Which of the following is the correct formula for calculating return on investment?

The ROI, an abbreviation for “return on investment”, measures the profitability of an investment by comparing the net profits received at exit to the original cost of the investment.

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How to Calculate ROI (Step-by-Step)

ROI stands for the “return on investment”, and is defined as the ratio between:

• Net Return → Total Profits Received
• Cost of the Investment → Total Amount Spent

The return on investment formula is straightforward, as the calculation simply involves dividing the net return on the investment by the investment’s corresponding cost.

In particular, the ROI is most commonly used for internal purposes within companies, such as for their decision-making processes regarding which projects to pursue and for decisions on how best to allocate their capital.

The higher the ROI on a project or investment, the greater the monetary benefits received — all else being equal.

However, what constitutes whether the ROI is adequate differs based on the target return specific to the investor and the length of the holding period, among other factors.

ROI Formula

The formula for calculating the return on investment is as follows.

ROI = (Gross Return – Cost of Investment) ÷ Cost of Investment

ROI = Net Return ÷ Cost of Investment

For purposes of comparability, the return on investment metric is typically expressed in percentage form, so the resulting value from the above formula must then be multiplied by 100.

The numerator in the formula, the return, represents the “net” return — meaning that the cost of the investment must be subtracted from either:

1. Gross Returns (or)
2. Total Exit Proceeds

Return on Investment Calculation Example

For example, if the gross return on an investment is $100k while the associated cost was $80k, the net return is $20k.

With that said, the return on investment can be calculated by dividing the $20k net return by the cost of $80k, which comes out to 25%.

• Return on Investment (ROI) = $20k ÷ $80k = 0.25, or 25%

How to Interpret Return on Investment (High vs. Low ROI)

What is a Good ROI?

The return on investment is a widespread metric due to its simplicity since only two inputs are necessary:

1. Net Return
2. Cost of Investment

However, one drawback is that the “time value of money” is neglected, i.e. a dollar received today in worth more than a dollar received in the future.

If there are two investments with the same return, yet the second investment requires twice the amount of time until it is realized, the ROI metric on its own fails to capture this important distinction.

Therefore, when making comparisons among different investments, investors must ensure the time frame is the same (or nearby) or otherwise remain cognizant of the timing discrepancies between investments when putting together rankings.

One variation of the metric is called the annualized return on investment, which adjusts the metric for differences in timing.

Annualized ROI = [(Ending Value / Beginning Value) ^ (1 / Number of Years)] – 1

Furthermore, a common mistake in calculating the metric is neglecting side expenses, which tends to be more applicable to projects in corporate finance.

The ROI calculation must factor in each and every profit and incurred cost associated with the project (e.g. unexpected maintenance fees) and investments (e.g. dividends, interest).

ROI Calculator — Excel Model Template

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Step 1. ROI Calculation Example and Ratio Analysis

Suppose an industrial company spent $50 million in capital expenditures (CapEx) to invest in new machinery and upgrade their factory.

By the end of the anticipated holding period – which in the context of a company purchasing fixed assets is the end of the PP&E’s useful life assumption – the company received $75 million.

The net return on the PP&E investment is equal to the gross return minus the cost of investment.

• Net Return = $75m – $50m = $25m

The net return of $25 million is then divided by the cost of investment to arrive at the return on investment (ROI).

• Return on Investment (ROI) = $25m ÷ $50m = 50%

Given the $50 million net return and $25 million cost of investment, the ROI is 50%, as shown in the screenshot below.

Step 2. Equity ROI Calculation Example

In the next example scenario, a hedge fund has purchased shares in a publicly-traded company.

On the date of the purchase, the company was trading at $10.00 and the hedge fund bought a total of 4 million shares.

Thus, the cost of investment to the hedge fund comes out to $40 million.

• Cost of Investment = $10.00 × 4m = $40m

Five years from the date of purchase, the hedge fund exits the investment – i.e. liquidates its position – when the shares are up 20% relative to the entry share price at $12.00 per share.

If we assume that 100% of their equity stake is sold, the total proceeds post-sale are $48 million.

• Total Proceeds from Sale = $12.00 * 4m = $48m

The net return comes out to $8m, which is the difference between the total proceeds from the sale ($48m) and the cost of investment ($40m).

The ROI on the hedge fund’s investment is therefore 20%.

Since we are given the holding period of the hedge fund in this particular investment (i.e. 5 years), the annualized ROI can also be calculated.

To calculate the annualized ROI, we’ll use the “RATE” function in Excel:

• Annualized ROI = RATE (5 Years, 0, -$40m Cost of Investment, $48m Total Proceeds from Sale)
• Annualized ROI = 3.7%

Alternatively, we could have divided the total sale proceeds by the cost of investment, raised it to the power of (1/5), and subtracted 1 – which also comes out to 3.7%, confirming our earlier calculation is correct.

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