Financial Management · Investment appraisal techniques

Capital Rationing and Profitability Index for ACCA FM

Updated 11 October 2026 · Fact-checked

Capital rationing means a firm has less capital than it needs to fund all positive-NPV projects. In a single period, rank divisible projects by profitability index (NPV ÷ capital invested), fund them in order, and split the last one. For indivisible projects, test combinations and pick the highest total NPV.

Understand Capital Rationing and Profitability Index

Normally you accept every project with a positive NPV. This maximises shareholder wealth. Capital rationing is the situation where there is not enough capital to do so. You must then choose which projects to fund.

There are two types. Hard capital rationing is imposed from outside, for example when banks or markets refuse to lend more. Soft capital rationing is imposed inside the firm, for example by a management budget limit, a policy of not raising new equity, or a wish to keep control. Soft rationing can be changed by management. Hard rationing cannot.

With rationing, the best project is not the one with the biggest NPV. It is the one that gives the most NPV for each unit of scarce capital. That is the idea behind the profitability index (PI). It is NPV per ₹1 (or $1) invested in the limited resource, here the capital in the year it is scarce.

The method depends on whether projects are divisible (you can do part of a project and earn a proportionate NPV) or indivisible (all or nothing). For divisible projects, rank by PI and fund in order until money runs out. For indivisible projects, ranking may not give the best answer, so you list feasible combinations and compare total NPV. The method also assumes capital is limited in one period only (single-period rationing) and that projects cannot be repeated.

Key rules to remember

Profitability index: PI = NPV ÷ capital invested in the rationed period; Use the outlay in the year capital is limited, usually Year 0. Some texts use PV of inflows ÷ outlay, which gives a different number, so follow the question's definition. The ranking is the same for single-period rationing.
Divisible projects rule: Rank by PI, fund highest first, take a fraction of the last project; Total NPV = sum of full NPVs + fraction × NPV of the part-funded project.
Indivisible projects rule: Choose the combination within the budget with the highest total NPV; Do not rank by PI alone. Leftover capital may be better used by a different combination.
Fraction of a project: Fraction = capital remaining ÷ project's full outlay; NPV earned = fraction × full NPV.

How to solve Capital Rationing and Profitability Index questions

Use this method for any single-period capital rationing question.

1Confirm capital is limited in one period only, and note the limit.
2Calculate the NPV of each project. Reject any with a negative NPV.
3Check whether projects are divisible or indivisible, and whether they are mutually exclusive.
4For divisible projects, calculate PI = NPV ÷ initial outlay for each project and rank them.
5Allocate capital in rank order. Give the last project only the fraction the remaining funds allow.
6Calculate the total NPV: full NPVs plus the fraction × NPV of the last project.
7For indivisible projects, list combinations that fit within the budget and compare total NPVs. Pick the highest.
8State the recommendation and any assumptions or limits, such as unused funds or no repeat projects.

Quickest way: PI ranking in under two minutes

When to use it: Use for divisible projects with single-period rationing, especially in Section A or an OT case where you only need the final NPV or the top-ranked project.

Write NPV and outlay for each project in one line each.
Divide NPV by outlay and rank.
Subtract outlays from the budget in rank order until you reach the project that does not fit.
Multiply its NPV by remaining funds ÷ its outlay.
Add all NPVs. For indivisible projects, check the two or three most plausible combinations and pick the highest.

Common mistakes in Capital Rationing and Profitability Index

Ranking projects by NPV instead of PI when projects are divisible.
Without rationing, NPV is the decision rule, so students keep using it.
Fix: Whenever capital is limited and projects are divisible, rank by PI.
Using PI ranking for indivisible projects and stopping.
PI is the method students remember, so they apply it everywhere.
Fix: For indivisible projects, test combinations. PI ranking can leave capital unused and give a lower total NPV.
Including projects with negative NPV to use up funds.
Students feel they must spend the whole budget.
Fix: Reject negative-NPV projects. Unused capital is acceptable.
Dividing the NPV by the wrong figure, such as total cash inflows.
Confusion between PI definitions.
Fix: Use NPV ÷ initial outlay unless the question defines PI differently, and state the formula.
Confusing hard and soft rationing.
Both mean limited funds, so the labels blur.
Fix: Hard means external, such as lenders or markets. Soft means internal, such as management policy or budgets.
Taking a fraction of an indivisible project.
Students apply the divisible method automatically.
Fix: Check the wording. Fractions are allowed only if the question says projects are divisible.

