Question

An investor has two bonds in his portfolio that have a face value of $1,000 and pay an 11% annual coupon. Bond L matures in 12 years, while Bond S matures in 1 year.

a. What will the value of each bond be if the going interest rate is 6%, 8%, and 12%? Assume that only one more interest payment is to be made on Bond S at its maturity and that 12 more payments are to be made on Bond L.

Answer 1

The value of each bond can be calculated using the present value formula. At different interest rates, the values of the bonds will vary. Bond L will have a higher value with lower interest rates and a lower value with higher interest rates. Bond S, with a shorter maturity period, will have a lower value compared to Bond L at the same interest rates.

Step-by-step explanation:

To calculate the value of each bond at different interest rates, we can use the present value formula. The formula for the present value of a bond is:

`PV = C/(1+r)^t`

Where PV is the present value, C is the annual coupon payment, r is the interest rate, and t is the number of years until maturity. Let's calculate the value of each bond at an interest rate of 6%, 8%, and 12%:

1. Bond L (12-year maturity) at 6% interest rate:
   
   `PV = $110/(1+0.06)^12 = $713.81`
2. Bond L (12-year maturity) at 8% interest rate:
   
   `PV = $110/(1+0.08)^12 = $583.19`
3. Bond L (12-year maturity) at 12% interest rate:
   
   `PV = $110/(1+0.12)^12 = $383.97`
4. Bond S (1-year maturity) at 6% interest rate:
   
   `PV = $110/(1+0.06)^1 = $103.77`
5. Bond S (1-year maturity) at 8% interest rate:
   
   `PV = $110/(1+0.08)^1 = $101.85`
6. Bond S (1-year maturity) at 12% interest rate:
   
   `PV = $80/(1+0.12)^1 = $71.43`

Therefore, the value of each bond for different interest rates is as follows:

• Bond L: $713.81 (6%), $583.19 (8%), $383.97 (12%)
• Bond S: $103.77 (6%), $101.85 (8%), $71.43 (12%)