Question

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A fund will need to pay out $2 million next year, $3 million the following year,...

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.

3.10
B.

2.98
C.

3.15
D.

3.20

Solutions

Expert Solution

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 A is correct.

jeff jeffy answered 1 year ago
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