Chapter 10, Problem 21SP

CALCULATING THE WACC Here is the condensed 2019 balance sheet for Skye Computer Company (in thousands of dollars):

Skye’s earnings per share last year were $3.20. The common stock sells for $55.00. last year’s dividend (D₀) was $2.10, and a flotation cost of 10% would be required to sell new common stock. Security analysts are projecting that the common dividend will grow at an annual rate of 9%. Skye’s preferred stock pays a dividend of $3.30 per share, and its preferred stock sells for $30.00 per share. The firm’s before-lax cost of debt is 10%, and its marginal tax rate is 25%. The firm’s currently outstanding 10% annual coupon rate, long-term debt sells at par value. The market risk premium is 5%, the risk-free rate is 6%, and Skye’s beta is 1.516. The firm’s total debt, which is the sum of the company’s short-term debt and long-term debt, equals $1.2 million.

1. a. Calculate the cost of each capital component, that is, the after-tax cost of debt, the cost of preferred stock, the cost of equity from retained earnings, and the cost of newly issued common stock. Use the DCF method to find the cost of common equity.
2. b. Now calculate the cost of common equity from retained earnings, using the CAPM method.
3. c. What is the cost of new common stock based on the CAPM? (Hint: Find the difference between r₁ and r_s as determined by the DCF method, and add that differential to the CAPM value for r_s.)
4. d. If Skye continues to use the same market-value capital structure, what is the firm’s WACC assuming that (1) it uses only retained earnings for equity and (2) if it expands so rapidly that it must issue new common stock?

Summary Introduction

To Determine: The after-tax cost of debt, cost of preferred stock, cost of common equity from retained earnings and cost of common equity from new common stock of Company SC.

Introduction: WACC is abbreviated as weighted average cost of capital, is a equation that computes the average rate of return that an organization requires to acquire to repay its security holders or investors. This computation is utilized to determine if a project is beneficial or in the event that it just repays the expense of subsidizing the project.

Answer to Problem 21SP

The after-tax cost of debt is 7.50%, cost of preferred stock is 11%, cost of common equity from retained earnings is 13.16% and cost of common equity from new common stock is 13.62%.

Explanation of Solution

Determine the after-tax cost of debt

$\begin{array}{c}AftertaxCostofDebt=\left[CostofDebt\left(r_d\right)\times \left(1-TaxRate\left(T\right)\right)\right]\\ =\left[10\%\times \left(1-25\%\right)\right]\\ =\left[10\%\times 75\%\right]\\ =7.50\%\end{array}$

Therefore the after-tax cost of debt is 7.50%.

Determine the cost of preferred stock

$\begin{array}{c}Costof\mathrm{Pr}eferredStock\left(r_P\right)=\left[\frac{\mathrm{Pr}eferredDividends\left(D_P\right)}{Costof\mathrm{Preferred}Stock}\right]\\ =\left[\frac{\$3.30}{\$30}\right]\\ =11\%\end{array}$

Therefore the cost of preferred stock is 11%.

Determine the cost of common equity from retained earnings

$\begin{array}{c}Costof\mathrm{Re}tainedEquity\left(r_s\right)=\left[\left(\frac{D_0\left(1+g\right)}{\left(P_0\right)}\right)+g\right]\\ =\left[\left(\frac{\$2.10\times \left(1+9\%\right)}{\$55}\right)+9\%\right]\\ =\left[0.04161+0.09\right]\\ =0.13161or13.16\%\end{array}$

Here,

D₀ - Current dividend

g - Growth rate

P₀ - Current price of bond

Therefore the cost of common equity from retained earnings is 13.16%.

Determine the cost of common equity from new common stock based on DCF

$\begin{array}{c}CostofCommonEquity\left(r_e\right)=\left[\left(\frac{D_0\times \left(1+g\right)}{P_0\times \left(1-F\right)}\right)+g\right]\\ =\left[\left(\frac{\$2.10\times \left(1+9\%\right)}{\$55\times \left(1-10\%\right)}\right)+9\%\right]\\ =\left[\left(\frac{\$2.289}{\$49.50}\right)+9\%\right]\\ =\left[0.046242+0.09\right]\\ =0.136242or13.62\%\end{array}$

Here,

D₀ - Current dividend

g - Growth rate

P₀ - Current price of bond

F - Flotation cost

Therefore the cost of common equity from new common stock based on DCF is 13.62%.

Summary Introduction

To Determine: The cost of common equity from retained earnings of Company SC utilising CAPM method.

Answer to Problem 21SP

The cost of common equity from retained earnings of Company SC utilising CAPM method is 13.58%.

Explanation of Solution

Determine the cost of common equity from retained earnings using CAPM

$\begin{array}{c}Costof\mathrm{Re}tainedEquity\left(r_s\right)=\left[r_F+\beta \times r_M\right]\\ =\left[6\%+1.516\times 5\%\right]\\ =\left[0.06+0.0758\right]\\ =0.1358or13.58\%\end{array}$

Here,

r_F - Risk free rate

r_M - Market risk premium

B - Beta of stock

Therefore the cost of common equity from retained earnings using CAPM is 13.58%.

Summary Introduction

To Determine: The cost of new common equity based on CAPM.

Answer to Problem 21SP

The cost of new common equity based on CAPM is 14.04%.

Explanation of Solution

Determine the difference between the cost of common equity from retained earnings and cost of common equity from new common stock

$\begin{array}{c}Difference=\left[\begin{array}{l}CostofCommonEquity\left(r_e\right)\\ -Costof\mathrm{Re}tainedEquity\left(r_s\right)\end{array}\right]\\ =\left[13.62\%-13.16\%\right]\\ =0.46\%\end{array}$

Therefore the difference between the cost of common equity from retained earnings and cost of common equity from new common stock is 0.46%

Determine the cost of new common equity based on CAPM

$\begin{array}{c}CostofNewCommonEquity\left(r_e\right)=\left[Costof\mathrm{Re}tainedEquity\left(r_s\right)+Difference\right]\\ =\left[13.58\%+0.46\%\right]\\ =14.04\%\end{array}$

Therefore the cost of new common equity based on CAPM is 14.04%.

