Methods of Investment Appraisal

UNIVERZITET U NOVOM PAZARU Suad Bećirović DYNAMIC AND STATIC METHODS OF INVESTMENT APPRAISAL Novi Pazar, 2006. DYNA

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UNIVERZITET U NOVOM PAZARU

Suad Bećirović

DYNAMIC AND STATIC METHODS OF INVESTMENT APPRAISAL

Novi Pazar, 2006.

DYNAMIC AND STATIC METHODS OF INVESTMENT APPRAISAL

CONTENTS 1. Investment and Finance......................................................................................................7 2. Acquisition Costs................................................................................................................7 3. Residual Value....................................................................................................................7 4. Useful Life..........................................................................................................................7 5. Cost of Capital....................................................................................................................8 1.1. Overview..........................................................................................................................9 1.2. Equivalent Annual Cost Method....................................................................................10

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DYNAMIC AND STATIC METHODS OF INVESTMENT APPRAISAL

List of Illustrations Illustration 1: Overview of the several types of investment..................................................4 Illustration 2: Steps in Project Appraisal...............................................................................5 Illustration 3: Different types of useful life.............................................................................8 Illustration 4: Factors for determining the cost of capital....................................................8 Illustration 5: Methods for Investment Appraisal.................................................................9 Illustration 6: Operands and Characteristics of the Static Methods...................................9 Illustration 7: Example for an Equivalent Annual Cost Method.......................................12 Illustration 8: Example for a Profit Comparison Method..................................................13 Illustration 9: Example for an Accounting Rate of Return Method..................................14 Illustration 10: Example for Simple Payback Method........................................................15 Illustration 11: Example for Non-Monetary Criteria in the Value Benefit Analysis.......17 Illustration 12: Example of Two Competing Investments..................................................18 Illustration 13: Example for a Net Present Value calculation............................................19 Illustration 14: Example for Using the Net Present Value Method in Comparing Two Alternatives..............................................................................................................................19 Illustration 15: Example for Determining the Internal Rate of Return with the Approximation Method..........................................................................................................21 Illustration 16: Example for Calculating an Annuity..........................................................22 Illustration 17: Example for Dynamic Payback Method....................................................23

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DYNAMIC AND STATIC METHODS OF INVESTMENT APPRAISAL

Introduction Organisations operate in a dynamic environment. Therefore they have to meet the challenges that the dynamic nature of the environment brings. To meet these challenges, a company has to invest large sums of money, in order to have an advantage compared to their competitors. The need for investments is a daily occurrence in a company: obsolescence and excess of age of machines, means of transportation and buildings; increasing expenses for maintenance 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 investments 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 Investment

− 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 personnel

Illustration 1: Overview of the several types of investment Source: Schulte, S., Script Investition und Finanzierung, p. 8

For a company, the decision for an investment means to give up liquidity. As compensation 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

4

DYNAMIC AND STATIC METHODS OF INVESTMENT APPRAISAL

Motivation for an Investment ⇓ Initial Investigation ⇓ Evaluation of the Investment

Investment Appraisal

⇓ Decision for an Investment ⇓ Implementation of the investment ⇓ Investment Controlling Illustration 2: Steps in Project Appraisal Source: Schulte, S., Script Investition und Finanzierung, p. 13

Firstly, there must be a reason or cause for an investment. The main motivation for an investment 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 decision, 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 order to make the correct decision, several methods for investment appraisal have been developed, 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 appraisal 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

2

Wöhe, G., Einführung in die Allgemeine Betriebswirtschaftslehre, p. 625 Ibid. 4 Ibid., p. 622 3

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DYNAMIC AND STATIC METHODS OF INVESTMENT APPRAISAL

Methodology 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.

6

DYNAMIC AND STATIC METHODS OF INVESTMENT APPRAISAL

I. Fundamental Terms 1. Investment and Finance The terms investment and finance have to be differentiated, because they describe contrasts. 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 longterm, 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 important 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 manufactured 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 purpose. 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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DYNAMIC AND STATIC METHODS OF INVESTMENT APPRAISAL

Technical Useful Life

Economic Useful Life

Average 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 maintenance and repair. Therefore the technical useful life is longer than the economic one. Determination is made according to statistical investigations or experience figures.

Useful life, which leads to the biggest possible profit of an investment object. Therefore, the main problem in determining the economic useful life is the calculation of the optimal replacement time, i.e. when an old object should be replaced by a new one.

Average useful life is usually determined by the tax authorities, in order to limit the maximum possible depreciation of an object. Therefore the main disadvantage of this type is that this useful life is determined according to the taxation policy and not according to economic aspects.

Important factors here are:

Legal Useful Life The legal useful life is in particular relevant for intangible assets like licences, property rights and furthermore for leasing contracts. This length is determined by the respective contracts.

