20 \%$
c. Interest rate of $13 \%,$ tax rate of $35 \%$
AG
Ankit Gupta
Numerade Educator
LL Incorporated's currently outstanding $11 \%$ coupon bonds have a yield to maturity of $8 \% .$ LL believes it could issue new bonds at par that would provide a similar yield to maturity. If its marginal tax rate is $35 \%$, what is LL's after-tax cost of debt?
Jennifer Stoner
Numerade Educator
Duggins Veterinary Supplies can issue perpetual preferred stock at a price of $\$ 50$ a share with an annual dividend of $\$ 4.50$ a share. Ignoring flotation costs, what is the company's cost of preferred stock, $r_{p s}$ ?
Carson Merrill
Numerade Educator
Burnwood Tech plans to issue some $\$ 60$ par preferred stock with a $6 \%$ dividend. A similar stock is selling on the market for $\$ 70 .$ Burnwood must pay flotation costs of $5 \%$ of the issue price. What is the cost of the preferred stock?
Oluwadamilola Ameobi
Numerade Educator
Summerdahl Resort's common stock is currently trading at $\$ 36$ a share. The stock is expected to pay a dividend of $\$ 3.00$ a share at the end of the year $\left(\mathrm{D}_{1}=\$ 3.00\right),$ and the dividend is expected to grow at a constant rate of $5 \%$ a year. What is its cost of common equity?
William Semus
Numerade Educator
Booher Book Stores has a beta of $0.8 .$ The yield on a 3 -month T-bill is $4 \%$ and the yield on a 10 -year T-bond is $6 \%$. The market risk premium is $5.5 \%$, and the return on an average stock in the market last year was $15 \% .$ What is the estimated cost of common equity using the CAPM?
Sanchit Jain
Numerade Educator
Shi Importer's balance sheet shows $\$ 300$ million in debt, $\$ 50$ million in preferred stock, and $\$ 250$ million in total common equity. Shi's tax rate is $40 \%, r_{d}=6 \%, r_{p s}=$ $5.8 \%,$ and $r_{s}=12 \% .$ If Shi has a target capital structure of $30 \%$ debt, $5 \%$ preferred stock, and $65 \%$ common stock, what is its WACC?
Linh Vu
Numerade Educator
David Ortiz Motors has a target capital structure of $40 \%$ debt and $60 \%$ equity. The yield to maturity on the company's outstanding bonds is $9 \%,$ and the company's tax rate is $40 \% .$ Ortiz's CFO has calculated the company's WACC as $9.96 \% .$ What is the company's cost of equity capital?
Amit Srivastava
Numerade Educator
A company's $6 \%$ coupon rate, semiannual payment, $\$ 1,000$ par value bond that $\mathrm{ma}-$ tures in 30 years sells at a price of $\$ 515.16 .$ The company's federal-plus-state tax rate is $40 \% .$ What is the firm's after-tax component cost of debt for purposes of calculating the WACC? (Hint: Base your answer on the nominal rate.)
Prashant Bana
Numerade Educator
The earnings, dividends, and stock price of Shelby Inc. are expected to grow at $7 \%$ per year in the future. Shelby's common stock sells for $\$ 23$ per share, its last dividend was $\$ 2.00,$ and the company will pay a dividend of $\$ 2.14$ at the end of the current year.
a. Using the discounted cash flow approach, what is its cost of equity?
b. If the firm's beta is $1.6,$ the risk-free rate is $9 \%,$ and the expected return on the market is $13 \%,$ then what would be the firm's cost of equity based on the CAPM approach?
c. If the firm's bonds earn a return of $12 \%$, then what would be your estimate of $\mathbf{r}_{\mathrm{s}}$ using the over-own-bond-yield-plus-judgmental-risk-premium approach? (Hint: Use the midpoint of the risk premium range.)
d. On the basis of the results of parts a through $c,$ what would be your estimate of Shelby's cost of equity?
