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# Interest Rate Risk: Philadelphia Electric

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Philadelphia Electric has many bonds trading on the New York Stock Exchange. Suppose the company'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?

#### Solution Preview

a. If the yield to maturity for all three bonds is 8%, what is the fair price of each bond?

The price of each bond is the present value of interest and principal. The semi annual interest (assuming bonds have semi annual interest) is 1,000 X 9.125%/2 = 45.625. The par value is \$1,000, discounting rate is 8%/2=4% and the periods to maturity are 2,14 and 30 (semi annual). Interest is an annuity and we use the PVIFA table to get the PV factor. For principal which is a lump sum we use the PVIF table

1 year bond
Price = 45.625 X PVIFA (2,4%) + 1,000 X PVIF (2,4%)
=45.525 X 1.8861 + 1,000 X 0.9246
= 86.05+924.56 = \$1,010.61

7 year bond
Price = 45.625 X PVIFA (14,4%) + 1,000 X PVIF (14,4%)
=45.525 X 10.5631+ 1,000 X 0.5775
= ...

#### Solution Summary

This solution provides a 600 word explanation regarding how to calculate the changes in bond prices given a change in interest rates. All calculations which are required are included within the response.

\$2.19