## Net present value

##### Published: Jun 2011

The net present value (NPV) of an asset is the sum total of the present values (PV) of that asset over a given period of time. It is used in the field of discounted cash flow analysis and allows an investor to calculate the likely returns on a prospective investment over its lifetime.

The NPV calculation is relatively straightforward. For each year of the investment, the net cash flow of the investment is divided by the discount rate to the power of the year of the investment.

$$\mathrm{NPV} = {C0 \:+ \: \frac{C1}{1 \:+ \: r} \: + \: \frac{C2}{1 \:+ \: r2} \: + \: \frac{C3}{ 1 \: + \: r3}} \:\:\:\:$$ etc.

Where r is the discount rate.

Or…

$$\frac{Rt}{1 \: + \: it}$$

Where 1 is the duration of the investment.

Rt is the net cash flow at time t .

### The discount rate

In the example below, for illustrative purposes, we have used a discount rate of 7% over the lifetime of the investment. The discount rate is the return that could be earned on an investment in the financial markets with similar risk.

It is not unknown for more nuanced NPV calculations to include more than one discount rate over the lifetime of the investment so that investors are able to map expected changes in the yield curve more closely.

### A worked example

Suppose a prospective five year investment costs $11,000. So the present value of the investment when t = 0 is -$11,000. Cash inflows are expected to total $10,000 a year and the new investment is expected to take$1,500 a year to maintain. The investor requires a minimum of 7% return on his/her investment.

Total inflows = $34,851.68 Total outflows =$18,500

Net present value = \$16,351.68

In which case, with NPV > 0, the investment would make a return and the investor should consider putting his/her money into the project.