Question

Pybus, Inc. is considering issuing bonds that will mature in 23 years with an annual coupon rate of 8 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 9.5 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 10.5 percent. What will be the price of these bonds if they receive either an A or a AA​ rating?

Answer 1

Answer : Calculation of Price of Bond in Case it receives AA rating :

Price of Bond = (Coupon * PVAF @ Yied for n years ) + (Par value * PVF @ Yied for nth year)

Coupon = Par Value * Coupon Rate

= 1000 * 8% = 80 / 2 = 40 (Divided by 2 as Coupon paid semiannually)

Yield = 9.5% / 2 = 4.75% Divided by 2 as Coupon paid semiannually)

n is the number of years to maturity i.e 23 * 2 = 46 (Multiplied by 2 as Coupon paid semiannually)

Price of Bond = (40 * PVAF @ 4.75% for 46 years ) + (1000 * PVF @ 4.75% for 46th year)

= (40 * 18.5625077982) + (1000 * 0.11828087927)

= 742.500311928 + 118.28087927

= 860.78

Calculation of Price of Bond in Case it receives A rating :

Price of Bond = (Coupon * PVAF @ Yied for n years ) + (Par value * PVF @ Yied for nth year)

Coupon = Par Value * Coupon Rate

= 1000 * 8% = 80 / 2 = 40 (Divided by 2 as Coupon paid semiannually)

Yield = 10.5% / 2 = 5.25% Divided by 2 as Coupon paid semiannually)

n is the number of years to maturity i.e 23 * 2 = 46 (Multiplied by 2 as Coupon paid semiannually)

Price of Bond = (40 * PVAF @ 5.25% for 46 years ) + (1000 * PVF @ 5.25% for 46th year)

= (40 * 17.237846941) + (1000 * 0.09501303527)

= 689.51387764 + 95.01303527

= 784.53