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In [[finance]], the '''net present value''' (NPV) of a investment project is the difference between the [[present value]] of the stream of [[cash flow]]s generated by this project and the value of the initial investment. If the result is positive, then the project could be undertaken, otherwise it should be refused.
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== Formula ==


The NPV of a project generating cash flows during n periods is given by the formula :
The present value of an investment is the sum of its [[discounting|discounted]] annual cash flows. . It can be expressed as a criterion for an investment project by requiring that the '''net present value'''  of its future cash flows, allowing for outflows during of its launch phase, should be positive. The corresponding  [[/Tutorials#net present expected value|net present expected value]]  is the sum of the net present values of  alternative outcomes after weighting each by its probability of occurrence.


<math>\mbox{NPV} = \sum_{t=1}^{n} \frac{C_t}{(1+r)^{t}} - {I}</math>
Calculations of net present value  are used for investment decisions by individuals and by companies and for [[cost-benefit analysis]] of proposals involving [[public goods]]. The [[discount rate]]s appropriate to those applications are discussed in the article on that subject.
 
Where
 
*<math>t</math> is the time of the cash flow <br>
*<math>r</math> is the [[discount rate]] <br>
*<math>C_t</math> is the net cash flow (the amount of cash) at time t. <br>
*<math>I</math> 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.

Revision as of 18:23, 2 October 2013

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The present value of an investment is the sum of its discounted annual cash flows. . It can be expressed as a criterion for an investment project by requiring that the net present value of its future cash flows, allowing for outflows during of its launch phase, should be positive. The corresponding net present expected value is the sum of the net present values of alternative outcomes after weighting each by its probability of occurrence.

Calculations of net present value are used for investment decisions by individuals and by companies and for cost-benefit analysis of proposals involving public goods. The discount rates appropriate to those applications are discussed in the article on that subject.

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