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)) Duration of the Bond a. $10,000 par value, coupon rate = 8.8%, rb = 0.18 years b. $10,000 par value, coupon rate = 10.8%, rb = 0.18 c. $10,000 par value, coupon rate = 12.8%, rb = 0.18

Answer 1

Solution:

a.

Year	CF	PVIF @ 18%	PV	PVxYear
1	880	0.84745763	745.7627	745.7627
2	880	0.71818443	632.0023	1264.005
3	880	0.60863087	535.5952	1606.786
4	880	0.51578888	453.8942	1815.577
5	10880	0.43710922	4755.748	23778.74
			7123.003	29210.87

Duration = 29210.87/7123.003 = 4.10 years

b.

Year	CF	PVIF @ 18%	PV	PVxYear
1	1080	0.84745763	915.2542	915.2542
2	1080	0.71818443	775.6392	1551.278
3	1080	0.60863087	657.3213	1971.964
4	1080	0.51578888	557.052	2228.208
5	11080	0.43710922	4843.17	24215.85
			7748.437	30882.56

Duration = 30882.56/7748.437 = 3.99 years

c.

Year	CF	PVIF @ 18%	PV	PVxYear
1	1280	0.84745763	1084.746	1084.746
2	1280	0.71818443	919.2761	1838.552
3	1280	0.60863087	779.0475	2337.143
4	1280	0.51578888	660.2098	2640.839
5	11280	0.43710922	4930.592	24652.96
			8373.871	32554.24

Duration = 32554.24/8373.871 = 3.89 years