methods of investment appraisal

UNIVERZITET U NOVOM PAZARU

Suad Bećirović

DYNAMIC AND STATIC METHODS OF INVESTMENT APPRAISAL

Novi Pazar, 2006.


CONTENTS

List of Illustrations....................................................................................................................3

Introduction...............................................................................................................................4

Methodology..............................................................................................................................6

1. Goals of the Thesis..............................................................................................................6

2. Means of Research..............................................................................................................6

I. Fundamental Terms..............................................................................................................7

1. Investment and Finance......................................................................................................7

2. Acquisition Costs................................................................................................................7

3. Residual Value....................................................................................................................7

4. Useful Life..........................................................................................................................7

5. Cost of Capital....................................................................................................................8

II. Overview over the Different Methods for Investment Appraisal....................................9

1. Static Methods.......................................................................................................................9

1.1. Overview..........................................................................................................................9

1.2. Equivalent Annual Cost Method....................................................................................10

1.3. Profit Comparison Method............................................................................................13

1.4. Accounting Rate of Return............................................................................................14

1.5. Simple (Static) Payback Method...................................................................................15

1.6. Value Benefit Analysis..................................................................................................16

2. Dynamic Methods...............................................................................................................18

2.1. Net Present Value Method.............................................................................................18

2.2. Internal Rate of Return Method.....................................................................................20

2.3. Annuity Method.............................................................................................................22

2.4. Dynamic Payback Method.............................................................................................23

2.5. Conditions for Using the Dynamic Methods.................................................................24

3. Conclusion...........................................................................................................................24

Bibliography.............................................................................................................................25

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List of Illustrations

Illustration 1: Overview of the several types of investment.......................................................4Illustration 2: Steps in Project Appraisal....................................................................................5Illustration 3: Different types of useful life................................................................................8Illustration 4: Factors for determining the cost of capital...........................................................8Illustration 5: Methods for Investment Appraisal.......................................................................9Illustration 6: Operands and Characteristics of the Static Methods............................................9Illustration 7: Example for an Equivalent Annual Cost Method..............................................12Illustration 8: Example for a Profit Comparison Method.........................................................13Illustration 9: Example for an Accounting Rate of Return Method..........................................14Illustration 10: Example for Simple Payback Method..............................................................15Illustration 11: Example for Non-Monetary Criteria in the Value Benefit Analysis................17Illustration 12: Example of Two Competing Investments........................................................18Illustration 13: Example for a Net Present Value calculation...................................................19Illustration 14: Example for Using the Net Present Value Method in Comparing Two Altern-

atives.................................................................................................................19Illustration 15: Example for Determining the Internal Rate of Return with the Approximation

Method..............................................................................................................21Illustration 16: Example for Calculating an Annuity................................................................22Illustration 17: Example for Dynamic Payback Method..........................................................23

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Introduction

Organisations operate in a dynamic environment. Therefore they have to meet the chal-lenges that the dynamic nature of the environment brings. To meet these challenges, a com-pany has to invest large sums of money, in order to have an advantage compared to their com-petitors. The need for investments is a daily occurrence in a company: obsolescence and ex-cess of age of machines, means of transportation and buildings; increasing expenses for main-tenance and servicing; innovation of modern production equipments and processes or changes in the markets of the manufactured products. All these causes require new investments. Figure 1 gives an overview of the several types of investment or reasons for an investment.

Type of investment Examples:

Diversification Investment A company decides to produce its product in a foreign country for the foreign market

Expansion Investment Due to high demand, the available capacity will be expanded

Modernisation Investment An existing IT-equipment will be replaced by a more powerful equipment

Rationalisation Investment A machine falls regularly out, so it has to be decided whether it should be replaced by a better machine

Contrary to a modernisation investment, rationalisation invest-ments are intended to change the production process, in order to minimize the production costs

Maintenance investment A machine will not be replaced, but repaired

First or Construction In-vestment

A supplier announces to increase its prices, so the company will produce the part on its own

Start-up of a company

Construction of a branch

Finance Investment A company wants to buy shares of a supplier for a strategic partnership

Temporary investment of excess liquidity in stocks and shares

Security Investment Increase of safety stock of raw materials

Personnel Investment Expenditures for education of personnelIllustration 1: Overview of the several types of investmentSource: Schulte, S., Script Investition und Finanzierung, p. 8

For a company, the decision for an investment means to give up liquidity. As compensa-tion of this abandonment and the fact that the company cannot use this liquidity anymore for other purposes, the company expects a profit, in order to have more liquidity in future. For this purpose, an investment can be defined as “spending of money now in the hope of higher returns in future.”1

As every investment contains risks, the decision for an investment takes place in several steps, which can be seen in illustration 2.

