Project Selection and Capital Rationing
With unlimited funds the rule is simple: accept every positive-NPV project. Under capital rationing, a fixed budget cannot fund them all, so the firm must rank. The profitability index (PI), defined as the present value of inflows divided by the initial outlay, ranks projects by value created per dollar invested and guides selection toward the bundle that maximises total NPV within the budget. PI is best for independent, divisible projects under a single binding constraint. With mutually exclusive choices or several constraints, the firm maximises total NPV directly, since raw PI ranking can then mislead.
Why it matters
NPV tells you how much value a project adds, but not how efficiently it uses scarce capital. When the budget binds, two projects with equal NPV are not equal if one needs half the cash. The profitability index fixes this by measuring value per dollar invested, so the firm can pack the most total value into a limited budget, much like filling a fixed-size knapsack with the most valuable items. The caveat is that the index ranks cleanly only when projects are independent and divisible and a single constraint binds.
Formulas
Worked examples
A firm has a A$10m budget. Project A needs A$6m and has an NPV of A$3m. Project B needs A$4m and has an NPV of A$2.4m. Project C needs A$6m and has an NPV of A$3.3m. Which projects maximise value?
Compute PI as 1 plus NPV over investment. A is 1 plus 3 over 6, that is 1.50. B is 1 plus 2.4 over 4, that is 1.60. C is 1 plus 3.3 over 6, that is 1.55. Ranked by PI the order is B, then C, then A. Within the A$10m budget, B (A$4m) plus C (A$6m) fits exactly and delivers A$2.4m plus A$3.3m, that is A$5.7m of NPV. A plus B would cost A$10m but yield only A$5.4m, so the PI ranking correctly picks the higher-value bundle.
Common mistakes
- ✗Always pick the projects with the highest individual NPV. Under a binding budget the goal is the most NPV per dollar, so the profitability index, not raw NPV, drives the ranking.
- ✗A profitability index above one is enough to accept a project. A PI above one signals value, but under rationing the project must also win its place against rivals competing for the same scarce capital.
- ✗PI works for any set of projects. PI ranking is reliable for independent, divisible projects under one constraint. With mutually exclusive projects or several constraints it can mislead.
- ✗Capital rationing means the firm has no positive-NPV projects left. Rationing means it cannot fund all of them, often by self-imposed limits, not that good projects are absent.
Revision bullets
- •With unlimited funds, accept every positive-NPV project
- •Capital rationing forces ranking under a fixed budget
- •The profitability index measures value created per dollar invested
- •PI equals one plus NPV divided by the initial investment
- •PI suits independent, divisible projects under one constraint
- •With mutually exclusive choices, maximise total NPV directly
Quick check
Under capital rationing, the profitability index is preferred to raw NPV for ranking because it measures
A project with a profitability index of 1.20 means that
Connected topics
Sources
- Titman & Martin, Ch. 7Titman, S., & Martin, J. D. Valuation: The Art and Science of Corporate Investment Decisions. Pearson.Covers project selection, the profitability index and ranking under capital rationing.
- Brealey, Myers & Allen (2020)Brealey, R. A., Myers, S. C., & Allen, F. Principles of Corporate Finance. 13th ed. McGraw-Hill Education, 2020.Standard treatment of the profitability index and capital rationing as a constrained NPV problem.