FYI on ROI: A Guide to Calculating Return on Investment

Return on investment (ROI) is a financial metric of profitability that is widely used to measure the return or gain from an investment. ROI is a simple ratio of the gain from an investment relative to its cost. It is as useful in evaluating the potential return from a stand-alone investment as it is in comparing returns from several investments.

In business analysis, ROI is one of the key metrics—along with other cash flow measures such as internal rate of return (IRR) and net present value (NPV)—used to evaluate and rank the attractiveness of a number of different investment alternatives. ROI is generally expressed as a percentage rather than as a ratio.

The ROI calculation is a straightforward one, and it can be calculated by either of the two following methods.

The first is this:

$ROI = \frac{\text{Net\ return \ on \ investment}}{\text{Cost \ of \ investment}}\times 100\%$ROI=Cost  of  investmentNet return  on  investment​×100%

The second is this:

$ROI = \frac{\text{Final value of investment} - \text{Initial value of investment}}{\text{Cost of investment}}\times100\%$ROI=Cost of investmentFinal value of investment−Initial value of investment​×100%

 There are some points to bear in mind with regard to ROI calculations:

• As noted earlier, ROI is intuitively easier to understand when expressed as a percentage instead of a ratio.
• The ROI calculation has "net return" rather than "net profit or gain" in the numerator. This is because returns from an investment can often be negative instead of positive.
•  A positive ROI figure means that net returns are in the black, as total returns exceed total costs. A negative ROI figure means that net returns are in the red (in other words, this investment produces a loss), as total costs exceed total returns.
• To compute ROI with greater accuracy, total returns and total costs should be considered. For an apples-to-apples comparison between competing investments, annualized ROI should be considered.

Let’s assume you bought 1,000 shares of hypothetical Worldwide Wicket Co. for $10 each. Exactly a year later, you sold the shares for $12.50. You earned dividends of $500 over the one-year holding period. You also spent a total of $125 on trading commissions when you bought and sold the shares. What is your ROI?

It can be calculated as follows:

$\textbf{ROI}=\frac{[(\$12.50-\$10.00)\times1,000]+\$500-\$125\times100\%=28.75\%}{[\$10.00\times1,000]}$ROI=[$10.00×1,000][($12.50−$10.00)×1,000]+$500−$125×100%=28.75%​

Let's deconstruct this calculation resulting in a 28.75% ROI step by step.

1. To calculate net returns, total returns and total costs must be considered. Total returns for a stock arise from capital gains and dividends. Total costs would include the initial purchase price as well as commissions paid.
2. In the above calculation, the first term [($12.50 - $10.00) x 1,000] shows the gross capital gain (i.e., before commissions) from this trade. The $500 amount refers to the dividends received by holding the stock, while $125 is the total commission paid.
3. Dissecting the ROI into its component parts would result in the following:

$\textbf{ROI}\mathbf{=}\textbf{Capital gains (23.75\%)}\mathbf{+}\textbf{Dividend yield (5.00\%)}$ROI=Capital gains (23.75%)+Dividend yield (5.00%)

Why is this important? Because capital gains and dividends are taxed at different rates in most jurisdictions.

Here's another way of calculating the ROI on your Worldwide Wicket Co. investment. Let's assume the following split of the $125 paid in total commissions—$50 when buying the shares and $75 when selling the shares.$\begin{aligned} &\textbf{Initial Value of Investment (i.e. cost of investment)}\mathbf{=\$10,000+\$50=\$10,050}\\ &\textbf{Final Value of Investment}\mathbf{=\$12,500+\$500-\$75=\$12,925}\\ &\mathbf{ROI}=\frac{\$12,925-\$10,050}{\$10,050}\times100\%=28.60\% \end{aligned}$​Initial Value of Investment (i.e. cost of investment)=$10,000+$50=$10,050Final Value of Investment=$12,500+$500−$75=$12,925​

The slight difference in the ROI values (28.75% vs. 28.60%) occurs because, in the second instance, the commission of $50 paid upon purchase of the shares was included in the initial cost of the investment. So while the numerator in both the equations was the same ($2,875), the slightly higher denominator in the second instance ($10,050 vs. $10,000) has the effect of marginally depressing the stated ROI figure.

