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324 CHAPTER 8 Cash Flow Estimation and Risk Analysis

that the study will produce favorable results, leading to the decision to move on to

Stage 2, and a 0.2 probability that the marketing study will produce negative results,

indicating that the project should be canceled after Stage 1. If the project is canceled,

the cost to the company will be the $500,000 for the initial marketing study, and it will

be a loss.

If the marketing study yields positive results, then United Robotics will spend

$1,000,000 on the prototype robot at Decision Point 2. Management estimates (be-

fore even making the initial $500,000 investment) that there is a 60 percent probabil-

ity that the television engineers will find the robot useful and a 40 percent probability

that they will not like it.

If the engineers like the robot, the firm will spend the final $10,000,000 to build

the plant and go into production. If the engineers do not like the prototype, the

project will be dropped. If the firm does go into production, the operating cash flows

over the project’s four-year life will depend on how well the market accepts the final

product. There is a 30 percent chance that acceptance will be quite good and net cash

flows will be $18 million per year, a 40 percent probability of $8 million each year, and

a 30 percent chance of losing $2 million. These cash flows are shown under Years 3

through 5.

In summary, the decision tree in Figure 8-3 defines the decision nodes and the

branches that leave the nodes. There are two types of nodes, decision nodes and out-

come nodes. Decision nodes are the points at which management can respond to new

information. The first decision node is at t 
1, after the company has completed the

marketing study (Decision Point 1 in Figure 8-3). The second decision node is at t 


2, after the company has completed the prototype study (Decision Point 2 in Figure

8-3). The outcome nodes show the possible results if a particular decision is taken.

There is one relevant outcome node (Decision Point 3 in Figure 8-3), the one oc-

curring at t 
3, and its branches show the possible cash flows if the company goes

ahead with the industrial robot project. There is one more decision node, Decision

Point 4, at which United Robotics terminates the project if acceptance is low. Note

that the decision tree also shows the probabilities of moving into each branch that

leaves a node.

The column of joint probabilities in Figure 8-3 gives the probability of occurrence

of each branch, hence of each NPV. Each joint probability is obtained by multiplying

together all probabilities on a particular branch. For example, the probability that the

FIGURE 8–3 United Robotics: Decision Tree Analysis (Thousands of Dollars)

Time

Joint Product:

t = 0 t = 1 t = 2 t = 3 t = 4 t = 5 Probability NPV Prob. 
NPV

$18,000 $18,000 $18,000 0.144 $25, 635 $3,691

($10,000)

➂

0.4$8,000 $8,000 $8,000 0.19 2$6,149 $1,181

($1,000)

➁

($2,000)  Stop 0.144 ($10,883) ($1,567)

($500)

➀

Stop 0.320 (1,397) (447)

Stop 0.200 (500) (100)

1.000 Expected NPV = $2,758

= $10,584

0.8

0.2

0.6

0.4

0.3

0.3

Cash Flow Estimation and Risk Analysis 323