## Introduction

Investment appraisal is very crucial before making commitment to huge capital investment. The appraisal process is characterized by two major activities. The first one is the assessment of the level of expected return accruing from the expenses incurred. The second one entails the estimates of future costs and benefits that are earned during the time that the project will run. During evaluation process, the costs and benefits that are incurred and earned over the estimated life of the project should be analyzed. The estimated life of the project is the period of time the noncurrent assets will be used in the project (Bierman, 2006). This means that estimation and evaluation of future benefits and costs of the project may take several years. Project appraisal is done to achieve better spending decisions on investment projects. There are a number of techniques that are used in project appraisal. They are divided into discounted and non-discounted project appraisal techniques. The discounted methods include Present Value, Net present value, and Internal Rate of Return among others. The non-discounted methods include Average Rate of Return and Pay Back period among others. A brief description of the two major categories of project appraisal methods will be discussed. The paper will specifically focus on Internal Rate of Return (IRR) and Net Present Value. Practitioners prefer Internal Rate of Return to Net Present Value in investment appraisal. The reason behind this claim will be the main agenda of this paper. The merits and limitations of the two methods will be discussed.

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## Investment Analysis

The motive behind every investment is to generate a return. The return gained is applied mainly in the following ways:

- The shareholders or owners of the company or the investment project are compensated for investing their money in the project. They also forego their current purchasing power for current and future returns.
- The capital used in the investment may have been obtained from lenders or creditors who expect to earn an interest and get the principle repaid. The return from investment is used to give regular payments to lenders or creditors in terms of interest and principle repayment.
- It enables the investors to retain part of their earnings for reinvestment purposes. This facilitates not only the company’s growth at present and the future but also has the implication of increasing the size of the company in terms of sales and assets (Pogue, 2004).
- Returns increase share prices. This is crucial for the credibility of the company and its ability to raise more funds.

The return is also necessary to keep the company’s operations moving smoothly. It forms part of operational capital that is used for daily running of the company.

A financial manager with present investment policies will be concerned with how efficiently the company’s funds are invested because it is from such investment that the company will survive in the market. In summary, investments are important because of the following reasons:

- They influence the company’s size.
- They Influence growth.
- They Influence company’s risks.

According to Hartman & Schafrick (2004), the investment decision making process is also regarded as capital budgeting. It involves the decision to invest the company’s current funds in viable ventures whose returns will be realized in the long run. Capital budgeting as financial planning method is characterized by the following factors:

- Their decisions are long term. They run for a period longer than one year. They are expected to generate returns within the period stipulated. The results of these decisions are, therefore, felt in future.
- They involve heavy capital injection. The investment involves huge amount of funds and calls for proper planning. Failure to plan properly can make the company to suffer huge losses and pose threats to its survival.
- These decisions are irreversible and any mistake may cause the company to incur heavy losses.

## Importance of Investment Decisions

- The company size is increased. The decision may involve purchase of fixed assets, sale of properties, and increase in retained earnings among others. All these contribute to increase in the size of the company.
- They increase the value of company’s shares and its credibility.
- The fact that they are irreversible means that they have to be made carefully to avoid any mistake which can lead to their failure.
- They involve heavy capital outflow. This calls for proper investment planning and more attention to ensure that the project succeeds. Failure to take necessary measures may make the company suffer huge losses or even close down.

Investment decisions are influenced by political and technological factors.

**Political factors**– according to Bruce (2003), under conditions of political unrest, heavy investment decisions cannot be made because it will entail an element of risk of failure of such investment. Thus political certainty has to be analyzed before such decisions are made. Such factors must be taken into consideration so that the company forecasts the inflows and outflows within given limitations. The limitations in this case would entail the degree of competition, performance of the economy, and changing tastes among others. They all influence ability to generate sufficient returns from a venture. This is a serious threat because the company will still be expected to pay only interest and principal on funds invested.**Technological factors**– The ability of the company to utilize its assets optimally depends on the technology adopted. In particular, assets may become obsolete and fail to generate good returns if outdated technology is adopted. For instance, the output of machines may be low with time and may not meet planned expectations which in most cases will have an impact on inflows from a venture.

## Methods of Analyzing Investment

They are also called Capital Budgeting Methods. There are two methods of analyzing the viability of an investment:

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### Traditional methods

- Payback period method.
- Accounting rate of return method.

