PV & NPV

Present Value (PV) and Net Present Value (NPV)

• Present Value (PV): the value today of a future cash flow.
• Net Present Value (NPV): the present value of all project cash inflows minus the initial investment.

Formulas:

$PV=\frac{FV}{(1+r{)}^n}$

$NPV={\sum }_{t=1}^n\frac{C_t}{(1+r{)}^t}-C_0$

Where:

• r = Discount Rate
• C_t = cash flow in period t
• C_0 = initial investment

Decision rule:

• NPV > 0: value is created
• NPV = 0: break-even at the required return
• NPV < 0: value is destroyed

DCF is an application of this same logic to valuing a business or asset.