Net present value: Difference between revisions

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


The '''net present value''' (NPV) of a  project is the sum of its discounted annual cash flows including those involved in its initial investment. Its '''net present expected value''' (NPEV) is the sum of the net present values of the alternative outcomes of the project after weighting each by its probability of occurrence. The formulae used to calculate NPV and NPEV are set out on the tutorials subpage.


== Formula ==


The NPV of a project generating cash flows during n periods is given by the formula :
Calculations of NPV or NPEV 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. The subject of risk-limitation  in investment decisions is discussed in the article on [[financial economics]]
 
<math>\mbox{NPV} = \sum_{t=1}^{n} \frac{C_t}{(1+r)^{t}} - {I}</math>
 
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 15:23, 25 February 2008

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The net present value (NPV) of a project is the sum of its discounted annual cash flows including those involved in its initial investment. Its net present expected value (NPEV) is the sum of the net present values of the alternative outcomes of the project after weighting each by its probability of occurrence. The formulae used to calculate NPV and NPEV are set out on the tutorials subpage.


Calculations of NPV or NPEV 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. The subject of risk-limitation in investment decisions is discussed in the article on financial economics

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