Question

You buy an 8 percent coupon, 10-year maturity bond when its yield to maturity is 9 percent. One year later, the yield to maturity is 10 percent. Assume the face value of the bond is $1,000.

(a) What is the price of the bond today?
(b) What is the price of the bond one year later?
(c) What is your rate of return over the one-year holding period?

Answer 1

Value of the bond is Present value of future cash inflows. So, the value of the bond is calculated by discounting the future cash inflows.

(a) Price of the bond today:

Year	Nature	Amount	PVF@9%	Present value
1-10	Coupon	$ 80	PVAF(9%,10)=6.4176	$513.408
10	Redemption	$1000	PVF(9%,10) =0.4224	$422.4
			Value of the Bond today	$935.808

(b) Price of the bond 1 year later:

Year	Nature	Amount	PVF@10%	Present value
1-9	Coupon	$ 80	PVAF(10%,9)=5.7590	$460.72
9	Redemption	$1000	PVF(10%,9) =0.4241	$424.1
			Value of the Bond after 1 yr	$884.82

(c) Rate of return over 1 yr holding period:

Rate of return = coupon received + (Sale price - purchase price) / Bond purchase price

= ($80 + ($884.82 - $935.808)) /$935.808

= ($80 - $50.98) / $935.808

= $29.02 / $935.808

=0.03101 (or) 3.101%