Advanced Financial Management · Advanced Capital Budgeting Decisions

Capital Rationing for CA Final AFM

Updated 5 October 2026 · Fact-checked

Capital rationing is choosing projects when funds are limited, so you cannot accept every positive-NPV project. Calculate NPV and profitability index, rank by PI for divisible projects, and fill the budget, taking a fraction of the last one. For indivisible projects, test combinations within the budget and pick the highest total NPV.

Understand Capital Rationing

Normal capital budgeting says: accept every project with a positive NPV. This works only if the firm can raise as much money as it needs. In real life it often cannot. When funds are limited, you must choose the best set of projects. This is capital rationing.

The objective does not change. You still want to maximise the total NPV of the projects you accept. The budget is now a constraint. A project with a high NPV may use up so much money that two smaller projects together would add more value.

There are two types. Hard capital rationing is an external limit, for example lenders or markets will not give more than a fixed amount. Soft capital rationing is an internal limit set by management, for example a budget cap for a division or a rule on borrowing. Soft limits can be relaxed. Hard limits cannot.

There are two kinds of projects. Divisible projects can be taken in part, and NPV scales in proportion to the share taken. Indivisible projects must be accepted fully or rejected. For divisible projects, ranking by profitability index (PI) gives the best answer for a single-period budget. For indivisible projects, PI ranking is only a starting point. You must check combinations, because PI ranking can leave money unused and miss a better mix.

When the budget applies over several years, or projects depend on each other, the problem is a linear programming one. You maximise total NPV subject to a budget limit in each period. For divisible projects the choice variable can be any fraction from 0 to 1. For indivisible projects it is either 0 or 1. In the exam you usually only need to set up the model, or solve a small one by listing combinations.

Key rules to remember

Profitability index (PI): PI = PV of cash inflows ÷ PV of cash outflows (initial outlay); Use present value of future inflows over the outlay. If outflows also occur in later years, use their present value in the denominator.
NPV and PI link: NPV = PV of inflows − PV of outflows; PI = 1 + (NPV ÷ Outlay); NPV > 0 means PI > 1. Some books define PI as NPV ÷ Outlay; read the question and stay consistent.
Divisible projects rule: Rank by PI (highest first); accept in order until budget ends; take a fraction of the last project = Balance funds ÷ Its outlay; Total NPV = full NPVs of accepted projects + fraction × NPV of the part-accepted project. Valid for a single-period budget.
Indivisible projects rule: Select the combination with Σ outlay ≤ budget that gives the highest Σ NPV; Check feasible combinations. Do not stop at PI ranking. Leftover funds can be assumed to earn only their cost, so they add no NPV unless stated.
Linear programming form: Maximise Σ (NPVj × xj) subject to Σ (Cjt × xj) ≤ Bt for each period t; 0 ≤ xj ≤ 1 (divisible) or xj = 0 or 1 (indivisible); Cjt is the cash outlay of project j in period t, and Bt is the budget available in period t. Add extra constraints for mutually exclusive or contingent projects.

How to solve Capital Rationing questions

Use this method for any capital rationing question. It works for divisible, indivisible and multi-constraint cases.

1Read the budget, the period(s) it applies to, and whether projects are divisible or indivisible. Note any mutually exclusive or dependent projects.
2Compute the NPV of each project at the given cost of capital, and its PV of inflows if not given.
3Compute PI for each project as PV of inflows ÷ outlay.
4Drop projects with NPV below zero (PI below 1). They never help.
5Divisible case: rank by PI, fill the budget in that order, and take a fraction of the last project that does not fit fully.
6Indivisible case: list all feasible combinations within the budget, add their NPVs, and pick the highest. Use the PI ranking only to shortlist.
7If the budget covers several years or there are other conditions, write the linear programming model: objective, constraints, and 0/1 or fractional limits.
8State the selected projects, funds used, funds left over and total NPV. Add one line on whether the limit is hard or soft if the question asks.

Quickest way: PI ranking with a combination check

When to use it: Single-period budget with up to five or six projects, when time is short.

Write outlay, NPV and PI for every project in one small table.
Rank by PI. If projects are divisible, fill the budget and take a fraction of the last one. You are done.
If projects are indivisible, take the PI-ranked set and note the unused funds.
Then test only the combinations that use the budget more fully. Swap one large project for two smaller ones.
Compare total NPVs. Pick the highest and state it clearly with funds used.

Common mistakes in Capital Rationing

Using PI ranking alone for indivisible projects
PI ranking is taught first and works perfectly for divisible projects, so students apply it everywhere.
Fix: For indivisible projects, always compare total NPV across feasible combinations. PI ranking can leave funds idle and miss a better mix.
Ranking by NPV instead of PI for divisible projects
NPV is the main decision criterion in ordinary capital budgeting.
Fix: Under a budget limit you want the most NPV per rupee of outlay. Rank by PI when projects are divisible.
Taking a fraction of an indivisible project
Students carry the divisible method over without checking the wording.
Fix: Read the question for the words divisible or indivisible. Fractions are allowed only when the project can be done in part.
Computing PI with NPV in the numerator
PI is confused with NPV ÷ outlay, which equals PI − 1.
Fix: Use PV of inflows ÷ outlay, so PI above 1 is acceptable. If you use NPV ÷ outlay, say so and rank consistently.
Ignoring unused funds and total NPV in the final answer
Students stop after naming the projects.
Fix: Always state the projects chosen, funds used, funds left and the total NPV. Leftover funds are assumed to add no NPV unless the question says otherwise.
Mixing up hard and soft capital rationing
Both mean a limited budget, so the cause is overlooked.
Fix: Hard means an external constraint the firm cannot change. Soft means a management-imposed limit that can be revised. Link the answer to who sets the limit.

