Financial Management and Strategic Management · Investment Decisions

Capital Rationing and Unequal Project Lives

Updated 4 October 2026 · Fact-checked

Capital rationing means choosing projects when funds are limited. Rank divisible projects by profitability index; for indivisible ones, test combinations within the budget and pick the highest total NPV. For mutually exclusive projects with different lives, divide each NPV by its annuity factor to get the equivalent annual annuity, then choose the higher.

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. The firm may have a fixed budget for the year. This is capital rationing. Now the goal changes. You must pick the set of projects that gives the highest total NPV within the budget.

There are two cases. If projects are divisible, you can take a part of a project and earn the same proportion of its NPV. Here you rank projects by profitability index (PI), because PI shows NPV-linked return per rupee of scarce funds. You fund the highest PI first, and the last project may be taken only in part. If projects are indivisible, you must take a project fully or not at all. Ranking by PI may then leave money unused, so you list the feasible combinations and pick the one with the highest total NPV.

A second problem arises when you compare mutually exclusive projects with different lives. A project that runs 5 years will usually show a bigger NPV than one that runs 3 years, simply because it runs longer. This is not a fair comparison. The fix is to convert each NPV into an equal yearly amount. This is the equivalent annual annuity (EAA). It is the annual cash flow, over the project's own life, that has the same present value as its NPV.

The project with the higher EAA is better. The other approach is the replacement chain method. You repeat each project until both reach a common time horizon (the LCM of the lives) and compare the NPVs over that horizon. Both methods assume the projects can be repeated on the same terms. EAA is shorter, so it is the usual exam choice.

Key rules to remember

Profitability Index: PI = PV of cash inflows ÷ PV of cash outflows = 1 + (NPV ÷ initial outlay); Use this to rank divisible projects under a single-period budget. Where the outlay is all at time 0, both forms give the same value.
Capital rationing rule (divisible): Rank by PI (highest first). Fund in order until the budget ends. Take the last project in proportion.; Partial NPV = (funds used ÷ full outlay) × NPV of that project.
Capital rationing rule (indivisible): Choose the feasible combination with the highest total NPV, with total outlay ≤ budget; A combination that uses the whole budget is not always the best. Compare NPVs, not PIs.
Present value annuity factor: PVAF(r, n) = [1 − (1 + r)^−n] ÷ r; Usually given in the PV annuity table. Use the factor for the project's own life.
Equivalent Annual Annuity: EAA = NPV ÷ PVAF(r, n); Use for mutually exclusive projects of unequal lives. Higher EAA is better.
Equivalent Annual Cost: EAC = PV of total costs ÷ PVAF(r, n); Use when projects have only costs, such as choosing between two machines. Lower EAC is better.

How to solve Capital Rationing and Unequal Project Lives questions

First identify which problem you have: a budget limit, unequal lives, or both. Then follow the steps for that case.

1Read the question and mark the budget limit, whether projects are divisible or indivisible, and whether they are independent or mutually exclusive.
2Compute NPV for each project at the given cost of capital if NPV is not given. Drop any project with a negative NPV.
3Under capital rationing, compute PI = PV of inflows ÷ outlay for each project and rank the projects.
4If divisible, fund in PI order until the budget ends. Take the last project only in part and scale its NPV by the same proportion. Add the NPVs.
5If indivisible, list all feasible combinations within the budget and their total NPVs. Pick the highest and state the unused funds.
6For unequal lives, find the PVAF for each project's own life at the cost of capital. Compute EAA = NPV ÷ PVAF for each project.
7Choose the project with the higher EAA (or lower EAC for cost-only projects). If asked, verify with the replacement chain over the LCM of the lives.
8Write a one-line conclusion with the selected projects, the total NPV or EAA, and the assumption (for example, projects can be repeated on the same terms).

Quickest way: PI ranking, then a quick combination check

When to use it: Use under exam time pressure for capital rationing questions with 4 to 6 projects and a single-period budget.

Write a small table with outlay, NPV and PI for each project. Compute PI as 1 + NPV ÷ outlay.
For divisible projects, fill the budget in PI order and scale the last NPV. This is the full answer.
For indivisible projects, start with the PI order, then test two or three other combinations that use the budget fully. Always compare total NPV.
For unequal lives, just divide each NPV by its PVAF. Do not build 15-year cash flow chains unless the question asks for it.
For MCQs: if one project has both higher NPV and a longer life, do not pick it directly. Check the EAA first. Since there is no negative marking, always attempt every MCQ.
In the written answer, show the table, the working for each combination or EAA, and the final conclusion. These earn step marks even if one figure is wrong.

Common mistakes in Capital Rationing and Unequal Project Lives

Ranking by NPV instead of PI under capital rationing.
Students are used to choosing the highest NPV in normal problems.
Fix: When funds are the scarce resource, rank by PI for divisible projects. For indivisible projects, compare total NPVs of feasible combinations.
Taking part of a project in the indivisible case.
Students apply the divisible method to all rationing questions.
Fix: Check the wording first. If projects cannot be split, only whole projects are allowed, and you must test combinations.
Comparing raw NPVs of projects with different lives.
The NPV rule looks complete, so students stop at the higher NPV.
Fix: For mutually exclusive projects with different lives, convert each NPV to EAA and compare. A bigger NPV over a longer life may have a lower EAA.
Using the wrong annuity factor in EAA.
Students take the factor for one project's life and use it for all projects, or read the wrong table row.
Fix: Use the PVAF for each project's own life and the same discount rate. Mark the factor next to each project before dividing.
Ignoring unused funds and a total that does not match the budget.
Students stop once a combination looks good and do not check the leftover amount.
Fix: Add outlays for each combination and confirm they do not exceed the budget. State the unused amount in the conclusion.
Treating PI as always giving the best answer under rationing.
PI ranking is taught as the rule, so students apply it even when projects are indivisible.
Fix: PI ranking is exact only for divisible projects. For indivisible projects, use it as a starting point and then check other combinations.

