There are several basic methods of evaluating an investments that are commonly used by decision makers in both private corporations and public agencies

There are several basic methods of evaluating an investments that are commonly used by decision makers in both private corporations and public agencies. Each of these measures is intended to be an indicator of profit or net benefit for a project under consideration. Some of these measures indicate the size of the profit at a specific point in time; others give the rate of return per period when the capital is in use or when reinvestments of the early profits are also included. If a decision maker understands clearly the meaning of the various profit measures for a given project, there is no reason why one cannot use all of them for the restrictive purposes for which they are appropriate. With the availability of computer based analysis and commercial software, it takes only a few seconds to compute these profit measures. However, it is important to define these measures precisely.

The internal rate of return (IRR)
The internal rate of return (IRR) is the discount rate often used in capital budgeting that makes the net present value of all cash flows from a certain project equal to zero. This in essence means that IRR is the rate of return that makes the sum of present value of future cash flows and the final market value of a project (or investment) equals its current market value. The higher a project’s internal rate of return, the more desirable it is to undertake the project. As a result, it is used to rank several prospective projects a firm is considering. As such the internal rate of return provides a simple hurdle, whereby any project should be avoided if the cost of capital exceeds this rate. A simple decision making criteria can be to accept a project if its internal rate of return exceeds the cost of capital and rejected if the IRR is less than the cost of capital. Although it should be noted that the use of IRR could result in a number of complexities such as a project with multiple IRRs or no IRR and also that IRR neglects the size of the project and assumes that cash flows are reinvested at a constant rate. Internal rate of return is the flip side of net present value (NPV), where NPV is discounted value of a stream of cash flows, generated from investment. IRR computes the break-even rate of return showing the discount rate.

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IRR can be mathematically calculated using the following formula:
C0+C11+r1+C21+r2+C31+r3+Cn1+rn=0
where
C0 – the Cash Outflow generated in period No= 0
C – the Cash Flow generated in the specific period (the last period being ‘n’).
IRR, denoted by ‘r’ is to be calculated by employing trial and error method or use built-in functions from Excel.
In addition to problems associated with calculating an IRR, there are a few issues with which the user should be aware. One of them, if the series of cash flows has more than one sign reversal (changes from a positive to a negative cash flow, or vice versa) then there are multiple solutions. For example, if we have two sign changes in the series of cash flows and thus we have two IRRs.
In fact, there are as many roots (solutions) as there are changes in signs, so a problem with 4 sign reversals would have 4 different solutions. To deal with this issue, a modified internal rate of return, or MIRR, is often used. Under this approach, all negative cash flows are first treated as a single problem and placed into an equivalent negative single present value.
Then, all positive cash flows are treated as a single problem and represented as a single positive future value. Finally, NPV methods are applied to the two values – the negative single initial value and the positive single future value as though these were the only two cash flows and therefore having only one solution.
Advantages of internal rate of return (IRR)
* It is considered to be straight forward and easy to understand.
* It recognizes the time value of money.
* It is uses cash flows.

Disadvantages of internal rate of return (IRR)
* It often gives unrealistic rates of return and unless the calculated IRR gives a reasonable rate of reinvestment of future cash flows, it should not be used as a yardstick to accept or reject a project.
* It may give different rates of return; in essence it entails more problems than a practitioner may think.
* It could be quite misleading if there is no large initial cash outflow.

