KatyDid Clothes has a $150 million ($1,000 face value) 15-year bond issue selling for 86 percent of par that carries a coupon rate of 8 percent, paid semiannually. What would be KatyDid's before-tax component cost of debt?

To calculate KatyDid Clothes' before-tax component cost of debt, we need to determine the yield to maturity (YTM) of the bond. The YTM represents the bond's annual return if held until maturity, and it is used as the before-tax cost of debt.

Given:
- Face value (par value) of the bond = $1,000
- Current price of the bond = 86% of par = $1,000 × 0.86 = $860
- Coupon rate = 8%
- Coupon payment frequency = Semiannual
- Time to maturity = 15 years

### Steps to Calculate the Before-Tax Cost of Debt:

1. **Determine the Coupon Payment:**
   Since the bond pays interest semiannually, the semiannual coupon payment is:
   \[
   \text{Semiannual Coupon Payment} = \frac{\text{Coupon Rate} \times \text{Face Value}}{2} = \frac{0.08 \times 1000}{2} = 40 \, \text{dollars}
   \]

2. **Determine the Number of Periods:**
   Since the bond has 15 years to maturity and pays semiannually:
   \[
   \text{Number of Periods} = 15 \times 2 = 30 \, \text{semiannual periods}
   \]

3. **Calculate the YTM:**
   The YTM can be found using the following relationship:
   \[
   P = \frac{C}{(1 + r)^1} + \frac{C}{(1 + r)^2} + \dots + \frac{C}{(1 + r)^{n}} + \frac{F}{(1 + r)^{n}}
   \]
   Where:
   - $ P $ = Current price of the bond = $860
   - $ C $ = Semiannual coupon payment = $40
   - $ F $ = Face value of the bond = $1,000
   - $ r $ = Semiannual yield (which needs to be solved)
   - $ n $ = Number of semiannual periods = 30

This is a complex equation that usually requires iterative methods or a financial calculator to solve directly, but it can be approximated using a financial calculator or Excel.

### Solving for $ r $:
Using a financial calculator or Excel’s RATE function:

\[
\text{Semiannual YTM} = \text{RATE}(n = 30, PMT = 40, PV = -860, FV = 1000) \approx 5.08\% \text{ (semiannual)}
\]

To find the annual YTM (which is the before-tax cost of debt):

\[
\text{Annual YTM} = 5.08\% \times 2 = 10.16\%
\]

### Answer:
KatyDid Clothes' before-tax component cost of debt is **10.16%**.

Would you like any further details or have any questions?

Here are some related questions you might find interesting:

1. How does the tax rate affect the after-tax cost of debt?
2. What is the difference between the coupon rate and the yield to maturity?
3. How would an increase in market interest rates affect the price of existing bonds?
4. What factors can influence a company's cost of debt?
5. How does bond maturity affect the cost of debt?

**Tip:** Remember, the cost of debt should be calculated before tax when computing WACC, but the after-tax cost is used when factoring in tax advantages.

Learn how to calculate KatyDid Clothes' before-tax component cost of debt using bond analysis techniques. Includes step-by-step calculations for determining the yield to maturity (YTM) of a bond selling at 86% of par value with an 8% coupon rate paid semiannually over 15 years.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation