266 Part Three Best Practices in Capital Budgeting
bre44380_ch10_249-278.indd 266 09/30/15 12:45 PM
round pegs, but, who knows, tomorrow square ones may be all the rage. In that case you need
a plant that provides the flexibility to produce a variety of peg shapes. In just the same way, it
may be worth paying up front for the flexibility to vary the inputs. For example, in Chapter 22
we will describe how electric utilities often build in the option to switch between burning oil
and burning natural gas. We refer to these opportunities as production options.Timing Options
The fact that a project has a positive NPV does not mean that it is best undertaken now. It
might be even more valuable to delay.
Timing decisions are fairly straightforward under conditions of certainty. You need to
examine alternative dates for making the investment and calculate its net future value at each
of these dates. Then, to find which of the alternatives would add most to the firm’s current
value, you must discount these net future values back to the present:Net present value of investment if undertaken at time t = net future value at date ____________________t
(1 + r)t
The optimal date to undertake the investment is the one that maximizes its contribution to the
value of your firm today. This procedure should already be familiar to you from Chapter 6,
where we worked out when it was best to cut a tract of timber.
In the timber-cutting example we assumed that there was no uncertainty about the cash
flows, so that you knew the optimal time to exercise your option. When there is uncertainty,
the timing option is much more complicated. An investment opportunity not taken at t = 0
might be more or less attractive at t = 1; there is rarely any way of knowing for sure. Perhaps
it is better to strike while the iron is hot even if there is a chance that it will become hotter. On
the other hand, if you wait a bit you might obtain more information and avoid a bad mistake.
That is why you often find that managers choose not to invest today in projects where the
NPV is only marginally positive and there is much to be learned by delay.More on Decision Trees
We will return to all these real options in Chapter 22, after we have covered the theory of
option valuation in Chapters 20 and 21. But we will end this chapter with a closer look at
decision trees.
Decision trees are commonly used to describe the real options imbedded in capital invest-
ment projects. But decision trees were used in the analysis of projects years before real options
were first explicitly identified. Decision trees can help to illustrate project risk and how future
decisions will affect project cash flows. Even if you never learn or use option valuation the-
ory, decision trees belong in your financial toolkit.
The best way to appreciate how decision trees can be used in project analysis is to work
through a detailed example.Drug development programs may last decades. Usually hundreds of thousands of compounds
may be tested to find a few with promise. Then these compounds must survive several stages
of investment and testing to gain approval from the Food and Drug Administration (FDA).
Only then can the drug be sold commercially. The stages are as follows:- Phase I clinical trials. After laboratory and clinical tests are concluded, the new drug is
tested for safety and dosage in a small sample of humans.
EXAMPLE 10.2 ● A Decision Tree for Pharmaceutical R&D