(Interest-rate risk) Philadelphia Electric has many bonds trading on the New Yor
ID: 2663378 • 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 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
Coupon Rate 9.13% Face value Assumed $1000 Coupon value 91.3 a. Yield to Maturity 8% Year Coupon Value 8% P.V.Factor Present value of interest 1 91.25 0.926 84.498 2 91.25 0.857 78.201 3 91.25 0.794 72.453 4 91.25 0.735 67.069 5 91.25 0.681 62.141 6 91.25 0.63 57.488 7 91.25 0.583 53.199 8 91.25 0.54 49.275 9 91.25 0.5 45.625 10 91.25 0.463 42.249 11 91.25 0.429 39.146 12 91.25 0.397 36.226 13 91.25 0.368 33.580 15 91.25 0.34 31.025 15 91.25 0.315 28.744 Year Face Value 8% P.V. Factor Present Value of Face value 1 1000 0.926 926 7 1000 0.583 583 15 1000 0.315 315 Year P.V. of Interest P.V. of Face Value Fair Value of bond 1 84.498 926 1010.498 7 475.048 583 1058.0475 15 780.918 315 1095.9175 b. Yield to Maturity 9% Year Coupon Value 9%P.V.Factor P.V.of Interest 1 91.25 0.917 83.676 2 91.25 0.842 76.833 3 91.25 0.772 70.445 4 91.25 0.708 64.605 5 91.25 0.65 59.313 6 91.25 0.596 54.385 7 91.25 0.547 49.914 8 91.25 0.502 45.808 9 91.25 0.46 41.975 10 91.25 0.422 38.508 11 91.25 0.388 35.405 12 91.25 0.356 32.485 13 91.25 0.326 29.748 15 91.25 0.299 27.284 15 91.25 0.275 25.094 Year Face Value 9% P.V. Factor Present Value of Face value 1 1000 0.917 917 7 1000 0.547 547 15 1000 0.275 275 Year P.V. of Interest P.V. of Face Value Fair Value of bond 1 83.676 926 1009.676 7 459.170 547 1006.17 15 735.475 275 1010.475 c. Yield to Maturity 7% Year Coupon Value 7% p.v. Factor P.V.of Interest 1 91.25 0.935 85.319 2 91.25 0.873 79.661 3 91.25 0.816 74.460 4 91.25 0.763 69.624 5 91.25 0.713 65.061 6 91.25 0.666 60.773 7 91.25 0.623 56.849 8 91.25 0.582 53.108 9 91.25 0.544 49.640 10 91.25 0.508 46.355 11 91.25 0.475 43.344 12 91.25 0.444 40.515 13 91.25 0.415 37.869 15 91.25 0.388 35.405 15 91.25 0.362 33.033 831.014 Year Face Value P.v factor Present value of face value 1 1000 0.935 935 7 1000 0.623 623 15 1000 0.362 362 Year P.V. of Interest Present value of face value Fair value of bond 1 85.319 935 1020.319 7 491.746 623 1114.746 15 831.014 362 1193.014 d. Fair value of bond year Yield 7% Yield 8% Yield 9% 1 1020.32 1010.50 1009.68 7 1114.75 1058.05 1006.17 15 1193.01 1095.92 1010.48 The value of bond depends upon interest rate.There is inverse realationship between the value of bond and the interest rate. The value of bond will decline when the depends interest rate risesand vice-versa.The value of 1, 7 and 15 year bonds comes down as interest is assumed to rise from 7% to 8% to 9%, resultinf loss to bondholders.Interest rates have tendency of rising and falling in practice.Thus, Investors investing their funds in bonds exposed to risk from increasing or falling interest rates.The intensity of interest risk would be higher on bonds with longer maturities than those in short periods. The value of long term bond will fluctuate more when rates fall below 7%.The differential value response to interest rates changes between short and long term bonds will always true. Thus, two bonds of same quality (in terms of the risk of default)would have different exposure to interest rate risk--the one with longer maturity is exposed to greater degree of risk from increasing interest rates.
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