You are provided the following information on a company. The total market value is $40 million. The capital structure, shown here, is considered to be optimal.
Accounting Value Market Value
Bonds, $1000 par, 6% coupon, 6% YTM $10,000,000 $10,000,000
Preferred Stock, 7%, $100 par, 100,000 shares $10,000,000 $8,000,000
Common Stock, $1 par, 100,000 shares $100,000
Capital in excess of par $400,000 $22,000,000 *
Retained Earnings $13,500,000
* Total market value of common equity
a. What is the after-tax cost of debt? (assume the company’s effective tax rate = 40%)
b. Assuming a $7 dividend paid annually, what is the required return for preferred shareholders (i.e. component cost of preferred stock)? (assume floatation costs = $0.00)
c. Assuming the risk-free rate is 2%, the expected return on the stock market is 9%, and the company's beta is 1.0, what is the required return for common stockholders (i.e., component cost of common stock)?
d. What is the company's weighted average cost of capital (WACC)?
a. To calculate the after-tax cost of debt, we need to find the yield to maturity (YTM). Given that the market value and accounting value of the bonds are the same, we can assume that the YTM is 6%.
The after-tax cost of debt formula is:
After-tax cost of debt = YTM * (1 - Tax Rate)
Using the given information, we can calculate:
After-tax cost of debt = 6% * (1 - 40%)
= 6% * 0.6
= 3.6%
Therefore, the after-tax cost of debt is 3.6%.
b. To calculate the required return for preferred shareholders, we need to use the dividend payment and the market value of preferred stock.
The required return for preferred shareholders is calculated as:
Required return for preferred stock = Dividend / Market Value of Preferred Stock
Using the given information, we can calculate:
Required return for preferred stock = $7 / $8,000,000
= 0.000875
= 0.0875 (or 8.75%)
Therefore, the required return for preferred shareholders is 8.75%.
c. To calculate the required return for common stockholders, we can use the Capital Asset Pricing Model (CAPM) formula:
Required return for common stock = Risk-free rate + Beta * (Market return - Risk-free rate)
Given:
Risk-free rate = 2%
Market return = 9%
Beta = 1.0
Using the CAPM formula, we can calculate:
Required return for common stock = 2% + 1.0 * (9% - 2%)
= 2% + 1.0 * 7%
= 2% + 7%
= 9%
Therefore, the required return for common stockholders is 9%.
d. To calculate the weighted average cost of capital (WACC), we need to calculate the weighted average of the component costs of debt, preferred stock, and common stock.
WACC formula:
WACC = (Weight of debt * Cost of debt) + (Weight of preferred stock * Cost of preferred stock) + (Weight of common stock * Cost of common stock)
Given:
Weight of debt = market value of debt / total market value
Weight of preferred stock = market value of preferred stock / total market value
Weight of common stock = market value of common equity / total market value
Using the given information, we can calculate:
Weight of debt = $10,000,000 / $40,000,000
= 0.25 (or 25%)
Weight of preferred stock = $8,000,000 / $40,000,000
= 0.2 (or 20%)
Weight of common stock = $22,000,000 / $40,000,000
= 0.55 (or 55%)
WACC = (0.25 * 3.6%) + (0.2 * 8.75%) + (0.55 * 9%)
= 0.009 + 0.0175 + 0.0495
= 0.076 (or 7.6%)
Therefore, the company's weighted average cost of capital (WACC) is 7.6%.