### Modern methods (Discounted cash flow techniques)

- NPV – Net present value method
- IRR – Internal rate of return method
- PI – Profitability index method

For the two major methods (traditional and modern) to be used, they must meet the following conditions:

- They should be able to rank the ventures according to their viability to enable the investor make informed choice. They should identify which project is more viable than the other.
- They should rank the venture according to how soon they generate returns. The investments bringing returns earlier and in large lump sum should be ranked high. If a venture brought in late and less inflows, it should be ranked accordingly.
- They should rank any other projects as and when it is available in the investment market.
- They methods should ensure that returns (inflows) come in form of cash. This helps the company in financing the cost of the venture.

Net Present Value and Internal Rate of Return are the main focus of this study. The computation of IRR depends on NPV technique. Their application in investment analysis raises interesting questions. Their computation is similar in a number of aspects but they yield different results in some cases. They may also give same results. The NPV method has been regarded as superior by most analysts but application of IRR in management decision making continue to gain prominence. The reason behind preference of IRR to NPV in decision making is the main agenda in the rest of this paper.

## The Internal Rate of Return

This is a discounted cash flow method of project appraisal. It employs the principle of Net Present Value. It is the rate at which the Net Present Value of a project’s future cash flows is zero (Greenberg & Weimer, 2001). This means that discounted cash inflows from a project are equal to its discounted cost.

IRR = Pv (cash inflows) = Pv (cash outflows) or IRR is the cost of capital when NPV = 0.

PV in this case stands for present value. IRR is also called internal rate of return because its computation entails only the cost of an investment and the associated income. There is no external information used in its computation. All information is gathered within the venture.

- A = inflow for each period
- C = Cost of investment

IRR is computed using a number of methods:

- Trial and error
- By interpolation
- By extrapolation

### Trial and error method

- A random rate is selected and used to compute Net present value of cash inflows. There is no specific criterion for selecting this rate.
- If the rate above gives NPV that is lower than cost, a lower rate is selected and a new NPV computed.
- If the rate selected in (a) above produces NPV greater than the cost, the next rate selected should be higher.
- The process is continued until zero NPV is obtained.
- The rate that will equate NPV to zero is the Internal Rate of Return.

This method is tedious and it may take a very long time and still fail to give actual results. However, the answer that could be obtained from the method will be very reliable compared to other methods.

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## Acceptance Rule of IRR

A project is accepted under IRR technique if it has a minimum required rate of return that is equal to or exceeds IRR. The minimum required rate of return is the cost of finance. It is also known as the cut off rate or hurdle rate. The IRR at this point will be the highest rate of interest a firm would be ready to pay to finance a project using borrowed funds and without being financially worse off by paying back the loan (the principal and accrued interest) out of the cash flows generated from the project (Moten & Thron, 2013). This description qualifies IRR to be taken as the break-even rate of borrowing from commercial banks. The project will be rejected if it has IRR that is less than the minimum required rate of return.

### Advantages of IRR

- The method considers time value of money because it uses discounted cash flows. Money changes value over time and it is important to discount future incomes in order to make investment decisions during the current period.
- IRR uses cash flows for the entire life of the project. This makes the method more reliable as an investment appraisal method.
- It is compatible with the maximization of owner’s wealth because, if it is higher than the cost of finance, owners’ wealth will be maximized. Such information will be very credible to the investors interested in the project. It will tell them if their investment will pay them them back or not.
- Unlike the NPV method, it does not use the cost of finance to discount inflows and for this reason it will indicate a rate of return of the project against which various ventures can be assessed for their viability.
- The method calculates the breakeven point of a project. This is the point at which a project is capable of paying for all its initial costs from the cash inflows. The investors are able to tell the point at which they will start making profit from the money they inject into the project.
- IRR provides an alternative cost of capital and removes the need to calculate it. It also gives an appropriate risk premium.

### Disadvantages of IRR

- The method is difficult to use because it involves a long process. Calculating IRR especially by trial and error method is a difficult task. Besides, one may not even arrive at the right answer at the end of the day (Sheeba, n. d).
- Since the method may involve inflows of large magnitude, trained manpower may be necessary. In some cases, computers will be needed in doing computation. This means that more resources will be needed to cater for training of manpower and purchasing computers. The method may, therefore, be expensive to employ.
- The methods used to compute IRR may produce multiple results. Decision criterion may pose a challenge because one result may reject the project while the other accepts it as viable.

