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==Net present value==
The present value of an investment generating cash flows C during n  years is given by:
::::<math>\mbox{V} = \sum_{t=1}^{n} \frac{C_t}{(1+r)^{t}}</math>
Where
*<math>t</math> is the time of the cash flow <br>
*<math>r</math> is the investor's [[discount rate]] <br>
*<math>C_t</math> is the  cash flow (the inflow  of cash) in year t  <br>
Tabulations of the factors to be applied each year at specified discount rates are to be found in many reference books [http://www.netmba.com/finance/time-value/present/].
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&nbsp;=&nbsp;PV
Where there are multiple possible outcomes y&nbsp;=&nbsp;1 ...n with probabilities ''P''<sub>y</sub> and present values ''V''<sub>y</sub>,
then the net present expected value is given by:
::::<math>\mbox{E} = \sum_{y=1}^{n} P_y V_y</math>
==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
<ref> Gaylon E. Greer and  Phillip T. Kolbe: ''Investment analysis for real estate decisions''[http://books.google.com/books?id=8ELJnEyWEl0C&pg=PA227&lpg=PA227&dq=inconsistent+OR+indeterminate+%22internal+rate+of+return%22&source=bl&ots=DdvKG7pFCo&sig=re1GDQMDmTfQqjMWyQk8CVnz0dY&hl=en&ei=KYY5TODMEs2HuAes1PWQBA&sa=X&oi=book_result&ct=result&resnum=6&ved=0CCwQ6AEwBQ#v=onepage&q=inconsistent%20OR%20indeterminate%20%22internal%20rate%20of%20return%22&f=false] (Google books extract), Dearborn Real Estate, 2003</ref>.
{{reflist}}

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Tutorials relating to the topic of Net present value.

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 Py and present values Vy,

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].

  1. Gaylon E. Greer and Phillip T. Kolbe: Investment analysis for real estate decisions[1] (Google books extract), Dearborn Real Estate, 2003