# Evaluation Methods: NPV, Profitability Index & IRR
## Net Present Value (NPV)
Definition: Sum of present values of all future cash inflows minus the initial investment, discounted at the cost of capital.
Decision Rule: NPV > 0 → Accept | NPV < 0 → Reject
### Advantages
| Advantage | Explanation |
|---|---|
| Considers Time Value of Money | All cash flows discounted to present value |
| Entire cash flow stream considered | No cash flow is ignored (unlike Payback) |
| Directly measures wealth addition | Positive NPV = direct addition to shareholder wealth |
| Expressed in current rupees | Facilitates meaningful comparison across projects |
| Projects independently comparable | Each project's NPV stands on its own merit |
### Limitations
| Limitation | Explanation |
|---|---|
| Difficult calculations | Requires accurate cash flow forecasts and appropriate discount rate |
| Accuracy-sensitive | Errors in either cash flows or discount rate compound significantly |
| Ignores project size | Does not adjust for differences in initial investment scale |
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## Profitability Index (PI)
Formula: PI = PV of Cash Inflows ÷ Initial Investment
Decision Rule: PI > 1 → Accept | PI < 1 → Reject | PI = 1 → Break-even (NPV = 0)
### Advantages
- Considers Time Value of Money
- Relative measure — useful for ranking projects of different sizes
### Limitations
- Fails under capital rationing when projects are indivisible
- A high-NPV large project may crowd out multiple small projects with a combined higher NPV
- A lower-PI project may generate early cash flows enabling another profitable project later, making total NPV higher
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## Internal Rate of Return (IRR)
Definition: The discount rate at which a project's NPV equals zero — the project's own rate of return.
Decision Rule: IRR > Cost of Capital → Accept | IRR < Cost of Capital → Reject
### Advantages
| Advantage | Explanation |
|---|---|
| Considers Time Value of Money | Uses discounted cash flows |
| All cash flows considered | Full project life is evaluated |
| Intuitive comparison | Directly compare IRR to cost of capital (hurdle rate) |
| Wealth maximisation | Projects where IRR > cost of capital add shareholder value |
### Limitations
| Limitation | Explanation |
|---|---|
| Tedious calculation | Requires trial-and-error or interpolation |
| Multiple IRRs possible | Non-conventional cash flow patterns (alternating signs) can yield multiple solutions |
| Unrealistic reinvestment assumption | Assumes interim cash flows reinvested at IRR — often not achievable |
| Misleading for mutually exclusive projects | IRR ranking can contradict NPV ranking; NPV is more reliable in such cases |
> Hierarchy for exam: For mutually exclusive projects, always prefer NPV over IRR. For capital rationing with divisible projects, use PI.