# Capital Rationing: How to Rank Projects When NPV and Budget Conflict

> A worked capital-rationing model showing when profitability-index rankings fail and how managers can select the highest-value feasible project portfolio.

- Canonical page: https://mtfinstitute.com/insights/capital-rationing-rank-projects-npv-profitability-index/
- Content type: Article
- Editorial category: Guides & Frameworks
- Publisher: MTF Institute of Management, Technology and Finance
- Author: MTF Institute Editorial Team- Published: 2026-08-18
- Updated: 2026-08-18
- Language: English
- Topics: Capital Allocation, Strategic Finance, NPV, Profitability Index, Investment Decisions

## Capital Rationing: How to Rank Projects When NPV and Budget Conflict

Net present value answers an important question: how much value should a project create at the chosen discount rate? It does not, by itself, solve a portfolio problem when several positive-NPV projects compete for a fixed investment budget.

Under capital rationing, managers must choose a feasible combination of projects. Profitability index can help compare value created per unit of initial capital, but a simple ranking can still select the wrong portfolio when projects are indivisible, timing differs or strategic constraints interact.

This guide provides a practical decision hierarchy, a worked example and a portfolio scorecard for managers allocating scarce capital.

## Three decisions that are often confused

1. **Standalone acceptance:** Does the project have positive NPV under consistent cash-flow and discount-rate assumptions?
2. **Capital efficiency:** How much present value does it create relative to constrained capital?
3. **Portfolio selection:** Which feasible combination maximizes value while respecting budget, risk, capacity and strategic constraints?

A project can pass the first test and still be excluded from the funded portfolio. That does not make it a bad project; it means another combination creates more value under the current constraint.

## The core measures

For a conventional project with an initial outlay at time zero:

**NPV = present value of future cash flows − initial outlay**

**Profitability index (PI) = present value of future cash flows / initial outlay**

Therefore:

**PI = 1 + NPV / initial outlay**

A PI above 1 corresponds to positive NPV under those assumptions. The measure is useful when the initial investment is the scarce resource. If projects have staged spending, shared resources or non-conventional cash flows, define the denominator explicitly rather than applying the shortcut mechanically.

## Worked portfolio example

Assume five indivisible projects, a €1.0 million capital ceiling and already risk-adjusted NPV estimates.

| Project | Initial outlay (€000) | NPV (€000) | PI | Standalone result |
|---|---:|---:|---:|---|
| A | 600 | 210 | 1.350 | Accept if unconstrained |
| B | 500 | 170 | 1.340 | Accept if unconstrained |
| C | 500 | 170 | 1.340 | Accept if unconstrained |
| D | 400 | 128 | 1.320 | Accept if unconstrained |
| E | 250 | 75 | 1.300 | Accept if unconstrained |

Every project has positive NPV. Ranking by PI puts A first. A greedy rule would then add D, using the full €1.0 million and producing €338,000 of NPV.

But B plus C also uses exactly €1.0 million and produces €340,000 of NPV. The simple PI ranking misses €2,000 because the projects are indivisible.

| Feasible portfolio | Outlay (€000) | Total NPV (€000) | Funded? |
|---|---:|---:|---|
| A + D | 1,000 | 338 | Feasible |
| B + C | 1,000 | **340** | **Value-maximizing in this set** |
| A + E | 850 | 285 | Feasible, capital remains |
| B + D | 900 | 298 | Feasible |
| C + D | 900 | 298 | Feasible |
| B + E | 750 | 245 | Feasible |
| C + E | 750 | 245 | Feasible |
| D + E | 650 | 203 | Feasible |

The example is intentionally simple. In a real portfolio, the difference can be material and constraints can include people, capacity, regulation, dependencies and concentration — not only cash.

## The seven-step CAPITAL decision hierarchy

### C — Confirm comparability

Use consistent treatment of inflation, tax, working capital, terminal value, financing and discount dates. A portfolio optimizer cannot repair inconsistent project models.

### A — Apply mandatory gates

Remove proposals that fail legal, safety, operational or strategic prerequisites. Record the reason; do not bury a mandatory failure inside a weighted score.

### P — Prove standalone economics

Calculate NPV and inspect the economic drivers. Stress-test volume, price, cost, timing and terminal assumptions. A positive base-case NPV is evidence, not certainty.

### I — Identify the binding constraint

Name the scarce resource: cash this year, specialist engineers, implementation capacity, management attention or risk appetite. PI is meaningful only when its denominator represents the true constraint.

### T — Test divisibility and dependencies

Can a project be partially funded? Must two projects be implemented together? Does one exclude another? Does a platform investment enable later projects? Record these relationships before ranking.