1 Wöhe, G., Einführung in die Allgemeine Betriebswirtschaftslehre, p. 618

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Illustration 2: Steps in Project AppraisalSource: Schulte, S., Script Investition und Finanzierung, p. 13

Firstly, there must be a reason or cause for an investment. The main motivation for an in-vestment is profit maximisation. To realise this goal, the types of investment, shown in figure 1, can be used. After realisation of the necessity of an investment and what type of investment the company wants to conduct, the investor has to check, whether the project is technically feasible and commercially viable. This involves assessing the risks and deciding whether the project is in line with the company's long-term strategic objectives. After making this de-cision, the investor has to check the economic efficiency of the project. Therefore, a detailed investigation will take place in order to examine the projected cash flows of the project. In or-der to make the correct decision, several methods for investment appraisal have been de-veloped, which will be discussed in detail in this paper. By means of these methods a decision will be made, which project is the most efficient and allows the greatest possible profit. At the stage of implementation of the investment proposal, responsibility for the project is assigned to a project manager or another responsible person. This person supervises that the project will be realised within the technical standards and the planned finance and time frame.2 After realisation of the project, the planned cash flows have to be compared with the actual cash flows. Such a comparison is important for two reasons. On the one hand, the investor has to implement retaliatory action, on the occasion of an accounting variance. On the other hand this assessment enables the investor to do a better forecast for future investments.3

This short description of the steps in a project appraisal shows what importance investment appraisals have in the framework of this process. Investment appraisals are aids to forecast and assess the future success of an investment. So these methods play an important role in the appraisal of a project. On the other hand, this also shows the danger, if an investment ap-praisal is not executed correctly, because this will lead to a misinvestment. A misinvestment occurs, when the actual cashflows are so much behind the original expectations that it would have been better for the investor not to undertake the investment.4

Methodology

2 Wöhe, G., Einführung in die Allgemeine Betriebswirtschaftslehre, p. 6253 Ibid.4 Ibid., p. 622

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Motivation for an Investment

Initial Investigation

Evaluation of the Investment

Decision for an Investment

Implementation of the investment

Investment Controlling

Investment Appraisal


1. Goals of the Thesis

Due to the great importance of the investment appraisals in project appraisal, this study has the goal to investigate the standard methods, which are mentioned in the literature for this purpose. So, we will investigate, whether these methods are able to meet the required tasks.

2. Means of Research

In order to fulfil the mentioned goals, the following steps will be carried out:

1. At the beginning of the study, we will clarify essential fundamental terms of finance and investment. Thus, the reader should be able to separate these terms, in order to have a better understanding of the methods of investment appraisal.

2. After this, we will present the different methods of investment appraisal. Besides the method, we will discuss the advantages and disadvantages of every single method. So, it will be possible to assess, whether these methods are useful or not.

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I. Fundamental Terms

1. Investment and Finance

The terms investment and finance have to be differentiated, because they describe con-trasts. These terms have the following meaning:

Finance: Investment:

Provision of liquid funds, e.g. by taking a credit to finance a project

An investment is the dedicated, usually long-term, capital lockup in order to receive future returns.5

2. Acquisition Costs

Normally there is no problem to determine the costs for the acquisition of an investment object. It has to be observed that all costs for the acquisition are recorded. Therefore it is im-portant to add all costs, which occur, until the investment object can be used. Examples for such additional costs, besides the acquisition price, can be:

- Costs for rebuilding due to changes and displacement of the available machines or other assets

- Installation costs for assembly, installation etc.

- Launching costs for implementing, test runs, orientation etc.

- Engineering costs for necessary investigations, advisory opinions etc.

Besides the acquisition of the investment object from outside, the object can be manufac-tured by the company itself. In this case it has to be calculated with the production costs.

3. Residual Value

Besides the acquisition costs, the value of the investment object at the end of the useful life has to be considered. The residual value is the expected sales revenue of an investment object at the end of the calculated useful life.

The residual value has to be considered, because it effectively decreases the acquisition costs in the calculation of the investment appraisal.

