Real options valuation

Overview

Real options valuation, also often termed real options analysis, (ROV or ROA) applies option valuation techniques to capital budgeting decisions. A real option itself, is the right—but not the obligation—to undertake certain business initiatives, such as deferring, abandoning, expanding, staging, or contracting a capital investment project. For example, real options valuation could examine the opportunity to invest in the expansion of a firm's factory and the alternative option to sell the factory. Real options are most valuable when uncertainty is high; management has significant flexibility to change the course of the project in a favorable direction and is willing to exercise the options.

Scope

Real options are generally distinguished from conventional financial options in that they are not typically traded as securities, and do not usually involve decisions on an underlying asset that is traded as a financial security. A further distinction is that option holders here, i.e. management, can directly influence the value of the option's underlying project; whereas this is not a consideration regarding the underlying security of a financial option. Moreover, management cannot measure uncertainty in terms of volatility, and must instead rely on their perceptions of uncertainty. Unlike financial options, management must also create or discover real options, and such creation and discovery process comprises an entrepreneurial or business task. Real options analysis, as a discipline, extends from its application in corporate finance, to decision making under uncertainty in general, adapting the techniques developed for financial options to "real-life" decisions. For example, R&D managers can use real options valuation to help them deal with various uncertainties in making decisions about the allocation of resources among R&D projects. Non-business examples might be evaluating the cost of cryptocurrency mining machines, or the decision to join the work force, or rather, to forgo several years of income to attend graduate school. It, thus, forces decision makers to be explicit about the assumptions underlying their projections, and for this reason ROV is increasingly employed as a tool in business strategy formulation. This extension of real options to real-world projects often requires customized decision support systems, because otherwise the complex compound real options will become too intractable to handle.

Types of real options

The flexibility available to management – i.e. the actual "real options" – generically, will relate to project size, project timing, and the operation of the project once established. In all cases, any (non-recoverable) upfront expenditure related to this flexibility is the option premium. Real options are also commonly applied to stock valuation - see Business valuation § Option pricing approaches - as well as to various other "Applications" referenced below.

Options relating to project size

Where the project's scope is uncertain, flexibility as to the size of the relevant facilities is valuable, and constitutes optionality.

Option to expand: Here the project is built with capacity in excess of the expected level of output so that it can produce at higher rates if needed. Management then has the option (but not the obligation) to expand – i.e. exercise the option – should conditions turn out to be favourable. A project with the option to expand will cost more to establish, the excess being the option premium, but is worth more than the same without the possibility of expansion. This is equivalent to a call option. Option to contract: The project is engineered such that output can be contracted in future should conditions turn out to be unfavourable. Forgoing these future expenditures constitutes option exercise. This is the equivalent to a put option, and again, the excess upfront expenditure is the option premium. Option to expand or contract: Here the project is designed such that its operation can be dynamically turned on and off. Management may shut down part or all of the operation when conditions are unfavorable (a put option), and may restart operations when conditions improve (a call option). A flexible manufacturing system (FMS) is a good example of this type of option. This option is also known as a Switching option.

Options relating to project life and timing

Where there is uncertainty as to when, and how, business or other conditions will eventuate, flexibility as to the timing of the relevant project(s) is valuable, and constitutes optionality.

Growth options: perhaps the most generic in this category – these entail the call option to exercise only those projects that appear to be profitable at the time of initiation. Initiation or deferment options: Here management has flexibility as to when to start a project. For example, in natural resource exploration a firm can delay mining a deposit until market conditions are favorable. This constitutes an American styled call option. Delay option with a product patent: A firm with a patent right on a product has a right to develop and market the product exclusively until the expiration of the patent. The firm will market and develop the product only if the present value of the expected cash flows from the product sales exceeds the cost of development. If this does not occur, the firm can shelve the patent and not incur any further costs. Option to abandon: Management may have the option to cease a project during its life, and, possibly, to realise its salvage value. Here, when the present value of the remaining cash flows falls below the liquidation value, the asset may be sold, and this act is effectively the exercising of a put option. This option is also known as a Termination option. Abandonment options are American styled. Sequencing options: This option is related to the initiation option above, although entails flexibility as to the timing of more than one inter-related projects: the analysis here is as to whether it is advantageous to implement these sequentially or in parallel. Here, observing the outcomes relating to the first project, the firm can resolve some of the uncertainty relating to the venture overall. Once resolved, management has the option to proceed or not with the development of the other projects. If taken in parallel, management would have already spent the resources and the value of the option not to spend them is lost. The sequencing of projects is an important issue in corporate strategy. Related here is also the notion of Intraproject vs. Interproject options.

Options relating to project operation

Management may have flexibility relating to the product produced and/or the process used in manufacture. As in the preceding cases, this flexibility increases the value but also the cost of the project; the latter corresponding, in turn, to the "premium" paid for the real option.

