Part 1Stancorp has a $ 11.3$11.3 million debt issue outstanding, with a 5.8 %5.8% coupon rate. The debt has semi-annual coupons, with the next coupon is due in six months. The debt matures in five years. It is currently priced at 94 %94% of par value.a. What is Stancorp's pre-tax cost of debt? Note: Compute the effective annual return.b. If Stancorp faces a 30 %30% tax rate, what is its after-tax cost of debt? Part 1a. The pre-tax cost of debt is [input]7.3837.383 % per year. (Round to four decimal places.)Part 2b. If Stancorp faces a 30 %30% tax rate, the after-tax cost of debt is [input]enter your response here %. (Round to four decimal places.)

Question

Part 1Stancorp has a $ 11.3$11.3 million debt issue​ outstanding, with a 5.8 %5.8% coupon rate. The debt has​ semi-annual coupons, with the next coupon is due in six months. The debt matures in five years. It is currently priced at 94 %94% of par value.a. What is​ Stancorp's pre-tax cost of​ debt? Note: Compute the effective annual return.b. If Stancorp faces a 30 %30% tax​ rate, what is its​ after-tax cost of​ debt? Part 1a. The​ pre-tax cost of debt is [input]7.3837.383 ​% per year. ​(Round to four decimal​ places.)Part 2b. If Stancorp faces a 30 %30% tax​ rate, the​ after-tax cost of debt is [input]enter your response here ​%. ​(Round to four decimal​ places.)

BlackTom AI · Accepted Answer

Yield to maturity (pre-tax cost of debt) is found by solving the bond present-value equation with semiannual coupons and then converting the semiannual rate to an effective annual rate (EAR).

Relevant concepts:
- Coupon per period = annual coupon rate / 2 = 5.8%/2 = 2.9% of par per half-year (0.029 per $1 of par).
- Number of periods n = 5 years × 2 = 10 semiannual periods.
- Price = 94% of par = 0.94 per $1 of par.
- PV equation: Price = Coupon × [1 − (1 + i)^−n]/i + 1 × (1 + i)^−n, where i is the semiannual yield.
- EAR = (1 + i)^2 − 1. After-tax cost = EAR × (1 − tax rate).

Step-by-step solution and intermediate calculations:
1) Set up PV equation using par = 1:
   0.94 = 0.029 × [1 − (1 + i)^−10]/i + (1 + i)^−10.
2) Solve numerically for the semiannual yield i. Using a financial calculator or iterative solution gives i ≈ 0.03626 (3.6258% per half-year).
3) Convert to effective annual yield:
   EAR = (1 + i)^2 − 1 = (1 + 0.0362576)^2 − 1 ≈ 1.073830 − 1 = 0.073830 → 7.3830% per year.
   (Intermediate: (1.0362576)^2 ≈ 1.073830.)
4) Compute after-tax cost with a 30% tax rate:
   After-tax cost = EAR × (1 − 0.30) = 0.073830 × 0.70 = 0.051681 → 5.1681%.

Why the correct answer is correct:
- The bond’s yield is the internal rate that equates discounted coupon and principal payments to the market price; converting the semiannual rate to an EAR correctly accounts for compounding. Tax deductibility of interest reduces the effective cost by the (1 − tax rate) factor.

Why other approaches are wrong:
- Using the coupon rate (5.8%) or the current yield (annual coupon ÷ price ≈ 6.1702%) ignores time value and capital gain/loss to maturity.
- Doubling the semiannual rate (nominal APR) misses compounding; the question asks for the effective annual return.

Final confirmation:
Pre-tax cost (EAR) = 7.3830% and after-tax cost = 5.1681%, matching the provided answers.

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