Question

compare how short term and long term bond values react differently to same interest rate change. In particular, determine two different maturities for two separate bonds: one short term and the other long term. Also, determine all the other relevant terms shared by these two bonds: the face value, the coupon interest rate together with payment frequency, and the discount rate or market interest rate used. Calculate bond values. Then let the discount rate or market interest rate increase by 1%, and recalculate bond values. Compare the changes of the values of each bond. Which one has a bigger change?  

Answer 1

C= Constant Cash flow

r= rate of interes

t= number of times payment made.

Present value anuity factor is used to calculate the present value of constant cashflows over a period of time. (However all my calculations were made using calculator shortcut)

r = rate of interest

n = year of cash flow

Present value formula is used to identify the present value of payment received in a particular year

Now as per the question:-

Short term bond:-

Bond Maturity Value	1000
Maturity years	6
Coupon rate	10%

Market rate	Interest	Present value anuity factor 6 years	PV of Cash flows (1)	Maturity Cash flows	PV factor 6th year	PV of Maturity Cash flows (2)	Pv of Bond (1+2)	Percentage of Change
12%	$100.00	4.11	$411.00	$1,000.00	0.51	$506.63	$917.63
13%	$100.00	3.99	$399.00	$1,000.00	0.48	$480.32	$879.32	4.18%
14%	$100.00	3.89	$389.00	$1,000.00	0.46	$455.59	$844.59	3.95%
15%	$100.00	3.78	$378.00	$1,000.00	0.43	$432.33	$810.33	4.06%
16%	$100.00	3.68	$368.00	$1,000.00	0.41	$410.44	$778.44	3.93%
17%	$100.00	3.58	$358.00	$1,000.00	0.39	$389.84	$747.84	3.93%

Long term bond :-

Bond Maturity Value	1000
Maturity years	15
Coupon rate	10%

Market rate	Interest	Present value anuity factor 15 years	PV of Cash flows (A)	Maturity Cash flows	PV factor 15th year	PV of Maturity Cash flows	Pv of Bond	Percentage of Change
12%	$100.00	6.81	$681.00	$1,000.00	0.18	$182.70	$863.70
13%	$100.00	6.46	$646.00	$1,000.00	0.16	$159.89	$805.89	6.693%
14%	$100.00	6.14	$614.00	$1,000.00	0.14	$140.10	$754.10	6.427%
15%	$100.00	5.84	$584.00	$1,000.00	0.12	$122.89	$706.89	6.259%
16%	$100.00	5.57	$557.00	$1,000.00	0.11	$107.93	$664.93	5.937%
17%	$100.00	5.32	$532.00	$1,000.00	0.09	$94.89	$626.89	5.721%
18%	$100.00	5.09	$509.00	$1,000.00	0.08	$83.52	$592.52	5.483%
19%	$100.00	4.87	$487.00	$1,000.00	0.07	$73.59	$560.59	5.389%
20%	$100.00	4.67	$467.00	$1,000.00	0.06	$64.91	$531.91	5.116%
21%	$100.00	4.48	$448.00	$1,000.00	0.06	$57.31	$505.31	5.000%
22%	$100.00	4.31	$431.00	$1,000.00	0.05	$50.65	$481.65	4.681%
23%	$100.00	4.15	$415.00	$1,000.00	0.0448	$44.81	$459.81	4.534%
24%	$100.00	4	$400.00	$1,000.00	0.0397	$39.69	$439.69	4.377%
25%	$100.00	3.89	$389.00	$1,000.00	0.0352	$35.18	$424.18	3.526%
26%	$100.00	3.72	$372.00	$1,000.00	0.03	$31.22	$403.22	4.942%

Consider two bonds of 6years (Short term) and 15 years (Long term); and as shown in the above table with 1% of change in market rates longterm bond is changed by 6% where as short term bond is changed only arround 4%. Therfore long term bond has more percentage of change wrt change in market rates.

Note: Market rates are used for discouting cash flows for present value.