A CIPM Principles candidate sent an email asking how to calculate the internal rate of return in the exercise shown in Exercise 36 in the CIPM Principles Curriculum (on page 234). In this example, the following information is given:
- Account market value on 1/1/10 is $237,000
- Dividends of $8,000 are paid on 7/1/10. These dividends are not reinvested (which means they are withdrawn from the account rather than remaining in the account).
- Contribution of $40,000 is made on 10/1/10
- Account market value is $329,000 on 12/31/10. There was also a dividend of $8,000 paid on this day that was not reinvested.
The above is the relevant information to the internal rate of return calculation; anything else that is given can be ignored for purposes of exercise 36.
In order to do this calculation, you need to determine the intervals at which cash flows will be entered into the calculator. I am going to use quarterly cash flows. Here is the information to be entered into the calculator:
CF(0) = -237,000 (this is the starting value of $237,000)
CF(1) = 0 (no cash flow occurs on 4/1)
F(1) = 1 (the cash flow of zero occurs once)
CF(2)= 8,000 (the withdrawn income of $8,000 on 7/1)
F(2)=1 (this cash flow occurs once)
CF(3)= -40,000 (the contribution of $40,000 on 10/1/10)
F(3)=1 (this cash flow occurs once)
CF(4)= 337,000 (combination of ending market value of $329,000 and the withdrawn income of $8,000)
F(4)=1 (this cash flow occurs just once)
This should give you an IRR of 6.378%. This is a quarterly number, and the exercise wants an annual return. Thus, you should do the following steps to convert the quarterly return to a annual return:
- add 1 to 6.378%
- raise 1.06378 to the 4th power (as there are four quarters in a year)
- subtract 1
- multiply by 100 to create the percentage
Thus the answer is 28.1%.
Having said all of that – stay tuned – on Wednesday I will show what many candidates may find to be a faster way of solving this particular problem.