When making a decision to invest capital in a particular project, the investor mostly uses standard financial management techniques as a basis for forecasting and analysis.
These techniques are known to be built on a linear economic model and data flows, which, of course, has little in common with practice. Therefore, basically all economic programs or business plans, as a rule, remain plans on paper, especially in the modern world of fast-moving processes of technology change.
To correct such imbalances in investment (mainly financial) analysis and management, there are a number of techniques that can be used in the formation and implementation of investment projects in conditions of market uncertainty, significant risk and a high degree of unreliability of initial information data.
One of these methods is the use of real options as a tool for insuring (hedging) investors against risks on different stages implementation of the investment project.
The first scientific and practical developments regarding the real options strategy appeared in the 70s of the last century and were published in an article by Myers. This theory was later developed in the Black-Scholes option model and in the works of other economists and financiers of that time.
Concerning classical definition option, then, as is known from the standard definition, an option is a contract or the ability of the buyer (seller) to make a transaction at a pre-agreed price before the expiration of such a contract. Actually, real options came to the industrial sector of the economy directly from financial technologies for managing securities portfolios and working with them on the stock market, where the factor of uncertainty is the main imperative like nowhere else.
Despite the fact that the theory of real options uses the methodology of financial options, there are significant differences between them, which will be presented in this article. There are also different kinds real options that are used at different stages of project development, for example, it can be a postponement, reduction, expansion of investments or a complete abandonment of the project.
The article analyzes an example of a real option to defer investment, which clearly shows the advantage this method over traditional methods of calculating accounting data.
The use of a real option in the simplest sense is the stage-by-stage implementation by the investor (his managers) of a project under conditions of uncertainty with the periodic (discrete) formation of new project conditions until the investment is fully implemented. Actually, initially the entire model for forecasting and analyzing investments was built on assessing future financial flows. Classical management uses well-known methods for calculating Discounted Cash Flows (DCF), calculated using formulas such as NPV (see), IRR (see) and others.
However, as mentioned above, these models not only do not take into account any significant market volatility, but even taking into account inflation (especially over long periods of calculation) distorts the data obtained by these algorithms. In the context of studying the behavior of an investment project in conditions of market turbulence and the lack of complete information, the use of real options is based on the “cost-risk model” (better known to stock traders as the “meme” - the greater the risk, the greater the profitability).
If you look at the graph of the systemic operation of real options, you can see that in the concept of this model, risk is not a threat, but a very real opportunity to increase the value of investment capital. The uncertainty that exists in this case, as the main problem for the investor, is taken into account as a certain reality that needs to be worked with and managed. This is where real options are needed. To make it completely clear how this works in practice, we can give a small example.
Let's pretend that construction company expects to invest $200 million in the construction of a residential complex. Upon completion of construction and commissioning of the development project, it is planned to receive an income of 225 million dollars.
There are two options for the development of events with the same degree of probability (0.5)+(0.5) or 50/50. The first involves an increase in cost to 270 million dollars, the second, negative, with the receipt of only 180 million. dollars. Also, as an option, the company has the opportunity to postpone construction for a period of one year.
Using a standard calculation using the DCF method with a discount rate (for example, the cost of a loan) of 10%, we obtain the cost of the project at the initial stage:
According to the rules of traditional investment analysis, an investment project can be accepted if the NPV is positive. The DCF method assumes that the project plan is unchanged and the project cost is determined for the entire investment period. However, in reality, if a company has a patent or license for new technology, then over time the present value of cash flows can change from being negative to positive.
Let’s say the company is satisfied with the return on the project at this stage. Now consider the positive and negative development of the project with equal probability.
Expected DCF for a positive forecast:
Expected DCF for a negative forecast:
Thus, after the first year, if the positive forecast is confirmed, the company will invest in the project; if not, the project will be terminated. The decision to delay the project for one year will ultimately net the company $21 million, while the decision to invest immediately using the DCF method will net the company only $4 million.
Thus, the cost of a call option is equal to the difference between the cost with and without the possibility of changing the project (21-4=17 million). It is also worth noting here that the DCF and real options methods perceive information differently. While DCF bases decisions on today's expectations of future information, real options pricing allows potential decisions to be made based on incoming information.
Despite the fact that there is much in common between real and exchange-traded options, the specifics of the former are related to the characteristics of investments in industrial business assets, which have their own differences.
In general, these differences can be summarized for clarity in one table:
However, technologies for accounting for future uncertainty used in financial markets have found wide application in economics, and there are several types of real options, which will be discussed below.
Main types of real options and features of their practical use
On this moment Investment practice has developed and applied several types of real options:
- Deferred transaction option, or option to defer. An option providing for deferment of the implementation of an investment project. For example, deferment of a transaction for the sale of an enterprise in anticipation of a change in value land plot where the business is located. Most often used in projects related to land use - agriculture, development projects, mining, etc.
- Sequential investment option (time-to-build option).
Organizing investment in the form of a certain sequence of projects allows you to stop the business if unfavorable information is received. Each investment stage is considered as a separate option, consisting of subsequent options and having total cost. It makes sense to use it in high-tech and venture investment projects, where each step requires its own separate analysis.
- Option to alter operation scale.
When particularly favorable market conditions occur, management may expand production or increase the use of resources. And, on the contrary, if market conditions worsen, the option of reducing the volume of operations is possible. In the worst case scenario, production may cease. They are most widespread in areas of the consumer sector - food and industrial retail, commercial real estate.
- Option to abandon operations.
If market conditions quickly deteriorate, management may cease current operations and sell assets in parts or the entire operating business as a whole. They are used in capital-intensive areas of industry, financial investments (portfolio management).
- Option to switch.
If the level of demand and prices for goods changes, management can flexibly change the production program or rearrange production to produce new goods. Mainly used in the consumer sector of the economy - consumer electronics, furniture manufacturing, household chemicals, i.e. where consumer preferences and fashion change rapidly.
- Growth options. For example, investments have been made in business infrastructure (purchase of oil reserves, a plot of land, R&D), as a result of which it becomes possible to start new projects, begin production of goods, and extract oil. Areas of application: industries with infrastructure (mining, R&D, high technology, computers). Foreign operations. Takeovers and acquisitions.
In addition to the listed main types of real options, there is the practice of combining or combining real options both with each other and with financial instruments for hedging risks (futures contracts and other derivative instruments).
Despite the widespread use by organizations of such traditional tools for economic analysis of the efficiency of capital investments as the calculation of net present value (MPV), internal rate of return (IRR) and payback periods, they are often mercilessly criticized for being static. All these methods take into account only tangible, material factors and ignore intangible ones: future competitive advantages, potential opportunities and flexibility in management. Relatively recently, a new method of investment planning has emerged - real options analysis. Its proponents argue that using the methodology used to value financial options, it is possible to calculate the portion of a project's value that is created through active management and strategic interaction.
Most books on real options tend to begin with the trivial observation that one of the main characteristics of the new business environment is uncertainty. Honestly, this is where you can find confirmation of the fallacy DCF in in the sense that “analysts, in an effort to justify their intuition, often manipulate the valuation process by forecasting unrealistic cash flows” (Amram, 1999). These books, moreover, openly acknowledge the fact that the pace real life usually does not fit within the intended planning horizon, as a result of which the rationale for investment decisions turns into an endless race. It is also argued that value measurement and its methodology are often viewed and presented differently in the absence of a full understanding and commitment to the concept of shareholder value. As an introduction, such books most often offer quite interesting examples real world uncertainties. One of the favorite examples is the long period of development of new products and low level success characteristic of the research, development and production of drugs. Another example is the possibility of a sharp increase in selling prices in dynamic markets without a corresponding increase in the prices of factors of production - although in practice the opposite happens. In the new century, unexpected changes in technology, prices, demand patterns and the nature of competition are inherent in almost every business.
There is no doubt that management faces uncertainty, especially when it comes to the results of research and development and the iterative process of gathering information as the project progresses.
By analogy with the pricing policy for financial options, we can conclude that as the uncertainty of project results increases, the cost of real options, that is, opportunities for managerial flexibility in decision making, also increases. A financial option is a contract that typically gives the right (but not the obligation) to buy or sell an asset at a pre-agreed price within a specified period (or at a specific point in time). The very word “option” (from English. option) means "power, right, or freedom of choice." However, R&D managers face uncertainty not only about project outcomes, but also about project budgets, product characteristics, market demands, and schedules. Chief real options expert Trigeorgis (Trigeorgis, 1993) identifies five main types of options: deferment, refusal, expansion, reduction and transition (for example, to another energy carrier or source of energy supply). To these we can add one more, sixth, type - improvement. But a real option is still easier to describe than to give it an exact definition.
From a business valuation point of view, we are interested in the following types of options.
Option to defer investment, for example, in the case of a choice between immediate expansion of production (and possible losses from a drop in demand) and delayed expansion (and possible lost profits).
Growth option for example, when deciding to invest capital to enter a new market.
Flexibility option for example, when choosing between the construction of one central facility and the construction of two facilities in different locations.
Exit option for example, when deciding to develop a new product in a volatile market.
Training option for example, with gradual investments in advertising.
The flexibility of project management creates significant value in options, which help enable incremental innovation with little variation in product performance and customer requirements. Management is expected to regularly conduct formal reviews to obtain information about all uncertainties. The concept of real options can be viewed as an optimization problem under conditions of uncertainty characteristic of a real asset (project, firm, land, etc.), taking into account available opportunities (options). When deciding what level of funding is most appropriate and which projects will bring the most benefit, a company faces a number of challenges that make accurate quantification very difficult.
Here are some of them:
- uncertainty of markets and technology success;
- uncertainty associated with the choice of time frame;
- the amount of capital costs required to organize mass production;
- Management's ability to respond in a timely manner to changes during the research and development process.
Unable to control all these aspects sufficiently to accurately estimate the value of their research and development portfolio, many companies simply abandon the most daring, innovative and intensive research projects in favor of more conservative ones, which long term may result in large losses.
However, analyzing investments in research and development does not necessarily have to be overly complex. According to real options theory, traditional valuation approaches can be improved by:
- understanding the stages of investment from research to the organization of mass production and determining where the main capital expenses arise during the project implementation;
- understanding the key factors and uncertainties (or risks) that affect value;
- formation of options at each stage in order to manage risks and realize opportunities, such as:
- alternative solutions to meet the same commercial or technical needs;
- approaches that will benefit from better than predicted outcomes;
- options to refuse or withdraw from the project.
To get an idea of what real options value the market assigns to a particular company, you first need to calculate the value of the business based on discounted cash flow. It is then compared with the market price. The greater the gap between the market price and the discounted cash flow, the more the real options held by the company are valued by the market.
In the literature on this topic, two main trends can be found. First, flexibility always seems to add value to any capital investment. Secondly, the preferred situation is when options are open. So, if the outgoing cash flow is characterized by extreme uncertainty, then it would be very reckless for a company that does not have production facilities to invest capital in the project. The reason is that since, for investment purposes, an option is available at a certain point in time in the future—a call option—it is best to hold it in stock but not exercise it (that is, ownership of the option is valued more than its implementation). Conversely, but for the same reason, companies that already have production capacity are best off retaining it and not using a put option to sell or abandon production. Thus, the desirability of owning production capacity depends on whether it is owned by the company or not (in the absence of a perfect market for production capacity, where the choice is obvious). Real options valuation moves from careful valuation of assets and the need to make the right forecasts for management to the precise determination of potential reactions to a range of possible future conditions.
