Question

ABC Co. issued 14-year bonds a year ago at a coupon rate of 7.7%. The bonds make semiannual payments. If the YTM on these bonds is 6.0%, what is the current bond price? (Do not round intermediate calculations. Round the final answer to 2 decimal places. Omit $ sign in your response.)

Answer 1

Solution:
	Current bond price is       1151.95
Working Notes:
	Since the bond was issued a year ago means , it remaining life other word years to maturity will 1 year lesser = 14-1 = 13 years
	Current bond price the present value of all the cash flow during the remaining life of the bond , and these cash flow is discounted by YTM of the bond in other word market interest rate for the bond . And the cash flow in the life of the bond are semi annual coupons and at end of life par value of bond as redemption value.
	Bond Price = Periodic Coupon Payments x Cumulative PVF @ periodic YTM (for t=0 to t=n) + PVF for t=n @ periodic YTM x Face value of Bond
	Coupon Rate = 7.7%
	Annual coupon = Face value of bond x Coupon Rate = 1,000 x 7.7% = $77
	Semi annual coupon = Annual coupon / 2 = $77/2=$38.5
	YTM= 6% p.a (annual)
	Semi annual YTM= 6%/2 = 3%
	n= no.of coupon = No. Of years x no. Of coupon in a year
	= 13 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
	= $38.5 x Cumulative PVF @ 3% for 1 to 26th + PVF @ 3% for 26th period x 1000
	= 38.5 x 17.8768424 + 1,000 x 0.463694727
	=1151.953159
	=$1,151.95
Hence	Current price of the bond is     1151.95
	Price is more than par value of 1000 as coupon rate is higher than YTM of the bond
Cumulative PVF @ 3% for 1 to 26th is calculated = (1 - (1/(1 + 0.03)^26) ) /0.03 =17.87684242
PVF @ 3% for 26th period is calculated by = 1/(1+i)^n = 1/(1.03)^26 =0.46369473
Please feel free to ask if anything about above solution in comment section of the question.