*Guest post by Jon Allen, Chief Compliance Officer, Bank of American Fork*

The goal of financial management in any company is to maximize the value for its owners. Managers need ways to determine whether projects will add value to their companies’ stocks. This is the third in a series of three articles that discuss methods for evaluating the financial benefits of projects. The first article discussed the **payback approach** and noted several serious shortcomings of that method, although for quick analysis of small-dollar projects it still makes sense to use. The second article discussed the **net-present-value approach**, a far-better method for evaluating larger projects. This article will discuss the internal-rate-of-return approach, a corollary of NPV. Neither NPV nor IRR has any of the drawbacks of the payback approach.

NPV is the present value of the cash inflows of a project less (net of) the required cash outlay. It accounts for the time value of money—that is to say that since the opportunity to do something productive with a dollar today that cannot be done without it today has value. Unlike the payback approach, NPV discounts future cash flows to the present to adjust for the time value of money. NPV does so using an interest rate that the company has set based on its views of the project’s risk, the uncertainty of its cash flows, any alternative uses of funds, and other factors.

IRR is simply the interest rate that if used in an NPV analysis will produce an NPV of zero. It is the discount rate at which the present value of a project’s costs equals the present value of its benefits. An NPV of zero is analogous to breaking even. A higher IRR correlates to a higher NPV and the reverse is also true. Therefore higher IRRs are more desirable than lower IRRs.

The IRR is useful because it gives managers an idea, expressed as a rate rather than a dollar amount, of how profitable a project will be. Even though some managers prefer to compare projects using rates rather than dollar amounts, the IRR approach should not be used to compare projects with significantly different initial costs, since they could have identical IRRs but very different NPVs. The one with the greater NPV is the one that should be chosen, even if it has a higher IRR. For that reason, the IRR approach should complement but not replace the NPV approach. Additionally, irregular cash-flow streams may produce unexpected results in IRR analyses.

Before we elaborate on the IRR, let’s discuss the appropriate interest rate for discounting to use in an NPV analysis. This rate can be thought of as a hurdle. If the firm thinks a project has high risk, is not confident in its projections, or has good alternative uses for the funds required for the project, then the project would have to meet a high hurdle in order to convince management to accept it. In other words, the firm would use a relatively high interest rate for its NPV analysis. A high interest rate will cause fewer projects to produce positive NPVs.

Now let’s think of the IRR as the cutoff point between high hurdles and low hurdles. For normal streams of cash flow, using any interest rate above the IRR will cause the NPV to be negative. Using any interest rate below the IRR will cause the NPV to be positive. All other things being equal, projects with negative NPVs should be rejected and projects with positive NPVs should be accepted.

Consider the same example we used in the previous two articles: Acme, Inc. is considering buying a new machine. The initial cost of that machine is $1 million. The machine has an expected life of five years and is expected to generate cash flows, net of all expenses, of $250,000 per year for each of those years. Assume Acme uses the NPV approach rather than the payback approach to analyze new projects, and has determined that it will only accept projects that have positive NPVs.

In Table 1, let’s assume that since Acme has a high degree of confidence in the projections and believes this project has little risk, it uses an interest rate of 5% to discount the cash flows. Using a financial calculator, we know that the NPV turns out to be $82,369, meaning that the expected future cash inflows of the project, discounted to the present by a rate of 5% and added together, exceed the initial investment of $1 million by $82,369, and therefore the project should be *accepted.*

Now let’s assume that Acme is not so confident in its projections and believes that because of risk, the appropriate interest rate for discounting the cash flows should be 10%. Table 2 uses the same expected cash flows as in Table 1 but changes the discount rate to 10%. In this case the expected cash flows are discounted to a greater degree and are not enough to make up for the initial project cost. Therefore the NPV is negative and the project should be *rejected.*

Using a financial calculator again, we determine that the IRR in both tables is 7.93%. Obviously the selection of an interest rate for discounting can make a big difference in the NPV of a project; however the interest rate does not affect the IRR.

If you recall from the first article, this same project reached “positive payback” at 4 years and Acme chose to *accept* it based on the payback approach. Table 2 shows that for a discount rate of 10%, that was the *wrong* decision. In fact, for any interest rate above 7.93% (these are high hurdles to overcome), the NPV will be negative and the project should be rejected. Conversely, for any interest rate below 7.93% (these are low hurdles), the NPV will be positive and the project should be accepted. If Acme felt that the appropriate interest rate was exactly 7.93%, then Acme would be indifferent as to accepting or rejecting the project.

Determining the IRR helps us to know how high our interest rate hurdle can be without making a project unprofitable. While the NPV approach has no significant flaws and is the preferred method for evaluating projects because it considers risk and the time value of money and has no arbitrary cutoff, the IRR approach should be used with caution. It is a useful complement to the NPV in cases of similar initial costs and normal cash-flow streams. The NPV shows expected returns expressed as dollar amounts, while the IRR marks the separation between interest rates that will yield positive NPVs and interest rates that will yield negative NPVs. Any interest rate below the IRR will cause the project to have a positive NPV, and any interest rate above the IRR will produce a negative NPV.

*Jon Allen (B.S. Brigham Young University, J.D. University of Idaho), teaches *Introduction to Corporate Finance* as an adjunct at Utah Valley University’s Woodbury School of Business. Before becoming Bank of American Fork’s Chief Compliance Officer, he was a commercial loan officer at Capital Community Bank. He volunteers on the Business Incubator Board of the Commission for Economic Development in Orem.*

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