Question

Bond X is noncallable and has 20 years to maturity, a 10% annual coupon, and a $1,000 par value. Your required return on Bond X is 12%; if you buy it, you plan to hold it for 5 years. You (and the market) have expectations that in 5 years, the yield to maturity on a 15-year bond with similar risk will be 10%. How much should you be willing to pay for Bond X today? (Hint: You will need to know how much the bond will be worth at the end of 5 years.) Do not round intermediate calculations. Round your answer to the nearest cent.

Answer 1

We need to calculate the price of the bond in 5 years.
Given that the coupon rate =10%
The appropriate discount rate we need to take for our calculations is 10%, and at that point the bond has 15 years to maturity, so the number of periods will be 15.
Let us take the face value of the bond equal to $1000 for our calculations.
Annual coupon payment = Face value* Coupon rate=$1000*10%=$100

The present value is $1000 (calculated in excel)

If we purchase the bond today, we will get an annual coupon of $100 for 5 years, and a sale price of the bond for $1000 (as calculated above by taking 15 years time period, coupon payment of $100 and discount rate of 10%)

At a discount rate of 12% (required return on Bond X), these cash flows will have a present value of $927.90 (calculated in excel)

We should pay an amount of $927.9 for bond X today.