NPV
GeneralNet Present Value
The difference between the present value of all future cash inflows and the present value of all cash outflows from an investment, discounted at a required rate of return. A positive NPV means the investment creates value.
Definition
Net Present Value (NPV) is the difference between the present value of cash inflows and the present value of cash outflows over a period of time. NPV is the fundamental measure of value creation or destruction from an investment or project, expressed in today's rupees.
The core intuition behind NPV: money today is worth more than money tomorrow (time value of money). A rupee received 5 years from now is worth less than a rupee today because today's rupee can be invested and grown. NPV accounts for this by discounting future cash flows to their present value using a discount rate that reflects the cost of capital and risk.
NPV > 0: Project creates value — invest NPV = 0: Project breaks even on cost of capital NPV < 0: Project destroys value — don't invest
Formula
NPV = Σ [Ct / (1 + r)^t] − C₀
Where:
- Ct = Net cash inflow in period t
- r = Discount rate (required rate of return)
- t = Time period (years)
- C₀ = Initial investment
Or equivalently:
NPV = −C₀ + C₁/(1+r) + C₂/(1+r)² + C₃/(1+r)³ + ...
Worked Example
You are evaluating a new retail outlet. Initial investment: ₹30 lakh. Expected annual cash flows for 5 years: Year 1: ₹5L, Year 2: ₹8L, Year 3: ₹10L, Year 4: ₹10L, Year 5: ₹12L. Discount rate (your required return): 12%.
| Year | Cash Flow | Discount Factor (1/(1.12)^n) | Present Value |
|---|---|---|---|
| 0 | −₹30,00,000 | 1.000 | −₹30,00,000 |
| 1 | ₹5,00,000 | 0.893 | ₹4,46,429 |
| 2 | ₹8,00,000 | 0.797 | ₹6,37,755 |
| 3 | ₹10,00,000 | 0.712 | ₹7,11,780 |
| 4 | ₹10,00,000 | 0.636 | ₹6,35,518 |
| 5 | ₹12,00,000 | 0.567 | ₹6,80,912 |
NPV = −₹30,00,000 + ₹31,12,394 = ₹1,12,394
The NPV is positive (₹1.12 lakh), so the project marginally clears the 12% hurdle rate. Use the ROI calculator to compare investment alternatives.
Key Things to Know
- NPV vs payback period: Payback period ignores the time value of money and what happens after payback. NPV accounts for both — it is the superior metric for financial decision-making, though payback period is simpler and useful for quick liquidity assessments.
- Sensitivity analysis: The NPV output is only as reliable as its inputs (cash flow estimates, discount rate). Run NPV under optimistic, base, and pessimistic scenarios. If NPV is positive only under optimistic assumptions, the project carries significant risk.
- Terminal value: For long-lived projects or businesses, the NPV calculation often includes a "terminal value" — the value of all cash flows beyond the explicit projection period, usually calculated using the Gordon Growth Model: TV = Final Year Cash Flow × (1 + g) / (r − g), where g is perpetual growth rate.
- NPV in project finance: For large infrastructure projects in India (roads, power plants), NPV analysis underpins lender feasibility assessments. Project finance NPVs are calculated over 15–30 year periods, making the discount rate choice critical — a 1% change in discount rate can alter NPV by several hundred crore on a ₹1,000 crore project.
- IRR complement: NPV and IRR together give a complete picture. If NPV > 0 and IRR > cost of capital, invest. When they conflict (scale or timing differences between projects), NPV wins — it measures absolute value creation, which is what matters.