Financial Management · Specific investment decisions (lease or buy, asset replacement, capital rationing)

Single-Period Capital Rationing for ACCA FM

Updated 11 October 2026 · Fact-checked

Single-period capital rationing means you have a fixed sum to invest now and cannot fund every positive-NPV project. For divisible projects, rank by profitability index (NPV ÷ capital invested) and fund in order. For indivisible projects, test feasible combinations and pick the one with the highest total NPV.

Understand Single-Period Capital Rationing

Normally you accept every project with a positive NPV. That maximises shareholder wealth. Capital rationing is the situation where you cannot do this because funds are limited. The limit is the scarce resource, so you must get the most NPV from each rupee or dollar available.

Single-period rationing means the shortage applies only to the initial outlay at time 0. Later years have enough funds. If funds are short in several periods, you need linear programming instead.

Hard rationing is imposed from outside, for example when banks or markets will not lend more. Soft rationing is imposed inside the business, for example by management budgets, a policy of no new equity, or a wish to limit risk. Soft rationing can in principle be changed. Hard rationing cannot.

Your method depends on whether projects are divisible. A divisible project can be done in part, and the NPV scales in proportion. An indivisible project is all or nothing. Divisible projects are solved by ranking on the profitability index (PI), which is NPV per unit of capital used. Indivisible projects need you to list the feasible combinations, because ranking can leave unused funds and give a worse total.

Only consider projects with a positive NPV. Also remember the assumptions: projects are independent, the limit lasts one period, and unused funds earn only the cost of capital, so they add no NPV. Mutually exclusive projects must not be chosen together.

Key rules to remember

Profitability index (PI): PI = NPV ÷ initial capital outlay; Use the capital that is rationed, usually the time 0 outlay. Some texts use PV of inflows ÷ outlay, which gives a different number, so follow the question's definition. The ranking is the same either way.
Divisible project selection: Rank by PI, fund highest first, take a fraction of the last project; Fraction = funds left ÷ full outlay of that project. NPV from it = fraction × full NPV.
Indivisible project selection: Choose the feasible combination with the highest total NPV; A combination is feasible if total outlay ≤ funds available. Ranking by PI may not give the best answer.
Decision rule: Only projects with NPV > 0 are considered; Reject negative-NPV projects even if capital is left over.

How to solve Single-Period Capital Rationing questions

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

1Check the type of question: is the limit in one period only, and are projects divisible, indivisible or mixed?
2Calculate the NPV of each project if not given. Discard any with a negative NPV.
3Calculate PI for each remaining project as NPV ÷ outlay.
4Divisible: rank by PI, allocate funds from the top, and take a fraction of the last project that fits. Total the NPV.
5Indivisible: list the feasible combinations within the limit, add up the NPV of each, and choose the highest. Note any unused funds.
6Check for mutually exclusive projects or fixed commitments and adjust the choices.
7State the plan clearly: which projects, how much invested, total NPV, and any assumptions or limitations.

Quickest way: PI ranking then a combination check

When to use it: Use it in Section C or an OT case when several projects compete for one limited sum at time 0.

Write a small table of outlay, NPV and PI for each project.
Rank by PI and fill the budget. If projects are divisible, you are finished after fractioning the last one.
If projects are indivisible, check whether the ranked set leaves funds unused. If it does, try swapping in a combination that uses more of the budget.
Compare totals of NPV only. Do not compare PIs across combinations.
Cross out negative-NPV projects first to save time.

Common mistakes in Single-Period Capital Rationing

Ranking by NPV instead of PI for divisible projects.
Students are used to choosing the highest NPV when there is no limit.
Fix: When capital is limited, rank by NPV per unit of scarce capital. Always compute PI.
Using PI ranking alone for indivisible projects.
The same method works for divisible projects, so students apply it everywhere.
Fix: Test combinations. Ranking can leave funds unused and give a lower total NPV.
Taking a fraction of an indivisible project.
Students fill the budget exactly without reading the question.
Fix: Underline the word indivisible or whole. If so, only accept or reject whole projects.
Including projects with a negative NPV to use up funds.
Students feel the budget must be fully spent.
Fix: Never invest in negative-NPV projects. Spare funds can be returned or invested at the cost of capital.
Choosing mutually exclusive projects together.
Students skim the scenario and treat all projects as independent.
Fix: Read for exclusivity statements and exclude invalid combinations before totalling NPV.
Mixing up hard and soft rationing.
Both words describe a limit, so the difference is easy to blur.
Fix: Hard means external limits such as lenders. Soft means internal management limits.

