Question

A fund will need to pay out $2 million next year, $3 million the following year, and then $5 million in the fifth year . If the discount rate is 7%, what is the Macaulay duration of this set of payments?

A. 2.98

B. 3.10

C. 3.20

D. 3.15

Answer 1

Given for a fund,

Cash flow are as follow:

CF1 = $2 million

CF2 = $3 million

CF5 = $5 million

Discount rate d = 10%

Duration is calculated as below table:

PV of cash flow = Cash flow/(1+d)^year

Total PV = sum of all PV = $8.05 million

weight = PV of cash flow/ Total PV

duration of each cash flow = year*weight

duration of the fund = sum of all duration = 3.10 years

Year	cash flow	PV of cash flow=cash flow/(1+YTM)^year	weight = PV of Cash flow/Price	Duration = weight*year
1	$                  2.00	$                  1.87	0.2321	0.2321
2	$                  3.00	$                  2.62	0.3253	0.6507
3	$                       -	$                       -	0.0000	0.0000
4		$                       -	0.0000	0.0000
5	$                  5.00	$                  3.56	0.4426	2.2130
	Total PV	$                  8.05	Duration	3.10

Option B is correct.