The Annualized ROI calculation counters one of the limitations of the basic ROI calculation, which is that it does not consider the length of time that an investment is held (the "holding period"). Annualized ROI is calculated as follows:

$\begin{aligned} &\text{Annualized } ROI = [(1 + ROI) ^{1/n} - 1]\times100\%\\ &\textbf{where:}\\ &n=\textbf{number of years for which the investment is held.} \end{aligned}$​Annualized ROI=[(1+ROI)1/n−1]×100%where:​

Assume you had an investment that generated an ROI of 50% over five years. What was the annualized ROI?

The simple annual average ROI of 10% (obtained by dividing ROI by the holding period of five years) is only a rough approximation of annualized ROI because it ignores the effects of compounding, which can make a significant difference over time. The longer the time period, the bigger the difference between the approximate annual average ROI (ROI / holding period) and annualized ROI. 

$\text{From the formula above, Annualized ROI}=[(1+0.50)^{1/5}-1]\times100\%=8.45\%$From the formula above, Annualized ROI=[(1+0.50)1/5−1]×100%=8.45%

This calculation can also be used for holding periods of less than a year by converting the holding period to a fraction of a year.

Assume you had an investment that generated an ROI of 10% over six months. What was the annualized ROI?

$\text{Annualized ROI}=[(1+0.10)^{1/0.5}-1]\times100\%=21.00\%$Annualized ROI=[(1+0.10)1/0.5−1]×100%=21.00%

(In the mathematical expression above, six months = 0.5 years).

Annualized ROI is especially useful when comparing returns between various investments or evaluating different investments.

Assume your investment in stock X generated an ROI of 50% over five years, while your stock Y investment returned 30% over three years. What was the better investment in terms of ROI

$\begin{aligned} &\text{Annualized ROI for stock } X=[(1+0.50)^{1/5}-1]\times100\%=8.45\%\\ &\text{Annualized ROI for stock } Y=[(1+0.30)^{1/3}-1]\times100\%=9.14\%\\ \end{aligned}$​Annualized ROI for stock X=[(1+0.50)1/5−1]×100%=8.45%Annualized ROI for stock Y=[(1+0.30)1/3−1]×100%=9.14%​

Stock Y had a superior ROI compared to stock X.

Leverage can magnify ROI if the investment generates gains, but by the same token, it can amplify losses if the investment proves to be a dud.

In an earlier example, we had assumed that you bought 1,000 shares of Worldwide Wickets Co. for $10 each. Let's further assume that you bought these shares on a 50% margin, which means that you put up $5,000 of your own capital and borrowed $5,000 from your brokerage as a margin loan. Exactly a year later, you sold the shares for $12.50. You earned dividends of $500 over the one-year holding period. You also spent a total of $125 on trading commissions when you bought and sold the shares. In addition, your margin loan carried an interest rate of 9%. What is your ROI?

There are two key differences from the earlier example:

• The interest on the margin loan ($450) should be considered in total costs.
• Your initial investment is now $5,000 because of the leverage employed by taking the margin loan of $5,000. 

* This is the margin loan of $5,000

Thus, even though the net dollar return was reduced by $450 on account of margin interest, ROI is substantially higher at 48.50%, compared with 28.75% if no leverage was employed.

But instead of rising to $12.50, what if the share price fell to $8.00, and you had no choice but to cut your losses and sell the full position? ROI, in this case, would be:

$\textbf{ROI}=\frac{[(\$8.00-\$10.00)\times1,000]+\$500-\$125-\$450}{[\$10.00\times1,000]-[\$10.00\times500]}\times100\%=-\frac{\$2,075}{\$5,000}=-41.50\%$ROI=[$10.00×1,000]−[$10.00×500][($8.00−$10.00)×1,000]+$500−$125−$450​×100%=−$5,000$2,075​=−41.50%

In this case, ROI of -41.50% is much worse than ROI of -16.25% that would have resulted if no leverage was employed.