Worked examples

Example 1

A company has a budget of ₹50 lakh. Four projects are available, all with a single outlay now. A: outlay ₹20 lakh, PV of inflows ₹30 lakh. B: outlay ₹15 lakh, PV of inflows ₹21 lakh. C: outlay ₹25 lakh, PV of inflows ₹32.5 lakh. D: outlay ₹10 lakh, PV of inflows ₹12 lakh. Find the best selection (i) if projects are divisible and (ii) if they are indivisible.

Show the solution

NPV = PV of inflows − outlay: A = ₹10 lakh, B = ₹6 lakh, C = ₹7.5 lakh, D = ₹2 lakh.
PI = PV of inflows ÷ outlay: A = 30 ÷ 20 = 1.5, B = 21 ÷ 15 = 1.4, C = 32.5 ÷ 25 = 1.3, D = 12 ÷ 10 = 1.2. All are above 1.
(i) Divisible: rank A, B, C, D. A uses ₹20 lakh, B uses ₹15 lakh, total ₹35 lakh. Balance ₹15 lakh goes to C.
Fraction of C = 15 ÷ 25 = 0.6. NPV from C = 0.6 × 7.5 = ₹4.5 lakh.
Total NPV = 10 + 6 + 4.5 = ₹20.5 lakh.
(ii) Indivisible: test feasible combinations within ₹50 lakh. A + B + D = ₹45 lakh, NPV = 10 + 6 + 2 = ₹18 lakh. A + C = ₹45 lakh, NPV = 17.5. B + C + D = ₹50 lakh, NPV = 15.5. A + B = ₹35 lakh, NPV = 16. B + C = ₹40 lakh, NPV = 13.5.
A + B + C costs ₹60 lakh and A + C + D costs ₹55 lakh, so both exceed the budget.
The highest NPV is from A + B + D at ₹18 lakh, with ₹5 lakh unused.

Answer: (i) Divisible: accept A, B and 60% of C; total NPV = ₹20.5 lakh. (ii) Indivisible: accept A, B and D; funds used ₹45 lakh; total NPV = ₹18 lakh.

Example 2

A firm has ₹40 lakh available this year and projects cannot be split. P: outlay ₹30 lakh, NPV ₹9 lakh. Q: outlay ₹20 lakh, NPV ₹5.4 lakh. R: outlay ₹20 lakh, NPV ₹5 lakh. Management first ranks projects by PI. Show whether PI ranking gives the best choice, and state whether the budget is hard or soft if the limit is set by the board to control risk.

Show the solution

PI = 1 + NPV ÷ outlay. P = 1 + 9 ÷ 30 = 1.30. Q = 1 + 5.4 ÷ 20 = 1.27. R = 1 + 5 ÷ 20 = 1.25.
PI ranking: P first. After P, ₹10 lakh remains. Q needs ₹20 lakh and R needs ₹20 lakh, so neither fits and they cannot be split.
PI-ranked choice: only P, NPV = ₹9 lakh, with ₹10 lakh unused.
Check other combinations: Q + R costs ₹40 lakh, which equals the budget. NPV = 5.4 + 5 = ₹10.4 lakh.
P + Q costs ₹50 lakh and P + R costs ₹50 lakh, so both are not feasible.
₹10.4 lakh is more than ₹9 lakh, so Q + R is better than the PI-ranked choice.
The limit is set by the board, so it is internal and can be changed. It is soft capital rationing.

Answer: PI ranking picks only P (NPV ₹9 lakh), which is not optimal. The best choice is Q + R, using ₹40 lakh, with total NPV ₹10.4 lakh. The board's limit is soft capital rationing.

Exam tips

Check the words divisible and indivisible before you start. They decide the whole method.
Show a small table of outlay, NPV and PI. Marks are given for the working and the ranking.
In indivisible questions, always show at least the competing combinations and their total NPV. A PI ranking alone loses marks.
End with funds used, funds left and total NPV. Mention hard or soft rationing if the question hints at the source of the limit.
For multi-period budgets or dependent projects, write the linear programming formulation clearly: objective function, constraints and conditions on the variables.

Practice questions from Advanced Capital Budgeting Decisions

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.

Capital Rationing: frequently asked questions

What is the difference between hard and soft capital rationing?

Hard capital rationing is an external limit on funds that the firm cannot change, such as limits from lenders or markets. Soft capital rationing is an internal limit set by management, such as a divisional budget cap. Soft limits can be revised, hard limits cannot.

How do I solve capital rationing for indivisible projects?

Compute NPV for each project and list all combinations whose total outlay is within the budget. Add the NPVs of each combination and pick the highest. PI ranking can help you shortlist, but it may not give the best result.

Why do we use profitability index in capital rationing?

PI shows the present value earned per rupee invested. When funds are limited, you want the most value from each rupee. For divisible projects in a single-period budget, ranking by PI gives the maximum total NPV.

Can capital rationing be solved by linear programming?

Yes. You maximise total NPV subject to a budget limit in each period. Divisible projects take any value from 0 to 1, and indivisible projects take only 0 or 1. In exams you are usually asked to formulate the model or solve a small case by hand.