# How to determine an accounting rate of return

An annual return, or annualized return, is a percentage that tells you how much an investment has increased in value on average per year over a period of time.

Annual return can be a preferable metric to use over simple return when you want to evaluate how successful an investment has been, or to compare the returns of two investments you’ve held over different time frames on equal footing: An investment that’s doubled in five years is obviously preferable to another investment that’s taken 50 years to double. An annual return allows you to compare the two.

How not to calculate an annual return
Your broker can help you determine what your returns have been on your investments — but if you don’t have a broker yet, come on over to our Broker Center, and we’ll help you get started. In the meantime, know that you can’t merely divide your simple return by the number of years held because of the compounding power of money. We can use a dramatic example to illustrate why.

Building-products manufacturer Patrick Industries is a dramatic produced an average annual return of close to 100% for the five years leading up to late 2015, meaning the stock doubled on average every year for five years. If you try to calculate its annual return by dividing its simple return by five, you’d get the wrong answer. (3,100% / 5 = 620%, not 100%.) That’s because returns compound — a double in year two doesn’t just double the original stock value, but it also doubles the previous years double.

How to calculate an annual return
Here’s how to do it correctly:

Look up the current price and your purchase price.

If the stock has undergone any splits, make sure the purchase price is adjusted for splits. If it isn’t, you can adjust it yourself. For example, if you held a stock for 4 years, during which time it has had a 2:1 and a 3:1 split, then you can calculate your split-adjusted purchase price by dividing your purchase price by 6 (2 x 3).

Simple Return = (Current Price-Purchase Price) / Purchase Price

Now that you have your simple return, annualize it:

Annual Return = (Simple Return +1) ^ (1 / Years Held)-1

Let’s use Campbell Soup as an example. Suppose it’s 2015, and you own shares (it doesn’t matter how many) of the stock. Campbell’s stock trades for \$48 per share, and you paid \$54 per share 20 years ago in 1995. In the meantime, the stock has undergone one split, a 2:1 split in 1997.

• The current price is \$48. Your purchase price was \$54.
• Your simple return would be 78% (\$48-\$27) / \$27).
• Your annual return would be 3% ((78% +1 ) ^ (1 / 20)-1).

Many companies pay their investors cash in the form of dividends. Since dividends can make up a substantial portion of investing returns, you may decide to calculate an annual return that takes them into account.

• Calculate your simple return using a historical dividend-adjusted historical price. (Also known as adjusted price or adjusted close price, a dividend-adjusted price usually will take into account any splits. It also implicitly assumes dividend reinvestment.)

Annual Dividend-Adjusted Return = (Simple Dividend-Adjusted Return +1) ^ (1 / Years Held)-1

Back to our Campbell Soup example. The company paid a bunch of dividends from 1995 to 2015. Here’s how you would include those in your annual return calculation:

The simple rate of return is calculated by taking the annual incremental net operating income and dividing by the initial investment. When calculating the annual incremental net operating income, we need to remember to reduce by the depreciation expense incurred by the investment.

### Watch IT

Let’s take a look at an example.

Hupana Running Company is looking at adding a stitcher that will add \$40,000 to the revenues of the company per year. The incremental (additional) cash operating expenses of this piece of equipment would be \$5,000 per year, and the equipment has a cost of \$100,000 with a 5 year life and no salvage value. So let’s pop these numbers into the formula:

Hupana Running Company—Stitcher Purchase
Annual incremental revenue \$40,000
Annual incremental operating expense \$5,000
Annual depreciation (\$100,000/5 years) \$20,000
Annual incremental expenses \$25,000
Annual incremental net operating income/(loss) \$15,000

So the simple rate of return would be: annual incremental net operating income/ initial investment cost

\$15,000/\$100,000= 15% simple rate of return

So it looks like the stitcher would be a good investment! What if we change up the numbers a bit. The stitcher will still add the \$40,000 to revenues, but will add \$10,000 to annual operating costs and only have a useful life of three years.

Hupana Running Company—Stitcher Purchase
Annual incremental revenue \$40,000
Annual incremental operating expense \$10,000
Annual depreciation (\$100,000/ years) \$33,333
Annual incremental expenses \$43,333
Annual incremental net operating income/(loss) −\$3,333

We now have a negative rate of return, so would probably pass on making this purchase. This brings home the point of how important it can be to know your numbers and do your research! Also noting, a small difference, can make a huge difference in the decision to make a capital budgeting decision, so as a manager, be clear on your information and perhaps use several of the available methods before making a final decision or before taking your analysis to your supervisor!

The real rate of return formula is the sum of one plus the nominal rate divided by the sum of one plus the inflation rate which then is subtracted by one. The formula for the real rate of return can be used to determine the effective return on an investment after adjusting for inflation.

The nominal rate is the stated rate or normal return that is not adjusted for inflation.

The rate of inflation is calculated based on the changes in price indices which are the price on a group of goods. One of the most commonly used price indices is the consumer price index(CPI). Although the consumer price index is widely used, a company or investor may want to consider using another price index or even their own group of goods that relates more to their business when calculating the real rate of return.

For quick calculation, an individual may choose to approximate the real rate of return by using the simple formula of nominal rate – inflation rate.

## Example of Real Rate of Return Formula

An example of the real rate of return formula would be an individual who wants to determine how much goods they can buy at the end of one year after leaving their money in a money market account that earns interest.

For this example of the real rate of return formula, we must assume that the individual wants to purchase the exact same goods and same proportion of goods that the consumer price index uses considering that it is used often to measure inflation.

For this example of the real rate of return formula, the money market yield is 5%, inflation is 3%, and the starting balance is \$1000. Using the real rate of return formula, this example would show

which would return a real rate of 1.942%. With a \$1000 starting balance, the individual could purchase \$1,019.42 of goods based on today’s cost. This example of the real rate of return formula can be checked by multiplying the \$1019.42 by (1.03), the inflation rate plus one, which results in a \$1050 balance which would be the normal return on a 5% yield.