Practical Management Science
6th Edition
ISBN: 9781337406659
Author: WINSTON, Wayne L.
Publisher: Cengage,
expand_more
expand_more
format_list_bulleted
Question
Chapter 11.3, Problem 25P
Summary Introduction
To simulate: The cash flows from the portfolio.
Introduction: Simulation model is the digital prototype of the physical model that helps to
Expert Solution & Answer
Trending nowThis is a popular solution!
Students have asked these similar questions
Company A's stock sells for $142 a share and has a 3-year average annual return of $27 per share. The beta value, a measure of risk, is 0.38. Company B sells for $149 a share and has a 3-year average annual return of $61 a share. The beta value is 1.23. Tori wants to spend no more than $12000 investing in these two stocks, but she wants to obtain at least $3000 in annual revenue. Tori also wants to minimize the risk, that is, the beta value. Determine how many shares of each stock Tori should buy.
Use excel for this problem
A trust officer at the Blacksburg National Bank needs to determine how to invest $150,000 in the following collection of bonds to maximize the annual return.
Bond
Annual Return
Maturity
Risk
Tax
Free
A
9.5%
Long
High
Yes
B
8.0%
Short
Low
Yes
C
9.0%
Long
Low
No
D
9.0%
Long
High
Yes
E
9.0%
Short
High
No
The officer wants to invest at least 40% of the money in short-term issues and no more than 20% in high-risk issues. At least 25% of the funds should go in tax-free investments, and at least 45% of the total annual return should be tax free.
Formulate the LP model for this problem.
Create the spreadsheet model and use Solver to solve the problem.
The Schoch Museum (see Problem 30 in Chapter 11) is embarking on a five-year fundraising campaign. As a nonprofit institution, the museum finds it challenging to acquire new donors, as many donors do not contribute every year. Suppose that the museum has identified a pool of 8,000 potential donors. The actual number of donors in the first year of the campaign is estimated to be somewhere between 60% and 75% of this pool. For each subsequent year, the museum expects that a certain percentage of current donors will discontinue their contributions. This is expected to be between 10% and 60%, with a most likely value of 35%. In addition, the museum expects to attract some percentage of new donors. This is assumed to be between 5% and 40% of the current year’s donors, with a most likely value of 10%. The average contribution in the first year is assumed to be $50 and will increase at a rate between 0% and 8% each subsequent year, with the most likely increase of 2.5%. Develop and analyze a…
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...
Knowledge Booster
Similar questions
- Suppose 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_forwardA European put option allows an investor to sell a share of stock at the exercise price on the exercise data. For example, if the exercise price is 48, and the stock price is 45 on the exercise date, the investor can sell the stock for 48 and then immediately buy it back (that is, cover his position) for 45, making 3 profit. But if the stock price on the exercise date is greater than the exercise price, the option is worthless at that date. So for a put, the investor is hoping that the price of the stock decreases. Using the same parameters as in Example 11.7, find a fair price for a European put option. (Note: As discussed in the text, an actual put option is usually for 100 shares.)arrow_forward
- In the financial world, there are many types of complex instruments called derivatives that derive their value from the value of an underlying asset. Consider the following simple derivative. A stocks current price is 80 per share. You purchase a derivative whose value to you becomes known a month from now. Specifically, let P be the price of the stock in a month. If P is between 75 and 85, the derivative is worth nothing to you. If P is less than 75, the derivative results in a loss of 100(75-P) dollars to you. (The factor of 100 is because many derivatives involve 100 shares.) If P is greater than 85, the derivative results in a gain of 100(P-85) dollars to you. Assume that the distribution of the change in the stock price from now to a month from now is normally distributed with mean 1 and standard deviation 8. Let EMV be the expected gain/loss from this derivative. It is a weighted average of all the possible losses and gains, weighted by their likelihoods. (Of course, any loss should be expressed as a negative number. For example, a loss of 1500 should be expressed as -1500.) Unfortunately, this is a difficult probability calculation, but EMV can be estimated by an @RISK simulation. Perform this simulation with at least 1000 iterations. What is your best estimate of EMV?arrow_forwardIn Problem 11 from the previous section, we stated that the damage amount is normally distributed. Suppose instead that the damage amount is triangularly distributed with parameters 500, 1500, and 7000. That is, the damage in an accident can be as low as 500 or as high as 7000, the most likely value is 1500, and there is definite skewness to the right. (It turns out, as you can verify in @RISK, that the mean of this distribution is 3000, the same as in Problem 11.) Use @RISK to simulate the amount you pay for damage. Run 5000 iterations. Then answer the following questions. In each case, explain how the indicated event would occur. a. What is the probability that you pay a positive amount but less than 750? b. What is the probability that you pay more than 600? c. What is the probability that you pay exactly 1000 (the deductible)?arrow_forwardBased on Grossman and Hart (1983). A salesperson for Fuller Brush has three options: (1) quit, (2) put forth a low level of effort, or (3) put forth a high level of effort. Suppose for simplicity that each salesperson will sell 0, 5000, or 50,000 worth of brushes. The probability of each sales amount depends on the effort level as described in the file P07_71.xlsx. If a salesperson is paid w dollars, he or she regards this as a benefit of w1/2 units. In addition, low effort costs the