Managing Risk through Phased Decisions: Decision Trees 323
discount rateapproach, under which differential project risk is dealt with by changing
the discount rate. Average-risk projects are discounted at the firm’s average cost of cap-
ital, higher-risk projects are discounted at a higher cost of capital, and lower-risk proj-
ects are discounted at a rate below the firm’s average cost of capital. Unfortunately,
there is no good way of specifying exactly how muchhigher or lower these discount
rates should be. Given the present state of the art, risk adjustments are necessarily judg-
mental and somewhat arbitrary.
How are risk-adjusted discount rates used to incorporate project risk into the
capital budget decision process?
Managing Risk through Phased Decisions: Decision Trees
Up to this point we have focused primarily on techniques for estimating a project’s
stand-alone risk. Although this is an integral part of capital budgeting, managers are
generally more interested in reducingrisk than in measuringit. For example, sometimes
projects can be structured so that expenditures do not have to be made all at one time,
but, rather, can be made in stages over a period of years. This reduces risk by giving
managers the opportunity to reevaluate decisions using new information and then ei-
ther investing additional funds or terminating the project. Such projects can be evalu-
ated using decision trees.
The Basic Decision Tree
For example, suppose United Robotics is considering the production of an industrial
robot for the television manufacturing industry. The net investment for this project
can be broken down into stages, as set forth in Figure 8-3:
Stage 1. At t 0, which in this case is sometime in the near future, conduct a
$500,000 study of the market potential for robots in television assembly lines.
Stage 2. If it appears that a sizable market does exist, then at t 1 spend $1,000,000
to design and build a prototype robot. This robot would then be evaluated by
television engineers, and their reactions would determine whether the firm
should proceed with the project.
Stage 3. If reaction to the prototype robot is good, then at t 2 build a production
plant at a net cost of $10,000,000. If this stage were reached, the project
would generate either high, medium, or low net cash flows over the following
four years.
Stage 4. At t 3 market acceptance will be known. If demand is low, the firm will ter-
minate the project and avoid the negative cash flows in Years 4 and 5.
A decision treesuch as the one in Figure 8-3 can be used to analyze such multi-
stage, or sequential, decisions. Here we assume that one year goes by between deci-
sions. Each circle represents a decision point, and it is called a decision node. The
dollar value to the left of each decision node represents the net investment required at
that decision point, and the cash flows shown under t 3 to t 5 represent the cash
inflows if the project is pushed on to completion. Each diagonal line represents a
branchof the decision tree, and each branch has an estimated probability. For exam-
ple, if the firm decides to “go” with the project at Decision Point 1, it will spend
$500,000 on a marketing study. Management estimates that there is a 0.8 probability
322 Cash Flow Estimation and Risk Analysis
