# Evaluating real options as a means for investment appraisal under uncertainty and its degree of utilisation by companies

Diplomarbeit 2003 116 Seiten

## Leseprobe

## III Table of Contents

I Abstract

II Acknowledgements

III Table of Contents

IV List of Figures

V List of Abbreviations

1 Introduction

2 Characteristics of Investment Decisions

2.1 What Is a Capital Investment?

2.2 Risk and Uncertainty

2.2.1 Definition

2.2.2 Measurement

3 Tools for Investment Appraisals

3.1 Static Methods

3.2 Discounted Cash Flow Approaches (Dynamic)

3.3 Approaches Which Try to Deal With Risk

3.3.1 Adjustments of NPV

3.3.2 Decision Tree Analysis (DTA)

3.3.3 Real Options

4 The Real Options Approach

4.1 Why Use Real Options to Evaluate Capital Investments?

4.1.1 Investment Decisions – Irreversibility, Uncertainty, and Flexibility

4.1.2 The Gap Between Quantitative and Qualitative Analysis

4.2 Financial Options

4.2.1 Calls and Puts

4.2.2 Estimating the Value of an Option

4.2.2.1 Variables Determining the Price of Options

4.2.2.2 Value of an Option at Expiry Date

4.2.3 Calculating the Price of an Option Before Expiry Date

4.2.3.1 Binomial Option Pricing Model (discrete)

4.2.3.2 Black-Scholes-Merton Option Pricing Model (continuous)

4.3 Real options explained by using a case study

4.3.1 Option to defer

4.3.2 Option to expand

4.3.3 Option to contract

4.3.4 Option to shut down and restart

4.3.5 Option to switch use

4.3.6 Option to abandon

4.3.7 Compound Options and Rainbow Options

4.4 Real Option Examples in Literature and Practical Applications

4.4.1 Land and Natural Resources

4.4.2 Production Facilities and Expansion of Production Capacities

4.4.3 Information System Projects

4.4.4 Real Options in R&D

4.4.5 Investments, Acquisitions, and Company Valuation

4.4.6 Product Launch and Market Entry

4.4.7 Other Applications

4.5 Advantages and Deficiencies of Real Options

4.5.1 Deficiencies

4.5.1.1 General shortcomings

4.5.1.2 Sophisticated Mathematics

4.5.1.3 Problems in Using the Black-Scholes Formula

4.5.1.4 Problems in Using the Binomial Approach

4.5.2 Advantages

5 Survey

5.1 Methodology

5.2 Evaluation of the Results

5.3 Discussion of Problems of the Survey and Relevance of the Findings

6 Conclusion – Is the Real Options Approach Really Necessary?

VI Appendix

1. Example of What Is Risk

2. Bounding the Value of an Option

3. Put-Call-Parity

4. Derivation of Binomial Option Pricing Formula

5. Derivation of risk-adjusted discount rate

6. Questionnaire

7. Used tools dependent on size of the company

8. Excel sheets for case study

VII References

VIII Affidavit

IX Curriculum Vitae

## IV List of Figures

Figure 1: Graph showing the distribution of the possible returns of two different investments with a standard deviation of 10 and 15, respectively

Figure 2: Example of a decision tree (only the part involving alternative A is depicted)

Figure 3: Summary of the effect of increasing one variable while keeping all others fixed on the price of a stock option (Hull, 2000).

Figure 4: One-step binomial tree

Figure 5: “Decision Radar” (Parrish, 2001)

Figure 6: Respondents classified by industrial sectors

Figure 7: Size classes used to evaluate the survey and number of companies of each size class in survey

Figure 8: Classification scheme of investment appraisal methods

Figure 9: Knowledge and application of ROA among the respondents

Figure 10: Importance of investments

Figure 11: Proportions of used methods for different investment decisions

Figure 12: Number of tools used to appraise different investments

Figure 13: Knowledge of ROA with regard to the three size classes

Figure 14: Knowledge of ROA in different industrial sectors.

Figure 15: Possible application of ROA for different investment decisions

Figure 16: Comparison of three investments with similar expected returns but different risk

Figure 17: Comparison of two portfolios consisting of a risk-free asset and a call, and shares and a put option, respectively

Figure 18: Screenshot of the questionnaire

Figure 19: Tools used for different investment decisions by companies of different size classes

V List of Abbreviations

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## 1 Introduction

The real options approach (ROA) is described by advocates as a powerful tool for investment appraisal^{[1]}, especially in regard to the uncertainty of such decisions and the value of flexibility of management decisions. The latter more than ever seems to be an important issue since the world’s economy has undergone a wrenching change towards globalisation. Studies by Dixit and Pindyck (1994), Trigeorgis (1996), and Amram and Kulatilaka (1999) indicate, that managerial flexibility is not valued by traditional investment appraisal techniques. Real options do take this flexibility into account. However, when reading more about this topic one notices that there seem to be only few companies which use this approach.

