# Opciones reales

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ANDERSON SARRIA HARRY NARVAEZ FINANCIAL MODELS AND SIMULATION
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A simple example of the option to expand
 ABC Corp. is considering replacing each of its existing

six widget machines withnew machines. The new machines cost \$1000 each and have a five year-life.
A
3 Year

B
0

C
1

D
2

E
3

F
4

G
5

4

CF of single machine

-1000

220

300

400

200150

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 The financial analyst working on the replacement

project has estimated a cost of capital for the project of 12%. Using these expected cash flows and a cost of capital of 12% for theproject; the analyst has concluded that the replacement of a single old machine by a new machine es unprofitable, since the NPV is negative:

220 300 400 200 150  1000       67.48 2 3 4 51.12 (1.12) (1.12) (1.12) (1.12)

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 Now comes the (real options) twist. The line manager

in charge of the widget line says: “I want to try one of the new machines for a year, if theexperiment is succesful, I want to replace five other similar machines on the line with the new machines. If I do not try one of the new machines, I will never know their true cash flows.”…  Does this changeour previously negative conclusion about replacing a single machine? The answer is “yes”..to see this, we now realize that what we is a package:
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 Replacing a single machine today. This has aNPV of -

67.48  The option of replacing five more machines in one year. Then we view each such option as a call option on a asset which has current value of:

220 300 400 200 150 S     932,52 2 3 4 5 1.12 (1.12) (1.12) (1.12) (1.12)
 A variance of 40% and an exercise price X=1000. Of

course, these call options can be exercised only if we purchase that first machine now, in effectthe real options model will be pricing the learning cost… Excel Example
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BINOMIAL MODELS AND THE ABANDONMENT OPTION
 Another way to view options is to use a bonomial

models first...