# Net present value/Tutorials

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## Net present value

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 .

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:

${\mbox{E}}=\sum _{y=1}^{n}P_{y}V_{y}$ ## 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. Gaylon E. Greer and Phillip T. Kolbe: Investment analysis for real estate decisions (Google books extract), Dearborn Real Estate, 2003