Worked examples

Example 1

A company has $100,000 available at time 0. Divisible projects: A outlay $40,000, NPV $10,000; B outlay $50,000, NPV $15,000; C outlay $60,000, NPV $12,000. Which plan maximises NPV, and what is the total NPV?

Show the solution

PI for A = 10,000 ÷ 40,000 = 0.25.
PI for B = 15,000 ÷ 50,000 = 0.30.
PI for C = 12,000 ÷ 60,000 = 0.20.
Ranking: B first, A second, C third.
Fund B in full: $50,000 used, $50,000 left, NPV $15,000.
Fund A in full: $40,000 used, $10,000 left, NPV $10,000.
Use the remaining $10,000 on C: fraction = 10,000 ÷ 60,000 = 1/6. NPV = 12,000 × 1/6 = $2,000.
Total NPV = 15,000 + 10,000 + 2,000 = $27,000.

Answer: Invest in all of B, all of A and one-sixth of C. Total NPV is $27,000.

Example 2

A company has $100,000 at time 0. Indivisible projects: P outlay $60,000, NPV $18,000; Q outlay $40,000, NPV $11,000; R outlay $50,000, NPV $14,000; S outlay $30,000, NPV $8,000. All are independent. Which projects should it accept?

Show the solution

PIs: P = 0.30, Q = 0.275, R = 0.28, S = 0.267 (to three decimal places).
Ranking by PI gives P, R, Q, S. P and R together cost $110,000, which is over the limit, so R cannot be added after P.
After P ($60,000), $40,000 is left. Add Q ($40,000): total outlay $100,000, NPV $29,000.
List other feasible combinations.
P + S = outlay $90,000, NPV $26,000.
R + Q = outlay $90,000, NPV $25,000.
R + S = outlay $80,000, NPV $22,000.
Q + S = outlay $70,000, NPV $19,000.
Check three-project sets: Q + S + R costs $120,000 and Q + S + P costs $130,000, both infeasible.
The highest NPV is P + Q at $29,000.

Answer: Accept P and Q, using all $100,000, for a total NPV of $29,000.

Exam tips

Read for the words divisible, indivisible, one period and mutually exclusive before you calculate anything.
Show a small table of outlay, NPV and PI. Markers can then give credit for method even if a figure is wrong.
In Section C, add a short comment on limitations: it covers one period only, ignores project interdependence and assumes NPVs are certain.
Be ready to explain hard and soft rationing, and to suggest ways to relax soft rationing, such as raising equity or delaying projects.
In OT questions, one wrong digit means zero marks. Recheck each PI and the final total NPV.

Practice questions from Specific investment decisions (lease or buy, asset replacement, capital rationing)

Single-Period 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.

Single-Period Capital Rationing: frequently asked questions

What is the difference between hard and soft capital rationing?

Hard rationing comes from outside the company, such as lenders refusing to provide more finance. Soft rationing comes from inside, such as management budget limits or a policy against raising new equity. Soft limits can be changed by management.

How do you calculate the profitability index in ACCA FM?

Divide the project's NPV by its initial outlay at the rationed period. For example, NPV of $15,000 on an outlay of $50,000 gives a PI of 0.30. Use the question's definition if it gives one.

Why can't you use PI for indivisible projects?

Because you cannot take part of a project, ranking may leave funds unused. A different combination can use the budget better and give a higher total NPV. So you test feasible combinations instead.

What does single-period capital rationing assume?

It assumes funds are short only at time 0 and are available freely later. It also assumes projects are independent and that NPV estimates are reliable. If funds are short in more than one period, you need linear programming.