## Net Present Value (NPV)

This method, just like IRR, recognizes time value of money. Time value of money states that money at hand is worthy more than the same amount receivable in future. A discounting rate is used that gives the present value of cash inflows and cash outflows receivable and expendable in future. To arrive at NPV, the discounted cash outflows are deducted from the discounted cash inflows to get a net figure. The difference is the Net Present Value. The rate used in NPV method is the one acceptable to the management or the cost of financing. The decision criterion is that if the Net Present Value is positive the project is accepted and if it is negative, the project is rejected.

- Pv (inflow) – Pv (outflows) = NPV

Initial outflow is at period zero and their value is their actual present value. With this method, an investor can ascertain the viability of an investment by discounting outflows. In this case, a venture will be viable if it has the lowest outflows.

Where:

- A = annual inflow
- K = Cost of finance
- C = Cost of investment
- N = Number of years

can be read from tables provided at the point of interception between the discounting rate and number of periods.

## Accept or Reject Rule of NPV

A positive NPV means that the company has more discounted cash inflows than outflows. All projects with positive NPV are acceptable. The company may also accept a project at a point where discounted cash inflows are equal to discounted cash outflows. This is a point where Net Present Value is equal to zero. The project is capable of paying for all its investment outlay (Bierman & Smidt, 2007). When evaluating more than one project and they all have positive NPV, the project with the highest NPV will be selected. A higher NPV means higher profits will be generated by the company. NPV can, therefore, be used to rank projects.

### Advantages of NPV

- Just like other techniques of project appraisal, NPV recognizes that the money at hand now is worth more than the same amount of money receivable in future. The principle of time value of money claims that a shilling today has more value than a shilling in future. Projects may have different working lives and they can only be compared at their present values. What the projects are worth today is what is very certain than what they will be worth tomorrow.
- The method accounts for all cash outflow and cash inflows throughout the life of a project. It is, therefore, a realistic gauge of the profitability of a venture.
- The method is consistent with share value. A positive Net Present Value will increase the value of a share.
- It is consistent with the objective of maximizing the welfare of the owner because a positive NPV will increase the net worth of owners. Positive NPV shows that the project will make profit and is worth venturing in.
- The method is a direct measure of contribution of a project. It obtains the different between income and cost which gives contribution. Incomes (cash inflows) and costs (cash outflows) are discounted to give the actual contribution over the working life of the project.

### Disadvantages of NPV

- Computation of NPV is also a difficult process. It involves discounting cash inflows and outflows and also obtaining their difference. This may also be an expensive process when computers may have to be used for large data size. Trained manpower may also be needed to do computation.
- Its calculation uses cost of finance which is a difficult concept because it considers both implicit and explicit whereas but NPV ignores implicit costs. The results may not be fully reliable.
- The method ignores the element of risk. It assumes that the project will continue giving cash inflows continuously throughout its working life. There is a lot of uncertainty in the future of a project (Hazen, 2003). This means that the project may not always give desired results. The method can only be used in evaluating an investment under certainty. For projects under uncertainty condition, the method will give unreliable results.
- The projects being evaluated may have different lives. Their NPV may not be the same and this may not give good assessment of alternative projects. The other factors that are likely to affect the use of the method are unequal project returns and costs.
- It ignores the Pay Back Period. This is the period of time that a project is expected to recoup its initial investment outlay. A project may have less NPV compared to another but it pays back sooner. The project with less payback period is preferred to the one with a longer period.

### Properties of NPV

- The net present value is usually high when income amounts are high. The discounted value of cash flows will increase and the amount of cash flows also increases.
- When the incomes of a project being evaluated come sooner, the Net Present Value will be high. It will be low when the incomes take a long time to be realized.
- The Net Present Value is different at different discounting rates. Increasing the discounting rate will reduce the amount of NPV.

## Comparing NPV and IRR

The Internal Rate of Return method assumes that cash flows from a project will be reinvested and generate more income. Net Present Value method does not make that assumption. The cash flows are not invested again in the business and they are evaluated as they are earned.

