Strategic Management and Corporate Finance · Project Evaluation

NPV vs IRR Conflicts and Capital Rationing Explained

Updated 11 October 2026 · Fact-checked

NPV and IRR can rank mutually exclusive projects differently because of differences in project size, timing of cash flows or project life. Choose the project with the higher NPV, since it adds more wealth. Under capital rationing, pick the combination of projects that maximises total NPV within the budget. For unequal lives, compare equivalent annual annuities.

Understand NPV vs IRR Conflicts and Capital Rationing

NPV (net present value) gives the rupee wealth a project adds. IRR (internal rate of return) gives the rate at which NPV is zero. For a single project with normal cash flows, both give the same accept or reject answer. Trouble starts when you must pick one of several mutually exclusive projects.

The rankings conflict for three main reasons. First, scale: a small project can have a high IRR but a small NPV, while a large project has a lower IRR but a bigger NPV. Second, timing: one project returns cash early and another late. Cash received late is hurt more by a high discount rate, so the ranking can flip as the rate changes. Third, unequal lives: a longer project can show a bigger NPV just because it runs longer. A fourth issue is non-conventional cash flows (signs change more than once). These can give multiple IRRs or none.

The reason NPV wins is the reinvestment assumption. NPV assumes interim cash flows are reinvested at the cost of capital. IRR assumes they are reinvested at the IRR itself. The cost of capital is the more realistic rate, and the aim of the firm is to maximise shareholder wealth. So when the two conflict, follow NPV.

The crossover rate is the discount rate at which two projects have equal NPV. It is the IRR of the incremental cash flows (larger project minus smaller). If the cost of capital is below the crossover rate, the NPV and IRR rankings conflict. If it is above, they agree.

Capital rationing means the firm has a limit on funds, so it cannot take every project with a positive NPV. The limit may be external (hard rationing, such as lenders capping credit) or internal (soft rationing, such as a budget set by management). The aim then is to maximise total NPV from the funds available. If projects can be taken in part (divisible), rank by profitability index. If they are all-or-nothing (indivisible), test the feasible combinations and pick the one with the highest total NPV.

For unequal lives, you cannot compare raw NPVs. Use the replacement chain method (repeat each project until both reach a common end point) or, more simply, the equivalent annual annuity (EAA). EAA converts each NPV into a yearly figure. The higher EAA is better.

Key rules to remember

Net present value: NPV = Σ [Cash flow in year t ÷ (1 + r)^t] − Initial outlay; r is the cost of capital. Use NPV as the final decision rule for mutually exclusive projects.
IRR condition: Σ [Cash flow in year t ÷ (1 + IRR)^t] − Initial outlay = 0; Accept if IRR is greater than the cost of capital. IRR is unreliable for ranking exclusive projects.
Crossover rate: Rate r at which NPV(A) = NPV(B), i.e. IRR of (B − A) cash flows; Below this rate the NPV ranking and IRR ranking can conflict. Above it they agree.
Profitability index: PI = Present value of cash inflows ÷ Initial outlay = 1 + (NPV ÷ Outlay); Use to rank divisible projects under single-period capital rationing.
Present value annuity factor: PVAF(r, n) = [1 − (1 + r)^−n] ÷ r; Used to find the EAA.
Equivalent annual annuity: EAA = NPV ÷ PVAF(r, n); Choose the project with the higher EAA when lives are unequal and projects are repeatable.
Capital rationing rule: Maximise Σ NPV subject to Σ Outlay ≤ Budget; Divisible: rank by PI and fill the budget, taking a fraction of the last project. Indivisible: compare feasible combinations.

How to solve NPV vs IRR Conflicts and Capital Rationing questions

Use this order for any question on NPV vs IRR conflict, capital rationing or unequal lives.

