**Project**

**11 (2525 words)**

**36**

**195**

Project appraisal techniques are used to evaluate possible investment opportunities and to determine which of these opportunities will generate the best return to the firm’s shareholders. Therefore, it is vital for the firm if they wish to continue receiving funds from shareholders to employ the best techniques available when analysing which investment opportunities will give the best return. There are two types of project appraisal techniques: non-discounted cash flows and discounted cash flows.

The Net Present Value and internal rate of return, examples of discounted cash flows, are in use in many large corporations and regarded as more effective than the traditional techniques of payback and accounting rate of return.

In this paper, I will examine the use of the Net Present Value, and the provisions it makes for specific cases, such as unequal lives and mutually exclusive projects. Then I will conclude with the technique that has been proved the best for investment appraisal through the analysis and comparison of project appraisal techniques.

The Net Present Value (NPV) method is used by 75% of firms when deciding on investment projects. The reasons for its wide use is that firstly, the NPV rule takes into account the time value of money, meaning that it recognises that a pound today is worth more than a pound tomorrow as the pound today can be invested to start earning interest immediately. Secondly, NPV depends solely on the forecasted cash flows from the project and the opportunity cost of capital.

And the final reason for its preference is because the present values are all measured in today’s pounds they have the property of additivity. This property is important as it helps managers to not be misled into accepting a low NPV project just because it is packaged with a high NPV project (Brealey and Myers 116-19). Other reasons for this widely used technique by managers are that it facilitates the managers’ work since the NPV calculation includes many of the aspects which must be evaluated by managers separately if they were to use the other investment appraisal methods.

Also, the NPV rule reflects the marginal return on the investment equal to the rate of interest on equivalent financial investments in the capital market allowing managers a facilitated comparison. Although the Net Present Value provides many advantages some extensions were made in order to include the special cases of unequal lives and mutually exclusive projects. Unequal lives The Net Present Value method is extended in the circumstance of unequal lives which is often referred to as the `horizon’ problem (Solomon) .

This problem arises when alternative investment projects have different lives, which has been the subject of much dispute. Unequal lives do not arise in independent projects, but can arise for mutually exclusive projects; but even in these cases it is unsure whether it is appropriate to extend the analysis to a common life. And it has been disputed that the extension should only be done if there is a high probability that the projects will actually be repeated at the end of their initial lives (Brigham and Houston 424-26). The first solution proposed was the replacement chain approach.

Those who are in favour of this method often argue that the cash flows of a project are realized earlier than those of another project so this gives the firm extra time to reinvest the money. This argument is not valid because a firm can always raise money at a specified rate, independent, of the project it wishes to execute. However there are three exceptions to this rule (Hirschleifer): when the investments are closely related to the project, when the projects use the same physical resource, and where replication is obvious.

Calculating mutually exclusive projects with different lives can be very complex. For example, if one project has a 5 year life versus one with a 20 year life, it would require a replacement chain analysis over twenty years. Therefore it is often simpler to calculate the equivalent annual annuity. The equivalent annual annuity method is often easier to apply than the replacement chain method, but the replacement chain method is easier to explain to decision makers. The two methods lead to the same decision as long as consistent assumptions are used.

There are several weaknesses with these types of analysis. First, if inflation is expected then the replacement equipment will have a higher price. Also, the sales and operating costs will change meaning that the conditions built into the analysis would be invalid. Another difficulty that could be encountered is if the replacements that occur at a future date employ a different technology which would change the cash flows. This could be fixed in the replacement chain analysis, but not with the equivalent annual annuity approach.

Lastly, it is very difficult to estimate the lives of projects so this may lead to speculations about the length of these projects. Consequently, due to all the uncertainties, managers for practical reasons will assume all projects to have the same life, but a problem will still exist if mutually exclusive projects have substantially different lives. Mutually exclusive projects Mutually exclusive projects are another situation for which NPV must extend its approach. In such projects, the chosen project is usually one which results in the greatest positive NPV because this will produce the greatest addition to shareholders’ wealth.

