Decision Tree

5/21/2018 Decision Tree

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http://www.bized.co.uk

Copyright 2006 Biz/ed

Decision Trees


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What is a Decision Tree?

A Visual Representation ofChoices, Consequences,Probabilities, andOpportunities.

A Way of Breaking Down

Complicated Situations Downto Easier-to-UnderstandScenarios. Decision Tree


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Easy Example

A Decision Tree with twochoices.

Go to Graduate School to

get my master in CS.

Go to Work in the RealWorld


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Notation Used in Decision

Trees A box is used to show a choice

that the

manager has to make.

A circle is used to show that a

probabilityoutcome will occur.

Lines connect outcomes to their


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Example Decision Tree

Decision

node

Chance

node Event 1

Event 2

Event 3


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Decision Trees


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Planning Tool


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Decision Trees

Enable a business to quantifydecision making

Useful when the outcomes areuncertain

Places a numerical value on likely

or potential outcomes Allows comparison of differentpossible decisions to be made


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Decision Trees

Limitations: How accurate is the data used

in the construction of the tree?

How reliable are the estimatesof the probabilities?

Data may be historical does this datarelate to real time?

Necessity of factoring in the qualitativefactors human resources, motivation,reaction, relations with suppliers and otherstakeholders


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Process


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The Process

Expand by opening new outlet

Maintain current status

Economic growth rises

Economic growth declines

0.7

0.3

Expected outcome300,000

Expected outcome-500,000

0

A square denotes the point where a decision is made, In this example, a business is contemplatingopening a new outlet. The uncertainty is the state of the economyif the economy continues to growhealthily the option is estimated to yield profits of 300,000. However, if the economy fails to grow asexpected, the potential loss is estimated at 500,000.

There is also the option to do nothing and maintain the current status quo! This would have an outcome of0.

The circle denotes the point where different outcomes could occur. The estimates of the probability and theknowledge of the expected outcome allow the firm to make a calculation of the likely return. In this exampleit is:

Economic growth rises: 0.7 x 300,000 = 210,000

Economic growth declines: 0.3 x 500,000 = -150,000

The calculation would suggest it is wise to go ahead with the decision ( a net benefit figure of +60,000)


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The Process

Expand by opening new outlet

Maintain current status

Economic growth rises

Economic growth declines

0.5

0.5

Expected outcome300,000

Expected outcome-500,000

0

Look what happens however if the probabilities change. If the firm is unsure of the potential for growth, it mightestimate it at 50:50. In this case the outcomes will be:

Economic growth rises: 0.5 x 300,000 = 150,000

Economic growth declines: 0.5 x -500,000 = -250,000

In this instance, the net benefit is -100,000the decision looks less favourable!


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Advantages


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Disadvantages


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Example Joes Garage

Joes garage is considering hiring another mechanic. The

mechanic would cost them an additional $50,000 / year in salary

and benefits. If there are a lot of accidents in Iowa City this year,they anticipate making an additional $75,000 in net revenue. If

there are not a lot of accidents, they could lose $20,000 off of

last years total net revenues. Because of all the ice on the roads,

Joe thinks that there will be a 70% chance of a lot of accidents

and a 30% chance of fewer accidents. Assume if he doesnt

expand he will have the same revenue as last year.

Draw a decision tree for Joe and tell him what he should do.


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Example - Answer

Hire new mechanic

Cost = $50,000

Dont hire new

mechanic

Cost = $0

70% chance of an increase in

accidents

Profit = $70,000

30% chance of a decrease inaccidents

Profit = - $20,000

Estimated value of Hire Mechanic =

NPV =.7(70,000) + .3(- $20,000) - $50,000 = - $7,000

Therefore you should not hire the mechanic


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Problem: Jenny Lind

Jenny Lind is a writer of romance novels.

A movie company and a TV network bothwant exclusive rights to one of her morepopular works. If she signs with thenetwork, she will receive a single lump

sum, but if she signs with the moviecompany, the amount she will receivedepends on the market response to hermovie. What should she do?


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Payouts and Probabilities

Movie company Payouts Small box office - $200,000

Medium box office - $1,000,000

Large box office - $3,000,000

TV Network Payout Flat rate - $900,000

Probabilities P(Small Box Office) = 0.3

P(Medium Box Office) = 0.6

P(Large Box Office) = 0.1


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Jenny Lind - Payoff Table

Decisions

States of Nature

Small Box

Office

Medium Box

Office

Large Box

Office

Sign with MovieCompany

$200,000 $1,000,000 $3,000,000

Sign with TVNetwork

$900,000 $900,000 $900,000

Prior

Probabilities0.3 0.6 0.1


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Jenny Lind Decision Tree

Small Box Office

Medium Box Office

Large Box Office

Small Box Office

Medium Box Office

Large Box Office

Sign with Movie Co.

Sign with TV Network

$200,000

$1,000,000

$3,000,000

$900,000

$900,000

$900,000


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Jenny Lind Decision Tree

Small Box Office

Medium Box Office

Large Box Office

Small Box Office

Medium Box Office

Large Box Office

Sign with Movie Co.


$200,000

$1,000,000

$3,000,000

$900,000

$900,000

$900,000

.3

.6

.1

.3

.6

.1

ER?

ER?

ER?


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Jenny Lind Decision Tree -Solved

Small Box Office

Medium Box Office

Large Box Office

Small Box Office

Medium Box Office

Large Box Office

Sign with Movie Co.


$200,000

$1,000,000

$3,000,000

$900,000

$900,000

$900,000

.3

.6

.1

.3

.6

.1

ER

900,000

ER960,000

ER960,000


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Marys Factory

Mary is the CEO of a gadget factory.

She is wondering whether or not it is a good idea to expand her

factory this year. The cost to expand her factory is $1.5M. If she

expands the factory, she expects to receive $6M if economy is goodand people continue to buy lots of gadgets, and $2M if economy is

bad.

If she does nothing and the economy stays good she expects $3M in

revenue; while only $1M if the economy is bad.

She also assumes that there is a 40% chance of a good economy and

a 60% chance of a bad economy.

Draw a Decision Tree showing these choices.


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Decision Tree Example

Expand Factory

Cost = $1.5 M

Dont Expand Factory

Cost = $0

40 % Chance of a Good Economy

Profit = $6M

60% Chance Bad Economy

Profit = $2M

Good Economy (40%)

Profit = $3M

Bad Economy (60%)

Profit = $1M

EVExpand= (.4(6) + .6(2))1.5 = $2.1M

EVNo Expand= .4(3) + .6(1) = $1.8M

$2.1 > 1.8, therefore you should expand the factory


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http://www.bized.co.ukMarys Factory Discounting

Before Mary takes this to the board, she wants to account for

the time value of money. The gadget company uses a 10%

discount rate (interest). The cost of expanding the factory is

paid in year zero but the revenue streams are in year one.

Compute the NPV again, this time accounts the time value

of money in your analysis. Should she expand the factory?

Decision Tree

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