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Risk and Flexibility Integration in Valuation

1.1. Introduction

The investment must be identified as an entry fee that provides access to future opportunities. Thus, the value of a project is not limited to the present value of anticipated cash flows, but must capture all the growth opportunities that will arise in the future. For this, real options offer a long-term vision. They have the advantage of incorporating future upside and downside cash flow opportunities through volatility representing the risk and, consequently, make it possible to incorporate the notion of flexibility into project management. In fact, depending on the cash flows, the project can, among other things, be carried, abandoned, strengthened or developed in sequence. Volatility is the key parameter of options, whether financial or real. Its usefulness lies in the fact that the value of derivative financial products or investment projects depends on the possibility of benefiting from favorable conditions or, otherwise, reducing losses. In practice, real options remain less used than the NPV criterion for determining the value of a project. However, Graham and Harvey's (2001) and Hartmann and Hassan's (2006) studies indicate that about a quarter of Chief Financial Officers (CFOs) surveyed use the real options approach to help them make investment decisions. Black and Scholes (1973), on the one hand, and Cox, Ross and Rubinstein (1979) models, on the other hand, form a basis for the valuation of investment projects by real options. Initially intended to enhance the value of financial options, these models are particularly relevant to evaluate a project taking into account a range of opportunities characterizing it.

After the realization of a pragmatic analogy as to the different parameters constituting these paradigmatic models, it is possible to apply the valuation of projects assimilated to real options. Thus, projects with growth options, abandonment options, combined options, sequential development options, or options for expanding or reducing the activity can be the subject of a dynamic and at least complementary analysis to that of the NPV criterion.

New parameters have been incorporated into the initial models in order to improve them by making them more precise. Thus, the notion of constant volatility established by Black and Scholes is questioned by some researchers who prefer a stochastic volatility with the objective of anticipating future developments in the price of the underlying. In addition, transaction costs complement the models by promoting a better definition of hedging strategies. Models with jumps are expected to consider important macroeconomic events. Finally, taking into account the payment of a discrete-time dividend within a continuous-time model would make it possible to refine the value of the project even better.

1.2. The scope of real options

Unlike financial options, real options focus on valuing "real" assets, i.e. investment projects. In this context, an analogy between financial and real options can be seen. In fact, an investment opportunity is similar to a call option because the company has the right, not the obligation, to invest in an asset, on a fixed date or during a given period, on a price known in advance. Thus, the five fundamental parameters that make it possible to evaluate a financial option can be similar when it comes to valuing an investment project. Amran and Kulatilaka (1999), who also believe that real options are an extension of the theory of financial options applied to real assets (non-financial), manage to distinguish seven categories of options. As a result, real options offer some flexibility in the management of an investment project, unlike traditional methods, as decisions can be made throughout project implementation.

In practice, Graham and Harvey (2001) find that, while the most commonly-used method of valuing an investment project is based on the NPV criterion, real options are used by almost a quarter of the CFOs surveyed. In other words, this method is more in demand than profitability index or value-at-risk. By refining the conclusions of these two researchers' study, we see that real options particularly convince large industrial companies, whose debt and growth are moderate and whose management is the responsibility of shareholders who pay little or no dividend(s). By focusing on the use of real options in the pharmaceutical industry, Hartmann and Hassan (2006) reach the same types of conclusions: about 25% of the pharmaceutical groups surveyed say they use real options.

The valuation models of real options rely on paradigms regarding the valuation of the option premium initially established for financial options. Black and Scholes (1973) set out to establish a continuous-time model, and Cox, Ross and Rubinstein (1979) consider a discrete-time model. A convergence between these two formulas allowed us to arrive at extensions such as taking into account the distribution of dividends.

1.2.1. The concept of real options

Real options involve real activities unlike financial options that exclusively incorporate financial assets. Luehrman (1998) attempts to draw an analogy between these two categories of options by presenting an analytical framework aimed at reconciling options theory with valuations of investment projects. He compares the similarities between the DCF method and the options approach by stating that an investment opportunity is similar to a call option, in that the company can, without being forced to, buy the assets necessary for the operation of a new activity. He also demonstrates that the value of the option linked to an investment opportunity has the same characteristics as that present on the financial markets and that, consequently, it is possible to evaluate an option falling within the investment process of real assets. The nuance, however, lies in the fact that investment opportunities only come once. Synthetic options need to be established with the ability to replicate payments from investment projects.

In this context, there is an analogy between the characteristics of an investment project and the five parameters used to calculate the price of an option. In fact, an investment opportunity is similar to a call option to the extent that the company has the right to purchase the equivalent of the underlying - namely, the assets required for the operation of the project - at a future date or before a future date (respectively, the equivalent of a European and American option) - at a certain price. The term "real" distinguishes this type of options from financial options of which the underlying is a financial asset. Financial options are specific contracts traded on organized or over-the-counter markets, while real options are more difficult to identify and specify. Just like a financial option, a real option is asymmetrical since it gives the holder the right and not the obligation to exercise it, that is to say, the right to undertake an investment or abandon it, the opportunity to take advantage of favorable developments and to leave behind unfavorable situations. Thus, by discounting the value of the assets held, we obtain the value of the underlying. If the investment action corresponds to the exercise of the option, the amount of the investment will be the exercise price of the option. The maturity of the option is the period during which the investment decision can be carried out. The risk-free interest rate remunerates the time value of money. The volatility of the underlying asset is the risk attached to the value of future cash flows of the project. Thus, the analogy is summarized in Table 1.1.

Table 1.1. Analogy between the parameters of the real option valuing an investment project and the financial option

Amran and Kulatilaka (1999) distinguish seven categories of real options:

• - the growth option gives the company the opportunity to expand into new markets or new activities. In other words, it is the junction between a current project and future opportunities. It is often essential to make an initial investment that can lead to new future growth opportunities if the circumstances are favorable. These are typically investments in a research and development project. The growth option is therefore similar to a European call option, of which the underlying asset is the current value of the cash flows generated by a future project and which depends on an initial investment. The exercise price corresponds to the additional investment to be undertaken to continue the project. Maturity is the time remaining until the project implementation. To proceed with the initial...