Net Present Value

The net present value (NPV) of a series of cash flows is found by calculating the present value of each cash flow and adding them together. The net present value indicates the magnitude of the cash flows.

The net present value is used to compare projects and to evaluate whether or not a project is worthwhile. It assumes that a project comprises a series of cash flows in or out of the business over a number of years.

Net Present Value Example

Consider as an example, the following cash flow diagram. At the start of year 1 (today) there is a cash out flow of 5,000 representing an investment in a project. For simplicity, with no further investment, the amount of 7,000 is returned in 3 years time at the end of year 3.

The business decides that the appropriate discount rate to use is 10%. The discount rate (value the business places on its money) is very important in the calculation. It will depend on a number of factors such as the risk involved and what other opportunities the business has for the funds. At the very least it should greater than the rate a business could earn at a bank (minimal risk), and is usually a lot higher.

The net present value of this project is the sum of the present values of each of the cash flows.

Cash flow 1
Cash flow 1 is paid out at the start of period 1, and therefore its present value is -5,000.

Cash flow 2
Cash flow 2 is received at the end of period 3, and therefore its present value is given by the present value of a lump sum formula.

```PV = FV / (1 + i)n
PV = 7,000 / (1 + 10%)3
PV = 5,259.20
```

How to Calculate Net Present Value

To get to the NPV, the present value of both cash flows is added together.

```Net present value = NPV = PV cash flow 1 + PV cash flow 2
NPV = -5,000 + 5,259.20
NPV = 259.20
```

The net present value formula results in a positive number, meaning that the return from the project must actually be greater than the 10% required by the business, and therefore the project is worth accepting. To prove this is the case, had the 5,000 been invested elsewhere at 10% then using the future value of a lump sum formula after 3 years we would have:

```FV = PV x (1 + i)n
FV = 5,000 x (1 + 10%)3
FV = 6,655.00```

At a discount rate of 10% the 5,000 would have grown into only 6,655 compared to the 7,000 received from the project.

Consider now what happens is the project returns only 6,000 at the end of year 3. The initial outlay on day one is -5,000, however, the present value of the year 3 cash flow is now given by:

```PV = FV / (1 + i)n
PV = 6,000 / (1 + 10%)3
PV = 4,507.89
```

and the NPV is

```Net present value = NPV = PV cash flow 1 + PV cash flow 2
NPV = -5,000 + 4,507.89
NPV = -492.11
```

In this case the net present value is negative meaning that the project should not be accepted as the return from the project must be less than the 10% required by the business.

NPV and Multiple Cash Flows

This exercise of calculating net present value can be repeated for any number of cash flows. Consider a project with the following cash flow diagram. In this case the initial cash is paid at at the start of period 1 (today). This is followed by receipts at the end of period 2 and the end of period 3.

Applying the present value of a lump sum formula to each payment we get the following

```NPV = -5,000 + 3,000 / (1 + 10%)2 + 7,000 / (1 + 10%)3
NPV = -5,000 + 2,479.34 + 5,259.20
NPV = 2,738.54
```

The net present value of the project is positive, the return must be greater than the 10% required by the business, and the project is accepted.

The calculations can be carried out using our present value of a lump sum tables can be used as follows:

From the tables at 10%, the factors for year 2 and 3 are 0.8264, and 0.7513, and the net present value is calculated as

```NPV = -5,000 + 3,000 x 0.8264 + 7,000 x 0.7513
NPV = -5,000 + 2,479.20 + 5,259.10
NPV = 2,738.30
```

The net present value calculation of a series of cash flows is simply the present value of each cash flow added together. Projects with a positive net present value at the required rate of return (discount rate) should be accepted, projects with a negative net present value should be rejected. If only one project can be undertaken, then the project with the highest net present value should be chosen.