Question

Arizona Public Utilities issued a bond that pays $70 in interest, with a $1000 par value. It matures in 25 years. The market's required yield to maturity on a comparable-risk bond is 8%.

A. Calculate the value of the bond.

B. How does the value change if the market's required yield to maturity on a comparable-risk bond (i)increases to 12 percent or (ii) decreases to 7%?

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 15 years instead of 25 years. REcompute your answers in a and 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 =25
Required Rate =8%
Annual Interest =70
a. Price of Bond =PV of Coupons +PV of Par Value =70*((1-(1+8%)^-25)/8%)+1000/(1+8%)^25 =893.2522

b. At Required Rate =12%
Price of Bond =PV of Coupons +PV of Par Value =70*((1-(1+12%)^-25)/12%)+1000/(1+12%)^25 =607.84
Price of bond decreases
At required rate =7%
Price of Bond =PV of Coupons +PV of Par Value =70*((1-(1+7%)^-25)/7%)+1000/(1+7%)^25 =1000
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 Price fluctuation less than in case of premium bonds.

d. If number of years =15
Price of Bond =PV of Coupons +PV of Par Value =70*((1-(1+8%)^-15)/8%)+1000/(1+8%)^15 =914.41

At Required Rate =12%
Price of Bond =PV of Coupons +PV of Par Value =70*((1-(1+12%)^-15)/12%)+1000/(1+12%)^15 =659.46
Price of bond decreases
At required rate =7%
Price of Bond =PV of Coupons +PV of Par Value =70*((1-(1+7%)^-15)/7%)+1000/(1+7%)^15 =1000
Price of bond increases

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