If this tool is so formidable, then why is it not widely used? The question evolves as to whether there is a need for a further investment appraisal technique. However, if this can be approved, then what are the reasons that companies stick to other methods of capital budgeting? During prior research by the author, three possible reasons have been identified which are examined in this paper:

- ROA is not well-known by companies, especially small- and medium-sized enterprises.

- ROA is only limitedly applicable.

- ROA is too difficult to use.

In this paper, the importance of investment decisions is illustrated and the investment appraisal methods used by companies are identified and briefly described. The real options approach is explained in more detail by means of a case study. Advantages and disadvantages are pointed out and literature is reviewed with regard to possible applications of ROA. In order to check its degree of utilisation by companies, a survey is conducted by using a questionnaire. Moreover, it shall be identified which capital budgeting tools are used by companies for different investment decisions and whether there exist size specific differences in this regard.

The second chapter starts by explaining what a capital expenditure is and why it is so important for companies. Risk and uncertainty are further key subjects of that chapter. Chapter three briefly outlines various tools of investment appraisal which can be found in all text books concerning this topic. It is important to have a common understanding of the advantages and disadvantages of the investment appraisal methods evaluated in chapter three in order to be able to view them in contrast to the real options approach. Options in general and real options in particular are dealt with in chapter four. Having evaluated all these tools for investment decision-making, in chapter five the conducted survey will be evaluated. Chapter six concludes this paper.

## 2 Characteristics of Investment Decisions

### 2.1 What Is a Capital Investment?

When a company is started, money has to be invested in order to get facilities and equipment for manufacturing products or providing services. Moreover, this initial investment^{[2]} is not enough to keep a company alive. Capital expenditures are needed for example to replace assets, to do necessary research and development in order to stay ahead of or keep pace with competitors, and to expand. Therefore, they are vital for companies. That is why capital expenditures in Germany amounted to €390 billion in 2002, which is approximately 18% of Germany’s GDP (Statistisches Bundesamt Deutschland, 2003). In 2001, capital expenditures in the UK totalled ₤116 billion which equals roughly 12% of Great Britain’s GDP (Office for National Statistics, 2003).

Investing means incurring costs now in order to get a stream of benefits in the future (Dixit and Pindyck, 1994; Levy and Sarnat, 1994; Lumby 1994). As a company only has limited resources, it has to decide whether an investment is worth undertaking. According to Lumby (1994), a decision situation is characterised by the existence of alternatives, and an objective or goal. For instance a company might want to increase shareholder value, or be the largest company in its sector, or simply survive in a highly competitive market. The company then has at least two alternatives in regard to capital expenditures in order to achieve that goal: either to invest in a project or not. Decisions relating to capital investment belong to the most important ones (Ryan and Ryan, 2002) since failure may affect the company’s profitability significantly because (Holmes, 1998):

- companies put a large amount of money in capital investments^{[3]}

- investments have a major impact on future cash flows and therefore on the company’s ability to meet its goal(s)

- returns of an investment are uncertain

- capital investments cannot be reversed or only with great losses

Investment appraisal techniques are formal approaches to support investment decisions and try to avoid personally motivated or intuitive decisions. However, some variables such as costs and revenues always have to be estimated, partly on basis of personal experience. Therefore, the quality of the result of the investment appraisal process depends heavily on the quality of the data which is used for the calculations (Holmes, 1998).

### 2.2 Risk and Uncertainty

#### 2.2.1 Definition

As mentioned before, variables needed for investment appraisal such as costs, revenues or discount rate have to be estimated. If all factors relating to the investment decision were known, a condition of certainty would exist and the decision maker can “determine precisely the outcome which will derive from any particular action” (Holmes, 1998:59). In this case, all tools for investment appraisal would, apart from their deficiencies, give an exact investment advice to the decision maker. However, investment appraisals are based on expectations and estimations. Therefore, the outcome of an investment may differ from the calculated expected value (Lumby, 1994). This is commonly referred to as risk.

Risk is defined by the Oxford Advanced Learner’s Dictionary of Current English (1989) as the “possibility of meeting danger or suffering harm, loss, etc”. In business life, one might refer to financial risk, business risk or economic risk. Each phrase means a possible negative impact on for example one’s firm. In contrast, derived from the Latin word *risicum*, risk had some positive connotations up to Middle Ages and referred to chance or luck both, good and bad (Levy and Sarnat, 1994). With investments, risk exists in the latter sense. One does not only suffer from the possibility of lower net cash flows^{[4]}, but may also profit from the chance of higher ones.

The concern is, how to identify and measure the level of risk of a particular investment and when having done that, how can it be incorporated in the investment appraisal. Therefore, one has to have a closer look at how risk can be measured. Although some authors differentiate between risk and uncertainty (e.g. Levy and Sarnat, 1994; Holmes, 1998), such a distinction is not drawn in this paper.

