In my last post, I covered a "fast" way to solve multiple choice internal rate of return exercises. In today's post, I look at a second quick method.

Recall the details from the last post:

- Account market value on 3/31 is $56.3 million
- Account market value on 4/11 is $58.2 million (prior to contribution on same day)
- Contribution of $9.8 million is made on 4/11
- Account market value of $69.6 million on 4/30

a) 9.3%, or

b) 2.7%, or

c) 5.6 ?

The second fast method involves use of the Modified Dietz formula. Modified Dietz is, in fact, a money-weighted return. It exhibits the following traits of money-weighted returns:

- the portfolio is valued only at the start and end of the period
- interim external cash flows are day-weighted within the evaluation period

Recall the formula for Modified Dietz is:

Plugging our data into this formula, we get the following:

From this it is clear that the answer is option c), the return of 5.6%. That wasn't painful at all! This method may be even faster than the last method!

Modified Dietz as an approximation to IRR should work fine for fairly short evaluation periods and non-extreme cash flows.

Hope this helps!

P.S. #1: Modified Dietz can, of course, be used to calculate sub-period returns, which we then geometrically link to get the time-weighted return. Recall the following traits of the time-weighted return:

- geometrically linked sub-period returns
- revaluation on a frequent basis (rather than just simply at the start and end of the period)
- if valuations are done on external cash flow dates, the geometrically linked return is the so-called "true time-weighted return"
- if valuations are done frequently but not on the cash flow dates, then the geometrically linked return is an estimate of the time-weighted return

Happy studying!

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