How do I handle capital rationing — when I can't fund all positive-NPV projects?

Question

AcadiFi · Accepted Answer

Capital rationing arises when a firm cannot fund all positive-NPV projects due to budget constraints. The optimal approach is to maximize total NPV within budget, not to rank by IRR.

Methods:
1. Profitability Index (PI) ranking: PI = NPV/Initial Investment + 1. Rank by PI descending, fund top until budget exhausted. Works for single-period rationing with divisible projects.

2. Integer programming: when projects are indivisible, use mixed-integer programming to maximize ΣNPV_i × x_i subject to Σ Cost_i × x_i ≤ Budget, x_i ∈ {0,1}.

3. Multi-period rationing: dynamic programming if budget constraints span multiple years.

Example: Quorrelton Industries has $80M capital budget for FY26, six candidate projects:

| Project | Cost | NPV | PI |
|---|---|---|---|
| A: automation | $25M | $12.5M | 1.50 |
| B: new product | $30M | $11.0M | 1.37 |
| C: expansion | $40M | $14.5M | 1.36 |
| D: IT upgrade | $15M | $4.5M | 1.30 |
| E: plant reno | $20M | $5.5M | 1.28 |
| F: warehouse | $35M | $7.5M | 1.21 |

Naive PI ranking: A ($25M) + B ($30M) + D ($15M) = $70M cost, $28.0M NPV. $10M unused.

Integer programming finds: A + C + D = $80M cost, $31.5M NPV. Better!

Or: A + B + E = $75M cost, $29.0M NPV. $5M leftover, not as good as A+C+D.

Quorrelton's CFO adopts A+C+D, forgoing B (new product) despite high PI. The $140M total positive-NPV projects reduced to $80M funded. Rejected projects (B, E, F) are re-considered in FY27.

Soft vs. hard rationing: soft rationing is internally imposed (signals management concerns or control); hard rationing reflects true external capital market constraints. Modern view: persistent soft rationing destroys value — firms should either relax budgets or issue equity/debt to fund unfunded positive-NPV projects.

How do I handle capital rationing — when I can't fund all positive-NPV projects?

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