Question

Altria has a 7% coupon 25 year bond (par value = 1,000). Assume that coupon payments are semiannual and that the yield-to-maturity is 6.5%. What is the price of this bond?

Answer 1

Solution:
	The price of this bond = $1061.38
Working Notes:
	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 = 7%
	Annual coupon = Face value of bond x Coupon Rate = 1,000 x 7% = $70
	Semi annual coupon = Annual coupon / 2 = $70/2=$35
	YTM= 6.5% p.a (annual)
	Semi annual YTM= 6.5%/2 = 3.25%
	n= no.of coupon = No. Of years x no. Of coupon in a year
	= 25 x 2 =50
	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
	= $35 x Cumulative PVF @ 3.25% for 1 to 50th + PVF @ 3.25% for 50th period x 1,000
	= 35 x 24.55176185 + 1000 x 0.20206774
	=$1061.37940475
	=$1,061.38
Cumulative PVF @ 3.25 % for 1 to 50th is calculated = (1 - (1/(1 + 0.0325)^50) ) /0.0325 = 24.55176185
PVF @ 3.25% for 50th period is calculated by = 1/(1+i)^n = 1/(1.0325)^50 =0.20206774
Please feel free to ask if anything about above solution in comment section of the question.