Pybus, Inc. is considering issuing bonds that will mature in 18 years with an annual coupon rate of 11 percent. Their par value will be $1,000, and the interest will be paid semiannually. Pybus is hoping to get a AA rating on its bonds and, if it does, the yield to maturity on similar AA bonds is 8.5 percent. However, Pybus is not sure whether the new bonds will receive a AA rating. If they receive an A rating, the yield to maturity on similar A bonds is 9.5 percent. What will be the price of these bonds if they receive either an A or a AA rating?
A. The price of the Pybus bonds if they receive a AA rating will be ?
.
(Round to the nearest cent.)
1)
Number of periods = 18 * 2 = 36
Semi annual yield = 8.5% / 2 = 4.25%
Semi annual coupon = [(11 / 100) * 1000] / 2 = 55
Price = Coupon * [1 - 1 / (1 + rate)^time] / time + Face value / (1 + rate)^time
Price = 55 * [1 - 1 / (1 + 0.0425)^36] / 0.0425 + 1000 / (1 + 0.0425)^36
Price = 55 * [1 - 0.223492] / 0.0425 + 223.491859
Price = 55 * 18.27078 + 223.491859
Price = $1,228.38
price of the Pybus bonds if they receive a AA rating will be $1,228.38
2)
Number of periods = 18 * 2 = 36
Semi annual yield = 9.5% / 2 = 4.75%
Semi annual coupon = [(11 / 100) * 1000] / 2 = 55
Price = Coupon * [1 - 1 / (1 + rate)^time] / time + Face value / (1 + rate)^time
Price = 55 * [1 - 1 / (1 + 0.0475)^36] / 0.0475 + 1000 / (1 + 0.0475)^36
Price = 55 * [1 - 0.188129] / 0.0475 + 188.128616
Price = 55 * 17.092029 + 188.128616
Price = $1,128.19
price of the Pybus bonds if they receive a A rating will be $1,128.19
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