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Interest is a cost, so we expect that higher interest will mean lower profits. Indeed, the profitability of an investment can be judged by the rate of interest it could pay and still be profitable. Here is the way that works.
An investment will require an outlay now, and will pay out net revenues only over some period in the future. Consider, for example, an investment that requires one to spend $100,000,000 in the first year, pays back nothing in the second year, and then pays back $10,000,000 every year for the next eighteen years. If we simply add up the 18 years of net revenue at $10 million per year, it seems that the investment pays back $180 million, and that sounds pretty good. But that's not right, because we haven't taken the opportunity cost of interest into account. For example, assume the rate of interest is 7%, and consider the $10 million payback in year 5. But $10 million in year five is not worth $10 million today. If I had the 10 million today, I could invest it at 7%, and in five years I would have $13.11 million, with four years of compound interest. To judge the profitability of the investment, we have to express the payback in terms of what the payments are worth in terms of dollars in hand today. If I were to invest $7,628,952.12, then in four years at 7% compound interest I would have $10,000,000. So that's all ten million five years from now is worth today -- $7,628,952.12. This is called "discounting to present value," and $7,628,952.12 is the present value of $10,000,000 in five years at 7% interest.
So the way to judge whether the investment is profitable or not is to discount the future net revenues for each year to present value, add them all up, and deduct the initial investment. If the net is positive, then the investment is profitable, and the profit is the difference -- discounted future net revenues minus present investment. Table 1 shows the discounted values for all years for the twenty-year investment in our example.
The discounted present value, and the profitability, will depend on the rate of interest we use for the calculation. In Table 1, three interest rates are shown: 5%, 6.25%, and 7%. At a rate of 7%, the investment is not profitable -- its net revenues over 20 years are only worth $94,010,158.03, and it loses $5,989,841.97. But at 5%, the opportunity cost of interest is less, and the net revenues of the investment are worth $111,329,399.07, for a profit of $11,329,399.07 in present value dollars. At an interest rate of 6.25%, the future revenues of the investment are worth exactly $100,000,000.00, and the investment just breaks even! (If you try this on your own spreadsheet, it might help to know that the 6.25% has been rounded off. The exact number is 6.252493909%).
Thus, 6.25% (plus a little) is the internal rate of return for the twenty-year investment in our example.
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