4. Useful Life

The useful life is the period, in which the investment object is used according to its pur-pose. In practice, there are several types of useful life, which are shown in the following table:

5 Gabler Wirtschaftslexikon, p. 1636

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Technical Useful Life Economic Useful Life Average Useful Life Legal Useful Life

Period, in which an asset (especially machines, buildings) is technically able to fulfil its purpose. It is possible to extend this period substantially by preventive mainten-ance and repair. There-fore the technical useful life is longer than the economic one. Determ-ination is made accord-ing to statistical investig-ations or experience fig-ures.

Useful life, which leads to the biggest possible profit of an investment object. Therefore, the main problem in de-termining the economic useful life is the calcu-lation of the optimal re-placement time, i.e. when an old object should be replaced by a new one.

Important factors here are:

Technical wear out

Technical develop-ment

Economic develop-ment

Average useful life is usually determined by the tax authorities, in order to limit the max-imum possible depreci-ation of an object. Therefore the main dis-advantage of this type is that this useful life is determined according to the taxation policy and not according to economic aspects.

The legal useful life is in particular relev-ant for intangible as-sets like licences, property rights and furthermore for leas-ing contracts.

This length is determ-ined by the respective contracts.

Illustration 3: Different types of useful lifeSource: See Script Investition und Finanzierung & Gabler Wirtschaftslexikon

For the investment appraisals, the economic useful life is the most important.

5. Cost of Capital

Cost of capital represents the minimum interest rate demanded by the investor. Therefore those costs are included into the calculation. Illustration 4 shows several methods for determ-ining the cost of capital.

Methods for Determining the Cost of Capital

Costs of Financing Opportunity Costs Other Methods

Cost for loan capital

Cost for equity capital

Choice of the interest rate of the next best excluded alternative as internal rate of return.

Determination via the in-ternal rate of return method

Rate of return of the company

Rate of return of sim-ilar companies

Bank interest modified by:

expected inflation rate

tax rate

risk surchargeIllustration 4: Factors for determining the cost of capitalSource: Schulte, S., Script Investition und Finanzierung, p. 9

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II. Overview over the Different Methods for Investment Appraisal

Methods for Investment Appraisal

Static Methods Dynamic Methods

- Equivalent Annual Cost Method

- Profit Comparison Method

- Accounting Rate of Return

- Static Payback Method

- Net Present Value Method

- Annuity Method

- Dynamic Payback Method

Illustration 5: Methods for Investment AppraisalSource: Own Picture

The methods for investment appraisal are divided into static and dynamic methods. The main difference between these types is that static methods usually consider only one period and particularly do not consider the interest on capital (especially compound interest). There-fore static methods are more and more ousted by the dynamic methods, which consider the time value of money in their appraisals.6

1. Static Methods

In the static methods, costs, revenues, profits and rate on returns are compared. They do not consider the time factor, i.e. they usually calculate only with one period. Therefore, the results are only useful for relatively short periods.

1.1. Overview

With regard to the used operands and number of planning periods, the following methods can be differentiated:

Operands Number of the considered periods

Equivalent Annual Cost Method costs one

Profit Comparison Method costs and revenues one

Accounting Rate of Return costs and revenues one

Static Payback Method cash flows severalIllustration 6: Operands and Characteristics of the Static MethodsSource: Wöhe, G., Einführung in die Allgemeine Betriebswirtschaftslehre, p. 629

In the following, we will present and discuss these methods.

6 Knapps Enzyklopädisches Lexikon des Geld-, Bank- und Börsenwesens, p. 1027

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1.2. Equivalent Annual Cost Method

1.2.1. Character

The equivalent annual cost method compares the costs of several investment alternatives. According to this method, the alternative with the minimal costs has to be chosen. Therefore, all occurring costs should be included into this calculation.

This method can be used in comparing, whether a replacement investment is favourable (comparison: old asset/new asset). Furthermore, it can be used in comparing several compar-able replacement investments.

In the following section, we will present the single types of costs, which should be in-cluded into this calculation.

1.2.2. Determination of the Single Types of Costs

1.2.2.1. Determination of the Cost of Capital

The cost of capital is calculated in order to consider the costs for the acquisition of the loan or equity capital. On the one hand, if a credit is taken from a bank, the interest on this loan has to be paid. On the other hand, if the project is financed by equity capital, it has to be con-sidered that this money could also be invested in interest-bearing investments, so the invest-ment causes opportunity costs.

