Question

Pybus, Inc. is considering issuing bonds that will mature in 21 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 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 ​$_. ​ (Round to the nearest​ cent.)

b. The price of the Pybus bonds if they receive a A rating will be ​$_. ​ (Round to the nearest​ cent.)

Answer 1

a. $1042.08

b. $961.20

Explanation

The formula to find bond price when interest is paid semi-annually is:

where C is the coupon payment i.e. Annual Coupon Rate * Face Value = 0.11* 1000 = 110

r is rate of return or YTM i.e. 10.5 or 11.5%

F is redemption value i.e. $1000

t is the time period i.e. 21 years

Case: 1

When thé bond receives AA rating i.e. YTM = 10.5%. Plugging in the figures, we get

B₀ = 110/2 [(1- (1+ 0.105/2)^-2*21)/0.105/2] + 1000/(1+0.105/2)^2*21

B₀ = 55 [(1- (1.0525)^-42)/0.0525] + 1000/(1.0525)⁴²

Using calculator we get the value of 1.0525⁴² and 1.0525^-42, we get

B₀ = 55 [(1- 0.1166)/0.0525] + 1000/8.577

B₀ = 55[0.8834/0.0525] + 116.591

B₀ = 55*16.827 + 116.591 = 925.485 + 116.591 = 1042.076

So, the price of bond if they receive AA rating is $1042.08

Case 2:

If the bonds get A rating i.e. YTM = 11.5%. Plugging in the figures, we get

B₁ = 110/2 [(1- (1+ 0.115/2)^-2*21)/0.115/2] + 1000/(1+0.115/2)^2*21

B₁ = 55 [(1- (1.0575)^-42)/0.0575] + 1000/(1.0575)⁴²

Using calculator we get the value of 1.0575⁴² and 1.0575^-42, we get

B₁ = 55 [(1- 0.095)/0.0575] + 1000/10.466

B₁ = 55 [0.905/0.0575] + 95.55

B₁ = 55* 15.739 + 95.55

B₁ = 865.645 + 95.55

B₁ = $961.195

So, the bond price when it receives A rating is $961.20.

Please note: Approximations may lead to slight deviation from actual figures.