A bond that has a $1,000 par value (face value) and a contract or coupon interest rate of 10.5%. The bonds have a current market value of $1123 and will mature in 10 years. The firm's marginal tax rate is 34%.
The cost of capital from this bond debt is _____ %
To calculate the cost of capital from this bond debt, you need to consider the after-tax cost of debt. Here are the steps to calculate it:
Step 1: Calculate the annual interest payment
The annual interest payment can be calculated by multiplying the par value of the bond by the coupon interest rate:
Annual interest payment = $1,000 * 10.5% = $105
Step 2: Calculate the after-tax interest payment
The after-tax interest payment is the interest payment adjusted for taxes. To calculate this, multiply the annual interest payment by (1 - tax rate):
After-tax interest payment = $105 * (1 - 34%) = $105 * 0.66 = $69.3
Step 3: Calculate the after-tax cost of debt
The after-tax cost of debt is the after-tax interest payment divided by the market value of the bond:
After-tax cost of debt = After-tax interest payment / Market value of the bond
After-tax cost of debt = $69.3 / $1,123 = 0.0617
Step 4: Convert the after-tax cost of debt to a percentage
Multiply the after-tax cost of debt by 100 to convert it to a percentage:
Cost of capital from this bond debt = After-tax cost of debt * 100
Cost of capital from this bond debt = 0.0617 * 100 = 6.17%
Therefore, the cost of capital from this bond debt is 6.17%.
To calculate the cost of capital from this bond debt, we need to consider two components: the coupon interest rate and the current market value (or price) of the bond.
1. Compute the annual interest payment:
The coupon interest rate is given as 10.5%. This represents the annual interest payment as a percentage of the bond's face value. Therefore, the annual interest payment would be (10.5/100) * $1,000 = $105.
2. Determine the after-tax interest payment:
The firm's marginal tax rate is provided as 34%, which means the firm receives a tax benefit because they can deduct the interest expense from their taxable income. To calculate the after-tax interest payment, we subtract the tax saving from the annual interest payment.
Tax saving = Tax rate * Interest payment
= 0.34 * $105 = $35.70
After-tax interest payment = Annual interest payment - Tax saving
= $105 - $35.70 = $69.30
3. Calculate the after-tax cost of debt:
The current market value of the bond is given as $1,123. This represents the price at which the bond is currently selling in the market.
After-tax cost of debt = After-tax interest payment / Current market value
= $69.30 / $1,123 ≈ 0.0616
4. Convert to a percentage:
To express the after-tax cost of debt as a percentage, multiply by 100.
After-tax cost of debt = 0.0616 * 100 ≈ 6.16%
So, the cost of capital from this bond debt is approximately 6.16%.