A bond that 1,000 par value 11.9 percent interest payment are $59.50 and are paid semiannually. The bond have a current market value of $1,120and will make in 10yrs. The firm marginal tax rate 34 percent. The after tax cost of debt is?
To calculate the after-tax cost of debt, we need to take into consideration the interest payment, the tax rate, and the market value of the bond.
1. First, we calculate the annual interest payment by multiplying the semiannual payment by the number of payments per year:
Annual interest payment = Semiannual payment * 2
Annual interest payment = $59.50 * 2
Annual interest payment = $119
2. Next, we calculate the annual interest expense by multiplying the annual interest payment by the number of years the bond will mature:
Annual interest expense = Annual interest payment * Number of years
Annual interest expense = $119 * 10
Annual interest expense = $1190
3. Then, we calculate the tax shield, which is the tax savings resulting from the interest expense. To calculate the tax shield, we multiply the annual interest expense by the tax rate:
Tax shield = Annual interest expense * Tax rate
Tax shield = $1190 * 0.34
Tax shield = $404.60
4. Finally, we calculate the after-tax cost of debt by subtracting the tax shield from the annual interest payment and dividing it by the market value of the bond:
After-tax cost of debt = (Annual interest payment - Tax shield) / Market value of the bond
After-tax cost of debt = ($119 - $404.60) / $1120
After-tax cost of debt = -$285.60 / $1120
After-tax cost of debt = -0.255
The after-tax cost of debt is -0.255 or -25.5%. Note that a negative cost of debt is unusual, and it may indicate that the company receives more tax benefits from the bond interest expense than the actual interest paid.
To calculate the after-tax cost of debt, we need to follow these steps:
Step 1: Calculate the annual interest payment.
Since the bond pays semiannual interest, we first need to find the semiannual interest payment and then multiply it by the number of semiannual periods in a year.
Given: Par value of the bond = $1,000, Interest payment = $59.50
Semiannual interest payment = $59.50
Annual interest payment = Semiannual interest payment * Number of semiannual periods in a year
= $59.50 * 2
= $119
Step 2: Calculate the before-tax cost of debt.
Given: Current market value of the bond = $1,120, Par value of the bond = $1,000, Time to maturity = 10 years
Before-tax cost of debt = (Annual interest payment) / (Current market value of the bond)
= $119 / $1,120
≈ 0.1063 or 10.63%
Step 3: Calculate the after-tax cost of debt.
Given: Marginal tax rate = 34%
After-tax cost of debt = Before-tax cost of debt * (1 - Marginal tax rate)
= 10.63% * (1 - 0.34)
≈ 0.0701 or 7.01%
Therefore, the after-tax cost of debt is approximately 7.01%.