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 $10,000 par value, coupon rate-9.5%, rb-0.15 |$10,000 par value, coupon rate 11.5%, rb 0.15 |$10,000 par value, coupon rate-13.5%, rb-0.15 4.01 years 3.91 3 82。 C.

Answer 1

a.

Period	Cash Flow from Bond	Discounting factor = 1/(1+R)^N	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
N	CF	Df = 1/(1+0.15)^N	PV = CF x Df	WCF = CF x N	WPV = WCF x Df
1	950.00	0.8696	826.0870	950.0000	826.0870
2	950.00	0.7561	718.3365	1900.0000	1436.6730
3	950.00	0.6575	624.6404	2850.0000	1873.9213
4	950.00	0.5718	543.1656	3800.0000	2172.6623
5	10950.00	0.4972	5444.0853	54750.0000	27220.4263
		Total = P = Price =	8156.3147	Total = Weighted Price = WP	33529.7698
Duration or Macaulay Duration = (WP/P) =		4.11 Years

b.

Period	Cash Flow from Bond	Discounting factor = 1/(1+R)^N	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
N	CF	Df = 1/(1+0.15)^N	PV = CF x Df	WCF = CF x N	WPV = WCF x Df
1	1150.00	0.8696	1000.0000	1150.0000	1000.0000
2	1150.00	0.7561	869.5652	2300.0000	1739.1304
3	1150.00	0.6575	756.1437	3450.0000	2268.4310
4	1150.00	0.5718	657.5162	4600.0000	2630.0649
5	11150.00	0.4972	5543.5206	55750.0000	27717.6030
		Total = P = Price =	8826.7457	Total = Weighted Price = WP	35355.2294
Duration or Macaulay Duration = (WP/P) =		4.01 Years

c.

Period	Cash Flow from Bond	Discounting factor = 1/(1+R)^N	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
N	CF	Df = 1/(1+0.15)^N	PV = CF x Df	WCF = CF x N	WPV = WCF x Df
1	1350.00	0.8696	1173.9130	1350.0000	1173.9130
2	1350.00	0.7561	1020.7940	2700.0000	2041.5879
3	1350.00	0.6575	887.6469	4050.0000	2662.9407
4	1350.00	0.5718	771.8669	5400.0000	3087.4675
5	11350.00	0.4972	5642.9559	56750.0000	28214.7797
		Total = P = Price =	9497.1767	Total = Weighted Price = WP	37180.6889
Duration or Macaulay Duration = (WP/P) =		3.91 Years