Simple Return vs. Compound Annual Growth Rate Formula

In order to better understand the return you get from your stocks, you don't have to be a math guru. All you need to do is to master several formulas.

The formulas will help you calculate the returns on your investment. This will further facilitate the identification of your current position as compared to where you should be regarding your financial goals.

The formulas have several applications. First of all through their use you will be able to establish your return when you sell a stock. Secondly, even if you don't plan to sell the stock you can see how much it returns you currently. On the other hand, the formula can be used as a criterion on whether you should sell a stock or keep it.

So, let's now see the formulas.

Simple Return Formula

The first formula is as follows:

Return = (Net Proceeds + Dividends) / Total Cost - 1

Example: John purchased 150 shares of company ABC. Each share costs $25. He paid $20 commission to his broker. So, the total cost incurred by John will be:

Total Cost = shares x price per share + commission fee

Total Cost = 150 x $25 + $20 = $3,770

John sold the stock at $30 per share. He also paid $20 commission fee to his broker for the transaction. John also received dividends that amounted to $1 per share. So, he got $150 in dividends.

Net Proceeds = shares x price per share - commission fee

Net Proceeds = 150 x $30 - $20 = $4,480

So, the simple return will be as follows:

Simple Return = ($4,480 + $150) / $3,770 - 1 = 1.23 - 1 = 0.23

So, the simple return is 23%. You should keep in mind that this percentage is only true for short-term investments. If you need an evaluation of the performance of a stock over a longer period of time you will need to use the next formula.

Compound Annual Growth Rate Formula

This formula gives you a better view on how your stock has done. This is so since it takes into consideration time value of money. It also evens out the ups and downs of the business cycle. This allows you to see the growth of your stock as one number.

In order to calculate the compound annual growth rate, you use the Simple Return formula and add some adjustments to it. The latter is expressed in the elimination of the -1 from the end of the formula.

The formula for compound annual growth rate is as follows:

Compound Annual Growth Rate = Adjusted Simple Return ^{(raised to the power)} - 1

So, let's return to the previous example. In order to get the compound annual growth rate, follow these steps:

Step 1

From the previous example we have Adjusted Simple Return of 1.23. We also take into account this time that John has held the stock of company ABC for 5 years.

Step 2

This step includes the calculation of the factor with which to adjust the return. It is estimated by dividing 1 by the number of years the stock has been held. In our example we have:

1/5 = 0.2 (this is the exponent)

Step 3

This is the final step in which we are ready to calculate the compound annual growth rate.

Compound Annual Growth Rate = 1.23 ^(0.2) - 1 = 0.04227

Therefore, the compound annual growth rate is equal to 4.2%.

As you can see you will not be able to do the calculations without a scientific calculator that allows for the entering of exponent. If you don't have such a calculator, you can make the calculations using Microsoft Excel.

Simple Return vs. Compound Annual Growth Rate

Returning back to John's example, we got 23% as a Simple Return. However, the compound annual growth rate we got is 5.1%. As you can see it is not such a good return for the longer period of time during which you will hold the stock. Inflation and taxes will further decrease your returns.

Compound annual growth rate allows for making a clearer evaluation of the performance of the stock. Additionally, the formula can be used to make after-tax estimations. All you need to do is to substitute after-tax proceeds and after-tax dividends.

Finally, use the compound annual growth rate formula whenever you need to make decisions regarding the performance of your stock over longer periods of time. It eliminates the ups and downs of the market and provides you with a constant number that greatly facilitates your decision making.

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