In financial terms, options mean the right (but not the obligation) to buy or sell securities of a company at a predetermined price at a certain point in time or before the end of a certain period. The main difference between real options is the non-financial nature of the acquired asset. It is not at all difficult to understand and imagine the so-called real option. The term "real option" was coined by Stuart Myers ( Myers, 1977). The theory of real options expands the concept of financial options (in particular, call options) and extends it to the sphere of economic analysis of the effectiveness of investments under conditions of uncertainty and the valuation of corporate assets or entire corporations. This is a continuation of the risk analysis within DCF. Real options approaches seek to bring the intellectual rigor and precision of option pricing models to the realm of valuation of non-financial assets and liabilities. Rather than viewing an asset or project as a single set of expected cash flows, it is represented as a series of complex options that, if exercised, give rise to other options and cash flows. This is quite a difficult concept to explain in a nutshell.
According to scientists, theoretically, any type of investment flexibility in the real world can be assessed using option pricing techniques borrowed from financial markets and commodity exchanges. Three methods are useful for this purpose:
- call option pricing model;
- put option pricing model;
- model for valuing stock options that pay dividends.
Advantages of the real options method
Proponents of this approach argue that the application of option pricing principles to non-financial assets overcomes the shortcomings of the traditional method of reduction to present value; This is especially true for the subjectivity of determining risk-adjusted discount rates. They argue that focusing on the assessment of flexibility provides a more appropriate evaluation criterion for the implementation of those projects that would otherwise appear to be unprofitable from an economic point of view. The real options method is consistent with the calculation of either fair value or enterprise-specific value. The difference, as with the more familiar present value, lies in the choice of assumptions. If a real option is universal, that is, available to any market participant, then its inclusion in the calculations corresponds to fair value. And if a real option is specific to a particular company, then the indicator that includes this option does not reflect its fair value, but can be a fairly reliable basis for determining its present value.
Advocates of the real options method have repeatedly made loud claims about its merits. Real options assess the value of managerial flexibility in making decisions in response to unexpected market changes. The real options method represents the most modern and advanced approach to the valuation and management of strategic investments. Real options analysis is particularly useful in estimating the value of intangible assets that are under development and whose commercial viability cannot be demonstrated. The real options method uses financial options theory to quantify the value of management flexibility in a world of uncertainty. When used as a conceptual tool, it allows management to characterize and communicate the strategic value of an investment project to all stakeholders. The Company creates shareholder value through the identification, management and exercise of real options associated with its investment portfolio.
Perhaps the most promising direction in the development of intangible asset valuation methodology is the concept of real options, as evidenced by the abundance of literature on the subject. Using financial options theory, it is possible to determine the cost of managerial flexibility under conditions of complete uncertainty. And the most impressive statement: the real options method allows corporate management to turn uncertainty into their favor and benefit from it, as well as limit the risk of a decline in the company's stock price. There is truly no limit to the wonders that real options can do. However, evidence of their successful practical application is far from impressive.
First mover and beta advantage
In practice, the one who gets up early does not always win - just look at the fairly typical history of video recording formats VHS And Betamax. Company format Sony Betamax lost VHS because he could not provide the same length of recording, and also because of moral and ethical considerations of management Sony. Company operating system Apple Computer gave the palm Windows due to short-sighted pricing policy. So it is reasonable to assume that value comes from the abundance and prevalence of a product, not from its scarcity. Even a completely free product distribution in short term can be considered a good start, if, of course, the company can afford it. Look at the browser Internet Explorer(not taking into account legal proceedings), programs Adobe Acrobat Reader, Sun Java or McFee Anti-Virus. It's extremely rare for a software manufacturer to not release a free beta version of their product in one form or another. The task comes down to creating new programs and constantly improving and updating them: inventing goods and services faster than they turn into consumer goods. Meanwhile, although the programs themselves may be free, technical assistance will not be cheap. Company Cygnus Solutions earned $20 million a year by supporting free software Unix. Apache is a free web server, and the company C2Net provides support and offers paid updates. On the other hand, a company may experience a rapid rise, climbing to the very top of the world for a short period of time, such as Nintendo but stay there only until other players, in this case Sony And Sega, they won't push her out of there. And everything that happened during the period of complete collapse in the field of assessing the value of Internet businesses does not at all prove the inconsistency of this comprehensive analysis.
Competitive advantage comes from constant innovation, flexibility and excellence. The cost of new business models that focus on the creation and development of options with high growth potential is extremely high. At least that's how it used to be. Mauboussin from the company Credit Suisse named Amazon.com"a smorgasbord of options" and identified four ways that real options have helped a company increase its value. Firstly, Amazon exercised diversification options, using its positions in key markets to launch similar projects. Second, it exercised its options to increase scale by expanding its distribution network to increase sales of existing units and new projects. Third, training options have emerged from marketing acquisitions, which may provide a platform for future value creation. Finally, Amazon.com invested in a number of young promising companies, the value of which, when assessed using the real options method, also turned out to be at a fairly high level.
How does the real options method work?
What do real options and information technology investing have in common?
Approaches to investment valuation, including the net present value method (NPV), often criticized for their inability to model uncertainty; this factor takes on particular significance in the context of making decisions about investments in information technology. Even if the net present value of an investment in IT is negative (which is usually taken as a reason not to invest in the project), these investments may still generate potentially valuable options that, under favorable circumstances (that is, unless technical risk or other sources of uncertainty reach critical levels), will make the initial investment worthwhile. The logic of real options also provides for the right of corporations to defer investment decisions until uncertainty is resolved, as opposed to immediate and possibly irreversible investments that may, under adverse circumstances, turn out to be unprofitable.
The real options method approaches the evaluation of research and development projects differently than DCF. Rather than struggling with myriad risks and uncertainties, a clear framework is developed that outlines the chronological sequence of capital investment decisions that will need to be made during the research and development process and identifies new opportunities that will need to be carefully explored before How to take on your next major investment commitment.
In this way, the company is able to determine a sequence of capital management decisions that will be made as the process progresses, rather than at the beginning, when many key factors are still unknown. While planning for future decisions and developing a decision tree, the key cost drivers and risks at each stage of the project should be identified.
For example, real options available to a company may include alternative approaches to achieving intended business and technical objectives, the ability to benefit from performance beyond those planned, and options to delay or exit a project.
In many cases, achieving the desired result will be cheaper in creating a joint venture than in developing the required technology on our own. This is because any competitive advantage gained through a new technology lasts only until another, better technology comes along. Another component of value that is often overlooked in traditional valuation approaches is the value of the knowledge accumulated during the research and development process. possible size and market share, as well as the flexibility of the company's response. This accumulated information has real value, even if the only possible use of it is the option to withdraw from the research project. However, such knowledge often forms the basis of the entire production strategy, since the relative benefits of licensing the technology, developing it in-house and further commercial exploitation depend on the final size of the market and the associated uncertainty. The cost of such training is not usually taken into account when valuing a business, but it can and should be calculated and included in the calculation of the cost of a research and development project. If the future of an organization depends on its scientific developments, then it is extremely important that the business valuation methodology used by the company reflects all the main components of the value that its scientific developments have.
Valuation of real options
The Black-Scholes model is most often associated with the valuation of options on financial securities that are publicly traded on an exchange. The same model is quite applicable to assessment IT-options, although, as noted in the literature on IT-topic, it is necessary to remember the assumptions that underlie the model.
The following variables are needed to calculate the value of a financial option using the Black-Scholes formula (similar variables needed to estimate the value of a real option are given in parentheses).
The Black-Scholes formula is as follows:
Where N(.)= probabilities from the cumulative normal distribution for weighting values V, X.
V T - X is the final value of the call option.
V T - e -τ f T X is the current value of the buy option;
(7.2)
(7.3)
Exercise of a buy option only in case of winning.
In practice, the real options method is extremely difficult to use, but such a possibility cannot be excluded. A number of case study articles have been published in the press exploring this issue, detailing how the option value of information technology investments should be valued and interpreted.
Cost of subsequent opportunities
Let's consider next example. By investment in equipment Mark I a negative net present value of $46 million is projected at an annual discount rate of 20%.
- However, investments in Mark I provide an opportunity (option) to invest in equipment Mark II and double in scale in three years.
Investment in equipment Mark II will cost $900 million; present value of projected cash flows from Mark II in three years is equal to $800 million (correspondingly, $463 million today). Thus,
Analysis DCF implies passive ownership of real company assets. Proponents of the real options method argue that DCF does not take into account cost management. Inclusion in analysis DCF Option pricing takes into account the cost of alternative investment opportunities.
- Technology A involves the use of custom computer-controlled equipment to produce parts complex shape, which are necessary for a new type of engine in large quantities and with low costs. But if the new engine does not find its buyer, then this equipment will be completely useless.
- Technology B involves the use of standard machines. Labor costs will be much higher, but the equipment can be sold or upgraded if the new engine type does not sell.
Option to Refuse
Technology B is similar to owning a put option.
Timing option
Let’s assume that the project does not belong to the “now or never” category, that is, you can invest money in it immediately, or you can wait. If the project is guaranteed to succeed, then waiting means losing or delaying the first positive cash flows in the near future. If the project is unsuccessful, then waiting can prevent a serious mistake.
The opportunity to invest in a project with a positive net present value is the equivalent of a call option. Optimal investment means exercising this option at the most favorable moment (this option is called an American option in the field of derivatives).
An option to buy shares that pay dividends.
Current cost = $200 million. If future demand is high, the cost of the project increases to $250 million, and if demand is low, it drops to $160 million.
If you wait to invest, you'll lose first-year cash flow ($16 million or $25 million), but you'll avoid the big mistake of investing $180 million in a project that may only cost $160 million in the future.
Buy option (call option). The cost if the outcome is favorable will be $70 million in next year; if unfavorable - 0; Today the call option is worth $22.9 million, which exceeds the $20 million gain from immediate exercise.
Option cost calculation
- American call option - no dividends. If not exercised before maturity, it can be treated as a European call option.
- European put option - no dividends. The value of a put option = the value of the call option - the value of the underlying financial instrument + the current value of the strike price.
- American put option - no dividends. Exercising an American put option before expiration to reinvest the strike price can sometimes make sense. Suppose that, immediately after you purchased an American put option, the price of the underlying financial instrument fell to zero. In such a case, it is undoubtedly better to exercise the put option immediately; It is extremely difficult to estimate its value; the Black-Scholes formula is not applicable in this case.
- European option to buy shares on which dividends are paid; it is necessary to reduce the price of shares in the Black-Scholes formula by the current amount of dividends paid before the option expires, since some part of today's share price is due to their share.
- An American option to buy shares that pay dividends. If the dividend is large enough, you may want to purchase the option and exercise it just before the date on which the stock becomes ineligible.
In practice, very complex real options are most often encountered. They come in two types: call options (call options) and put options (put options). A call option implies the right, but not the obligation, to purchase an asset at fixed price(exercise price) on a specific date (European call option) or before the expiration of a specific date (American call option). Examples of real buy options are an option to develop a construction project at a certain point in the future (American option) or an option to expand production before a competitor decides to do so (American option). A put option represents the right, but not the obligation, to sell an asset at a fixed price at a future date; they also come in American and European varieties. Examples of (American) put options: option to abandon a field, option to manufacture products under a contract. But in general they are much less common than real call options. Real European options are very rare and are perhaps more dependent on financial and accounting aspects than purely commercial considerations.
