Question

Suppose you purchase a 10-year, 4% semi-annual coupon bond for 78.681. If the yield remains constant and you reinvest the coupons you receive at that yield, what will be the value of those coupons when the bond matures in 10 years?

Answer 1

1]	The first step is to find the YTM of the bond.
	YTM is that discount rate at which the price
	o the bond of $786.81 equals the PV of the
	cash flows from the bond if it is held till
	maturity.
	The cash flows are:
	*The maturity value of $1,000 receivable at
	EOY 10, and
	*The semi-annual coupons of $20 [for 20
	hal years] which, is an annuity.
	Such a discount rate has to be found out by
	trial and error.
	Discounting with 6% [3% for half year]:
	PV = 1000/1.03^20+20*(1.03^20-1)/(0.03*1.03^20) =	$         851.23
	Discounting with 7% [3.5% for half year]:
	PV = 1000/1.035^20+20*(1.035^20-1)/(0.035*1.035^20) =	$         786.81
	As the PV of the cash flows equal the price
	of the bond at 3.5% semi-annual discount
	rate, the YTM = 3.5%*2 = 7.00%
2]	The FV of the coupons [annuity] = 20*(1.035^20-1)/(0.035) =	$         565.59