## Net Present Value (NPV) and Internal Rate of Return (IRR)

### Definition

A net present value (NPV) is the net total of several present values (arising from cashflows at different future dates) added together, some of which may be positive and some negative.

An internal rate of return (IRR) is the one single interest rate (rate of discount) which it is necessary to use when discounting a series of future values to achieve a given net present value or, equivalently, the interest rate which it is necessary to use when discounting a series of future values including an initial cashflow now, to achieve a zero net present value.

### How are they used?

#### NPV

Suppose that we have a series of future cashflows, some of which are positive and some negative. Each ...