# Interest Rate Risk: Philadelphia Electric

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

...77.50 = \$1,059.44

15 year bond
Price = 45.625 X PVIFA (30,4%) + 1,000 X PVIF (30,4%)
=45.525 X 17.7920 + 1,000 X 0.3083
= 788.95+308.30 = \$1,097.25

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?

The fair price would be the present value of interest and principal now discounted at 7%/2=3.5%
1 year bond
Price = 45.625 X PVIFA (2,3.5%) + 1,000 X PVIF (2,3.5%)
=45.525 X 1.8897 + 1,000 X 0.9335
= 86.67+933.5 = \$1,020.18

7 year bond
Price = 45.625 X PVIFA (14,3.5%) + 1,000 X PVIF (14,3.5%)
=45.525 X 10.9205 + 1,000 X 0.6178
= 498.25+617.8 = \$1,116.03

15 year bond
Price = 45.625 X PVIFA (30,3.5%) + 1,000 X PVIF (30,3.5%)
=45.525 X 18.3920 + 1,000 X 0.3563
= ...