Question

Bond value and time-Changing required returns Personal Finance Problem Lynn Parsons is considering investing in either of two outstanding bonds. The bonds both have $1,000 par values and 12% coupon interest rates and pay annual interest. Bond A has exactly 10 years to maturity, and bond B has 20 years to maturity a. Calculate the present value of bond A if the required rate of return is: (1) 9%, (2) 12%, and (3) 15%. b. Calculate the present value of bond B if the required rate of return is: (1) 9%, (2) 12%, and (3) 15%. c. From your findings in parts a and b, discuss the relationship between time to maturity and changing required returns. d. If Lynn wanted to minimize interest rate risk, which bond should she purchase? Why?

Answer 1

The present value of bond A and bond B is calculated using different required rates of return. The relationship between time to maturity and changing required returns is discussed. For minimizing interest rate risk, bond B is recommended to be purchased by Lynn.

Step-by-step explanation:

The present value of a bond is calculated by discounting the future cash flows associated with the bond using the required rate of return.

a. To calculate the present value of bond A, we need to discount the future cash flows using the required rate of return:

1. At a required rate of return of 9%, the present value of bond A is $922.75.
2. At a required rate of return of 12%, the present value of bond A is $829.68.
3. At a required rate of return of 15%, the present value of bond A is $743.40.

b. To calculate the present value of bond B, we need to discount the future cash flows using the required rate of return:

1. At a required rate of return of 9%, the present value of bond B is $457.15.
2. At a required rate of return of 12%, the present value of bond B is $423.05.
3. At a required rate of return of 15%, the present value of bond B is $393.52.

c. The relationship between time to maturity and changing required returns can be observed from the calculations. As the time to maturity decreases, the present value of the bond becomes more sensitive to changes in the required rate of return. In other words, the value of the bond fluctuates more when the time to maturity is shorter.

d. To minimize interest rate risk, Lynn should purchase bond B. As it has a longer time to maturity, the present value of bond B is less sensitive to changes in the required rate of return compared to bond A.