Practical Management Science
6th Edition
ISBN: 9781337406659
Author: WINSTON, Wayne L.
Publisher: Cengage,
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Chapter 11, Problem 55P
The DC Cisco office is trying to predict the revenue it will generate next week. Ten deals may close next week. The probability of each deal closing and data on the possible size of each deal (in millions of dollars) are listed in the file P11_55.xlsx. Use simulation to estimate total revenue. Based on the simulation, the company can be 95% certain that its total revenue will be between what two numbers?
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Chapter 11 Solutions
Practical Management Science
Ch. 11.2 - If the number of competitors in Example 11.1...Ch. 11.2 - In Example 11.1, the possible profits vary from...Ch. 11.2 - Referring to Example 11.1, if the average bid for...Ch. 11.2 - See how sensitive the results in Example 11.2 are...Ch. 11.2 - In Example 11.2, the gamma distribution was used...Ch. 11.2 - Prob. 6PCh. 11.2 - In Example 11.3, suppose you want to run five...Ch. 11.2 - In Example 11.3, if a batch fails to pass...Ch. 11.3 - Rerun the new car simulation from Example 11.4,...Ch. 11.3 - Rerun the new car simulation from Example 11.4,...
Ch. 11.3 - In the cash balance model from Example 11.5, the...Ch. 11.3 - Prob. 12PCh. 11.3 - Prob. 13PCh. 11.3 - The simulation output from Example 11.6 indicates...Ch. 11.3 - Prob. 15PCh. 11.3 - Referring to the retirement example in Example...Ch. 11.3 - A European put option allows an investor to sell a...Ch. 11.3 - Prob. 18PCh. 11.3 - Prob. 19PCh. 11.3 - Based on Kelly (1956). You currently have 100....Ch. 11.3 - Amanda has 30 years to save for her retirement. At...Ch. 11.3 - In the financial world, there are many types of...Ch. 11.3 - Suppose you currently have a portfolio of three...Ch. 11.3 - If you own a stock, buying a put option on the...Ch. 11.3 - Prob. 25PCh. 11.3 - Prob. 26PCh. 11.3 - Prob. 27PCh. 11.3 - Prob. 28PCh. 11.4 - Prob. 29PCh. 11.4 - Seas Beginning sells clothing by mail order. An...Ch. 11.4 - Based on Babich (1992). Suppose that each week...Ch. 11.4 - The customer loyalty model in Example 11.9 assumes...Ch. 11.4 - Prob. 33PCh. 11.4 - Suppose that GLC earns a 2000 profit each time a...Ch. 11.4 - Prob. 35PCh. 11.5 - A martingale betting strategy works as follows....Ch. 11.5 - The game of Chuck-a-Luck is played as follows: You...Ch. 11.5 - You have 5 and your opponent has 10. You flip a...Ch. 11.5 - Assume a very good NBA team has a 70% chance of...Ch. 11.5 - Consider the following card game. The player and...Ch. 11.5 - Prob. 42PCh. 11 - You now have 5000. You will toss a fair coin four...Ch. 11 - You now have 10,000, all of which is invested in a...Ch. 11 - Suppose you have invested 25% of your portfolio in...Ch. 11 - Prob. 47PCh. 11 - Based on Marcus (1990). The Balboa mutual fund has...Ch. 11 - Prob. 50PCh. 11 - Prob. 52PCh. 11 - The annual demand for Prizdol, a prescription drug...Ch. 11 - Prob. 54PCh. 11 - The DC Cisco office is trying to predict the...Ch. 11 - A common decision is whether a company should buy...Ch. 11 - Suppose you begin year 1 with 5000. At the...Ch. 11 - You are considering a 10-year investment project....Ch. 11 - Play Things is developing a new Lady Gaga doll....Ch. 11 - An automobile manufacturer is considering whether...Ch. 11 - It costs a pharmaceutical company 75,000 to...Ch. 11 - Prob. 65PCh. 11 - Rework the previous problem for a case in which...Ch. 11 - Prob. 68PCh. 11 - The Tinkan Company produces one-pound cans for the...Ch. 11 - Prob. 70PCh. 11 - In this version of dice blackjack, you toss a...Ch. 11 - Prob. 76PCh. 11 - It is January 1 of year 0, and Merck is trying to...Ch. 11 - Suppose you are an HR (human resources) manager at...Ch. 11 - You are an avid basketball fan, and you would like...Ch. 11 - Suppose you are a financial analyst and your...Ch. 11 - Software development is an inherently risky and...Ch. 11 - Health care is continually in the news. Can (or...
