An Internal Rate of Return exercise - HP 12C keystrokes

In a previous post, I covered an internal rate of return sample exam question, and I covered the keystrokes used on one of the calculators that may be used on the CIPM exam, the Texas Instruments Business Analyst II Plus (TI-BA II Plus).

There is, of course, another financial calculator that CIPM candidates may use on the exams, and that is the Hewlett Packard 12C.  In this post, I will cover the keystrokes to do the exercise on the HP 12C.

Recall the particulars of the exercise:

The Millers deposited $50,000 into their account on 1 May 2005 and another $40,000 on 1 July 2005. The portfolio also received and reinvested dividends of $30,000 on 1 July, plus another $30,000 on 31 December. The Miller's investment adviser, Greenbush Investments, uses a daily pricing system that shows account values (inclusive of dividends and contributions) of $2,375,000 and $2,460,000 on 1 May and 1 July, respectively. The account was valued at $2,225,000 on 1 January 2005 and at $2,445,000 on 31 December 2005.  

What is the annual internal rate of return?

I also remind candidates that I covered the steps to calculating internal rate of return in this previous blog post.

Next, we should identify the important information in this problem; i.e., the cash flows that must be entered into the calculator - and those that should be ignored. The important cash flows are:

• the initial market value of $2,225,000 on 1/1/2005
• the contribution of $50,000 on 5/1/2005
• the contribution of $40,000 on 7/1/2005
• the ending market value of $2,445,000 on 12/31/2005

You can ignore the dividends that are described because they are "reinvested" - this means they remain in the portfolio and are not an external cash flow. If they were "not reinvested," that would mean that they should be treated as withdrawals at the time of payment... but that is not the case here.

You can also ignore the other valuations that are given. With internal rate of return calculations, only the initial value and the ending value are needed.

In order to enter this into your financial calculator, you will need to evenly space the cash flows (in time) and "zero fill" the empty periods. In this problem, you can assume monthly occurring cash flows if you treat the initial market value as being for 12/31/2004, and the contributions as occurring on 4/30/2005 and 6/30/2005 (rather than 5/1/2005 and 7/1/2005).

The "zero filled" cash flows will be on the following dates: 1/31, 2/28, 3/31, 7/31, 8/31, 9/30, 10/31 and 11/30.

Thus, the following keystrokes may be used on the HP 12C calculator: 

[f] CLEAR [REG]                     (clears the registry)

2225000 [CHS] [g] [CF0]         (enters -2,225,000 as CF0)

0  [g] [CFj]                                (enters 0 as CF1)                        

3  [g] [Nj]                                  (indicates that CF1 occurs three times)

50000 [CHS] [g] [CFj]              (enters -50,000 as CF2)

0 [g] [CFj]                                 (enters 0 as CF3)

40000 [CHS] [g] [CFj]             (enters -40,000 as CF4)

0  [g] [CFj]                               (enters 0 as CF5)                        

5  [g] [Nj]                                 (indicates that CF5 occurs five times)

2445000 [g] [CFj]                    (enters 2,445,000 as CF6)

[f] [IRR]                                   (computes the IRR)

At this point, the calculator should tell you the solution is 0.4636%. But, this is a monthly return, because the spacing of our cash flows was monthly. We now need to convert this to an annual return. To do this, do the following steps:

• divide by 100 (converting the percentage to a decimal)
• add 1 (creating a wealth relative)
• raise the result of the last step to the 12th power
• subtract 1
• multiply by 100

This should give you an annual return of 5.70%

Happy studying!

An Internal Rate of Return exercise...

A CIPM Expert Level candidate sent me the following question, asking what are the proper keystrokes to obtain the solution:

The Millers deposited $50,000 into their account on 1 May 2005 and another $40,000 on 1 July 2005. The portfolio also received and reinvested dividends of $30,000 on 1 July, plus another $30,000 on 31 December. The Miller's investment adviser, Greenbush Investments, uses a daily pricing system that shows account values (inclusive of dividends and contributions) of $2,375,000 and $2,460,000 on 1 May and 1 July, respectively. The account was valued at $2,225,000 on 1 January 2005 and at $2,445,000 on 31 December 2005.

