Question

Wolfpack Enterprises plans to issue $1,000,000, 5-year, bonds payable with a stated
interest rate of 12%. The bonds pay interest semi-annually and the market rate is 10%.
What amount of money can Wolfpack Enterprises expect to receive when they sell their bonds?

Answer 1

Solution:
	Wolfpack Enterprises expect to receive when they sell their bonds	$             1,077,217.35
		$                   1,077,217	(rounded to nearest dollar)
	[The total market price of the bond issued]
Working Notes:
	market price of the bond issued = $1,077,217.35
	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 = 12%
	Annual coupon = Face value of bond x Coupon Rate = 1,000,000 x 12% = $120,000
	Coupon is paid semi annually therefore periodic Coupon payments = Annual Coupon/ No. of coupon in a year = 120,000/2 = $60,000
	YTM= 10% p.a (market interest rate annual)
	YTM = 10%/2 = 5% Semi annual
	n= no. of coupon = No. Of years x no. Of coupon in a year
	= 5 x 2 = 10
	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
	= $60,000 x Cumulative PVF @ 5% for 1 to 10th + PVF @ 5% for 10th period x 1,000,000
	= 60,000 x    7.721734929 + 0.613913254 x 1000,000
	=$1,077,217.35
	=$1,077,217
Cumulative PVF @ 5% for 1 to 10th is calculated = (1 - (1/(1 + 0.05)^10) ) /0.05 = 7.721734929
PVF @ 5% for 10th period is calculated by = 1/(1+i)^n = 1/(1.05)^10 = 0.613913254
Please feel free to ask if anything about above solution in comment section of the question.