Question

what is the fair price for the $1000 par value 10-year bond, which was issued 3 years ago and carries coupon rate of 3,50%. coupon is paid semi-annually. investors required rate of return for similar securities is 2,50%

Answer 1

Solution:
	Fair price of the Bond is $1063.85
Working Notes:
	Fair price of the Bond is the present value of all the cash flows during the life Bond.
	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 = 3.50%
	Annual coupon = Face value of bond x Coupon Rate = 1000 x 3.5% = $35
	Semi annual coupon = Annual coupon / 2 = $35/2=$17.50
	YTM= 2.50% p.a (annual)   is investors required rate of returns
	Semi annual YTM= 2.5%/2 = 1.25%
	Bond life is 10 years but issued 3 years ago , means remaining life is 7 years only
	n= no.of coupon = No. Of years x no. Of coupon in a year
	= 7 x 2 =14
	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
	= $17.50 x Cumulative PVF @ 1.25% for 1 to 14th + PVF @ 1.25% for 14th period x 1,000
	= 17.50 x 12.77055275+ 1000 x 0.840368091
	=1063.852764
	=$1,063.85
	Cumulative PVF @ 1.25 % for 1 to 14th is calculated = (1 - (1/(1 + 0.0125)^14) ) /0.0125 = 12.77055275
	PVF @ 1.25% for 14th period is calculated by = 1/(1+i)^n = 1/(1.0125)^14 =0.840368091
Please feel free to ask if anything about above solution in comment section of the question.