NPV gives different results for different discounting rates. This means that it is not reliable because it does not give consistent results. For Internal Rate of Return, the same result is given because the focus is to get NPV that is equal to zero.

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## Why is IRR still popular among practitioners?

In many cases, the Internal Rate of Return and Net Present Value techniques will lead to same decisions. However, IRR may give different decisions from those of NPV. When such cases of contradicting results arise, the Net Present Value tends to give better decisions. The IRR can be used in a way that yields similar results as NPV. This is only possible if the rate of discount appropriate for discounting future cash flows is the same throughout the life of the project. In case the rates of interest are not the same, the two procedures may not yield similar results. NPV method is easier to use correctly but IRR is much more difficult to apply correctly.

In some cases, the investments may be mutually exclusive. In this case, the undertaking of one eliminates the proceeds of the other. If a company has two or more investments which are mutually exclusive, only one of them can be accepted even when all are economically viable. IRR method does not recognize the size of investment and, therefore, gives less reliable results for mutually exclusive investments compared with Net Present Value.

The IRR method still remains commonly used by practitioners in capital budgeting despite its shortcomings. The method is said to have reporting simplicity. The NPV method is relatively complex and is based on assumptions at every stage. The assumptions could be with regard to discount rate and likelihood of receiving cash payments among others. The IRR simplifies the entire project into a single figure that management of a company finds easier to use in assessing the economic viability of its projects. However, the simple IRR may not be good for long projects with multiple and uncertain cash flows. It may also not be the best for evaluating projects where different discounting rates are used.

IRR is a rate quantity. It indicates the quality, yield, and efficiency of an investment. The Net Present Value is just an indicator of the value of magnitude of a project or projects. The management prefers IRR because it provides more information than NPV.

Decision making under IRR is done in favor of the project when IRR is greater than the minimum acceptable rate of return (Mertens & Wilson, 2012). For a firm that has shareholders, the cost of capital (minimum rate) shows that the investment is backed by its shareholders. A project is considered economically viable when IRR is greater than the cost of capital.

Managers tend to understand better the concept of returns expressed in percentage. They find it easier to compare IRR with the required cost of capital. IRR is also suitable because NPV cannot yield proper results in case the project has different discount rates.

IRR is preferred by practitioners because they find it imperative to know the difference between the proposed investments’ IRR and the rate of return needed. The IRR is considered as a measure of safety that makes it easier to assess the return on investment and the risk. For instance, if a project has IRR of 0.30 and required rate of return of 0.12, the difference is big enough and allows for error. For NPV, such information is not provided making IRR more popular.

Based on the analysis, the Internal Rate of Return is preferred in practice to Net Present Value. However, the NPV method seems superior to most analysts. For reporting purposes, IRR gives more information than IRR. Practitioners value reporting and prefer a method that will give adequate information. The two methods may yield similar results in some cased. However, this based on some conditions. For instance, the discount rate should not vary over the life of the project.

## Reference

Bierman, H 2006, *Implementation of Capital Budgeting Techniques*, FMA, New York.

Bierman, H & Smidt, S 2007, *The Capital Budgeting Decision, 9th ed*, Routledge, New York.

Bruce, J 2003, *Investment Performance Measurement*, Wiley, New York.

Greenberg, B & Weimer, V 2001, *Cost-Benefit Analysis, 2nd edition*, Prentice Hall, Pearson Education.

Hartman, J & Schafrick, C 2004, ‘The relevant internal rate of return’, *The Engineering Economist*, Vol. 49, no. 2, Pp. 139–158.

Hazen, G 2003, ‘A new perspective on multiple internal rates of return’, *The Engineering Economist*, vol. 48, no. 2, pp. 31–51.

Mertens, D & Wilson, A 2012, *Program Evaluation Theory and Practice: A Comprehensive Guide*, The Guilford Press, New York.

Moten, J & Thron, C 2013, ‘Improvements on Secant Method for Estimating Internal Rate of Return’, *International Journal of Applied Mathematics and Statistics*, vol. 42, no. 2, pp. 23-56.

Pogue, M 2004, ‘Investment Appraisal: A New Approach’, *Managerial Auditing Journal*, Vol. 19, No. 4, pp. 565–570.

Sheeba, K n. d, *Financial Management*, Pearson Education India, New Delhi