In [[Principles of Corporate Finance]] the concept of //net present value// or //NPV// is defined as a project's net contribution to wealth ([[Present Value]]) minus initial investments. [[NPV]] is a measure of the difference between how much an asset is worth and what it costs. When it is worth more than it costs, the project has a positive NPV and the cooperation goes ahead and invests.  A very simple to understand interpretation of the NPV is that it is your net profit at the end of the investment period corrected for inflation.

Put in another way; the NPV = PV(expected benefit cash flows) //minus// PV (capital expenditure). The decision is to invest if the NPV > 0. 

Net present value is calculated as present value plus any immediate cash flow:

$\Large \text{Net Present Value (NPV)} = C_0 + \frac{C_1}{1+r}$

If $\large C_0$ is negative the immediate cash flow is an investment or [[Cash Outflow]]. For example, if a dentist wishes to purchase a new dental practice, he may calculate the net present value over a number of years to see if he will recover his investment in a reasonable period of time. If the ask price for the dental practice is \$500,000, this is the present cash outflow used in the calculation. If the discounted cash inflow over, say, two years, is greater than or equal to \$500,000, then the investment will likely be profitable. For multiple varying discount factors and multiple years the formula becomes:

$\Large NPV = C_0 + \sum{\frac{C_t}{(1+r_t)^t}}$

There are three points to make about NPV:
1) A dollar today is worth more than a dollar tomorrow
2) The NPV depends on the forecasted cash flows from a project and takes the [[Opportunity Cost]]s into account
3) Because the present values are translated to 'dollars today' NPV's can be added up:

$\Large NPV (A+B) = NPV(A) + NPV(B)$

See also:
* [[Present Value]]
* [[IRR]]
* this [[excel sheet|/static/files/MBI/Module%209/Exercize%20Arosa%20Brixen%20Chamonix.xlsx]] example for comparison: 
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finance_public
created
Thu, 19 Jan 2012 15:50:43 GMT
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dirkjan
modified
Thu, 19 Jan 2012 15:50:43 GMT
modifier
dirkjan
tags
M12
Principles of Corporate Finance
Term
creator
dirkjan