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# Decision Tree Analysis

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Situation

An entrepreneur is considering whether to open a new computer store. He wants to proceed cautiously since the market potential for another computer store is uncertain. His options are:
? Open a small store now
? Open a large store now
? Drop the idea now
? Have a market potential survey conducted for \$5000.

The survey would suggest either a favorable or unfavorable market for a new computer store.

Based on his own preliminary calculations, the entrepreneur believes that if a small store is opened, he would earn a 1st year profit of \$30,000 in a favorable market, but lose \$35,000 in the 1st year in a n unfavorable market. Without the insight from the market potential survey, he believes there is a 50% chance that the market will be favorable. In initial discussions with the marketing research firm, the marketing analyst guessed there was a 60% chance that a survey would suggest a favorable market. Reluctantly, the analyst admitted that marketing surveys do not always assess markets correctly. Upon further prodding by the entrepreneur, the analyst estimated that if the survey suggested a favorable market, then the chance of the market actually being favorable was 90%. But if the survey suggested an unfavorable market, there would still be a 15% chance that the market would actually be favorable. At this point, the entrepreneur is perplexed.

Required:
1. Why do you think the decision of what to do seems difficult to the entrepreneur?
2. Construct a decision tree representing all possible actions, events and payoffs.
3. Analyze the decision tree, computing all the expected values, and recommend what the entrepreneur should do - explain completely (the grade awarded will depend on the quality of this response!!)
4. With your recommendation (from question 3), what is the best case 1st year net financial result to which he would be exposed? What is the worst case 1st year net financial result to which he would be exposed? Show all calculations and net final \$\$\$ impact.
5. The entrepreneur has now decided that he does not want to be exposed to any 1st year net loss over \$25,000. This means he no longer wants to consider opening a large store. What is your final recommendation to him now? Explain completely.

#### Solution Preview

See the attached Excel file for decision tree and payoff calculations.

1. Why do you think the decision of what to do seem difficult to the entrepreneur?

? No data is available for the expected payoffs in case of opening a large store.
? Because of the unpredictable nature survey (given posterior probabilities) it is difficult to make a decision just by looking at the data.
? Expected payoffs can be calculated only for the first year. Some long term estimates would have helped in taking a decision.

2. Construct a decision tree representing all possible actions, events and payoffs

The decision tree is in attached file : 74018_decisiontree.xls

3. Analyze the decision tree, computing all the expected values, and recommend what the entrepreneur should do.

Analysis of the decision tree starts with the calculation of expected payoffs from right to left as shown in the decision tree.
1. The expected monetary value(EMV) or expected payoff of activity node (1) ( the node dealing with conducting survey) is :
0.6*(0.9* 30000+ 0.1*(-35000)) + 0.4*(0.15* 30000+ 0.85*(-35000))
= \$ 4000 Profit.

Considering the survey cost as \$ 5000, the actual profit/loss becomes:
\$ 4000- \$5000 = -\$1000 i.e. Loss of \$ 1000.

2. As there is no data available about conducting a survey for large store, the EMV for activity node (1) is Loss of \$ 1000.

3. EMV ...

#### Solution Summary

This posting contains a detailed decision tree analysis of a business situation with construction of decision tree, calculation of Posterior probabilities and Expected payoffs and choosing the best alternative among the available ones based on the analysis.

\$2.19

## Decision Tree Analysis: Use decision tree analysis to recommend a production schedule and decide whether to publish the book.

Harvey Publishing Company, a small publisher in Columbus, is considering a new book. Typesetting and related costs to prepare for the production are \$10,000. It will cost \$2 per copy to produce the book. If additional copies are needed at a later time, the set-up cost will be\$5,000 and the cost per copy will again be \$2. The book will sell for \$14 a copy. Royalties, commissions, shipping costs, and so on will be \$4 a copy. If the book gets good reviews, it can be expected to sell 5,000 copies a year for 3 years. If it gets bad reviews, sales will be 2000 copies in the first year and will then cease. There is a 0.3 probability of a favorable review. Sally Harvey, president, faces a choice between ordering an immediate production run of 15,000 copies or a production run of 5,000 copies, followed by an additional production runs at the end of the first year if the book is successful. All production runs must be in increments of 5,000 copies. Harvey uses a 10% required return for evaluating new investments. She will pay no taxes because of previous losses and her capital is very limited. Use decision tree analysis to recommend a production schedule and decide whether to publish the book.

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