#### 2.2.2 Measurement

A definition of risk is how spread-out the possible returns of an investment are (Ross, Westerfield and Jaffe, 1993)^{[5]}. Yet there might not only be a few scenarios but various different outcomes. Considering all of them and estimating probabilities can become time-consuming work. Statistics show that if one would have the opportunity to do the same investment over and over again, the average return of all these repetitions would converge to the expected return E(R). All other outcomes are distributed around that expected return in a way that is called normal distribution. Thus, the standard deviation (s) can be used as a measure for risk (Markowitz, 1952). Obviously, there is not only the danger of returns below the expected return (downside risk) but also the chance of higher gains (upside potential) (Lumby, 1994).

Levy and Sarnat (1994:237) also define the “expected (mean) profit as an indicator of an investment’s anticipated profitability and variance (or standard deviation) as an indicator of its risk”. The larger the standard deviation, the greater the dispersion of the possible outcomes around the expected return and thus the greater the risk. Expected return and variance are calculated (Levy and Sarnat, 1994):

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where: s2 … Variance of the returns

n … Number of possible outcomes (returns)

Ri … Possible return associated with outcome i

Pi … Probability of return i

Having both, expected return and variance, one can plot a graph of the frequency distribution of the returns as shown in the following diagram (figure 1). Both projects have an expected return of 100 but different standard deviations. The possible outcomes are shown on the x-axis. On the y-axis one can see the probability of each possible outcome.

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Figure 1: Graph showing the distribution of the possible returns of two different investments with a standard deviation of 10 and 15, respectively

## 3 Tools for Investment Appraisals

Most authors speak of traditional tools of investment appraisal when talking about methods which take not into account the time value of money (e.g. Levy and Sarnat, 1994; Lumby, 1994). Thus, these approaches are also referred to as static (Holmes, 1998). In this paper the phrase “traditional” is extended to net present value and internal rate of return since at least the former has been known for more than a century. A calculation of a net present value can be found in “Calculation of the Value which Forest Land and Immature Stands Possess for Forestry” published by Martin Faustmann in 1849 (Faustmann, 1849). At least Irving Fisher states the expression “net present value” in his 1907 book “The Rate of Interest: Its Nature, Determination and Relation to Economic Phenomena” (Fisher, 1977).

### 3.1 Static Methods

Static investment appraisals are relatively straightforward as they consider a pound in the future to be as valuable as a pound today. Therefore, future cash flows can be easily compared with the initial investment outlay. The static methods are rather quick and simple to calculate and can be understood by everyone in a company. Furthermore, they provide definitive investment rules when to invest and when not.

A very simple method to analyse investments is the cost comparison method (e.g. Bestmann, 1997; Horvath, 2002) which contrasts two or more alternative investment possibilities in order to determine the most cost-effective investment. The technique is not used to make decisions whether or not to do an investment but to compare different alternatives of a project when a positive decision to undertake this project has already been made.

The return on investment (ROI), also known as return on capital employed (ROCE) or accounting rate of return (ARR) relates the forecasted average annual profit to the average capital employed over the whole time of the investment (e.g. Ross, Westerfield and Jaffe, 1993; Holmes, 1998; Brealey and Myers, 2000). Hence, it is an enhancement of the cost comparison method as it also takes the revenues into account and calculates the profit. Since shareholders pay considerable attention to book measures, ROI can be applied by choosing a minimum ROI (i.e. one that meets the expectations of the shareholders) and accepting only those projects which meet this requirement (Holmes, 1998; Brealey and Myers, 2000).

There are several ways of calculating the ROI (see Ross, Westerfield and Jaffe, 1993; Levy and Sarnat, 1994; Lumby, 1994; Holmes, 1998). A further variation is the so-called CFROI (Cash-Flow Return On Investment). Since the ROI uses accounting figures it can be distorted by the use of different accounting practices (as for example UK-GAAP or German accounting principles allow a company to use different valuation methods under the same circumstance). The CFROI uses cash flows or operating profits since these figures do not vary very much under different accounting methods (Gabler Wirtschaftslexikon, 2003).

A further static capital budgeting technique is the payback method. It measures how many years it takes the project to amortise, i.e. when the cumulative forecasted cash flow equals the initial outlay (Lumby, 1994; Brealey and Myers, 2000). In order to make a decision as to whether or not to accept a project, the decision maker has to select a cut-off point in time. All projects that have a payback period of equal or less than the cut-of point are accepted. If the projects are mutually exclusive, the one with the shortest payback period is chosen (Lumby, 1994; Bestmann, 1997; Holmes, 1998).

Static methods are considered to be “rules of thumb” (Levy and Sarnat, 1994:157) and have some shortcomings in common. Firstly, they ignore the time value of money (Holmes, 1998, Brealey and Myers, 2000). Earlier cash flows are less risky and money received early can be reinvested somewhere else. Payback and ROI give no hint that one should favour the project with high cash flows in the initial stage (assuming all other factors are the same with both projects). Secondly, cut-off date and minimum ROI are arbitrary choices (Ross, Westerfield and Jaffe, 1993). Using these as an investment rule may lead to under-investment as many long-life projects with large initial outlays might not be undertaken (Holmes, 1998) or unprofitable strategic projects which are necessary for a profitable follow-up investment might be rejected. Finally, they do not take into account the scale of the investment.