Worked examples

Example 1

A firm has a capital budget of ₹8,00,000 for the year. Four independent projects are available. Outlay and NPV (at the firm's cost of capital) are: A: outlay ₹4,00,000, NPV ₹1,60,000. B: outlay ₹3,00,000, NPV ₹1,50,000. C: outlay ₹5,00,000, NPV ₹1,50,000. D: outlay ₹2,00,000, NPV ₹20,000. Select the projects (a) if the projects are divisible and (b) if they are indivisible.

Show the solution

Compute PI = 1 + NPV ÷ outlay. A: 1 + 1,60,000 ÷ 4,00,000 = 1.40. B: 1 + 1,50,000 ÷ 3,00,000 = 1.50. C: 1 + 1,50,000 ÷ 5,00,000 = 1.30. D: 1 + 20,000 ÷ 2,00,000 = 1.10.
Rank by PI: B (1.50), A (1.40), C (1.30), D (1.10).
(a) Divisible: fund B fully = ₹3,00,000, leaving ₹5,00,000. Fund A fully = ₹4,00,000, leaving ₹1,00,000. Use ₹1,00,000 for C, which is 1,00,000 ÷ 5,00,000 = 20% of C.
NPV from 20% of C = 20% × 1,50,000 = ₹30,000.
Total NPV = 1,50,000 + 1,60,000 + 30,000 = ₹3,40,000.
(b) Indivisible: list feasible combinations within ₹8,00,000. A + B: outlay ₹7,00,000, NPV ₹3,10,000. B + C: outlay ₹8,00,000, NPV ₹3,00,000. C + D: outlay ₹7,00,000, NPV ₹1,70,000. A + D: outlay ₹6,00,000, NPV ₹1,80,000. B + D: outlay ₹5,00,000, NPV ₹1,70,000.
Other combinations are not feasible: A + C costs ₹9,00,000 and A + B + D costs ₹9,00,000, both above the budget.
The highest NPV is from A + B at ₹3,10,000, with ₹1,00,000 of funds unused. B + C uses the whole budget but gives a lower NPV.

Answer: (a) Divisible: take B and A in full and 20% of C. Total NPV = ₹3,40,000. (b) Indivisible: take A and B. Total NPV = ₹3,10,000, with ₹1,00,000 unused.

Example 2

A company must choose one of two mutually exclusive machines. Cost of capital is 10%. Machine P has a life of 3 years and an NPV of ₹1,24,345. Machine Q has a life of 5 years and an NPV of ₹1,70,586. PV annuity factors at 10%: 3 years = 2.4869; 5 years = 3.7908. Which machine should the company choose? Assume each can be replaced on the same terms.

Show the solution

Raw NPV favours Q (₹1,70,586 against ₹1,24,345). But the lives differ, so this is not a fair comparison.
Compute EAA for P = NPV ÷ PVAF(10%, 3) = 1,24,345 ÷ 2.4869 = ₹50,000.
Compute EAA for Q = NPV ÷ PVAF(10%, 5) = 1,70,586 ÷ 3.7908 = ₹45,000.
Compare: P gives an equivalent annual benefit of ₹50,000 and Q gives ₹45,000.
P has the higher EAA, so it creates more value per year when both are repeated on the same terms.

Answer: Choose Machine P. Its EAA is ₹50,000 against ₹45,000 for Machine Q, even though Q has the higher NPV.

Exam tips

Read the wording for 'divisible' or 'indivisible' before doing any working. It decides your method, and examiners often change it between sub-parts of the same question.
Show a clean table with outlay, NPV and PI. Ranking and combinations are easy to follow from it, and step marks depend on it.
In indivisible problems, list every feasible combination briefly. Writing only the final choice risks losing marks if your pick is wrong.
In unequal-life questions, write the PVAF with the rate and year (for example, PVAF at 10%, 3 years) before dividing. It shows the method even if a table value is misread.
For MCQs, a quick check works well: a longer-lived project with a higher NPV is not automatically better. Calculate EAA and choose the higher figure.

Practice questions from Investment Decisions

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?

Capital rationing is a situation where a firm has less money than the good projects need. So it cannot accept every project with a positive NPV. It picks the set of projects that gives the highest total NPV within its budget.

Why do we use PI and not NPV for ranking under capital rationing?

NPV is an absolute amount and favours large projects. PI measures value per rupee of scarce funds, so it ranks divisible projects correctly. For indivisible projects PI is only a starting point, and you must compare the total NPV of feasible combinations.

How do I calculate equivalent annual annuity?

Calculate the project's NPV at the cost of capital. Then divide it by the present value annuity factor for the project's own life at the same rate. The result is the equal yearly amount that has the same present value as the NPV. The project with the higher EAA is preferred.

When should I use the replacement chain method instead of EAA?

Use the replacement chain when the question asks for it or gives the cash flows over a common horizon. You repeat each project until both end together, usually at the LCM of their lives, and compare total NPVs. EAA is faster and gives the same ranking under the same assumptions.