Hira Hussain
Numerade Educator
Radon Homes' current EPS is $\$ 6.50 .$ It was $\$ 4.42$ five years ago. The company pays out $40 \%$ of its earnings as dividends, and the stock sells for $\$ 36$
a. Calculate the historical growth rate in earnings. (Hint: This is a 5-year growth period.)
b. Calculate the next expected dividend per share, $D_{1}$. (Hint: $D_{0}=0.4(\$ 6.50)=$ \$2.60.) Assume that the past growth rate will continue.
c. What is Radon Homes' cost of equity, $r_{s}$ ?
Kevin Zaborsky
Numerade Educator
Spencer Supplies' stock is currently selling for $\$ 60$ a share. The firm is expected to earn $\$ 5.40$ per share this year and to pay a year-end dividend of $\$ 3.60$
a. If investors require a $9 \%$ return, what rate of growth must be expected for Spencer?
b. If Spencer reinvests earnings in projects with average returns equal to the stock's expected rate of return, then what will be next year's EPS? (Hint: $\mathrm{g}=\mathrm{ROE} \times$ Retention ratio.)
Nick Johnson
Numerade Educator
Messman Manufacturing will issue common stock to the public for $\$ 30 .$ The expected dividend and the growth in dividends are $\$ 3.00$ per share and $5 \%$, respectively. If the flotation cost is $10 \%$ of the issue's gross proceeds, what is the cost of external equity, $r_{c}$ ?
Nick Johnson
Numerade Educator
Suppose a company will issue new 20 -year debt with a par value of $\$ 1,000$ and a coupon rate of $9 \%$, paid annually. The tax rate is $40 \%$. If the flotation cost is $2 \%$ of the issue proceeds, then what is the after-tax cost of debt? Disregard the tax shield from the amortization of flotation costs.
Prashant Bana
Numerade Educator
On January $1,$ the total market value of the Tysseland Company was $\$ 60$ million. During the year, the company plans to raise and invest $\$ 30$ million in new projects. The firm's present market value capital structure, shown below, is considered to be optimal. There is no short-term debt.
New bonds will have an $8 \%$ coupon rate, and they will be sold at par. Common stock is currently selling at $\$ 30$ a share. The stockholders' required rate of return is estimated to be $12 \%,$ consisting of a dividend yield of $4 \%$ and an expected constant growth rate of $8 \%$. (The next expected dividend is $\$ 1.20$, so the dividend yield is $\$ 1.20 / \$ 30=4 \% .$ The marginal tax rate is $40 \%$
Hira Hussain
Numerade Educator
Suppose the Schoof Company has this book value balance sheet:The current liabilities consist entirely of notes payable to banks, and the interest rate on this debt is $10 \%$, the same as the rate on new bank loans. These bank loans are not used for seasonal financing but instead are part of the company's permanent capital structure. The long-term debt consists of 30,000 bonds, each with a par value of $\mathrm{SI}, 000,$ an annual coupon interest rate of $6 \%,$ and a 20 -year maturity. The going rate of interest on new long-term debt, $r_{d},$ is $10 \%,$ and this is the present yield to maturity on the bonds. The common stock sells at a price of $\$ 60$ per share. Calculate the firm's market value capital structure.
Oluwadamilola Ameobi
Numerade Educator
The table below gives the balance sheet for Travellers Inn Inc. (TII), a company that was formed by merging a number of regional motel chains.
The following facts also apply to TII.
(1) Short-term debt consists of bank loans that currently cost $10 \%,$ with interest payable quarterly. These loans are used to finance receivables and inventories on a seasonal basis, so bank loans are zero in the off-season.
(2) The long-term debt consists of 20-year, semiannual payment mortgage bonds with a coupon rate of $8 \%$. Currently, these bonds provide a yield to investors of $r_{d}=$ $12 \% .$ If new bonds were sold, they would have a $12 \%$ yield to maturity.
(3) TII's perpetual preferred stock has a $\$ 100$ par value, pays a quarterly dividend of $\$ 2,$ and has a yield to investors of $11 \% .$ New perpetual preferred would have to provide the same yield to investors, and the company would incur a $5 \%$ flotation cost to sell it.