And this is a big problem, because the Black-Scholes formula cannot be used to estimate the value of options on stocks that pay dividends. The Black-Scholes model is really only suitable for valuing the European call option. However, it can be easily proven that early exercise of an American option to purchase shares that do not pay dividends is not advisable. Therefore, the Black-Scholes formula can be used to value an American call option on a dividend-free stock. This model can also be used to value a European put option. There is a well-known relationship between the value of call and put options, which is based on the fact that the payoff at the time of expiration of holding a call option is similar to the payoff from holding the stock and a put option combined at an exercise price equal to the price of the call option. Both allow the investor to hedge against a fall in the stock price and benefit from the difference between the stock price and the strike price if the stock price rises. The only difference is that an options-only strategy requires less investment because the strike price will not have to be paid until the option expires.
Thus, the difference between the two alternatives is equal to the current strike price.
Therefore we have:
The value of the call option + the current value of the strike price = the value of the put option + the stock price, and by rearrangement we get:
Put option value = call option value - stock price + current strike price.
This is sometimes also called call and put option parity. This model is useful in estimating the value of a European put option (using either the Black-Scholes formula or binomial models), but for American put options it can only provide an approximate figure. The reason is that under certain circumstances, exercising the option if it wins will be justified, and in fact the value of an American put option cannot be less than the value of a European put option.
The Black-Scholes model is not suitable for valuing an American option on dividend-paying stocks, since, provided the dividends are large enough, early exercise of the option with a gain may be quite justified. However, under such circumstances, the binomial model can be applied, if, of course, the size of dividend payments is known. When we're talking about about investment projects, real options are most often found, similar to an American option on stocks that pay dividends, because their implementation is possible at any time, and also because the projects generate intermediate cash flows similar to dividend payments.
When valuing real options, the general principle is that flexibility always increases the value of a project. Moreover, the relationship between them is straightforward, despite possible difficulties options valuation procedures. Theoretically, the value of an investment with an option can be broken down into two components: the value of the investment without any alternative options and the value of the option. According to real options theory, the value of an option can be estimated using one or more option pricing models, and the principles of DCF-analysis.
For example, how can you use the real options method to value an asset if its value depends on the risk of changes in the price of natural gas? First of all, it is necessary to determine and, if necessary, build a model of the behavior of market prices of futures contracts for natural gas. The model is created to provide, at any point in time, data on the probability distribution of gas prices in this moment taking into account gas prices for the previous period. The cash flow is then estimated based on the price of natural gas futures contracts, with a risk-adjusted set of probabilities derived from the current or historical volatility data. This cash flow is then discounted at the risk-free rate.
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Share price S- present value at a rate of 12% of projected cash flows from the moment the project is launched, excluding costs for launching the project and for research and development | |
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Execution price (cost of launching the project) | |
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Time until expiration t | |
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Volatility | |
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Black-Scholes call option value - current value (at 6%) of R&D costs ($119 million - $98 million) |
In traditional DCF-analysis, all cash flows are discounted at a rate of 12%, while in the Black-Scholes model, costs for research and development, as well as for launching a project (if it is launched) are discounted at a risk-free rate (6%). And the difference, by the way, is $27 million. The Black-Scholes approach undoubtedly seems more adequate, since it recognizes the fact that the costs of research, development and launch of the project are not associated with risk, and therefore there is no need to discount them at higher rate.
Example: extension option
Let's say a corporation Uberqualitat Hotel Group, which is engaged in the hotel business, has the opportunity to acquire a closed joint stock company Quality Hotels Ltd, located in the UK. Company value determined based on DCF using free cash flow analysis, was $95 million. Unfortunately, management Quality Hotels Ltd insists on a sale price of $100 million. The situation is complicated by the fact that the property Quality Hotels Ltd There are several valuable areas of land in Scotland and Wales that could be exploited if the current favorable economic conditions continue. However, if there is a downturn in business activity in the British economy, then their development is unlikely to be advisable. The optimal moment for the development of a hotel business in these areas will come in exactly five years (this is a controversial statement in itself, but for the sake of our example, let’s assume that it is so), and the cost of development will reach $120 million; Based on projected cash flows, the present value of cash flows (discounted over a five-year term) would be only $100 million, indicating that the investment was not profitable. Therefore, none of the associated cash flows were included in the present value estimate. However, due to market uncertainty, the standard deviation in the value of these projected cash flows is quite significant—about 60% per year.
Therefore, it is quite possible that the purchase Quality Hotels Ltd may result in access to a market with greater growth potential. But how to estimate the value of an option to buy this company?
We will need additional information about the cost of capital for the new business (say 23% per year) and the risk-free interest rate - let's say it is 10% per year on a continuously compounded basis. Since in in this example the decision to start construction will be made no earlier than five years later, then the option being valued is essentially a European call option. As for the input parameters for calculating the value of the option, the exercise price is $120 million, and the today's value of the assets that underlie the option is $100 million; when discounted for five years at a rate of 23%, we obtain their current value in the amount of $35.52 million.
In the original formula S means stock price, X— the execution price, and e— discount factor based on continuously compounded interest on t years at the risk-free rate, where t— the number of years until the option expires. In our case, all variables remain unchanged, with the exception of S, - this parameter means the current value of the acquired asset.
Thus, we have established that, by agreeing to a deal, Uberqualitat AG receives an option with an approximate value of $11.39 million. After adding to the present value of the cash flows from existing business we get the final cost Quality Hotels Ltd, equal to $106.21 million, and then the acquisition price of $100 million becomes much more attractive.
In reality, additional complications are likely to arise. For example, approval of an expansion project may in turn lead to options for further expansion, say new hotels. On the other hand, if the corporate creditworthiness as a whole is limited, this may prevent other options from being created and negatively impact total value.
Option to abandon investment
Returning to the example with Quality Hotels Ltd, Let's assume that the company has an almost completed hotel property in Cornwall as part of its assets. Given the current state of the Cornish economy and the recently published pessimistic forecasts for its development, there is uncertainty surrounding the value of this hotel and its long-term viability. The present value of the hotel's expected cash flows is estimated at $5 million, but management Quality Hotels Ltd guarantees the buyback of the hotel for $4 million in a year if the new owners so desire. Estimated Uberqualitat AG, The standard deviation of the hotel's net present value next year will be 30%. The risk-free rate is again set at 10% per year.
Thus, one can imagine that Uberqualitat AG has an option to sell an asset with a current value of $5 million and an exercise price of $4 million. Since the opportunity to exercise the option is one-time, the option can be considered European and valued using the Black-Scholes model, as well as the parity of put and call options, which is discussed mentioned above. To do this, you need to take the following steps: 1) evaluate the buy option at the same price and exercise date as the sell option; 2) calculate the current (discounted) value of the execution price; 3) calculate the value as the cost of the call option - stock price + current value of the exercise price. As a result of applying this model, we obtain the value of the call option equal to $1.472 million.
One of the problems associated with valuing divestment options is that option pricing models are built on the assumption that reliable information about the exercise price is available. In the example discussed above, this was the case, but a more realistic situation is when the value of the option to abandon the asset depends primarily on the market conditions prevailing at the time of the transaction.
Option to defer investment
Let's say a company is considering a $4 million project and its final outcome depends on demand for the product during the first year. Currently, it is extremely difficult to predict demand, since it directly depends on the ability to produce a competing product, which, in turn, depends on the success of a new, never-before-tested technology. However, all this uncertainty will be completely eliminated by the end of the first year. If demand during the first year is high, at $600 thousand in real terms, then demand from the second year to infinity is also expected to be at $600 thousand (again in real terms and very simplified). We also assume that the appropriate real discount rate is 10%, so that the value of this cash flow over an infinite period will be $6 million. If, on the contrary, demand is low at the end of the first year ($300 thousand), then this will remain the case forever , and the current cost of the project will be $3 million. So, at the end of the first year, the return will be either high ($6 million + in the first year $600 thousand = $6.6 million) or low ($3 million + in the first year $300 thousand = $3.3 million). For the sake of simplicity, let us assume that both scenarios have an equal probability of occurrence and that demand uncertainty is unsystematic. It follows that the required discount rate remains at the same level of 10%, and the present value is somewhere in the middle, that is, $4.5 million.
Using the traditional approach DCF We calculate the net present value: $4.5 million - $4 million (capital costs) = $500 thousand. So the project can be launched immediately.
But what if we instead waited until the end of the first year before making an investment decision? In the language of real options, we retain our option to buy this project. This option is worth either $6 million - $4 million = $2 million in the case of high demand, or nothing in the case of low demand (at the limit). The underlying asset of the option, the project, is worth either $6.6 million or $3.3 million at the end of the first year, including the project's cash flow, which is similar to a stock dividend. This again depends on demand. To calculate the delta, you can use the binomial option pricing model.
Let's say the risk-free rate is 5%. We can insure our portfolio against a possible price drop if we write down 1 / 0.6061 = 1.65 buy options on the project. Since the guaranteed return will be no less than $3.3 million, the value of the call option, WITH, can be found from the following equation:
(4.5 million - 1.65 C) × 1.05 = 3.3 million
Solving the equation yields an option value of $0.8225 million if retained, or just $0.5 million (net present value) if exercised immediately. In other words, based on the information available, deferring the investment is a more valuable option than starting the project immediately. Or, to put it another way, the company will be worth $0.3225 million more due to having the option to defer the investment.
This option can also be valued using the risk neutral method. The synthetic probability of an increase in value is 0.4318 compared to the real probability of 0.5. Based on the synthetic probability, the expected payoff from the option is calculated, which is then discounted at the risk-free rate. The resulting option value remains the same ($0.832 25 million). One extremely important assumption to keep in mind is that the value of any of the potential cash flows is assumed to be independent of delays in the project. In some cases this assumption is quite acceptable. For example, this approach to option pricing is used in the valuation of fields and oil wells. Taking into account the volatility of prices for these products, deferring investments in this case provides a certain advantage. However, companies that compete on the basis of inherent technological advantages are unlikely to benefit from the ability to defer investment, which would then give competitors a greater chance of catching up and overtaking them. So, when evaluating a deferment option, one should take into account the possible loss of competitive advantage as a result of deferring the investment to a later date.
Business decisions based on real options theory
Examples of such solutions include: merger Time Warner And AOL in order to expand the distribution network through the online environment; portal solution Yahoo! on developing the online auction business; purchase eBay companies such as Half.com And Butterfield & Butterfield. “This was a strategic move for each of these companies to drive value,” said one analyst. Real options are attracting the attention of both company executives and financial advisors, but many still have no idea about them. Judging by the short list of business decisions above, this may even be for the best.
Company project PwC entitled "Assessment Toolkit" high technology» ( High-Tech Toolkit), which is almost unheard of now, unlike in the late 1990s, is a practical application of real options theory in the valuation of high-tech companies in the early stages of development. PwC divides its toolkit into three parts. The first is market analysis, which includes technology adoption and life cycle, market definition and segmentation, models of competitive market dynamics, models of customer purchasing decisions, and scenario analysis. Further specialists PwC offer clients a specialized financial model of the product, including a highly detailed cash flow model, which, thirdly, provides for an assessment of flexibility (real options) taking into account the results of market analysis. “The life cycle of a technology consists of four stages: research, invention, innovation, diffusion and higher development. Each of them is extremely important. At the heart of our approach is the key premise that each stage can be viewed as a real option to purchase the next stage... [or] as an offer of an option to abandon the next stage of development and recover all or part of the costs by receiving the salvage value of the assets in that case , if the product's prospects turn out to be disappointing."
