Question

An investor has two bonds in his portfolio that have a face value of $1000 and pay a 10% annual coupon. Bond A matures 20 years and Bond B matures in 5 years. a) Estimate the value of each bond if the required return is 9% b)Estimate the value of each bond of the required return is 11%. (Please explain the answer in detail, do not provide answer in excel and pls attach all the formulas used clearly)

Answer 1

a)	When the interest rate is .09
	Years to maturity	20
	Par/Face value	1000
	Annual coupon rate	10%
	Annual coupon	100
	Present Value = Future value/ ((1+r)^t)
	where r is the interest rate that is 9% and t is the time period
	Value of the bond = sum of present values of future cash flows
	r	0.09
	t	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20
	future cash flow	100	100	100	100	100	100	100	100	100	100	100	100	100	100	100	100	100	100	100	1100
	present value	91.74	84.17	77.22	70.84	64.99	59.63	54.70	50.19	46.04	42.24	38.75	35.55	32.62	29.92	27.45	25.19	23.11	21.20	19.45	196.27
	value of the bond	1091.29
	Years to maturity	5
	Par/Face value	1000
	Annual coupon rate	10%
	Annual coupon	100
	Present Value = Future value/ ((1+r)^t)
	where r is the interest rate that is 9% and t is the time period
	Value of the bond = sum of present values of future cash flows
	r	0.09
	t	1	2	3	4	5
	future cash flow	100	100	100	100	1100
	present value	91.74	84.17	77.22	70.84	714.92
	value of the bond	1038.90
b)	When the interest rate is .11
	Years to maturity	20
	Par/Face value	1000
	Annual coupon rate	10%
	Annual coupon	100
	Present Value = Future value/ ((1+r)^t)
	where r is the interest rate that is 11% and t is the time period
	Value of the bond = sum of present values of future cash flows
	r	0.11
	t	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20
	future cash flow	100	100	100	100	100	100	100	100	100	100	100	100	100	100	100	100	100	100	100	1100
	present value	90.09	81.16	73.12	65.87	59.35	53.46	48.17	43.39	39.09	35.22	31.73	28.58	25.75	23.20	20.90	18.83	16.96	15.28	13.77	136.44
	value of the bond	920.37
	Years to maturity	5
	Par/Face value	1000
	Annual coupon rate	10%
	Annual coupon	100
	Present Value = Future value/ ((1+r)^t)
	where r is the interest rate that is 11% and t is the time period
	Value of the bond = sum of present values of future cash flows
	r	0.11
	t	1	2	3	4	5
	future cash flow	100	100	100	100	1100
	present value	90.09	81.16	73.12	65.87	652.80
	value of the bond	963.04
	Interest rate	Value of 20 yr bond	Value of 5 yr bond
	9%	1091.29	1038.90
	11%	920.37	963.04