Every entrepreneur runs the risk that some unusual event wil

Every entrepreneur runs the risk that some unusual event will wipe out his business. Examples are a customer lawsuit, a dishonest employee, a tornado, a flood, or a broken waterpipe. Let\'s assume the rate of events is constant at 3 percent per year with each event costing $10,000. Assume each event is independent of any other.

A. Which distribution represents this risk?

B. What is the probability of one or more disasters in 20 years?

C. How much capital does the entrepreneur need for at least an 85 percent chance of surviving for 20 years? Assume that all the business earnings are paid out each year, so the business does not build capital internally.

D. One entrepreneur does not want to tie up his capital waiting for a disaster. He has asked you to sell insurance to him. What should you charge to fully insure every disaster? Assume that you can sell a large number of similar policies. (This risk is similar to the risk of an automobile accident, so your answers should be in the same ballpark of your annual payment.)

Solution

p = Prob for unusual event which wipes out his business = 0.03

cost = 10000

Each even is independent of the other

and there are two outcomes, either event occurs or not.

A)Hence X - no of unusual events is binomial.

B) the probability of one or more disasters in 20 years

= P(X>=1)

=1-P(X=0)

= 1-(0.97)²⁰

=0.4562

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c) For one or more diasters prob = 0.4562

If 85% survival should be there then prob for disaster <0.15

Hence 2 or more diasters can be tolerated for 85% survival.

For this capital fund to be invested >20000

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