A bond that has a $1000 par value (face value) and a contract or coupon interest rate of 11.1%. The bonds have a current market value of $1125 and will mature in 10 years. The firms marginal tax rate is 34%. The cost of capital from this bond debt is what percent? (round to two decimal places.)
To calculate the cost of capital from this bond debt, we need to determine the yield to maturity (YTM) of the bond. The YTM represents the annualized rate of return an investor would earn if they hold the bond until maturity.
Given information:
- Par value (face value) = $1000
- Coupon interest rate = 11.1%
- Current market value = $1125
- Time to maturity = 10 years
- Marginal tax rate = 34%
Step 1: Calculate the annual coupon payment.
Coupon payment = Par value * Coupon interest rate
Coupon payment = $1000 * 11.1% = $111
Step 2: Calculate the yield to maturity.
Using financial calculators or software, we find that the YTM is approximately 8.90%.
Step 3: Calculate the after-tax cost of debt.
After-tax cost of debt = YTM * (1 - Marginal tax rate)
After-tax cost of debt = 8.90% * (1 - 34%) = 5.86%
Step 4: Convert the after-tax cost of debt to a percentage.
Cost of debt percent = After-tax cost of debt * 100
Cost of debt percent = 5.86%
Therefore, the cost of capital from this bond debt is approximately 5.86%.
To find the cost of capital from this bond debt, we need to calculate the yield to maturity (YTM) of the bond. The YTM represents the total return anticipated on a bond if it is held until it matures.
To calculate the YTM, we can use the following formula:
YTM = (Annual Interest Payment + ((Face Value - Current Market Value) / Number of Years)) / ((Face Value + Current Market Value) / 2)
Let's calculate the YTM using the given information:
Par Value (Face Value) = $1000
Coupon Interest Rate = 11.1%
Current Market Value = $1125
Number of Years = 10
First, calculate the annual interest payment:
Annual Interest Payment = Par Value * Coupon Interest Rate
Annual Interest Payment = $1000 * 11.1% = $111
Next, calculate the difference between the face value and market value over the number of years:
(Face Value - Current Market Value) / Number of Years = ($1000 - $1125) / 10 = -$12.50
Now, substitute the values into the YTM formula:
YTM = ($111 + -$12.50) / (($1000 + $1125) / 2)
YTM = $98.50 / ($2125 / 2)
YTM = $98.50 / $1062.50
YTM ≈ 0.0928
Next, we need to calculate the after-tax cost of debt. The formula to calculate the after-tax cost of debt is:
After-Tax Cost of Debt = YTM * (1 - Tax Rate)
Given the marginal tax rate of 34%, we can calculate the after-tax cost of debt:
After-Tax Cost of Debt = 0.0928 * (1 - 0.34)
After-Tax Cost of Debt ≈ 0.0611
Finally, to express the cost of debt as a percentage, we can multiply by 100:
Cost of Debt = After-Tax Cost of Debt * 100
Cost of Debt ≈ 6.11%
Therefore, the cost of capital from this bond debt is approximately 6.11%.