NPV

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:

${\text{Net Present Value (NPV)}}=C_{0}+{\frac {C_{1}}{1+r}}$

If $C_{0}$ 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:

$NPV=C_{0}+\sum {\frac {C_{t}}{(1+r_{t})^{t}}}$

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 Costs into account 3) Because the present values are translated to 'dollars today' NPV's can be added up:

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

See also:

• Present Value
• IRR
• this

excel sheet

example for comparison: