Question
In: Finance
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 agoRelated Solutions
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