# Net present value/Tutorials

## Net present value

The present value of an investment generating cash flows C during n years is given by:

Where

- is the time of the cash flow
- is the investor's discount rate
- is the cash flow (the inflow of cash) in year t

Tabulations of the factors to be applied each year at specified discount rates are to be found in many reference books [2].

Present value becomes net present value when C is taken to be the net cash inflow after allowing for outflows at the time of purchase of an asset or during the launch phase of a project.

## Net present expected value

The net present expected value, E of a project having a probability P of a single outcome whose net present value is V is given by:

- E = PV

Where there are multiple possible outcomes y = 1 ...n with probabilities *P*_{y} and present values *V*_{y},

then the net present expected value is given by:

## Internal rate of return

The internal rate of return is that value of the discount rate, r in the above equations at which the present value V is zero. It is not recommended as an investment criterion because it is capable of producing inconsistent results
^{[1]}.