## Definition of Present Value (PV)

*Present value* or PV is the result of discounting one or more future amounts to the present. The greater the discount rate, the smaller the present value.

## Examples of Present Value

A cash amount of $10,000 received at the end of 5 years will have a *present value (PV)* of $6,210 when the $10,000 is discounted at 10% compounded annually. If the $10,000 is discounted at 12% compounded annually, the present value will be $5,670.

## Definition of Net Present Value (NPV)

*Net present value* is the result of discounting *all of the cash inflows and outflows* and then combining all of their present values. This means that the original outflow (often the investment made at the present time) is a deduction from the other present values.

A positive net present value indicates that an investment is earning more than the discount rate. A negative net present value indicates an investment is earning less than the discount rate, but may be earning a positive rate. For example, if the cash flows are discounted by 12%, a slightly negative NPV could mean that the investment is earning 11%.

## Examples of Net Present Value

Assume that an investment of $5,000 today will result in one cash receipt of $10,000 at the end of 5 years. If the investor requires a 10% annual return compounded annually, the *net present value (NPV)* of the investment is $1,210. This is the result of combining the present value of the cash inflow $6,210 (from the example above) and the $5,000 (which is the present of the $5,000 paid today).

Assuming the same information, except that the rate for discounting the cash amounts is 12%, the net present value (NPV) is $670. This is the $5,670 present value of the cash inflow combined with the present value of the $5,000 cash outflow.