Companies solve the problem of time value of money by discounting the cash flows before calculating the payback period or the CFROI. Discounting the cash flows accounts for the time value of money (Brealey and Myers, 2000), but still all other drawbacks are ignored. However, if a project pays back at all, it must have a positive net present value^{[6]} (Shin, 2003)

### 3.2 Discounted Cash Flow Approaches (Dynamic)

Discounted cash flow (DCF) approaches solve the problem of taking into account the time value of money. This is important as with an investment there are present outlays and future benefits. It depends on the possible alternative use one has for the money (Levy and Sarnat, 1994). Clearly, 1 pound (or dollar, euro, etc.) today is worth more than 1 pound in the future. Therefore, cash flows occurring at different times cannot be compared directly but have to be converted to a common point in time; such as different currencies have to be converted to a common currency to be able to judge the value (Lumby, 1994).

One can convert the cash flows to any point in time, but the most sensible is the present day, i.e. the day of the initial outlay. Thus, with a capital investment the question is what are the future cash flows worth today? In other words: what amount of money invested today (PV) at rate r equals the cash flow received in the future (FV) at time t?

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Solving for PV leads to

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where: FV … Future value

PV … Present value

r … Annual interest rate (decimal)

t … Time in years

This is the formula to calculate the present value of a future cash flow as given by Levy and Sarnat (1994). The calculation is called discounting and has to be done for every future cash flow.

Net present value (NPV), internal rate of return (IRR), and Economic Value Added (EVA) use this concept of discounting. For calculating the NPV, all future cash receipts are discounted to the time of the initial investment outlay at an interest rate that reflects the value of the alternative use of the capital. Then these present values are added up and the initial outlay is deducted (Lumby, 1994).

illustration not visible in this excerpt

where: I … Initial outlay

CFi … Cash flow in year i

n … Number of periods with cash flows

r … Annual interest rate (decimal)

The net present value is positive when the sum of the discounted future cash flows is greater than the initial investment outlay. In that case it is worth investing. There is no need of an additional figure such as a cut-off date with which to compare the NPV. If NVP < 0 the company should not invest, since the alternative use of the funds (e.g. investing in the capital market) is preferable to this capital expenditure and firms operate to maximise profit (Levy and Sarnat, 1994).

The internal rate of return (IRR) is the average rate of return which leads to a zero NPV, thereby enabling the decision maker to compare more easily the return of the project with interest rates on the capital market (Ross, Westerfield and Jaffe, 1993; Lumby, 1994; Holmes, 1998). In order to calculate the IRR one has to solve the following equation for r (if necessary by using iteration):

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Having calculated the internal rate of return, this has to be compared with an appropriate cut-off rate in order to come to a decision. Lumby (1994) suggests the market rate of interest as a cut-off rate since this is the opportunity cost. Other authors (e.g. Ross, Westerfield and Jaffe, 1993; Holmes, 1998; Brealey and Myers, 2000) favour the cost of capital because the IRR should be greater than this in order to satisfy the providers of capital.

Economic Value Added, or EVA^{[7]}, has been developed by the consulting firm Stern Stewart & Co. It is the amount by which earnings exceed the required minimum rate of return (Stern Stewart & Co., 2003).

illustration not visible in this excerpt

where Net Sales

– Operating Expenses

– Taxes

= Net Operating Profit After Taxes (NOPAT)

(EVANOMICS, 2003)

One should be aware that for calculating the NOPAT needed for EVA it may be necessary to make up to 164 adjustments to transform a normal income statement into an EVA one (Roztocki, 2003). The calculation shown above can be done for every year of the project’s life. Then the EVAs have to be discounted and added to see what the investment is worth today (the so-called Market Value Added [MVA]). It has been shown by several authors that NPV and EVA/MVA are generally similar (e.g. Day, 1999; Back, 2003; Anon., 2003; Damodaran, 2003a). The differences between NPV and EVA are in regard to their calculation and their further use.

Clearly, DCF techniques have some great advantages. They do not only take into account the time value of money, but furthermore consider all cash flows and are, despite the iteration necessary for IRR, rather easy to calculate (Ross, Westerfield and Jaffe, 1993). Moreover, mutually exclusive projects can be ranked and those with the highest NPV, EVA or IRR, respectively, should be chosen.

On the other hand, they also suffer from one major shortcoming. Exactly as with the static methods before, all future cash flows have to be known with certainty (Holmes, 1998). Due to the fact that market developments, inflation rates, and other factors cannot be known beforehand, this certainty does not exist. Hence, one can surely not compare a high risk investment generating an uncertain return with a low risk investment yielding a certain profit such as a bank deposit or a government bond by using the same discount rate.

