Question

Make sure to show all work.

1. An 8% coupon bond paying interest annually and with 5 years remaining until maturity is selling for $1150 for every $1000 of face value. A) Find its yield to maturity. B) Find the duration of the bond in part A , at its existing yield to maturity. C) Using the duration measure calculated in part B, forecast the percentage change in the bond’s price if its yield rises by 50 basis points (.5%).

Answer 1

A). Using financial calculator, Yield to maturity of the bond can be calculated.

Use follwoing value in financial calculator to compute YTM

FV = 1000

price = -1150

n = 5

PMT = 8% of 1000 = 80

compute for I/Y, we get I/Y = 4.58%

So Yield to maturity of the bond is 4.58%

B). duration is calculated as below

Year	Coupon	discount factor	PV of coupon	weight	duration
1	80	0.9562	76.4995	0.0665	0.0665
2	80	0.9144	73.1521	0.0636	0.1272
3	80	0.8744	69.9512	0.0608	0.1825
4	80	0.8361	66.8904	0.0582	0.2327
5	1080	0.7995	863.5069	0.7509	3.7544
		Price	1150	Duration	4.36

Here, Discount factor = 1/(1+YTM)^year

PV of coupon = coupon * discount factor

weight = PV of coupon/ price of the bond

duration of each coupon = weight *duration

total duration = sum of duration of all coupon = 4.36 years

C). so macaulay duration calculated = 4.36 years

So modified duratio = macaulay duration/(1+YTM) = 4.36/1.0458 = 4.17 years

So, change in price of the bond = -D*P*dr

so when yield rises by 50 basis points, change in price = -4.17 * 1150 * 0.005 = $-23.99

So, new price of the bond = 1150-23.99 = $1126.01

So, percentage change in price (final price-initial price)/initial price = (1126.01-1150)/1150 = -2.09%