Question

1. What is the value of a semi-annual pay 9% coupon bond 2 years from now that was bought in 2019 and matures in 15 years if rates go to 10% in 2 years.

1. 1000
2. 923
3. 928
4. 965

Answer 1

Solution:
	Answer is C. 928
Working Notes:
Notes:	Value of bond is the cash flow during the remaining life of bond , after two year life remain will be 13 YEARS and market rate will be 10% so the cash flows will be discount at this 10% to get bond value( the present value of all cash flows )
	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 = 9%
	[Coupon rate does not change it will remain same]
	Annual coupon = Face value of bond x Coupon Rate = 1,000 x 9% = $90
	Semi annual coupon = Annual coupon / 2 = $90/2=$45
	YTM= 10% p.a (annual)
	Semi annual YTM= 10%/2 = 5%
Notes:	YTM at end of 2nd year becomes 10%
	n= no.of coupon = No. Of years x no. Of coupon in a year
	= (15-2) x 2 = 26
	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
	= $45 x Cumulative PVF @ 5% for 1 to 26th + PVF @ 5% for 26th period x 1,000
	= 45 x 14.3751853 + 1000 x 0.281240735
	=$928.1240735
	=$928
Cumulative PVF @ 5 % for 1 to 26th is calculated = (1 - (1/(1 + 0.05)^26) ) /0.05 = 14.3751853
PVF @ 5% for 26th period is calculated by = 1/(1+i)^n = 1/(1.05)^26 =0.281240735
Please feel free to ask if anything about above solution in comment section of the question.