Question

Bond value and timelong dash—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 13​% 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)

10​%,

​(2)

13​%,

and​ (3)

16​%.

b.  Calculate the present value of bond B if the required rate of return​ is: (1)

10​%,

​(2)

13​%,

and​ (3)

16​%.

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

Par value of the bonds = $ 1,000

NA = 10 years

NB​​​​​​ = 20 years

Coupon rate = 13% paid annually

Annual coupon value = 1,000 * 0.13 = $ 130

a)

If YTM = 10%

Bond Value = (130 / 1.1) + (130 / 1.12) + (130 / 1.13) + (130 / 1.14​​​​​​​) + (130 / 1.15​​​​) + ......(130 / 1.19​​​​​​​) + (130 + 1000/ 1.110​​​​​​​) = $ 1,184.33

If YTM = 13%

Bond Value = (130 / 1.13) + (130 / 1.132) + (130 / 1.133​​​​​​​) + (130 / 1.134​​​​​​​) + (130 / 1.135​​​​) + ......(130 / 1.139​​​​​​​) + (130 + 1000/ 1.1310​​​​​​​) = $ 1,000

If YTM = 16%

Bond Value = (130 / 1.16) + (130 / 1.162) + (130 / 1.163​​​​​​​) + (130 / 1.164​​​​​​​) + (130 / 1.165​​​​) + ......(130 / 1.169​​​​​​​) + (130 + 1000/ 1.1610​​​​​​​) = $ 855

b)

If YTM = 10%

Bond Value = (130 / 1.1) + (130 / 1.12) + (130 / 1.13​​​​​​​) + (130 / 1.14​​​​​​​) + (130 / 1.15​​​​) + ......(130 / 1.119​​​​​​​) + (130 + 1000/ 1.120​​​​​​​) = $ 1,255.40

If YTM = 13%

Bond Value = (130 / 1.13) + (130 / 1.132) + (130 / 1.133​​​​​​​) + (130 / 1.134​​​​​​​) + (130 / 1.135​​​​) + ......(130 / 1.1319​​​​​​​) + (130 + 1000/ 1.1320​​​​​​​) = $ 1,000

If YTM = 16%

Bond Value = (130 / 1.16) + (130 / 1.162) + (130 / 1.163​​​​​​​) + (130 / 1.164​​​​​​​) + (130 / 1.165​​​​) + ......(130 / 1.1619​​​​​​) + (130 + 1000/ 1.1620​​​​​​​) = $ 822.13

C) As the years to marturity increases, the required rate of return or yield increases.

For the same face value and yield to maturity(YTM), if the years to maturity changes, the present value of the bond also changes.

For same YTM, the bond with more years to maturity will be available at more premium or more discounted price than a bond with less years to maturity.

d) To minimize the interest rate risk, she should purchase Bond A. Because the chances of interest rate fluctuation is often higher when the horizon gets longer. So, if she buys bond B, she will be exposed to a lot of uncertainity due to the longer time horizon. If Bond B offers sufficient maturity premium to compensate for the interest rate risk, then she can also go for it. But in idea situation, Bond A works the best.