Suppose that Skipper's insurer views him as having the following distribution for the present value of losses: (i) (ii) Probability 0.02 0.04 0.10 0.84 Loss $20,000 5,000 1,000 0 What is the fair premium for full coverage if the competitive loading (administrative costs and capital costs) equals 15% of expected claim cost? Suppose that Skipper believes his probabilities of losses are one-half of what the insurer believes (expected claim). What is the loading- as a dollar value, and as a percentage of the expected claim on the policy from Skipper's perspective?
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- Michelle owns a house in which she keeps valuables worth 100,000 which can get stolen with probability 1%. She can purchase coverage C of the amount C ∈ [0; 100,000] at premium π = 0.05 dollars for each dollar covered. Her Bernouilli utility function is u(w) = ln(w). Assume she has no other assets. 1. Set up her maximization problem. 2. How much insurance will she choose to buy? 3. How much profits does the insurance company earn on insuring Michelle? 4. Does the fact that the insurance company earn profits mean that Michelle is worse off com-pared to the situation in which she is not insured? Explain what is happening. 5. How much insurance will she buy if insurance companies charge an actuarially fair insurance rate?Suppose we are considering the question of how much capacity to build in the face of uncertain demand. Assume that the cost is $20 per unit of lost sales due to insufficient capacity. Also assume that there is a cost of $7 for each unit of capacity built. The probability of various demand levels is as follows: Demand—X Units Probability of X 0 .05 1 .10 2 .15 3 .20 4 .20 5 .15 6 .10 7 .05 a. How many units of capacity should be built to minimize the total cost of providing capacity plus lost sales? b. State a…Stocks A and B have the following probability distributions ofexpected future returns:Probability A B0.1 (10%) (35%)0.2 2 00.4 12 200.2 20 250.1 38 45a. Calculate the expected rate of return, r⁄B, for Stock B (r⁄A =12%).b. Calculate the standard deviation of expected returns, σA, for Stock A (σB =20.35%).Now calculate the coefficient of variation for Stock B. Is it possible that most investorswill regard Stock B as being less risky than Stock A? Explain.c. Assume the risk-free rate is 2.5%. What are the Sharpe ratios for Stocks A and B? Arethese calculations consistent with the information obtained from the coefficient ofvariation calculations in part b? Explain
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- We are thinking of filming the Don Harnett story. Weknow that if the film is a flop, we will lose $4 million, andif the film is a success, we will earn $15 million. Beforehand,we believe that there is a 10% chance that the Don Harnettstory will be a hit. Before filming, we have the option ofpaying the noted movie critic Roger Alert $1 million for hisview of the film. In the past, Alert has predicted 60% of allactual hits to be hits and 90% of all actual flops to be flops.We want to maximize our expected profits. Use a decisiontree to determine our best strategy. What is EVSI? What isEVPI?A 5-year annuity of ten $5,300 semiannual paymentswill begin 9 years from now, with the first payment coming 9.5 years from now. If thediscount rate is 12 percent compounded monthly, what is the value of this annuityfive years from now? What is the value three years from now? What is the currentvalue of the annuity?Your manager is quite concerned about the recent deterioration of a section of the roof on a building that houses your firm's computer operations. According to your assistant there are three options which merit consideration: A, B, and C. Moreover, there are three possible future conditions that must be included in the analysis: I, which has a probability of occurrence of .5; II, which has a probability of .3; and III, which has a probability of .2. If condition I materializes, A will cost $12,000, B will cost $20,000, and C will cost $16,000. If condition II materializes, the costs will be $15,000 for A, $18,000 for B, and $14,000 for C. If condition III materializes, the costs will be $10,000 for A, $15,000 for B, and $19,000 for C. (A) Draw a decision tree for this problem (B) Using expected monetary value, which alternative should be chosen? Explain your Answer.