Option to abandon the project, Valuing an Option to Abandon: An Illustration

Table 1 Parameters of a project and related real options. Source: own elaboration. The consideration of real options in the assessment of a project is useful both in offering an alternative approach and in providing more concrete material for calculation [ 9 ]. The use of real options involves the prior identification of the options presented in the project [ 10 ] and the subsequent determination of their value.

The real options which are initially considered may help the manager to modify the project if necessary to enable a more accurate valuation to be carried out. It is in fact normally used only by companies dealing with very large capital such us those supplying energy or healthcare, or in the technology sector.

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The findings of previous surveys cite the complexity of its implementation, together with lack of familiarity, as the reasons for the infrequent use of real options. This leads them to believe that any error in use may be very difficult to detect [ 12 ]. Option pricing constitutes one of the most challenging problems in computational finance and derivative modelling [ 13 ]. Although these two types of options are not of the same nature, they have many similarities. For example, in both cases, the value of an option is directly related to its maturity and to the volatility of the underlying asset.

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The existing literature about real option valuation indicates two identifiable approaches, namely, discrete and continuous, depending on the complexity and nature of the analysed option [ 15 — 18 ]. More specifically, discrete models are more popular when valuing real options, given their simplicity [ 19 — 22 ].

In this paper we will use the binomial options pricing model [ 23 ], initially for one defined period, then for two periods, and, finally, for periods. And this is because the aforementioned model, used in the context of financial options appraisal, is also applicable to the case of real options [ 2425 ].

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In particular, the option to abandon provides the investor with the opportunity of liquidating the entire investment project in exchange for an amount called the residual value [ 26 ].

This option can be considered as a put option which follows a multiplicative binomial pricing process [ 27 ].

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Thus, the option to abandon will be exercised if the operation proves to be inefficient, that is to say, when the present value of cash flows is less than its residual value, thereby indicating the optimal time to abandon the investment [ 28 ]. These options are frequently used by venture capital companies because most of their investments are carried out in innovative sectors with a high degree of uncertainty [ 29 ].

Assessing the Option to Abandon an Investment Project by the Binomial Options Pricing Model

The option to abandon increases the project value because it reduces the difficulties to terminate the project activity when it becomes a bad investment. The residual value of the project can be constant if its value has been agreed upon in a prior contract. Nevertheless, the residual value is usually variable, which makes its estimation more difficult.

The residual value does not have to depend on the project value; in this case, the option to abandon has two stochastic variables which complicate its estimation: the future cash flows of the project and its residual value [ 30 ].

Therefore, the aim of this paper is to obtain a mathematical expression for the value of the option to abandon a project, terminating the business activity and liquidating assets, after one, two, and periods of time.

The Option to Abandon a Project

This type of option, along with the options to extend, to reduce, and to defer, is one of the real options most used in business practice and engineering projects.

In general, the total value of an investment project can be divided into two components: the static NPV and the value of the real option [ 31 ]. Thus, the steps to be taken into account to obtain the expression of the price of the option to abandon are the following: i First, the value of an investment project is calculated by including the flexibility represented by the possession of an option to abandon.

This paper is organized as follows.

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After this Introduction, Section 2 introduces the methodology to be used in the rest of the paper to obtain the mathematical expression of the option to abandon a project within a period.

Section 3 presents the generalization of Section 2 to two periods and allows us to derive the mathematical expression for periods, shown in Section 4.

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Finally, Section 5 summarises and concludes. Option to Abandon within a Period The value of the option to abandon a project at any time prior to the expiry of the first period denoted byusing a continuous stochastic process, is given by where is the riskless interest rate, represents the random variable which describes the value of the project cash flows at instant 1, denotes the stochastic residual value of the project at instant 1, and is the joint probability density function of and.

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  4. Valuing an Option to Abandon: An Illustration

Nevertheless and for the sake of simplicity, we have opted for the use of the discrete stochastic model called the binomial options pricing model. Accordingly, starting from the present value of cash flows and the present value of the residual valueit is assumed that there are only two possible scenarios for both and whose probabilities of occurrence are andrespectively.

Sometimes closing a project, abandoning a project is the right thing to do, okay? Of course all projects have to be constantly reevaluated, right? In fact, one of the topics we're going to talk about in module four is how to evaluate ongoing projects and divisions, that's one of our topics. For now, let's talk about the value of this option to abandon.

Option to abandon the project, the first scenario describes an upward movement of andwhilst the second scenario represents a downward movement of and with probability. Therefore, both the value of cash flows option to abandon the project the residual value at instant 1 can be described by the following dichotomous random variables representing their evolution: where and are, respectively, the upward and downward possible movements of.

As previously indicated, it is assumed that the residual value is also a dichotomous random variable.

Real Options in Capital Budgeting. Pricing the Option to Delay and the Option to Abandon a Project

This is because, according to the Gordon and Shapiro model [ 32 ], the residual value of the project at instant can be calculated as follows: where is the value of cash flow at instantis the market discount rate, and is the cumulative increase rate of cash flows. So, the evolution of the residual value of a project can be expressed as follows: where and are, respectively, the upward and downward possible movements of.

ACCA AFM 6 12 Application of options theory in investment decisions Real Options

Thus, the project value with the option to abandon will be determined according to the factors representing the upward and downward movements applied to the present value of the future cash flows, where andbeing the volatility of the present value during one period.

Analogously, the upward and downward factors concerning the residual value of the project are andrespectively, where we have assumed that. That is to say, the relative range of is less than that corresponding to.

By using the option to abandon the project options pricing distribution, these factors will allow us to foresee the value of the project in a favourable or an unfavourable situation whose probabilities of occurrence are andrespectively. Consequently, the NPV of a project with the option to abandon within a period is given by the following expression: where is the initial investment.

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As and are random variables, the project value will depend on the relative position of the residual value with respect to the value of the cash flows both in the case of an unfavourable and a favourable evolution. Nevertheless, as the residual value under the favourable condition,is always less than the value of cash flow under the same conditions,the value of a project with the option to abandon within a period will depend on the relative position of.