1Read the question and decide the type: mutually exclusive projects, a budget limit, or unequal lives. Note whether projects are divisible.
2List cash flows year by year and the cost of capital. Check whether the cash flows are conventional.
3Compute NPV of each project using present value factors. Show the working.
4Compute IRR (or use the IRR given) and the PI if the question asks for it. Show the two rankings side by side.
5If the rankings conflict, name the cause: scale, timing or life. If asked, find the crossover rate from incremental cash flows.
6For capital rationing, rank by PI if divisible. If indivisible, list all combinations within the budget and add their NPVs.
7For unequal lives, compute EAA = NPV ÷ PVAF for each project, or use a common-life replacement chain.
8State the final recommendation based on NPV or EAA, with one line on why IRR misleads here.

Quickest way: NPV first, then fit the budget

When to use it: Use when time is short and the question gives cost of capital, outlays and cash flows.

Compute NPV for each project once. Everything else builds on it.
Conflict question: recommend the higher NPV and give the one-line reason (reinvestment at cost of capital, wealth maximisation).
Rationing question with divisible projects: compute PI = 1 + NPV ÷ outlay, rank, fill the budget, take a fraction of the last project.
Rationing question with indivisible projects: list only the combinations that fit the budget and add NPVs. Do not rely on PI ranking alone.
Unequal lives: divide each NPV by its annuity factor and compare. Do this before anything else.

Common mistakes in NPV vs IRR Conflicts and Capital Rationing

Recommending the project with the higher IRR when it conflicts with NPV for mutually exclusive projects.
IRR looks like a rate of return and feels easier to compare.
Fix: Follow NPV when the two conflict. State that IRR assumes reinvestment at the IRR, while NPV assumes the cost of capital.
Comparing raw NPVs of projects with different lives.
Students forget that a longer project earns for more years.
Fix: Convert each NPV to an EAA using the annuity factor for that project's life and compare the EAAs.
Ranking by PI and stopping when projects are indivisible.
PI ranking works cleanly only for divisible projects, and students apply it everywhere.
Fix: For indivisible projects, list every combination within the budget and choose the highest total NPV.
Taking a fraction of a project when the question says projects cannot be split.
Students copy the divisible-project method without checking the condition.
Fix: Underline 'divisible' or 'indivisible' in the question before choosing the method.
Calling any project with a positive NPV acceptable under capital rationing.
Students forget that the budget limit is binding.
Fix: Accept only the set that maximises total NPV within the limit. Say that some positive-NPV projects are rejected because of the budget.
Finding the crossover rate from the two projects' IRRs instead of incremental cash flows.
Confusion between the IRR of a project and the rate at which two NPVs are equal.
Fix: Subtract one project's cash flows from the other's year by year, then find the rate at which that incremental NPV is zero.

Worked examples

Example 1

Aarav Industries Ltd must choose one of two mutually exclusive projects. Cost of capital is 10%. Project A: outlay ₹10,00,000, inflow ₹13,00,000 at the end of year 1. Project B: outlay ₹10,00,000, inflow ₹17,28,000 at the end of year 3. Find NPV and IRR of each, find the crossover rate, and recommend a project.

Show the solution

NPV of A = 13,00,000 ÷ 1.10 − 10,00,000 = 11,81,818 − 10,00,000 = ₹1,81,818.
NPV of B = 17,28,000 ÷ (1.10)³ − 10,00,000. (1.10)³ = 1.331, so 17,28,000 ÷ 1.331 = 12,98,272. NPV = ₹2,98,272.
IRR of A: 13,00,000 ÷ (1 + r) = 10,00,000, so 1 + r = 1.30 and IRR = 30%.
IRR of B: 17,28,000 ÷ (1 + r)³ = 10,00,000, so (1 + r)³ = 1.728, 1 + r = 1.20 and IRR = 20%.
The rankings conflict: A has the higher IRR (30% vs 20%), B has the higher NPV (₹2,98,272 vs ₹1,81,818). The cause is timing: A returns cash in one year, B holds it for three years at a higher total.
Crossover rate: equate NPVs. 13,00,000 ÷ (1 + r) = 17,28,000 ÷ (1 + r)³, so (1 + r)² = 17,28,000 ÷ 13,00,000 = 1.3292. 1 + r = 1.1529, so r is about 15.29%.
The cost of capital (10%) is below the crossover rate (about 15.29%), so a conflict is expected. At a cost of capital above 15.29%, A would have the higher NPV as well.
Recommend B, because it adds more wealth and NPV assumes reinvestment at the cost of capital, which is more realistic than reinvestment at 30%.

