NPV vs IRR Conflict: Mutually Exclusive Projects Worked Examples
When NPV and IRR disagree on which project to pick, NPV wins — and here is exactly why, with the crossover rate, the reinvestment-rate assumption, the multiple-IRR trap, and worked examples.
What You'll Learn
- ✓Explain why NPV and IRR can rank mutually exclusive projects differently.
- ✓Compute and interpret the crossover (Fisher) rate.
- ✓Recognize the multiple-IRR problem and when to use MIRR.
1. Direct Answer: When NPV and IRR Disagree, Use NPV
For a single independent project with conventional cash flows (one sign change), NPV and IRR always agree on accept/reject: NPV greater than zero corresponds to IRR greater than the discount rate. The conflict appears only with MUTUALLY EXCLUSIVE projects — where choosing one means rejecting the other — and only when they differ in SCALE (size of investment) or in the TIMING of their cash flows. When they disagree on ranking, ALWAYS choose the higher-NPV project, because NPV measures the absolute dollar value added to the firm, while IRR is only a percentage rate. The deep reason is the reinvestment-rate assumption: IRR implicitly assumes interim cash flows are reinvested at the IRR itself (often unrealistically high), whereas NPV assumes reinvestment at the discount rate (the firm's cost of capital), which is the economically correct assumption.
Key Points
- •NPV and IRR agree for a single conventional project; conflict arises with mutually exclusive ones.
- •Conflicts come from differences in scale or in cash-flow timing.
- •When rankings disagree, choose the higher NPV — it measures absolute value added.
2. Why the Reinvestment Assumption Matters
The hidden engine behind the conflict is what each method assumes happens to cash flows received during the project. IRR assumes every interim cash flow is reinvested at the project's own internal rate of return. If a project has a 25% IRR, that assumes you can keep redeploying its cash at 25% — rarely true. NPV assumes interim cash flows are reinvested at the discount rate (the WACC), which reflects the firm's realistic opportunity cost of capital. Because the NPV reinvestment assumption is the defensible one, NPV gives the economically correct ranking. This is also why a project with a very high IRR but a small scale can lose to a larger project with a lower IRR but a much bigger NPV: the percentage looks better, but the dollars created are smaller.
Key Points
- •IRR assumes reinvestment at the IRR (often unrealistic).
- •NPV assumes reinvestment at the cost of capital (realistic).
- •A high IRR on a small project can create fewer dollars than a lower IRR on a large one.
3. The Crossover (Fisher) Rate
The crossover rate, or Fisher intersection, is the discount rate at which two projects have EQUAL NPV. Below the crossover rate, the project with the larger or later cash flows has the higher NPV; above it, the ranking flips. To find it, take the differences between the two projects' cash flows period by period and solve for the IRR of that incremental cash-flow stream — that incremental IRR is the crossover rate. The practical insight: if your firm's discount rate is below the crossover, NPV and IRR may rank the projects differently; if it is above the crossover, they agree. Knowing the crossover rate tells you exactly when to worry about a conflict. Always compare your actual cost of capital to the crossover to see which side of the flip you are on.
Key Points
- •Crossover rate = the discount rate where two projects have equal NPV.
- •Find it as the IRR of the incremental (difference) cash flows.
- •Below the crossover, rankings can conflict; above it, NPV and IRR agree.
4. Worked Example: Scale Conflict
Two mutually exclusive projects, cost of capital 10%. PROJECT A: invest $10,000, receive $13,000 in one year. NPV = -10,000 + 13,000/1.10 = -10,000 + 11,818 = $1,818; IRR = 30%. PROJECT B: invest $100,000, receive $120,000 in one year. NPV = -100,000 + 120,000/1.10 = -100,000 + 109,091 = $9,091; IRR = 20%. IRR ranks A first (30% > 20%); NPV ranks B first ($9,091 > $1,818). This is a classic SCALE conflict: A has the higher percentage return but B creates five times the absolute value. Choose B — the firm is $9,091 richer versus $1,818, and you cannot 'spend' a percentage. If A and B were independent (both could be funded), you would take both; the conflict only forces a choice because they are mutually exclusive.
Key Points
- •Project A: NPV $1,818, IRR 30%. Project B: NPV $9,091, IRR 20%.
