From Ken Little,
Your Guide to Stocks.
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Many people find math challenging, but there are a couple of simple formulas that can help you understand your return from stock investments.

These formulas answer the question: What is the return on my investment? You use them to figure out where you are (how much profit or loss) and what your next step should be.

You use the formulas when you sell an investment to calculate your return. You can also use these formulas to see where you are at any particular point in time, even if you don’t plan to sell or if you want to know the return as a factor in your sell or hold decision.

The first formula is known as the Simple Return. It gives you a quick number, but it has some limitations, as you’ll see in a minute.

Formula

The formula is:

Return = net proceeds + any dividends / what you paid - 1

Now let’s plug some numbers in and see how it works. If you bought 200 shares of Kumquat Ltd. for $30 per share and paid an $18 commission, the total cost would be $6,018 (200 x $30 = $6,000 + $18 = $6,018).

You sold the stock for $36 per share and paid an $18 commission. If you received dividends of $1 per share, that equals $200.

Plugging those numbers in, we get: $36 x 200 = $7,200 - $18 = $7,182 for net proceeds.

Putting it all together:

Simple Return = $7,182 + $200 / $6,018 - 1

Simple Return = $7,382 / $6,018 -1

Simple Return = 1.23 – 1

Simple Return = .23 or 23%

Helpful

While this is helpful information, it doesn’t tell the whole story and is really only valid for investment held for very short periods.

To get a valid picture of how a stock or other investment has done over time, you need to calculate the compound annual growth rate.

The compound annual growth rate gives you a better picture of what an investment has done for you because it takes into account the time value of money and evens out the ups and downs so you can see the growth as a single number.

To get the compound annual growth rate, you use the Simple Return with an adjustment. The adjustment is eliminating the subtraction of 1 at the end of the calculation.

Simple Return

From our example above, the Adjusted Simple Return would be 1.23.

The next step is to factor in the length of time you have held an investment. Let’s assume you have held the Kumquat stock for 4 years.

Divide 1 by the number of years the investment has been held (4) and this will give you the factor to adjust the return:

1 / 4 = .25 power or exponent

Compound annual growth rate = adjusted simple return ^{(raised to the power)} - 1

Compound annual growth rate = 1.23 ^(.25) -1

Compound annual growth rate = 1.05311 -1

Compound annual growth rate = .05311 or 5.31 percent

Need Calculator

You will need a calculator that allows you to enter the exponent or power. You can also make the calculations using Microsoft Excel.

In the “Insert Function” under the “Insert” menu, pick “Math & Trig” from the drop down box and scroll down to “POWER.” This function allows you to enter the number and the power you want to raise it to.

As you can see, our 23 percent Simple Return looked pretty good until we factored in the time you held the stock. The Annual Compound Growth Rate of 5.31 percent is nothing to get excited about. By the time you pay taxes and factor in inflation, this investment lost money.

Once you have the compounded annual growth rate you are in a better position to see what the stock has actually done. If you want an after-tax calculation, substitute after tax proceeds and after-tax dividend numbers.

Conclusion

Compound annual growth rate calculations give you an accurate picture of how your investment is doing over time and let you get beyond the “peaks and valleys” to a constant number that you can confidently use in your decision making.