**Net present value (NPV) or present worth**

This is defined as the present value of discounted inflows less discounted outflows.

If the NPV > 0 at the required interest rate then the project may be accepted.

If the NPV < 0 at the required interest rate then the project should be rejected.

Using the same sample figures as for the calculation of payback, the NPV can be calculated as shown in Table 11.11.

**TABLE 11.11 ****Calculating NPV**

**Internal rate of return (IRR) or DCF yield**

The internal rate of return is the rate at which the NPV of a project is zero; that is, the project breaks even. This is found by trial and error (or using the 'goal seek' function).

Using the same sample data as for payback and NPV, the IRR can be found by increasing the required rate to 37.617 per cent, at which rate the NPV is exactly zero (Table 11.12). A higher required or discount rate would cause the NPV to be negative.

If the IRR > the required rate then a project may be accepted. If the IRR < the required rate then a project should be rejected.

**TABLE 11.12 ****Calculating the IRR**

**NPV or IRR - which should be used?**

If a project is viable, it is likely that both NPV and IRR will meet a company's appraisal hurdles. Also, when choosing between two or more projects, unless the profile of cash flows is quite different - in other words, the projects are of quite different natures - NPV and IRR analysis will indicate the same choice.

One way of summing up the message revealed by NPV is to say that at the required rate, if NPV is positive (at a sufficiently high level), the project will satisfy the company's criteria. NPV analysis is for 'committed' investors - those who wish to be or get into a particular business and who require a certain return - higher if possible!

IRR could be summed up as the measure for 'disinterested' investors, that is, investors with no particular attachment to a specific type of investment or strategy apart from maximizing the company's rate of return.

Worldwide, companies and multinationals such as the oil majors use IRR in preference to NPV. Are they all disinterested investors? Maybe to the extent that they do not focus on one or more restricted types of investment and business activity, settling for some desired rate (higher if possible). They rather look to maximize return, that is, maximize shareholder value.

There is the basic model, namely the expected cash flows discounted at the required rate to arrive at the NPV or at the rate at which the project breaks even - the IRR. It is possible to look at the project at other points in time; for example, all the cash flows could be compounded forward to give their future values. The decision to invest or not in a single or competing projects should be the same, as the cash flows are identical and the adjustment for future values simply the inverse of discounting. However, the future values would be more difficult or confusing to comprehend as you would be asking the decision maker to consider values where time and components of the rate used, such as inflation, have had an effect.

A much more useful measure, again using the same cash flow model, is to consider all the cash flow categories as annual worths or values.