The interest charges are calculated on the basis of the average capital employed. The aver-age capital employed bases on a simple calculation of the average. However, if a residual value exists, this has to be considered at calculating the average. So we can conclude the fol-lowing formula for this calculation:

Cc = cost of capital

C = acquisition costs

RV = residual value

i = interest rate

1.2.2.2. Determination of the Cost Accounting Depreciation

With the cost accounting depreciation, the depreciation of the investment object is con-sidered. In investment appraisals, linear depreciation is usually used. The cost accounting de-preciation can be calculated with the following formula:

Cd = cost accounting depreciation

C = acquisition costs

RV = residual value

UL = useful life

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If there is a residual value at the end of the period, it has to be subtracted from the acquisi -tion costs, in order to get the real depreciation of the investment object.

1.2.2.3. Determination of the Operating Costs

The operating costs consist especially of the following types of costs:

Personnel costs:

- Wages

- Salaries

- Fringe benefits

Material costs:

- Raw materials

- Auxiliary material

- Operating supplies

Maintenance costs:

- Repair costs

- Inspection costs

- Service costs

Occupancy costs

Energy costs

Tooling charges

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1.2.3. Example

The following table shows two investment alternatives with their respective costs. Machine 1 Machine 21. Acquisition Costs 100,000 € 50,000 € 2. Useful Life (years) 5 53. Residual Value 10,000 € 04. Utilisation (units/year) 10,000 10,000

5. Depreciation (€/year) 18,000 € 10,000 € 6. Cost of Capital (interest rate of 10%) 5,500 € 2,500 € 7. Other Fixed Costs 1,000 € 700 €

8. Total Fixed Costs 24,500 € 13,200 € 9. Labour Costs 4,700 € 12,000 € 10. Material Costs (€/year) 1,500 € 1,500 € 11. Energy and other costs 800 € 2,000 €

12. Total Variable Costs 7,000 € 15,500 € 13. Variable costs per unit 0.70 € 1.55 € 13. Total Costs 31,500 € 28,700 €

Illustration 7: Example for an Equivalent Annual Cost MethodSource: Own Illustration

We can see that machine 2 has smaller total costs. Therefore, according to this method, machine 2 has to be chosen as an investment.

1.2.4. Assessment

Advantages:

Simple application

Relatively easy data collection

Disadvantages:

Possible accrual of costs at different times is not considered

Only period is assessed, which leads to inaccuracies

At comparing alternatives, different useful lives are not considered, because only the costs of one period are taken into account

Future differences in quality and capacity are not considered

In practice, it is often difficult to separate the costs in variable and fixed

The extent of capital expenditure is not considered adequately

1.3. Profit Comparison Method

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1.3.1. Character

The profit comparison method is an extension of the equivalent annual cost method. Here, besides the costs, the revenues are also included into the calculation. If the possible revenues of the alternatives are different, the profit comparison method has to be carried out, because the equivalent annual cost method would lead to wrong conclusions.

Reasons for different profits could be:7

a) The investment alternatives have different performance features (e.g. maximum output)

b) The investment alternatives have different qualitative characteristics, so it could be pos-sible that the output quantity is the same, but the products of one alternative are qualitat -ively superior and could be sold at a higher price

However, some authors are of the opinion that the profit comparison method should not be used, because in all cases, in which different revenues occur, a comparison of the rate of re -turn should be executed.8

1.3.2. Example

We will use the same example, as in the previous section. For example the products of machine 1 can be sold at 4 € per unit and the products of machine 2 for 3.50 € per unit. So we receive the following results:

Machine 1 Machine 2

Revenues 40,000 € 35,000 €

Costs 31,500 € 28,700 €

Profit 8,500 € 6,300 €Illustration 8: Example for a Profit Comparison MethodSource: Own Illustration

In this case, machine 1 is more favourable than machine 2.

1.3.3. Assessment

Advantages:

Besides the costs, the revenues are taken into account, so investment objects with different revenues can be compared

Simple application


Disadvantages:

Short-term, static method

Different extent of profits in the single periods are not considered

Assignment of the revenues to the single investment objects is usually very difficult

Already realised profits are compared with future possible ones7 Schulte, S., Script Finanzierung und Investition, p. 228 Boegelspacher, K., Script Investition & Finanzierung, p. 26

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This method only compares absolute profits, but does not compare the rates of return

1.4. Accounting Rate of Return

1.4.1. Character

One of the essential disadvantages of the equivalent annual cost method and profit compar-ison method is that they assess investment opportunities without consideration of the neces-sary employment of capital. Therefore the accounting rate of return determines the relative advantage of an investment.

