Question

The YTM on a bond is the interest rate you earn on your investment if interest rates don’t change. If you actually sell the bond before it matures, your realized return is known as the holding period yield (HPY).

a.	Suppose that today you buy a bond with an annual coupon rate of 6 percent for $1,080. The bond has 13 years to maturity. What rate of return do you expect to earn on your investment? Assume a par value of $1,000. (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
b-1.	Two years from now, the YTM on your bond has declined by 1 percent, and you decide to sell. What price will your bond sell for? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
b-2.	What is the HPY on your investment? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Answer 1

Solution:
a.	Expected rate of return	5.14%
Working Notes:
	As the bond is paying coupon annually , its Ytm can be calculated by Excel or financial calculator
	No. of period = years to maturity x no. of coupon in a year = 13 x 1 =nper = N = 13
	Face value of bond = FV= $1,000
	Price of the bond = PV = -$1080
	Annual Coupon amount = PMT = coupon rate x face value = 6% x $1,000 =$60
	For calculation YTM by excel
	type above data in below format
	=RATE(N,pmt,PV,FV)
	=RATE(13,60,-1080,1000)
	5.141103748%
	=5.141103748%
	=5.14%
	YTM = Expected rate of return = 5.14%
b-1.	Bond price   $1,161.62
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 = 6 %
	Annual coupon = Face value of bond x Coupon Rate = 1,000 x 6 % = $ 60
	YTM= 5.141103748% - 1% = 4.141103748% p.a (annual) the required rate of return
	n= no.of coupon = No. Of years x no. Of coupon in a year
	= (13 - 2) x 1 = 11
	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 x Cumulative PVF @ 4.141103748% for 1 to 11th + PVF @ 4.141103748% for 11th period x 1,000
	= 60 x 8.694185424 + 1000 x 0.639964762
	=$1,161.61589
	=$1,161.62
Cumulative PVF @ 4.141103748 % for 1 to 11th is calculated = (1 - (1/(1 + 0.04141103748)^11) ) /0.04141103748 = 8.694185424
PVF @   4.141103748% for 11th period is calculated by = 1/(1+i)^n = 1/(1.04141103748)^11 = 0.639964762
b-2.	HPY	9.17%
Working Notes:
Notes:	HPY for 2 years returns is calculated
	As the bond is paying coupon annually , its Ytm can be calculated by Excel or financial calculator
	No. of period = period expired x no. of coupon in a year = 2 x 1 =nper = N = 2
	Face value of bond = FV= $1,161.61589 received at end 2 year
	Price of the bond = PV = -$1080 amount paid before 2 years
	Annual Coupon amount = PMT = coupon rate x face value = 6% x $1,000 =$60
	For calculation YTM by excel
	type above data in below format
	=RATE(N,pmt,PV,FV)
	=RATE(2,60,-1080,1161.61589)
	9.168446025%
	=9.168446025%
	=9.17%
Please feel free to ask if anything about above solution in comment section of the question.