The payback period
The payback period is defined as the time required to recover the initial investment in a project from operations. The payback period method of financial appraisal is used to evaluate capital projects and to calculate the return per year from the start of the project until the accumulated returns are equal to the cost of the investment at which time the investment is said to have been paid back and the time taken to achieve this payback is referred to as the payback period.
The payback method is computed as follows:
Payback Period= Initial InvestmentCash Inflow per Period
The payback decision rule states that acceptable projects must have less than some maximum payback period designated by management. Payback is said to emphasize the management’s concern with liquidity and the need to minimize risk through a rapid recovery of the initial investment. It is often used for small expenditures that have obvious benefits that the use of more sophisticated capital budgeting methods is not required or justified.
It should be noted that the required payback period sets the threshold barrier (hurdle rate) for the project acceptance. It often appears that in many cases that the determination of the required payback period is based on subjective assessments, taking into account past experiences and the perceived level of project risk.
Typically, the payback period expected by managers appears to be in the range of two to four years. The payback method by definition, only takes into account project returns up to the payback period. However, for certain projects which are long term by nature and whose benefits will accrue some time in the future and well beyond the normal payback may not be accepted based on the calculation used by the payback method, although such projects may actually be vital for the long-term success of the business. It is therefore important to use the payback method more as a measure of project liquidity rather than project profitability. The payback method (PB) is commonly used for appraisal of capital investments in companies despite its deficiencies. In many companies, the payback period is used as a measure of attractiveness of capital investments. This method is commonly used in pure profit evaluations as a single criterion and also sometimes used when focusing on aspects such as liquidity and project time risk.
The major deficiencies of the payback method are that it ignores cash flows after the payback period and that it does not measure the time value of money in correct manner. To help reduce these deficiencies, the maximum acceptable payback period (PP) should be chosen in a somewhat more sophisticated way. For instance, in practice the maximum acceptable payback period is usually chosen as a fixed value, for example, three years and in some cases the limit value of the payback period has been related to the economic life of the investment, for example a payback period that is shorter than half the economic life.
The second issue that it does not measure the time value of money in correct manner in other words that it ignores the timing of the returns has, to some extent, been addressed by the introduction of the discounted payback methods.

Advantages of the payback period
* It is widely used and easily understood.
* It favours capital projects that return large early cash flows.
* It allows a financial manager to cope with risk by examining how long it will take to recoup initial investment, although it does not treat risk directly.
* It addresses capital rationing issues easily.
* The ease of use and interpretation permit decentralization of the capital budgeting decision which enhances the chance of only worthwhile items reaching the final budget.
* It contains a built-in safeguard against risk and uncertainty in that the earlier the payback the lower the risk.
* It remains a major supplementary tool in investment analysis.

Disadvantages of the payback method
* It ignores any benefits that occur after the payback period i.e. it does not measure total income.
* The time value of money is ignored.
* It is difficult to distinguish between projects of different size when initial investment amounts are vastly divergent.
* It over-emphasizes short run profitability.
* The overall payback periods are shortened by postponing replacement of depreciated plant and equipment. This policy may do more harm than good to the production process.

Net present value (NPV)
The Net Present Value is defined as the different between the present value of the cost inflows and the present value of the cash outflows. In other words, a project’s net present value, usually computed as of the time of the initial investment is the present value of the project’s cash flows from operations and disinvestment less the amount of the initial investment. For instance, in computing the projects net present value, the cash flows occurring at different points in time are adjusted for the time value of money using a discount rate that is the minimum rate of return required for the project to be acceptable. Projects with positive net present values (or values at least equal to zero) are acceptable and projects with negative net present values are unacceptable. In case the project is rejected, it is rejected because cash flows will also be negative.
NPV is used in capital budgeting to analyse the profitability of an investment or project and it is sensitive to the reliability of future cash flows that the investment or project will yield. For instance, the NPV compares the value of the dollar today to the value of that same dollar in the future taking inflation and returns into account.

The NPV is computed as follows:
NPV=n=0NCn1+rn
where
C – the Cash Flow generated in the specific period,
n – time index
N – the last period when cash flows take place
r – relevant discount rate
Note that higher NPVs are more desirable. The specific decision rule for NPV is as follows:
NPV ? 0, reject project
NPV > 0, accept project
Advantages of net present value (NPV)
* It is considered to be conceptually superior to other methods.
* It does not ignore any period in the project life or any cash flows.
* It is mindful of the time value of money.
* It is easier to apply NPV than IRR.
* It prefers early cash flows compared to other methods.
Disadvantages of net present value (NPV)
* The NPV calculations unlike IRR method, expects the management to know the true cost of capital.
* NPV gives distorted comparisons between projects of unequal size or unequal economic life. In other to overcome this limitation, NPV is used with the profitability index.

Capital investment decision is one of the most important decisions, because it is thought to be affecting the short and long run situations of firms, and according to theory, it is thought to be affecting shareholders’ wealth.
It is true that in many situations reliable estimates of cash proceeds are difficult to make. Fortunately, there are a large number of investment decisions in which cash proceeds can be predicted with a fair degree of certainty. But even with an accurate, reliable estimate of cash proceeds, the wrong decision is frequently made because incorrect methods are used in evaluating this information.

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