Profitability Index (PI) Calculator
Calculate the Profitability Index (PI) to evaluate the relationship between the present value of future cash flows and the initial investment cost.
Enter Investment Data
Enter the initial cost and the expected future cash flows for each period, along with the discount rate.
Future Cash Flows ($)
Understanding Profitability Index (PI)
The Profitability Index (PI), also known as the Value Investment Ratio (VIR) or Profit Investment Ratio (PIR), is a capital budgeting tool used to evaluate the attractiveness of a potential investment or project. It measures the ratio between the present value of future expected cash flows and the initial amount invested.
Formula:
The primary formula is:
$PI = \frac{\text{Present Value of Future Cash Flows}}{\text{Initial Investment}}$
Where the Present Value (PV) of Future Cash Flows is calculated as:
$PV = \sum_{t=1}^{n} \frac{CF_t}{(1 + r)^t} = \frac{CF_1}{(1+r)^1} + \frac{CF_2}{(1+r)^2} + ... + \frac{CF_n}{(1+r)^n}$
- $CF_t$ = Net cash flow in period $t$ (Year 1, 2, ... n)
- $r$ = Discount Rate per period
- $n$ = Number of periods
- Initial Investment is the cost at time $t=0$.
An alternative formula relates PI to Net Present Value (NPV):
$PI = \frac{NPV + \text{Initial Investment}}{\text{Initial Investment}} = 1 + \frac{NPV}{\text{Initial Investment}}$
Interpretation of the PI Value:
The PI rule for decision making is simple:
- PI > 1.0: Accept the project. Indicates that the present value of future cash flows is greater than the initial cost, suggesting the project will generate value.
- PI < 1.0: Reject the project. Indicates that the present value of future cash flows is less than the initial cost, suggesting the project will destroy value.
- PI = 1.0: Indifferent. Indicates that the present value of future cash flows exactly equals the initial cost (NPV = 0). The project is expected to earn exactly the required rate of return (discount rate).
Uses and Advantages:
- Ranking Projects:** PI is particularly useful for ranking projects when a company has limited capital (capital rationing). It shows the value generated *per dollar invested*, helping prioritize projects that offer the most "bang for the buck".
- Considers Time Value of Money:** Like NPV, it accounts for the fact that money today is worth more than money in the future by using a discount rate.
- Relative Measure:** Provides a ratio indicating efficiency, which can be easier to compare across projects of different sizes than the absolute dollar value of NPV.
Limitations:
- Scale Ignored:** While good for ranking relative efficiency, it doesn't show the absolute dollar value created (NPV does). A small project might have a high PI but contribute less overall value than a large project with a slightly lower PI.
- Mutually Exclusive Projects:** If projects are mutually exclusive (you can only choose one), NPV is generally the preferred decision criterion because it selects the project that adds the most absolute value.
- **Discount Rate Sensitivity:** The PI calculation is sensitive to the chosen discount rate.
- Cash Flow Estimates:** Accuracy depends heavily on the reliability of future cash flow predictions.
Frequently Asked Questions (FAQs)
1. What is the Profitability Index (PI)?
It's a ratio comparing the present value of an investment's future cash inflows to its initial cost. A PI greater than 1 suggests a profitable investment.
2. How does PI differ from NPV (Net Present Value)?
NPV calculates the *absolute dollar value* added by a project (PV of Inflows - Initial Cost). PI calculates a *relative ratio* (PV of Inflows / Initial Cost), indicating value generated per dollar invested.
3. When is PI particularly useful?
When comparing and ranking multiple independent projects under conditions of limited capital (capital rationing). It helps select the projects offering the highest return per unit of investment.
4. What discount rate should be used?
The discount rate should typically be the company's required rate of return, cost of capital (WACC), or the opportunity cost of investing in this project versus alternatives of similar risk.
5. What does a PI of 1.3 mean?
It means that for every $1 invested, the project is expected to generate $1.30 in present value terms, resulting in a net value creation of $0.30 per dollar invested.
