<THE FOOLISH FOUR>

Foolish Four Report
by Robert Sheard

LEXINGTON, KY. (Mar. 2, 1998) -- A number of readers wrote to me this weekend after my column Friday on the Beardstown Ladies' mathematical woes. In that column I outlined a procedure (using the XIRR function in Excel) for calculating one's actual return when faced with the complication of additional cash infusions (or withdrawals) along the route.

For example, if you start with $10,000 on January 1, 1997, add another $1,000 on April 1, July 1, and October 1, and finish the year with a total value of $16,000, what's your real return?

You started with $10,000 and finished with $16,000, so your return is 60%, right? Well, not exactly. You can't count the additional $3,000 you deposited over the course of the year as portfolio growth. That's new money and each deposit was in the account for a different time period. Yet, that is apparently what the Beardstown Ladies did.

What about simply measuring the growth from the $13,000 to the $16,000? Isn't the return 23%? That, too, is wrong, but in the other direction. The three $1,000 deposits weren't in your portfolio the whole year, so you can't calculate the return as if you began the year with $13,000; that understates your actual gain.

You must take into account the time value of money. And as I wrote Friday, the easiest way to do that is with the XIRR function in Microsoft Excel. (I understand that Quicken software has a similar function.)

But if you don't have Excel, all is not lost. You can use a method that requires nothing more than a little time (and a calculator if you like). Let's use our example above of the investor who starts the year with $10,000, adds $3,000 more over the course of the year, and finishes with $16,000.

By using the unit value method (the same basic method mutual funds must use since they are constantly receiving and paying out cash to individual investors), you can calculate an accurate overall return. Let's go through the steps.

When a fund opens for the first time, it issues an arbitrary number of shares (or units) at an equally arbitrary price. Let's say the Joe Stock Fund opens on January 1, 1997 with $10,000, valued as 100 units at $100.00 each. (You could choose 10 units at $1,000 each; it doesn't matter.)

From now on, though, the value of the units will be tied to the growth of the portfolio itself.

Let's say at the close on March 31, the Joe Stock Fund has grown to $10,600. There are still 100 units outstanding, so the new Unit Value is $106.00 ($10,600 divided by 100 units). To add the first new money to the Joe Stock Fund, you divide the amount you're adding ($1,000 in this case), by the new Unit Value ($106.00) to see how many additional units you're purchasing. In this case, it would be 9.434 units ($1,000 / $106.00 = 9.434).

So at this point, the Joe Stock Fund has a total of 109.434 units outstanding (the original 100 plus the newly acquired 9.434), each valued at $106.00 for a total value of $11,600. You'll notice that equals the value of the portfolio at the close on Mar. 31 ($10,600) plus the new $1,000.

Zoom ahead to the year's halfway mark. Let's say the Joe Stock Fund's value has increased to $12,300 at the close on June 30. To calculate the new Unit Value, divide that dollar amount by the number of units outstanding. So, $12,300 divided by 109.434 gives us a new Unit Value of $112.40. Investing a new $1,000 at $112.40 per unit buys the Joe Stock Fund another 8.897 units. The fund now has a total of 118.331 units, each valued at $112.40, for a total value of $13,300.40. (The numbers won't come out precisely unless you carry the decimals out to more places, but we're talking micro amounts, so don't sweat it.)

Zoom ahead again to the end of the third quarter. On September 30, let's say the Joe Stock Fund portfolio is now worth $14,100. Divide that by the units outstanding (118.331) to get the new Unit Value of $119.16. Adding another $1,000 at that unit cost buys the fund an additional 8.392 units. The Joe Stock Fund now has a total of 126.723 units, valued at $119.16 each, worth a total value of $15,100.31

And finally, sprint forward to New Year's Eve. The year ends with the Joe Stock Fund sitting on 126.723 units and a total value of $16,000. What's the new unit value? That's right; $16,000 divided by 126.723 units equals $126.26 per unit.

So how do we calculate the total return? It's simple now. Just calculate the percentage difference between the original Unit Value of $100.00 and the current one of $126.26 and you get a gain of 26.3%. That's all there is to it. (FYI, putting the same values through the XIRR function in Excel generates an annualized return of 26.3% as well.)

One caution: the unit value method calculates only your total return since inception. It does not figure your annualized return for periods other than one year, so if you're applying this method to a portfolio that has been open for less than a year or for several years, you'll still have to calculate the annualized return based on how long the portfolio's been open.

Nevertheless, using unit value is one relatively easy way to calculate the total return for your portfolio if you don't have access to Excel or Quicken and still want to account accurately for additional savings you've added or money you've withdrawn. As a number of you are setting up DRiP or "Dozens" portfolios, these calculations are especially important on order to know how well you're really doing. Don't count the reinvestment of dividends as new deposits, however. Dividends are part of your normal portfolio growth; they are not new funds you're adding out of your own pocket.

Fool on!

[Want to be the first Fool on your block to get a copy of Robert Sheard's forthcoming book? Click here to pre-order your copy of The Unemotional Investor.]

TODAY'S NUMBERS

Stock Change Last -------------------- UK + 11/16 47.13 IP +1 5/8 48.25 MO - 1/16 43.38 EK +1 7/8 67.50

Day Month Year FOOL-4 +1.98% 1.98% 7.22% DJIA +0.06% 0.06% 8.12% S&P 500 -0.16% -0.16% 7.96% NASDAQ -0.67% -0.67% 11.99% Rec'd # Security In At Now Change 12/31/97 289 Int'l Pape 43.13 48.25 11.88% 12/31/97 206 Eastman Ko 60.56 67.50 11.46% 12/31/97 291 Union Carb 42.94 47.13 9.75% 12/31/97 276 Philip Mor 45.25 43.38 -4.14% Rec'd # Security In At Value Change 12/31/97 289 Int'l Pape 12463.13 13944.25 $1481.13 12/31/97 206 Eastman Ko 12475.88 13905.00 $1429.13 12/31/97 291 Union Carb 12494.81 13713.38 $1218.56 12/31/97 276 Philip Mor 12489.00 11971.50 -$517.50 CASH $77.19 TOTAL $53611.32