Question

Consider the following:

Bond A	Bond B
Term to Maturity: 10 years from today	Term to Maturity: 20 years from today
Face Value: $1,000	Face Value: $1,000
Coupon Rate: 10% annual coupons	Coupon Rate: 10% annual coupons
Repayment of Face Value: On last coupon date	Repayment of Face Value: On last coupon date

1) Assume discount rate is 10%. Use the PV function to calculate the prices for these two bonds.

2) Make a Data Table to compare the bond prices when discount rate varies from 1% to 20% incrementing by 1%.

3) Is the longer-term bond's price more sensitive to changes in discount rate? Make a connected scatter chart with both series of bond prices calculated above in the same chart and explain it in a textbox by comparing the slopes.

Answer 1

1)

	Bond A	Bond B
Future Value	$                         1,000.00	$                       1,000.00
Coupon	$                             100.00	$                          100.00
Years to Maturity	10	20
YTM	10%	10%
Excel formula	PV(0.1,10,100,1000)	PV(0.1,20,100,1000)
Price	$                         1,000.00	$                       1,000.00

2)

rate	Price of bond A	Price of Bond B
1%	$                         1,852.42	$                       2,624.10
2%	$                         1,718.61	$                       2,308.11
3%	$                         1,597.11	$                       2,041.42
4%	$                         1,486.65	$                       1,815.42
5%	$                         1,386.09	$                       1,623.11
6%	$                         1,294.40	$                       1,458.80
7%	$                         1,210.71	$                       1,317.82
8%	$                         1,134.20	$                       1,196.36
9%	$                         1,064.18	$                       1,091.29
10%	$                         1,000.00	$                       1,000.00
11%	$                             941.11	$                          920.37
12%	$                             887.00	$                          850.61
13%	$                             837.21	$                          789.26
14%	$                             791.36	$                          735.07
15%	$                             749.06	$                          687.03
16%	$                             710.01	$                          644.27
17%	$                             673.90	$                          606.06
18%	$                             640.47	$                          571.78
19%	$                             609.50	$                          540.92
20%	$                             580.75	$                          513.04

3)

Yes longer term bond ie bond B is more sensitive to price change as the scatter plot has more slope. More the slope it means there is more pirce sensitivity as there is a greater price range