Financial Management and Business Data Analytics · Capital Budgeting

NPV vs IRR Conflict, Unequal Lives and Replacement Decisions

Updated 10 October 2026 · Fact-checked

When projects are mutually exclusive, NPV and IRR can rank them differently. Trust NPV, because it measures the rupee gain in wealth, or check the incremental cash flows. For projects with unequal lives, compare the equivalent annual annuity (NPV ÷ annuity factor) or equivalent annual cost, not raw NPV.

Understand Comparing Projects: Ranking Conflicts and Unequal Lives

Mutually exclusive projects are alternatives where choosing one rules out the others, such as two machines for the same job. For a single independent project, NPV and IRR always give the same accept or reject answer. Conflicts only appear when you must rank projects.

Why do NPV and IRR disagree? There are three usual causes. First, scale: a small project can have a high IRR but a small rupee gain. Second, timing: one project returns cash early, another late. Third, unequal lives. IRR is a percentage return. NPV is a rupee increase in wealth. The firm's goal is wealth maximisation, so when they conflict, NPV wins. NPV also assumes cash flows are reinvested at the cost of capital, which is a more realistic assumption than IRR's assumption of reinvestment at the IRR itself.

You can also settle a conflict with the incremental (differential) project. Subtract the cash flows of the smaller or cheaper project from the larger one. If the incremental IRR is above the cost of capital, the extra investment is worthwhile, so choose the larger project. This gives the same answer as NPV.

When lives are unequal, a higher NPV may only mean the project runs longer. Two fixes exist. The replacement chain method repeats each project until both reach a common life (the LCM of lives). The equivalent annual annuity (EAA) method converts each NPV into a yearly amount. For cost-only projects, use equivalent annual cost (EAC). EAA is faster and is preferred in exams.

In a replacement decision, you compare keeping the old asset with buying a new one. Use only relevant, incremental cash flows: sale value of the old asset, its tax effect, savings in operating cost, and extra depreciation tax shield. Past cost of the old asset is sunk and ignored. Under capital rationing, funds are limited, so you pick the combination of projects with the highest total NPV within the budget, usually guided by the profitability index.

Key rules to remember

Net present value: NPV = Σ [Cash inflow(t) ÷ (1 + k)^t] − Initial outlay; k is the cost of capital. In a conflict, the higher NPV project is preferred for mutually exclusive projects.
Incremental IRR rule: Choose larger project if IRR of (Larger − Smaller) cash flows > k; Gives the same decision as NPV. Compute incremental flows year by year.
Equivalent annual annuity (EAA): EAA = NPV ÷ PVAF(k, n); PVAF is the present value annuity factor for the project's own life n. Higher EAA is better.
Equivalent annual cost (EAC): EAC = PV of all costs ÷ PVAF(k, n); Use for cost-only machines. Lower EAC is better.
Profitability index: PI = PV of cash inflows ÷ Initial outlay; Used to rank projects under capital rationing when projects are divisible.
Replacement chain: Common life = LCM of project lives; Repeat each project over the common life, then compare total NPVs.

How to solve Comparing Projects: Ranking Conflicts and Unequal Lives questions

Use this method for conflict, unequal life, replacement and rationing questions.

1Read the question and mark whether projects are independent or mutually exclusive, and whether lives are equal.
2List the relevant cash flows for each project. Ignore sunk costs and include tax effects and salvage value if given.
3Compute NPV at the given cost of capital. Compute IRR only if asked.
4If NPV and IRR rank differently on mutually exclusive projects, state the cause (scale, timing or life) and prefer the higher NPV. Support it with incremental cash flows if the question asks.
5If lives are unequal, calculate EAA (or EAC for costs) using the annuity factor of each project's own life, or use the replacement chain.
6For a replacement decision, build incremental cash flows: old asset sale value, savings, extra depreciation shield, and compare NPV of replacing with keeping.
7For capital rationing, compute PI, rank, pick projects within the budget, and check combinations if projects are indivisible.
8Write a clear final recommendation with the reason.

Quickest way: Rank by NPV, then fix the life

When to use it: Use when time is short and the question gives discount factors or annuity factors.

Compute NPV for each project first. This is the decision basis for mutually exclusive projects.
If lives differ, divide each NPV (or PV of cost) by its own annuity factor and compare the annual figures.
For a quick conflict check, subtract the cash flows and compare incremental IRR with the cost of capital.
Under rationing, divide NPV or PV of inflows by outlay, rank, and fill the budget. Test one alternative combination if a project does not fit exactly.
State the decision in one line with the reason.

