## Net Present Value (NPV)

NPV is the sum of present values of all future cash inflows minus the initial investment, discounted at the firm's cost of capital (WACC).

> NPV = Σ [CFt ÷ (1+r)^t] − Initial Outflow

Decision Rule:

NPV > 0 → Accept (project adds to shareholder wealth)
NPV < 0 → Reject
NPV = 0 → Indifferent

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### Advantages

#	Advantage	Why Important
1	Accounts for Time Value of Money	All cash flows discounted to present value
2	Considers the entire stream of cash flows	No cash flow is ignored, unlike Payback
3	Directly measures addition to shareholder wealth	NPV = value created for owners
4	Uses discounted cash flows	All values expressed in today's rupees—economically meaningful
5	Projects can be evaluated independently	Each project's NPV stands on its own; NPVs of independent projects are additive

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### Limitations

#	Limitation	Consequence
1	Calculation complexity	Requires estimation of WACC and multi-year cash flows—more effort than Payback or ARR
2	Sensitive to input accuracy	Small errors in cash flow or discount rate estimates lead to large NPV swings
3	Ignores scale differences	A large project with NPV ₹10 lakh vs. a small project with NPV ₹8 lakh—NPV favours the large project even if the smaller project delivers better return per rupee invested

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> Exam tip: NPV is considered the theoretically superior method for capital budgeting because it directly measures wealth creation and satisfies all three criteria: TVM, full cash flow consideration, and wealth maximisation objective.

Worked example

### Example 1

Initial outflow: ₹2,00,000. Cash inflows: Year 1: ₹80,000; Year 2: ₹90,000; Year 3: ₹70,000. WACC = 10%. PV Year 1 = 80,000/1.10 = ₹72,727. PV Year 2 = 90,000/1.21 = ₹74,380. PV Year 3 = 70,000/1.331 = ₹52,592. Total PV = ₹1,99,699. NPV = 1,99,699 − 2,00,000 = −₹301 → Reject (barely).

### Example 2

Project A: Initial outlay ₹50 lakh, NPV = ₹12 lakh. Project B: Initial outlay ₹10 lakh, NPV = ₹9 lakh. Under pure NPV, Project A is preferred. But Project B may be better on a per-rupee-invested basis (PI of B = 1.9 vs. A = 1.24). This illustrates the scale limitation of NPV—Profitability Index should be used alongside NPV under capital rationing.

⚠️ Common exam mistakes

Discounting the initial outflow—if the outflow occurs at Time 0, it is already in present value terms and should not be discounted.
Using a fixed arbitrary discount rate rather than WACC—the discount rate must reflect the firm's actual cost of capital.
Concluding NPV = 0 means the project is bad—NPV of zero means the project exactly earns the required rate of return, which is acceptable.
Comparing NPVs of projects with different lives without adjusting (e.g., using Equivalent Annual Annuity)—direct NPV comparison is only valid for projects with equal lives.

Reference:

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Net Present Value (NPV) — Merits and Limitations

Worked example

⚠️ Common exam mistakes