Calvin and Andre both have bonds they bought at par value which pay a 9.75% coupon...

Calvin and Andre both have bonds they bought at par value which pay a 9.75% coupon rate. Calvin's bond has 10 years to maturity and Andre's bond has 20 years to maturity. If interest rates suddenly rise to 11.75%, what is the approximate change in value of Andre's bond?

Solutions

Expert Solution

1. Calvin's Bond with 'No Change in Coupon Rate' with 10 year of Maturity.

Bond Valuation Formula:

P = Present Value

C=Coupon Rate

i = Interest Payable

y=Yield

t=time

T=Year of Maturity

F=FaceValue

Example:

Bond Face Value	Years	Coupon Rate	Interest Compounded Annualy	Discounted Cash Flow
1000	1	0.0975	97.5	88.83827
	2	0.0975	97.5	80.94603
	3	0.0975	97.5	73.75493
	4	0.0975	97.5	67.20267
	5	0.0975	97.5	61.2325
	6	0.0975	97.5	55.79271
	7	0.0975	97.5	50.83618
	8	0.0975	97.5	46.31998
	9	0.0975	97.5	42.205
	10	0.0975	1097.5	432.8717	1000

We can find there is no change in the Bond Valuation.

Andre's Bond

Bond Face Value	Years	Coupon Rate	Interest Compounded Annualy	Discounted Cash Flow
1000	1	0.1175	117.5	87.24832
	2	0.1175	117.5	78.07456
	3	0.1175	117.5	69.86538
	4	0.1175	117.5	62.51935
	5	0.1175	117.5	55.94573
	6	0.1175	117.5	50.06329
	7	0.1175	117.5	44.79937
	8	0.1175	117.5	40.08892
	9	0.1175	117.5	35.87375
	10	0.1175	117.5	32.10179
	11	0.1175	117.5	28.72644
	12	0.1175	117.5	25.70598
	13	0.1175	117.5	23.00312
	14	0.1175	117.5	20.58445
	15	0.1175	117.5	18.42009
	16	0.1175	117.5	16.4833
	17	0.1175	117.5	14.75015
	18	0.1175	117.5	13.19924
	19	0.1175	117.5	11.8114
	20	0.1175	1117.5	10.56949	739.8341385

If the coupon rate goes high in future the present value of the Bond gets reduced to $739 approximate to 26% of change.

jeff jeffy answered 1 year ago

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