(Interest-rate risk) Philadelphia Electric has many bonds trading on the New Yor
ID: 2673108 • Letter: #
Question
(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?
Explanation / Answer
a. 1. CALC: n = 1 x 2 = 2 r = 8% / 2 = 4% PV = ? PMT = 9.125% x 1000 / 2 = $45.625 FV = $1000 PV = -$1,010.61 2. CALC: n = 7 x 2 = 14 r = 8% / 2 = 4% PV = ? PMT = 9.125% x 1000 / 2 = $45.625 FV = $1000 PV = -$1,059.42 3. CALC: n = 15 x 2 = 30 r = 8% / 2 = 4% PV = ? PMT = 9.125% x 1000 / 2 = $45.625 FV = $1000 PV = -$1,097.27 Neo b. 1. CALC: n = 1 x 2 = 2 r = 7% / 2 = 3.5% PV = ? PMT = 9.125% x 1000 / 2 = $45.625 FV = $1000 PV = -$1,020.18 2. CALC: n = 7 x 2 = 14 r = 7% / 2 = 3.5% PV = ? PMT = 9.125% x 1000 / 2 = $45.625 FV = $1000 PV = -$1,116.03 3. CALC: n = 15 x 2 = 30 r = 7% / 2 = 3.5% PV = ? PMT = 9.125% x 1000 / 2 = $45.625 FV = $1000 PV = -$1,195.42 c. 1. CALC: n = 1 x 2 = 2 r = 9% / 2 = 4.5% PV = ? PMT = 9.125% x 1000 / 2 = $45.625 FV = $1000 PV = -$1,001.17 Eon 2. CALC: n = 7 x 2 = 14 r = 9% / 2 = 4.5% PV = ? PMT = 9.125% x 1000 / 2 = $45.625 FV = $1000 PV = -$1,006.39 3. CALC: n = 15 x 2 = 30 r = 9% / 2 = 4.5% PV = ? PMT = 9.125% x 1000 / 2 = $45.625 FV = $1000 PV = -$1,010.18 d. Interest rate risk varies directly with maturity. The longer maturity bonds have higher price changes when interest rates change.
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