Department of Management Science & Engineering
Stanford University

Number 12/Autumn 2003

Investment Science Newsletter

By Professor David G. Luenberger

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This Newsletter has become quite popular, for many people are ordering it through the website Recently, we attended the conference Real Options Valuation 2003 in San Diego, where we met a number of other real options researchers and practitioners, presented our work, and gave people a brochure on the Real Options Calculator. It was a nice intimate conference with many good ideas. It was clear from the presentations and discussions that the field is maturing and real options is becoming well-accepted. We believe that there is still a great deal of room for further advance - particularly through the incorporation of more general investment science concepts in business problems. It is a tradition of this Newsletter to include a short technical article. We obtained quite a bit of positive feedback about the article "Strategy and the State Framework" contained in the last Newsletter. This is a powerful approach that we are still developing. It is likely that there will be more about it in future issues. This current issue features an article "Interacting Options" by the guest contributor Robert Luenberger. As you may know, Robert has led the development of investment science at Onward, Inc. and teaches the Stanford course Investment Science Practice each Spring quarter. In this class, students work in teams on actual industry problems on a real-time basis. By now, dozens of such projects have been completed, to the satisfaction of both the industry sponsor and the students, and we have learned a great deal from them. Robert's article in this issue deals with a common phenomenon in real options analysis. As always, we welcome comments on the article.

Short Course

The two-day course Investment Science for Industry is described on the website There have been a number of requests to have this course offered again soon, and we are making plans to do so. If you have an interest in this, either individually or to be offered in your company, please let us know by responding as indicated in the website.

Interacting Options

When analyzing a set of investment decisions or options within an investment project, it often seems natural to analyze each potential choice on an individual basis. This approach, however, ignores the interaction between the various choices. The best course of action, when each choice is analyzed independently, may not be the same as when the full spectrum of choices is analyzed together.

Here we describe two common ways in which this is manifested.

First, a choice may lead to future opportunities down the line. For instance, an investment in a platform technology may lead to only modest (or no) direct sales, but will enable several products that would not have been possible otherwise. Similarly, certain expansions are naturally sequential and must be conducted one step at a time. The value associated with taking each step must account for these future possibilities.

As an example, consider a manufacturing facility whose capacity can be expanded to accommodate demand growth. Suppose capacity may be added sequentially in two phases so that the second can only be conducted after the first is complete. When determining the value of executing the first expansion, the value associated with the (newly-created) ability to conduct further expansion must be included.

We can represent the above situations diagrammatically. For the case of a platform technology, the ovals in Figure 1 represent the possible cash-flow scenarios and the arrows represent available strategic options. The value of each scenario may depend on one or many uncertain variables and also on the value of the subsequent decisions and their corresponding (uncertain) cash-flows. Figure 2 represents a simple sequential capacity expansion diagram.

Figure 1: Platform technology investment


Figure 2: Sequential capacity expansion

The second type of option interaction is often of a more subtle nature. Several options may be mutually exclusive in the sense that exercising one of them precludes the exercise of the others. While this may lead one to think that it is sufficient to know which one is more valuable on a standalone basis, this may not be the case. Exercise of an option may be optimally postponed in order to capture greater value at a later date. However, such postponement opens the door to future exercise of all other available options as well. Thus, there is a complex interaction between all options within a project even when they are mutually exclusive; and knowing which option is most valuable in an individual, disconnected way is not enough to ensure one's decisions maximize value of a project.

Consider, for example, a real estate investor who holds some land and is considering developing it into office space to be sold. In general, the best time to do this will depend on the future prices of real estate in that area. The investor, however, is exposed to price movements in each direction: he gains as the office space prices rise and loses as prices drop. Due to the fixed costs that he is likely incurring, it may be optimal for him to develop and sell immediately. Imagine, that, in addition to the development prospect, the developer has a standing fixed offer for the land itself for a certain period of time. In that case, the investor can profit from positive price changes while having limited exposure to decreases in value. Therefore, the development option is more valuable as the investor can now afford to wait longer for possible price rises. Figure 3 shows a strategy map for this situation.

Figure 3: Real estate development with fixed downside protection

There are interesting implications of option interaction when designing projects. Asking certain questions may lead to the discovery of options that, while not necessarily directly related to where you think value lies, may in fact create significant additional value. Are there new opportunities that exercising a certain option opens up? Are there (salvage) options that would become valuable if things do not go as hoped?

Let us consider again the real estate example mentioned above. The quarterly maintenance on the property is $750,000 and there is no rent or other income being generated from the property. The county has made a standing offer of $6 million for the property. Alternatively, they could develop the land themselves - this would cost $50 million if carried out immediately, and this figure would rise 10% for each year of delay. Once developed, they expect the land to be worth $65 million, though this value carries an annual volatility of 40%.

Ignoring the county's offer, one can work out that the best decision would be to develop and sell immediately, leading to a net present value of $8.89 million.

Considering both options simultaneously, however, leads to a more interesting (and profitable) strategy. Specifically, one would monitor the current land price each quarter, and develop the land if it is above a pre-defined threshold, sell to the county if it is below another pre-defined level, and wait if the price remains in between these two levels. The net present value associated with following this strategy is $12.24 million.

The details of this example can be found at