6. What does a PI of 0.8 mean?
It means that for every $1 invested, the project is expected to generate only $0.80 in present value terms, resulting in a net loss of $0.20 per dollar invested. The project should likely be rejected.
7. Can PI be negative?
No, because the initial investment (denominator) is positive, and the present value of future cash flows (numerator) is usually assumed to be positive or zero in standard project evaluations. If the PV of future flows were negative, the project would be clearly rejected long before calculating PI.
8. If two projects are mutually exclusive, should I choose the one with the higher PI?
Not necessarily. For mutually exclusive projects, NPV is generally the better criterion. A larger project with a slightly lower PI might generate a much higher NPV (more total value) than a smaller project with a very high PI.
9. Does this calculation include taxes?
It depends on the cash flow inputs. For accurate capital budgeting, the cash flows ($CF_t$) entered should ideally be *after-tax* cash flows, and the discount rate ($r$) should also be appropriate for the cash flows being used (e.g., an after-tax WACC).
10. Where do the cash flow estimates come from?
Estimating future cash flows is a critical part of capital budgeting. It involves forecasting revenues, operating costs, changes in working capital, and capital expenditures associated with the project over its life.
Examples (USD)
Assume Discount Rate = 10% for all examples.
- Project A:** Initial Inv: $10,000; CFs: $4k, $4k, $4k, $4k (4 yrs).
- PV of Future CFs ≈ $12,679.46
- PI = $12,679.46 / $10,000 ≈ **1.27** (Accept)
- Project B:** Initial Inv: $20,000; CFs: $6k, $7k, $8k, $9k (4 yrs).
- PV of Future CFs ≈ $21,836.35
- PI = $21,836.35 / $20,000 ≈ **1.09** (Accept, but less efficient per $ than A)
- Project C:** Initial Inv: $5,000; CFs: $1k, $1k, $1k, $1k, $1k (5 yrs).
- PV of Future CFs ≈ $3,790.79
- PI = $3,790.79 / $5,000 ≈ **0.76** (Reject)
- Project D (High Initial Return):** Initial Inv: $50,000; CFs: $30k, $20k, $10k, $5k (4 yrs).
- PV of Future CFs ≈ $51,774.03
- PI = $51,774.03 / $50,000 ≈ **1.04** (Marginally Acceptable)
- Project E (Break-Even):** Initial Inv: $10,000; CFs: $3,333, $3,333, $3,333 (3 yrs). (Approximate)
- PV of Future CFs ≈ $8,288.71 (Using 3333 exactly)
- PI = $8,288.71 / $10,000 ≈ **0.83** (Reject) *Note: Requires slightly higher CFs to reach PI=1*
- *If CFs were ~$4021/yr:* PV ≈ $10,000, PI ≈ 1.00 (Indifferent)
- Ranking (Limited Capital $20k):** Project A (Cost $10k, PI 1.27) vs Project B (Cost $20k, PI 1.09). Choose Project A as it gives more value per dollar invested, leaving $10k capital potentially for other uses. (Though Project B has higher NPV).
- Zero Cash Flows:** Initial Inv: $1000; CFs: $0, $0, $0. -> PV = $0, PI = **0.00** (Reject).
- Single Future Cash Flow:** Initial Inv: $1000; CFs: $0, $0, $1500 (Yr 3). -> PV = $1500 / (1.10)^3 ≈ $1126.97. PI ≈ **1.13** (Accept).
- Negative Cash Flow:** Initial Inv: $2000; CFs: $1000, -$500 (Yr 2), $1000 (Yr 3). -> PV ≈ $909.09 - $413.22 + $751.31 ≈ $1247.18. PI ≈ **0.62** (Reject).
- Higher Discount Rate:** Project A data, Discount Rate 15%. -> PV ≈ $11,419.64. PI ≈ **1.14** (Still acceptable, but less attractive than at 10%).
