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# 2010-02-27_122228_Philadelphia - \$45.625 FV = \$1,000 PV...

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Solutions Guide: (Interest-rate risk) Philadelphia Electric has many bonds trading on the New York Stock Exchange. Suppose PhilElÂ’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? a. 1. CALC: n = 1 x 2 = 2 r = 8% / 2 = 4% PV = ? PMT = 9.125% x 1,000 / 2 = \$45.625 FV = \$1,000 PV = -\$1,010.61 2. CALC: n = 7 x 2 = 14 r = 8% / 2 = 4% PV = ? PMT = 9.125% x 1,000 / 2 =

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Unformatted text preview: \$45.625 FV = \$1,000 PV = -\$1,059.42 3. CALC: n = 15 x 2 = 30 r = 8% / 2 = 4% PV = ? PMT = 9.125% x 1,000 / 2 = \$45.625 FV = \$1,000 PV = -\$1,097.27 b. 1. CALC: n = 1 x 2 = 2 r = 7% / 2 = 3.5% PV = ? PMT = 9.125% x 1,000 / 2 = \$45.625 FV = \$1,000 PV = -\$1,020.18 2. CALC: n = 7 x 2 = 14 r = 7% / 2 = 3.5% PV = ? PMT = 9.125% x 1,000 / 2 = \$45.625 FV = \$1,000 PV = -\$1,116.03 3. CALC: n = 15 x 2 = 30 r = 7% / 2 = 3.5% PV = ? PMT = 9.125% x 1,000 / 2 = \$45.625 FV = \$1,000 PV = -\$1,195.42 c. 1. CALC: n = 1 x 2 = 2 r = 9% / 2 = 4.5% PV = ? PMT = 9.125% x 1,000 / 2 = \$45.625 FV = \$1,000 PV = -\$1,001.17 2. CALC: n = 7 x 2 = 14 r = 9% / 2 = 4.5% PV = ? PMT = 9.125% x 1,000 / 2 = \$45.625 FV = \$1,000 PV = -\$1,006.39 3. CALC: n = 15 x 2 = 30 r = 9% / 2 = 4.5% PV = ? PMT = 9.125% x 1,000 / 2 = \$45.625 FV = \$1,000 PV = -\$1,010.18 d. Interest-rate risk varies directly with maturity. The longer maturity of the bonds, the larger the price change is when interest rates change....
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