Suppose we have a bond issue currently outstanding that has 25 years left to maturity. The coupon rate is 9% and coupons are paid semiannually. The bond is currently selling for $908.72. If the firm's marginal tax rate is 20%. What's the firm's after-tax cost of debt? O 8.0% O 9.0% O 10.0% O 11.0%

Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
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**Problem Statement:**

Suppose we have a bond issue currently outstanding that has 25 years left to maturity. The coupon rate is 9% and coupons are paid semiannually. The bond is currently selling for $908.72. If the firm's marginal tax rate is 20%, what's the firm's after-tax cost of debt?

**Options:**

- 8.0%
- 9.0%
- 10.0%
- 11.0%

**Analysis:**

To find the firm's after-tax cost of debt, calculate the yield to maturity (YTM) first, then adjust for taxes. Here's how you can calculate it:

1. **Yield to Maturity (YTM):** Use the bond pricing formula to find the YTM, considering:
   - Coupon Payment = (Coupon Rate/2) * Face Value (assuming Face Value is $1,000)
   - Number of Periods = Years to Maturity * 2

2. **After-Tax Cost of Debt Formula:**
   \[
   \text{After-Tax Cost of Debt} = \text{YTM} \times (1 - \text{Tax Rate})
   \]

Once you compute the YTM and apply the tax adjustment, compare it with the provided options to find the correct answer.
Transcribed Image Text:**Problem Statement:** Suppose we have a bond issue currently outstanding that has 25 years left to maturity. The coupon rate is 9% and coupons are paid semiannually. The bond is currently selling for $908.72. If the firm's marginal tax rate is 20%, what's the firm's after-tax cost of debt? **Options:** - 8.0% - 9.0% - 10.0% - 11.0% **Analysis:** To find the firm's after-tax cost of debt, calculate the yield to maturity (YTM) first, then adjust for taxes. Here's how you can calculate it: 1. **Yield to Maturity (YTM):** Use the bond pricing formula to find the YTM, considering: - Coupon Payment = (Coupon Rate/2) * Face Value (assuming Face Value is $1,000) - Number of Periods = Years to Maturity * 2 2. **After-Tax Cost of Debt Formula:** \[ \text{After-Tax Cost of Debt} = \text{YTM} \times (1 - \text{Tax Rate}) \] Once you compute the YTM and apply the tax adjustment, compare it with the provided options to find the correct answer.
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