(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%.
a. To calculate the cost of debt for the bond, we need to determine the after-tax coupon payment and the after-tax market price of the bond.
The after-tax coupon payment can be calculated as:
Coupon payment = Par value * Coupon rate = $1,000 * 11.6% = $116
After-tax coupon payment = Coupon payment * (1 - Marginal tax rate) = $116 * (1 - 0.34) = $76.56
The after-tax market price of the bond is $1,124.
The cost of debt can be calculated using the following formula:
Cost of debt = (After-tax coupon payment + (Par value - Market price) / Number of years to maturity) / (Par value + Market price) / 2
Cost of debt = ($76.56 + ($1,000 - $1,124) / 10) / ($1,000 + $1,124) / 2 = 0.0767 or 7.67%
b. If the firm's bonds are not frequently traded, determining the cost of debt can be challenging. In such cases, an alternative approach is to estimate the yield to maturity (YTM) of similar bonds in the market or use the yield on a bond index that closely matches the characteristics of the firm's bonds.
c. To calculate the cost of equity for the new common stock issue, we can use the dividend growth model. The cost of equity can be calculated using the following formula:
Cost of equity = Dividend per share / Current market price + Dividend growth rate
Cost of equity = $1.74 / $27.98 + 8.8% = 0.0805 or 8.05%
d. The cost of preferred stock can be calculated as the dividend rate divided by the market price of the preferred stock.
Cost of preferred stock = Dividend rate / Market price
Cost of preferred stock = 9.9% / $145.53 = 0.068 or 6.8%
e. To calculate the cost of debt for the bond, we need to adjust the bond yield for taxes.
After-tax yield = Bond yield * (1 - Marginal tax rate) = 12.4% * (1 - 0.34) = 8.184%
The cost of debt can be calculated using the after-tax yield:
Cost of debt = Bond yield * (1 - Marginal tax rate) = 8.184% or 8.18%