17. Suppose a risk-neutral power plant needs 10,000 tons of coal for its operations next month. It is uncertain about the future price of coal. Today it sells for $60 a ton but next month it could be $50 or $70 (with equal probability). How much would the power plant be willing to pay today for an option to buy a ton of coal next month at today's price? (Ignore discounting over the short period of a month.) а. 5 b. 4 с. 3 d. 0
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- 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?Q. 4 Suppose you, owner and CEO of a corporation, are considering a $25 million project that constructs a building in the downtown area of Toronto. The current market price of the similar building is about $20 million. The future price is uncertain. It may be either $28 million or $22 million in one year from now, depending on the economic situation. The company can borrow at a risk-free rate of 5 percent per year. What is the value of this project? Use a binomial model to value this real option.Assume Person A is offered the following game: If they want to participate in the game, theywill need to pay £5. If they participate, they can choose between Option A and Option B.Option A consists of spinning a roulette wheel with 37 different numbers (18 red, 18 black,and 1 green). If the outcome is red, the participant receives £10 and £0 otherwise. Option B isa fair coin flip that yields £5 when heads comes up and £10 when tails comes up.(a) What is the expected value of Option A?(ii) What is the expected value of Option B?(iii) What is the expected value of participating in the game and choosingOption A?(iv) What is the expected value of participating in the game and choosingOption B?(v) How much would the game need to cost to make it a fair game when youchoose Option A?(vi) How much would the game need to cost to make it a fair game when youchoose Option B?(b) Person A chooses to participate in the above described game. Which of thefollowing options can be true regarding…
- 5. Investor attitudes toward risk Suppose an investor, Erik, is offered the investment opportunities described in the table below. Each investment costs $1,000 today and provides a payoff, also described below, one year from now. Option Payoff One Year from Now 1 100% chance of receiving $1,100 2 50% chance of receiving $1,000; 50% chance of receiving $1,200 3 50% chance of receiving $200; 50% chance of receiving $2,000 If Erik is risk averse, which investment will he prefer? The investor will choose option 1. The investor will choose option 2. The investor will choose option 3. The investor will be indifferent toward these options. Suppose the market risk premium is currently 6%. If investors were to become more risk-averse, the market risk premium might increase to 8%. What effect would you expect this to have on the prices of most financial assets? Prices would be unaffected. Prices would decrease. Prices would increase.Uncertainty 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?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 635
- Suppose that instead Einar short sells 200 shares of German Power Weak Inc. at $40 each. NASDUCK now sets a margin requirement of 30%.(e) How much cash does Einar need to invest?(f) Calculate the margin call of NASDUCK if the price increases to $44.(g) Suppose the price falls to $25. How much cash can Einar take out from his margin account?(h) Suppose he takes out 50% of the amount in part (g). At what price threshold will Einar face a margin call by NASDUCK?7 3. How would the utility of a risk lover look like? a. Graph the utility function. Will this person be willing to pay for insurance?You are evaluating the possibility that your company bids $150,000 for a particular construction job. (a) If a bid of $150,000 corresponds to a relative bid of 1.20, what is the dollar profit that your company would make from winning the job with this bid? Show your work. (b) Calculate an estimate of the expected profit of the bid of $150,000 for this job. Assume that, historically, 55 percent of the bids of an average bidder for this type of job would exceed the bid ratio of 1.20. Assume also that you are bidding against three other construction companies. Show your work.
- 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…Microeconomics Wilfred’s expected utility function is px1^0.5+(1−p)x2^0.5, where p is the probability that he consumes x1 and 1 - p is the probability that he consumes x2. Wilfred is offered a choice between getting a sure payment of $Z or a lottery in which he receives $2500 with probability p = 0.4 and $3700 with probability 1 - p. Wilfred will choose the sure payment if Z > CE and the lottery if Z < CE, where the value of CE is equal to ___ (please round your final answer to two decimal places if necessary)A lottery system has balls numbered 1 to 65 and randomly selects 6 of the lottery balls. There is only one prize of $ 10,000,000.00 which is awarded only it a lottery player selects the correct set of 6 lottery balls. a) If a lottery ticket costs $ 5.00, what is a lottery player's expected value? b) How much would the lottery prize have to be worth if it was to be a fair game? (Note: Include dollar signs in your answer)