Question

Bond value and timelong-Changing required returns  

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 7 years to​ maturity, and bond B has 17 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

Price of Bond A

a. par value of Bond A =1000
Coupon = 12%*1000 = 120
Number of Periods =7

PV of Bond at 9% YTM = 100*(1-(1+9%)^-7)/9%+1000/(1+9%)^7=1150.99
PV of Bond at 12% YTM =100*(1-(1+12%)^-7)/12%+1000/(1+12%)^7=1000
PV of Bond at 15% YTM =100*(1-(1+15%)^-7)/15%+1000/(1+15%)^7=875.19

b. par value of Bond B =1000
Coupon = 12%*1000 = 120
Number of Periods =17

1) PV of Bond at 9% YTM = 120*(1-(1+9%)^-17)/9%+1000/(1+9%)^17=1292.90
2) PV of Bond at 12% YTM =120*(1-(1+12%)^-17)/12%+1000/(1+12%)^17=1000
3) PV of Bond at 15% YTM =120*(1-(1+15%)^-17)/15%+1000/(1+15%)^17=818.59

c. Higher the Maturity and higher the YTM lower is the price of bond and vice versa

d. To minimise risk she should purchase Bond A because lower the maturity lower is the interest risk.There is lower interest rate risk in Bond A.