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 9%; 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 9%. 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

Price of the bond = Sum of PV of all the cash inflows

Price of the bond at the end of 5 years = Sum of PV of all the cash inflows from year 6 to year 20

Please refer to the table for the calculations-

Time	Cash Inflows	PV of cash inflows @9% interest rate
6	100	59.6
7	100	54.7
8	100	50.2
9	100	46.0
10	100	42.2
11	100	38.8
12	100	35.6
13	100	32.6
14	100	29.9
15	100	27.5
16	100	25.2
17	100	23.1
18	100	21.2
19	100	19.4
20	1100	196.3
Price at the end of 5 years	702.3

We will be willing to pay $702.3 for Bond X today