In the case of mutually exclusive investments, ranking becomes crucial as only one of a group of projects can be chosen. Mutually exclusive investment decisions can be made because of two important assumptions underlying the analysis (Pike and Neale 79-85). The first assumption is the existence of a perfect capital market so a market where managers will never find themselves unable to take on a positive NPV project because of the lack of finance. The second assumption is that the discount rate correctly reflects the degree of risk involved in the project.

The discount rate should represent the return available elsewhere in the capital market on a similar risk investment. And finally in the case of mutually exclusive projects with unequal lives, a third assumption that must be made is that mutually exclusive projects are isolated investments. This means that they do not form part of a replacement chain so it is assumed that the nature of the mutually exclusive project chosen will not be replaced when it reaches the end of its life. Without this assumption, then it requires a more complex decision rule (Brealey and Myers 126-29).

Although the NPV method has been able to include modifications for these special cases, not all of the other appraisal techniques have been as successful. The internal rate of return is the average annual return earned through the life of an investment and it computes a break-even rate of return which shows the discount rate below which an investment results in a positive NPV and above which an investment results in a negative NPV. My analysis of evaluative techniques will not focus on the non-discounted cash flow techniques as they do not take into account the timing of cash flows which is unsuitable for appraisal techniques.

My analysis, however, will focus on the comparison of the two discounted cash flow techniques: Net Present Value (NPV) and internal rate of return (IRR), in order to determine which of the two has the optimal investment criterion for a wealth-maximising firm. The most important comparison is that NPV’s calculation automatically compares the project with the alternative capital market investment forgone, unlike the IRR method that does not give a consistently reliable indication of how much better or worse the project is relative to the capital market investment alternative.

Mutually exclusive projects As discussed above, in the case of mutually exclusive projects, ranking becomes crucial as only one of a group of mutually exclusive alternatives can be executed. NPV can be used to give the correct decision advice with just a small modification to the basic rule. While the use of IRR in this case involves a more complex decision rule (Dorfman) which arises because IRRs of the differential cash flows have to be computed.

In the case of mutually exclusive projects, many prefer NPV because of the simpler calculation. For example, if a company is faced with more than two alternatives, using the NPV rule would simply require the calculation of each project’s NPV and the project with the largest positive NPV would be selected. On the other hand, the IRR rule requires IRRs of pairs of projects and their differential cash flow to be calculated, requiring a choice between each pair of projects until the best option is found.

Furthermore, it is very unlikely that any company actually uses this modified IRR decision rule because to use it Implies a belief in the correctness of the NPV decision rule since the modified IRR rule is designed to give the same advice as NPV so it would be simpler and easier to use the NPV rule itself. Reinvestment assumption Another notable difference between NPV and IRR is their reinvestment assumption. The NPV decision rule assumes that project-generated cash flows are reinvested to earn a rate of return equal to the discount rate used in NPV analysis.

While, the IRR method assumes project-generated cash flows are reinvested to earn a rate of return equal to the IRR of the project that generated those cash flows The difficulty with the IRR is that it assumes that the project cash flow can yield a return equal to the IRR of the project that generated those cash flows, but investments yielding such returns may well be available to the company independently of whether or not the company accepts the project. The NPV model accepts this argument by taking the market rate of interest as the opportunity cost of the project cash flows.

For that reason, in a perfect capital market, NPV model makes the correct assumption about the opportunity cost of a project’s cash flow and therefore gives the correct decision advice. Multiple IRRs A further issue with the IRR decision rule arises out of the mathematics of its formula when the investment time horizon is extended. The IRR of a project’s cash flow is the root of a polynomial equation and there are possible solutions to polynomial equations for each change of sign. Consequently, any particular investment project may have more than one internal rate of return or may not have an IRR at all.