Company tools PwC was intended to help technology companies determine their value. First, “a multidisciplinary team was assembled that included specialists in market valuation and analysis, technology research and financial and legal due diligence, operations and strategy assessment, cash flow modeling and decision analysis methods.” By studying as closely as possible the potential market for a high-tech product, they sought to explore those factors that most influence a company's ability to create value, develop and bring new products to market. They started with market analysis: technology adoption and life cycle, market definition and segmentation, models of competitive market dynamics, purchasing decision models, evaluation of operations and strategy, scenario analysis. Then came the turn of the second stage, which specialists PwC named Venture Kit, which included specialized financial model, detailed cash flow model, scenario builder and automated sensitivity analysis. Experts tried to answer a number of interrelated questions: how can an early-stage technology company create a viable business strategy? How reliable and durable will it be? How much is the company itself worth? And what is its funding requirement? They offered their tools to companies that had developed or were looking to acquire new technology to help them fully realize the potential for value creation from such investments. In addition, the company PwC provided its clients from the technology, information, communications and venture capital sectors with services in the areas of investment decision making, strategy assessment, investment audit, IPO, providing financing for venture investors, mergers and acquisitions, supporting business sale transactions ( Michael Churchil, PwC Sydney).
A careful study of the value created at each stage of the mass production process, according to PwC gives companies amazingly deep insight into the sources of value through their research and development. Specialists PwC also stated that they observed that this process allowed companies to “create more dynamic strategies to continuously maximize market value research and development,” whatever that means. Independent experts argue that integrating options thinking into the strategic management of information technology is an emerging area of research with the goal of identifying management techniques for controlling the value of options over time, including the ability to forgo options that are unlikely to provide positive future performance. Is this binomial option pricing method just another application of decision tree analysis? Yes, but with one caveat: option pricing theory is a very compact and powerful way to construct certain types of decision trees (Figure 7.1).
Company PwC stated that its tools can radically improve traditional DCF- analysis when forecasting company revenues in the medium term. However, the question remains unanswered about how closely a company's revenue and its valuation are interconnected.
A decision tree for a simplified two-phase project where a choice must be made between developing the technology in-house and an alternative approach (for example, a joint venture or a license). In practice, there are usually many other stages, including prototype development and testing, and the uncertainty of profit and success, in turn, depends on a host of other uncertainties.
Among the relatively new tools for business valuation, first of all, is the method of real options (hereinafter the abbreviation ROV method will be used from English - “Real Options Valuation”), proposed by a number of foreign authors in the mid-1980s, and according to certain species options already in 1977-1978, and has found practical application since the mid-1990s.
The most important feature of this method is its compliance with the rapidly changing economic conditions in which enterprises operate. At present, the ROV method has not yet been fully recognized; active discussions continue about the possibilities and limits of its application. Nevertheless, the attention to the method shown by specialists in the field of assessment in various countries allows us to conclude that its study is an urgent task in Russia.
Since the publication of Fisher Black and Myron Scholes's article "Option Pricing and Corporate Obligations" in 1973, option pricing has often been used by investors, stockbrokers, and others to calculate the theoretical value of stock options, interest rate options, and other types of options common throughout the world. . The idea of option pricing was preceded by the determination of the adjusted theoretical option price, in order to determine whether the option was overvalued or undervalued in the market. Only in the last few years has the option method become recognized as an alternative to standard net present value calculations in determining the value of investment opportunities in the real market as a tool for determining the value of companies and projects.
A financial option gives the owner the right to buy (call option) or sell (put option) underlying certain assets (stock, bond, gold, etc.) at a certain price during a certain period of time, but not the obligation to do so. For these rights, the owner pays a premium (option price).
The precursor to real options is the idea of financial options. Consider the example of a company that determines the prospects of a project that meets the required investment today and certain requirements in 6 months. If the opportunities look promising (promising), i.e. If the project's expected net present value is greater than the option value, then the project moves forward. If the project does not look promising, that is, the net present value of the project is lower than the option price, the option is not used, and losses occur - the option price, a premium, is paid. Determining the value of a real option, which involves considering the elasticity (flexibility) inherent in many projects (or an entire company), does not involve the DCF (discounted cash flow) model. Real options management allows you to expand investments or abandon the project.
Many literature sources describe the methodology for estimating DCF / NPV, which is further compared with the real options method. The main problem with the DCF method is that it does not take into account the concept of flexibility at the point of decision making. When an investment decision is made definitively and without flexibility, the opportunity to respond to new information is lost. This opportunity is assessed as an opportunity cost that is not considered in traditional DCF/NPV analysis. While attempting to incorporate these costs into the analysis may facilitate option pricing, an alternative method is to incorporate option models used in financial asset pricing into the investment process. According to the opinion of the authors of foreign literature, this fact is interpreted as follows: “The DCF model is not only unfinished, but can also lead to serious errors. Investors must decide when to invest, how to adjust the project's operating forecasts, and when to sell the investment.
Real options valuation is more applicable in some industries than others. In particular, real options pricing is a powerful tool in high-growth industries where companies make investments that consistently experience a high degree of uncertainty (high risk). A small investment today provides the opportunity to continue a project with a larger subsequent investment or to abandon the project altogether, much like a stock option, where a small premium is paid today to have the right, but not the obligation, to buy shares later. Examples of such industries include energy (especially oil and gas), all R&D intensive industries such as biotechnology, pharmaceuticals and advanced technology, as well as industries with large marketing investments.
Last time financial specialists prove that real options pricing is a valuation tool for determining the value of almost any company. All unexplored directions of future cash flows, such as new products, new segments, or new markets, can be, or even better can be, valued through real options. It is proposed to divide the determination of the company's value as follows:
Current operating cost is calculated using one of the costing models mentioned above, such as the DCF model (discounted cash flow model). The company's value is then calculated relative to other opportunities in that industry or related industries using real options valuation. The two values obtained are added together to form the final value of the company.
As a rule, real options are more of a conceptual framework about a company's projects, investments and capabilities than a practical technique for determining value. When used in practice, real options are valued using the Black-Scholes model. When the value of a real option is calculated, the details are calculated key indicators projects, investments or the entire company.
So, the concept of “real option” was formed by analogy with the concept of an option in the securities market, which is a derivative security that gives its buyer the right to sell or buy a certain amount of goods (other securities) at a certain point in time at a certain price. For example, an American stock option gives its owner the right to buy (a call option) or sell (a put option) a specific share (the underlying asset) during a specified period at a predetermined price. (base price). If we are talking about a European type option, its execution date is fixed (on the last day of the validity period). Depending on future exchange rate dynamics, the owner of the option may or may not exercise his right, and the seller of the option has the obligation to buy or sell. Thus, an option always represents the possibility of performing one or another action.
A feature of modern entrepreneurship is that the management of an enterprise can make decisions based on future external conditions, and the obligation to perform one or another action is often absent.
Accordingly, it becomes possible to use elements of the mathematical theory of options in assessing the value of a business. The general diagram of the logical correspondence between the parameters of financial options (using stock options as an example) and real options is given in Table. 5.
Table 5
Characteristics of financial and real options
When extrapolating the described dependencies to objects in the real sector of the economy, it becomes possible to describe and systematize the set possible solutions, which is of decisive importance in business valuation.
Since the NAU method was introduced into valuation practice relatively recently, discussions are still ongoing about its place in the general system of approaches and methods for enterprise valuation.
According to the classification of approaches to valuation used in Russia, the NOU method refers, first of all, to the income approach, since it is focused on determining the future profitability of a business, taking into account the possibility of management making active decisions. However, as it seems to some participants in the ongoing discussion, it is conceptually quite close to the comparative approach, since it is focused on the consideration of many alternatives.
From a theoretical point of view, the real options method is a further development in the methodology for assessing ways to solve the “economic problem of time”. The time factor in economics is always associated with significant uncertainty of future events, which necessitates a “spatial representation of time” in the form of a functional or stochastic dependence. In principle, all methods of the income approach to valuation are aimed at solving the “economic problem of time”. The ROV method greatly refines the understanding of the future dynamics of the business, taking into account the possibility of making active decisions at any time and, thus, provides appraisers with a more accurate “picture” of future events.
While the real options method has been established in practice, the methodologies for using this type of analysis are different. The methods vary in level of sophistication and range from detailed models based on the pricing of financial options to procedures used in real estate and similar fields. For example, despite differences in the ability to incorporate flexibility into decision making, in many cases technical aspects real options methods include NPV and DCF calculations as a separate part of the assessment. In this case, the real options method is not a replacement for the DCF method, since DCF analysis is often necessary to understand the value of the asset in question. In the process of interaction with other methods that I work using Excel, the real options method has the opportunity to enhance everyday professional practice.
To consider the relationship between real and financial options, as well as the role of NPV in the methodology of real options, let us turn to one of the foreign sources, which describes the indicators commercial activities in relation to a call option. This publication discusses the definition and main properties of an option: expected cash flows; the period for which the option can be deferred; predicted costs of exercising the option. Further, these indicators are correlated with similar requirements of the buy option (Fig. 17).
The first two components, asset value (S) and cost (X), are obtained from the calculations of the traditional DCF method. Therefore, DCF analysis is the starting point when considering an option. Since DCF calculations do not include the added value provided by the option, the remaining factors form the necessary components for assessing flexibility. These factors consist of the option exercise period (t), the return that can be earned by incurring the cost (the risk-free rate r/), and the level of risk/fluctuation of the real asset (a).
Of all the above parameters, the most difficult to determine is the error/fluctuation of the asset (a). For example, in engineering systems, historical error information is usually not available. At the same time, this indicator is significant because it measures the level of future uncertainty, and the cost of project flexibility is the ability to respond to future uncertainty. For financial options, swing (a 2) can be defined as standard deviation from the annualized annual return based on available information. When this indicator is considered in the real options methodology, it is recommended to consider a range of 30-60% per year if information is limited. When searching for information, the parameters needed for comparison will mainly be publicly traded stocks with a future business opportunity that will be of a similar level of risk. For real estate, the fluctuation is usually taken to be in the range of 10-25% per year.
Rice. 17.
Financial asset management pursues the goal of achieving a certain economic effect in the future. The future is uncertain and management takes place under conditions of uncertainty regarding the future state of financial assets and their economic environment. Uncertainty creates the risk of ineffective management - such that the intended management goals are not achieved. For example, an investment decision that was initially considered economically justified may no longer be so due to deteriorating market conditions. Therefore, the task of minimizing the risk of ineffective financial management is linked to the task of an all-out fight against uncertainty.
The fundamental book by L. Zadeh presents the theory of fuzzy sets. The original intention of this theory was to build a functional correspondence between fuzzy linguistic descriptions (for example, “tall”, “warm”, etc.) and special functions expressing the degree of membership of the values of measured parameters (length, temperature, weight, etc.) the aforementioned vague descriptions. “Linguistic probabilities” were also introduced there, i.e. probabilities specified not quantitatively, but using a fuzzy semantic assessment.
Subsequently, the range of applicability of fuzzy set theory expanded significantly. The author himself defined fuzzy sets as a tool for constructing a theory of possibilities. Since then, the scientific categories of chance and possibility, probability and expectedness have received a theoretical distinction.
