Chapter 10, Problem 21SP

CALCULATING THE WACC Here is the condensed 2016 balance sheet for Skye Computer Company (in thousands of dollars):

		2016
Current assets		$2,000
Net fixed assets		3,000
Total assets		$5,000
Accounts payable and accruals		$900
Short-term debt		100
Long-term debt		1,100
Preferred stock (10,000 shares)		250
Common stock (50,000 shares)		1.300
Retained earnings		1,350
Total common equity		52,650
Total liabilities and equity		$5,000

Skye’s earnings per share last year were $3.20. The common stock sells for $55.00, Last year's dividend (Do) 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-tax cost of debt is 10%, and its marginal tax rate is 35%. 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 r_c 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? (2) If it expands so rapidly that it must issue new common stock?

Summary Introduction

To identify: The cost of preferred stock, after tax cost of debt, the cost of equity from retained earnings and the cost of newly issued common stock.

Introduction:

Weighted Average Cost of Capital (WACC):

WACC refers to the average of cost of capital, raised from debt, equity, and preference shares. It represents the weights assigned to the components of cost of capital.

Explanation of Solution

Given information:

Current price is $55.

Last year’s dividend is $2.10.

Growth rate is 9%.

Before tax cost of debt is 10%.

Tax rate is 35%.

Formula to calculate after tax cost of debt,

$\text{After}\text{tax}\text{cost}\text{of}\text{debt}=\text{Before}\text{tax}\text{cost}\text{of}\text{debt}\times \left(100\%-\text{Tax}\text{rate}\right)$

Substitute 10% for before taxcost of debt and 35% for tax rate.

$\begin{array}{c}\text{After}\text{tax}\text{cost}\text{of}\text{debt}=10\%\times \left(100\%-35\%\right)\\ =10\%\times 65\%\\ =6.5\%\end{array}$

Formula to calculate cost of preferred stock,

$\text{Cost}\text{of}\text{preferred}\text{stock}=\frac{\text{Preferred}\text{stock}\text{dividend}}{\text{Current}\text{price}}\times 100$

Substitute $3.30 for preferred stock dividend and $30 for current price.

$\begin{array}{c}\text{Cost}\text{of}\text{preferred}\text{stock}=\frac{\$3.30}{\$30}\times 100\\ =11\%\end{array}$

Using DCF (discounted cash flow) method,

Formula to calculate cost of equity,

$\text{Cost}\text{of}{\text{equity (r}}_{\text{e}}\text{)}=\frac{\text{Dividend}}{\text{Current}\text{price}}\times 100+\text{Growth}\text{rate}$

Substitute $2.10 for dividend and $55 for current price and 9% for growth rate.

$\begin{array}{c}\text{Cost}\text{of}\text{equity}=\frac{\$2.10}{\$55}\times 100+9\%\\ =3.82\%+9\%\\ =12.82\%\end{array}$

Formula to calculate cost of newly issued common stock,

$\text{Cost}\text{of}\text{newly}\text{issued}{\text{equity (r}}_{\text{s}}\text{)}=\frac{\text{Dividend}}{\text{Current}\text{price}\left(1-\text{Flotation}\text{cost}\right)}+\text{Growth}\text{rate}$

Substitute $2.10 for dividend and $55 for current price, 0.1 for flotation cost and 9% for growth rate.

$\begin{array}{c}\text{Cost}\text{of}\text{newly}\text{issued}\text{equity}=\frac{\$2.10}{\$55\left(1-0.10\right)}\times 100+9\%\\ =\frac{\$2.10}{\$49.50}\times 100+9\%\\ =4.24\%+9\%\\ =13.24\%\end{array}$

Conclusion

Thus, the after tax cost of debt is 6.5%, the cost of preferred stockis 11%, the cost of equity from retained earningsis 12.82% and the cost of newly issued common stock is 13.24%.

Summary Introduction

To identify: The common equity cost from retained earnings using CAPM method.

Explanation of Solution

Using CAPM method,

Formula to calculate cost of retained earnings,

${\text{k}}_{\text{s}}={\text{r}}_{\text{f}}+\text{b}\left({\text{r}}_{\text{m}}-{\text{r}}_{\text{f}}\right)$

Where,

• k_sis the cost of retained earnings.
• r_f is risk free rate of return.
• r_m is market risk premium.
• b_i is the beta of the company.

Substitute 0.06 for r_f, 1.516 for b_i and 0.05 for r_m.

$\begin{array}{c}{\text{k}}_{\text{s}}=0.06+1.516\left(0.05-0.06\right)\\ =0.06-0.01516\\ =0.04484\text{or}4.48\%\end{array}$

Conclusion

Thus, the common equity’s cost from retained earnings using CAPM method is 4.48%.

Summary Introduction

To identify: The new common stock’s cost based on the CAPM method.

Explanation of Solution

Formula to calculate cost of new common stock based on the CAPM method,

$\text{Cost}\text{of}\text{new}\text{common}\text{stock}={\text{r}}_{\text{s}}-{\text{r}}_{\text{e}}+{\text{k}}_{\text{s}}$

Where,

k_sis the cost of retained earnings.

r_s is cost of newly issued common stock (using DCF method).

r_e iscost of equity.