### 3.3 Approaches Which Try to Deal With Risk

#### 3.3.1 Adjustments of NPV

New techniques have been proposed in order to account for risk. However, Brealey and Myers (2000) vehemently argue in favour of net present value and vote against authors who say that NPV should be replaced by better tools of investment appraisal. According to the them, adjustments of NPV are capable of dealing with risk.

Since most people dislike risk, i.e. they are risk-averse (Pilbeam, 1998), they expect a rate of return from investments which compensates them for the risk they incur (e.g. Lumby, 1994; Holmes, 1998). Therefore, high-risk projects have to be discounted at a higher discount rate. Using a risk-adjusted discount-rate is common practice in companies which utilize NPV. Levy and Sarnat (1994) discuss several methods of risk adjustment to get a proper discount rate. Brealey and Myers (2000) furthermore argue, that the risk of a project may vary in its various stages (e.g. R&D stage is more risky than production stage). Therefore, one should decide for appropriate discount rates for each stage.

Sensitivity analysis is an approach to determine the factors (such as input prices, labour costs, sales) of an investment project which are of most concern. Principally, there are two ways of doing this. On the one hand, the decision maker can alter each variable by a certain rate (e.g. 20%) and see, how the NPV changes (Holmes, 1998). On the other hand one can check to what extend each item can vary before a positive NPV becomes zero (Lumby 1994; Proctor, 2002). Ross, Westerfield and Jaffe (1993) and Brealey and Myers (2000) refer to this as break-even analysis because it shows how bad the estimates can be before losses are made (negative NPV). If a small error proves critical, Levy and Sarnat (1994) consider the project to be risky.

Adversely, sensitivity analysis focuses on only one variable at a time. It therefore ignores the fact that two or more variables may be related to each other and vary simultaneously. A solution to the problem of interrelated variables is to use simulation models such as Monte Carlo simulation. This method has to be done with a computer because possible net present values are calculated at least some hundred times by simultaneously changing all variables within a certain range (Holmes 1998). One can then plot a graph of the frequency distribution and calculate the expected NPV and variance.

The scenario approach (also: Expected Net Present Value (ENPV)) which also allows for interrelationships between variables (Ross, Westerfield and Jaffe, 1993) is a smaller version of this. The decision maker draws several scenarios (e.g. recession, steady growth, boom). For each scenario he has to estimate the value of each variable which enters NPV and calculate the NPV accordingly. Using the probabilities of the scenarios it is possible to reckon a weighted average of the scenario NPVs – the expected net present value (Holmes, 1998).

All these approaches are valuable in an uncertain world as the decision maker gets a feeling of how uncertainty can influence the outcome. Companies use risk-adjusted discount rates for both, sensitivity analysis and scenario approach. However, a key drawback of these methods is this risk-adjustment. Furthermore, Monte Carlo simulation and scenario approach are based on the statistical assumption that when one does the investment over and over again, the average outcome of all these similar investments will converge to the expected net present value. However, since in most cases a capital expenditure can not be repeated in the same way, the statistical model of an expected value is, according to Holmes (1998), not of much value. Furthermore, with the scenario approach one does not only have to estimate the cash flows of a project but also the probabilities of the possible scenarios.

#### 3.3.2 Decision Tree Analysis (DTA)

While ENPV assumes that the company will be faced with a certain scenario for the remainder of the project’s life, decision tree analysis provides a more realistic picture as the state of economy might change for example (Holmes, 1998). Furthermore, decisions made today can affect one’s options in the future (Brealey and Myers, 2000). Outcomes, therefore, depend on the state of nature (e.g. how does the economy develop) and the decisions made. An example for a decision tree is depicted in figure 2.

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Figure 2: Example of a decision tree (only the part involving alternative A is depicted)

Clearly, DTA has its major advantage in forcing the underlying strategy into the open and making alternative courses of action more transparent (Lumby, 1994; Brealey and Myers, 2000). Furthermore, it reveals the manager’s flexibility during the whole life of the project to make decisions of how the project is going to be continued depending on the outcome of other decisions and the states of nature which occur. On the other hand, there are many figures and lots of sums which become unmanageable when trying to consider all possible outcomes (Holmes, 1998). Brealey and Myers (2000) add that a decision tree can become very complex very quickly and can nevertheless only show a small fraction of possible future outcomes.

#### 3.3.3 Real Options

Decision tree analysis is a rather good method regarding its ability to deal with risk. Often there is no time to waste and decisions have to be made very quickly. But there might be some occasions when a company is able to wait before committing an investment. Suppose that a company can wait and undertake the project in the future. In one year the top management of the company will know what the state of the economy will be and can be certain about future cash flows. This option to wait must have some value since the managers would remain flexible regarding their decision and could make their choice under conditions of perfect certainty. The real options approach (ROA) tries to value this flexibility.

