(individual or component costs of capital)Compute the cost of the 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 11.7%. The bonds have a current market value of $1,125 and will mature in 10 years. The firms marginal tax rate is 34%.
b. A new common stock issue that paid a $1.76 dividend last year. The firms dividends are expected to continue to grow at 6.2% per year forever. The price of the firm’s common stock is now %27.39.
c. A preferred stock paying 8.6% dividend on a $112 par value.
d. A bond selling to yield 12.4% where the firm’s tax rate is 34%.
To compute the cost of capital for each case, we need to calculate the individual or component costs of capital. These components include the cost of debt, cost of equity, and cost of preferred stock.
a. Cost of Debt:
The cost of debt is obtained using the yield to maturity (YTM) of the bond. The YTM represents the market interest rate on the bond and can be calculated using financial calculators or specialized software. Alternatively, you can use trial-and-error or approximation methods to find the YTM. In this case, the bond is selling at a premium ($1,125 > $1,000), so the YTM will be less than the coupon rate. Once the YTM is determined, we can use it along with the firm's marginal tax rate to get the after-tax cost of debt.
b. Cost of Equity:
The cost of equity is the return required by the shareholders or investors to hold the stock of the company. One common method to estimate the cost of equity is by using the dividend growth model, also known as the Gordon Growth Model. The formula for this model is: Cost of Equity = Dividend / Current Stock Price + Dividend Growth Rate. Using the given information, we can calculate the cost of equity.
c. Cost of Preferred Stock:
The cost of preferred stock is the dividend rate paid divided by the current market price of the stock. In this case, the preferred stock has a fixed dividend rate of 8.6%, so we can directly use this rate to calculate the cost of preferred stock.
d. Since the bond is selling to yield 12.4%, we can use this yield as the before-tax cost of debt. We also need to account for taxes, so we need to calculate the after-tax cost of debt by multiplying the before-tax cost of debt by (1 - tax rate).
By calculating these individual components, we can determine the weighted average cost of capital (WACC) for the firm by taking the weighted sum of the cost of each component using the appropriate weights (proportions of each component in the firm's capital structure).
a. To calculate the cost of capital for the bond, we will use the formula for the after-tax cost of debt:
Cost of Debt = Coupon Interest Rate * (1 - Marginal Tax Rate)
Cost of Debt = 11.7% * (1 - 34%) = 0.117 * 0.66 = 0.07722 or 7.72%
Therefore, the cost of the capital for the bond is 7.72%.
b. To calculate the cost of capital for the common stock, we will use the Dividend Growth Model formula:
Cost of Equity = (Dividends per Share / Stock Price) + Growth Rate
Cost of Equity = ($1.76 / $27.39) + 6.2% = 0.0641 + 0.062 = 0.1261 or 12.61%
Therefore, the cost of the capital for the common stock is 12.61%.
c. The cost of capital for preferred stock is simply the dividend rate, as preferred stockholders are paid dividends before common stockholders. Therefore, the cost of capital for the preferred stock is 8.6%.
d. To calculate the cost of capital for the bond selling to yield 12.4%, we will use the formula for the after-tax cost of debt:
Cost of Debt = Yield to Maturity * (1 - Marginal Tax Rate)
Cost of Debt = 12.4% * (1 - 34%) = 0.124 * 0.66 = 0.08184 or 8.184%
Therefore, the cost of the capital for the bond selling to yield 12.4% is 8.184%.