Consider the problem of moral hazard where a firm has the choice of two projects: a safe project with $1300 revenue, and a risky project with $2500 revenue with probability ½ or nothing. A $1000 bond can fund either project and the CD rate is 10%. Select the answer that makes most sense for the following questions. Question: Profit from the safe project is: $50 $200 $100 can't be determined
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- 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 $154Uncertainty and willingness to pay for insurance. Utility = (Wealth)1/3 Prob(flood) = .04 Prob(no flood) = .96 Total wealth if flood = $100,000. Total Wealth if no flood = $800,000. Find: (i) expected value, (ii) expected utility, (iii) certainty equivalent, and (iv) maximum willingness to pay for a policy that provides 100% flood insurance coverage. Draw the utility function and include all solved values on the diagram. What is the average gross profit per insurance customer, if each customer is charged his own maximum willingness to pay?A plaintiff believes that there is a 30% chance that he will winIf he wins, he will gain $50,000. It costs him $5000 in non‐recoverable litigation costs to take the case to court. If the plaintiff is risk‐neutral, which of the following is true? A) The plaintiff will take the case to court with an expected net‐gain of $10,000 B) The plaintiff will take the case to court with an expected net‐gain of $15,000 C) The plaintiff will not take the case to court because he is afraid of losing. D) None of the above
- 4.7 Hudson Corporation is considering three options for managing its data processing operation: continuing with its own staff, hiring an outside vendor to do the managing (referred to as outsourcing), or using a combination of its own staff and an outside vendor. The cost of the operation depends on future demand. The annual cost of each option (in thousands of dollars) depends on demand as follows: Demand Staffing Options High Medium Low Own staff 650 650 600 Outside vendor 900 600 300 Combination 800 650 500 If the demand probabilities are 0.2, 0.5, and 0.3, and the table below shows the total cost of the different options, construct a risk profile for the optimal decision in the table. Option Total Cost Own Staff 635 Outside Vendor 570 Combination 635D & R A1 10 - 9 Question 10. Minimum Variance Commodity Hedge Choc Full of Good Inc., a producer of powdered hot chocolate, has just received a large order that will require the purchase of 800 metric tons of cocoa in 3 months. The current spot price of cocoa is US $3,055 per metric ton. The standard deviation of the change in spot cocoa price is 0.2. Mr. Dulce, the CFO of Choc Full, is considering a minimum-variance hedge of this future cocoa purchase using the three-month cocoa futures contract. The contract size is 10 metric tons. The standard deviation of the change in cocoa futures price is 0.25. The covariance between the change in the spot and futures cocoa price is 0.035. The annually compounded interest rate faced by the company is 5%, the three-month storage cost is $2.5 per metric ton, and the convenience yield is $0.5 per metric ton. Calculate the gain/loss on spot position, the gain/loss on futures position, and the profits from this hedged position by hypothesizing…D & R A1 10 - 8 Question 10. Minimum Variance Commodity Hedge Choc Full of Good Inc., a producer of powdered hot chocolate, has just received a large order that will require the purchase of 800 metric tons of cocoa in 3 months. The current spot price of cocoa is US $3,055 per metric ton. The standard deviation of the change in spot cocoa price is 0.2. Mr. Dulce, the CFO of Choc Full, is considering a minimum-variance hedge of this future cocoa purchase using the three-month cocoa futures contract. The contract size is 10 metric tons. The standard deviation of the change in cocoa futures price is 0.25. The covariance between the change in the spot and futures cocoa price is 0.035. The annually compounded interest rate faced by the company is 5%, the three-month storage cost is $2.5 per metric ton, and the convenience yield is $0.5 per metric ton. What is the profit from this hedged position if the spot cocoa price in three months turns out to be $3,100?
- Correct answer What is the formula for risk free rate ##############Givenu(x)=x0.5 Lottery A Probability 0.50 0.25 0.25 Outcome 64 16 0 For automatic grading, give all numerical answers to exactly two decimal places. Do not include currency signs 1) What is the expected value? (Give the answer as 36.00, not 36) 2) What is the expected utility? 3) What is the certainty equivalent? (Number only) 4) What is the risk premium? 5) Would this person rather receive 20 for sure than play Lottery A? (Answer should be Y or N for auto-grading to work) 6) (Harder) In many applications of expected utility, it is possible to lose money. The usual way of handling this is to interpret utility in terms of final wealth. Suppose it costs money to play this lottery. If starting wealth is 100, calculate the expected utility of playing lottery A if the price of playing is 15. Your answer should be to two decimal places. (Note: calculating the certainty equivalent of the lottery would be a little different than we've done in class. Squaring your EU result would give…8) Three decision makers have assessed utilities for the problem whose payoff table appearsbelow.s1 s2 s3d1 500 100 -400d2 200 150 100d3 -100 200 300probability.2 .6 .2Indifference Probability for PersonPayoff A B C300 .95 .68 .45200 .94 .64 .32150 .91 .62 .28100 .89 .60 .22-100 .75 .45 .10a. Plot the utility function for each decision maker.b. Characterize each decision maker's attitude toward risk.c. Which decision will each person prefer?
- After analyzing the costs of various options for obtaining brackets, Ross White (see Problems 6-27 through 6-29) recognizes that although he knows that the lead time is 2 days and the demand per day averages 10 units, the demand during the lead time often varies. Ross has kept very careful records and has determined that lead time demand is normally distributed with a standard deviation of 1.5 units. What Z value would be appropriate for a 98% service level? What safety stock should Ross maintain if he wants a 98% service level? What is the adjusted ROP for the brackets? What is the annual holding cost for the safety stock if the annual holding cost per unit is $1.50?5. An individual has a utility function given by (W) - √W, and initial wealth of $100. If he plays a costless lottery in which he can win or lose $10 at the flip of a coin, compute his expected utility. What is the expected gain? Will such a person be categorized as risk neutral?The Utility fct is U = W2/3 + 1000Flood occurs with Probabilities=1/20. The Value of house ✩540,000 if no flood. After aflood, the value is ✩40,000. Cost of insurance is 20 cents per dollar.a. Calculate EUb. Calculate EVc. Calculate CEd. Calculate RPe. Calculate the variance and standard deviationf. How much insurance should you buy? Assume your are paying premium in all event.g. What is the expected profit of the insurance company?h. Calculate the coefficient of absolute risk aversioni. Calculate the coefficient of relative risk aversion