Barry’s Steroids Company has $1,000 par value bonds outstanding at 13 percent interest. The bonds will mature in 40 years.

If the percent yield to maturity is 10 percent, what percent of the total bond value does the repayment of principal represent? Assume interest payments are annual. 

To find what percent of the total bond value the repayment of the principal represents, we need to calculate two things:

1. **The total present value of the bond**, which includes both the present value of the interest payments and the present value of the repayment of the principal.
2. **The present value of the repayment of the principal (par value)**.

Let's go step by step:

### Step 1: Present Value of Interest Payments
The bond pays 13% annual interest on a $1,000 par value, meaning the annual interest payment is:

\[
\text{Interest Payment} = 13\% \times 1000 = 130 \text{ dollars annually}
\]

The present value of these interest payments is calculated using the formula for the present value of an annuity:

\[
PV_{\text{interest}} = C \times \left(1 - (1 + r)^{-n}\right) / r
\]

Where:
- $ C = 130 $ (annual coupon payment)
- $ r = 0.10 $ (yield to maturity as a decimal)
- $ n = 40 $ (number of years)

### Step 2: Present Value of Principal Repayment
The present value of the principal repayment (which is $1,000 at maturity) is calculated using the formula for the present value of a lump sum:

\[
PV_{\text{principal}} = \frac{F}{(1 + r)^n}
\]

Where:
- $ F = 1,000 $ (face value of the bond)
- $ r = 0.10 $
- $ n = 40 $

### Step 3: Total Present Value of the Bond
The total present value of the bond is the sum of the present value of the interest payments and the present value of the principal repayment:

\[
PV_{\text{total}} = PV_{\text{interest}} + PV_{\text{principal}}
\]

### Step 4: Percent of Total Value Represented by Principal Repayment
Finally, the percentage of the total bond value that the repayment of the principal represents is given by:

\[
\text{Percent of Total Bond Value} = \frac{PV_{\text{principal}}}{PV_{\text{total}}} \times 100
\]

Now, I'll calculate these values.Here are the results:

- Present value of interest payments: \$1,271.28
- Present value of the principal repayment: \$22.09
- Total present value of the bond: \$1,293.37
- **Percent of total bond value that the repayment of the principal represents**: 1.71%

This means that the repayment of the principal represents **1.71%** of the total bond value.

Would you like further details on any of these steps or calculations?

Here are five related questions:
1. How does changing the interest rate affect the bond's total value?
2. What happens if the yield to maturity increases to 12%?
3. How is the present value of a bond's coupon payment calculated over different periods?
4. What is the difference between bond price and face value?
5. How does bond maturity affect the proportion of principal in total value?

**Tip:** When yield to maturity is lower than the bond's coupon rate, the bond will be priced higher than its face value (premium bond).

Barry’s Steroids Company has $1,000 par value bonds outstanding at 13 percent interest. The bonds will mature in 40 years. If the percent yield to maturity is 10 percent, what percent of the total bond value does the repayment of principal represent? Assume interest payments are annual.

Explore how to calculate the percentage of the total bond value represented by the repayment of principal for Barry’s Steroids Company bond. Learn about bond valuation, including present value of interest payments and principal repayment, using a detailed solution for a bond with 13% coupon rate and 10% yield to maturity. Suitable for finance students.

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