Ross, Westerfield and Jaffe (1993) remark that NPV calculates the value of a project for a certain life time. In practice, a project can be altered in scope or even abandoned or the company can have the opportunity to wait. According to the authors such options should be included in the value of a project. Therefore, the market value of a project consists of its NPV and option value. Brealey and Myers share this opinion and state:

“Books about capital budgeting sometimes create the impression that, once the manager has made an investment decision, there is nothing to do but sit back and watch the cash flows unfold. In practice, companies are constantly modifying their operations. If cash flows are better than anticipated, the project may be expanded; if they are worse, it may be contracted or abandoned altogether. Good managers take account of these options when they value a project.”

(Brealey and Myers, 2000:283)

Of course one can take such options into consideration just by common sense and experience. However, to be objective and to base an investment decision on facts and figures rather than on feelings is a major point of investment appraisals. Therefore, the next chapter will deal with how such options can be valued.

## 4 The Real Options Approach

Before the valuation of real options is considered, reasons are given to illustrate the importance of why this capital budgeting method emerged. Financial options will be used in chapter 4.2 to demonstrate the fundamentals of option valuation. Chapter 4.3 will then deal with some basic real options while applications of real options are considered in chapter 4.4. Subsequently, different opinions about advantages and disadvantages of real options will be contrasted.

### 4.1 Why Use Real Options to Evaluate Capital Investments?

When there are already so many investment appraisal techniques, why develop a further one? To answer this question, one has to have a closer look at investments.

#### 4.1.1 Investment Decisions – Irreversibility, Uncertainty, and Flexibility

Dixit and Pyndick (1994) argue that an investment is partially or completely irreversible. If for example a company builds a plant which can be used to produce product A, and sales for this product turn out to be bad, then the investment is sunk. It cannot be recovered by for example selling the plant because nobody would buy the plant at a price equal to building costs since it is of no use for him either. Furthermore, there will always be uncertainty about the future returns of the investment. The authors state that one can possibly postpone the investment decision and wait for further information about the future, thereby reducing uncertainty.

Managerial flexibility is the key factor for Trigeorgis (1996). He puts forward that traditional approaches to investment appraisal were originally developed to value passive investments in stocks or bonds. However, when valuing capital investments, one should be aware of the possibilities to defer, to alter the scope of, or to abandon a project. DCF tools do not take into account this flexibility and implicitly assume that companies hold real assets passively and ignore the options embedded in investments (Brealey and Myers, 2000).

According to Amram and Kulatilaka (1999), uncertainty creates opportunities and should therefore be welcomed. While NPV requires a high risk-premium for high-risk projects, thereby reducing the project’s NPV, real options do also take into account the positive side of risk since the outcome may also be higher-than-average. With globalisation being only one key factor of today’s economic environment, uncertainty has even increased because markets have moved together, thereby increasing competition.

#### 4.1.2 The Gap Between Quantitative and Qualitative Analysis

A major problem associated with traditional tools of investment appraisal is that all tools require a forecast of future cash flows. Since most methods do only use one single estimate, the question arises whether this forecast is realistic. A solution is to use different scenarios. Nevertheless, the inputs are subjective (Amram and Kulatilaka, 1999).

According to Dixit and Pyndick (1994), a further disadvantage of traditional tools is that they do not value the possibility to delay investment. If for example NPV is used, the calculation only shows whether the investment should be undertaken now or never. As a further example, NPV does also not capture the value of the possibility to switch inputs or outputs.

Trigeorgis (1996) adds that an option can alter the risk of a project (e.g. the government offers the option to buy the results of an R&D project for a fixed price however the outcome will be). He shows that traditional tools underestimate the value of this option. Moreover, traditional techniques are biased against investments with operating and strategic adaptability, since such projects often require a higher initial outlay which makes them less profitable. In real life, managers often prefer investments with high flexibility to opportunities which offer a high return but are less adaptive to changing circumstances.

Thus, investment advice given by traditional tools of investment appraisal is often ignored (Copeland, 2001; Copeland and Howe, 2002). However, the decision then is rather qualitative and based on intuition and experience. Even though this qualitative analysis might work if one person makes the decision, a problem arises when there are several people in a project team who have divergent views or when several hierarchical levels have to agree. Then, a common agreement might not be found. Investment appraisal tools, on the other hand, try to base decisions on quantitative data. The real options approach expresses flexibility in figures and creates a well-founded basis for discussion. Since the models for option valuation were initially developed for financial options, these will be described first.

### 4.2 Financial Options

When opening the finance section of a newspaper, one can see that there are, for example, commodity options, currency options, interest rate options and stock options (Brealey and Myers, 2000). The item to which an option refers is called underlying asset (Hull, 2000). Ross, Westerfield and Jaffe (1993) describe options as a unique financial contract because they give the buyer the right, but not the obligation to do something. In the following, options are explained by means of stock options. Due to the restrictions of this paper, this topic will only briefly be outlined in a way that is sufficient to provide a basis for discussing real options.