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- If you want to replicate the results of a simulation model with Excel functions only, not @RISK, you can build a data table and let the column input cell be any blank cell. Explain why this works.arrow_forwardSuppose you begin year 1 with 5000. At the beginning of each year, you put half of your money under a mattress and invest the other half in Whitewater stock. During each year, there is a 40% chance that the Whitewater stock will double, and there is a 60% chance that you will lose half of your investment. To illustrate, if the stock doubles during the first year, you will have 3750 under the mattress and 3750 invested in Whitewater during year 2. You want to estimate your annual return over a 30-year period. If you end with F dollars, your annual return is (F/5000)1/30 1. For example, if you end with 100,000, your annual return is 201/30 1 = 0.105, or 10.5%. Run 1000 replications of an appropriate simulation. Based on the results, you can be 95% certain that your annual return will be between which two values?arrow_forwardSuppose you currently have a portfolio of three stocks, A, B, and C. You own 500 shares of A, 300 of B, and 1000 of C. The current share prices are 42.76, 81.33, and, 58.22, respectively. You plan to hold this portfolio for at least a year. During the coming year, economists have predicted that the national economy will be awful, stable, or great with probabilities 0.2, 0.5, and 0.3. Given the state of the economy, the returns (one-year percentage changes) of the three stocks are independent and normally distributed. However, the means and standard deviations of these returns depend on the state of the economy, as indicated in the file P11_23.xlsx. a. Use @RISK to simulate the value of the portfolio and the portfolio return in the next year. How likely is it that you will have a negative return? How likely is it that you will have a return of at least 25%? b. Suppose you had a crystal ball where you could predict the state of the economy with certainty. The stock returns would still be uncertain, but you would know whether your means and standard deviations come from row 6, 7, or 8 of the P11_23.xlsx file. If you learn, with certainty, that the economy is going to be great in the next year, run the appropriate simulation to answer the same questions as in part a. Repeat this if you learn that the economy is going to be awful. How do these results compare with those in part a?arrow_forward
- In August of the current year, a car dealer is trying to determine how many cars of the next model year to order. Each car ordered in August costs 20,000. The demand for the dealers next year models has the probability distribution shown in the file P10_12.xlsx. Each car sells for 25,000. If demand for next years cars exceeds the number of cars ordered in August, the dealer must reorder at a cost of 22,000 per car. Excess cars can be disposed of at 17,000 per car. Use simulation to determine how many cars to order in August. For your optimal order quantity, find a 95% confidence interval for the expected profit.arrow_forwardRerun the new car simulation from Example 11.4, but now introduce uncertainty into the fixed development cost. Let it be triangularly distributed with parameters 600 million, 650 million, and 850 million. (You can check that the mean of this distribution is 700 million, the same as the cost given in the example.) Comment on the differences between your output and those in the example. Would you say these differences are important for the company?arrow_forwardIt is surprising (but true) that if 23 people are in the same room, there is about a 50% chance that at least two people will have the same birthday. Suppose you want to estimate the probability that if 30 people are in the same room, at least two of them will have the same birthday. You can proceed as follows. a. Generate random birthdays for 30 different people. Ignoring the possibility of a leap year, each person has a 1/365 chance of having a given birthday (label the days of the year 1 to 365). You can use the RANDBETWEEN function to generate birthdays. b. Once you have generated 30 peoples birthdays, how can you tell whether at least two people have the same birthday? One way is to use Excels RANK function. (You can learn how to use this function in Excels online help.) This function returns the rank of a number relative to a given group of numbers. In the case of a tie, two numbers are given the same rank. For example, if the set of numbers is 4, 3, 2, 5, the RANK function returns 2, 3, 4, 1. (By default, RANK gives 1 to the largest number.) If the set of numbers is 4, 3, 2, 4, the RANK function returns 1, 3, 4, 1. c. After using the RANK function, you should be able to determine whether at least two of the 30 people have the same birthday. What is the (estimated) probability that this occurs?arrow_forward
