1.         Represent the following decision making problem by a Decision Tree.

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Pay off in 00 (`)

Action

S1

S2

S3

A1

200

420

– 120

A2

550

70

250

Probability

0.3

0.5

0.2

(Ans.  :   EMV (A1), = 23400; EMV (A2) = 25,000)

 

2.         A firm has developed a new product X, they can either test market or abandon the project. The details are set out below.

Test market cost ` 50, 000 likely outcomes are favourable (P = 0.7) or failure (P = 0.3). If favourable, they could either abandon or produce it when demand anticipated to be

Low                P = 0.25                                 Low                 ` 1,00,000

Medium         P = 0.6                                    Profit               ` 1,50,000

High               P = 0.15                                 Profit               ` 4,50,000

If the test market indicate failure, the project would be abandoned. abandonment at any stage results in a gain of ` 30, 000 from machinery used.

(i)      Draw decision tree showing the nodes of possibilities.

(ii)     Evaluate the decision tree.

3.         A company has the opportunity of marketing a new package of computer games. It has two possible courses of action to test market on limited scale or to give up the project completely. A test market would cost ` 1,60,000 and current evidence suggests that consumer reaction is equally likely for ‘positive’ or ‘negative’. If the reaction to test marketing is ‘positive’, the company could either market the computer games nationally or still give up the project completely.

Research suggests that a national launch might result in the following sales.

Sales

Contribution (` Millions)

Probability

High

1.2

0.25

Average

0.3

0.50

Low

– 0.24

0.25

If the test marketing were to yield ‘negative’ results. the company would give up the project. Giving up the project at any point would result in contribution of ` 60, 000 from the sales of copyright etc. to another manufacturer. All contributions have been discounted to present value.

You are required to :

(a)     Draw decision tree to represent this situation including all relevant probabilities and financial values.

(b)     Recommend a course of action for the company on the basis of expected value.

 

4.         Draw decision tree for the following problem and by applying an appropriate decisions criterion suggest a best course of action.

States of Economy (E)

Courses of Action

P

Q

R

P(E)

Fair

900

400

0

0.2

Good

2900

4400

5000

0.5

Best

5900

6700

7900

0.3

 

5.         An economist in a company has predicted returns for two stocks A1 and A2 under four economic conditions as below. The predicted 18 months returns of ` 2000 investment in each stock under each economics condition is also mentioned in the table. Construct a decision tree and suggest the best stock to buy using  (i)  EMV Criteria  (ii)  EOL Criteria…

ACT (Stocks)

Economic Condition

Recession

Stable Economy

Moderate Growth

Boom

A1

50

90

120

170

A2

– 30

50

270

420

Best

0.10

0.25

0.30

0.35

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