• Technical wear out • Technical development • Economic development

Illustration 3: Different types of useful life Source: 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 determining the cost of capital. Methods for Determining the Cost of Capital Costs of Financing

Opportunity Costs

Other Methods

− Cost for loan capital

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

− Rate of return of the company

− Cost for equity capital

− Determination internal rate method

via the of return

− Rate of return similar companies

of

Bank interest modified by: − expected inflation rate − tax rate − risk surcharge

Illustration 4: Factors for determining the cost of capital Source: Schulte, S., Script Investition und Finanzierung, p. 9

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DYNAMIC AND STATIC METHODS OF INVESTMENT APPRAISAL

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

Dynamic Methods

Equivalent Annual Cost Method

Net Present Value Method

Profit Comparison Method

Annuity Method

Accounting Rate of Return

Dynamic Payback Method

Static Payback Method Illustration 5: Methods for Investment Appraisal Source: 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). Therefore 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

costs

one

Profit Comparison Method

costs and revenues

one

Accounting Rate of Return

costs and revenues

one

cash flows

several

Equivalent Annual Cost Method

Static Payback Method

Illustration 6: Operands and Characteristics of the Static Methods Source: 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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DYNAMIC AND STATIC METHODS OF INVESTMENT APPRAISAL

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 comparable replacement investments. In the following section, we will present the single types of costs, which should be included 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 considered that this money could also be invested in interest-bearing investments, so the investment causes opportunity costs. The interest charges are calculated on the basis of the average capital employed. The average 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 following formula for this calculation: Cc =

C + RV *i 2

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 considered. In investment appraisals, linear depreciation is usually used. The cost accounting depreciation can be calculated with the following formula: Cd =

C − RV UL

Cd = cost accounting depreciation C = acquisition costs RV = residual value UL = useful life 10

DYNAMIC AND STATIC METHODS OF INVESTMENT APPRAISAL

If there is a residual value at the end of the period, it has to be subtracted from the acquisition 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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DYNAMIC AND STATIC METHODS OF INVESTMENT APPRAISAL

1.2.3. Example The following table shows two investment alternatives with their respective costs. Machine 1 Machine 2 1. Acquisition Costs 100,000 € 50,000 € 2. Useful Life (years) 5 5 3. Residual Value 10,000 € 0 4. 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 Method Source: 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 12

DYNAMIC AND STATIC METHODS OF INVESTMENT APPRAISAL

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 possible that the output quantity is the same, but the products of one alternative are qualitatively 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 return 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 Method Source: 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 − Relatively easy data collection 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 7 8

Schulte, S., Script Finanzierung und Investition, p. 22 Boegelspacher, K., Script Investition & Finanzierung, p. 26

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DYNAMIC AND STATIC METHODS OF INVESTMENT APPRAISAL

− Already realised profits are compared with future possible ones − 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 comparison method is that they assess investment opportunities without consideration of the necessary 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 Accounting

Rate

of Return

=

Corrected Average Capital

Profit Em ployed

* 100

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 Method Source: 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 relative terms, machine 2 is more favourable.

1.4.3. Assessment 9

Wöhe, G., Einführung in die Allgemeine Betriebswirtschaftslehre, p. 631 For the calculation of the average capital employed see section 1.2.2.1

10

14

DYNAMIC AND STATIC METHODS OF INVESTMENT APPRAISAL

The greatest advantage of the accounting rate of return method is that it determines the relative 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 return. So, it supposes that the differences in the acquisition costs can be invested at the respective accounting rate of return (i.e. practically at every interest rate).11 However, this assumption 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 investment 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 years

Illustration 10: Example for Simple Payback Method Source: 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

15

DYNAMIC AND STATIC METHODS OF INVESTMENT APPRAISAL

Advantages: − Simple application − Shows how fast the acquisition costs return to the company − Relatively easy data collection 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 social criteria. Therefore this method should complete every investment appraisal. The single criteria are weighted and every investment alternative receives certain points according to its fulfilment of the criteria. The alternative with the most points is chosen. Illustration 11 shows some examples for such criteria.

16

DYNAMIC AND STATIC METHODS OF INVESTMENT APPRAISAL

Market Criteria

Labour- and Procurement Criteria

Labour Physiological Criteria

Infrastructure Criteria

Technical Criteria

Environmental Criteria



Market Share



Saturation of the Market



Product Range



Market Strategy



Availability of Qualified Labour



Availability of Raw Material



Service



Delivery Time



Accident Prevention



Dust, Noise and Other Annoyances



Intellectual Capability



Manual Capability



Handling



Internal and external transport possibilities



Energy Supply



Pre- and Post-Capacity



Waste Disposal



Universal Availability



Capacity Reserves



Degree of Automation



Maturity of Construction



Disturbances during Installation



Accordance with Magisterial Planning



Environmental Impact due to Emissions



Image Improvement in the market



Meeting Socio-Political Needs

Illustration 11: Example for Non-Monetary Criteria in the Value Benefit Analysis Source: Bögelspacher, K., Script Investition & Finanzierung, p. 29/30

17

DYNAMIC AND STATIC METHODS OF INVESTMENT APPRAISAL

2. Dynamic Methods 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 expressed 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