For the calculation of the rate of return, this method uses the results of the annual cost and profit comparison method. Here the corrected profit of a period is related to capital employed on average. The corrected profit contains, besides the actual profits, the costs of capital. In that way this method wants to consider greater differences in the acquisition costs.9

According to this method, an investment is advantageous, when the rate of return is greater than the minimum rate of return or the investment with the greatest rate of return is the most favourable.

1.4.2. Example

Machine 1 Machine 2

Revenues 40,000 € 35,000 €

Costs 31,500 € 28,700 €

Profit 8,500 € 6,300 €

Cost of Capital 5,500 € 2,500 €

Corrected Profit 14,000 € 8,800 €

Average Capital Employed10 55,000 € 25,000 €

Accounting Rate of Return 25.5 % 35.2 %Illustration 9: Example for an Accounting Rate of Return MethodSource: Own Illustration

It is interesting that according to this method, machine 2 is more favourable, while the profit comparison method proposed machine 1. The reason for this is that machine 1, despite its greater absolute profits, has much a greater average capital employed. Therefore, in relat-ive terms, machine 2 is more favourable.

1.4.3. Assessment

9 Wöhe, G., Einführung in die Allgemeine Betriebswirtschaftslehre, p. 63110 For the calculation of the average capital employed see section 1.2.2.1

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The greatest advantage of the accounting rate of return method is that it determines the rel-ative advantage of an investment. Furthermore, this method has the same advantages as the profit comparison and equivalent annual cost method.

This method has the same disadvantages as the profit comparison method. Furthermore, this method does not take into account the time value of money in determining the rate of re-turn. So, it supposes that the differences in the acquisition costs can be invested at the respect-ive accounting rate of return (i.e. practically at every interest rate).11 However, this assump-tion is not very realistic.

1.5. Simple (Static) Payback Method

1.5.1. Character

The static payback method is the only static method, which uses data of several periods. This method calculates the period, which is necessary to compensate the acquisition costs by the annual cash flows of the investment. An investment is advantageous when it has a short payback period. The payback period is the period in which the acquisition costs of the invest-ment are “paid back”, i.e. returned to the company.

The methods, discussed so far, use costs and revenues. However, in order to calculate the cash flow, the profits have to be corrected by the depreciation. The depreciation is subtracted from the revenues at calculation of the profit, but the depreciation is not affecting payment, so it has to be added to the profits. So the approximate cash flow can be determined.

In this method it is assumed that the whole cash flow is used exclusively for the payback of the investment.

1.5.2. Example

Machine 1 Machine 2

Acquisition Costs 100,000 € 50,000 €

Useful Life (years) 5 5

Cash Flow Year 1 (cumulative) 26,500 € (26,500 €) 16,300 € (16,300 €)

Cash Flow Year 2 27,500 € (54,000 €) 16,700 € (33,000 €)

Cash Flow Year 3 25,000 € (79,000 €) 15,000 € (48,000 €)

Cash Flow Year 4 21,000 € (100,000 €) 12,000 € (60,000 €)

Payback Period 4 years 3.17 yearsIllustration 10: Example for Simple Payback MethodSource: Own Illustration

According to this method, machine 2 has to be chosen.

1.5.3. Assessment

11 Knapps Enzyklopädisches Lexikon des Geld-, Bank- und Börsenwesens, p. 1028

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Advantages:

Simple application

Shows how fast the acquisition costs return to the company


Disadvantages:

Simple payback does not take into account the time value of money

It ignores cash flows received after the end of the payback period

It does not take into account the overall profitability of the project.

1.6. Value Benefit Analysis

The value benefit analysis is not a classical method for investment appraisal. It is a method to assess alternatives according to non-monetary criteria, e.g. technical, psychological or so-cial criteria. Therefore this method should complete every investment appraisal.

The single criteria are weighted and every investment alternative receives certain points ac-cording to its fulfilment of the criteria. The alternative with the most points is chosen.

Illustration 11 shows some examples for such criteria.

