Why can the project with the higher IRR have the lower NPV?

Define the comparison before ranking anything

NYU Stern’s investment-return teaching material distinguishes NPV, a discounted sum including the initial investment, from IRR, the discount rate setting that sum to zero. It discusses why percentage and dollar measures can rank projects differently.

Stipulate two mutually exclusive fictional projects, both ending after one year. Assume their stated cash flows occur exactly as modeled, use one currency and have the same stipulated 10% annual discount rate. Ignore taxes, financing effects, fees, intermediate cash flows and any value after the final receipt. These simplifications are not a risk assessment.

Compute both measures on the same timeline

Project A pays 100 at time 0 and receives 130 at time 1. Its IRR is 130/100−1=30%. Its NPV at 10% is−100+130/1.10=18.181818, approximately 18.18 in currency units.

Project B pays 1,000 at time 0 and receives 1,200 at time 1. Its IRR is 20%, but its NPV at 10% is−1,000+1,200/1.10=90.909091, approximately 90.91. A has the higher modeled percentage; B has the larger modeled present-value surplus. The two statements are consistent.

Inspect the extra outlay and receipt

The B-minus-A comparison requires an additional 900 at time 0 and yields an additional 1,070 at time 1. Its incremental IRR is 1,070/900−1=18.888889%. Discounting that incremental receipt at 10% gives an incremental NPV of−900+1,070/1.10=72.727273.

That 72.727273 equals 90.909091−18.181818, so the original and incremental ledgers reconcile. The calculation exposes which extra cash-flow commitment is being compared. It does not assume that the unused capital under A could earn any particular return or that additional financing is actually available.

Change the discount assumption visibly

The NPV difference becomes zero at 1,070/900−1, approximately 18.888889%. This is the crossover rate for these particular one-year cash flows. At a 25% discount rate, A’s NPV is−100+130/1.25=4, while B’s is−1,000+1,200/1.25=−40.

The crossover is a sensitivity result, not a measured cost of capital. A discount rate must be appropriate for the modeled cash flows and risk; changing it solely to obtain a preferred ranking would conceal the decision’s dependence on assumptions.

State what the worksheet has not decided

A capital budget, different risks, unequal lives, strategic constraints or omitted follow-on expenditure could alter a real comparison. Cash-flow patterns with several sign changes can also have multiple IRRs or no useful single IRR. Our one-outflow/one-inflow examples avoid that ambiguity.

The lesson is to report both the percentage and the currency calculation with their timeline. Neither a high IRR nor a positive NPV alone verifies that a cash-flow forecast is credible, executable or suitable for an investor. No project should be selected from these invented numbers.

Method, sources, and limits

All cash flows, discount assumptions and the crossover check are original hypothetical teaching inputs, recomputed on 27 October 2026. The source supplies conceptual definitions; no source project’s empirical returns are reproduced. This AI-assisted worksheet is not a qualified human valuation or investment review.