19

Illustration 12: Example of Two Competing Investments Source: 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, project B has a smaller average profit, but greater profits at the beginning of the period. Therefore 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 advantageous, the greater the net present value is. The net present value is calculated according to this formula: n

NPV = -A 0 + ∑ i =1

NPV I O t n

12

It - Ot qt

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

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

18

DYNAMIC AND STATIC METHODS OF INVESTMENT APPRAISAL

q A0

= interest rate13 = 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 investment 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 acquisition 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 -100,000 1 55,000 15,000 40,000 36,364 2 50,000 20,000 30,000 24,793 3 45,000 20,000 25,000 18,783 4 40,000 22,000 18,000 12,294 5 38,000 28,000 10,000 6,209 Residual Value 10,000 0 10,000 6,209 Net Present Value 4,653 Illustration 13: Example for a Net Present Value calculation Source: 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 2 0 -100,000 -100,000 -50,000 -50,000 1 40,000 36,364 20,000 18,182 2 30,000 24,793 15,000 12,397 3 25,000 18,783 15,000 11,270 4 18,000 12,294 10,000 6,830 5 10,000 6,209 5,000 3,105 Residual Value 10,000 6,209 0 0 Net Present Value 4,653 1,783 Illustration 14: Example for Using the Net Present Value Method in Comparing Two Alternatives Source: Own Illustration

This example shows that machine 1 is more favourable than machine 2. It has to be mentioned 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

19

DYNAMIC AND STATIC METHODS OF INVESTMENT APPRAISAL

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 positive (NPV2).15 The calculated values are inserted into the formula below: q int = q1 - NPV1 *

q 2 - q1 NPV2 - NPV1

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

14 15

Knapps Enzyklopädisches Lexikon des Geld-, Bank- und Börsenwesens, p. 1030 Bögelspacher, K., Script Investition & Finanzierung, p. 32

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DYNAMIC AND STATIC METHODS OF INVESTMENT APPRAISAL

2.2.2. Example 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 -100,000 1 40,000 36,364 40,000 35,398 2 30,000 24,793 30,000 23,494 3 25,000 18,783 25,000 17,326 4 18,000 12,294 18,000 11,040 5 10,000 6,209 10,000 5,428 Residual Value 10,000 6,209 10,000 5,428 Net Present Value 4,653 -1,886 Illustration 15: Example for Determining the Internal Rate of Return with the Approximation Method Source: Own Illustration

When we insert the data into the formula, mentioned above, we receive the following result: q int

=1,13 - (-1886)

*

1.10 - 1.13 4653 - (-1886)

=1,121

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 example, 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 6 11 6 also receive an IRR of 0 %. Because − 1 + 1 − 2 + 3 = 0 . However, this project has two 1 1 1 (!) further IRRs, qint = 100 % and qint = 200 %, because the equations 6 11 6 6 11 6 − 1 + 1 − 2 + 3 = 0 and − 1 + 1 − 2 + 3 = 0 are also solved. Such results make no 2 2 2 3 3 3 sense, especially when we calculate the maximum possible interest rate for loans and moreover the question, which IRR of this example is the correct one, is not answered.16 16

Knapps Enzyklopädisches Lexikon des Geld-, Bank- und Börsenwesens, p. 1031

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DYNAMIC AND STATIC METHODS OF INVESTMENT APPRAISAL

− IRR cannot accommodate changes in interest rates over the life of a project − It assumes funds are re-invested at a rate equivalent to the IRR itself, which may be unrealistically 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 mentioned above shows. The NPV method assumes that the cash flows can be invested on the calculated 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. Therefore, 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 version of the net present value method. The annuity can be calculated with the following formula: a = NPV *

2.3.2. Example Year 0 1 2 3 4 5 Residual Value Net Present Value Annuity

Cash Flow -100,000 40,000 30,000 25,000 18,000 10,000 10,000

q n (q - 1) q n −1

Present Value -100,000 36,364 24,793 18,783 12,294 6,209 6,209 4,653 1,227

Illustration 16: Example for Calculating an Annuity Source: 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 17

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

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DYNAMIC AND STATIC METHODS OF INVESTMENT APPRAISAL

2.4.1. Character 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 0 1 2 3 4 5 Residual Value Net Present Value

-100,000 40,000 30,000 25,000 18,000 10,000 10,000

-100,000 36,364 24,793 18,783 12,294 6,209 6,209 4,653

Cumulative Value Present Value -100,000 -63,636 -38,843 -20,060 -7,766 -1,557 +4,653

Illustration 17: Example for Dynamic Payback Method Source: 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 -

18

For every investment object it must be possible to assign the cash inflows and outflows, which is not very easy in practice Gabler Wirtschaftslexikon, p. 1645

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DYNAMIC AND STATIC METHODS OF INVESTMENT APPRAISAL

-

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

-

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 unrealistic 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 investment 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 investment 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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DYNAMIC AND STATIC METHODS OF INVESTMENT APPRAISAL

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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