Output mix options: The option to produce different outputs from the same facility – product flexibility – is known as an output mix option. These options are particularly valuable in industries where demand is volatile or where quantities demanded in total for a particular good are typically low, and management would wish to change to a different product quickly if required. Input mix options: An input mix option – process flexibility – allows management to use different inputs to produce the same output as appropriate. For example, a farmer will value the option to switch between various feed sources, preferring to use the cheapest acceptable alternative. An electric utility, for example, may have the option to switch between various fuel sources to produce electricity, and therefore a flexible plant, although more expensive may actually be more valuable. Operating scale options: Management may have the option to change the output rate per unit of time or to change the total length of production run time, for example in response to market conditions. These options are also known as Intensity options.

Valuation

Given the above, it is clear that there is an analogy between real options and financial options, and we would therefore expect options-based modelling and analysis to be applied here. At the same time, it is nevertheless important to understand why the more standard valuation techniques may not be applicable for ROV.

Applicability of standard techniques

ROV is often contrasted with more standard techniques of capital budgeting, such as discounted cash flow (DCF) analysis / net present value (NPV). Under this "standard" NPV approach, future expected cash flows are present valued under the empirical probability measure at a discount rate that reflects the embedded risk in the project; see CAPM, APT, WACC. Here, only the expected cash flows are considered, and the "flexibility" to alter corporate strategy in view of actual market realizations is "ignored"; see below as well as Corporate finance § Valuing flexibility. The NPV framework (implicitly) assumes that management is "passive" with regard to their Capital Investment once committed. Some analysts account for this uncertainty by (i) adjusting the discount rate, e.g. by increasing the cost of capital, or (ii) adjusting the cash flows, e.g. using certainty equivalents, or (iii) applying (subjective) "haircuts" to the forecast numbers, or (iv) via probability-weighting these as in rNPV. Even when employed, however, these latter methods do not normally properly account for changes in risk over the project's lifecycle and hence fail to appropriately adapt the risk adjustment. By contrast, ROV assumes that management is "active" and can "continuously" respond to market changes. Real options consider "all" scenarios (or "states") and indicate the best corporate action in each of these contingent events. Because management adapts to each negative outcome by decreasing its exposure and to positive scenarios by scaling up, the firm benefits from uncertainty in the underlying market, achieving a lower variability of profits than under the commitment/NPV stance. The contingent nature of future profits in real option models is captured by employing the techniques developed for financial options in the literature on contingent claims analysis. Here the approach, known as risk-neutral valuation, consists in adjusting the probability distribution for risk consideration, while discounting at the risk-free rate. This technique is also known as the "martingale" approach, and uses a risk-neutral measure. For technical considerations here, see below. For related discussion – and graphical representation – see Datar–Mathews method for real option valuation. Given these different treatments, the real options value of a project is typically higher than under NPV. As outlined, the difference will be most marked in projects with major flexibility, contingency, and volatility; and more generally, as for financial options, a higher volatility of the underlying leads to a higher project ROV. It is thought that this difference in valuations is one reason for the slower adoption of real options, both in practice and academia; studies have shown though that when input values are properly identified, ROV models are reliable estimators of underlying asset value.

Options based valuation

Although there is much similarity between the modelling of real options and financial options, ROV is distinguished from the latter, in that it takes into account uncertainty about the future evolution of the parameters that determine the value of the project, coupled with management's ability to respond to the evolution of these parameters. It is the combined effect of these that makes ROV technically more challenging than its alternatives.

First, you must figure out the full range of possible values for the underlying asset. ... This involves estimating what the asset's value would be if it existed today and forecasting to see the full set of possible future values ... [These] calculations provide you with numbers for all the possible future values of the option at the various points where a decision is needed on whether to continue with the project. When valuing the real option, the analyst must therefore consider the inputs to the valuation, the valuation method employed, and whether any technical limitations may apply. Conceptually, valuing a real option looks at the premium between inflows and outlays for a particular project. Inputs to the value of a real option (time, discount rates, volatility, cash inflows and outflows) are each affected by the terms of business, and external environmental factors that a project exists in. Terms of business as information regarding ownership, data collection costs, and patents, are formed in relation to political, environmental, socio-cultural, technological, environmental and legal factors that affect an industry. Just as terms of business are affected by external environmental factors, these same circumstances affect the volatility of returns, as well as the discount rate (as firm or project specific risk). Furthermore, the external environmental influences that affect an industry affect projections on expected inflows and outlays.

