In each scenario, the value will be the larger of the value of exercising the option by building the plant at that point for a cost of $800 million and the value of keeping the option alive—deferring the decision on whether to spend the $800 million on building the plant until the next period. If the event tree looks a little crude, don’t worry. One large South American conglomerate we know of measures its exercise performance by tracking the time lag between the resolution of uncertainty (for example, when the price of a particular commodity hits a trigger point for opening or closing a mine) and an appropriate action by the company. We now work back from the end of year three to determine the project’s potential values at the end of year two. If the plant’s value falls to $833 million, the year-two potential values are $1 billion and $694 million. We do not maintain, however, that simply switching to a binomial model will put everything right, for the biggest problem with real options (though it is seldom voiced) is more managerial than technical. 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. At that point, the project’s incremental value is the value of the right to invest $800 million in building the plant over the following two years less the $400 million the firm must invest in order to have that option—but if the result of that subtraction is negative, the project’s value is zero. But in most cases, companies can find a compromise solution that reveals the quality of their processes without divulging strategically sensitive performance goals. The seven sets of bars represent seven hypothetical option holders, ranging from fairly patient on the left to very itchy on the right. Using the binomial model to value this investment project as a compound option is a two-step process. Many of the problems with real-options analysis stem from the use of the Black-Scholes-Merton model, which isn’t suited to real options. But some evidence suggests that home owners routinely exercise that option too late, even if they know that the arithmetic works out in favor of refinancing. The truth is, all models are simplified representations of reality, and all involve assumptions. But it doesn’t, we regret, go to the heart of the problem many managers have with real options: Managers suspect that the options approach routinely overvalues a company’s growth opportunities. The values the plant could have a year hence, two years hence, and three years hence are as shown: Copano’s managers use the values from the event tree to begin their calculation of the values on the decision tree. All rights reserved. Should they commit to investing the full amount needed? The factor for a down movement is the inverse of the up factor—that is, 1/e__t. To determine the value of that right to invest, we simply work backward from the possible values at the end of year two that we have already calculated using the replicating portfolio technique, just as we worked back from year three to get the potential values at the end of year two. To build that decision tree, they calculate how much the plant would be worth if it existed today and what its value could be at points in the future. They are decisions like shutting down unprofitable operations or waiting until conditions improve. Real options don’t have to be a black box. Working back from these using the replicating portfolio technique, we find that the right to invest $400 million in a year’s time is worth $71 million, $11 million more than the $60 million cost of permits and preparation. Indeed, a survey of 4,000 CFOs published in 2001 by John Graham and Campbell Harvey found that 27% of the respondents claimed they “always or almost always” used some sort of options approach to evaluating and deciding upon growth opportunities.
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