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Market Criteria Market Share

Saturation of the Market

Product Range

Market Strategy

Labour- and Procurement Criteria Availability of Qualified Labour

Availability of Raw Material

Service

Delivery Time

Labour Physiological Criteria Accident Prevention

Dust, Noise and Other Annoy-ances

Intellectual Capability

Manual Capability

Handling

Infrastructure Criteria Internal and external transport possibilities

Energy Supply

Pre- and Post-Capacity

Waste Disposal

Technical Criteria Universal Availability

Capacity Reserves

Degree of Automation

Maturity of Construction

Disturbances during Installation

Environmental Criteria Accordance with Magisterial Planning

Environmental Impact due to Emissions

Image Improvement in the mar-ket

Meeting Socio-Political NeedsIllustration 11: Example for Non-Monetary Criteria in the Value Benefit AnalysisSource: Bögelspacher, K., Script Investition & Finanzierung, p. 29/30

2. Dynamic Methods

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The dynamic methods are said to be more superior to the static methods, because they take into account the time value of money. These methods assume that one Euro today is worth more than one Euro this time next year. Because today’s one Euro can be invested and receive income from it. Therefore, the dynamic methods stress that future cash flows should be ex-pressed in terms of what they are worth now when cash is expended on the project. The present values of these future cash flows can then be compared with what we are spending now on the project. In other words, the net present value is saying that one should compare like with like, which of course is a fair statement. By setting the future cash inflows from the project without discounting them against the initial capital cost, one is not being realistic and fair.12

The following example will show the differences between the dynamic and static methods:

Project Profits in the years Average

1 2 3

A 10 20 30 20

B 27 20 10 19Illustration 12: Example of Two Competing InvestmentsSource: Knapps Enzyklopädisches Lexikon des Geld-, Bank- und Börsenwesens, p. 1027

In this case, if we want to conduct an investment appraisal according to the static methods, we will choose Project A. Because the static methods only use one period and calculate with average values, project A will be chosen. However, the dynamic methods try to consider all periods, in which the investment object is used. We can see that project A has on the one hand a greater average profit, but has small profits at the beginning of its use. Contrary to this, pro-ject B has a smaller average profit, but greater profits at the beginning of the period. There-fore it has to be investigated, whether the combination of profits of project B are probably more favourable than of project A. The dynamic methods give an answer to this question, as we will see in the following sections.

2.1. Net Present Value Method

2.1.1. Character

This method compares the present values of cash outflows and inflows. If the result gives a positive net present value, then the project is favourable. An investment is more advantage-ous, the greater the net present value is.

The net present value is calculated according to this formula:

NPV = net present valueI = cash inflows in the years1 to nO = cash outflows in the years1 to nt = period (t = 0, 1, 2, ..., n)n = useful life of the investment object

12 O Idowu, S., Capital investment appraisal - part 1

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q = interest rate13

A0 = Acquisition Costs in period 0

A positive net present value can be interpreted as follows: The internal interest rate of the investment is higher than the interest rate, which was used in the calculation. So the net present value shows the profit of the investment. If the net present value is zero, the invest-ment only produces the minimum rate of return. In this case the cash flow can only cover the acquisition costs and the cost of capital for the capital employed. This is especially important, when the investment is financed with loan capital.

2.1.2. Example

In the following example, we will calculate the net present value of an investment, with ac-quisition costs of 100,000 € and a residual value of 10,000 € in period 5. Furthermore we will calculate with an interest rate of 10% and with the following cash inflows and outflows:

Year Cash Inflows Cash Outflows Difference Present Value

0 100,000 -100,000 -100,0001 55,000 15,000 40,000 36,3642 50,000 20,000 30,000 24,7933 45,000 20,000 25,000 18,7834 40,000 22,000 18,000 12,2945 38,000 28,000 10,000 6,209Residual Value 10,000 0 10,000 6,209Net Present Value 4,653

Illustration 13: Example for a Net Present Value calculationSource: Own Illustration

We can see that the investment has a net present value of 4,653 €. Therefore the internal rate of the investment is higher than the interest rate of 10 %.

The net present value method can also be used in comparing two competing investments. This shows the following example:Year Machine 1 Machine 20 -100,000 -100,000 -50,000 -50,0001 40,000 36,364 20,000 18,1822 30,000 24,793 15,000 12,3973 25,000 18,783 15,000 11,2704 18,000 12,294 10,000 6,8305 10,000 6,209 5,000 3,105Residual Value 10,000 6,209 0 0Net Present Value 4,653 1,783

Illustration 14: Example for Using the Net Present Value Method in Comparing Two AlternativesSource: Own Illustration

This example shows that machine 1 is more favourable than machine 2. It has to be men-tioned that the residual value at the end of the period is treated as a cash inflow and therefore has to be discounted.

