Chapter 12: homework 9 Cost of Capital

Which statement is correct, all else held constant?

A decrease in a firm's WACC will increase the attractiveness of the firm's investment options.

Black Stone Furnaces wants to build a new facility. The cost of capital for this investment is primarily dependent on which one of the following?

The nature of the investment

When evaluating a project, the dividend growth model

is relatively simply to use

cost of capital

-reflects the average riskiness of all the securities the firm has issued -provides indication of how the market views the risk of those assets

WACC also ?

-reflects the risk and the target capital structure of the firms existing assets as a whole

Market Value of a Firm

-the sum of the MV of each capital

capital structure weights

-the weights of each source of funds

Traditional Bank has an issue of preferred stock with an annual dividend of $7.50 that just sold for $62 a share. What is the bank's cost of preferred stock?

7.50/62 = 12.10%

Which one of the following statements is correct? Assume the pretax cost of debt is less than the cost of equity.

A firm may change its capital structure if the government changes its tax policies. Correct

The common stock of Silent Motors has a beta that is 5 percent greater than the overall market beta. Currently, the market risk premium is 8.25 percent while the U.S. Treasury bill is yielding 2.8 percent. What is the cost of equity for this firm?

B= 5% more than market beta (1) MRP= 8.25% RF= 2.8% RE = Rf + β × (E(RM) − Rf ) RE = .028 + 1.05 × .0825 RE = .1146, or 11.46%

S&W has 21,000 shares of common stock outstanding at a price of $29 a share. It also has 2,000 shares of preferred stock outstanding at a price of $71 a share. The firm has 7 percent, 12-year bonds outstanding with a total market value of $386,000. The bonds are currently quoted at 100.6 percent of face and pay interest semiannually. What is the capital structure weight of the firm's preferred stock if the tax rate is 21 percent?

Common stock = 21,000 × $29 = $609,000 Preferred stock = 2,000 × $71 = $142,000 Debt = $386,000 Value = $609,000 + 142,000 + 386,000 = $1,137,000 Weight of preferred = $142,000/$1,137,000 = .1249, or 12.49%

Dee's Dress Emporium has 50,000 shares of common stock outstanding at a price of $27 a share. It also has 1,000 shares of preferred stock outstanding at a price of $20 a share. There are 800 bonds outstanding that have a semiannual coupon payment of $25. The bonds mature in four years, have a face value of $1,000, and sell at 97 percent of par. What is the capital structure weight of the common stock?

Common stock = 50,000 × $27 = $1,350,000 Preferred stock = 1000 × $20 = $20,000 Debt = 800 × (.97 × $1,000) = $776,000 Value = $1,350,000 + 20,000 + 776,000 = $2,146,000 Weight of common stock = $1,350,000/$2,146,000 = .6291, or 62.91%

Santa Claus Enterprises has 87,000 shares of common stock outstanding at a current price of $39 a share. The firm also has two bond issues outstanding. The first bond issue has a total face value of $230,000, pays 7.1 percent interest annually, and currently sells for 103.1 percent of face value. The second bond issue consists of 5,000 bonds that are selling for $887 each. These bonds pay 6.5 percent interest annually and mature in eight years. The tax rate is 21 percent. What is the capital structure weight of the firm's debt?

Common stock = 87,000 × $39 = $3,393,000 Debt = (1.031 × $230,000) + (5,000 × $887) = $4,672,130 Weight of debt = $4,672,130/($3,393,000 + 4,672,130) = .5793, or 57.93%

Western Electric has 21,000 shares of common stock outstanding at a price per share of $61 and a rate of return of 15.6 percent. The firm has 11,000 shares of $8 preferred stock outstanding at a price of $48 a share. The outstanding debt has a total face value of $275,000 and currently sells for 104 percent of face. The yield to maturity on the debt is 8.81 percent. What is the firm's weighted average cost of capital if the tax rate is 25 percent?

Common stock: 21,000 × $61 = $1,281,000 Preferred stock: 11,000 × $48 = $528,000 Debt: 1.04 × $275,000 = $286,000 Value = $1,281,000 + 528,000 + 286,000 = $2,095,000 WACC = ($1,281,000/$2,095,000)(.156) + ($528,000/$2,095,000)($8/$48) + ($286,000/$2,095,000)(.0881)(1 − .25) = .1464, or 14.64%

Musical Charts just paid an annual dividend of $1.84 per share. This dividend is expected to increase by 2.1 percent annually. Currently, the firm has a beta of 1.12 and a stock price of $31 a share. The risk-free rate is 4.3 percent, and the market rate of return is 12.3 percent. What is the cost of equity capital for this firm?

D= 1.84 Rf= 4.3% G= 2.1% R(M)= 12.3 Po= 3.1 B= 1.12 R(E)= 1.84 (1 + 0.021)/31 + 0.021 = 8.16% R(E)= 0.043 +1.12 x ( 0.1230 - 0.0430 ) = 13.26% 8.16+ 13.26 /2 = 10.71%

Commercial Construction Builders has a beta of 1.34, a dividend growth rate of 2.1 percent for the foreseeable future, a stock price of $15 per share, and an expected annual dividend of $.45 per share next year. The market rate of return is 12.8 percent, and the risk-free rate is 4.2 percent. What is the firm's average cost of equity?

