(Interest-rate risk) Philadelphia Electric has many bonds trading on the New York Stock

Exchange. Suppose PhilEl’s bonds have identical coupon rates of 9.125% but that one issue
matures in 1 year, one in 7 years, and the third in 15 years. Assume that a coupon payment
was made yesterday.
a. If the yield to maturity for all three bonds is 8%, what is the fair price of each bond?
b. Suppose that the yield to maturity for all of these bonds changed instantaneously to 7%.
What is the fair price of each bond now?
c. Suppose that the yield to maturity for all of these bonds changed instantaneously again,
this time to 9%. Now what is the fair price of each bond?
d. Based on the fair prices at the various yields to maturity, is interest-rate risk the same,
higher, or lower for longer- versus shorter-maturity bonds?

To calculate the fair price of each bond, we need to use the bond pricing formula. The formula for calculating the fair price of a bond is:

Fair Price = (Coupon Payment / (1 + Yield to Maturity) ^ Time to Maturity) + (Coupon Payment / (1 + Yield to Maturity) ^ (Time to Maturity - 1)) + ... + (Coupon Payment + Par Value) / (1 + Yield to Maturity) ^ (Time to Maturity)

Where:

- Coupon Payment: The fixed periodic interest payment made by the bond.
- Yield to Maturity: The rate of return an investor would earn if they held the bond until maturity.
- Time to Maturity: The number of periods remaining until the bond matures.
- Par Value: The face value or principal amount of the bond.

Now let's calculate the fair price of each bond based on the given information:

a. If the yield to maturity for all three bonds is 8%:
- Coupon Rate = 9.125%
- Yield to Maturity = 8%

For the bond maturing in 1 year:
- Coupon Payment = (9.125% * Par Value) / 2 (since it pays semi-annually)
- Time to Maturity = 1 year

Using the bond pricing formula, we can calculate the fair price of the bond.

Similarly, we can calculate the fair price for the bonds maturing in 7 years and 15 years.

b. If the yield to maturity for all three bonds changes to 7%:
- Yield to Maturity = 7%

Using the bond pricing formula, calculate the fair price of each bond now.

c. If the yield to maturity for all three bonds changes to 9%:
- Yield to Maturity = 9%

Using the bond pricing formula, calculate the fair price of each bond now.

d. Based on the fair prices at the various yields to maturity, we can compare the prices of the bonds with different maturities. If the prices of longer maturity bonds (15 years) are more sensitive to changes in the yield to maturity compared to shorter maturity bonds (1 year), then interest-rate risk is higher for longer-maturity bonds. If the prices of longer maturity bonds are less sensitive to changes in the yield to maturity compared to shorter-maturity bonds, then interest-rate risk is lower for longer-maturity bonds.