Valuation inputs

Given the similarity in valuation approach, the inputs required for modelling the real option correspond, generically, to those required for a financial option valuation. The specific application, though, is as follows:

The option's underlying is the project in question – it is modelled in terms of: Spot price: the starting or current value of the project is required: this is usually based on management's "best guess" as to the gross value of the project's cash flows and resultant NPV; Volatility: a measure for uncertainty as to the change in value over time is required: the volatility in project value is generally used, usually derived via monte carlo simulation; sometimes the volatility of the first period's cash flows are preferred; see further under Corporate finance for a discussion relating to the estimation of NPV and project volatility. some analysts substitute a listed security as a proxy, using either its price volatility (historical volatility), or, if options exist on this security, their implied volatility. Dividends generated by the underlying asset: As part of a project, the dividend equates to any income which could be derived from the real assets and paid to the owner. These reduce the appreciation of the asset. Option characteristics: Strike price: this corresponds to any (non-recoverable) investment outlays, typically the prospective costs of the project. In general, management would proceed (i.e. the option would be in the money) given that the present value of expected cash flows exceeds this amount; Option term: the time during which management may decide to act, or not act, corresponds to the life of the option. As above, examples include the time to expiry of a patent, or of the mineral rights for a new mine. See Option time value. Note though that given the flexibility related to timing as described, caution must be applied here. Option style and option exercise. Management's ability to respond to changes in value is modeled at each decision point as a series of options, as above these may comprise, i.a.: the option to contract the project (an American styled put option); the option to abandon the project (also an American put); the option to expand or extend the project (both American styled call options); switching options or composite options which may also apply to the project.

Valuation methods

The valuation methods usually employed, likewise, are adapted from techniques developed for valuing financial options. Note though that, in general, while most "real" problems allow for American style exercise at any point (many points) in the project's life and are impacted by multiple underlying variables, the standard methods are limited either with regard to dimensionality, to early exercise, or to both. In selecting a model, therefore, analysts must make a trade off between these considerations; see Option (finance) § Model implementation. The model must also be flexible enough to allow for the relevant decision rule to be coded appropriately at each decision point.

Closed form, Black–Scholes-like solutions are sometimes employed. These are applicable only for European styled options or perpetual American options. Note that this application of Black–Scholes assumes constant — i.e. deterministic — costs: in cases where the project's costs, like its revenue, are also assumed stochastic, then Margrabe's formula can (should) be applied instead, here valuing the option to "exchange" expenses for revenue. (Relatedly, where the project is exposed to two (or more) uncertainties — e.g. for natural resources, price and quantity — some analysts attempt to use an overall volatility; this, though, is more correctly treated as a rainbow option, typically valued using simulation as below.) The most commonly employed methods are binomial lattices. These are more widely used given that most real options are American styled. Additionally, and particularly, lattice-based models allow for flexibility as to exercise, where the relevant, and differing, rules may be encoded at each node. Note that lattices cannot readily handle high-dimensional problems; treating the project's costs as stochastic would add (at least) one dimension to the lattice, increasing the number of ending-nodes by the square (the exponent here, corresponding to the number of sources of uncertainty). Specialised Monte Carlo Methods have also been developed and are increasingly, and especially, applied to high-dimensional problems. Note that for American styled real options, this application is somewhat more complex; although recent research combines a least squares approach with simulation, allowing for the valuation of real options which are both multidimensional and American styled; see Monte Carlo methods for option pricing § Least Square Monte Carlo. When the Real Option can be modelled using a partial differential equation, then Finite difference methods for option pricing are sometimes applied. Although many of the early ROV articles discussed this method, its use is relatively uncommon today—particularly amongst practitioners—due to the required mathematical sophistication; these too cannot readily be used for high-dimensional problems. Various other methods, aimed mainly at practitioners, have been developed for real option valuation. These typically use cash-flow scenarios for the projection of the future pay-off distribution, and are not based on restricting assumptions similar to those that underlie the closed form (or even numeric) solutions discussed. Recent additions include the Datar–Mathews method (which can be understood as an extension of the net present value multi-scenario Monte Carlo model with an adjustment for risk aversion and economic decision-making), the fuzzy pay-off method, and the simulation with optimized exercise thresholds method. By contrast, methods focusing on, for example, real option valuation in engineering design may be more sophisticated. These include analytics based on decision rules, which merge physical design considerations and management decisions through an intuitive "if-then-else" statement e.g., if demand is higher than a certain production capacity level, then expand existing capacity, else do nothing; this approach can be combined with advanced mathematical optimization methods like stochastic programming and robust optimisation to find the optimal design and decision rule variables. A more recent approach reformulates the real option problem as a data-driven Markov decision process, and uses advanced machine learning like deep reinforcement learning to evaluate a wide range of possible real option and design implementation strategies, well suited for complex systems and investment projects. These help quantify the value of flexibility engineered early on in system designs and/or irreversible investment projects. The methods help rank order flexible design solutions relative to one another, and thus enable the best real option strategies to be exercised cost effectively during operations. These methods have been applied in many use cases in aerospace, defense, energy, transport, space, and water infrastructure design and planning.

Limitations

The relevance of Real options, even as a thought framework, may be limited due to market, organizational and / or technical considerations. When the framework is employed, therefore, the analyst must first ensure that ROV is relevant to the project in question. These considerations are as follows.