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Probability and Expected Value of a Payoff

Charles and Millie Jackson (a married couple in their 40's) have decided to invest a portion of their accumulated retirement "nest-egg" in a new business venture. It is an opportunity that Millie found while exploring one of her hobbies. Her idea is to embroider logos for small companies and organizations. They have already priced the equipment to be a $10,000 investment, and after estimating variable costs, expect to make a profit of about $10 per shirt. Based on preliminary contacts, they believe there is a .30 probability (30 percent chance) that they could land a 3-year commitment from a local company, but only if they've made the investment and proven their product. This would lead to production of 3,000 shirts and a net profit of $30,000. If that were to fall through, they believe they could easily land deals with several local clubs, organizations and churches to sell shirts, but at a reduced profit of only $5 per shirt, leading to a 3-year net return of $15,000. Both figures must be reduced by the initial start-up cost of $10,000.

State of Nature Payoff Probability Expected Value
Contract with Company $20,000 0.3
No Contract $5,000 0.7

1. Complete the table above so that you can show the Jackson's what their expected payoff is.

2. Assuming that they have this $10,000 currently invested in low yield market funds that at the end of 3 years will be worth $12,200, and assuming no withdrawal penalties for using the money and no "emotional attachment" to the business, what would you recommend the Jackson's do purely from a monetary perspective?

3. Is this an appropriate way to make this decision? If yes, Why, or if no, why not?

Solution Summary

Probability and Expected Value of a Payoff are investigated. The solution is detailed and well presented.