What is the annual internal rate of return?

First, I suggest that readers of this blog review my post from a few months ago suggesting a series of steps to solve internal rate of return problems. That post is here.

Next, we should identify the important information in this problem; i.e., the cash flows that must be entered into the calculator - and those that should be ignored. The important cash flows are:

• the initial market value of $2,225,000 on 1/1/2005
• the contribution of $50,000 on 5/1/2005
• the contribution of $40,000 on 7/1/2005
• the ending market value of $2,445,000 on 12/31/2005

You can ignore the dividends that are described because they are "reinvested" - this means they remain in the portfolio and are not an external cash flow. If they were "not reinvested," that would mean that they should be treated as withdrawals at the time of payment... but that is not the case here.

You can also ignore the other valuations that are given. With internal rate of return calculations, only the initial value and the ending value are needed.

In order to enter this into your financial calculator, you will need to evenly space the cash flows (in time) and "zero fill" the empty periods. In this problem, you can assume monthly occurring cash flows if you treat the initial market value as being for 12/31/2004, and the contributions as occurring on 4/30/2005 and 6/30/2005 (rather than 5/1/2005 and 7/1/2005).

The "zero filled" cash flows will be on the following dates: 1/31, 2/28, 3/31, 7/31, 8/31, 9/30, 10/31 and 11/30.

Thus, the following keystrokes may be used (TI BA II Plus calculator):

[CF][2nd][CLR WORK] Clears cash flow worksheet

-2225000[ENTER] Enters 2,225,000 as CF0

[down arrow] 0 [ENTER] Enters 0 as CF1

[down arrow] 3 [ENTER] The frequency of this flow is three times

[down arrow] -50000 [ENTER] Enters 50,000 as CF2

[down arrow] 1 [ENTER] The frequency of this flow is once

[down arrow] 0 [ENTER] Enters 0 as CF3

[down arrow] 1 [ENTER] The frequency of this flow is once

[down arrow] -40000 [ENTER] Enters 40,000 as CF4

[down arrow] 1 [ENTER] The frequency of this flow is once

[down arrow] 0 [ENTER] Enters 0 as CF5

[down arrow] 5 [ENTER] The frequency of this flow is five times

[down arrow] 2445000 [ENTER] Enters 2,445,000 as CF6

[down arrow] 1 [ENTER] The frequency of this flow is once

[IRR][CPT] Computes the IRR


At this point, the calculator should tell you the solution is 0.4636%. But, this is a monthly return, because the spacing of our cash flows was monthly. We now need to convert this to an annual return. To do this, do the following steps:

• divide by 100 (converting the percentage to a decimal)
  
• add 1 (creating a wealth relative)
• raise the result of the last step to the 12th power
• subtract 1
• multiply by 100

This should give you an annual return of 5.70%

Steps for calculating IRR

The following steps may be used to calculate internal rate of return using one of the financial calculators (HP 12C and TI BA II Plus):

1. Identify all external cash flows, including beginning and ending market values, and arrange them in chronological order.

2. Arrange the cash flows so that they are evenly spaced with respect to time. The financial calculators expect cash flows to occur at a regular frequency, so the cash flows entered must be evenly spaced, with zero cash flows used to fill in any missing data. I will describe how this can be done below.

3. Create the present value equation, equating the sum of the present value of outflows (beginning market value and any contributions) with the sum of the present value of in-flows (ending market values, and any withdrawals). I recommend ordering cash flows on each side of the equation in chronological order, from the first through to the last.

4. Identify simultaneously occurring cash flows. These are cash flows that occur on the same date, including both outflows and in-flows. These will be netted for purposes of entry into the financial calculator.

5. Using the appropriate keystrokes, enter the cash flows into the financial calculator’s cash flow worksheet, and compute the IRR.

6. The solution obtained in step 5 will be an internal rate of return for the interval of the cash flow spacing (step 2). Using exponents, convert the internal rate of return to a return for the desired period.