Question

A two-year, 8% coupon bond with a face value of $1,000 has a current price of $1,000. Assume that the bond makes annual coupon payments. The term structure of interest rates is flat.

(a) What is the bond’s yield-to-maturity?

(b) Using the concept of duration, find the approximate percentage change in the price of the bond if the yield-to-maturity drops by 1%.

(c) Compared with the coupon bond in this problem, would the price of a two-year, U.S. Treasury STRIP change more or less in response to the change in interest rates? Why?

Answer 1

a) Yield to maturity = 8%

Reason : When current price and value of the bond is same, then yield to maturity rate would be same that of coupon interest.

Hence yield to maturity equals to coupon interest @ 8%

b) Calculation of Macaulay duration:

Year	Cash flows	Present value (P. V.) factor @8%	P. V. Of cash flows	Weight of P. V. Of cash flows	(Weight of P.V. of cash flows * Years
1	$80	0.9259	$74.07	0.0741	0.0741
2	$1080	0.8573	$925.88	0.9259	1.8518
Total			999.95	1	1.9259

Macaulay duration = 1.9259

Now,

If yield to maturity decreases then price of bond decreases and if yield to maturity increases then price of bond increases.

Here, decrease in yield to maturity leads to increase in bond price.

% of change in price of bond = Duration * % change in yield to maturity

% change in price = 1.9259 * 1% = 1.9259% (increase)

c) New bond price after change in yield to maturity = Old price + % change in price (increse)

New bond price = $1000 + 1.9259% = $1019.26

Price of the bond change less but increased due to change in yield to maturity.

As longer period of bond will affect more change due to change in yield than short period of bond. Hence price of the bond changed less due to it's short duration ie. 2 years.