CP

318 CHAPTER 8 Cash Flow Estimation and Risk Analysis

Finally, the project’s coefficient of variation is:

The project’s coefficient of variation can be compared with the coefficient of variation

of RIC’s “average” project to get an idea of the relative riskiness of the proposed

project. RIC’s existing projects, on average, have a coefficient of variation of about 1.0,

so, on the basis of this stand-alone risk measure, we conclude that the project is much

riskier than an “average” project.

Scenario analysis provides useful information about a project’s stand-alone risk.

However, it is limited in that it considers only a few discrete outcomes (NPVs), even

though there are an infinite number of possibilities. We describe a more complete

method of assessing a project’s stand-alone risk in the next section.

Monte Carlo Simulation

Monte Carlo simulationties together sensitivities and probability distributions. It

grew out of work in the Manhattan Project to build the first atomic bomb, and was

so named because it utilized the mathematics of casino gambling. While Monte Carlo

simulation is considerably more complex than scenario analysis, simulation software

packages make this process manageable. Many of these packages are included as

add-ons to spreadsheet programs such asMicrosoft Excel.

In a simulation analysis, the computer begins by picking at random a value for

each variable—sales in units, the sales price, the variable cost per unit, and so on.

CVNPV

NPV

E(NPV)

$69,267

$30,135

2.30.

High-Tech CFOs

Recent developments in technology have made it easier for
corporations to utilize complex risk analysis techniques.
New software and higher-powered computers enable finan-
cial managers to process large amounts of information, so
technically astute finance people can consider a broad range
of scenarios using computers to estimate the effects of
changes in sales, operating costs, interest rates, the overall
economy, and even the weather. Given such analysis, finan-
cial managers can make better decisions as to which course
of action is most likely to maximize shareholder wealth.
Risk analysis can also take account of the correlation be-
tween various types of risk. For example, if interest rates and
currencies tend to move together in a particular way, this
tendency can be incorporated into the model. This can en-
able financial managers to make better estimates of the like-
lihood and effect of “worst-case” outcomes.
While this type of risk analysis is undeniably useful, it is
only as good as the information and assumptions used in the

models. Also, risk models frequently involve complex calcula-

tions, and they generate output that requires financial man-

agers to have a fair amount of mathematical sophistication.

However, technology is helping to solve these problems, and

new programs have been developed to present risk analysis in

an intuitive way. For example, Andrew Lo, an MIT finance

professor, has developed a program that summarizes the risk,

return, and liquidity profiles of various strategies using a new

data visualization process that enables complicated relation-

ships to be plotted along three-dimensional graphs that are

easy to interpret. While some old-guard CFOs may bristle at

these new approaches, younger and more computer-savvy

CFOs are likely to embrace them. As Lo puts it: “The video-

game generation just loves these 3-D tools.”

Source:“The CFO Goes 3-D: Higher Math and Savvy Software Are Cru-

cial,” reprinted from October 28, 1996 issue of Business Weekby special per-

mission, copyright © 1996 by The McGraw-Hill Companies, Inc.

Cash Flow Estimation and Risk Analysis 317