Question

An insurance company is analyzing the following three bonds, each with five years to maturity, annual interest payments, and is using 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))

Duration of the bond

a.$10,000 par value, coupon rate = 9.5%, rb = 0.15years

b.$10,000 par value, coupon rate = 11.5%, rb = 0.15

c.$10,000 par value, coupon rate = 13.5%, rb = 0.15

Answer 1

a.

Bond duration > 4.11 years

Period	Cash Flow	Discounting factor = 1/(1+R)^Y	PV of the cash flows = Cash flow x Df	Weighted cash flow = Period x Cash flow	Present value of weighted cash flow = Weighted Cash flow x Df
Y	CF	Df = 1/(1+15%)^Y	PV = CF x Df	WCF = CF x Y	WPV = WCF x Df
1	950	0.8696	826.0870	950.00	826.0870
2	950	0.7561	718.3365	1900.00	1436.6730
3	950	0.6575	624.6404	2850.00	1873.9213
4	950	0.5718	543.1656	3800.00	2172.6623
5	10950	0.4972	5444.0853	54750.00	27220.4263
		Total = P =	8156.3147	Total = WP =	33529.7698
		Duration = WP/P =	4.11

b.

Bond duration > 4.01 years

Period	Cash Flow	Discounting factor = 1/(1+R)^Y	PV of the cash flows = Cash flow x Df	Weighted cash flow = Period x Cash flow	Present value of weighted cash flow = Weighted Cash flow x Df
Y	CF	Df = 1/(1+15%)^Y	PV = CF x Df	WCF = CF x Y	WPV = WCF x Df
1	1150	0.8696	1000.0000	1150.00	1000.0000
2	1150	0.7561	869.5652	2300.00	1739.1304
3	1150	0.6575	756.1437	3450.00	2268.4310
4	1150	0.5718	657.5162	4600.00	2630.0649
5	11150	0.4972	5543.5206	55750.00	27717.6030
		Total = P =	8826.7457	Total = WP =	35355.2294
		Duration = WP/P =	4.01
					#REF!

c.

Bond duration > 3.91 years

Period	Cash Flow	Discounting factor = 1/(1+R)^Y	PV of the cash flows = Cash flow x Df	Weighted cash flow = Period x Cash flow	Present value of weighted cash flow = Weighted Cash flow x Df
Y	CF	Df = 1/(1+15%)^Y	PV = CF x Df	WCF = CF x Y	WPV = WCF x Df
1	1350	0.8696	1173.9130	1350.00	1173.9130
2	1350	0.7561	1020.7940	2700.00	2041.5879
3	1350	0.6575	887.6469	4050.00	2662.9407
4	1350	0.5718	771.8669	5400.00	3087.4675
5	11350	0.4972	5642.9559	56750.00	28214.7797
		Total = P =	9497.1767	Total = WP =	37180.6889
		Duration = WP/P =	3.91

-----

Note:

+ or - 2 bps is possible