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- A common decision is whether a company should buy equipment and produce a product in house or outsource production to another company. If sales volume is high enough, then by producing in house, the savings on unit costs will cover the fixed cost of the equipment. Suppose a company must make such a decision for a four-year time horizon, given the following data. Use simulation to estimate the probability that producing in house is better than outsourcing. If the company outsources production, it will have to purchase the product from the manufacturer for 25 per unit. This unit cost will remain constant for the next four years. The company will sell the product for 42 per unit. This price will remain constant for the next four years. If the company produces the product in house, it must buy a 500,000 machine that is depreciated on a straight-line basis over four years, and its cost of production will be 9 per unit. This unit cost will remain constant for the next four years. The demand in year 1 has a worst case of 10,000 units, a most likely case of 14,000 units, and a best case of 16,000 units. The average annual growth in demand for years 2-4 has a worst case of 7%, a most likely case of 15%, and a best case of 20%. Whatever this annual growth is, it will be the same in each of the years. The tax rate is 35%. Cash flows are discounted at 8% per year.arrow_forwardYou are considering a 10-year investment project. At present, the expected cash flow each year is 10,000. Suppose, however, that each years cash flow is normally distributed with mean equal to last years actual cash flow and standard deviation 1000. For example, suppose that the actual cash flow in year 1 is 12,000. Then year 2 cash flow is normal with mean 12,000 and standard deviation 1000. Also, at the end of year 1, your best guess is that each later years expected cash flow will be 12,000. a. Estimate the mean and standard deviation of the NPV of this project. Assume that cash flows are discounted at a rate of 10% per year. b. Now assume that the project has an abandonment option. At the end of each year you can abandon the project for the value given in the file P11_60.xlsx. For example, suppose that year 1 cash flow is 4000. Then at the end of year 1, you expect cash flow for each remaining year to be 4000. This has an NPV of less than 62,000, so you should abandon the project and collect 62,000 at the end of year 1. Estimate the mean and standard deviation of the project with the abandonment option. How much would you pay for the abandonment option? (Hint: You can abandon a project at most once. So in year 5, for example, you abandon only if the sum of future expected NPVs is less than the year 5 abandonment value and the project has not yet been abandoned. Also, once you abandon the project, the actual cash flows for future years are zero. So in this case the future cash flows after abandonment should be zero in your model.)arrow_forwardBased on Kelly (1956). You currently have 100. Each week you can invest any amount of money you currently have in a risky investment. With probability 0.4, the amount you invest is tripled (e.g., if you invest 100, you increase your asset position by 300), and, with probability 0.6, the amount you invest is lost. Consider the following investment strategies: Each week, invest 10% of your money. Each week, invest 30% of your money. Each week, invest 50% of your money. Use @RISK to simulate 100 weeks of each strategy 1000 times. Which strategy appears to be best in terms of the maximum growth rate? (In general, if you can multiply your investment by M with probability p and lose your investment with probability q = 1 p, you should invest a fraction [p(M 1) q]/(M 1) of your money each week. This strategy maximizes the expected growth rate of your fortune and is known as the Kelly criterion.) (Hint: If an initial wealth of I dollars grows to F dollars in 100 weeks, the weekly growth rate, labeled r, satisfies F = (I + r)100, so that r = (F/I)1/100 1.)arrow_forward
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