For most investments, neither total expenditures nor total earnings occur at a single point in time, but in flows of different quantities in different years. Investors use the concept of net present value to equilibrate amounts of expenditures or gains occurring at different points in time. Net present value represents the comparison of an amount of money at the present time and its value in the future.
For any risky investment, once the flow of expenditures and gains has stopped, investors can calculate the internal rate of return based on these values. In effect, this calculation answers the following question for the investor: Suppose there were a savings account with a constant interest rate that could have been invested in, instead of making the investment actually made. What would that theoretical interest rate have to be to make the investor equally content to have made the investment?
The internal rate of return allows for a concise and objective method of comparing the relative success of different investments. Suppose one investment involved an initial expenditure of $100 and yielded a single gain, 1 year later, of $105, while another investment also involved an initial investment of $100, but yielded a single gain of $106.12 after 3 years. In this example, the first investment would be regarded as economically preferable, even though the specific amount of money received was less, because it had an internal rate of return of 5 percent, while the second investment had an internal rate of return of only 2 percent. The superiority of the first investment is evidenced by the fact that the investor could have recycled the earnings in the same investment for 2 more years, which would have rendered a total of $115.76 after 3 years instead of $106.12.
For any given income stream of expenditures and gains from a research project or collection of projects, with expenditures represented by negative numbers and gains by positive numbers, the internal rate of return can be interpreted mathematically as the hypothetical interest rate that would cause the net present value of the income stream to be zero. It can be calculated by solving an equation in which the sum of all time-adjusted expenditures and gains is set to zero.*
From its definition, the internal rate of return can be calculated once all the gains, losses, and timeframes are known. Estimating rates of return for scientific research is difficult because of inherent problems that exist in estimating a project's potential gains and losses. For instance, research in one area may be interdependent with research in a related area, making it difficult for investors to separate their individual effects. Furthermore, society often gains more from a successful scientific advancement than does the organization conducting the research. Consequently, there are two rates of return: the private rate of return, which is based on the expenses incurred and profits made by the company conducting the research, and the social rate of return, which is based on the overall effects on society, including the firm conducting the research.
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