Common mistakes in Comparing Projects: Ranking Conflicts and Unequal Lives

Choosing the project with the higher IRR when NPV disagrees
Percentage returns look more impressive and are easy to compare.
Fix: For mutually exclusive projects, choose the higher NPV at the cost of capital, and say why IRR misleads (scale or timing).
Comparing NPVs of projects with different lives directly
Students assume a higher NPV always means a better project.
Fix: Convert to EAA or EAC, or extend to a common life using the replacement chain.
Using the annuity factor of the wrong life
Students use one factor for both projects to save time.
Fix: Each project's EAA or EAC uses its own life's annuity factor at the same rate.
Including the original cost or book value of the old asset as a cash flow in replacement
Sunk cost feels relevant because it is on the balance sheet.
Fix: Only the sale value of the old asset and its tax effect are relevant. Book value matters only for the tax calculation.
Picking the cheapest machine by PV of costs when lives differ
Lower total cost looks cheaper, but it buys fewer years of service.
Fix: Compare EAC, which is cost per year of service.
Ranking only by NPV under capital rationing
Students forget the budget limit changes the objective.
Fix: Rank by PI and choose the combination with the highest total NPV within the budget.

Worked examples

Example 1

Cost of capital is 10%. Project A needs ₹1,00,000 now and returns ₹1,30,000 after one year. Project B needs ₹5,00,000 now and returns ₹6,25,000 after one year. They are mutually exclusive. Rank by NPV and IRR, and recommend one.

Show the solution

NPV of A = 1,30,000 ÷ 1.10 − 1,00,000 = 1,18,181.82 − 1,00,000 = ₹18,181.82.
NPV of B = 6,25,000 ÷ 1.10 − 5,00,000 = 5,68,181.82 − 5,00,000 = ₹68,181.82.
IRR of A = 1,30,000 ÷ 1,00,000 − 1 = 30%. IRR of B = 6,25,000 ÷ 5,00,000 − 1 = 25%.
IRR ranks A first, NPV ranks B first. The conflict arises from scale: B is five times larger.
Incremental project (B − A): outlay ₹4,00,000, inflow ₹4,95,000 after one year. Incremental IRR = 4,95,000 ÷ 4,00,000 − 1 = 23.75%, which is above 10%.
Incremental NPV = 4,95,000 ÷ 1.10 − 4,00,000 = 4,50,000 − 4,00,000 = ₹50,000, which equals 68,181.82 − 18,181.82.

Answer: Choose Project B. It has the higher NPV (₹68,181.82 against ₹18,181.82) and the extra investment earns 23.75%, more than the 10% cost of capital.

Example 2

A firm must choose one machine at a cost of capital of 10%. Machine P costs ₹3,00,000, lasts 3 years and has annual operating cost of ₹60,000. Machine Q costs ₹4,50,000, lasts 5 years and has annual operating cost of ₹50,000. Neither has salvage value. PVAF at 10%: 3 years = 2.4869; 5 years = 3.7908. Which machine should be bought?

Show the solution

PV of costs of P = 3,00,000 + 60,000 × 2.4869 = 3,00,000 + 1,49,214 = ₹4,49,214.
PV of costs of Q = 4,50,000 + 50,000 × 3.7908 = 4,50,000 + 1,89,540 = ₹6,39,540.
These totals cover different lives, so they cannot be compared directly.
EAC of P = 4,49,214 ÷ 2.4869 = ₹1,80,632 (approx.).
EAC of Q = 6,39,540 ÷ 3.7908 = ₹1,68,709 (approx.).
Q has the lower annual cost.

Answer: Buy Machine Q. Its equivalent annual cost of about ₹1,68,709 is lower than P's about ₹1,80,632, even though its total PV of costs is higher.

Exam tips

In a conflict question, always name the cause (scale, timing or life) and state that NPV is preferred because it maximises wealth.
Show incremental cash flows in a small table when asked to resolve a conflict. It earns step marks and checks your NPV.
Use the annuity factor given in the question for each life. Do not recompute from scratch if factors are supplied.
In replacement problems, list relevant cash flows first and write clearly that sunk cost is ignored.
For MCQs, remember: independent projects give no conflict, and cost-only projects use the lowest EAC, not the highest.

Practice questions from Capital Budgeting

Comparing Projects: Ranking Conflicts and Unequal Lives in other exams

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

CFA Level IConflicts Between NPV and IRR Rankings

Comparing Projects: Ranking Conflicts and Unequal Lives: frequently asked questions

Why do NPV and IRR give different rankings?

They differ when projects have different scale, timing of cash flows or lives. NPV assumes reinvestment at the cost of capital, while IRR assumes reinvestment at the IRR itself. For mutually exclusive projects, the NPV ranking is preferred.

When should I use equivalent annual annuity?

Use it when mutually exclusive projects have unequal lives and can be repeated. Divide each NPV by the annuity factor of its own life. Choose the higher EAA, or for costs the lower EAC.

What is the difference between replacement chain and EAA?

The replacement chain repeats each project until a common life, such as the LCM of lives, and compares total NPVs. EAA converts each NPV into a yearly amount. Both lead to the same decision, but EAA is quicker.

How is capital rationing solved?

Compute the profitability index of each project, rank them, and select projects until the budget is used. If projects are indivisible, check combinations and choose the one with the highest total NPV within the budget.