CP

Summary 325

company will, if Stage 1 is undertaken, move through Stages 2 and 3, and that a strong

demand will produce $18,000,000 of inflows, is (0.8)(0.6)(0.3) 
0.144 
14.4%.

The company has a cost of capital of 11.5 percent, and management assumes ini-

tially that the project is of average risk. The NPV of the top (most favorable) branch

as shown in the next to last column is $25,635 (in thousands of dollars):

The NPVs for other branches were calculated similarly.

The last column in Figure 8-3 gives the product of the NPV for each branch times

the joint probability of that branch, and the sum of these products is the project’s ex-

pected NPV. Based on the expectations set forth in Figure 8-3 and a cost of capital of

11.5 percent, the project’s expected NPV is $2.758 million.

As this example shows, decision tree analysis requires managers to explicitly artic-

ulate the types of risk a project faces and to develop responses to potential scenarios.

Note also that our example could be extended to cover many other types of decisions,

and could even be incorporated into a simulation analysis. All in all, decision tree

analysis is a valuable tool for analyzing project risk.

A relatively new area of capital budgeting is called real options analysis. We discuss

this in much more detail in Chapter 17, but a real option exists any time a manager has

an opportunity to alter a project in response to changing market conditions. Chapter

17 shows several methods for evaluating real options, including the use of decision

tree analysis.^13

What is a decision tree? A branch? A node?

Summary

Throughout the book, we have indicated that the value of any asset depends on the

amount, timing, and riskiness of the cash flows it produces. In this chapter, we devel-

oped a framework for analyzing a project’s cash flows and risk. The key concepts cov-

ered are listed below.


 The most important (and most difficult) step in analyzing a capital budgeting proj-

ect is estimating the incremental after-tax cash flowsthe project will produce.


 Project cash flowis different from accounting income. Project cash flow reflects:

(1) cash outlays for fixed assets,(2) the tax shield provided by depreciation,

and (3) cash flows due to changes in net operating working capital.Project cash

flow does not include interest payments.


 In determining incremental cash flows, opportunity costs(the cash flows for-

gone by using an asset) must be included, but sunk costs(cash outlays that have

$25,635.

NPV
$500

$1,000

(1.115)^1



$10,000

(1.115)^2



$18,000

(1.115)^3



$18,000

(1.115)^4



$18,000

(1.115)^5

(^13) In the United Robotics example we glossed over an important issue, namely, the appropriate cost of capi-
tal for the project. Adding decision nodes to a project clearly changes its risk, so we would expect the cost of
capital for a project with few decision nodes to have a different risk than one with many nodes. If this were
so, we would expect the projects to have different costs of capital. In fact, we might expect the cost of capi-
tal to change over time as the project moves to different stages, since the stages themselves differ in risk. We
discuss these issues in more detail in Chapter 17.

324 Cash Flow Estimation and Risk Analysis