Substitute 12.82 % for r_e, 13.24% for r_s and 4.48% for k_s.

$\begin{array}{c}\text{Cost}\text{of}\text{new}\text{common}\text{stock}=13.24\%-12.82\%+4.48\%\\ =0.42\%+4.48\%\\ =4.9\%\end{array}$

Conclusion

Thus, the cost of new common stock based on the CAPM method is 4.9%.

Summary Introduction

To identify: The WACC when (1) firm utilises only retained earnings for equity and (2) firm expands so rapidly that it must issue new common stock.

Explanation of Solution

Debt is $1,200,000.

Equity is $1,300,000.

Preferred stock is $250,000.

Retained earnings are $1,350,000.

Formula to calculate weight of equity,

$\text{Weight}\text{of}\text{equity}=\frac{\text{Equity}}{\text{Equity}+\text{Debt}+\text{Preference}\text{share}+\text{Retained}\text{earnings}}$

Substitute $1,300,000 for equity, $1,200,000 for debt, $250,000 for preference shares and $1,350,000 for retained earnings.

$\begin{array}{c}\text{Weight}\text{of}\text{equity}=\frac{\$1,300,000}{\$1,300,000+\$1,200,000+\$250,000+\$1,350,000}\\ =\frac{\$1,300,000}{\$4,100,000}\\ =0.32\end{array}$

Formula to calculate weight of debt,

$\text{Weight}\text{of}\text{debt}=\frac{\text{Debt}}{\text{Equity}+\text{Debt}+\text{Preference}\text{share}+\text{Retained}\text{earnings}}$

Substitute $1,300,000 for equity, $1,200,000 for debt, $250,000 for preference shares and $1,350,000 for retained earnings.

$\begin{array}{c}\text{Weight}\text{of}\text{debt}=\frac{\$1,200,000}{\$1,300,000+\$1,200,000+\$250,000+\$1,350,000}\\ =\frac{\$1,200,000}{\$4,100,000}\\ =0.29\end{array}$

Formula to calculate weight of preference shares,

$\text{Weight}\text{of}\text{preference}\text{share}=\frac{\text{Preference}\text{share}}{\text{Equity}+\text{Debt}+\text{Preference}\text{share}+\text{Retained}\text{earnings}}$

Substitute $1,300,000 for equity, $1,200,000 for debt, $250,000 for preference shares and $1,350,000 for retained earnings.

$\begin{array}{c}\text{Weight}\text{of}\text{preference}\text{share}=\frac{\$250,000}{\$1,300,000+\$1,200,000+\$250,000+\$1,350,000}\\ =\frac{\$250,000}{\$4,100,000}\\ =0.061\end{array}$

Formula to calculate weight of retained earnings,

$\text{Weight}\text{of}\text{retained}\text{earnings}=\frac{\text{Retained}\text{earnings}}{\text{Equity}+\text{Debt}+\text{Preference}\text{share}+\text{Retained}\text{earnings}}$

Substitute $1,300,000 for equity, $1,200,000 for debt, $250,000 for preference shares and $1,350,000 for retained earnings.

$\begin{array}{c}\text{Weight}\text{of}\text{retained}\text{earnings}=\frac{\$1,350,000}{\$1,300,000+\$1,200,000+\$250,000+\$1,350,000}\\ =\frac{\$1,350,000}{\$4,100,000}\\ =0.33\end{array}$

Formula to calculate WACC,

$\text{WACC}=\left[\begin{array}{l}\left(\text{Weight}\text{of}\text{equity}\times \text{Cost}\text{of}\text{equity}\right)\\ +\left(\text{Weight}\text{of}\text{preference}\text{shares}\times \text{Cost}\text{of}\text{preference}\text{shares}\right)\\ +\left(\text{Weight}\text{of}\text{retained}\text{earning}\times \text{Cost}\text{of}\text{retained}\text{earning}\right)\\ +\left(\text{Weight}\text{of}\text{debt}\times \text{Cost}\text{of}\text{debt}\times \left(1-\text{Tax}\text{rate}\right)\right)\end{array}\right]$

Substitute 0.32 for weight of equity, 13.24% for cost of equity, 0.29 for weight of debt, 11%for cost of preference share, 0.061 for weight of preference share, 0.33 for weight of retained earnings, 12.82% for cost of retained earnings, 6.50% for cost of debt and 35% tax.

$\begin{array}{c}\text{WACC}=\left[\begin{array}{l}\left(0.32\times 13.24\%\right)+\left(0.061\times 11\%\right)\\ +\left(0.33\times 12.82\%\right)+\left(0.29\times 6.50\%\left(1-35\%\right)\right)\end{array}\right]\\ =\left(0.042\right)+\left(0.00671\right)+\left(0.042\right)+\left(0.01885\times 0.65\right)\\ =0.103\\ =10.3\%\end{array}$

Conclusion

Thus, the WACC is 0.103 or 10.30%.