Topic: Decision Analysis

Question $1$: $(13$ marks$)$

Cal Bender and Becky Addison have known each other since high school. Two years ago they

entered the same university and today they are taking undergraduate courses in the business

school. Both hope to graduate with degrees in finance. In an attempt to make extra money and to

use some of the knowledge gained from their business courses, Cal and Becky have decided to

look into the possibility of starting a small company that would provide word processing services

to students who needed term papers or other reports prepared in a professional manner. Using a

systems approach, Cal and Becky have identified three strategies. Strategy $1$ is to invest in a

fairly expensive microcomputer system with a high$-$quality laser printer. In a favorable market,

they should be able to obtain a net profit of $$41,000$ over the next $2$ years. If the market is

unfavorable, they can lose $$29,000.$ Strategy $2$ is to purchase a less expensive system. With a

favorable market, they could get a return during the next $2$ years of $$33,000.$ With an unfavorable

market, they would incur a loss of $$15,000.$ Their final strategy, strategy $3,$ is to do nothing.

Cal and Becky have estimated that there is a $65\%$ chance that the market is favorable.a$)$ Draw a simple decision tree for this problem. What is the best alternative based on Expected

Monetary Value $($EMV$)$ criterion?

b$)$ Cal and Becky are also considering hiring a business analyst at a cost of $$3,000$ to get

additional information on the future market. The additional information can be positive $($i$.$e$.,$

a favorable market is likely$)$ or negative $($i$.$e$.,$ an unfavorable market is likely$).$

In the past, if the market was favorable, the analyst predicted positive information $82\%$ of the

times. If the market was unfavorable, the analyst predicted negative information $78\%$ of the

times. Calculate the following posterior probabilities:

$P($Favorable $|$ Positive Information$)|$

$P($Favorable $|$ Negative Information$)$

$($Keep answers to four decimal places$)|$

c$)$ Draw a complex decision tree and answer the following questions: $[5]$

Should Cal and Becky hire the business analyst? Why?

If the answer is Yes and the analyst gives positive information, then which decision

alternative should Cal and Becky choose? Why?

If the answer is Yes and the analyst gives negative information, then which decision

alternative should Cal and Becky choose? Why?

If the answer is No$,$ then which decision alternative should Cal and Becky choose?

d$)$ Based on the Expected Value of Sample Information, how much might Cal and Becky be

willing to pay for this additional information? Why? $[2]$

e$)$ Calculate the efficiency of this sample information and interpret its meaning.