# The Concept of Net Present Value

By using discounted cash flow techniques and calculating present values, we can compare the return on an investment in capital projects with an alternative equal risk investment in securities traded in the financial market, Suppose a firm is considering four projects (all of which are risk-free) as shown in below photo. You can see that each of the projects is identical with the investment in the risk-free security shown in below photo because you can cash in this investment for \$10,000 in year 1, \$121,000 in year 2, \$133,100 in year 3 and \$146,410 in year 4. in other words your potential cash receipts from the risk-free security are identical to the net cash flows for projects A, B, C and D shown in below photo. Consequently, the firm should be indifferent as to whether it uses the funds to invest in the projects or invests the funds in securities of identical risk traded in the financial markets.

The most straightforward way of determining whether a project yields a return in excess of the alternative equal risk investment in traded securities is to calculate the net present value (NPV). This is the present value of the net cash inflows less the project’s initial investment outlay if the rate of return from the project is greater than the return from
an equivalent risk investment in securities traded in the financial market, the NPV will be positive. Alternatively, if the rate of return is lower, the NPV will be negative. A positive NPV therefore indicates that an investment should be accepted, while a negative value indicates that it should be rejected. A zero NPV calculation indicates that the firm should be indifferent to whether the project is accepted or rejected.

You can see that the present value of each of the projects shown in below photo is \$100,000. You should now deduct the investment cost of \$100,000 to calculate the project’s NPV. The NPV for each project is zero. The firm should therefore be indifferent to whether it accepts any of the projects or invests the funds in an equivalent risk-free security. This was our conclusion when we compared the cash flows of the projects with the investment in a risk-free security shown in below photo You can see that it is better for the firm to invest in any of the projects shown in Above photo if their initial investment outlays are less than e 100 000. This is because we have to pay \$100,000 to obtain an equivalent stream of cash flows from a security traded in the financial markets. Conversely, we should reject the investment in the projects if their
initial investment outlays are greater than 1100 000. You should now see that the NPV rule leads to a direct comparison of a project with an equivalent risk security traded in the financial market Given that the present value of the net cash inf lows for each project is \$100,000, their NPVs will be positive (thus signifying acceptance) if the initial
investment outlay is less than \$100,000 and negative (thus signifying rejection) if the initial outlay is greater than \$100,000.