A husband and wife are planning for retirement and they believe that a compariso

Question

A husband and wife are planning for retirement and they believe that a comparison over a five-year period would be appropriate. They are given the following information about one mutual fund that they are considering. Assume that all remaining assets under management are withdrawn by the family at the end of 5 years. What is the money-weighted annual return for the fund? You can calculate the annual cash flow (either additional investment or withdrawal by the couple) at year t as the difference between the beginning assets under management at year t and ending assets under management at year t-1.

Explanation / Answer

A money-weighted rate of return is identical in concept to an internal rate of return: it is the discount rate on which the NPV = 0 or the present value of inflows = present value of outflows.

where

discount factor = (1 + IRR)^( corresponding time of cashflow - 1)

Discount CF = CF/discount factor

MWAR is the discount factor that causes the sum of discounted cashflows to be 0. I have used excel goal seek to calculate it wherein I specified that cell containing value of sum of discounted cash flows to be set as 0 , by changing the value of cell for MWAR.

MWAR= 3.23% Year Beginning AUM Net return Ending AUM Cashflow at start of year Discount factor Discounted CF 1 30 10% 33 -30 1 -30 2 40 -15% 34 -7 1.032331648 -6.780766638 3 25 8% 27 9 1.065708632 8.445085015 4 25 16% 29 2 1.100164749 1.817909547 5 20 9% 21.8 9 1.135734889 7.924384546 6 21.8 1.17245507 18.59346304 SUM= 7.5508E-05

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