A 6% coupon bond has a par value of $1,000 and a yield-to-maturity of 8%. You purchase the bond when it has exactly 14 years remaining until maturity. You hold the bond for 6 months, collect the coupon payment, and then sell the bond immediately. If the bond's yield-to-maturity is 8% when you sell it, what is your percentage return over this 6-month holding period? Enter your answer as a decimal and show 4 decimal places. For example, if your answer is 6.25%, enter .0625.

To calculate the percentage return over the 6-month holding period, we need to follow these steps:

### Step 1: Coupon Payment Received
The bond has a 6% annual coupon rate, and its par value is $1,000. Since coupon payments are typically made semi-annually, you will receive half of the annual coupon in 6 months.

\[
\text{Coupon Payment} = \frac{6\% \times 1,000}{2} = \frac{0.06 \times 1,000}{2} = 30
\]

### Step 2: Initial Price of the Bond
The bond's price when purchased can be found using the present value of its cash flows, which include the present value of future coupon payments and the present value of the par value. Since the yield-to-maturity (YTM) is 8%, this is the discount rate to use.

The bond has 14 years remaining until maturity, which means 28 semi-annual periods. The coupon payment is $30 every 6 months. We need to calculate the present value of the bond using the following formula:

\[
\text{Price} = \sum_{t=1}^{28} \frac{C}{(1 + \frac{r}{2})^t} + \frac{F}{(1 + \frac{r}{2})^{28}}
\]

Where:
- $ C = 30 $ (the semi-annual coupon payment)
- $ r = 8\% $ (the yield-to-maturity)
- $ F = 1,000 $ (the par value)
- $ t = 1, 2, \dots, 28 $ (the number of semi-annual periods)

Let's calculate the price using this formula.

### Step 3: Selling Price of the Bond
Since the yield-to-maturity remains 8% when you sell the bond after 6 months, and there are now 13.5 years (27 semi-annual periods) left, the selling price of the bond will also be the present value of future cash flows using the same discount rate of 8%.

Now let's compute the bond price at both times.The initial price of the bond when you purchased it is approximately $ 833.3694 $ dollars, and the selling price after 6 months is approximately $ 836.7041 $ dollars.

### Step 4: Total Return Over the 6-Month Period
Your return comes from two sources:
1. The coupon payment you received, which is \$30.
2. The change in the bond price, which is $ 836.7041 - 833.3694 = 3.3347 $ dollars.

Thus, your total gain over the 6-month period is:
\[
\text{Total Gain} = 30 + 3.3347 = 33.3347 \, \text{dollars}
\]

### Step 5: Percentage Return
To calculate the percentage return, divide your total gain by the initial bond price:
\[
\text{Percentage Return} = \frac{33.3347}{833.3694} = 0.0400
\]

So, your percentage return over the 6-month holding period is approximately **0.0400**, or **4.00%**.

Would you like further details on this calculation or have any questions?

Here are 5 related questions to consider:
1. How does a change in yield-to-maturity affect bond prices?
2. What is the difference between current yield and yield-to-maturity?
3. How are semi-annual bond payments treated differently from annual payments?
4. What happens to bond prices when interest rates rise?
5. How is the duration of a bond used to measure interest rate risk?

**Tip:** In bond investing, the relationship between bond prices and yields is inverse: when yields rise, bond prices fall, and vice versa.

Learn how to calculate the percentage return on a 6% coupon bond with a par value of $1,000, a yield-to-maturity of 8%, and a 6-month holding period. This problem demonstrates bond valuation, present value of cash flows, and percentage return calculations.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation