Strategic Financial Management · Investment Decisions, Project Planning and Control

Capital Rationing and Unequal Project Lives Explained

Updated 11 October 2026 · Fact-checked

Capital rationing means choosing projects when funds are limited, so you maximise total NPV within the budget, using profitability index ranking for divisible projects and combination testing for indivisible ones. For mutually exclusive projects with different lives, compare them using the replacement chain method or the equivalent annual annuity, not raw NPV.

Understand Capital Rationing and Unequal Project Lives

Normal NPV logic says accept every project with a positive NPV. This assumes you can raise any amount of money at the cost of capital. In real life you often cannot. A board may fix a budget for the year. That is capital rationing. Now the goal changes: pick the set of projects that gives the highest total NPV within the budget.

The tool is the profitability index (PI), which is NPV per rupee of outlay (plus one). If projects are divisible (you can take part of a project), rank by PI and fund from the top until money runs out. If projects are indivisible (all or nothing), PI ranking can mislead because leftover money may sit idle. Then you list feasible combinations and pick the one with the highest total NPV. If the budget also applies to next year, the problem becomes multi-period and usually needs linear programming, so in exams read what the question permits.

The second issue is unequal project lives. Suppose you must choose one of two mutually exclusive machines, one lasting 3 years and the other 6 years. The 6-year machine will usually show a higher NPV simply because it earns for longer. That is not a fair comparison. You need to put both on the same time footing.

There are two ways. In the replacement chain method, you assume each project is repeated until both end together, at the lowest common multiple of their lives, and compare the total NPVs. In the equivalent annual annuity (EAA) method, you convert each NPV into a yearly amount over its own life and pick the higher one. Both give the same ranking when the assumption of repeating at the same terms holds. For machines that only cost money and earn no direct revenue, use the equivalent annual cost and pick the lower one.

Both methods assume that the project can be repeated on the same terms. If costs, prices or technology are likely to change, say so in your answer. That is where marks for judgement come from.

Key rules to remember

Profitability index: PI = PV of cash inflows ÷ Initial outlay = 1 + (NPV ÷ Initial outlay); Some books define it as NPV ÷ outlay. Check the question and state your definition. Both give the same ranking.
Capital rationing objective: Maximise Σ NPV of selected projects, subject to Σ outlay ≤ budget; For indivisible projects, test combinations. For divisible projects, rank by PI and part-fund the last project.
Annuity factor: PVAF(r, n) = [1 − (1 + r)^(−n)] ÷ r; Use the table value given in the question if provided.
Equivalent annual annuity: EAA = NPV ÷ PVAF(r, n); n is the project's own life. Choose the project with the higher EAA.
Equivalent annual cost: EAC = PV of all costs ÷ PVAF(r, n); Use when projects only have costs. Choose the lower EAC.
Replacement chain NPV: Chain NPV = NPV + NPV ÷ (1 + r)^n + NPV ÷ (1 + r)^(2n) + ... over the common life; Common life is the lowest common multiple of the project lives. Add each repeat's NPV discounted back to today.

How to solve Capital Rationing and Unequal Project Lives questions

First decide which problem you have: a budget limit across many projects, or a choice between mutually exclusive projects with different lives. Some questions combine both.

1Read the question for the budget, whether projects are divisible, and whether they are independent or mutually exclusive.
2Compute the NPV of each project at the given cost of capital, using its own cash flows and life.
3For capital rationing, compute the PI of each project and rank them from highest to lowest.
4If projects are divisible, fund in PI order and take only a fraction of the last project that fits. Add up the NPV.
5If projects are indivisible, list every combination that fits within the budget and compare total NPVs. Do not trust PI order alone.
6For unequal lives, find the lowest common multiple of the lives and build the replacement chain, or compute EAA = NPV ÷ PVAF for each project.
7Compare on the common basis and state the recommendation in a sentence, with the assumption that projects can be repeated on the same terms.
8Mention unused funds, and any qualitative factors, if the question asks for comments.

Quickest way: PI ranking then combination check, and EAA over replacement chain

When to use it: Use when time is short and the question has many projects or a long common life, such as 4 years against 6 years or 5 years against 7 years.

For rationing, compute PI for every project in one table with outlay, NPV and PI columns.
Fund in PI order and note how much budget is left. If the leftover is large and projects are indivisible, test two or three swaps that use the budget fully.
For unequal lives, skip the chain. Compute EAA = NPV ÷ PVAF for each project and compare.
Use the replacement chain only when the question asks for it, or when the lowest common multiple is small.
Write one line of recommendation, since that is what the examiner looks for.

Common mistakes in Capital Rationing and Unequal Project Lives

Ranking by PI and stopping, even when projects are indivisible.
PI ranking is taught first and it feels complete.
Fix: With indivisible projects, always check whether another combination uses the budget better and gives a higher total NPV.
Comparing raw NPVs of projects with different lives.
NPV is the standard decision rule, so students apply it automatically.
Fix: Whenever mutually exclusive projects have different lives, convert to EAA or use a replacement chain first.
Using the wrong life when computing EAA.
Students use the common life of 6 years for both projects.
Fix: EAA uses each project's own life in the annuity factor.
Choosing the higher EAC for cost-only projects.
Students carry over the 'higher is better' rule from EAA.
Fix: For costs, lower equivalent annual cost is better. Label the figure as cost.
Forgetting to discount the later repeats in the replacement chain.
Students add the same NPV twice without adjusting for time.
Fix: Discount each repeat's NPV back to year 0 by the year in which the repeat starts.
Selecting projects with PI below 1 just to use up the budget.
Students want to spend the full amount.
Fix: A project with a negative NPV (PI below 1) reduces value. Leave unused funds idle or invest them elsewhere.

Worked examples

Example 1

A company has a capital budget of ₹100 lakh for the year. Five independent projects are available with the following outlay and NPV (₹ lakh): A: 40 and 18; B: 30 and 12; C: 50 and 22; D: 20 and 10; E: 60 and 21. Select the best set of projects if (a) projects are divisible and (b) projects are indivisible.

Show the solution

Compute PI = 1 + NPV ÷ outlay. A = 1 + 18/40 = 1.45. B = 1 + 12/30 = 1.40. C = 1 + 22/50 = 1.44. D = 1 + 10/20 = 1.50. E = 1 + 21/60 = 1.35.
Rank by PI: D (1.50), A (1.45), C (1.44), B (1.40), E (1.35).
(a) Divisible: fund D fully (₹20 lakh, NPV 10). Budget left is ₹80 lakh. Fund A fully (₹40 lakh, NPV 18). Budget left is ₹40 lakh. Take C partly: 40/50 = 0.8 of C, NPV = 0.8 × 22 = 17.6.
Total NPV for (a) = 10 + 18 + 17.6 = ₹45.6 lakh.
(b) Indivisible, PI order only: D (20) + A (40) = 60. C (50) does not fit. B (30) fits, total outlay 90, NPV = 10 + 18 + 12 = 40.
Test other combinations. B + C + D = 30 + 50 + 20 = 100, NPV = 12 + 22 + 10 = 44. A + C = 90, NPV 40. A + E = 100, NPV 39. A + B + D = 90, NPV 40. D + E = 80, NPV 31. B + E = 90, NPV 33. No other combination within ₹100 lakh beats 44.

Answer: (a) Divisible: take D, A and 80% of C for a total NPV of ₹45.6 lakh. (b) Indivisible: take B, C and D, using the full ₹100 lakh, for a total NPV of ₹44 lakh. PI order alone would give only ₹40 lakh in (b).

Example 2

Choose between two mutually exclusive machines at a cost of capital of 10%. Machine A costs ₹6,00,000, has a life of 3 years and gives a net cash inflow of ₹3,00,000 a year. Machine B costs ₹10,00,000, has a life of 6 years and gives a net cash inflow of ₹3,00,000 a year. Use PVAF at 10%: 3 years = 2.4869, 6 years = 4.3553. PV factor at 10% for year 3 = 0.7513. Evaluate by (a) equivalent annual annuity and (b) replacement chain.

Show the solution

NPV of A = 3,00,000 × 2.4869 − 6,00,000 = 7,46,070 − 6,00,000 = ₹1,46,070.
NPV of B = 3,00,000 × 4.3553 − 10,00,000 = 13,06,590 − 10,00,000 = ₹3,06,590.
The raw NPV favours B, but the lives differ, so compare on a common basis.
(a) EAA of A = 1,46,070 ÷ 2.4869 ≈ ₹58,736. EAA of B = 3,06,590 ÷ 4.3553 ≈ ₹70,395.
(b) The common life is 6 years. Machine A is repeated once, starting at year 3. NPV of the repeat at year 0 = 1,46,070 × 0.7513 ≈ ₹1,09,742.
Chain NPV of A over 6 years = 1,46,070 + 1,09,742 = ₹2,55,812.
Chain NPV of B = ₹3,06,590, since it already runs for 6 years.
Both methods rank B above A.

Answer: Choose Machine B. Its EAA of about ₹70,395 beats A's ₹58,736, and its 6-year NPV of ₹3,06,590 beats A's replacement chain NPV of ₹2,55,812. This assumes A can be repeated on the same terms.

Exam tips

Read whether projects are divisible, indivisible or mutually exclusive before starting. The method depends on it.
Show a PI table with outlay, NPV and PI in one place. It earns marks and prevents slips.
In indivisible cases, show the combinations you tested and say which is best. Do not just state the answer.
Write the recommendation and the key assumption (projects can be repeated on the same terms) in one or two lines.
Use the annuity factors given in the question. Do not recalculate them, since small rounding differences can change your figure.

Practice questions from Investment Decisions, Project Planning and Control

Capital Rationing and Unequal Project Lives in other exams

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

Capital Rationing and Unequal Project Lives: frequently asked questions

What is capital rationing in simple words?

It is a situation where the company has a limited budget and cannot take up all projects with positive NPV. You then pick the set of projects that gives the highest total NPV within the budget.

When does PI ranking fail under capital rationing?

It can fail when projects are indivisible. After funding the top-ranked ones, some money may be left over that no remaining project can use. A different combination can then give a higher total NPV.

Which is better, the replacement chain or the equivalent annual annuity method?

Both give the same ranking under the same assumptions. EAA is faster when the common life is long, and the replacement chain is easier to explain when the common life is short. Use the one the question asks for.

Do I use EAA for projects with only costs?

Yes, but compute the equivalent annual cost instead, which is the present value of costs divided by the annuity factor. The project with the lower equivalent annual cost is preferred.