Net present value/Tutorials

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

${\mbox{V}}=\sum _{t=1}^{n}{\frac {C_{t}}{(1+r)^{t}}}$

Where

• $t$ is the time of the cash flow
  
• $r$ is the investor's discount rate
  
• $C_{t}$ 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 [1].

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.

${\mbox{r}}=\sum _{j=1}^{n}{y_{j}}{B_{i}j}$

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:

${\mbox{E}}=\sum _{y=1}^{n}P_{y}V_{y}$