Since the late 70s, methods of fuzzy set theory have begun to be used in economics. A. Kofman's monograph “Introduction of the Theory of Fuzzy Sets” presents a wide range of possible applications of this theory - from assessing the effectiveness of investments to personnel decisions and equipment replacements. The publication provides the corresponding mathematical models.
In the case of using fuzzy numbers to predict parameters, it is necessary not to generate point probabilistic estimates, but to set an estimated corridor for the values of the predicted parameters. Then the expected effect is assessed by the expert in the same way as a fuzzy number with its calculated spread (degree of fuzzyness).
As for assessing the risk of decision-making under conditions of uncertainty, it is worth noting that the degree of stability of decisions is verified by analyzing the sensitivity of the decision to fluctuations in the initial data. Such stability can be assessed analytically.
Let's consider a simplified presentation of the fuzzy set method. The entire work process is divided into 9 stages.
Stage 1. Introduction of basic sets and subsets.
For example, a set of company states is introduced ( E), in which subsets are located (extremely unfavorable), Ez(unfavorable), Ez(average quality), etc. Accordingly, a set of bankruptcy risk degrees (C) is introduced, consisting of subsets C/ (marginal bankruptcy risk), NW(bankruptcy risk is high), NW(average risk of bankruptcy), etc. Number of subplots. 27-30.
gestures E And WITH must match. Index WITH takes a value from 0 to 1.
It is also necessary to enter an arbitrary management or financial indicator X, which has many values (IN,). Accordingly, the indicator IN, will be divided into the number of subsets, how many of them will there be? and & As an example, the names of the subsets 5 would be as follows: In and(very low level of indicator^,), IN12 (low level of indicator^), etc.
It is assumed that the growth of a separate indicator X is associated with a decrease in the degree of bankruptcy risk and with an improvement in the well-being of the enterprise in question.
Stage 2. Construction of sets of indicators.
At this stage, a set of individual indicators X with a total number of X is constructed, which not only affect the assessment of the risk of bankruptcy of the company, but also evaluate various aspects of its business and financial life.
Stage 3. Determining the significance level.
Each indicator X is associated with its level of significance P. To evaluate this level, it is necessary to arrange all indicators in descending order of importance so that the rule is satisfied:
G/> G2.>... Hm
If the system of indicators is ranked in descending order of their importance, then the significance of the i-th indicator r should be determined according to Fishburne’s rule, proposed in his publication “Utility Theory for Decision Making”.
Stage 4. Classification of risk level.
For each subset of bankruptcy risk degrees C, an interval is determined in which the value lies g(risk level indicator WITH). For example, if there is a subset WITH/(marginal risk of bankruptcy), then it will correspond to the value g in the range 0-8
Stage 5. Classification of indicator values.
At the current stage, a classification of the current values of x indicators X is built, compared with the values of subsets Sun.
Stage 6. Assessing the level of indicators.
The current level of indicators is assessed, and the obtained values of x indicators X-, are summarized in a single table.
Stage 7. Classification of indicator levels.
The obtained values are classified according to the Stage 5 table:
where R,y = 1 if /)/(y-/yy, and Hu= 0 in the opposite case (when the value does not fall within the selected classification range).
Stage 8. Risk assessment.
Here arithmetic operations are performed to assess the degree of bankruptcy risk g. The actions are as follows. Initially, we estimate the weights of one or another subset of IN in assessing the state of the enterprise? and assessing the degree of risk WITH. These weights subsequently participate in external summation to determine the average value of g, where gi is nothing more than the average g score from the corresponding range from Stage 4.
Stage 9. Conclusions.
We classify the resulting risk value based on the range data from Step 4.
From the above example, it is worth noting that fuzzy-set approaches are convenient in engineering application and have an increased degree of validity, since all possible scenarios for the development of events fall into the fuzzy-set calculation.
The fact that DCF is not used when pricing financial options indicates that this method does not comply with the fundamentals of option pricing. The central concept in option theory is the right to choose the future. According to a foreign author, there are only two cases when the flexibility of decision-making during a project does not affect the quality of investment decisions. The first is when decisions are made in the presence of complete and reliable information. In this case, the optimal trajectory of the project's development is predetermined, and the investment decision comes down to choosing the best alternative at the current moment in time. The second case is when all decisions are 100% reversible without the risk of losses. Under these conditions, assessing the effectiveness of investment decisions comes down to traditional discounting of future cash flows. The lack of flexibility in decision making, the relative lack of risk and certainty can also be seen in the features of traditional assessment methods. However, the distinctive characteristics of decision making in a real situation are certainty and irreversibility, which are not taken into account by the DCF method.
Flexibility in decision-making as the project progresses is a necessary condition for increasing the effectiveness of projects in conditions of irreversibility and uncertainty. It allows you to respond to emerging risks in a timely manner and minimize possible losses.
To illustrate this statement (see Figure 18), flexibility is defined as “the ability economic system respond to unexpected changes inside and outside the system, allowing you to achieve your goals.”
Flexibility can be “defensive” or “offensive.” An example of the first is the ability to switch to alternative input factors of production (resources, technologies) that reduce losses, as opposed to continuing dependence on a single source even when prices for input factors increase. On the other hand, the ability to expand your influence in the current and new markets when the actual demand for a product increases above the expected one is an example of “attacking” flexibility. “Defensive” flexibility allows you to reduce losses, while “offensive” flexibility allows you to take advantage of the positive potential of the project in conditions of uncertainty and irreversibility.
Rice. 18.
In the graph, under the influence of both types of flexibility, an asymmetric risk curve is formed, while a static project, implying the absence of the possibility of making a decision, is described in a symmetric risk envelope. The impact of flexibility shifts the risk envelope to the right, increasing the value of the investment project. The obvious conclusion from the above example is the fact that the value of real projects is underestimated by traditional analysis methods.
Of course, it can be argued that traditional cost estimation models allow you to evaluate a project taking into account several scenarios that may include various options management behavior. However, such approaches do not take into account the possibility of developing intermediate scenarios, but rather the construction of multi-scenario approaches in which the number of possible events is significant.
As already noted, the theory of real options is based on the assumption that investment projects in the real sector can be represented in the form of a diagram of the operation of a financial option.
As in financial options, the basis of a real investment project is the possession of a certain asset that allows you to make a choice in the future. In financial options, this asset is a contract that gives the right to purchase/sell the underlying asset for a certain period of time before the final moment of execution (American option). In real options, they can be various types of assets, the possession of which allows the company to launch some investment project.
Such an asset could be:
- a patent that gives the right to use a certain technology in the future during its validity period;
- technology itself, which, due to its uniqueness, allows you to launch production and introduce a certain product to the market. The duration of the option in this case is the period of time during which this product will be relevant. A product may lose its relevance as a result of the disappearance of demand for this product or the creation of alternative technology by competitors;
- fixed assets, which represent a fixed part of the project costs and allow, when investing in the required resources that make up the variable part of the costs, to begin production of a certain product. Such fixed assets can be land, premises, factory, etc.;
- conserved or unexplored resources, the possession of which gives the right to begin development if external conditions are favorable or additional information is obtained based on the results of geological research;
- in addition to all of the above, an asset that allows an investment opportunity to be realized can be contacts, connections, acquaintances, benefits, privileges, agreements - almost everything that makes it possible to receive Money or other tangible and intangible benefits.
The cost of acquiring an asset that gives us the opportunity to implement a certain investment project is the payment for the option (pregshsp). If the option price, i.e. the average projected cash flows from the exercise of the option will exceed the option fee, its exercise is profitable.
The exercise price of an option is a parameter that is the present value of all costs expected during the period of implementation of the investment opportunity. These expenses are necessary to exercise the option. This could be an investment to implement the technology; investments in oil field development; costs for purchasing resources and hiring work force required to start production at the factory.
The underlying asset can be the actual asset that represents the investment opportunity. In this case, its cost coincides with the fee for owning the option. Most often it occurs when the underlying asset is projected cash flows reduced to time zero. In this case, traditional approaches to estimating future cash flows and methods for valuing real options are simultaneously applied.
Thus, a “golden mean” is achieved between an abstract management assessment and a mathematical justification, and the assessment process itself is, as it were, divided into two stages. The first is to determine the value of future cash flows under the average market scenario. This stage is based on management's vision and uses the DCF method, which does not take into account the cost of flexibility. The second stage is the evaluation of real options, which allows you to re-evaluate the project taking into account the possibility of making a decision. The underlying asset when valuing options is the value of discounted cash flows. The essence of further assessment is to model various trajectories of changes in the value of the asset, i.e. deviations from the mean value found using the DCF approach; and determining the current value of the option, taking into account the possibility of neutralizing losses in a negative set of circumstances and maximizing profits in favorable market conditions.
A few caveats should be noted. First of all, in an efficient market, the valuation of any options held by a company should be reflected in the share price of any listed company. Of course, this rule is absolutely inapplicable to companies closed type. Second, the pricing of timing options does not take into account factors such as temporary business advantages due to market primacy. Finally, option pricing assumes that the strike price is known reliably, when in fact determining it is part of the problem.
According to proponents of real options theory, one of the problems is that risks and flexibility are not adequately defined and assessed. Discount rates do not take into account different stages of the project and different states of the global economy. As APV proponents have always argued, the CAPM's assumptions do not always hold true at the project level—betas may not reflect actual risk—and historical data is not always useful in estimating future betas. Most DCF-based approaches do not distinguish between agile and inflexible projects. The first of the above caveats also means that if any analysis uses data on similar companies with the same options, the value of the options will be factored into the beta or P/E estimate. The second caveat includes, for example, avoiding high discount rates as a rational response to high risk because it may be more than offset by the value that a company will receive by becoming the first supplier to a particular product market. And the third caveat may mean that options are often overpriced. In the case of real options, this is hardly possible: if, for example, a project is rejected due to low demand for the product, then one can reasonably expect that this will affect the selling price of the manufacturing plant.
The real options method is considered dynamic in the sense that it includes uncertainty that changes over time, as well as the types, methods and timing of the implementation of the relevant real options. However, some still believe that the real options method is little better than dynamic programming of investment regimes under conditions of uncertainty. But in general, the real options method significantly enriches economic theory in the field of capital investment under conditions of uncertainty.
In table Figure 6 presents the chronology of the development of the concept of real options within the framework of finance theory.
Table 6
Stages of development of the real options concept
|
Contribution to the theory and practice of the option method |
||
|
Criticism of underestimation of invested projects when using the DCF method. Introduction of decision tree analysis method |
Dean, Hayes, Garvin |
|
|
Formation general principles option valuations |
Black, Scholes, Merton, Cox, Ross |
|
|
Recognition of the possibility of using the real options method in business valuation. Creation of an apparatus that allows the use of unified valuation methods for financial and real options |
Riggs, Mason, Cox, Ross, Rubinstein |
|
|
Creation of a classification of modern options |
Merton, Trigeorgis, Brennan, Marcus |
|
|
Development of rules for valuing certain types of options |
Siegel, Ingersoll, McDonald, Ross, Pindyck, Majd |
|
|
Analysis of complex options and relationships between options |
Trigeorgis, Dos Santos |
It may be noted that recent empirical research based on real options theory has been largely limited to resource industries due to the ease with which certain asset characteristics can be manipulated, allowing for the use of several simplified assumptions:
3. Price is a non-constant random variable; the trend of movement cannot be traced.
Modern researchers identify a wide variety of real options. For business valuation highest value have the types of options indicated in table. 7.