Summary Introduction

To Determine: The WACC if the firm utilises only retained earnings for equity and if the firm expands rapidly in order to issue new common stock.

Answer to Problem 21SP

The WACC if the firm uses only retained earnings for equity and if the firm expands rapidly in order to issue new common stock

Explanation of Solution

Determine the market value of preferred stock

 $\begin{array}{c}MarketValu{e}_{\mathrm{Pr}eferredStock}=\left[\frac{\mathrm{Pr}ic{e}_{\mathrm{Pr}eferredStock}\times SharesOuts\tan ding}{FaceValue}\right]\\ =\left[\frac{\$30\times 10,000}{\$1,000}\right]\\ =\left[\frac{\$300,000}{\$1,000}\right]\\ =\$300\end{array}$

Therefore the market value of preferred stock is $300

Determine the market value of debt

 $\begin{array}{c}MarketValu{e}_{Debt}=\left[LongTermDebt+ShortTermDebt\right]\\ =\left[\$1,100+\$100\right]\\ =\$1,200\end{array}$

Therefore the market value of debt is $1,200

Determine the market value of common stock

$\begin{array}{c}MarketValu{e}_{CommonStock}=\left[\frac{\mathrm{Pr}ic{e}_{CommonStock}\times SharesOuts\tan ding}{FaceValue}\right]\\ =\left[\frac{\$55\times 50,000}{\$1,000}\right]\\ =\left[\frac{\$2,750,000}{\$1,000}\right]\\ =\$2,750\end{array}$

Therefore the market value of common stock is $2,750

Determine the total market value

$\begin{array}{c}TotalMarketValue=\left[\begin{array}{l}MarketValu{e}_{CommonStock}+MarketValu{e}_{Debt}+\\ MarketValu{e}_{\mathrm{Pr}eferredStock}\end{array}\right]\\ =\left[\$2,750+\$1,200+\$300\right]\\ =\$4,250\end{array}$

Therefore the total market value is $4,250

Determine the weight of preferred stock

 $\begin{array}{c}Weigh{t}_{\mathrm{Pr}eferredStock}=\left[\frac{MarketValu{e}_{\mathrm{Pr}eferredStock}}{TotalMarketValue}\right]\\ =\left[\frac{\$300}{\$4,250}\right]\\ =0.07058or7.06\%\end{array}$

Therefore the weight of preferred stock is 7.06%

Determine the weight of debt

 $\begin{array}{c}Weigh{t}_{Debt}=\left[\frac{MarketValu{e}_{Debt}}{TotalMarketValue}\right]\\ =\left[\frac{\$1,200}{\$4,250}\right]\\ =0.28235or28.24\%\end{array}$

Therefore the weight of debt is 28.24%

Determine the weight of common stock

 $\begin{array}{c}Weigh{t}_{CommonStock}=\left[\frac{MarketValu{e}_{CommonStock}}{TotalMarketValue}\right]\\ =\left[\frac{\$2,750}{\$4,250}\right]\\ =0.64705or64.71\%\end{array}$

Therefore the weight of common stock is 64.71%

Determine the WACC if the firm uses only retained earnings for equity

For the rate of common stock, the average of old and new common stock values are considered.

$\begin{array}{c}WACC=\left[\left(w_d\times r_d\times \left(1-T\right)\right)+\left(w_p\times r_p\times \right)+\left(w_e\times r_e\right)\right]\\ =\left[\begin{array}{l}\left(28.24\%\times 10\%\times \left(1-25\%\right)\right)+\left(7.06\%\times 11\%\right)+\\ \left(64.71\%\times \left(\frac{13.16\%+13.58\%}{2}\right)\right)\end{array}\right]\\ =\left[\begin{array}{l}\left(28.24\%\times 7.50\%\right)+\left(7.06\%\times 11\%\right)+\\ \left(64.71\%\times 13.37\%\right)\end{array}\right]\\ =\left[0.02118+0.007766+0.086517\right]\end{array}$

$=0.115463or11.55\%$

Here,

w_d - Weight of debt

r_d - Rate of debt

T - Tax rate

w_p - Weight of preferred stock

r_p - Rate of preferred stock

w_e - Weight of common stock

r_e - Rate of common stock

Therefore the WACC if the firm uses only retained earnings for equity is 11.55%.

Determine the WACC if the firm expands rapidly in order to issue new common stock.

For the rate of common stock, the average of cost of new common equity based on CAPM and the cost of new common equity based on DCF values are considered.

$\begin{array}{c}WACC=\left[\left(w_d\times r_d\times \left(1-T\right)\right)+\left(w_p\times r_p\right)+\left(w_e\times r_e\right)\right]\\ =\left[\begin{array}{l}\left(28.24\%\times 10\%\times \left(1-25\%\right)\right)+\left(7.06\%\times 11\%\right)+\\ \left(64.71\%\times \left(\frac{14.04\%+13.62\%}{2}\right)\right)\end{array}\right]\\ =\left[\begin{array}{l}\left(28.24\%\times 7.50\%\right)+\left(7.06\%\times 11\%\right)+\\ \left(64.71\%\times 13.83\%\right)\end{array}\right]\\ =\left[0.02118+0.007766+0.089494\right]\\ =0.11844or11.84\%\end{array}$

Therefore the WACC if the firm expands rapidly in order to issue new common stock is 11.84%.