# Incremental internal rate of return

The incremental internal rate of return is an analysis of the financial return to an investor or entity where there are two competing investment opportunities involving different amounts of investment. The analysis is applied to the difference between the costs of the two investments. Thus, you would subtract the cash flows associated with the less expensive alternative from the cash flows associated with the more expensive alternative to arrive at the cash flows applicable to the difference between the two alternatives, and then conduct an internal rate of return analysis on this difference.

Based just on quantitative analysis, you would select the more expensive investment opportunity if it has an incremental internal rate of return higher than the minimum return you consider acceptable. However, there are qualitative issues to consider as well, such as whether there is an incremental increase in risk associated with the more expensive investment. Therefore, realistically, the investor must weigh a variety of factors besides just the incremental internal rate of return before making an investment decision. This rate of return may not even be the deciding factor in making an investment decision.

If the investor believes that there is a considerable amount of additional risk associated with the more expensive investment opportunity, he or she can adjust for this risk by increasing the minimum return considered acceptable. For example, the minimum rate of return threshold for a low-risk investment might be 5%, while the threshold might be 10% for a high-risk investment.

Incremental Internal Rate of Return Example

ABC International is considering obtaining a color copier, and it can do so either with a lease or an outright purchase. The lease involves a series of payments over the three-year useful life of the copier, while the purchase option involves more cash up-front and some continuing maintenance, but it also has a resale value at the end of its useful life. The following analysis of the incremental differences in the cash flows between the two alternatives reveals that there is a positive incremental internal rate of return for the purchasing option. Barring any other issues (such as available cash to buy the copier), the purchasing option therefore appears to be the better alternative.

 Year Lease Buy Difference 0 -\$7,000 -\$29,000 -\$22,000 1 -7,000 -1,500 5,500 2 -7,000 -1,500 5,500 3 -7,000 -1,500 5,500 Resale +\$15,000 15,000 Incremental IRR 13.3%