G= 2.1 B= 1.34 Po= $15 R(m)= 12.8 D1= 0.45 Rf= 4.2 Re= 0.45/15 + 0.0210 = 5.16% Re= 0.0420 + (1.34 x (0.1280 - 0.0420 ) = 15.72% Average= 15.72 + 5.16/2 = 10.41%

Which one of the following will decrease the aftertax cost of debt for a firm?

Increase in tax rates

Which one of the following will increase the cost of equity, all else held constant?

Increase in the dividend growth rate

Three years ago, the Fairchildress Company issued 20-year, 7.75 percent semiannual coupon bonds at par. Today, the bonds are quoted at 102.6. What is this firm's pretax cost of debt?

N= (20-3) x 2 = 34 I/y=--------- 3.73 x 2 = 7.47% Pv= 1.0260 x 1000 = 1026 PMT= 0.0775 x 1000/2 = 38.75 Fv= 1000

USA Manufacturing issued 30-year, 7.2 percent semiannual bonds 6 years ago. The bonds currently sell at 101 percent of face value. What is the firm's aftertax cost of debt if the tax rate is 21 percent?

N= (30-6)x2 = 48 I/Y=----------3.55 x 2 = 7.11 PV= 1.01 x 1000 = 1010 PMT= 0.0720 x 1000/2 = 36 Fv=1000 After tax cost of debt? =Rd x (1-tx) =7.11 x (1-0.2100) = 5.61%

Spartans has 6.5 percent bonds outstanding that mature in 18 years. The bonds pay interest semiannually and have a face value of $1,000. Currently, the bonds are selling for $985 each. What is the firm's pretax cost of debt?

N= 18 x 2 = 36 YTM= ? ------------3.32x2= 6.64% Pv= 9.85 PMT= 0.0650 x1000/2 = 32.50 Fv= 1000

Madison Square Stores has a $20 million bond issue outstanding that currently has a market value of $19.6 million. The bonds mature in 6.5 years and pay semiannual interest payments of $35 each. What is the firm's pretax cost of debt?

N= 6.5 x 2= 13 I/Y= --------- 3.69% x 2 = 7.39% Pv= -980 PMt= 35 Fv=1000

Electronic Products has 22,500 bonds outstanding that are currently quoted at 101.6. The bonds mature in 8 years and pay an annual coupon payment of $90. What is the firm's aftertax cost of debt if the applicable tax rate is 21 percent?

N= 8 I/Y= -------- 8.71= Rd PV= 1.016 x 1000= 1016 PMT= 90 Fv= 1000 After tax? =Rd x (1-tc) =8.71 x (1- 0.2100) = 6.89%

Pride of Lions has bonds outstanding that carry an annual coupon of 5.75 percent. The bonds mature in 9 years and are currently priced at 98 percent of face value. What is the firm's pretax cost of debt?

N= 9x 2 =18 I/Y=----------3.02% x 2 = 6.04% Pv=-980 PMT= 28.75 FV= 1000

The market rate of return is 12.65 percent, and the risk-free rate is 3.1 percent. Galaxy Company has 15 percent more systematic risk than the overall market and has a dividend growth rate of 3.75 percent. The firm's stock is currently selling for $53 a share and has a dividend yield of 4.53 percent. What is the firm's average cost of equity?

Po= 53 E(Rm)=12.65 D= 4.53 RF= 3.1 G= 3.75 15% more systematic R(E)= 0.0453 x 53/53 + 0.0375 = 8.28% Re= 0.0310 + ( 1.15 x( 0.1265 - 0.0310)= 14.08% 8.28+ 14.08/2 = 11.18%

KellyAnne Public Relations just paid an annual dividend of $1.27 on its common stock and increases its dividend by 3.4 percent annually. What is the rate of return on this stock if the current stock price is $38.56 a share?

RE = D1/P0 + g RE = 1.31318/38.56 + .034 RE = .068055 RE = .0681, or 6.81%

The common stock of Serenity Homescapes has a beta of 1.21 and a standard deviation of 17.8 percent. The market rate of return is 13.5 percent, and the risk-free rate is 3.2 percent. What is the cost of equity for this firm?

RE = Rf + β × (E(RM) − Rf) RE = .032 + 1.21 × (.135 − .032) RE = .1566, or 15.66%

Precision Cuts has a target debt-equity ratio of .48. Its cost of equity is 16.4 percent, and its pretax cost of debt is 8.2 percent. If the tax rate is 21 percent, what is the company's WACC?

RE= 16.40 Rd= 8.20% Tc= 21% D/E= 0.48 D= 0.48 E=1 V= 1.48 Wd=D/V= .48/1.48= 0.3243 We= E/V=1/1.48= 0.6757 WACC= ( 0.3243 x 0.082 x (1- 0.2100) + ( 0.6757 x 0.1640) WACC= 13.18%

Gulf Coast Tours currently has a weighted average cost of capital of 12.4 percent based on a combination of debt and equity financing. The firm has no preferred stock. The current debt-equity ratio is .47 and the aftertax cost of debt is 6.1 percent. The company just hired a new president who is considering eliminating all debt financing. All else constant, what will the firm's cost of capital be if the firm switches to an all-equity firm?

