# What is the net present value of a project

## Definition – Net present value (NPV)

NPV is defined as the sum of present value of all cash inflows minus sum of present value of all cash outflows.

## Decision Rule

• If NPV is positive, accept the project
• If NPV is negative, reject the project
• When you are choosing a project out of several options, accept the project with the highest NPV

## Formula

Net Present Value (NPV) = Present Value of inflows – Present Value of outflows

## Explanation – Net present value of a project

NPV is the net funds generated by the project after cost of capital. It is an absolute measure and is considered as the most reliable method in investment appraisal. Let’s say a project needs a \$1,000 investment in year 0 and will generate returns for 3 years. Suppose the Present Value (PV) of these inflows is \$3,500. So overall, the project generates a net benefit of \$2,500.

To understand the concept of NPV, you must learn its relationship with the cost of capital. If you remember, the cost of capital is the total cost that the business has to return to its providers of finance. Consider another example of a business that has calculated NPVs of \$500, \$0, and (\$400) of a project at discount rates of 9% 12%, and 15% respectively. Now, what does this mean?

• If the business borrows funds at a rate of 15% to finance the project, the business will face a loss of \$400 because the inflows generated by the project are not enough to cover its investment.
• If the business borrows funds at the rate of 12%, the project would break even i.e., the total present value of inflows will cover the present value of an investment in the project thus resulting in no profit-no loss.
• If the business borrows funds at the rate of 9%, the project will yield a return of \$500 because the interest cost to be paid back to lenders is lower and the PV of inflows exceeds outflows.

From this, you can estimate that at higher costs of capital, the NPV of a project decreases because the business has to return a greater amount to lenders. This is shown in the graph below:

## Calculation – NPV

There are two steps to calculate the NPV of a project:

1. Discount the future cash flows using an appropriate discount rate (mostly, the cost of capital of the company)
2. Subtract the PV of outflows from the PV of inflows to calculate the NPV of the project.

## Example – What is the net present value of a project

A manufacturing company, Argos Limited, is planning to invest in a new assembly machine for its production department. The cost of the machine is \$150,000. It is estimated that it will reduce material wastage in the production process and therefore result in production cost savings. The life of the machine is expected to be 5 years after which it will be sold as scrap for \$10,000. The machine is expected to generate the following inflows in the form of savings:

Since the investment in the machine is in year 0, it does not need to be discounted.

Net Present Value (NPV) = PV of inflow – PV of outflow

NPV = \$156,280 – \$150,000

NPV = \$6,280

Since the NPV of the project is positive, management should invest in the project.