A CIPM Principles candidate sent an email asking how to calculate the internal rate of return in the exercise shown in Example 26 in the CIPM Principles Curriculum (on page 198).  In this example, the following information is given:

• 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

 You can ignore the market value on 4/11; this information is not needed to calculate IRR.

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 daily cash flows.  Here is the information to be entered into the calculator:

CF(0) = -56.3      (this is the starting value of $56.3 million)
CF(1) = 0            (no cash flows occur from 4/1 through 4/10)
F(1) = 10            (ten days of zeros)
CF(2)=-9.8         (the contribution of $9.8 million on 4/11)
F(2)=1                (this contribution occurs just once)
CF(3)=0             (no cash flows occur from 4/12 through 4/29)
F(3)=18             (18 days of zeros)
CF(4)=69.6       ($69.6 million is the ending value)
F(4)=1              (this cash flow occurs just once)
Compute IRR

This should give you an IRR of 0.1819%.  This is a daily number, and the exercise wants a monthly return.  Thus, you should do the following steps to convert the daily return to a monthly return:

• add 1 to 0.1819%
• raise 1.001819 to the 30th power (as there are 30 days in April)
• subtract 1
• multiply by 100 to create the percentage

 Thus the answer is 5.60%.