Unfortunately, we cannot determine, a priori, what that discount rate should be, because the risk of the option on the project is different from the risk of the project itself. If the plant is to be built at the end of year two and its value turns out to be $1.44 billion (the highest of the potential values at that period as shown on the event tree), then the value of the project if the firm chooses to build immediately is $1.44 billion less the $800 million exercise cost, or $640 million. The four sets of bars represent four hypothetical option holders, ranging from fairly alert on the left to very sleepy on the right. But in most cases, companies can find a compromise solution that reveals the quality of their processes without divulging strategically sensitive performance goals. How do you estimate the volatility of a chemical plant’s value? The shaded bars represent the value gap for an option on a stock whose price volatility is 20%; the unshaded bars represent the gap for an option on a stock with much higher volatility—80%. Using the right valuation model will make real-options-based management work a lot better. American-style call options give holders the right to buy the stock at any time through the maturity date, and sometimes it is best to exercise an option early rather than sell it to someone else. While current-day options are protected against stock splits—the exercise prices and number of options are adjusted in response to splits—investors still have to vigilantly keep track of stock dividends, because most options are not dividend protected. In some cases, the values of the assets underlying real options are similarly observable. Some critics of the real-options tool feel that these kinds of assumptions render option-based valuation models useless. A 1999 study by Chip Heath, Steven Huddart, and Mark Lang revealed that corporate officers who hold executive stock options also have a tendency to exercise their options too early if there has been a recent run-up in the stock price. Other formulas can be used in cases where the distribution of the possible underlying asset values is not lognormal. The trigger points should not only tell managers when they need to decide on exercise but also specify rules governing the exercise decisions. REAL OPTION ANALYSIS EXAMPLE 1 A company is considering investing in a project. How did Copano’s managers derive the numbers on the decision tree? The right choice for managers, therefore, is to defer building and to keep the option alive; that choice gives them a project value of $699 million. In particular, work by John Cox, Steve Ross, and Mark Rubinstein has led to the creation of binomial, or lattice, models that are built around decision trees and are ideally suited to real-option valuation. Should they commit to investing the full amount needed? The right to exercise financial options is unambiguous. This contrasts with the net present value of minus $9 million, which a conventional NPV analysis would give ($1 billion less the present value of the three capital outlays, which come to $1.009 billion if we assume a discount rate of 10.83% for the industry). Using our real-option model would force them to do this, and by looking at how the values of their previous chemical plants—and those of competitors—have evolved in the past, they can construct plausible scenarios for those different possible futures. 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. For simplicity, the exhibit models not a real option but a stock option—a put option with a year to maturity. Even if it is relatively clear what the underlying asset is—a new plant, for instance—the maturity of an option can be indeterminate: Does the opportunity to expand a business last forever or until a competitor takes away the opportunity by expanding first? Real options don’t have to be a black box. The present value (PV) of future discounted expected cash flows is either 3000 if the market goes up or 500 if the market goes down next year. If holders of financial options don’t always behave optimally, we can scarcely expect holders of far more complex real options to behave any better. So it is important for companies to identify clearly and in advance who will have responsibility for acting on the trigger. Real-World Example of Real Options . Real options in capital budgeting allow a company’s management to make future decisions that may change the value of capital budgeting decisions made today. Corporate financial officers may have the same problem in managing their companies’ debt portfolios. The reasons for this high defection rate seem just as sensible as the reasons for using the tool and are usually based on technical grounds. Obviously, triggers should not be precise dates or numbers but rather ranges around which there can be some flexibility and debate. 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. Once the managers responsible for the exercise decisions have been assigned, the company needs to make sure those people are properly motivated. In a year, therefore, the plant will be worth either $1.2 billion or $833 million. As MBA graduates may remember from their finance courses, any option on a share can be expressed as a portfolio consisting of a certain number of shares and a certain number of bonds. They could give up on real options, throwing away a tool that ideally captures the contingencies in managing growth opportunities. To use the binomial model, you must create an “event tree” to figure out the full range of possible values for the plant during the project’s lifetime—next year, at the end of the design phase, upon completion. They are right about the differences but wrong to assume that they are insurmountable. In this case, that number is greater than the value of exercising the option by building the plant. In some cases, companies may find it useful to share their trigger points with investors and analysts, as the information will enable these stakeholders to assess the quality of the company’s decision making. Each corporate growth project is an option, in the sense that managers face choices—push ahead or pull back—along the way. They worked backward from the end of year three, using the values from the event tree, and they relied on the replicating portfolio technique, which is explained in the sidebar with that title.