(4) The company has 4 million shares of common stock outstanding. $P_{0}=\$ 20,$ but the stock has recently traded in the price range from $\$ 17$ to $\$ 23 . \mathrm{D}_{0}=\$ 1$ and $\mathrm{EPS}_{0}=\$ 2 .$ ROE based on average equity was $24 \%$ in $2008,$ but management expects to increase this return on equity to $30 \%$; however, security analysts and investors generally are not aware of management's optimism in this regard.
(5) Betas, as reported by security analysts, range from 1.3 to $1.7 ;$ the T-bond rate is $10 \% ;$ and $\mathrm{RP}_{\mathrm{M}}$ is estimated by various brokerage houses to be in the range from $4.5 \%$ to $5.5 \% .$ Some brokerage house analysts report forecasted growth dividend growth rates in the range of $10 \%$ to $15 \%$ over the foreseeable future.
(6) TII's financial vice president recently polled some pension fund investment managers who hold TII's securities regarding what minimum rate of return on TII's common would make them willing to buy the common rather than TII bonds, given that the bonds yielded $12 \% .$ The responses suggested a risk premium over TII bonds of 4 to 6 percentage points.
(7) TII is in the $40 \%$ federal-plus-state tax bracket.
(8) TII's principal investment banker predicts a decline in interest rates, with $r_{d}$ falling to $10 \%$ and the T-bond rate to $8 \%$, although the bank acknowledges that an increase in the expected inflation rate could lead to an increase rather than a decrease in interest rates.
Assume that you were recently hired by TII as a financial analyst and that your boss, the treasurer, has asked you to estimate the company's WACC under the assumption that no new equity will be issued. Your cost of capital should be appropriate for use in evaluating projects that are in the same risk class as the assets TII now operates.
Heather Duong
Numerade Educator
Start with the partial model in the file Cb 09 PI 8 Build a Model.xls on the textbook's Web site. The stock of Gao Computing sells for $\$ 50,$ and last year's dividend was \$2.10. A flotation cost of $10 \%$ would be required to issue new common stock. Gao's preferred stock pays a dividend of $\$ 3.30$ per share, and new preferred could be sold at a price to net the company $\$ 30$ per share. Security analysts are projecting that the common dividend will grow at a rate of $7 \%$ a year. The firm can issue additional long-term debt at an interest rate (or a before-tax cost) of $10 \%,$ and its marginal tax rate is $35 \%$. The market risk premium is $6 \%$, the risk-free rate is $6.5 \%$, and Gao's beta is $0.83 .$ In its cost-of-capital calculations, Gao uses a target capital structure with $45 \%$ debt, $5 \%$ preferred stock, and $50 \%$ common equity.
a. Calculate the cost of each capital component-in other words, the after-tax cost of debt, the cost of preferred stock (including flotation costs), and the cost of equity (ignoring flotation costs). Use both the DCF method and the CAPM method to find the cost of equity.
b. Calculate the cost of new stock using the DCF model.
c. What is the cost of new common stock based on the CAPM? (Hint: Find the difference between $r_{e}$ and $r_{s}$ as determined by the DCF method and then add that difference to the CAPM value for $r_{s}$.
d. Assuming that Gao will not issue new equity and will continue to use the same target capital structure, what is the company's WACC?
e. Suppose Gao is evaluating three projects with the following characteristics.
(1) Each project has a cost of $\$ 1$ million. They will all be financed using the target mix of long-term debt, preferred stock, and common equity. The cost of the common equity for each project should be based on the beta estimated for the project. All equity will come from reinvested earnings.
(2) Equity invested in Project A would have a beta of 0.5 and an expected return of $9.0 \%$
(3) Equity invested in Project B would have a beta of 1.0 and an expected return of $10.0 \%$
(4) Equity invested in Project $C$ would have a beta of 2.0 and an expected return of $11.0 \%$
f. Analyze the company's situation and explain why each project should be accepted or rejected.
Heather Duong
Numerade Educator