Table 7
Main types of real options
|
Option type |
characteristic |
applications |
|
Deferment option (use) |
Start the project immediately or defer for X periods |
Mining, agriculture, construction |
|
Construction time option |
Having a choice between continuing or stopping investment in the business |
Knowledge-intensive industries industry, pharmaceuticals |
|
Option on regulation scale |
Increasing or decreasing the scale of business |
Real estate, mining industry |
|
Option to terminate operations |
If market conditions worsen, sale of assets or complete cessation of business |
Capital intensive industries, financial services |
|
Option to change products |
Changing the assortment without significant investment |
Small-scale or single-piece production of goods |
|
Growth options |
Implementation of new projects through the implementation of the current one |
All types of production depending on the state of infrastructure |
|
Multifunctional options |
Many projects provide a large number of alternative possibilities at once, forming certain combinations. The valuation of options in this group is carried out according to the principle of the sum of private options. |
Most large projects in all industries mentioned above |
Most of those listed in table. 7 types of real options cannot be used in practice without proper knowledge of mathematics by decision makers. But there are some exceptions. The most common types of decisions made by business leaders with a lesser degree of formalization include:
- 1. Decision to postpone the project.
- 2. Deciding on construction time.
Let us illustrate this with the example of a “deferment option”. A standard decision-making rule based on the DCF method (according to which a project with positive value IRU must be approved and implemented immediately) assumes that any project with IRU > 0 that is not immediately approved and implemented is forever lost.
This does not take into account the fact that sometimes a certain delay in the implementation of the project can be useful, since it allows you to make some improvements to increase the profitability of the project, or makes it possible to protect the enterprise from possible errors leading to negative consequences. In this regard, let's look at a short example.
Let's say the management of an enterprise is faced with the task of choosing the optimal moment for investment. The MRU of any hypothetical project, if it is implemented immediately, will be denoted as MRU0, and the MRU of this project, if it is implemented at a later date, will be denoted as NRUb.
Thus, the decision-making system about the start time of the project will be based on the following algorithm:
Immediate implementation of the project if
Postponement of project implementation if
In other cases (with MRUY
Along with the mentioned options, the objects of which are assets, options can also be allocated in relation to the liabilities of the enterprise. The subject of analysis in this case are those items of funding sources that are probabilistic in nature and influence the amount of capital costs. Options are liabilities, however, within the framework of the discussion about business valuation methods, they are still of secondary importance.
As noted above, the traditional DCF method is based on the idea of a certain “pre-foreseen”, that is, a rigid cash flow scenario, and is based on a kind of “obligation” of management to adhere to the strategy it has currently chosen. However, the real situation on the market is characterized by a high degree of uncertainty, so flexibility and adaptability of management become the most important parameters activities of the enterprise. This necessitates the correction of the main indicators calculated within the framework of the DCF method by the value of the real option valuation. However, one should not assume that the SHEA method is an alternative to DCF; on the contrary, it only complements DCF, making the valuation obtained using discounted cash flows better and more appropriate to the unstable and constantly changing market situation. This is largely reflected in the basic formula of the real options method, where the NOU method “corrects” the DCF method under conditions of high uncertainty. Accordingly, the basic formula on which the use of options is based is the following:
KRUb - KRU strategic indicator,
KRUr - passive value of KRU, calculated on the basis of the traditional cash flow method,
nuclear power plant - the cost of options for active actions by the management of the company being valued.
Accordingly, the key problem of the real options method is calculating the cost of nuclear weapons. The NRU value, adjusted for the value of the nuclear reactor, may differ significantly from the amount of the NRU calculated on the basis of traditional methods. For example, if an enterprise is characterized by increased flexibility and the ability to adapt to environmental changes, the NRU, taking into account nuclear weapons, increases significantly. On the contrary, if an enterprise practically cannot (without significant costs) change the nomenclature and volume of production, the NRU according to the nuclear-powered control method decreases.
In table 8 describes the differences between the real options method and the classical DCF in three main parameters.
To answer the question in the affirmative about the significance of option theory for valuation, it is necessary to find out whether its application increases the accuracy of calculating the value of a business. Therefore, we should consider the basic provisions of the theory of option pricing.
The valuation of financial options is based on the principle of freedom to carry out arbitrage operations, therefore, in a perfect financial market, the prices of assets with the same yield are equal. In a full financial market, it is possible to build a portfolio that, under the same external conditions, would generate the same income as an option. For example, payments on a call option on a stock can be replicated by taking out a loan and simultaneously purchasing the corresponding amount of the underlying securities. The price of the call option corresponds, under the described conditions, to the price of the constructed duplicate portfolio.
Table 8
Distinctive features of the DDP and NDC methods
|
Influence of the parameter on the cost of the object |
||
|
Volatility |
In conditions of uncertainty, investors demand an additional risk premium, which leads to a decrease in cash flow and a decrease in enterprise value |
The value of an enterprise increases if it has “space” for decision-making, since in this case it is possible to develop measures to protect against the negative impact of the external environment |
|
Risk-free interest rate |
Increasing risk-free interest rate leads to greater discounting of future cash flow and, as a result, to a decrease in enterprise value |
An increase in the risk-free interest rate leads to an increase in enterprise value as capital is allocated in the form of risk-free investments and then used as part of a strategic alternative |
|
Forecast period |
Valuation of an enterprise for a longer term is associated with greater discounting of cash flows and, as a result, causes a decrease in its value |
When valuing a business over the longer term, there is a higher likelihood that positive cash flows from future investments will exceed negative flows from current investments and the value of the business will increase |
Another way to price an option that does not involve constructing the portfolio described above is risk-neutral pricing. The method describes hypothetically possible risk-neutral behavior, i.e. a probability distribution is studied that, under risk-neutral conditions, leads to the formation of identical market prices. These prices should remain in equilibrium when the risk appetite of market participants changes. The sought probabilities are therefore called conditional. In this regard, consider the following example.
EXAMPLE OF DETERMINING THE PRICE OF A FINANCIAL OPTION
Initial data:
one-period binomial process, i.e. On the day the option is exercised (in a year), only two options for changing the share price are possible. It is necessary to evaluate the option to buy shares of the European type (E). The current rate is 110 monetary units. It is possible that the share price may increase by 30% (b = 1.3) or decrease by 20% (b = 0.8). Hence, changes in the stock price are expressed in the price on the execution day equal to 143 or 88 monetary units. The risk-free interest rate r is 5%.
It is not difficult to determine the appropriate option price on the exercise day. If the stock price rises, it makes sense to exercise the option. The option price in this case is calculated as the difference between the stock price on the exercise day and the base price. If, on the contrary, the stock price falls, the owner of the option does not exercise it. The option has zero value because the market rate prevailing on the day of exercise is lower than that specified in the option. These kinds of dependencies also explain the risk asymmetry inherent in real options.
The next step is to determine the value of the option on the day of valuation. Further reasoning is based on the fact that, under the assumed conditions of risk neutrality, the expected return is equal to the risk-free interest rate. The conditional probability p of a stock price increase is calculated as follows:
Finally, using conditional probabilities, we calculate the expected price of the option:
By discounting using the risk-free interest rate, we obtain the value of the call option at the time of making the decision to purchase it in the amount of 15.7 monetary units.
To carry out an assessment using this method, information is required on subjective probabilities reflecting external conditions or on the individual risk appetite of the investor. Individual risk appetites may be implicitly reflected in the market price of the underlying asset.
The most well-known models for determining the price of an option, regardless of individual preferences, are the binomial model and the Black-Scholes model.
The binomial model underlying the example discussed above corresponds to discrete random variable. In contrast, stock price dynamics in the Black-Scholes model are described by continuous random variable.
The Black-Scholes model is often considered as a kind of “limiting” case of the binomial model, when the number of periods I tends to infinity (i.e., there is a transition from discrete probabilities characteristic of specific periods to continuous probability distributions). The initial premise of the model is a normal probability distribution. Based on this premise, the basic formula of the model is compiled (relative to the European option to purchase an asset):
Wherein:
V- current value of the asset,
I - the price for purchasing an asset in the future established at the time of purchasing the option (i.e., the cost of future investments),
(5 - standard deviation of probabilities (about 2 - dispersion),
T - option duration (in years),
yy- risk-free interest rate,
N((11 ) and N((12 ) - cumulative probabilities according to With normal distribution.
The Black-Scholes model is traditionally considered more complex than the binomial one, but the development information technologies gradually makes it relatively easy to apply in practice.
Both models are generally effective for valuing real options, but the binomial model, which can be used more flexibly in many cases, has advantages over the Black-Scholes model. Moreover, the use of the binomial model, while reducing the duration of periods and simultaneously increasing the number of intervals, makes it possible to bring the accuracy of calculations closer to the Black-Scholes model.
When evaluating real options, it must be remembered that the analogy drawn with financial options is very limited. The significant difference lies primarily in the fact that the emergence of real options, unlike financial ones, usually does not occur in the organized capital market. It follows that in the case of real options, their owner does not have an exclusive right. Therefore, the assessment process must additionally take into account the impact of competition.
EXAMPLE OF PRACTICAL USE OF REAL OPTIONS
It has already been noted that the value assessed using real options consists of two parts: fixed and variable, the latter of which is considered as an option.
The methodology for valuing real options can be shown using a simplified two-part one process 1 . The object of assessment is a fully self-sustaining object intended for sale, with expected income in the period And in the amount of 1000 monetary units, and in the period b- 2000 monetary units. Taxes are excluded from consideration. Subsequently, a constant discount rate of 15% is introduced into the model. The cost of the object, calculated on the basis of these data, is 2381.9 monetary units.
Additionally, the cost of the entrepreneurial opportunity, assessed separately, must be included in the payment stream. Let's say in the period And the buyer is given the opportunity to use the facility’s know-how to begin production of a new group of goods. To do this, it is necessary to carry out in the period b investments of 300 monetary units. The size of the investment represents the base price of the entrepreneurial opportunity. Managers' decision to exercise an option depends on external conditions in the period And. It is assumed that offensive and non-offensive necessary conditions equally probable. According to scenario 1, favorable conditions arise for a new group of goods, which, when making additional investments, allow b expect an income of 500 monetary units.
Scenario 2, due to future external conditions, gives a pessimistic forecast, according to which in the period 2 , you can count on additional income of only 200 monetary units. Obviously, the production of a new product group makes sense only when scenario 1 occurs. The present value of additional income in the amount of 434.8 monetary units in this case
1 Krag ./., Kasperzak R. Grundzuge der Unternehmensbewertung. Verlag Vahlen, 2000.
exceeds an investment of 300 monetary units (the base price), while in scenario 2 this does not happen: the present value of cash income is only 173.9 monetary units, which is obviously lower than the base price.
Entrepreneurial opportunity can be measured as the present value of a European call option on additional income. To estimate the value of a call option at time 1o, the market price of the option object must be known, which implicitly reflects the preferences of market participants. As noted above, unlike financial options, as a rule, there is no explicit data on the dynamics of the price of the real option object. However, there are two fundamental approaches to calculating the option price. The first is to replace the option object with a “twin asset” or “mimicking portfolio” that would be traded in the market. In this case, the substitute asset must have a high degree of correlation with the real option object. This approach can be used when assessing those enterprises whose cash flows are closely related to the dynamics of prices for Natural resources, such as gold, oil, etc. In cases where a suitable “twin asset” cannot be selected, it is recommended to estimate the market price of the option object using discounted cash flows.
