Exploring Internal Rate of Return: A Comprehensive Analysis

The internal rate of return is simply the unique discount rate that, when applied to both cash inflows and cash outflows over the investment’s economic life, provides a zero net present value—that is, the present value of the inflows is exactly equal to the present value of the outflows. Stated another way, if cash flow estimates are achieved, the principal of an investment will be amortized over its specified economic life, while earning the exact return implied by the underlying discount rate.

The project’s IRR might coincide with the return standard desired, might exceed it, or might fall short of the standard. These three conditions parallel those of net present value. One of the attractions of the internal rate of return for many practitioners is its ease of comparison with the return standard, and/or the cost of capital, being stated in percentage terms. Naturally, the result of a given project will vary with changes in the economic life and the pattern of cash flows.

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In fact, the internal rate of return is found by letting it become a variable that is dependent on cash flows and economic life. In the case of net present value and profitability index, we had employed a specified return standard to discount the investment’s cash flows. As a ranking device for investments, the internal rate of return isn’t without problems. First, there’s the mathematical possibility that a complex project with many varied cash inflows and outflows over its economic life might in fact yield two different internal rates of return.

Although a relatively rare occurrence, such an inconvenient outcome is caused by the specific pattern and timing of the various cash inflows and outflows.

OPEN BOOK FACTS IN DETERMINING THE DISCOUNT RATE FOR A PARTICULAR PROJECT OR INVESTMENT

We have seen that when we have projects that have equal investment at the beginning and equal economic life, the different methods give us a tool in selection of the best project. These can be referred to as “independent projects”, as execution of the projects does not depend upon other factors.

However, there could be “dependent” projects that are dependent upon other factors like required civil construction etc Further, as already listed under demerits even in the case of “modern methods”, projects that are equal in scale of investment or have equal economic life are rare to come by simultaneously. In reality, most of the times we have projects that are not equal with each other. We do encounter problems while applying the “DCF” techniques to such projects in ranking them properly. A mutually exclusive project is one whose acceptance precludes the acceptance of one or more alternative proposals.

For example, if the firm is considering investment in one of two computer systems, acceptance of one system will rule out the acceptance of the other. Two mutually exclusive proposals cannot both be accepted simultaneously. Ranking such projects based on IRR or NPV may give contradictory results. The conflict in rankings will be due to one or a combination of the following differences:

1. Scale of investment – cost of projects differ
2. Cash flow pattern – timing of cash flows differs. For example, the cash flows of one project increase over time while those of another decrease.
3. Project life – projects have unequal economic lives.

It is important to note that one or more of the above constitute a necessary but not sufficient condition for a conflict in rankings. Thus it is possible that mutually exclusive projects could differ on all these dimensions (scale, pattern and life) and still not show any conflict between rankings under the IRR and NPV methods.

PRACTICAL ISSUE

More important, however, is the practical issue of choosing among alternative Projects that involve widely differing net investments and that have internal rates of return inverse to the size of the project (the smaller investment has the higher return).

A $10,000 investment with an internal rate of return of 50 percent cannot be directly compared to an outlay of $100,000 with a 30 percent internal rate of return, particularly if the risks are similar and the company normally requires a 15 percent earnings standard. While both projects exceed the desired return and thus create value, it might be better to employ the larger sum at 30 percent than the smaller sum at 50 percent, unless sufficient funds are available for both projects to be undertaken.

If the economic life of alternative projects differs widely, it might similarly be advantageous to employ funds at a lower rate for a longer period of time than to opt for a brief period of higher return. This condition applies if a choice must be made between two investments, both of which exceed the return standard. With respect of Different projects when the internal rates of return of different projects are compared, there’s also the implied assumption that the cash flows thrown off during each project’s economic life can in fact be reinvested at their unique rates.

We know, however, that the company’s earnings standard usually is an expression of the long-run earnings power of the company, even if only approximate. Thus, managers applying a 15 or even 20 percent return standard to investments must realize that a project with its own internal rate of return of, say, 30 percent, cannot be assumed to have its cash flows reinvested at this unique higher rate. Unless the general earnings standard is quite unrealistic, funds thrown off by capital investments can only be expected to be reemployed over time at this lower average rate.

This apparent dilemma does not, however, invalidate the internal rate of return measure, because any project will certainly yield its calculated internal rate of return if all conditions hold over its economic life, regardless of what is done with the cash generated by the project. Therefore, it’s appropriate to rank projects by their respective IRRs. There’s an obvious fallacy in this line of discussion. It stems from the use of accounting earnings to represent the benefits of the project and comparing these to the after-tax cost of the debt capital used to finance it. This isn’t a proper economic comparison,. Only a discounted cash flow analysis can determine the true economic cost/benefit trade-off. We could say that the project was exactly yielding the specific cost of the debt capital associated with it only if the net present value of the project was exactly zero when we discount the incremental annual cash flows.

All of these results can at one time or another enter into the deliberations, but considerable judgment must be exercised to determine their relevance in the particular case. In most situations, the discounted cash flow approach will be the conceptually most convincing measure, despite the difficulties of estimating the cash flow pattern in specific terms.

WHAT THE FINANCIAL MANAGER THINKS?

To keep all the things in the mind the following is a recap of the key issues raised directly or indirectly . They are enumerated here to help the reader keep the techniques discussed within the perspective of financial theory and business practice.

1. The concept of value is not independent of the purpose for which it is used, and its definition and meaning can vary widely with respect to the conditions and circumstances to which it is applied.
2. The value of a security is a function of the expectations about future performance placed upon it, which can be individual judgments as well as collective judgments representing a market.
3. Investors approach the valuation of an investment proposition in terms of their individual risk preferences and thus will differ widely in assessing the attractiveness of an investment.
4. While the securities markets provide momentary indications, the relative value of a share of common stock in the market at any time is a combination of future expectations, residual claims, and assessments of general and specific risk, subject to economic and business conditions and the decisions of management and the board of directors. It’s also affected by the breadth of trading in the security.
5. Valuation techniques are essentially assessment tools that attempt to quantify available objective data and estimates. Yet such quantification will always remain in part subjective, and in part impacted by forces beyond the individual parties’ control.
6. Valuation of a security or a business is distorted by the same elements that distort other types of financial analysis: price-level changes, accounting conventions, economic conditions, market fluctuations, and many subjective intangible factors.
7. Validation of results achieved from valuation projects ultimately has to await actual performance in the future; this is why the importance of sound judgments at the time of the analysis cannot be overstated. We pointed out that net present value and internal rate of return are both discounted Cash-flow measures. In other words, each measure depends only on the project’s cash Flows and the opportunity cost of capital. But when companies report to shareholders On their performance, they do not show simply the cash flows. Instead they report the Firm’s book income and book assets.