13 Instead of the interest rate, the inflation rate can be used, in order to make the cash flows of different years comparable

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2.1.3. Assessment

Advantages:

Considers the time value of money

Shareholder wealth is maximised

It is based on cash flows, which are less subjective than profits.

Disadvantages:

It assumes that there is no difference between the interest rate for equity capital and for loan capital.

It assumes that money can be invested on the same interest rate during the whole period14

it can be difficult to identify an appropriate discount rate

Cash flows are usually assumed to occur at the end of a year, but in practice this is over simplistic

It is assumed that the cash flows can be assigned directly to the investment object

It is difficult to compare alternatives with different useful lives with this method

2.2. Internal Rate of Return Method

2.2.1. Character

This method allows determining the real rate of return of an investment. So in such a case the net present value of an investment would be zero. The internal rate of return therefore is the maximum rate of discount that will be used to finance a project without making a loss from it. This is especially an important question, when the project is financed by loan capital. So the investor knows what the maximum possible interest rate of the loan could be.

In order to calculate the internal rate of return, the equation for determining the net present value has to be solved for qt. This is a very complicated mathematic operation. Therefore there are two possibilities to solve this problem. First, software (e.g. MS Excel) can be used to calculate the internal rate of return or an approximation method can be used.

In the approximation method two net present values (NPV 1 and NPV2) for two arbitrarily determined interest rates. However, these interest rates should not be too far from another (< 5 %). The first net present value has to be negative (NPV1), while the second one must be pos-itive (NPV2).15 The calculated values are inserted into the formula below:

The investment is advantageous, when the internal rate of return is not below the expected minimum interest rate.

2.2.2. Example14 Knapps Enzyklopädisches Lexikon des Geld-, Bank- und Börsenwesens, p. 103015 Bögelspacher, K., Script Investition & Finanzierung, p. 32

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For this example, we will use the same data as in the example of the previous section. As second interest rate, we will use an interest rate of 13%, which results in a negative net present value.Year i = 10% i = 13 %0 -100,000 -100,000 -100,000 -100,0001 40,000 36,364 40,000 35,3982 30,000 24,793 30,000 23,4943 25,000 18,783 25,000 17,3264 18,000 12,294 18,000 11,0405 10,000 6,209 10,000 5,428Residual Value 10,000 6,209 10,000 5,428Net Present Value 4,653 -1,886

Illustration 15: Example for Determining the Internal Rate of Return with the Approximation MethodSource: Own Illustration

When we insert the data into the formula, mentioned above, we receive the following res-ult:

So machine 1 has an internal rate of return of 12.1 %.

2.2.3. Assessment

Advantages:

It takes into account the time value of money, which is a good basis for decision-making

Results are expressed as a simple percentage and therefore are more easily understood than some other methods

It indicates how sensitive decisions are to a change in interest rates.

Disadvantages:

Projects with unconventional cash flows can have either negative or multiple IRRs. For ex-ample, a project has the following cash flows: A0 = 1, CF1 = 6, CF2 = -11 und CF3 = 6. If we use the simple payback method, we would refuse this investment, because the payback period is at the end of the useful life. If we use the internal rate of return method, we would

also receive an IRR of 0 %. Because . However, this project has two (!)

further IRRs, qint = 100 % and qint = 200 %, because the equations and

are also solved. Such results make no sense, especially when we cal-

culate the maximum possible interest rate for loans and moreover the question, which IRR of this example is the correct one, is not answered.16

IRR cannot accommodate changes in interest rates over the life of a project16 Knapps Enzyklopädisches Lexikon des Geld-, Bank- und Börsenwesens, p. 1031

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It assumes funds are re-invested at a rate equivalent to the IRR itself, which may be unreal-istically high.

It may give conflicting recommendations to net present value

The question arises, what to do, when the internal rate of return method and net present value method calculate different results? Then the net present value method should be used. Because the internal rate of return method leads to inexpedient results, as the example men-tioned above shows. The NPV method assumes that the cash flows can be invested on the cal-culated interest rate. However, the IRR method assumes that funds are re-invested at a rate equivalent to the IRR itself. This assumption is very unrealistic, especially for non-monetary investments.17

2.3. Annuity Method

2.3.1. Character

The annuity method distributes the net present value into commensurate annuities. There-fore, an investment is advantageous, when the annuity is not negative. The annuity method leads to the same results, like the net present value method. Therefore, it can be called a ver-sion of the net present value method.

