Question

A six-year bond with a par value of $1,000 with a coupon rate of 9% (paid annually) is selling to yield 8.5% per annum. This bond has a modified duration of Select one: a. 3.23 years. b. 3.49 years. c. 3.25 years. d. 4.23 years. e. 4.47 years.

Answer 1

Given for the bond,

Face value = $1000

Coupon rate = 9% annually

coupon = 9%*1000 = $90

Yield to maturity = 8.5%

Duration is calculated as below table:

Coupon in year 6 includes Face value of $1000

PV of coupon = Coupon/(1+YTM)^t

Price = sum of all PV = $1022.77

weight = PV of coupon/ price

duration of each coupon = year*weight

duration of the bond = sum of all duration = 4.90 years

So modified duration = duration/(1+yield) = 4.9/1.085 = 4.5 years

So, approximately option e is correct

Year	Coupon	PV of cash flow=coupon/(1+YTM)^year	weight = PV of Coupon/Price	Duration = weight*year
1	$                90.00	$                82.95	0.0811	0.0811
2	$                90.00	$                76.45	0.0747	0.1495
3	$                90.00	$                70.46	0.0689	0.2067
4	$                90.00	$                64.94	0.0635	0.2540
5	$                90.00	$                59.85	0.0585	0.2926
6	$          1,090.00	$             668.11	0.6532	3.9194
	Price	$          1,022.77	Duration	4.90