Question

.You own a bond that pays $120 in annual​ interest with a $1,000 par value. It matures in 20 years. Your required rate of return is 11 percent.

a. Calculate the value of the bond.

b. How does the value change if your required rate of return​ (1) increases to 16 percent or​ (2) decreases to 6 ​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 5 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

Par Value =1000
Number of Periods =20
Required Rate =11%
Annual Interest =120
a. Price of Bond =PV of Coupons +PV of Par Value =120*((1-(1+11%)^-20)/11%)+1000/(1+11%)^20 =1079.63
b.At Required Rate =16%
Price of Bond =PV of Coupons +PV of Par Value =120*((1-(1+16%)^-20)/16%)+1000/(1+16%)^20 =762.85
Price of bond decreases
At required rate =6%
Price of Bond =PV of Coupons +PV of Par Value =120*((1-(1+6%)^-20)/6%)+1000/(1+6%)^20 =1688.20
Price of bond increases
c. Higher the maturity more will be the fluctuation in price during change in YTM due to maturity risk . Change in YTM causes huge change price particularly in premium bonds because of the interest rate risk.In discount bonds the risk increases but i=Price fluctuation less than in case of premium bonds.

d. Number of years =5
Price of Bond =PV of Coupons +PV of Par Value =120*((1-(1+11%)^-5)/11%)+1000/(1+11%)^5 =1036.96
b.At Required Rate =16%
Price of Bond =PV of Coupons +PV of Par Value =120*((1-(1+16%)^-5)/16%)+1000/(1+16%)^5 =869.03
Price of bond decreases
At required rate =6%
Price of Bond =PV of Coupons +PV of Par Value =120*((1-(1+6%)^-5)/6%)+1000/(1+6%)^5=1252.74

e. Lower the maturity in both discount and premium bonds lower is the fluctuations of price due to lower maturity risk.