Question

​(Bond valuation​) You own a bond that pays ​$100 in annual​ interest, with a ​$1,000 par value. It matures in 20 years. Your required rate of return is 12 percent.

a. Calculate the value of the bond.

b. How does the value change if your required rate of return​ (1) increases to 14 percent or​ (2) decreases to 7 ​percent?

c. Explain the implications of your answers in part ​(b​) as they relate to interest rate​ risk, premium​ bonds, and discount bonds.

d. Assume that the bond matures in 4 years instead of 20 years. Recompute your answers in part ​(b​).

e. Explain the implications of your answers in part ​(d​) as they relate to interest rate​ risk, premium​ bonds, and discount bonds.

Answer 1

Coupon =100
Par value =1000
Required rate =12%
a. Value of the bond = PV of Coupons + PV of Par Value =100*(1-(1+12%)^-20)/12% +1000/(1+12%)^20 =850.61

b. At rate of 14%
Value of the bond = PV of Coupons + PV of Par Value =100*(1-(1+14%)^-20)/14%+1000/(1+14%)^20 =735.07
Change in value of bond =(735.07-850.61)/850.61=-13.58%
At Rate of 7%
Value of the bond = PV of Coupons + PV of Par Value =100*(1-(1+7%)^-20)/7%+1000/(1+7%)^20 =1317.82
Change in value of bond =(1317.82-850.61)/850.61=54.93%

c. If discount rate is higher than required rate then we get discount bonds and if it is lower then required rate we get premium bonds.

d.Value of the bond = PV of Coupons + PV of Par Value =100*(1-(1+12%)^-4)/12% +1000/(1+12%)^4 =939.25

At rate of 14%
Value of the bond = PV of Coupons + PV of Par Value =100*(1-(1+14%)^-4)/14%+1000/(1+14%)^4 =883.45
Change in value of bond =(883.45-939.25)/939.25=-5.94%
At Rate of 7%
Value of the bond = PV of Coupons + PV of Par Value =100*(1-(1+7%)^-4)/7%+1000/(1+7%)^4=1101.62
Change in value of bond =(1101.62-939.25)/939.25=17.29%

e) Lower the maturity lower is the decrease in price with change in required rate. It is a discount bond
Higher the maturity higher is the increase in price with change in required rate.It is a premium bond.