(individual or component costs of capital) Your firm is considering a new investment proposal and would like to calculate its weighted average cost of capital. To help in this, compute the cost of capital for the firm for the following:
a. A bond that has a $1,000 par value (face value) and a contract or coupon interest rate of 11.6%. The bonds have a current market value of $1,124 and will mature in 10 years. The firms marginal tax rate is 34%.
b. If the firm’s bonds are not frequently traded, how would you go about determining a cost of debt for this company?
c. A new common stock issue that paid a $1.74 divided last year. The par value of the stock is $16, and the firm’s dividends per share have grown at a rate of 8.8% per year. This growth rate is expected to continue into the foreseeable future. The price of this stock is now $27.98.
d. A preferred stock paying a 9.9% dividend on a $112 par value. The preferred shares are currently selling for $145.53.
e. A bond selling to yield 12.4% for the purchaser of the bond. The borrowing firm faces a tax rate of 34%.
To calculate the weighted average cost of capital (WACC), you need to determine the cost of each component of capital: cost of debt, cost of equity, and cost of preferred stock.
a. Cost of Debt:
The cost of debt is the interest rate the firm pays on its debt. In this case, you have a bond with a $1,000 par value, a coupon rate of 11.6%, a market value of $1,124, and a maturity of 10 years. To calculate the cost of debt, you can use the yield to maturity (YTM) formula.
YTM = (Coupon Payment + ((Face Value - Market Value) / Maturity)) / ((Face Value + Market Value) / 2)
First, calculate the annual coupon payment:
Coupon Payment = Par Value * Coupon Rate = $1,000 * 11.6% = $116
Next, calculate the YTM using the given information:
YTM = ($116 + (($1,000 - $1,124) / 10)) / (($1,000 + $1,124) / 2)
b. Cost of Debt for Infrequently Traded Bonds:
If the firm's bonds are not frequently traded, it can be challenging to determine the cost of debt directly from the market. In this case, you can estimate the cost of debt by analyzing similar bonds issued by comparable companies in the same industry. You can look for publicly available data on interest rates or ask for quotes from investment bankers to obtain an estimate of the cost of debt.
c. Cost of Equity:
The cost of equity is the return required by the company's investors. In this case, the firm is issuing new common stock with a dividend of $1.74, a par value of $16, and a current price of $27.98. To calculate the cost of equity, you can use the dividend growth model (also known as the Gordon Growth Model).
Cost of Equity = (Dividends per Share / Current Stock Price) + Dividend Growth Rate
First, calculate the dividend growth rate:
Dividend Growth Rate = 8.8% = 0.088
Next, calculate the cost of equity using the given information:
Cost of Equity = ($1.74 / $27.98) + 0.088
d. Cost of Preferred Stock:
The cost of preferred stock is the dividend rate paid to preferred stockholders. In this case, the preferred stock pays a 9.9% dividend on a $112 par value and is currently selling for $145.53. To calculate the cost of preferred stock, you can use the dividend yield formula.
Cost of Preferred Stock = Annual Dividend / Market Price
First, calculate the annual dividend:
Annual Dividend = $112 * 9.9% = $11.088
Next, calculate the cost of preferred stock using the given information:
Cost of Preferred Stock = $11.088 / $145.53
e. Cost of Capital (WACC):
To calculate the WACC, you need to weight the cost of each component of capital by its proportion in the firm's capital structure. The formula for WACC is:
WACC = (Weight of Debt * Cost of Debt) + (Weight of Equity * Cost of Equity) + (Weight of Preferred Stock * Cost of Preferred Stock)
The weights can be calculated by dividing the market value of each component by the total market value of all components.
For example, if the firm's capital structure is 40% debt, 50% equity, and 10% preferred stock, you would calculate the WACC as follows:
WACC = (0.4 * Cost of Debt) + (0.5 * Cost of Equity) + (0.1 * Cost of Preferred Stock)
Note: The tax rate is incorporated into the cost of debt calculation as interest expenses are tax-deductible.
By following these steps, you can calculate the weighted average cost of capital for the firm.