Question

In this lesson, we learned that almost all capital budgeting decisions faced by the firm contain embedded real options. Discuss ways that you can apply "real options" analysis to everyday decisions in your life.

Answer 1

Choosing the Right Model

Critics of options-based approaches to valuing and managing growth opportunities often point out that there is a world of difference between relatively simple financial options and highly complex real options. These differences, they argue, make it practically impossible to apply financial-option models to real-option decisions. They are right about the differences but wrong to assume that they are insurmountable. Valuation models can accurately capture even the most complex real options.

There are two main differences between financial and real options. First, the information necessary to value financial options and make decisions about exercising them is typically much more readily available than for real options.

The Binomial Model in Action

Using the binomial model to value this investment project as a compound option is a two-step process. First, you must figure out the full range of possible values for the underlying asset—in this case, the plant—during the project’s lifetime. 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 of the plant. Once you know that, you work back from the

Modeling the Value of the Underlying Asset.

Modeling the asset’s value involves drawing what we call an event tree, which shows the possible future values of the plant under plausible market scenarios. The first step in drawing a tree for Copano is estimating what the value of the plant would be if it existed today, a figure that may be derived from traditional nonoption valuation techniques, such as discounted cash flow. The second step is estimating how much this value is likely to move up or down during the period in question. If we assume that the distribution of possible plant values is fairly standard (what statisticians refer to as lognormal), the factor to apply for an up movement is given by the formula e to the power of (sigma multiplied by the square root of the time elapsed), where e is the base of the natural logarithm (2.718), sigma is the volatility of the asset (the likely change in the plant’s value), and the time, t, is measured in years. The factor for a down movement is the inverse of the up factor—that is, 1/e__t. Other formulas can be used in cases where the distribution of the possible underlying asset values is not lognormal.

plant’s value at completion, factoring in the various later investments, to determine the value of the plant-development project today. These second-step 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.

Valuing Your Options.

To calculate the possible values of the project as an option at each stage in the decision tree, you have to begin from the end, the point furthest in the future. If you abandon the project, its value is zero. Otherwise, the value at the end of year three is the difference between the value of the plant at the end of year three and the cost of building it. If the plant’s value at the end of year three is $1.728 billion, then the project’s incremental value at that point is $1.728 billion minus the remaining cost of $800 million needed to build the plant, or $928 million. But if the value of the completed plant turns out to be $579 million—that is, less than the construction cost—the project’s incremental value is zero, because you would not invest the $800 million to build the plant. Looking down the right hand side of the exhibit “Copano’s Decision Tree,” we see three potential scenarios in which the project’s incremental value at the end of year three is positive and one in which the costs of the project exceed the plant’s value, so the project value is zero.