You are a hotel manager considering four projects that yield different payoffs, depending upon whether there is an economic boom or a recession. The potential payoffs and corresponding payoffs are summarized in the accompanying table. Project A B с D Multiple Choice Which project has the highest variance? O с A D Boom (50%) $40 -$10 B $ 50 $ 60 Recession (50%) - $ 20 $30 -$ 50 $ 60
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- 1 Consider the two investments listed below with possible outcomes and probabilities: INVESTMENT (in $1000) P SAFE RISKY INVESTMENT AMOUNT 40+ 40+ GOOD SCENARIO OUTCOME 45+ 80+ AVERAGE+ SCENARIO PROB+ OUTCOME 0.40+ 0.40 42+ 45 BAD+ SCENARIO PROB OUTCOME PROB 0.20 35+ 0.20 10 0.40€ 0.40 a) What are the expected payoffs (E(x)) and standard deviations for each investment? b) Suppose I have utility function U(*) = √(x). What is the expected utility from each investment? c) Which investment will I choose, if any? Show and explain your work and provide the intuition.< d) What is the value of the risk premium for the SAFE investment? Show and explain your work and provide the intuition. e) What is the value of the risk premium for the RISKY investment? Show and explain your work and provide the intuition.< 43 A ✔ →10) a) What are the probability distributions for the annual benefit and life for the following project? The annual benefit's most likely value is $7000 with a probability of 60%. There is a 30% probability that it will be $4000, and the highest value that is likely $9,000. A life of 6 years is twice as likely as a life of 9 years. b) The project has a first cost of $25,000. The firm uses an interest rate of 8%. Assume that the probability distributions for annual benefit and life are unrelated or statistically independent. Calculate the probability distribution for the PW c) The first cost of the project is $25,000. Use the expected values for annual benefits and life to estimate the present worth. Use an interest rate of 8%. d) Use the probability distribution function of the PW to calculate the EV(PW). Does this indicate an attractive project? F) Using the probability distribution for the PW, calculate the PW's standard deviation.(8 points) A taxpayer (of a particular profile) can either comply with the IRS code, orcheat and receive some benefit. The IRS can either audit the taxpayer at a cost or donothing. If the taxpayer cheats and the IRS audits then the tax payer faces penalty (fineplus possibly jail time) and the IRS receives the fine. The payoff matrix:IRSAudit (q) Not Audit (1-q)Cheat (p) -50000, 4000 1000, 0Tax PayerComply (1-p) -500, -300 0, 0Assume the tax payer cheats with probability p and complies with probability 1 − p, andIRS audits with probability q and does not audit with probability 1 − q. Find the mixedstrategy Nash equilibrium. Express probabilities in percentage forms and keep two digitsafter the decimal point, for example p = 2.34%.
- 1. In a one-period model, the share price starts at $12 and in one year's time is either $24 or $6. Simple interest on USD is 20% per year. (a) Construct a replicating portfolio for a one year call option with strike K = $15. (b) Explain how The Law of One Price allows you to calculate the pre- mium of the call option. (c) Construct risk-neutral probabilities for the model for the share price and verify the risk-neutral value for the call option is the same as the value given by the replicating portfolio. |3DDetermine the two best decision alternatives by a conservative decision maker. Decision dl d2 d3 d4 d1 and d4 -350 d2 and d3 d3 and d4 sl States of Nature 900 d1 and d2 d1 and d3 500 700 750 -380 210 -360 $3 1100 600 -370 700MKBIC Systems is evaluating four projects A, B, C and D that have risks associated with the producing benefits. Based on the data given in the table below, which project is the best alternative? Project A Project B Project C Project D EUAW Prob. EUAW Prob. EUAW Prob. EUAW Prob. $2,500 0.3 $3,000 0.1 -$5,000 0.25 $4,000 0.35 $1,800 0.45 -$2,500 0.3 $6,500 0.45 $2,500 0.4 $3,200 0.25 $4,000 0.6 $2,000 0.3 -$1,500 0.25 A. Project A B. Project B C. Project C D. Project D
- McBurger Inc., wants to redesign its kitchen to improve productivity and quality. Three designs,called B1, B2, and B3, are under consideration. No matter which design is used, daily demandfor sandwiches at a typical McBurger restaurant is 500 sandwiches. A sandwich costs 500 baizato produce. Non-defective sandwich sell, on average, for 1 OR per sandwich. Defective sandwichcannot be sold and are scrapped. The goal is to chose a design that maximizes the expected profitat a typical restaurant over a period of one year (365 days). Designs B1, B2, and B3 cost 40,0003OR, 50,000 OR, and 70,000 OR, respectively. Under design B1, there is 0.8 chance that 90 outof each 100 sandwiches are non-defective and 0.2 chance that 70 out of each 100 sandwiches arenon-defective. Under design B2, there is 0.85 chance that 90 out of each 100 sandwiches are nondefective and 0.15 chance that 75 out of each 100 sandwiches are non-defective. Under design B3,there is 0.9 chance that 95 out of each 100 sandwiches…1) When and why should a utility approach be applied?2) Explain how utility could be used in a decision where performance is not measuredby monetary value.3) What are the key traits and differences of Project and Review Technique(PERT)/Critical Path Method (CPM)?4) Why perform sensitivity analysis?5) Explain how and why all predecessor activities must be considered when finding theearliest start timeYou're managing a project using the earned value management for cost management. The project planned value (PV) is $200,000. The project earned value (EV) is $100,000. The actual cost (AC) is $150,000. What is the cost variance (CV) for the project? a. -50,000 b. 100,000 c. -100,000 d. 150,000
- During your first month as an employee atGreenfield Industries (a large drill-bit manufacturer),you are asked to evaluate alternatives forproducing a newly designed drill bit on a turningmachine. Your boss’ memorandum to you haspractically no information about what the alternativesare and what criteria should be used. The same taskwas posed to a previous employee who could notfinish the analysis, but she has given you the followinginformation: An old turning machine valued at $350,000exists (in the warehouse) that can be modified for thenew drill bit. The in-house technicians have givenan estimate of $40,000 to modify this machine, andthey assure you that they will have the machine readybefore the projected start date (although they havenever done any modifications of this type). It is hopedthat the old turning machine will be able to meetproduction requirements at full capacity. An outsidecompany, McDonald Inc., made the machine sevenyears ago and can easily do the same…20 O It costs a pharmaceutical company $35,000 to produce a 1000-pound batch of a drug. The average yield from a batch is unknown but the best case is 90% yield (that is, 900 pounds of good drug will be produced), the most likely case is 85% yield, and the worst case is 70% yield. The annual demand for the drug is unknown, with the best case being 22,000 pounds, the most likely case 18,000 pounds, and the worst case 12.000 pounds. The drug sells for $60 per pound and leftover amounts of the drug can be sold for $8 per pound. To maximize annual expected profit, how many batches of the drug should the company produce? You can assume that it will produce the batches only once, before demand for the drug is known. You should consider a range of batches between 13 and 22.D.I. Aelitau, a line manufacturer, wants to select one of three feasible prototype designs for a new tire; A, B, C. Revenues Low Medium High (0.30) (0.50) (0.20) A 120,000 255,000 390,000 B 130,000 295,000 460,000 C 100,000 300,000 480,000 What is the minimum expected opportunity loss? (Hint: EV of PI) $43,500 $6,500 $9,000 $7,000