Taking into account the above, the current price of the option object R0 is calculated as follows:
From here you can derive the values of the rate of increase or decrease in value. In a positive scenario, the current value of the option object increases by 434.8 monetary units, thus the growth rate is 1.643, and in a negative scenario, the current value drops to 173.8 monetary units, and the decrease in value is 0.657. To complete the data necessary to calculate the value of the option, we enter the value of the risk-free interest rate. It is assumed that it is constant and amounts to 5%.
The next step is to estimate the conditional probabilities. To do this, we will make the following calculations:
Finally, using conditional probabilities, you can calculate the value of the call option at the time of valuation:
Co = (0.3985 x 134.8 + 0.6015 * 0) /1.05 = 51.2.
According to the calculation results, the enterprise value obtained above in the amount of 2381.9 monetary units, which does not take into account entrepreneurial opportunities, should be increased by their valuation and will amount to 2433.1 monetary units.
In the above example, the inclusion of real options contributed to the fact that the value of the project's NRU became more favorable for the investor. This result is not accidental and is associated with the general tendency of the IIOU method to increase the value of the enterprise with an increase in uncertainty and the number of strategic alternatives compared to the DCF method. This trend is shown in Fig. 19.
Rice. 19. Enterprise value under conditions of uncertainty (comparison of COU and DCF methods)
Proponents of the option method of business valuation argue that entrepreneurial opportunities cannot be adequately assessed using traditional methods of calculating present value. “Naive” calculations of the current value of objects are criticized, when the assessment of future income is carried out on the basis of strict planning. At the same time, the appraiser often agrees with previously made, including negative, decisions, neglecting future entrepreneurial opportunities.
One of the main advantages of the option method is that option pricing models can be used to value any asset that has option characteristics, although with some caveats. In general, the NOU method can be used in various situations to evaluate many objects, including:
- options on various assets (exchange options);
- shares (as a “call” option on the company’s assets or part of the pledged property);
- instruments with options features, including some types of bonds;
- patents (considered as options on products);
- minerals and certain other natural resources;
- investment projects that provide a choice of options;
- long-term contracts (with the right to prolongation);
- leasing transactions and lease agreements (with the right to extend).
Also, the LOU method can be used in the field of property insurance, in financial management (making decisions on discounts for regular customers, wholesale discounts, purchasing batches of goods, etc.), as well as in analyzing the effectiveness of the process of mergers and acquisitions of companies.
The advantages of the option method include the absence of the need to determine subjective assessments of entrepreneurial opportunities. This, at first glance, significant advantage arises due to the acceptance of the known market price of the option object. However, if the option object is not traded on the market and it is impossible to select a “twin asset,” the option method, strictly speaking, loses its attractiveness. The proposal to use a different valuation method to determine the value of an object does not solve the problem, since in this case the application of the same discounted cash flow method will lead to less objective results.
The advantages and disadvantages of the option approach can be noted in the context of the flexible planning tool. The disadvantages include the use of a single, constant interest rate in calculations based on the construction of a decision tree. There is a fundamental possibility of including in the model the necessary variable discounting factors that depend on time and external conditions, but their practical application is fraught with great difficulties.
As already noted, research on real options long years were significantly limited to resource industries due to the ease of transferring financial options pricing models to this type of real assets. It is obvious that the process of capital investment, for example, in a coal or oil project, has much in common with the exercise of a financial option. But at present, the field of use of the nuclear-powered laser method has increased significantly at the expense of other industries.
Some critical researchers do not recognize that option pricing theory makes a significant contribution to business valuation. At the same time, they refer to the developed technique of flexible investment planning, which allows using the decision tree method to assess entrepreneurial flexibility.
Thus, it is impossible to give a definitive answer about the unambiguously high efficiency of the option method. However, the NOU method can be successfully used in cases where there is acceptable and reasonable data on the market prices of option objects. The use of the real options method for making decisions on R&D allows us to take into account the possibility of a flexible response of the company's management to changing external conditions.
- Simians C.F. Research on Discounted Cash Flow Models // Real Estate Finance. - 13 (4). - 1997. P. 93-95.
- Price is the main source of uncertainty; Fluctuations in costs and inventories are of secondary importance.
- A capital market is called complete when there are many linearly independent securities.
senior lecturer of the department
accounting and finance
Severodvinsk branch
St. Petersburg State
maritime technical university
Smart and targeted investment activities are important for any company. Investments in the implementation of various projects carry the task of achieving certain goals, depending on the company’s policies. The goals can be very different: increasing the profitability of the production process, expanding or modernizing production, increasing market share, technological breakthrough, etc.
The implementation of investment projects is a new and insufficiently studied area of activity of enterprises in Russian market. An investment project is a process of implementing a set of interrelated actions aimed at achieving certain financial, economic, social, infrastructural and, in some cases, political results.
Currently, the main method for estimating the value of any income-generating project is to determine its net present value (NPV) for the current period. This cost is nothing more than the difference between the discounted cash flows generated by the project in the future and the necessary current investments to implement this project. If the present net value is positive, the project is considered profitable and is implemented, otherwise the project is rejected. The problem of forecasting profit is a separate issue, but in any case it is assumed that for each future period it is predetermined.
Even when the probabilities of income are determined for each period depending on possible situations (realistic forecast, pessimistic, optimistic), only the average statistical profit for each period is considered. But in many cases, management can make decisions as the project develops in order to increase its profitability. So, if the situation worsens, you can terminate or suspend the project; if circumstances are successful, you can increase capacity and increase the scale of the project to obtain greater profits. In an uncertain situation, you can postpone the main initial investments, and maintain only the possibility of their rapid implementation when favorable events occur. One way or another, many investment projects are flexible. Naturally, such a right to influence the course of the investment process has a certain value. The real options method is primarily aimed at determining the value of this right, determining the value of real options built into the project.
Real options terminology developed by Stephen Marglin. In 1970, he described the concept of real options (real-estate options) as follows: “When private investors have monopoly power in an investment sector, the right to undertake a project becomes an economic object that has a certain value, regardless of the investment process itself. In principle, there is no obstacle to such a right being bought or sold, although markets for such rights are the exception to the rule. Real options are special occasion a formal instrument that determines the relationship between the right to make investments and the investment itself. Usually the relationship itself is much less formal, market position or special knowledge creates hidden options associated with a particular investment, options for which there are no markets, but which are no less real.
Real option concept determine as the right of its owner, but not the obligation, to perform a certain action in the future. Financial options provide the right to buy (sell) a specific underlying asset and insure financial risks. Real options give the right to change the course of the project and insure strategic risks. Typically, real options are identified with a specific company asset, such as a patent or license. A patent or product license provides a firm with the right to develop a product and its market. Possessing a patent, a company can begin selling a product at any favorable moment, making initial investments in its development.
The analogy between investment projects and financial options explains the appearance of the term “real option”, i.e. the value potentially contained in the flexibility of management in making operational decisions when carrying out strategic investment projects. “Real options”, their recognition, understanding and sometimes evaluation is nothing more than a range of methods for flexible use of the assets and liabilities of an enterprise.
Valuation of investment projects using the real options method is based on the assumption that any investment opportunity for a company can be considered as a financial option, that is, the company has the right, not the obligation, to create or acquire assets over a period of time.
However, a real option should not be confused with a choice. If the company does not have the opportunity to carry out the project in stages or, in case of failure, to exit the project before its completion, minimizing losses, then the company is faced with a choice (to invest now or not) that does not contain real options.
Real options are an important tool for strategic and financial analysis because traditional approaches, such as NPV calculation, ignore flexibility. The discounted cash flow (DCF) method, the net present value (NPV) method, which is widely used in practice to this day, first began to be criticized in the mid-70s. Its obvious disadvantage is the static, “conservative” nature of the investment situation under consideration.
When using the DCF method, the analyst tries to avoid uncertainty at the time of analyzing the investment project. As a result, one or more scenarios for the future development of events appear. However, scenario analysis does not solve the main problem - staticity, since in the end an averaged option is adopted, which shows how uncertainty will be resolved in accordance with the underlying premises.
The real options method assumes a fundamentally different approach. Uncertainty remains, and management adapts over time (makes optimal decisions) to the changing situation. In other words, real options provide the opportunity to change and make optimal decisions in the future in accordance with new incoming information. Moreover, the ability to make and change decisions in the future is quantified at the time of analysis. It should be noted that, regardless of the chosen method of evaluating an investment project, management in most cases has the opportunity to make optimal decisions and change those already made. The problem with the DCF method is that it does not take into account such possibilities at the stage of assessing the effectiveness of an investment project.
Unlike the DCF method, which takes into account only cash inflows and outflows, the real options method allows you to take into account a larger number of factors. These include the period over which the investment opportunity remains open, the uncertainty of future earnings, the present value of future cash receipts and expenditures, and the value lost during the life of the investment opportunity.
Presenting a corporation as a portfolio of projects, each of which has a certain NPV, creates a static picture of investments and investment opportunities. In many cases, this mechanism allows you to monitor the situation, but often this is not enough.
Ultimately, option valuation includes the cost of knowledge. This is important because strategic decisions are rarely immediate affairs, especially in capital-intensive industries. NPV analysis often shows inadequate results because the value of knowledge in this case cannot be accurately taken into account until all obligations are fully allocated. This problem considered in the real options model.
In essence, NPV analysis overlooks flexibility, especially that related to uncertainty regarding cash flow growth rates, since it focuses on only two factors: key points creating value. This approach assumes that the present value of both cash inflows and cash outflows is static. Experts who understand the limitations of evaluating a project using NPV alone try to use scenario analysis to take into account the need to rank key indicators.
Using pessimistic, optimistic and realistic scenarios helps limit uncertainty, but static remains at the level of each of these scenarios. The scenario approach recognizes the existence of uncertainty, but does not take into account the value of flexibility that is inherent in the situation itself, and thus is not very useful in decision making. In contrast to this approach, the use of real options provides a comprehensive assessment of the strategic decision even in the presence of uncertainty.
The application of the real options methodology to the evaluation of investment projects is advisable when the following conditions are met:
When considering any project, management must understand what its flexibility is, what real options may be present in it. You also need to consider how much it costs to exercise an option, in what cases this exercise is possible and what benefits it will bring.
Depending on the conditions under which the option acquires value for the company, the following main types of real options are distinguished.
First option- possibility of deferment. Delay occurs when a company can delay decisions about major investments until some point in the future, thereby reducing the risk of the project. Moreover, when deferring, the company must have relatively unique assets in order to be sure that other companies will not take its niche by investing in more early date(patents, proprietary developments, and unique technologies provide this opportunity).
Second option- one of the most common is the ability to change the scale of the project. The option is that management can increase or decrease the scope of the project. Accordingly, in a favorable situation (customer growth, demand for products, etc.), investments can be made into the project additional funds, and if the situation worsens, the project can be reduced until the reduction in marginal costs has a positive effect on profits. Such an option may be valuable in industries subject to cyclical development, in which a decline in production alternates with its sharp increase.
Third option- exit option - allows the company to abandon the project if market conditions sharply deteriorate. The company can then sell the assets externally, recouping some of its losses, or use them in other investments.
Example
The company plans to put into operation a line for the production of new products. The project is designed for two years. An initial investment of 200 thousand euros will be required to complete the preparatory stage of the project, which lasts one year. A year later, at the start of production, it is necessary to invest another 190 thousand euros.
