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percent of equity value. The option-pricing valuation with shut-down/reopen and abandonment options gave a valuation of Kryptonite Mining's equity of 116 percent of its current market value.

The shut-down, reopen, and abandonment option values, as fractions of the corresponding site option-pricing values, ranged between 5 and 15 percent for a spot price range of $1.75/ounce to $2.25/ounce. These option values were much higher for lower spot prices and much lower for higher spot prices.

A major benefit of the analysis was the insight it provided into the economics of opening and shutting down each site. Given that a mine was open, it was optimal to keep it open even when the marginal revenue from a ton of output was less than the marginal cost of extraction. The intuitive explanation is that the fixed cost of closing an operation might be incurred needlessly if the commodity price rose in the near future. The opposite result applies to a closed mine. The optimal decision might be to keep it closed because of reopening costs until the commodity price rose substantially above the marginal cost of production.

Multiphase Investment (Compound Option)

CHEMCO was considering a $650 million investment in a new chemical plant. Traditional NPV methodology estimated a value of negative $71.2 million. This result was based on a spread between the input and output chemical prices that was volatile, near a high, given current market conditions, and was mean reverting. Mean reversion implied that since the spread was currently high, the probability that it might decrease was deemed to be greater than the probability that it would increase further. Management decided to use an option-pricing approach because it could start the project now, then abandon after an initial design phase, or after a pre-construction phase, if the spread decreased as expected (see Exhibit 20.13).

The project was a compound option because the second phase was conditional on the results of the first phase and on improvement in the spread, and the third phase was contingent on approval of the second phase. It was appropriate to think of the first phase as a platform on which the other phases were contingent. When the additional flexibility was valued, the project's NPV increased from -$71.2 million (without flexibility) to $354.5 (with flexibility).

Compound options are appropriate for a wide range of managerial decisions. They might even be used for distinguishing between a single acquisition and an acquisition program—a sequence of acquisitions. Often the initial deal in an acquisition program is a platform or stepping-stone to other acquisitions. The first deal might be negative NPV when viewed in isolation, but the entire program might have a positive value because it is a compound option.

Compound Rainbow Option (Learning Option)

A compound rainbow option is a sequence of decisions that is affected by two or more sources of uncertainty. The example in Exhibit 20.14 is what we call a learning option. It is applicable to exploration and production decisions, to research and development programs, and to product development programs. Our client was a large integrated oil company that had an extensive natural gas field. The field was 60 percent explored and 40 percent unexplored.

Management was divided about whether to develop the field now or to complete exploration. Those in favor of immediate development argued that Exhibit 20.13 The Value of Compound Options in a Multiphase Investment

flexibility,3n(j therefore destroyed option value

Exhibit 20.14 Compound Rainbow Option

Exhibit 20.14 Compound Rainbow Option

doing so would pull the expected future cash inflows of the project into the present and thereby add cash and value to the company. Others were concerned that early development might result in expensive ''wrong sizing" of the billion-dollar investment in refineries, pipelines, and storage facilities. Current development would have to be based on estimates of reserves in the unexplored portion of the field—estimates that had a wide range of error. Once the investment was in place, it would be oversized and have excess capacity if the unexplored part of the field proved to have less natural gas than expected. If it turned out to have more natural gas than expected, the development would be undersized. To resolve the debate, management decided to try a real options approach.

The decision tree in Exhibit 20.14 shows the compound options that were involved. A decision had to be made about whether to start or defer the development of the field. If development were started, another decision had to be made about the scale of investment. If development were deferred, there was the decision about whether to explore, and if so at what level. If exploration took place, should the development decision be made in year 3 or deferred further?

There were two sources of uncertainty. First is the price of natural gas, which is known today, but which becomes more uncertain. Second is the uncertainty about the quantity of natural gas in the ground. It has a wide range of uncertainty today, but the range narrows if the company decides to explore the field.

When the analysis was completed the highest value was obtained by making the decision to explore now, by deferring the development decision until year 3, and making an expansion decision in year 11. The value of this set of decisions was 125 percent higher than the value of the base case, which was to develop the field now and wait for three years before deciding to explore.

It is easy to see from these examples that asset options can substantially alter the value of a business. The fact that the options exist does not mean that they are optimally managed. There are two problems. First, managers are not trained to recognize real options. Second, they are usually not familiar with the methodological advances that have made real options easier to apply and to understand. Understanding asset options can provide insight into managing flexibility as a new approach for dealing with uncertainty.

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