Tuesday, October 1, 2013

Fast Calculation of Internal Rate of Return (in Multiple Choice Situations...), Part I

I have covered the steps to calculating internal rate of return in a few different posts on the blog, including here, here and here.  I have also covered the steps to use the cash flow worksheets of the TI BA II Plus and the HP 12 C

You may have read the curriculum and the steps in the blog posts cited above, and you may have thought to yourself, "Wow, that's a lot of steps!"

It is possible that a question could be phrased in such a way (given that you are taking a multiple choice exam) that allows you to use a strategy to quickly calculate the internal rate of return.

For example, assume the question is as follows:
  • 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
Given the above, is the monthly internal rate of return closest to:
a)  9.3%, or
b) 2.7%, or
c) 5.6 ?

Recall that internal rate of return is the rate R that equates the ending market value for a period with the sum of:

- the future value of the beginning market value growing at the rate R for the entire period
- each contribution and withdrawal growing at the rate R for the fraction of the period that remains at the time of the given cash flow.

Thus, internal rate of return is the rate R that satisfies the following equation:

If you are given a question along the lines of the above exercise, where you are given three choices for a valid answer, rather than doing all of the steps to solve IRR that I outlined here, you could  simply plug each of the possible answers into the above equation, and see if you get equality.  If you do, that's the correct answer.  If you don't get equality, you should try a different multiple choice option.

To illustrate, using the first possible answer, option a),  of 9.3%:

 In the above, 69.6 represents the ending value of 69.6 million, 56.3 is the beginning value and 9.8 is the external cash flow, which occurs on the 11th day of a 30 day month.  Once we take the future value of all cash flows (i.e., the beginning value and the one contribution), and sum those future values, it is not equal to the ending value.  Thus, option a) is not the correct answer.  So, we try the return of 2.7%, which is option b):

Again, the sum of the future values does not equal the ending value, so option b) is not the correct answer.

At this point, if you trust your calculations and wanted to save time, you should be able to conclude that option c), the return of 5.6%, is the correct answer.  But, if you want to confirm this, you can take a few more minutes to prove that to yourself:

Chances are that if you apply this "process of elimination" method, you will arrive at the correct answer faster than if you executed the longer set of steps to calculate IRR.  Now keep in mind that you may encounter an exam question that is not structured in a way that you can do these "fast" steps, but if it is, and if you can recognize that, you have a good process to use.

Hopefully this gives you a good test taking tip, and also reinforces your understanding of the internal rate of return.  Later this week, I will show you a second "fast" method.

Happy studying!

P.S.:  the athlete in the picture above is Jamaica's Usain Bolt, the world's fastest person!

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