# Real options method for valuation

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Email: eduardo. This paper provides an overview of the real options approach to valuation mainly from the point of view of the author who has worked in this area for over 30 years. After a general introduction to the subject, numerical procedures to value real options are discussed. Recent developments in the valuation of complex American options has allowed progress in the solution of many interesting real option problems.

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Two applications of the real options approach are discussed in more detail: the valuation of natural resource investments and the valuation of research and development investments. JEL classification: G12 1. Options are contingent decisions that provide the opportunity to make a decision after uncertainty unfolds.

Uncertainty and the agent's ability to respond to it flexibility are the source of value of an option. Whenever possible, real options valuations are aligned with financial market valuations. Most investments are subject to options valuation.

## Investment appraisal and real options | ACCA Qualification | Students | ACCA Global

There are four main types of options associated with investment projects-the option to expand, to postpone, to abandon, and to temporarily suspend an investment.

For example, the option to expand a project is valuable when a firm may want to invest in a negative net present value NPV project if it provides the firm the possibility of developing a new project. Consider the valuation of a mine of which, at current commodity prices, only half is economically feasible for development. This investment will provide the option to develop the remainder of the mine when and if market prices change.

In this case, the option to expand is valuable and must be considered when quantifying the value of the mine. On the other hand, even with a positive NPV project, the option to delay the investment is valuable as it gives the firm the opportunity to wait until more market information is available.

- THE REAL OPTIONS APPROACH TO VALUATION: CHALLENGES AND OPPORTUNITIES
- A real option is an economically valuable right to make or else abandon some choice that is available to the managers of a company, often concerning business projects or investment opportunities.

Finally, the option to temporarily suspend production is valuable whenever a firm has the opportunity to open and temporarily close a facility. For instance, when a commodity price is low, the firm can choose to close its facility and re-open it later when prices are higher.

Thus, flexibility can be an important real options method for valuation of value for many investment projects and the option-pricing framework provides a powerful tool for analyzing such flexibility.

### Adjusting for Cost

Furthermore, the real options approach to valuation is currently being applied in practice and extended in several directions. In particular, this method has been broadened to take into account competitive interactions and their impact on option exercise strategies. The remainder of this paper is organized as follows. Section 2 compares the two main approaches to value how to make money easily with ideas projects.

## Real Option Definition

Section 3 briefly describes three procedures used to solve option valuation problems. Section 4 presents two particular applications of the real option approach in investment projects.

Finally, Section 5 concludes. The traditional valuation technique, known as discounted cash-flows DCF or net present value NPVrequires forecasts.

It uses a single expected value of future cashflows. A simplified version of the traditional approach is: where Ct is the expected cash flow in period t and k is the risk-adjusted discount rate. By defining cash flows as the profits obtained by the investment project, Equation 1 can be rewritten as: where qt is the quantity produced and St is the spot price, assumed to be the only source of uncertainty in this simplified version.

There are two main drawbacks to the traditional approach that makes it inappropriate for valuing projects in many practical situations.

## Real options valuation - Wikipedia

First, DCF assumes that future firm decisions are fixed at the outset and ignores the flexibility in decision making during the course of the investment project. Second, when there are options e.

Alternatively, the risk-neutral RN valuation or certainty-equivalent CE approach can effectively capture the flexibility embedded in real options valuation. In the CE approach, the adjustment real options method for valuation risk is in the probability distribution of real options method for valuation flows instead of the discount rate. The NPV of a project is then calculated by discounting the certainty equivalent cash flows CEQt by the risk-free rate: As can be observed in Equation 3in order to calculate the certainty equivalent cash flows, futures prices Ft are used instead of the spot prices St.

Futures prices are the expected future spot prices under the risk-neutral distribution. Cox and RossReal options method for valuation and Krepsand Harrison and Pliska show that the absence of arbitrage implies the existence of a probability distribution, such that securities are priced at their discounted at the risk-free rate expected cash flows under these risk-neutral or risk-adjusted probabilities.

Moreover, these probabilities are unique if markets are complete-all risks can be hedged. If, on the other hand, markets are not complete, their probabilities are not unique, but any of them can be used for pricing. The first case is when the risk-neutral distribution is known, as in the Black-Scholes framework; unfortunately, the only pure example of this case in the real world are gold mines. The second case is when the risk-neutral distribution is unknown but can be obtained from futures prices or other traded assets e.

In Section 4 this topic will be explored further. The last case is when the risk-neutral distribution is unknown and futures prices do not exist. In this case the risk-neutral distribution can be obtained by using an equilibrium model, such as the CAPM.

### Integrating Options and Discounted Cash Flow

The first approach uses dynamic programming techniques to lay out possible future outcomes and folds back the value of the optimal future real options method for valuation using risk-neutral distributions. The binomial method is a dynamic programming approach widely employed to value simple options.

It can also be used to price American-type options. However, this solution method becomes inadequate when there are multiple factors affecting the value of the option or when there are path dependencies. The second method directly solves the partial differential equations PDE that result from most option pricing problems. This approach leads to closed-form solutions in very few cases, such as the Black-Scholes equation for European call options.

In most option valuation problems the PDE has to be solved numerically. This is a very flexible method, and it is appropriate for valuing American options.

Finding a solution however becomes extremely complicated when there are more than three state variables; thus, PDE is an inadequate method for solving the more complex real option problems. Furthermore, this method is technically sophisticated as it needs to approximate boundary conditions.

- Making Real Options Really Work
- CFOs tell us that real options overestimate the value of uncertain projects, encouraging companies to overinvest in them.

In general option pricing problems can also be solved by simulation. The simulation approach is very powerful; however, it is forward-looking whereas the optimal exercise of an American option has dynamic programming features.

Longstaff and Schwartz developed a simulation approach to valuing American options. An American option gives its holder the right to exercise at multiple points in time finite number before its maturity date.

At each exercise point, the holder optimally compares the immediate exercise value with the value of continuation. As standard theory implies real options method for valuation the value of continuation can be expressed as the conditional expected value of discounted future cash flows, the basic idea behind the simulation approach is that the conditional expected value of continuation can be estimated from the cross-sectional information from the simulation by least-squares.

The conditional expectation function is estimated by regressing discounted ex-post realized cash flows from continuation on functions of the current or past values of the state variables. The fitted value from this cross-sectional regression is shown to be an efficient estimator of the conditional expectation function. Thus, by estimating the conditional expectation function for each exercise date in each of the possible simulated paths, an optimal stopping rule for the option and hence its current value can be accurately estimated.