When evaluating a business proposal, one often has to contend with unequal cash flows. This means that the returns from an investment will fluctuate from one year to the next.

The calculation of ROI in such cases is more complicated and involves using the internal rate of return (IRR) function in a spreadsheet or calculator.

Assume you have a business proposal to evaluate that involves an initial investment of $100,000 (shown under Year 0 in the "Cash Outflow" row in the following Table). The investment generates cash flows over the next five years, as shown in the "Cash Inflow" row. The "Net Cash Flow" row sums up the cash outflow and cash inflow for each year. What is the ROI?

Using the IRR function, the calculated ROI is 8.64%.

The final column shows the total cash flows over the five-year period. Net cash flow over this five-year period is $25,000 on an initial investment of $100,000. What if this $25,000 was spread out equally over five years? The cash flow table would then look like this:

Note that the IRR, in this case, is now only 5.00%.

The substantial difference in the IRR between these two scenarios—despite the initial investment and total net cash flows being the same in both cases—has to do with the timing of the cash inflows. In the first case, substantially larger cash inflows are received in the first four years. Because of the time value of money, these larger inflows in the earlier years have a positive impact on IRR.

The biggest benefit of ROI is that it is an uncomplicated metric, easy to calculate and intuitively easy to understand. ROI's simplicity means that it is a standardized, universal measure of profitability with the same connotation anywhere in the world, and hence not liable to be misunderstood or misinterpreted. "This investment has an ROI of 20%" has the same meaning whether you hear it in Argentina or Zimbabwe.

Despite its simplicity, the ROI metric is versatile enough to be used to evaluate the efficiency of a single stand-alone investment or to compare returns from different investments.

ROI does not take into account the holding period of an investment, which can be an issue when comparing investment alternatives. For example, assume investment X generates an ROI of 25% while investment Y produces an ROI of 15%. One cannot assume that X is the superior investment unless the timeframe of investment is also known. What if the 25% ROI from X is generated over a period of five years, but the 15% ROI from Y only takes one year? Calculating annualized ROI can overcome this hurdle when comparing investment choices.

ROI does not adjust for risk. It is common knowledge that investment returns have a direct correlation with risk – the higher the potential returns, the greater the possible risk. This can be observed firsthand in the investment world, where small-cap stocks typically have higher returns than large-cap stocks but are accompanied by significantly greater risk. An investor who is targeting a portfolio return of 12%, for example, would have to assume a substantially higher degree of risk than an investor who wants a return of 4%. If one focuses only on the ROI number without evaluating the concomitant risk, the eventual outcome of the investment decision may be very different from the expected result.

ROI figures can be exaggerated if all the expected costs are not included in the calculation, whether deliberately or inadvertently. For example, in evaluating the ROI on a piece of real estate, associated expenses such as mortgage interest, property taxes, insurance and maintenance costs must be considered because they can take a hefty chunk out of ROI. Not including all these expenses in the ROI calculation can result in a grossly overstated return figure.

Like many profitability metrics, ROI only emphasizes financial gain and does not consider ancillary benefits such as social or environmental ones. A relatively new ROI metric known as "Social Return on Investment" (SROI) helps quantify some of these benefits.

Return on investment (ROI) is a simple and intuitive metric of profitability used to measure the return or gain from an investment. Despite its simplicity, it is versatile enough to be used to evaluate the efficiency of a single stand-alone investment or to compare returns from different investments. ROI's limitations are that it does not consider the holding period of an investment (which can be rectified by using the annualized ROI calculation) and is not adjusted for risk. Despite these limitations, ROI finds widespread application and is one of the key metrics—along with other cash flow measures such as IRR and NPV—used in business analysis to evaluate and rank returns from competing investment alternatives.