The annuity can be calculated with the following formula:

2.3.2. ExampleYear Cash Flow Present Value

0 -100,000 -100,0001 40,000 36,3642 30,000 24,7933 25,000 18,7834 18,000 12,2945 10,000 6,209Residual Value 10,000 6,209Net Present Value 4,653Annuity 1,227

Illustration 16: Example for Calculating an AnnuitySource: Own Illustration

This investment has an annuity of 1,227 €. Therefore the investor is able to take annually 1,227 € and the investment has still an internal rate of return of 10%.

2.4. Dynamic Payback Method

2.4.1. Character

17 Wöhe, G., Einführung in die Allgemeine Betriebswirtschaftslehre, p. 644

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The dynamic payback method determines in which period the capital employed plus the expected interest rate returned to the company. The payback period is in particular dependent on the interest rate. A high interest rate leads to a long payback period, while a short interest rate leads to a short payback period.

2.4.2. Example

We will calculate the payback period for machine 1. Year Machine 1 Present Value Cumulative Value

Present Value0 -100,000 -100,000 -100,0001 40,000 36,364 -63,6362 30,000 24,793 -38,8433 25,000 18,783 -20,0604 18,000 12,294 -7,7665 10,000 6,209 -1,557Residual Value 10,000 6,209 +4,653Net Present Value 4,653

Illustration 17: Example for Dynamic Payback MethodSource: Own Illustration

We can see that the payback period of this investment is about 4 years.

2.4.3. Assessment

Advantages:

Considers the time value of money

It is based on cash flows, which are less subjective than profits

Shows how fast the acquisition costs plus interest return to the company

Disadvantages:

It ignores cash flows received after the end of the payback period

It does not take into account the overall profitability of the project.

2.5. Conditions for Using the Dynamic Methods

For using the dynamic methods, the following conditions have to be fulfilled:18

- For every investment object it must be possible to assign the cash inflows and outflows, which is not very easy in practice

- The cash flows have to be reinvested immediately and they must be able to produce a yield at the calculated interest rate at minimum

18 Gabler Wirtschaftslexikon, p. 1645

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- The liquidity of the company is assured in any case, i.e. no matter what kind of investment will be undertaken

- The company is able to sell its products at a predetermined price, in unlimited quantity

3. Conclusion

We have shown in this study, what alternatives a company has, in order to determine the possible success of an investment. The single methods have been investigated according to their advantages and disadvantages. Due to their disadvantages, especially because they use only one period and ignore the time value of money, the static methods are more and more ousted by the dynamic methods. The most important advantage of the dynamic methods is that they consider the time value of money. However, these methods are based on some un-realistic assumptions:19

The cash flows can be invested on the same interest rate during the whole useful life of an investment object

There is no difference between the interest rate for equity capital and for loan capital.

It is difficult, sometimes impossible, to assign cash inflows and outflows to the invest-ment object

Every investment contains risks. These risks have to be considered in the investment appraisals

All these assumptions are not very realistic, but they are fundamental for the application of the dynamic methods. Due to these constraints, new methods have been developing for in-vestment appraisals, which try to compensate the disadvantages of the traditional methods. Examples for these new methods are the DEAN-model, methods of operations research and approaches for a simultaneous investment and finance planning.

19 See also Wöhe, G., Einführung in die Allgemeine Betriebswirtschaftslehre, p. 654

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Bibliography

1. Bögelspacher, K., Script: „Investition & Finanzierung“

2. Gabler Wirtschaftslexikon, 15th edition, Wiesbaden, 2000.

3. Irons, A., Capital investment appraisal, article at http://www.accaglobal.com/publications/studentaccountant/1105038

4. Knapps Enzyklopädisches Lexikon des Geld-, Bank- und Börsenwesens, 4th edition, Frankfurt am Main, 1999.

5. O Idowu, S., Capital investment appraisal - part 1, article at http://www.accaglobal.com/publications/studentaccountant/39869

6. Schulte, S., Script: „Finanzierung und Investition“

7. Wöhe, G., Einführung in die Allgemeine Betriebswirtschaftslehre, 20th edition, München, 2000.

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