### A — Assemble feasible portfolios

For a small set, enumerate combinations. For a larger set, use an integer optimization model with binary fund/not-fund variables and explicit constraints. The objective can maximize total NPV, but strategic and risk requirements must be represented rather than discussed after the answer appears.

### L — Lock governance and learning

Approve milestones, funding tranches, benefits owners and stop rules. Capital allocation should continue after approval through evidence-based release or withdrawal of funds.

## A portfolio model managers can audit

For each project *i*, define:

- `x_i = 1` if funded, `0` otherwise;
- `NPV_i` as risk-adjusted net present value;
- `Cost_i` as constrained capital required.

Maximize:

**Σ NPV_i × x_i**

Subject to:

**Σ Cost_i × x_i ≤ capital budget**

Then add constraints that reflect reality. For example:

- dependency: `x_B ≤ x_A` if B requires A;
- mutual exclusion: `x_C + x_D ≤ 1`;
- mandatory program: `x_E = 1`;
- risk limit: total exposure to one market must remain below a defined threshold.

The mathematical answer is only as good as the cash flows and constraints. Preserve the model, assumptions and override reasons so the final decision remains auditable.

## When profitability index is useful

PI is most useful as a screening and diagnostic measure when:

- initial capital is the main binding constraint;
- projects have conventional cash-flow patterns;
- projects are reasonably comparable;
- small or divisible investments can be ranked incrementally.

It becomes less reliable when:

- projects are large and indivisible;
- future capital requirements differ materially;
- projects share costs or benefits;
- one project creates an option for another;
- risk is concentrated or correlated;
- the discount rate or cash-flow treatment is inconsistent.

In those cases, compare complete portfolios, not only project ratios.

## The executive allocation scorecard

Use the financial result as the center of the decision, then expose non-financial constraints without turning them into unexplained points.

| Decision layer | Question | Evidence | Treatment |
|---|---|---|---|
| Economics | Does the project create value? | NPV, sensitivities and scenario drivers | Mandatory positive case unless an explicit strategic exception is approved |
| Constraint efficiency | What value is created per scarce unit? | PI or value per constrained resource | Comparative signal |
| Portfolio fit | Is the combination feasible and value-maximizing? | Enumeration or optimization | Portfolio decision |
| Strategic necessity | Is there an obligation or capability dependency? | Strategy map, regulation or architecture | Explicit constraint or documented override |
| Delivery capacity | Can the organization execute now? | Named team, milestones and dependency load | Capacity constraint |
| Risk concentration | Does the portfolio create correlated exposure? | Scenario and concentration analysis | Limit or diversification rule |
| Learning value | Can funding be staged as evidence arrives? | Tranches, milestones and stop rules | Governance design |

## Common failure modes

**Ranking by IRR alone.** A high percentage return on a small project can create less absolute value than a lower-return larger project. See MTF's [NPV vs IRR decision guide](https://mtfinstitute.com/insights/npv-vs-irr-conflicting-investment-signals/).

**Treating the budget as permanent.** If a rejected project has compelling NPV, management should examine whether the capital ceiling reflects financing capacity, risk appetite or an arbitrary planning convention.

**Optimizing a single year.** A project may consume little current cash but create large future commitments. Use a multi-period constraint where required.

**Using weighted scores to overwrite value.** Strategic considerations matter, but an unexplained score can conceal weak economics. State the constraint or approved exception directly.

**Ignoring option value and sequencing.** Pilot, platform and compliance investments can unlock later choices. Model the decision tree rather than forcing all value into one static NPV.

## Practical conclusion

When capital is constrained, the objective is not to identify the project with the highest NPV or PI. It is to fund the feasible portfolio that creates the most defensible value. Confirm comparable models, identify the real constraint, calculate capital efficiency, enumerate combinations and document every strategic or risk override.

Managers who want to develop stronger capital-allocation, valuation and financial decision skills can explore MTF Institute's [Strategic Finance: M&A, Corporate Valuation and Investment Banking](https://mtfinstitute.com/lp/strategic-finance/). It is a professional education program, not an academic degree.

## Sources and related reading

- [Microsoft: NPV function](https://support.microsoft.com/en-us/office/npv-function-8672cb67-2576-4d07-b67b-ac28acf2a568)
- [UK Government: The Green Book — appraisal and evaluation](https://www.gov.uk/government/publications/the-green-book-appraisal-and-evaluation-in-central-government)
- [MTF: DCF Sensitivity Analysis](https://mtfinstitute.com/insights/dcf-sensitivity-analysis-wacc-terminal-growth-valuation-risk/)
- [MTF: WACC Explained for Managers](https://mtfinstitute.com/insights/wacc-explained-for-managers-hurdle-rate/)


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