Question

A bond you are evaluating has a 6.5 percent coupon rate (compounded semiannually), a $1,000 face value, and is 10 years from maturity. (LG 3-4)

a. If the required rate of return on the bond is 6 percent, what is its fair present value?

b. If the required rate of return on the bond is 8 percent, what is its fair present value?

c. What do your answers to parts (a) and (b) say about the relation between required rates of return and fair values of bonds?

Answer 1

a)

Semi annual coupon = (6.5% of 1000) / 2 = 32.5

Number of periods = 10 * 2 = 20

Semi annual rate = 6% / 2 = 3%

Fair present value = Coupon * [1 - 1 / (1 + r)^n] / r + FV / (1 + r)^n

Fair present value = 32.5 * [1 - 1 / (1 + 0.03)^20] / 0.03 + 1000 / (1 + 0.03)^20

Fair present value = 32.5 * [1 - 0.553676] / 0.03 + 553.675754

Fair present value = 32.5 * 14.877475 + 553.675754

Fair present value = $1,037.19

b)

Semi annual coupon = (6.5% of 1000) / 2 = 32.5

Number of periods = 10 * 2 = 20

Semi annual rate = 8% / 2 = 4%

Fair present value = Coupon * [1 - 1 / (1 + r)^n] / r + FV / (1 + r)^n

Fair present value = 32.5 * [1 - 1 / (1 + 0.04)^20] / 0.04 + 1000 / (1 + 0.04)^20

Fair present value = 32.5 * [1 - 0.456387] / 0.04 + 456.386946

Fair present value = 32.5 * 13.590326 + 456.386946

Fair present value = $898.07

c)

There is an inverse relationship between required rate and fair value of bond. The price will decrease when interest rates increase.