## Profitability Index (PI)
PI (also called Benefit-Cost Ratio) is a relative measure of a project's value—how much present value is generated per rupee of investment.
> PI = Total PV of Future Cash Inflows ÷ Initial Investment
(Alternatively: PI = 1 + NPV/Initial Investment)
Decision Rule:
- PI > 1 → Accept
- PI < 1 → Reject
- PI = 1 → Indifferent
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### Advantages
| # | Advantage |
|---|---|
| 1 | Incorporates Time Value of Money (uses discounted cash flows, like NPV) |
| 2 | Relative profitability measure—useful when comparing projects of different sizes (overcomes NPV's scale problem) |
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### Limitations
| # | Limitation | Detail |
|---|---|---|
| 1 | Fails under capital rationing with indivisible projects | Cannot fractionally select projects; a project with PI = 1.5 cannot be split to use partial funds |
| 2 | May exclude high-NPV projects | Accepting a single large project with high NPV prevents several smaller projects with collectively higher NPV |
| 3 | Sequencing effects ignored | A lower-PI project chosen now might free up resources to undertake another project in Year 2, producing higher total NPV—PI misses this dynamic |
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> When to prefer PI over NPV: In capital rationing situations (limited funds, divisible projects), rank projects by PI to maximise total NPV per rupee of budget. When projects are indivisible, use integer programming or trial combinations.