Question

(Related to Checkpoint​ 9.3)  ​(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 11.5 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 12.5 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 an A rating will be ​$

​ (Round to the nearest​ cent.)

Answer 1

Solution:
a.	The price of the Pybus bonds if they receive a AA rating will be ​$	963.02
b.	The price of the Pybus bonds if they receive an A rating will be ​$	895.28
Working Notes:
a.	The price of the Pybus bonds if they receive a AA rating		=$963.02
	Bond Price = Periodic Coupon Payments x Cumulative PVF @ periodic YTM (for t= to t=n) + PVF for t=n @ periodic YTM x Face value of Bond
	Coupon Rate = 11%
	Annual coupon = Face value of bond x Coupon Rate = 1,000 x 11 % = $110
	Semi annual coupon = Annual coupon / 2 = $110/2=$55
	YTM= 11.5% p.a (annual)
	Semi annual YTM= 11.5%/2 = 5.75%
	n= no.of coupon = No. Of years x no. Of coupon in a year
	= 17 x 2 = 34
	Bond Price = Periodic Coupon Payments x Cumulative PVF @ periodic YTM (for t= to t=n) + PVF for t=n @ periodic YTM x Face value of Bond
	= $55 x Cumulative PVF @ 5.75% for 1 to 34th + PVF @ 5.75% for 34th period x 1,000
	= 55 x 14.7923457 + 1000 x 0.149440122
	=$963.0191355
	=$963.02
Cumulative PVF @ 5.75% for 1 to 34th is calculated = (1 - (1/(1 + 0.0575)^34) ) /0.0575 = 14.7923457
PVF @ 5.75% for 34th period is calculated by = 1/(1+i)^n = 1/(1.0575)^34 =0.149440122
b.	The price of the Pybus bonds if they receive a A rating		=$895.28
	Bond Price = Periodic Coupon Payments x Cumulative PVF @ periodic YTM (for t= to t=n) + PVF for t=n @ periodic YTM x Face value of Bond
	Coupon Rate = 11%
	Annual coupon = Face value of bond x Coupon Rate = 1,000 x 11 % = $110
	Semi annual coupon = Annual coupon / 2 = $110/2=$55
	YTM= 12.5% p.a (annual)
	Semi annual YTM= 12.5%/2 = 6.25%
	n= no.of coupon = No. Of years x no. Of coupon in a year
	= 17 x 2 = 34
	Bond Price = Periodic Coupon Payments x Cumulative PVF @ periodic YTM (for t= to t=n) + PVF for t=n @ periodic YTM x Face value of Bond
	= $55 x Cumulative PVF @ 6.25% for 1 to 34th + PVF @ 6.25% for 34th period x 1,000
	= 55 x 13.96325778 + 1000 x 0.127296389
	=$895.2755669
	=$895.28
Cumulative PVF @ 6.25% for 1 to 34th is calculated = (1 - (1/(1 + 0.0625)^34) ) /0.0625 = 13.96325778
PVF @ 6.25% for 34th period is calculated by = 1/(1+i)^n = 1/(1.0625)^34 =0.127296389
Please feel free to ask if anything about above solution in comment section of the question.