- •IRR favors the small high-percentage project; NPV favors the large value-creating one.
- •Choose Project B — it adds far more absolute value.
5. The Multiple-IRR Problem and MIRR
When a project has NON-CONVENTIONAL cash flows — more than one sign change in the cash-flow stream (for example, a large cleanup cost at the end of a mining project) — the IRR equation can have MULTIPLE solutions or none at all. A project with two sign changes can have two different IRRs, neither of which is meaningful for a decision. NPV has no such problem and remains valid. The fix when you still want a rate is the MODIFIED INTERNAL RATE OF RETURN (MIRR), which assumes interim cash flows are reinvested at the cost of capital (not the IRR), producing a single, defensible rate. MIRR resolves both the multiple-IRR issue and the unrealistic reinvestment assumption. The hierarchy to remember: NPV is the primary rule; MIRR fixes IRR's flaws; plain IRR is for intuition and communication only.
Key Points
- •Non-conventional cash flows (multiple sign changes) can produce multiple or no IRRs.
- •NPV is unaffected; MIRR gives a single rate using cost-of-capital reinvestment.
- •Hierarchy: NPV primary, MIRR to fix IRR, IRR for intuition only.
6. Solving NPV vs IRR Problems in FinanceIQ
Snap a photo of a capital-budgeting problem and FinanceIQ computes NPV, IRR, and MIRR for each project, finds the crossover rate from the incremental cash flows, identifies whether a scale or timing conflict exists, and recommends the higher-NPV choice with the reasoning shown step by step. It also flags non-conventional cash flows that trigger the multiple-IRR problem. This content is for educational purposes only and does not constitute financial advice.
Key Points
- •Computes NPV, IRR, and MIRR and the crossover rate.
- •Identifies scale vs timing conflicts and flags multiple-IRR cases.
- •Recommends the higher-NPV project with the reasoning shown.
Key Takeaways
- ★Conflicts arise only with mutually exclusive projects differing in scale or timing.
- ★Always defer to NPV — it measures absolute value added; IRR is only a percentage.
- ★IRR assumes reinvestment at the IRR; NPV assumes reinvestment at the cost of capital.
- ★Crossover (Fisher) rate = IRR of the incremental cash flows; below it, rankings can flip.
- ★Non-conventional cash flows cause multiple IRRs — use NPV or MIRR.
Practice Questions
1. Project X: NPV $5,000, IRR 18%. Project Y: NPV $8,000, IRR 14%. They are mutually exclusive. Which do you choose?
2. What does the crossover rate represent?
3. A project's cash flows are -100, +260, -165. Why might IRR mislead?
FAQs
Common questions about this topic
NPV measures the actual dollar value a project adds to the firm and uses the realistic assumption that interim cash flows are reinvested at the cost of capital. IRR is a percentage that assumes reinvestment at the IRR itself, which is often unrealistic, and it can mislead with mutually exclusive projects of different scale or timing and break down entirely with non-conventional cash flows. When the two disagree, NPV gives the value-maximizing decision.
Only for mutually exclusive projects — where you must pick one — that differ in scale (one is much larger) or in the timing of their cash flows (one front-loaded, one back-loaded). For independent projects with conventional cash flows, NPV and IRR always agree on accept or reject. The conflict is a ranking problem specific to having to choose between alternatives.
The modified internal rate of return assumes interim cash flows are reinvested at the firm's cost of capital rather than at the IRR, producing a single rate that fixes IRR's unrealistic reinvestment assumption and the multiple-IRR problem. Use it when you want a percentage measure but the project has non-conventional cash flows or when IRR's reinvestment assumption distorts the comparison. NPV remains the primary decision rule.
Yes, when its cash flows are non-conventional — meaning the cash-flow signs change more than once over the project's life, such as an initial outflow, then inflows, then a large final cleanup outflow. Each sign change can introduce another root to the IRR equation, so a project with two sign changes can have two IRRs. Neither is meaningful for the decision; rely on NPV or MIRR instead.
Snap a photo of the capital-budgeting problem and FinanceIQ computes NPV, IRR, and MIRR for each project, finds the crossover rate, identifies whether a scale or timing conflict exists, flags non-conventional cash flows, and recommends the higher-NPV choice with the full reasoning. This content is for educational purposes only and does not constitute financial advice.