Advanced Financial Management · Financial strategy formulation

Financial Planning, Constraints and Capital Rationing in ACCA AFM

Updated 11 October 2026 · Fact-checked

Financial planning sets targets for growth, funding and returns, then tests them against constraints. Capital rationing is a limit on funds: hard if imposed externally, soft if set internally. With one rationed period, rank divisible projects by profitability index (NPV ÷ capital used). For indivisible projects, test combinations. Growth is also capped by retention × ROE.

Understand Financial Planning, Constraints and Capital Rationing

Financial planning turns strategy into numbers. You set targets for growth, profit, investment, dividends and funding. Then you check whether the business can deliver them with the money and capacity it has.

A constraint is anything that stops the plan being delivered. Internal constraints include management limits on borrowing, a dividend policy the board will not change, limited management time and a minimum return the board demands. External constraints include lenders' covenants, a weak equity market, the cost and availability of debt, regulation and the economic cycle.

Capital rationing means a firm cannot fund every project that has a positive NPV. Hard rationing is imposed from outside. Examples are lenders refusing to lend or the market refusing a share issue. Soft rationing is imposed inside the firm. Examples are a head office budget for a division, or a wish to avoid new shares so as to keep control. The distinction matters because soft limits can be questioned and changed. Hard limits cannot.

When funds are short, the aim changes. You no longer accept every project with a positive NPV. You choose the set of projects that gives the highest total NPV within the limit. If projects can be done in part (divisible), rank them by profitability index. If they are all-or-nothing (indivisible), test the affordable combinations. Where funds are limited in more than one period, you need linear programming, which AFM tests mainly through interpretation of a given solution and shadow prices.

Growth is a planning constraint too. A firm that funds growth only from retained profit and keeps its gearing constant can grow at about retention ratio × return on equity. Planning for faster growth means more external finance, a lower payout, a higher ROE or higher gearing. Each has a cost and a risk, and the exam wants you to discuss them.

Key rules to remember

Profitability index (single-period rationing): PI = NPV ÷ capital invested in the rationed period; Rank divisible projects by PI, highest first, and fund down the list until the money runs out. The last project is taken in part.
Total NPV with a partial project: NPV of partial project = fraction funded × full NPV; Assumes the project is divisible and that its NPV scales in proportion. State this assumption.
Retention ratio: b = 1 − dividend payout ratio = (PAT − dividends) ÷ PAT; b is the share of profit kept in the business.
Return on equity: ROE = profit after tax ÷ shareholders' equity; Use the same equity basis (opening or closing) throughout. Say which you use.
Sustainable growth rate: g = b × ROE; Growth in equity and earnings that can be funded from retained profit, if ROE and gearing stay constant. It is an estimate, not a limit that can never be passed.
Rule for rationing type: Hard = imposed externally; Soft = imposed internally; Under single-period rationing, the NPV rule changes from accept all positive-NPV projects to maximise total NPV within the limit.

How to solve Financial Planning, Constraints and Capital Rationing questions

Use this method for any question on planning, constraints or rationing. Do the numbers first, then the discussion.

1Read the requirement. Decide whether it wants calculations, discussion of constraints, or both.
2Identify the constraint: which period is short of funds, and is the limit hard or soft? Check whether projects are divisible, indivisible, mutually exclusive or linked.
3Calculate the NPV of each project first. Discard any with a negative NPV before you ration.
4For divisible projects, work out PI for each project, rank them, and allocate funds in rank order. Take the last project in part.
5For indivisible projects, list every affordable combination, add the NPVs, and pick the highest. Leftover funds can be assumed to earn a zero NPV unless told otherwise.
6For growth questions, find b and ROE, then g = b × ROE. Compare it with the planned growth and work out the gap in funding or the change needed in payout, ROE or gearing.
7Write the commentary. Cover assumptions, whether the limit is hard or soft, whether it can be removed, effects on shareholder wealth and risks.
8Answer the requirement in a clear closing line, using the scenario's names and numbers.

Quickest way: PI ranking table for divisible projects

When to use it: Use it when one period is rationed and projects can be done in part. It takes about two minutes once the NPVs are known.

Make a four-column list: project, investment, NPV, PI.
Divide each NPV by its investment and rank by PI.
Subtract investment from the budget down the ranking until a project does not fit.
Fund the fraction that fits: remaining money ÷ that project's investment.
Add the NPVs, and show the partial NPV as fraction × NPV.
If the projects are indivisible, do not use the ranking as your answer. Check combinations that use the budget best.

Common mistakes in Financial Planning, Constraints and Capital Rationing

Ranking projects by NPV or IRR instead of profitability index when funds are limited.
NPV ranking is the habit from unconstrained appraisal.
Fix: Under rationing in one period, rank divisible projects by NPV per unit of the scarce resource, which is the PI.
Using the PI ranking as the final answer for indivisible projects.
Students learn one method and apply it to every question.
Fix: Check the affordable combinations. A lower-PI project that uses the funds more fully can give a higher total NPV.
Calculating PI as (PV of inflows ÷ investment) and mixing it with NPV ÷ investment.
Both versions exist and look alike.
Fix: Use NPV ÷ investment in the rationed period throughout. Never mix versions in the same table.
Not saying whether rationing is hard or soft, or not discussing what it means.
Students treat rationing as pure calculation.
Fix: State the type and its cause. For soft rationing, question the limit. It may destroy value if good projects are rejected. For hard rationing, discuss alternative finance.
Mixing up opening and closing equity when computing ROE, or using the dividend payout where retention is needed.
Students rush the sustainable growth formula.
Fix: Calculate b = 1 − payout first and write the equity basis next to ROE.
Treating sustainable growth as a hard ceiling.
The formula looks exact.
Fix: Say it holds if ROE and gearing stay constant and no new equity is raised. A firm can grow faster with borrowing, a rights issue or higher margins.

