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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 6%, what is the Macaulay duration of this set of payments?

A. 3.05
B. 3.12
C. 2.85
D. 3.50

Solutions

Expert Solution

Given about a fund,

Payment in year 1 = $2 million

Payment in year 2 = $3 million

Payment in year 5 = $5 million

discount rate d = 6%

Duration is calculated as below table:

PV of payment = payment/(1+d)^year

Total PV = sum of all PV = $8.29 million

weight = PV of payment/ price

duration of each coupon = period*weight

duration of the bond = sum of all duration = 3.12 years

Year payment PV of Cash flow=Payment/(1+d)^year weight = PV of Payment/Price Duration = weight*year
1 $                  2.00 $                  1.89 0.2275 0.2275
2 $                  3.00 $                  2.67 0.3220 0.6439
3 $                       -   $                       -   0.0000 0.0000
4 $                       -   $                       -   0.0000 0.0000
5 $                  5.00 $                  3.74 0.4505 2.2527
Total PV $                  8.29 Duration 3.12

Option B is correct.

jeff jeffy answered 1 year ago
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