#### 4.2.1 Calls and Puts

There are two different basic types of options: calls and puts. Brealey and Myers (2000:586) define, that “a call option gives its owner the right to buy stock at a specified exercise price on or before a specified exercise date.” A put option, on the other hand, is the right to sell stock at a specified price on or before a specified date (Lumby, 1994). All authors furthermore clarify that the owner of an option does not have the obligation to exercise it.

An option can be acquired by paying a so-called option premium to the seller of the option. If the buyer of an option wants to exercise it, the seller of that option has the obligation to fulfil the contract (Uszczapowski, 1999). Therefore, the seller of a call has to deliver shares and the seller of a put has to pay the exercise price if the owners of the options should request it (Brealey and Myers, 2000). Later in this chapter will be explained that a capital investment is similar to acquiring an option. Therefore, the focus will be on buying options while the position of selling an option will not be considered.

A further important distinction has to be drawn between American options and European ones. While an American option can be exercised at any date up to the expiry date, a European option can only be exercised at its expiry date (Brealey and Myers, 2000)^{[8]}.

#### 4.2.2 Estimating the Value of an Option

The variables which have impact on the value of an option are now going to be elucidated. The assumptions made within this chapter are the same as in Hull (2000):

1) There are no transactions costs.

2) All trading profits (net of trading losses) are subject to the same tax rate.

3) Borrowing and lending at the risk-free interest rate is possible.

##### 4.2.2.1 Variables Determining the Price of Options

According to Hull (2000; see also Uszczapowski, 1999), there are six variables which determine the price of an option. The following table (figure 3) shows the influence of an increase in these variables on the option price. A “+” indicates an increase in option value, a “–“ a decrease.

illustration not visible in this excerpt

Figure 3: Summary of the effect of increasing one variable while keeping all others fixed on the price of a stock option (Hull, 2000).

Stock price (S) and exercise price (E)

As the buyer of a call, one has the right to request delivery of the underlying stock for paying the exercise price. Then, one can sell the stock on the stock market. Thus, the payoff of a call option is the amount by which the stock price exceeds the exercise price of the option (S – E). Therefore, the value of a call option must be greater the higher the stock price and the lower the exercise price. A put option is the more valuable the higher the exercise price and the lower the stock price because one can buy stock on the market and sell it for a higher price by exercising the option. The payoff is E - S (Hull, 2000).

Time to expiration (time to maturity; t) and volatility (v)^{[9]}

Considering two American-style options which only differ in their time to expiration, it is obvious that the option with the longer life must have a higher value. Ross, Westerfield and Jaffe (1993) and Hull (2000) state, that the owner of the option with the longer time to maturity has the same rights as the owner of the short-life option, but even more time within which he can exercise these rights. Therefore, the long-life option must be worth at least as much as the short-life one. For options in general^{[10]}, Levy and Sarnat (1994) and Brealey and Myers (2000) reason that the longer the time to expiration, the greater the chance that the option becomes more valuable. Moreover, with increasing volatility the chance that the stock price rises or drops very much also increases. The difference between a stock and an option is, that while the owner of stock participates from gains as well as from losses, a high volatility does not alter the downside risk of options (outcome cannot be below 0) but increases the chance of larger profits (Lumby, 1994).

Risk-free interest rate (i)

The impact of the risk-free interest rate on the price of a call is explained in different ways by different authors. Hull (2000) explains the impact of the interest rate on options with the help of economic theory. A simpler explanation is given by Ross, Westerfield and Jaffe (1993) and Brealey and Myers (2000) who argue that the buyer of a call only has to invest a smaller sum then the buyer of stocks and can, therefore, invest the rest of the money at the risk-free interest rate but participates from upward movements of the underlying. Levy and Sarnat (1994) argue that with an increasing interest rate the present value of the exercise price E/(1+r)t declines which makes a call more and a put less valuable.

Dividends (D)

If a company has paid a dividend, the share price will drop. Therefore, the price of a call will drop while the price of a put increases (Hull, 2000). Additionally, even if the share price rises to its previous level or even higher, only the owner of the share receives a dividend payment while the buyer of a call does not. If a dividend is significantly high, it might be worth for the holder of an American call option to exercise his option before the dividend payment and to receive the dividend (see Uszczapowski, 1999). In summary, dividend payments make a call less and a put more valuable.

In this section, all the variables have already been introduced. Further notations, which will be used are:

C … value of an American call option to buy one share

c … value of an European call option to buy one share

P … value of an American put option to sell one share

p … value of an European put option to sell one share

##### 4.2.2.2 Value of an Option at Expiry Date

Emphasis will now be put on the value of the option when it expires. For the reader who is more interested in details of option valuation the boundaries of the value of an option and the so-called put-call-parity are explained in the appendix.

At maturity, t is zero. A call is only exercised if S > E. The buyer of a put will only make use of his right if E > S. Otherwise, the owners of the call and put respectively will let their options expire. The value of an option at expiry date, therefore, is (Hull, 2000)

illustration not visible in this excerpt

illustration not visible in this excerpt

For both types of options, call and put, this is also called the intrinsic value of the option (Lumby, 1994; Uszczapowski, 1999). The intrinsic value of an option is the lower limit of the option price during the whole life of the option (Brealey and Myers, 2000). This can be said to be true, although Hull (2000) is more accurate in terms of the intrinsic value of a European option before expiry which he says is

Abbildung in dieser Leseprobe nicht enthalten^{[11]}

illustration not visible in this excerpt

because E is only needed at expiry date.