It is expected that cash flows from the sale of the new product will be available to the enterprise by the end of the second year of the project. However, at present it is difficult to determine whether the new product will be in demand. The probability of an optimistic development of events (expected income of 600 thousand euros) is 80%, and a pessimistic one (expected income of 10 thousand euros) is 20%. The required rate of return of the project is 15%.
Let's calculate NPV using the standard approach:
NPV = (–200) + (–190) / 1.15 + (0.8 x 600 + 0.2 x 10) / 1.152 = –0.76. |
Since the net present value of the project is less than zero, it is logical to refuse its implementation. Let's assume that within a year it will become clear whether the new products will be in demand. This way, the company's management will have the opportunity to decide whether to continue the investment. In case of negative changes, it is more profitable to stop the project.
The possibility of choosing in a year in this case is a real option for the enterprise to exit (refuse). Then NPV of the project, taking into account the option to refuse, will be:
NPV = (–200) + 0.8 x (–190) / 1.15 + (0.8 x 600 + 0.2 x 0) / 1.152 = 30.78. |
Since, taking into account the real option, the net present value of the project is positive, it can be recommended for execution.
Methods for calculating options are presented in detail in.
Let's denote the main characteristics that affect the cost of projects that include real options. The main characteristic of a project that increases its cost is uncertainty. A more risky project, all other things being equal, provides the highest profitability, and the refusal option allows you to hedge the risk of a worsening situation (the greater the risk, the more the right of refusal and the project itself are worth). The high uncertainty of the project also lies in the ability to make an over-optimistic forecast of the development of events with a certain probability; accordingly, by taking into account the expansion option, the cost of the project increases significantly.
Another important factor affecting the cost of a project is the cost of maintaining the option. Thus, a company can maintain unprofitable business models for years, spend huge amounts of money on improving technology, so that in the future, with the help of this business model, under favorable circumstances, it can occupy its niche in the market. Another important factor is the duration of the option, which is directly proportional to its value. The more we can own a certain right, the more that right is worth. As already indicated above, the value of an option depends on its uniqueness and the ability of competitors to copy it.
The Black-Scholes option pricing model can be used to determine the value of real options.
This model is simple both in presentation and in application. However, it has a number of limitations:
The value of a real option is calculated using the Black-Scholes formula, developed for valuing call-type financial options:
standard deviation of stock returns over the period. For real options, this is “asset price volatility” (market priced risk). For real assets in the usual way assessment is the analysis of statistical data for past periods; |
||
current share price. For a real option, this is the present value of cash flows from the implementation of the investment opportunity that the company will receive as a result of the investment project; |
||
PV(X) = Xe-rt |
present value of investment for the implementation of the project or liquidation value upon abandonment of the project; |
|
option exercise price (for real options - project implementation costs); |
||
a number that is the base of the natural logarithm (rounded value 2.71828); |
||
short-term risk-free rate of return; |
||
the time until the option expires (realization of the opportunity contained in the option) or the time until the next decision point. |
From the analysis of this formula it follows that the price of a real option is higher if:
In this case, the greatest influence on the increase in the value of the option is the present value of the expected cash flows. Therefore, to increase the investment attractiveness of a project, it is more advisable for companies to focus on increasing income rather than reducing costs.
The main difficulties that may arise when applying this model are associated with obtaining reliable initial data necessary for the calculation (time until the implementation of the project's capabilities, variance value, etc.).
Example
Replacement of equipment for hydrogeological drilling of wells.
Real call option, Black-Scholes model
LLC "Vodyanoy" provides services to gardening partnerships in the Moscow region for drilling water wells. In total, the LLC has ten drilling rigs operating at various sites and in various areas of the region. The management of the enterprise is considering the possibility of significant modernization of drilling units, which will reduce operating costs, increase the productivity of installations and, accordingly, receive more orders from potential clients. It is necessary to justify the modernization. Unfortunately, calculations for the most likely scenario show that the benefits of modernization do not cover the capital costs of it.
Here are the initial data for calculations for this scenario per machine:
Indicator name |
Indicator value |
|
Basic option |
New technology |
|
Productivity, m/machine shift |
||
Equipment utilization rate over time |
||
Average number of shifts per year |
||
Average price of one drilled meter, dollars. |
||
Average current costs per machine tool shift, dollars. |
||
Net capital costs, including the purchase of new units minus the net salvage value of old ones, dollars. |
||
There are no additional costs or benefits associated with the increase in working capital in the project. The depreciation rate for equipment is 20%; after a five-year period, the net value from the disposal of the equipment is zero.
Weighted average cost of capital of LLC:
a) in real terms - 12%;
b) risk-free rate - 4% per year;
c) income tax rate - 24%.
At the same time, the management had serious doubts about the results of calculations related to the accuracy of cash flow predictions. The point is the uncertainty that the initial assumptions regarding:
a) the number of orders and associated current costs per drilled meter (savings on semi-fixed costs are possible) and equipment utilization rate;
b) trouble-free operation new technology and frequency of repairs;
c) the average depth of wells drilled (payment is made not by footage, but by the result of drilling - the number of productive wells), etc.
As a result, the accuracy of calculating the effect is s = 40%.
In order not to risk the entire business as a whole and to obtain more accurate information about the results of the project, the management of the LLC decides to conduct an experiment: despite the negative results of the calculations, carry out modernization on one of the drilling units. If the result turns out to be successful (which will be clear within a year), it will be possible to replicate the experience on the other nine installations.
Solution
Calculations carried out according to traditional technology, really show the unprofitability of modernization at any one, let alone ten installations.
Calculation of cash flow for replacing one machine
Indicator name |
Indicator value by year |
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0th period |
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Productivity, m/machine shift: new equipment; |
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comparison bases |
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Equipment utilization rate |
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Average number of shifts per year |
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Additional volume, m/year |
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Average price of one meter, dollars. |
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Additional revenue per year, dollars |
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Average current costs for 1 machine tool shift, dollars: |
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new technology; |
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comparison bases |
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Average number of shifts per year |
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Additional operating costs, dollars per year |
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Additional capital costs |
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Depreciation rate, % |
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Depreciation of additional capital investments, dollars. |
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Additional profit per year, dollars |
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Income tax (24%), USD |
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Net cash flow of the project, dollars. |
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Project evaluation without options |
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Cost of capital, % |
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Risk-free rate, % |
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NPV of the project, dollars |
The result of discounting at a rate of 12% |
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Each of the projects reduces the wealth of the owners by 1.7 thousand dollars, which is a considerable amount by the standards of this enterprise.
At the same time, the first draft gives us information about what may happen to the next nine and reveals their uncertainty. In fact, it gives the right to invest money in nine more such projects within a year under favorable circumstances (positive results of the first project). This right represents a real call option on 9 projects (or 9 options, each on one project).
If we value these options using the Black-Scholes model and add their premiums to the effect of the base project, the result changes:
Option pricing
Indicators |
Values |
Number of options in the project |
|
S for each option, dollars |
18 285, 27 (20 000 – 1714,73) |
X for each option, dollars. |
|
Premium per option |
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Project NPV with options |
21,051 (2529.61 x 9 – 1714.73) |
Thus, despite the seeming unprofitability of modernization, the project is completely justified.
You can learn more about option calculations in.
Using the real options method has not only advantages, but also disadvantages.
Uncritical application of this methodology can negatively affect the company's business and its competitive position. Maintaining excessive flexibility in decisions can lead to frequent revision of plans, loss of “strategic focus” and, as a result, to the fact that the company will never achieve its strategic goals. Another important point is the correct accounting of the cost of creating and maintaining real options. For example, the opportunity to increase production output (investment in capacity reserves) may not be in demand, and not all the costs of creating such an option will be justified.
In addition, the introduction of a real options model requires a change in the company’s internal culture and approaches to doing business, which often becomes an insurmountable obstacle.
The main problem with using the real options methodology is the lack of qualified specialists, as well as the shortage of Russian experience its application.
Despite the fact that the real options method is widely known only among specialists - theorists in the field of business valuation - recently it has become increasingly widespread for the evaluation of investment projects.
The use of a tool such as real options in company management allows management to pay less attention to creating “ideal” forecasts and direct more efforts to identifying alternative ways of developing the company. The use of the traditional DCF method leads to the fact that during the implementation of a project it is difficult for management to abandon planned actions and see new opportunities that will bring big profits to the company.
Taking into account that the scope of this technique is practically unlimited and that real options can be found wherever there is uncertainty, within three to four years the number of companies adopting this method will increase significantly.
According to S. Faiz, who successfully introduced real options valuation methods into Texaco practice, real options are a method of the 21st century. . Companies that adopt it first will secure a competitive advantage in the future.
Among the enterprises that successfully use options methods are the following:
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the largest international pharmaceutical company Merck has been using option methods for many years to evaluate billions of dollars in investments in the development of new drugs; |
Rhino Tinto, an English mining group with annual sales of over £9 billion, carries out mine assessment and decision-making; |
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RTZ-CRA was assessing zinc deposits in Peru for possible acquisition; |
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Texaco evaluates oil fields that are in the early stages of development and objectively resolves conflict between management groups regarding the strategy for their further development; |
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British Petroleum assessed and developed a strategy for the development of oil fields in the North Sea, the economic viability of which was questionable in the early 90s. |
Methods for valuing real options are becoming increasingly recognized among investors: banks and other financial institutions, in particular the EBRD.
Such major Russian companies as Gazprom, Lukoil, Tatneft, Severstal, as well as companies working with Internet technologies, patents, licenses, etc., use the options methodology in their practice.
LITERATURE
1. Braley R., Myers S. Principles of corporate finance. - M.: Olimp-Business, 1997.
2. Bruslanova N. Evaluation of investment projects using the real options method // Financial Director. - 2004. - No. 7.
3. Bukhvalov A.V. Real options in management // Russian Journal of Management. - 2004. - No. 2.
4. Damodaran A. Investment assessment. Tools and techniques for assessing any assets. - M.: Alpina Business Books, 2004.
5. Kalinin D. New methods for assessing the value of companies and making investment decisions // Securities Market. - 2000. - No. 8.
6. Kovalev V.V. Methods for evaluating investment projects. - M.: Finance and Statistics, 2000.
7. Kovalishin E. A., Pomansky A. B. Real options: the optimal moment of investment // Economics and mathematical methods. - 1999. - No. 35.
8. Kozhevnikov D. Application of “real options” models for valuation strategic projects. - M.: MIPT, 2001.
9. Knysh M. I., Perekatov B. A., Tyutikov Yu. P. Strategic planning of investment activities: Textbook. allowance. - St. Petersburg: Business press, 1998.
10. Limitovsky M. A. Investment projects and real options in emerging markets. - M.: Delo, 2004.
11. Pirogov N.K. Real options and reality // Modern aspects of regional development: Collection of articles. - Irkutsk: BIBMM ISU, 2003.
12. Ramzaev M. Cost flexibility // Finance and economics on the Internet: http://ecommerce.al.ru/analis/newecon/valuefl.htm
13. Sisoshvili S. Development of an investment project // Economics and life. - 2001. - No. 7.
14. Sysoev A. Yu. The use of “real options” models in assessing the effectiveness of investment projects // Vestnik FA. - 2003. - Issue. 4.
15. Topsakhalova F. M. Features of making an investment decision under conditions of uncertainty and risk // Economic analysis: theory and practice. - 2005. - No. 12.
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