However, it can be shown that with most project cash flows, the variations in the project’s NPV between the IRRs are usually very small, and the value of the NPV itself is likely to be close to zero. Regardless the problem of multiple IRRs does cause difficulties in the case of mutually exclusive investment decisions as the differential cash flow may have multiple IRRs which cause the decision rule to become invalid. There is a solution for multiple IRRs called the extended yield method (Lumby and Jones 94-116).

This method solves the problem by eliminating the second change in sign achieved by discounting the unwanted cash flow back to the present value at the hurdle rate and then netting the figure off against the year 0 outlay (Drury 298-302). Yet, this solution only gets around the problem of multiple IRRs and does not solve it. A further concern that arises with the IRR is it evaluates projects on the basis of a percentage rate of return meaning it examines a project’s rate of return relative to its outlay, rather than in absolute terms as NPV.

NPV by automatically examining and comparing the incremental cash flows against the cost of capital ensures the firm will reach the optimal scale of investment while the IRR expressed in percentage ignores this important feature of an investment decision. Moreover most firms have their goals set out in terms of absolute returns and not in percentage terms and since NPV reflects absolute returns this ensures optimality when mutually exclusive choice situations arise.

But it is easier to communicate a percentage rather than an absolute return to other managers and employees, who many not be familiar with project appraisal techniques, so percentage terms have the added appeal of quick recognition and understanding. Conclusion The Net Present Value and the internal rate of return methods of selecting capital investment proposals are closely related. They both are time-adjusted methods of profitability and even their math formulas are almost identical in form.

Although both criteria give equivalent results with regard to independent conventional projects, they do not rank projects in a similar way. Most managers’ use NPV because of its various advantages, such as, the NPV reflects the absolute magnitude of the projects while the IRR does not. NPV implicitly assumes reinvestment proceeds at the cost of capital; IRR assumes reinvestment at the project’s own rate of return. The reinvestment assumption is of crucial importance if we assume a changing cost of capital in future years.

Under such circumstances the IRR rule breaks down because of the comparison of a single-valued rate of return with a series of different short-term discount rates holds little significance. Also, NPV is not only theoretically superior to the IRR but also has important technical advantages. When non-conventional cash flows are considered, a real solution for the project’s IRR may not exist or multiple IRRs may be found for a single project. The popularity of the IRR rule is in part psychological; as a survey of managers suggests that the measure of investment which is set out in ercentage terms is appealing and better understood by managers. The rate of return can readily be compared with the cost of funds to yield a margin of profit. However, the appeal of the IRR should not obscure the fundamental fact that when mutually exclusive decisions have to be made they should be made by the NPV method which has led to the development of modified IRR. Modified IRR is an attempt to overcome the theoretical difficulties of IRR, while retaining an evaluation based on percentage returns to avoid the ‘user-unfriendliness’ of NPV.

The modified IRR is founded on NPV analysis which is then converted into a rate of return. The modification to IRR has two technical advantages: that it eliminates any problem of multiple IRRs and that it will not provide decisions involving mutually exclusive projects which contradict that given by the NPV method. In many ways, the modified IRR has proven itself to be the best investment appraisal technique as it has theoretical background in NPV, but its method of evaluation uses a user-friendly percentage rate of return.

Works Cited

Brealey, Richard A. and Steward C. Myers. Principles of Corporate Finance. McGrawHill-Irwin, 2009. Brigham, Eugene F. and Joel Houston. Fundamentals of Financial Management. Cengage Learning, 2007. Dorfman, R. “The Meaning of Itnernal Rates of Return.” Journal of Finance (1981). Drury, Colin. Management and Cost Accounting. Cengage Learning, 2008. Hirschleifer, Jack. “On Theory of Optimal Investment Decision.” Journal of pOlitical Economy (August 1958). Lumby, Steve and Chris Jones. Corporate Finance: thoery and practice. Cengage Learning, 2003. Pike, Richard and Bill Neale. Corporate Finaance and Investment: decisions and strategies. Prentice Hall, 2008. Solomon, Erza. “The Arithmetic of Capital Budgetting Decisions.” Journal of Business (April 1956).

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