Worked examples

Example 1

Alpha Co has $500,000 available now. No funds will be rationed later. Projects A, B, C and D each need an immediate outlay and have the following NPVs: A outlay $200,000, NPV $50,000; B outlay $300,000, NPV $60,000; C outlay $150,000, NPV $45,000; D outlay $250,000, NPV $40,000. (a) Find the best plan if projects are divisible. (b) Find the best plan if projects are indivisible. Assume no project can be repeated.

Show the solution

Calculate PI = NPV ÷ outlay. A: 50,000 ÷ 200,000 = 0.25. B: 60,000 ÷ 300,000 = 0.20. C: 45,000 ÷ 150,000 = 0.30. D: 40,000 ÷ 250,000 = 0.16.
Rank: C (0.30), A (0.25), B (0.20), D (0.16).
(a) Fund C fully: $150,000 used, $350,000 left. Fund A fully: $200,000 used, $150,000 left.
Fund B in part: 150,000 ÷ 300,000 = 50% of B. NPV = 0.5 × 60,000 = $30,000.
Total NPV = 45,000 + 50,000 + 30,000 = $125,000.
(b) List the affordable combinations: C+A costs $350,000, NPV $95,000. C+B costs $450,000, NPV $105,000. C+D costs $400,000, NPV $85,000. A+B costs $500,000, NPV $110,000. A+D costs $450,000, NPV $90,000. B+D costs $550,000, which is not affordable. Single projects have lower NPVs. Three-project sets cost at least $550,000 (C+A+D = $600,000, C+A+B = $650,000), so none are affordable.
The highest total is A+B at $110,000, which uses all the funds.

Answer: (a) Divisible: invest in C and A in full and 50% of B, for a total NPV of $125,000. (b) Indivisible: invest in A and B, for a total NPV of $110,000. The answer to (b) is lower than (a) because B cannot be part-funded, and the PI ranking does not give the best combination.

Example 2

Beta Co reports profit after tax of $12m and pays dividends of $4.8m. Opening shareholders' equity is $80m. Management plans to grow at 12% a year. Assume ROE is based on opening equity, and that ROE and gearing stay constant. (a) Calculate the sustainable growth rate. (b) Find the payout ratio that would make 12% growth sustainable. (c) Comment on other ways to reach 12%.

Show the solution

(a) Retention = (12 − 4.8) ÷ 12 = 7.2 ÷ 12 = 0.6. ROE = 12 ÷ 80 = 15%.
g = 0.6 × 15% = 9%.
(b) Required b = g ÷ ROE = 12% ÷ 15% = 0.8. Payout = 1 − 0.8 = 20%.
Check: 0.8 × 15% = 12%. The dividend would be 20% × $12m = $2.4m, down from $4.8m.
(c) The firm could raise ROE by improving margin or asset use. It could take on more debt, which raises financial risk and may breach covenants. It could issue new equity, which dilutes control and has issue costs.

Answer: Sustainable growth is 9%. To make 12% sustainable with the same ROE, the payout would need to fall to 20%, which means cutting the dividend to $2.4m. The alternatives are a higher ROE, more gearing or new equity. Each has a cost in risk, signalling or dilution, and the board should weigh these against shareholder expectations.

Exam tips

Always state the assumptions: divisibility, one-period rationing, no repeat of projects and that unused funds earn a zero NPV. The marker looks for these.
Do not stop at the calculation. Say whether rationing is hard or soft and what the board could do about it, and use the scenario's facts.
In Section A case studies, link constraints to the scenario's wider strategy: covenants, investor expectations, dividend policy and governance. This earns professional skills marks for analysis and commercial acumen.
If a question gives a multi-period or linear programming output, interpret the shadow prices. A shadow price shows how much total NPV rises for one extra unit of the scarce resource, which shows what extra finance is worth.
Show every PI and NPV in a tidy table. Even if a figure is wrong, method marks follow from a clear layout.

Practice questions from Financial strategy formulation

Financial Planning, Constraints and 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.

Financial Planning, Constraints and Capital Rationing: frequently asked questions

What is the difference between hard and soft capital rationing?

Hard rationing comes from outside the firm, for example lenders or the equity market refusing to supply more funds. Soft rationing is set inside the firm, for example a divisional budget or a policy against new equity. Soft limits can be reviewed. Hard limits usually need a change in finance or strategy.

How do I solve capital rationing questions with divisible projects?

Work out each project's NPV, divide by the investment in the rationed period to get the profitability index, and rank from highest. Fund projects in order until the money runs out, taking the last one in part. Total NPV is the sum of the full and part NPVs.

What is the sustainable growth rate formula in AFM?

It is g = b × ROE, where b is the retention ratio (1 − payout) and ROE is return on equity. It shows the growth that can be funded from retained profit if ROE and gearing stay constant. Say which equity figure you used.

Does ranking by profitability index always give the best answer?

No. It works for one rationed period when projects are divisible. If projects are indivisible, test combinations. If more than one period is rationed, you need linear programming.