Real-World Complications

By recognizing your ability to shut down the gas turbine plant, you are able to estimate a much more precise value than you would assuming a stupid “always running” plant value. However, many problems remain with the $28.6 million value estimate. Even if you cannot address each and every one, you want to at least recognize them.
Your most important concern is that you need to estimate the electricity price process for 2000, not for 1999. This is a self-contained task—you can do so, even before you ever consider the plant itself.
1. Your $28.6 million calculation was for profits if you had operated in 1999. Alas, it is more sensible to assume that 1999 would only be indicative of 2000 in terms of the electricity price process (e.g., mean and standard deviation). Moreover, you know that 1999 closed with a price of $28.89, not the average price of $28.09. Can you make use of this knowledge? In any case, you should assume that history will not repeat itself, but that it can teach you a lot about the future. This is exactly analogous to our earlier assumption in the investments sections of this blog, where we stipulated that historical return statistics (means and standard deviations) are indicative of future statistics, but that the exact future return realization could end up quite different from the past.
2. Even if you use 1999 data to estimate the statistical process for 2000, it could be that the historical process is not a good guide for your future. If your experience in electricity management makes you capable of better estimating the price of electricity in 2000, then you can come up with a better cash flow estimate. But to improve your estimate of the value of the plant, you must be able not only to forecast the mean electricity price, but also the standard deviation in the electricity price. (In retrospect, we know that the past turned out not to be indicative of the future. California experienced a famous energy crisis in 2000, partially due to price manipulation by the energy producers themselves!)
3. If you look at the historical prices, you will see that each weekly price is not exactly a random draw from a fixed distribution. When the price the previous week was high, chances are that the price this week is also high. For example, at the end of the year, the price stood at $28.89. This implies that the next price is unlikely to be $50 or $18, but more likely something between $26 and $32. In contrast, when the price was $50 last week, you would expect it to be something, say, between $44 and $52. (Note that this is not necessarily symmetric around $50!)
You know that in order to value your plant, you must forecast some process for the electricity price in 2000. Your technique itself can range from the simple to the fancy. In the real-world, the better you are at electricity price process estimation, the better will be your value estimates. Typically, the best forecasts combine qualitative managerial knowledge of the industry and business with quantitative statistical modeling techniques. We shall explore two kinds of electricity forecasting processes in the next two sections: a simple qualitative version, in which you write down a reasonable and intuitive binomial tree; and a quantitative statistical time-series estimation, in which you estimate a time-series model from the historical electricity price data.