Profitability Index (PI)
Ratio of the present value of future cash flows to the initial investment. PI > 1 means the project creates value; PI < 1 means it destroys value. Mathematically equivalent to NPV/|initial investment| + 1.
When to use: Use to rank capital-rationed projects of different sizes — PI gives a normalized "bang for the buck" measure that NPV alone doesn't. Especially useful when you have more attractive projects than capital to fund them all.
Formula
Variables
| Symbol | Name | Description | Unit |
|---|---|---|---|
| PI | Profitability Index | Ratio of PV of future cash flows to the initial investment | integer |
| CashFlows | Cash Flows | Sequence of cash flows starting at period 0 (negative for outflows, positive for inflows) | $ |
| k | Discount Rate | Cost of capital or required rate of return as a decimal (e.g. 0.10 for 10%) | % |
Real-Life Examples
Example 1: 4-Year Project
Invest $1,000, receive $400/year for 4 years at 10% required return.
Given
Step-by-Step
PI of 1.27 — every $1 invested generates $1.27 of present value. Accept (and prefer to a competing project with PI=1.10 if capital is limited).
Example 2: Below-Hurdle Project
$5,000 invested, receiving $1,200, $1,500, $1,800, $2,000 at 12% required return.
Given
Step-by-Step
PI < 1 — every $1 in produces only $0.96 of present value. Reject.
Frequently Asked Questions
When you have capital constraints. NPV ranks by absolute dollar value created — a $50M project with $5M NPV ranks above a $1M project with $4M NPV, but the smaller project is more capital-efficient (PI 5.0 vs 1.1). Under capital rationing, PI tells you which projects to pick first.
PI = 1 + NPV/|CF₀|. They always agree on accept/reject decisions (PI > 1 ↔ NPV > 0), but disagree on rankings when projects have different sizes.
In the canonical form, PI uses just CF₀ as the denominator. For projects with negative cash flows in multiple early years, sum the PV of all negative CFs and use that as the denominator instead — this implementation uses the magnitude of CF₀ only, which is the standard textbook form.