Rd=6.1% WACC= 12.4% Re=? WACC= (Wd x Rd x (1-Tc) + (We x Re) V= 0.47 +1 = 1.47 E=1 Wd= D/v= 0.47/1.47 = 31.9 we=E/v= 1/1.47= 68.02 0.1240= (0.3197 x 0.0610) + (0.6803 x Re) 0.1240= 0.0195 + (0.6803 x Re) RE= 15.36%

The Five and Dime Store has a cost of equity of 14.8 percent, a pretax cost of debt of 6.7 percent, and a tax rate of 21 percent. What is the firm's weighted average cost of capital if the debt-equity ratio is .46?

Re= 14.8 Rd= 6.7 Tc= 21 D/E= 0.46 D= 0.46 E=1 V= 1.46 Wd=D/V=0.46/1.46= 0.2150 We=E/V=1/1.46= 0.6849 WACC= (Wd x Rd X (1-Tc) + (WE x Re) WACC= 0.3150 x 0.0670 x (1-0.2100) + ( 0.6849 x 0.1480) = 11.80%

Country Cook's cost of equity is 16.2 percent and its aftertax cost of debt is 5.8 percent. What is the firm's weighted average cost of capital if its debt-equity ratio is .42 and the tax rate is 21 percent?

Re= 16.2 Rd=5.8 Tc=21% D/E= 0.42 V= 1.42 Wd=D/V= 0.42/1.42= 0.2958 We=E/V= 1/1.42= 0.7042 WACC= Wd x Rd x (1-Tc) + (We x Re) WACC=(0.2958 x 0.0580 x (1-0.2100) + (0.7042 x 0.1620)= 13.12%

Ted is trying to decide what cost of capital he should assign to a project. Which one of the following should be his primary consideration in this decision?

Risk level of the project

The 5.25 percent preferred stock of Robert Bruce Security is selling for $50.26 a share. What is the firm's cost of preferred stock if the tax rate is 21 percent and the par value per share is $100?

Rp = (.0525 × $100)/$50.26 = .1045, or 10.45%

Which statement is true?

The cost of preferred stock is unaffected by the issuer's tax rate.

Which one of the following is the primary determinant of an investment's cost of capital?

The investment's level of risk

Healthy Snacks has a target capital structure of 60 percent common stock, 3 percent preferred stock, and 37 percent debt. Its cost of equity is 16.8 percent, the cost of preferred stock is 11.4 percent, and the pretax cost of debt is 8.3 percent. What is the company's WACC if the applicable tax rate is 21 percent?

WACC = .60(.168) + .03(.114) + .37(.083)(1 − .21) = .1285, or 12.85%

A firm wants to create a WACC of 11.2 percent. The firm's cost of equity is 16.8 percent, and its pretax cost of debt is 8.7 percent. The tax rate is 25 percent. What does the debt-equity ratio need to be for the firm to achieve its target WACC?

WACC= 11.2% Re= 16.8% Rd= 8.7% TC= 25% WACC = .112 = (1 − x)(.168) + x(.087)(1 − .25) x = .5450 Debt-equity ratio = .5450/(1 − .5450) = 1.20

The Color Box uses a combination of common stock, preferred stock, and debt financing. The company wants preferred stock to represent 7 percent of the total financing. It also wants to structure the firm in a manner that will produce a weighted average cost of capital of 9.5 percent. The aftertax cost of debt is 4.8 percent, the cost of preferred is 8.9 percent, and the cost of common stock is 14.7 percent. What percentage of the firm's capital funding should be debt financing?

WACC= 9.5% Rd= 4.8% PS= 8.9% CS= 14.7% .095 = (1 − .07 − x)(.147) + (.07)(.089) + (x)(.048) x = .4842, or 48.42%

WACC equation

Wd*Rd(1-T) + (We*Re) + (Wps*Rps) or Wd*Rd(1-T) + (We*Re)

capital

a firms resources of financing to fund its assets

Lester lent money to The Corner Store by purchasing bonds issued by the store. The rate of return that he and the other lenders require is referred to as the:

cost of debt

A firm that uses its weighted average cost of capital as the required return for all of its investments will:

increase the risk level of the firm over time

Total Return Equation

dividend yield + capital gains yield

Which one of the following will decrease the aftertax cost of debt for a firm?

increase in tax rates

Weighted Average Cost of Capital (WACC)

represents the overall return the firm must earn on its existing assets to maintain the value of the firm

cost of debt

required return that lenders require on the companys new debt

Cost of Preferred Stock

the ratio of the preferred stock dividend to the firm's net proceeds from the sale of preferred stock

capital structure

the relative proportions of debt, equity, and other securities that a firm has outstanding

YTM

the return bond purchasers would earn if they held the debt to maturity and received all the payments as promised

cost of equity

the return that equity investors require on their investment in the firm

Which one of the following represents the minimum rate of return a firm must earn on its assets if it is to maintain the current value of its securities?

weighted average cost of capital