Question

An insurance company is analyzing the following three bonds, each with five years to maturity, annual coupon payments, and duration as the measure of interest rate risk. What is the duration of each of the three bonds? (Do not round intermediate calculations. Round your answers to 2 decimal places. (e.g., 32.16))

a. $10,000 par value, coupon rate = 10.0%, rb = 0.2

b. $10,000 par value, coupon rate = 12.0%, rb = 0.2

c. $10,000 par value, coupon rate = 14.0%, rb = 0.2

Answer 1

Bond A	period	cash flow	present value of cash flow = cash flow/(1+r)^n r= 20%	present value of cash flow*period
	1	1000	833.3333	833.3333
	2	1000	694.4444	1388.889
	3	1000	578.7037	1736.111
	4	1000	482.2531	1929.012
	5	11000	4420.653	22103.27
	value of bond = sum of present value of cash flow		7009.388
	sum of present value of cash flow*period			27990.61
	Duration of bond	(sum of present value of cash flow* period)/value of bond	27990.61/7009.388	3.99
Bond B	period	cash flow	present value of cash flow = cash flow/(1+r)^n r= 20%	present value of cash flow*period
	1	1200	1000	1000
	2	1200	833.3333	1666.667
	3	1200	694.4444	2083.333
	4	1200	578.7037	2314.815
	5	11200	4501.029	22505.14
	value of bond = sum of present value of cash flow		7607.51
	sum of present value of cash flow*period			29569.96
	Duration of bond	(sum of present value of cash flow* period)/value of bond	29569.96/7607.51	3.89
Bond C	period	cash flow	present value of cash flow = cash flow/(1+r)^n r= 20%	present value of cash flow*period
	1	1400	1166.667	1166.667
	2	1400	972.2222	1944.444
	3	1400	810.1852	2430.556
	4	1400	675.1543	2700.617
	5	11400	4581.404	22907.02
	value of bond = sum of present value of cash flow		8205.633
	sum of present value of cash flow*period			31149.31
	Duration of bond	(sum of present value of cash flow* period)/value of bond	31149.31/8205.633	3.80