4. A car owner is willing to pay £500 at the start of the year to insure against a loss L (in£) if the car was stolen. The car owner has initial capital of £15,000 and the probabilityof the can being stolen is 0.2. If the car owner's utility function is U(w) = ½ w½ forw > 0, calculate L.

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Answered: 4. A car owner is willing to pay £500…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 25P

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A project does not necessarily have a unique IRR. (Refer to the previous problem for more information on IRR.) Show that a project with the following cash flows has two IRRs: year 1, 20; year 2, 82; year 3, 60; year 4, 2. (Note: It can be shown that if the cash flow of a project changes sign only once, the project is guaranteed to have a unique IRR.)
Assume the demand for a companys drug Wozac during the current year is 50,000, and assume demand will grow at 5% a year. If the company builds a plant that can produce x units of Wozac per year, it will cost 16x. Each unit of Wozac is sold for 3. Each unit of Wozac produced incurs a variable production cost of 0.20. It costs 0.40 per year to operate a unit of capacity. Determine how large a Wozac plant the company should build to maximize its expected profit over the next 10 years.
It is January 1 of year 0, and Merck is trying to determine whether to continue development of a new drug. The following information is relevant. You can assume that all cash flows occur at the ends of the respective years. Clinical trials (the trials where the drug is tested on humans) are equally likely to be completed in year 1 or 2. There is an 80% chance that clinical trials will succeed. If these trials fail, the FDA will not allow the drug to be marketed. The cost of clinical trials is assumed to follow a triangular distribution with best case 100 million, most likely case 150 million, and worst case 250 million. Clinical trial costs are incurred at the end of the year clinical trials are completed. If clinical trials succeed, the drug will be sold for five years, earning a profit of 6 per unit sold. If clinical trials succeed, a plant will be built during the same year trials are completed. The cost of the plant is assumed to follow a triangular distribution with best case 1 billion, most likely case 1.5 billion, and worst case 2.5 billion. The plant cost will be depreciated on a straight-line basis during the five years of sales. Sales begin the year after successful clinical trials. Of course, if the clinical trials fail, there are no sales. During the first year of sales, Merck believe sales will be between 100 million and 200 million units. Sales of 140 million units are assumed to be three times as likely as sales of 120 million units, and sales of 160 million units are assumed to be twice as likely as sales of 120 million units. Merck assumes that for years 2 to 5 that the drug is on the market, the growth rate will be the same each year. The annual growth in sales will be between 5% and 15%. There is a 25% chance that the annual growth will be 7% or less, a 50% chance that it will be 9% or less, and a 75% chance that it will be 12% or less. Cash flows are discounted 15% per year, and the tax rate is 40%. Use simulation to model Mercks situation. Based on the simulation output, would you recommend that Merck continue developing? Explain your reasoning. What are the three key drivers of the projects NPV? (Hint: The way the uncertainty about the first year sales is stated suggests using the General distribution, implemented with the RISKGENERAL function. Similarly, the way the uncertainty about the annual growth rate is stated suggests using the Cumul distribution, implemented with the RISKCUMUL function. Look these functions up in @RISKs online help.)
A martingale betting strategy works as follows. You begin with a certain amount of money and repeatedly play a game in which you have a 40% chance of winning any bet. In the first game, you bet 1. From then on, every time you win a bet, you bet 1 the next time. Each time you lose, you double your previous bet. Currently you have 63. Assuming you have unlimited credit, so that you can bet more money than you have, use simulation to estimate the profit or loss you will have after playing the game 50 times.
You now have 10,000, all of which is invested in a sports team. Each year there is a 60% chance that the value of the team will increase by 60% and a 40% chance that the value of the team will decrease by 60%. Estimate the mean and median value of your investment after 50 years. Explain the large difference between the estimated mean and median.
Pricing Decisions at Madison The Madison Company manufactures and retails a certain product. The company wants to determine the price that maximizes its profit from this product. The unit cost of producing and marketing the product is 50. Madison will certainly charge at least 50 for the product to ensure that it makes some profit. However, there is a very competitive market for this product, so that Madisons demand falls sharply when it increases its price. How should the company proceed?2 In the pricing model in Example 7.1 with the constant elasticity demand function, the assumption is that all units demanded are sold. Suppose the company has the capacity to produce only 200 units. If demand is less than capacity, all of demand is sold. If demand is greater than or equal to capacity, only 200 units are sold. Use Solver to find the optimal price and the corresponding profit. Then use SolverTable to see how sensitive these answers are to the production capacity, letting it vary from 170 to 230 in increments of 10. Discuss your findings relative to the original solution in Example 7.1. In other words, what is the effect of capacity on the optimal price and profit?

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4. A car owner is willing to pay £500 at the start of the year to insure against a loss L (in £) if the car was stolen. The car owner has initial capital of £15,000 and the probability of the can being stolen is 0.2. If the car owner's utility function is U(w) = ½ w½ for w > 0, calculate L.