Answer: NPV: A ₹1,81,818, B ₹2,98,272. IRR: A 30%, B 20%. Crossover rate is about 15.29%. Select Project B on the NPV criterion.

Example 2

Meera Textiles Ltd has a capital budget of ₹50 lakh. Four projects are available: P (outlay ₹20 lakh, NPV ₹6 lakh), Q (outlay ₹30 lakh, NPV ₹8 lakh), R (outlay ₹25 lakh, NPV ₹9 lakh) and S (outlay ₹15 lakh, NPV ₹3.5 lakh). (a) Select projects if they are indivisible. (b) Select projects if they are divisible.

Show the solution

(a) List combinations within ₹50 lakh: P+Q = ₹50 lakh, NPV 14. P+R = ₹45 lakh, NPV 15. P+S = ₹35 lakh, NPV 9.5. Q+S = ₹45 lakh, NPV 11.5. R+S = ₹40 lakh, NPV 12.5. Q+R = ₹55 lakh exceeds the budget. Any three-project set exceeds ₹50 lakh (the cheapest three, P+R+S, cost ₹60 lakh).
The highest total NPV is from P+R at ₹15 lakh, using ₹45 lakh. ₹5 lakh stays unused.
(b) Compute PI = 1 + NPV ÷ outlay. P = 1 + 6/20 = 1.30. Q = 1 + 8/30 = 1.267. R = 1 + 9/25 = 1.36. S = 1 + 3.5/15 = 1.233.
Rank by PI: R, P, Q, S.
Take R in full (₹25 lakh, NPV 9) and P in full (₹20 lakh, NPV 6). Total spent ₹45 lakh. ₹5 lakh remains.
Use the balance in Q: 5 ÷ 30 = 1/6 of Q. NPV from this part = 8 × 1/6 = ₹1.33 lakh (approx).
Total NPV = 9 + 6 + 1.33 = ₹16.33 lakh (approx).

Answer: (a) Indivisible: select P and R, total NPV ₹15 lakh. (b) Divisible: select R and P in full plus one-sixth of Q, total NPV about ₹16.33 lakh.

Exam tips

Show NPV and IRR side by side in a small working table, then write one clear line naming the cause of the conflict. Marks go for the reason as well as the numbers.
Always end with a firm recommendation and the reason (wealth maximisation, reinvestment at cost of capital). A computation without a conclusion loses marks.
In rationing questions, state your assumption on divisibility if the question is silent, and show the rejected combinations briefly.
For unequal lives, write the EAA formula first, then the annuity factor, then the division. Method marks are easy to get this way.
Keep present value factors and the annuity formula ready. If the question gives a table, use its factors rather than recomputing.

Practice questions from Project Evaluation

NPV vs IRR Conflicts and Capital Rationing in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

NPV vs IRR Conflicts and Capital Rationing: frequently asked questions

Why do NPV and IRR give different rankings?

They differ when projects have different sizes, different timing of cash flows, or different lives. NPV assumes reinvestment at the cost of capital, while IRR assumes reinvestment at the project's own IRR. The two methods can therefore rank the same projects differently.

Which should I follow when NPV and IRR conflict?

Follow NPV for mutually exclusive projects. It measures the absolute rupee wealth added and uses a more realistic reinvestment rate. In the exam, say this in one line along with your numbers.

What is capital rationing and how is it solved?

Capital rationing is a limit on the funds available for investment, so not all positive-NPV projects can be taken. If projects are divisible, rank them by profitability index and fill the budget. If they are indivisible, test feasible combinations and choose the one with the highest total NPV.

How do I compare projects with unequal lives?

Compute the NPV of each project, then divide it by the annuity factor for that project's life at the cost of capital. This gives the equivalent annual annuity. The project with the higher EAA is preferred, assuming the projects can be repeated.