Question

Suppose you buy a 30-year, $1,000 par value bond for $975. The coupon rate is 8% and coupon payments are issued annually. You plan to sell the bond in 12 years, at which point you believe the bond's yield to maturity will be 9%. You also forecast a reinvestment rate on the coupons of 7%. What is the annualized compound return on this investment?

		-6.42%
		3.93%
		4.99%
		7.58%
		11.62

Answer 1

Purchase price at t=0			975
Plus All returns from holding the bond at t=12:
Future value of all the annual coupons(compounded at the YTM on the date of purchase)	80*((1+8.23%)^11-1)/8.23%=	1348.09
Future value of all the reinvestments of annual coupons (compounded at the YTM on the date of purchase)	5.6*((1+8.23%)^10-1)/8.23%=	82.02
# Price at the date of selling--given the YTM at t=12 as 9%	(80*(1-1.09^-18)/0.09)+(1000/1.09^18)=	912.44
Total returns from holding the bond			2342.54
Annualized compound return on this investment	(2342.54/975)^(1/12)-1=		7.58%
((Ending Price+All holding period returns-Purchase price)/Purchase price)^(1/n)-1-----n=no.of periods of holding
ANSWER: d.   7.58%

Workings

YTM to find the FV of coupon +reinvestment cash flows , is the YTM at the purchase date

ie.975=(80*(1-(1+r)^-30)/r)+(1000/(1+r)^30))

Solving for, r, we get the effective interest rate or the YTM as

r=8.23%

Reinvestment CFs- $ 80*7%=

5.6

earns & compounds interest for 10 periods

Coupon CFS of $ 80 to be compounded for 11 periods

# Price at the date of selling is----- $ 912.44

PV of remaining(30-12)=18 coupons+PV of Face value, 1000 to be recd. At maturity----both discounted at the YTM as at end yr. 12, ie. Given as 9%