Question

Last year Janet purchased a $1,000 face value corporate bond with an 7% annual coupon rate and a 20-year maturity. At the time of the purchase, it had an expected yield to maturity of 6.03%. If Janet sold the bond today for $1,080.57, what rate of return would she have earned for the past year? Do not round intermediate calculations. Round your answer to two decimal places.

Answer 1

Solution:
	Rate of return would she have earned for the past year = 3.56%
Working Notes:
	First of the bond price when she bought is calculated.
	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
	YTM= 6.03% p.a (annual)
	n= no.of coupon = No. Of years x no. Of coupon in a year
	= 20 x 1 = 20
	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
	= $ 70 x Cumulative PVF @6.03% for 1 to 20th + PVF @ 6.03% for 20th period x 1,000
	= 70 x 11.442039 + 1000 x 0.310045028
	=$1,110.98776
	Cumulative PVF @ 6.03 % for 1 to 20th is calculated = (1 - (1/(1 + 0.0603)^20) ) /0.0603 = 11.442039
	PVF @ 6.03% for 20th period is calculated by = 1/(1+i)^n = 1/(1.0603)^20 =0.310045028
Now
	She would have also received annual coupon of $70 that is 7% x$1000=$70
	Selling price of Bond = $1,080.50
	Buying price= $1,110.98776
	Rate of return would she have earned for the past year =( Selling price of Bond + Annual coupon received - Buying price of Bond )/Buying price of bond
		=($1,080.57+$70 - $1,110.98776)/$1,110.98776
		=0.035627971
		=3.56 %
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