Worked examples

Example 1

A company has ₹10,00,000 available this year. Three divisible projects, which cannot be repeated, have these figures. Project A: outlay ₹4,00,000, NPV ₹1,20,000. Project B: outlay ₹5,00,000, NPV ₹1,00,000. Project C: outlay ₹3,00,000, NPV ₹90,000. Find the best plan and total NPV.

Show the solution

PI of A = 1,20,000 ÷ 4,00,000 = 0.30.
PI of B = 1,00,000 ÷ 5,00,000 = 0.20.
PI of C = 90,000 ÷ 3,00,000 = 0.30.
A and C tie at 0.30, then B at 0.20. Fund A and C in full: 4,00,000 + 3,00,000 = ₹7,00,000.
Remaining funds = 10,00,000 − 7,00,000 = ₹3,00,000. B needs ₹5,00,000, so take 3,00,000 ÷ 5,00,000 = 0.6 of B.
NPV from B = 0.6 × 1,00,000 = ₹60,000.
Total NPV = 1,20,000 + 90,000 + 60,000 = ₹2,70,000.

Answer: Invest in A and C fully and 60% of B. Total NPV is ₹2,70,000.

Example 2

Capital available is $100,000. Projects are indivisible and not repeatable. Project W: outlay $60,000, NPV $18,000. Project X: outlay $40,000, NPV $10,000. Project Y: outlay $50,000, NPV $14,000. Project Z: outlay $30,000, NPV $7,000. Which combination maximises NPV?

Show the solution

PIs: W = 18,000 ÷ 60,000 = 0.30. X = 10,000 ÷ 40,000 = 0.25. Y = 14,000 ÷ 50,000 = 0.28. Z = 7,000 ÷ 30,000 = 0.233.
Ranking by PI gives W, Y, X, Z. W ($60,000) then Y would need $110,000, which does not fit. W + X = $100,000 fits, NPV $28,000.
Because projects are indivisible, test other combinations within $100,000.
W + Z = $90,000, NPV $25,000.
X + Y = $90,000, NPV $24,000.
Y + Z = $80,000, NPV $21,000.
X + Y + Z = $120,000, which exceeds the budget.
W + X = $28,000 is the highest.

Answer: Accept W and X. Total NPV is $28,000, using all $100,000.

Exam tips

Read for the words divisible or indivisible. They decide your method.
In OT questions, show the PI calculation on your scratch pad and check the ranking twice. A wrong rank means zero for the question.
In written answers, state your assumptions: single period, projects not repeatable, funds not carried forward.
If asked to discuss rationing, name hard and soft types with an example of each, and say soft rationing may be removed by management.
Always say that only positive-NPV projects should be considered, and note any unused funds.

Practice questions from Investment appraisal techniques

Capital Rationing and Profitability Index 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 Profitability Index: frequently asked questions

What is the difference between hard and soft capital rationing?

Hard capital rationing comes from outside the firm, such as lenders refusing to provide more finance. Soft capital rationing is set by the firm itself, for example through a management budget. Soft rationing can be changed, hard rationing cannot.

How do you calculate the profitability index in ACCA FM?

Divide the project's NPV by the capital invested in the rationed period, usually the Year 0 outlay. Rank projects from highest to lowest PI. Always follow the question if it gives its own definition.

Why can't you use PI ranking for indivisible projects?

Indivisible projects must be accepted whole or not at all. Ranking by PI may leave capital unused or block a better pairing. You must test feasible combinations and choose the highest total NPV.

What is single-period capital rationing?

It is when capital is limited in the current period only, and later periods have enough funds. This allows the simple PI method. If funds are limited in several periods, linear programming is needed.