Chapter 9, Problem 17P

The following table gives the current balance sheet for Travellers Inn Inc. (TII), a company that was formed by merging a number of regional motel chains.

Travellers Inn (Millions of Dollars)

The following facts also apply to TII.

1. (1) The long-term debt consists of 29,412 bonds, each having a 20-year maturity, semiannual payments, a coupon rate of 7.6%, and a face value of $1,000. Currently, these bonds provide investors with a yield to maturity of 11.8%. If new bonds were sold, they would have an 11.8% yield to maturity.
2. (2) TII’s perpetual preferred stock has a $100 par value, pays a quarterly dividend per share of $2, and has a yield to investors of 10%. New perpetual preferred stock would have to provide the same yield to investors, and the company would incur a 3.85% flotation cost to sell it.
3. (3) The company has 3.8 million shares of common stock outstanding, a price per share = P₀ = $20, dividend per share = D₀ = $1, and earnings per share = EPS₀ = $5. The return on equity (ROE) is expected to be 10%.
4. (4) The stock has a beta of 1.6%. The T-bond rate is 6%, and RP_M is estimated to be 5%.
5. (5) 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 11.8%. The responses suggested a risk premium over TII bonds of 3 percentage points.
6. (6) TII is in the 25% federal-plus-state tax bracket.

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. Based on your analysis, answer the following questions.

1. a. What are the current market value weights for debt, preferred stock, and common stock? (Hint: Do your work in dollars, not millions of dollars. When you calculate the market values of debt and preferred stock, be sure to round the market price per bond and the market price per share of preferred to the nearest penny.)
2. b. What is the after-tax cost of debt?
3. c. What is the cost of preferred stock?
4. d. What is the required return on common stock using CAPM?
5. e. Use the retention growth equation to estimate the expected growth rate. Then use the expected growth rate and the dividend growth model to estimate the required return on common stock.
6. f. What is the required return on common stock using the own-bond-yield-plus-judgmental-risk-premium approach?
7. g. Use the required return on stock from the CAPM model, and calculate the WACC.

Summary Introduction

To determine: The market value weights of debt, common stock and preferred stock.

Answer to Problem 17P

The market value weights of debt are 20%, common stock is 76% and preferred stock is 4%.

Explanation of Solution

Determine the market value weights of debt, common stock and preferred stock

Excel Spreadsheet:

Excel Workings:

Therefore, the market value weights of debt are 20%, common stock is 76% and preferred stock is 4%.

Summary Introduction

To determine: The after-tax cost of debt.

Answer to Problem 17P

The after-tax cost of debt is 8.85%.

Explanation of Solution

Determine the after-tax cost of debt

$\begin{array}{c}Aftertax\mathrm{Cos}tofDebt=\left[\mathrm{Pr}etax\mathrm{Cos}tofDebt\times \left(1-TaxRate\right)\right]\\ =\left[11.80\%\times \left(1-25\%\right)\right]\\ =0.0885or8.85\%\end{array}$

Therefore, the after-tax cost of debt is 8.85%.

Summary Introduction

To determine: The cost of preferred stock.

Answer to Problem 17P

The cost of preferred stock is 10.40%.

Explanation of Solution

Determine the cost of preferred stock

$\begin{array}{c}\mathrm{Cos}tof\mathrm{Pr}eferredStock=\left[\frac{Annual\mathrm{Pr}eferredDividend}{Stock\mathrm{Pr}ice\times \left(1-Flotation\mathrm{Cos}ts\right)}\right]\\ =\left[\frac{\$100\times 10\%}{\$100\times \left(1-3.85\%\right)}\right]\\ =\left[\frac{\$10}{\$96.15}\right]\\ =0.104004or10.40\%\end{array}$

Therefore, the cost of preferred stock is 10.40%.

Summary Introduction

To determine: The required return on common stock using CAPM.

Answer to Problem 17P

The required return on common stock using CAPM is 14%.

Explanation of Solution

Determine the required return on common stock using CAPM

$\begin{array}{c}\mathrm{Cos}tofCommonStoc{k}_{CAPM}=\left[RiskfreeRate+Beta\times MarketRisk\mathrm{Pr}emium\right]\\ =\left[6\%+1.6\times 5\%\right]\\ =14\%\end{array}$

Therefore, the required return on common stock using CAPM is 14%.

Summary Introduction

To determine: The required return on common stock using dividend growth model.

Answer to Problem 17P

The required return on common stock using dividend growth model is 13.40%.

Explanation of Solution

Determine the payout ratio

$\begin{array}{c}PayoutRatio=\left[\frac{Dividendpershare}{Earningspershare}\right]\\ =\left[\frac{\$1}{\$5}\right]\\ =20\%\end{array}$

Therefore, the payout ratio is 20%.

Determine the growth rate

$\begin{array}{c}GrowthRate=\left[ROE\times \left(1-PayoutRatio\right)\right]\\ =\left[10\%\times \left(1-20\%\right)\right]\\ =8\%\end{array}$

Therefore, the growth rate is 8%.

Determine the required return on common stock using dividend growth model

$\begin{array}{c}\mathrm{Cos}tofCommonStoc{k}_{DividendGrowth}=\left[\left(\frac{Dividends\times \left(1+GrowthRate\right)}{Stock\mathrm{Pr}ice}\right)+GrowthRate\right]\\ =\left[\left(\frac{\$1\times \left(1+8\%\right)}{\$20}\right)+8\%\right]\\ =\left[0.054+0.08\right]\\ =13.40\%\end{array}$

Therefore, the required return on common stock using dividend growth model is 13.40%.

Summary Introduction

To determine: The required return on common stock using own-bond-yield-plus-judgmental- risk-premium approach.

Answer to Problem 17P

The required return on common stock using own-bond-yield-plus-judgmental- risk-premium approach is 14.80%.

Explanation of Solution

Determine the required return on common stock using own-bond-yield-plus-judgmental- risk-premium approach

$\begin{array}{c}\mathrm{Cos}tofCommonStoc{k}_{BondYieldJudgemental}=\left[BondYield+Risk\mathrm{Pr}emiumPercentagePo\mathrm{int}s\right]\\ =\left[11.8\%+3\%\right]\\ =14.80\%\end{array}$

Therefore, the required return on common stock using own-bond-yield-plus-judgmental- risk-premium approach is 14.80%.

Summary Introduction

To determine: The WACC.

Answer to Problem 17P

The WACC is 12.83%.

Explanation of Solution

Determine the WACC

$\begin{array}{c}WACC=\left[\begin{array}{l}\left(\left(Weigh{t}_{Debt}\times Rat{e}_{Debt}\right)\times \left(1-Tax\right)\right)+\\ \left(Weigh{t}_{\mathrm{Pr}eferredStock}\times Rat{e}_{\mathrm{Pr}eferredStock}\right)+\\ \left(Weigh{t}_{CommonStock}\times Rat{e}_{CommonStock}\right)\end{array}\right]\\ =\left[\left(\left(20\%\times 8.85\%\right)\right)+\left(4\%\times 10.40\%\right)+\left(76\%\times 14\%\right)\right]\\ =\left[1.77\%+0.42\%+10.64\%\right]\\ =12.83\%\end{array}$

Therefore, the WACC is 12.83%.