Question

 ​(Bond valuation)  ​Pybus, Inc. is considering issuing bonds that will mature in 17 years with an annual coupon rate of 11 percent. Their par value will be ​$1 comma 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 10.5 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 11.5 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 ​$ nothing. ​ (Round to the nearest​ cent.)

Answer 1

a). Bond's Market Value = PV of Coupon Payment + PV of Maturity Value

= [Periodic Coupon Payment * {(1 - (1 + r)^-n) / r}] + [Face Value / (1 + r)^n]

= [{(11%/2)*$1,000} * {(1 - (1 + 0.105/2)^-(17*2)) / (0.105/2)}] + [$1,000 / {1 + (0.105/2)}^(17*2)]

= [$55 * {0.8244 / 0.0525}] + [$1,000 / 5.6958]

= [$55 * 15.7034] + $175.57

= $863.69 + $175.57 = $1,039.26

b). Bond's Market Value = PV of Coupon Payment + PV of Maturity Value

= [Periodic Coupon Payment * {(1 - (1 + r)^-n) / r}] + [Face Value / (1 + r)^n]

= [{(11%/2)*$1,000} * {(1 - (1 + 0.115/2)^-(17*2)) / (0.115/2)}] + [$1,000 / {1 + (0.115/2)}^(17*2)]

= [$55 * {0.8506 / 0.0575}] + [$1,000 / 6.6916]

= [$55 * 14.7923] + $149.44

= $813.58 + $149.44 = $963.02