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 = 8.4%, rb = 0.14	years
b.	$10,000 par value, coupon rate = 10.4%, rb = 0.14
c.	$10,000 par value, coupon rate = 12.4%, rb = 0.14

Answer 1

Par value = $10,000

Maturity = 5 years (Annual payments)

R = 14%

a). Coupon Rate = 8.4%

Time(t)	CF	PV of CF	PV of CF x t
1	$840	$ 736.84	$ 736.84
2	$840	$ 646.35	$1,292.71
3	$840	$ 566.98	$1,700.93
4	$840	$ 497.35	$1,989.39
5	$840	$ 436.27	$2,181.35
Total		$2,883.79	$7,901.21

Duration = $7,901.21/$2,883.79 = 2.74 years

b). Coupon Rate = 10.4%

Time(t)	CF	PV of CF	PV of CF x t
1	$1,040	$ 912.28	$ 912.28
2	$1,040	$ 800.25	$1,600.49
3	$1,040	$ 701.97	$2,105.91
4	$1,040	$ 615.76	$2,463.05
5	$1,040	$ 540.14	$2,700.72
Total		$3,570.40

$9,782.45

Duration = $9,782.45/$3,570.40 = 2.74 years

c). Coupon Rate = 12.4%

Time(t)	CF	PV of CF	PV of CF x t
1	$1,240	$1,087.72	$ 1,087.72
2	$1,240	$ 954.14	$ 1,908.28
3	$1,240	$ 836.96	$ 2,510.89
4	$1,240	$ 734.18	$ 2,936.72
5	$1,240	$ 644.02	$ 3,220.09
Total		$4,257.02

$11,663.70

Duration = $11,663.70/$4,257.02 = 2.74 years