2. Advanced Valuation I Real Options

1. the option to wait for the optimal time to invest

2. the option to grow in the future

3. the option to abandon a poorly performing project

For Merck, investing in R&D is like purchasing a call option. When research results on early-stage drug development projects are favorable, Merck commits ad- ditional resources to the next stage of product development. If research results are not promising, Merck stops funding the project. Merck, by selectively investing in those technologies that prove to be the most promising, exercises its option to develop a product: The additional investment is equivalent to paying the strike price and acquir- ing the underlying asset—in this case, the benefits of further product development. By choosing not to make further investments (thereby mothballing or abandoning the research and development project) Merck chooses not to exercise its option.

A real option is the right to make a particular business decision, such as a capital investment, after new information is learned. A key distinction between a real option and a financial option is that real options, and the underlying assets on which they are based, are often not traded in competitive markets; for example, there is no market for Merck’s R&D in a particular drug.

Despite this distinction, many of the principles that we developed in the last two chapters for financial options also apply to real options. In particular, because real options allow a decision maker to choose the most attractive alternative after new information becomes available, the presence of real options adds value to an investment opportunity. This value can be substantial, especially in environments with a great deal of uncertainty. Thus, to make the most accurate investment decisions, the value of these options must be included in the decision-making process.

Decision tree: A graphical representation that shows current and future decisions and their corresponding risks and outcomes over time

A decision tree differs from the binomial trees used in Chapter 21. In a binomial tree, the branches of the tree represent uncertainty that cannot be controlled. In a decision tree, we also include branches to represent different choices available to the decision maker.

Notice that the decision tree now contains two kinds of nodes: square decision nodes (invest versus do nothing), and circular information nodes in which uncertainty is re- solved that is out of the control of the decision maker

A decision node that occurs after an information node in a decision tree is a real option

Once the decision tree is created, we can value the investment opportunity by working backwards from the end of the tree. At each

(i) Decision node: determine the optimal choice by comparing the present value of the remaining payoffs along each branch; and at each

(ii) Information node: compute the expected present value of the payoffs from the subsequent branches.

This option to delay is common in practice. Typically, there are costs from delaying the investment decision: interim profits from the project are lost, costs might rise, competitors may enter, etc. On the other hand, by delay- ing you will gain additional information regarding the value of the investment. In general, one must trade off the costs from delay with the benefit from gaining information before making a decision

Figure 22.5 plots the NPV of investing today and the value of waiting as we vary the expected first-year free cash flow of the dealership, and thus its current operating value. As the figure makes clear, you should invest today (and give up the option to wait) only if the current value of the dealership exceeds $6.66 million. Thus, your optimal investment strategy is to invest today only if the NPV of the investment opportunity exceeds $6.66 million - 5 million = $1.66 million.

The red line denotes the NPV of investing today. The yellow curve shows the value today of waiting one year to make the decision (i.e., the value of the call option). The black curve indicates the value of the contract, which gives us the option to invest today, in one year, or not at all. The optimal investment strategy is to invest today only if the value of an operating dealership exceeds $6.66 million.

Current NPV:

Without the option of when to invest, it is optimal to invest as long as NPV > 0. But when you have the option of deciding when to invest, it is usually optimal to invest only when the NPV is substantially greater than zero.

To understand this result, think of the timing decision as a choice between two mutually exclusive projects: (1) invest today or (2) wait. Faced with mutually exclusive choices, we should choose the project with the higher NPV. That is, we should invest today only if the NPV of investing today exceeds the value of the option of waiting. If we can always walk away from the project, the option of waiting will be positive, so the NPV of investing today must be even higher for us to choose not to wait.

Thus, given the option to wait, an investment that currently has a negative NPV can have a positive value.

Volatility:

By delaying an investment, we can base our decision on additional informa- tion. The option to wait is most valuable when there is a great deal of uncertainty regard- ing what the value of the investment will be in the future. If there is little uncertainty, the benefit of waiting is diminished.

Dividends:

Recall that absent dividends, it is not optimal to exercise a call option early. In the real option context, the dividends correspond to any value from the investment that we give up by waiting. It is always better to wait unless there is a cost to doing so. The greater the cost, the less attractive the option to delay becomes.

Notice that the beta of a corporation with the option to open a dealership (that is, 6.4) is considerably larger than the beta of a dealership itself (2.0). Moreover, the beta of the corporation will fluctuate with the value of the option, and it will only be equal to the beta of a dealership if it is optimal to open the dealership immediately.

As this example shows, when comparing firms in the same industry, betas may vary depending upon the firms’ growth opportunities. All else equal, firms for which a higher fraction of their value depends on future growth will tend to have higher betas.

The fact that the beta of the firm includes the beta of the firm’s growth options has implications for capital budgeting. Because the beta of growth options tend to be higher than the beta of the firm’s investments in place, the beta of the firm typically overstates the beta of its existing assets. Hence, when financial analysts estimate an individual project beta by using the beta of a firm with substantial growth options, they may be overestimating the project beta.

When a firm has a real option to invest in the future, as in the dealership example, it is known as a growth option. In other situations, the firm may have the option to reduce the scale of its investment in the future; the option to disinvest is known as an abandonment option. Because these options have value, they contribute to the value of any firm with future possible investment opportunities.

Future growth opportunities can be thought of as a collection of real call options on poten- tial projects. Out-of-the-money calls are riskier than in-the-money calls, and because most growth options are likely to be out-of-the-money, the growth component of firm value is likely to be riskier than the ongoing assets of the firm. This observation might explain why young firms (and small firms) have higher returns than older, established firms. It also explains why R&D-intensive firms often have higher expected returns even when much of the R&D risk is idiosyncratic.

While we don’t know the true probability of each outcome, we can compute the present value using risk-neutral probabilities, as we showed in Chapter 21. To find the risk-neutral probabilities, we solve for the probabilities so that the expected return of all financial assets is equal to the current risk-free rate.

That is, a risk-neutral possibility of x that interest rates will rise is required for the annuity to have an expected return equal to the risk-free rate of 6% over the next year.

In this example, even though the cash flows of the project are known with certainty, the uncertainty regarding future interest rates creates substantial option value for the firm. The firm’s ability to use the patent and grow should interest rates fall is worth close to a quarter of a million dollars.

This project is an example of a strategy that many firms use when they undertake big projects. Rather than commit to the entire project initially, a firm experiments by undertak- ing the project in stages. It implements the project on a smaller scale first; if the small-scale project proves successful, the firm then exercises the option to grow the project.

The previous two examples consider cases in which the firm has the option to grow or expand if the project proves successful. Alternatively, when a project is unsuccessful, the firm may be able to mitigate its loss by abandoning the project. An abandonment option is the option to walk away. Abandonment options can add value to a project because a firm can drop a project if it turns out to be unsuccessful.

It is easy to ignore or understate the importance of the option to abandon. In many applications killing an economically unsuccessful venture can add more value than starting a new venture. Often, however, managers focus on the value created by starting new ven- tures and de-emphasize the value created by abandoning old ventures. Some of this behaviour undoubtedly results from the same behavioural biases that we discussed in Chapter 13 that cause individual investors to hold onto losers. It is also closely tied to the sunk cost fallacy, the idea that once a manager makes a large investment, he should not abandon a project. As we pointed out in Chapter 8, sunk costs should have no bearing on an invest- ment decision. If continuing a project is a negative-NPV undertaking, you can create value by abandoning, regardless of how much investment has already been sunk into the project.