Net Present Value (NPV)

Also known as: NPV Formula

NPV = \sum_{t=0}^{N} \frac{C_t}{(1+r)^t}

NPV = Σ Ct / (1+r)^t

What It Calculates

Evaluates the profitability of an investment by summing the present values of all future cash flows. A positive NPV means the investment creates value.

variables

Symbol	Name	Unit	Description
NPV	Net Present Value	$	The difference between the present value of cash inflows and outflows
C_t	Cash Flow at time t	$	Net cash flow during period t (negative for initial investment)
r	Discount Rate	decimal	Rate of return required
N	Total Periods	—	Number of time periods

Worked Examples

1PV of Year 1: 3000/1.10 = 2727

2PV of Year 2: 3000/1.21 = 2479

3PV of Year 3: 3000/1.331 = 2254

4PV of Year 4: 3000/1.4641 = 2049

5PV of Year 5: 3000/1.6105 = 1863

6NPV = -10000 + 2727 + 2479 + 2254 + 2049 + 1863 = $1,372

Result: $1,372

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Related Formulas

Present Value Formula

PV = FV / (1 + r/n)^(nt)

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