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Return on Investment
Return on investment (ROI) is the ratio of the net change in an investment's value (positive and negative) to the value of the original investment. The basic return on investment formula is ROI = (Cn/V0), where C is the net change in value for the investment, n is the elapsed time since the initial investment, and V0 is the initial value of that investment (at Time 0). This evaluation can be made for past, present, and future investments and their actual or projected changes in value.
Applications
While ROI can be expressed as a simple ratio, difficulties arise when a decision maker must compare investments that differ in their initial investment amounts and in the amounts and timing of their subsequent changes in investment value. Furthermore, difficulties are caused when tax rates, inflation, and expectations for what constitutes an adequate return on investment are considered in the analysis.
Medical Decision Making
ROI is an important factor in medical decision making because it provides a metric for use in comparing the relative economic attractiveness of alternative medical investments. All other factors being equal, one would assume that investments with higher ROIs would be preferred to investments with lower ROIs.
Expanding the Formula
The ROI formula can be elaborated as ROI = (Vn − V0/V0), where Vn is the value of the investment at Time n and V0 is the investment's initial value. This expansion makes it clear that the numerator includes all changes in the initial investment's value (gains and losses, realized and unrealized) as well as any cash flows (positive and negative) resulting from that investment. Using the example of an investment in a new clinic building, changes in the initial investment's value would include changes in the value of the building as well as cash flows from revenues and expenses involved
in the ownership and operation of the building (e.g., interest payments for loans, property tax, and building maintenance costs).
Cash Flow Timing and Valuation Adjustments
When the investment period (time between Vn and V0) is relatively short, differences in the timing of cash flows (between the initial investment and subsequent returns) is not an issue, and ROI is calculated without further adjustment. However, when cash flows occur over a longer period of time, they can have a significant impact on one's assessment of the value of alternative investment options, and special techniques are required to adjust for these differences. These adjustments take two forms:
- Compounding: adjustments to the ROI estimate to account for previous cash flows and to account for the investment's changing value over time
- Discounting: adjustments to individual cash flow values to account for the time lag between the initial investment and subsequent cash flow
Two additional types of adjustment may be used in ROI calculations. These are for taxes and inflation. Since both of these rates may be different for different years in the ROI analysis, it is customary to incorporate their effects in the annual calculations of net change in value (annual net cash flows).
Compounding
Assume an investment with an initial value of $100 that reaches a final value of $130 at the end of 3 years. One way of expressing the annual ROI is to take the arithmetic average of the change in value ($10 = $30/3). This yields an estimate of 10% ROI per annum 10% = $10/$100). However, this method does not account for the fact that if the annual ROI is actually 10%, the investment's initial value at the beginning of the second year will be the $100 initial investment plus a 10% annual return on that investment during the first year. Therefore, using an arithmetic average overestimates the annual ROI. To calculate the annual ROI after adjusting for changes in the value of the initial investment, one must solve the following equation for r: Vn – V0 = V0 (1 + r)n – V0, where r is the annualized rate of return on investment and n is the number of years in the investment period. Subtracting the initial investment value, this formula shows that the final value of an investment can be expressed as the investment's initial value compounded at an annual rate over a period of years (Vn = V0 (1 + r)n) In this example, the value for r that yields a final investment value of $130 for a $100 initial investment over a 3-year period is 9.1%. This is considerably smaller than the original estimate of a 10% annual ROI.
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