Net present value

Eduzendium article

The net present value (NPV) of a project is the sum of its discounted annual cash flows including those involved in its initial investment.

Formula

The NPV of a project generating cash flows during n periods is given by the formula :

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

Where

• $t$ is the time of the cash flow
  
• $r$ is the discount rate
  
• $C_{t}$ is the net cash flow (the amount of cash) at time t.
  
• $I$ is the initial investment outlay.

Principle

The NPV enables to compare the cost of an investment and the income it generated in regard of the opportunity cost of capital and sometimes of the level of risk associated to it.

Comparing the cost of a project and the income it generated is not enough to conclude whether it is a good project or not. Indeed the value of a amount of money today and the value of the same amount at time t in the future are different, because this amount could be deposited in a bank account from today to time t and yield interest. The NPV takes into account this parameter.

Conclusions

• When investors evaluate a investment project, they undertake it when its NPV is positive.
• When they evaluate several projects mutually exclusive they choose the project with the highest positive NPV.