#### 4.2.3 Calculating the Price of an Option Before Expiry Date

The market value of an option before expiry date will always be greater than its intrinsic value. Thus, there must be some additional value. As already said, the greater t and v, the higher the price of an option. Since at maturity t is zero, volatility and time to maturity must have an impact on the “additional” value of an option. For that reason, this value is also called time value (Lumby, 1994; Uszczapowski, 1999).

##### 4.2.3.1 Binomial Option Pricing Model (discrete)

In October 1979, Cox, Ross and Rubinstein published an article called “Option Pricing: A Simplified Approach” in the Journal of Financial Economics. Their approach to value options is based on the assumptions, that there are only two possible outcomes for the price of a stock after a time period t and that no arbitrage^{[12]} opportunity exists. Because of the first assumption, a so-called binomial tree can be constructed which shows the different possible paths the stock price might take during the life of the option (Hull, 2000).

The binomial tree below has only one step and shows on the left hand side the price of a stock at the beginning of time period t (S) as well as the price of a call on this stock (c). The stock price can either move up to a level Su (u>1) or down to Sd (d<1) resulting in an option price of either cu or cd (figure 4).

illustration not visible in this excerpt

Figure 4: One-step binomial tree

The derivation of the binomial option pricing formula as shown below is adapted from Hull (2000) and can be seen in the appendix.

illustration not visible in this excerpt

where Abbildung in dieser Leseprobe nicht enthalten

With this equation an option can be priced according to the binomial option pricing model. Variables cu and cd are the values of the option at maturity when the stock moves up or down respectively. Since S can be observed today, one can draw a scenario containing two possible outcomes of the stock price and then use these figures to calculate u and d. As in the case of stocks the historic volatility is most often known and used for projecting the stock price for the future, u and d are set as follows.

illustration not visible in this excerpt

illustration not visible in this excerpt

The formulas used in this section are valid for European call and put options. In practice, of course, one step is far too less to get a good approximation of an option price. According to Hull (2000), analysts divide the life of an option into 30 or more steps which leads to 230 (about a billion) possible stock price paths. When valuing American options, one has to work backwards node by node, looking at each node whether early exercise is optimal. Thus, Hull (2000) argues, the value of an American option at each node is the greater of the value given by the equation for one step and the payoff from early exercise.

**[...]**

^{[1]} Also referred to as “capital budgeting” or “capital investment appraisal” (Oxford Dictionary of Accounting, 1999).

^{[2]} The terms “investment”, “capital investment”, “capital expenditure” and “investment expenditure” are used interchangeably within this paper.

^{[3]} In 2001, Rolls-Royce invested ₤636 mn (9.5% of its turnover) in R&D (Rolls-Royce, 2002). BP’s investments in that year account for $13.2 bn (7.6% of its turnover) (BP, 2002).

^{[4]} Net cash flow = revenues – costs. Therefore a net cash flow can decrease by either falling revenues, or increasing costs, or both.

^{[5]} A brief example can be found in the appendix.

^{[6]} Net present value is dealt with in chapter 3.2

^{[7]} Copyright © 1999 Stern Stewart & Co. All rights reserved. EVA®, The EVA Company® and FINANSEER® are trademarks of Stern Stewart & Co.

^{[8]} The geographical expressions “American” and “European” do not matter any more regarding to where the options are traded. Both types of options are traded in America as well as Europe and in other parts of the world (Uszczapowski, 1999).

^{[9]} Hull (2000) defines the volatility (v) of a stock price so that v ´ ∆t½ is the standard deviation of the return of the stock in the period of time ∆t.

^{[10]} For a more detailed discussion of the impact of time and volatility on European options see Hull (2000).

^{[11]} Hull uses continuous discounting instead of a discrete discount rate. Therefore (1+r)-t becomes e-rt with e … Euler’s constant (base of natural logarithm).

^{[12]} Riskless profit that can be made by e.g. buying a stock on one market and selling it instantly on another market where it is higher priced. This can be applied in many more cases such as whole portfolios, different interest rates in different countries which are not compensated by exchange rate changes or by different forward rates.

## Details

- Seiten
- 116
- Erscheinungsform
- Originalausgabe
- Jahr
- 2003
- ISBN (eBook)
- 9783832473075
- ISBN (Buch)
- 9783838673073
- Dateigröße
- 1.2 MB
- Sprache
- Englisch
- Katalognummer
- v222605
- Institution / Hochschule
- Fachhochschule Aachen – Wirtschaft
- Note
- 1,0
- Schlagworte
- realoptionen investitionsrechnung investitionsanalyse discounted cash flow controlling