Asked by Patricia Christian on Jun 23, 2024
Verified
Assume a firm has 20-year, 8% coupon bonds with a current market yield of 10%. With a combined federal and state corporate tax rate of 40%, the firm's after-tax cost of debt is:
A) 3.2%
B) 4.0%
C) 4.8%
D) 6.0%
After-tax Cost
The cost of an investment or expense after deducting the tax advantages, reflecting the actual financial impact on an individual or company.
Coupon Bonds
Bonds that pay the holder a fixed interest rate (the coupon) over a specified period, typically until maturity when the principal, or face value, is repaid.
Market Yield
The rate of return anticipated on a bond if it is held until the maturity date, factoring in its current price, interest payments, and term length.
- Acquire knowledge on how to calculate the debt cost for bonds with varying conditions.
- Apply tax considerations to understand the after-tax cost of debt.
Verified Answer
OA
Osama AhmedJun 24, 2024
Final Answer :
D
Explanation :
First, find the bond's price using the current market yield:
PV = (8/0.08) [1 − 1/(1+0.1)20] + 1000/ (1+0.1)20 = $667.38
Next, calculate the after-tax cost of debt:
Coupon payment = 0.08 * $1000 = $80
After-tax coupon payment = $80 * (1-0.4) = $48
PV of after-tax coupon payments = (48/0.1) [1 - 1/(1+0.1)20] = $443.86
PV of principal repayment = $1000 / (1+0.1)20 = $148.64
Total after-tax cost of debt = ($443.86 + $148.64)/$667.38 = 0.06 or 6.0%
PV = (8/0.08) [1 − 1/(1+0.1)20] + 1000/ (1+0.1)20 = $667.38
Next, calculate the after-tax cost of debt:
Coupon payment = 0.08 * $1000 = $80
After-tax coupon payment = $80 * (1-0.4) = $48
PV of after-tax coupon payments = (48/0.1) [1 - 1/(1+0.1)20] = $443.86
PV of principal repayment = $1000 / (1+0.1)20 = $148.64
Total after-tax cost of debt = ($443.86 + $148.64)/$667.38 = 0.06 or 6.0%
Learning Objectives
- Acquire knowledge on how to calculate the debt cost for bonds with varying conditions.
- Apply tax considerations to understand the after-tax cost of debt.