A New Perspective on Multiple Internal Rates of Return

The most commonly cited drawback to using the internal rate of return to evaluate deterministic cash flow streams is the possibility of multiple conflicting internal rates, or no internal rate at all. We claim, however, that contrary to current consensus, multiple or nonexistent internal rates are not contradictory, meaningless or invalid as rates of return. There is, moreover, no need to carefully examine a cash flow stream to rule out the possibility of multiple internal rates, or to throw out or ignore “unreasonable” rates. What we show is that when there are multiple (or even complex-valued) internal rates, each has a meaningful interpretation as a rate of return on its own underlying investment stream.It does not matter which rate is used to accept or reject the cash flow stream, as long as one identifies the underlying investment stream as a net investment or net borrowing. When we say it does not matter which rate is used, we mean that regardless of which rate is chosen, the cash-flow acceptance or rejection decision will be the same, and consistent with net present value.