You live in an area where there is a possibility of a massive earthquake, so consider purchasing earthquake insurance for your home at an annual cost of $180. The probability of an earthquake damaging your home in the course of a year is 0.001. If this occurs, you estimate that the cost of the damage (fully covered by insurance) will be $160,000. Your total assets (including the house) are worth $250,000.  a) Apply the maximum expected value decision rule to determine the alternative (to buy insurance or not) that maximizes the value of your assets after one year. b) You developed a utility function that measures the value of your assets in x dollars (x ≥ 0). This utility function is U(x) = √x. Compare the utility of reducing the total of your assets for the next year by a value equal to the value of the insurance, with the expected utility next year of not purchasing tremor insurance. Should you purchase the insurance?

In the table below x denotes the X-Tract Company’s projected annual profit (in $1,000).  The table also shows the probability of earning that profit.  The negative value indicates a loss.   x f(x)   x = profit   -100 0.01   f(x) = probability -200 0.04       0         100 0.26       200 0.54       300 0.05       400 0.02         8 What is the expected value of profit? a $136     b $142     c $148     d $154

Your company has a new project to be considered. You are given the following information on the best guess of related outcomes for the project. The cost of developing and market testing the product over the next year is $225 million. If the test is successful, which has a 65% chance, the company will spend another $800 million to put the production capabilities in place. The expected cash flows after tax for a successful project are $225 million each year for the next six years with a probability of.8; there is a 20% chance of a zero NPV. If the test fails the cash flows associated with continuing through the sixth year are $125 million per year after tax. The company uses a 12% discount rate for these types of projects. Draw and label the decision tree. Explain what decisions management would make at each node upon their realization.

St. John's Brewery (SJB) is getting ready for a busy tourist season. SJB wants to either increase production or produce the same amount as last year, depending on the demand level for the coming season. SJB estimates the probabilities for high, medium and low demands as 0.2, 0.3, and 0.5 respectively, on the basis of the number of tourists forecasted by the local recreational bureau. If SJB increases production, the expected profits corresponding to high, medium and low demands are $750,000, $325,000 and $100,000 respectively. If SJB does not increase production, the expected profits are $450,000, $325,000 and $150,000 respectively. (NOTE: Text answers are case sensitive and the value of different parts of this question is indicated in square brackets [*/*]) Construct a decision tree for SJB. On the basis of the EV, what should SJB do? What is the expected value of increasing production? What is the expected value of not increasing production? Should SJB increase production (enter…

= 1. (i) A utility function has the form U(w) aw³ +bw² where a, b E R. Assuming w > 0 and a 0, is U(w) ever suitable for a non-satiated and risk-averse investor? If it is, state the range of values of w this holds for as a function of a and b. You must include your working. (ii) Give an example of a utility function with DARA. Show all your working. (iii) An investor has IRRA. Would this investor prefer a fair gamble or to do nothing? Provide a short explanation of your answer.

Assume that 5% of the people who receive Treatment A die. The sixty percent who fully recover live another 10 years. The treatment is only partially successful for 35% of the patients, who live another 4 years. What is the expected value of Treatment A, expressed as additional years of life?

Thelma is indifferent between $100 and a bet with a 0.6 chance of no return and a 0.4 chance of $200. If U(0) = 20 and U(200) = 220, then U(100) = :

The Gorman Manufacturing Company must decide whether to manufacture a component part at its Milan, Michigan, plant or purchase the component part from a supplier. The resulting profit is dependent upon the demand for the product. The following payoff table shows the projected profit (in thousands of dollars):                                             state of nature   low demand medium demnad high demand Decision alternative s1 s2 s3 manufacture d1 -20 40 100 purchase d2 10 45 70 The state-of-nature probabilities are P(s1) = 0.35, P(s2) = 0.35, and P(s3) = 0.30. a. Use expected value to recommend a decision. b. Use EVPI to determine whether Gorman should attempt to obtain a better estimate of demand.

The gain from a project is equally likely to have any value between - $0.15 million and + $0.85 million. What is the 99% value at risk? A) $0.145 million B) $0.14 million C) $0.13 million D) $0.10 million