salesperson 0 benefit units, whereas high effort costs 50 benefit units. If a salesperson were to quit Fuller and work elsewhere, he or she could earn a benefit of 20 units. Fuller wants all salespeople to put forth a high level of effort. The question is how to minimize the cost of encouraging them to do so. The company cannot observe the level of effort put forth by a salesperson, but it can observe the size of his or her sales. Thus, the wage paid to the salesperson is completely determined by the size of the sale. This means that Fuller must determine w0, the wage paid for sales of 0; w5000, the wage paid for sales of 5000; and w50,000, the wage paid for sales of 50,000. These wages must be set so that the salespeople value the expected benefit from high effort more than quitting and more than low effort. Determine how to minimize the expected cost of ensuring that all salespeople put forth high effort. (This problem is an example of agency theory.)arrow_forward
- A market analyst working for a small appliance manufacturer finds that if the firm produces and sells x blenders annually, a model for the total profit (in dollars) is P(x) = 8x + 0.3x2 − 0.001x3 − 372. Graph the function P in an appropriate viewing rectangle, and use the graph to answer the following questions. (a) When just a few blenders are manufactured, the firm loses money (profit is negative). (For example, P(10) = −263, so the firm loses $263.00 if it produces and sells only 10 blenders.) How many blenders must the firm produce to break even? (Round your answer to the nearest whole number.) blenders(b) Does profit increase indefinitely as more blenders are produced and sold? YesNo If not, what is the largest possible profit the firm could have? (If profit increases indefinitely, enter your answer as ∞. Otherwise, round your answer to the nearest cent.)arrow_forwardShow cells in excel with step by step using solver and the sum product function show how to calculate weighted risk Wall Street firms commonly use linear programming models to select their bond portfolios. A firm is considering the following 5 bonds: Bond Annual Return rate (%) Risk measure Bond 9.2 5 Bond 5 3 Bond 6.1 2 Bond 3.5 4 Bond 1.2 1 In the table above, “risk measure” has a value between 1 and 5 with 5 indicating the riskiest bond and 1 the least risky bond. The firm has a budget of 1 million dollars for this investment. The firm wants to decide its investments in the 5 bonds to maximize the expected return of the portfolio, subject to constraints listed below: The weighted average risk of the portfolio should not exceed 4. At least 30% of the total investment can be invested in bond 3. To diversify the portfolio, the investment on each bond should be at least 10% of the total investment. The sum of investments made in…arrow_forwardThe purchased and installation costs of some pieces of equipment are given as a function of weight rather than capacity. An example of this is the installed costs of large tanks. The 1980 cost for an installed aluminum tank weighing 100,000 lb was $390,000. For a size range from 200,000 to 1,000,000 lb, the installed cost-weight exponent for aluminum tanks is 0.93. If an aluminum tank weighing 700,000 lb is required, what is capital investment needed in 2002? Notice: If you can't find exponent (x), you can use the value 0.6arrow_forward
- A trust officer at the Blacksburg National Bank needs to determine how to invest $100,000 in the following collection of bonds to maximize the total annual return (before tax). Bond Annual Return Maturity Risk Tax-Free A 9.5% Long High Yes B 8.0% Short Low Yes C 9.0% Long Low No D 9.0% Long High Yes E 9.0% Short High No The officer wants to invest as least 50% of the money in short-term issues and no more than 50% in high-risk issues. At least 30% of the funds should go in tax-free investments, and at least 40% of the total annual return should be tax free. Suppose the decision variable represents the amount of money invested in bond for . Formulate a linear programming (LP) model to solve the optimal strategy. 1. Write down the constraint using the defined decision variables requiring “invest as least 50% of the money in short-term issues”. 2. Write down the constraint using the defined decision…arrow_forwardDataware is trying to determine whether to give a $10 rebate, cut the price $6, or have no price change on a software product. Currently, 40,000 units of the product are sold each week for $45 apiece. The variable cost of the product is $5. The most likely case appears to be that a $10 rebate will increase sales 30%, and half of all people will claim the rebate. For the price cut, the most likely case is that sales will increase 20%.a. Given all other assumptions, what increase in sales from the rebate would make the rebate and price cut equally desirable?b. Dataware does not really know the increase in sales that will result from a rebate or price cut. However, the company is sure that the rebate will increase sales by between 15% and 40% and that the price cut will increase sales by between 10% and 30%. Perform a sensitivity analysis (two-way data table) that could be used to help determine Dataware’s best decision.arrow_forwardYou have $50,000 to invest in three stocks. Let Ri be the random variable representing the annual return on $1 invested in stock i. For example, if Ri = 0.12, then $1 invested in stock i at the beginning of a year is worth $1.12 at the end of the year. The means are E(R1) = 0.17, E(R2) = 0.15, and E(R3) = 0.12. The variances are Var R1 = 0.25, Var R2 = 0.18, and Var R3 = 0.14. The correlations are r12 = 0.6, r13 = 0.9, and r23 = 0.7. Determine the minimum-variance portfolio that attains a mean annual return of at least 0.14. If needed, round your answers to three decimal digits. Investment decision Stock 1 Stock 2 Stock 3 Fractions to investarrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Practical Management ScienceOperations ManagementISBN:9781337406659Author:WINSTON, Wayne L.Publisher:Cengage,
Practical Management Science
Operations Management
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:Cengage,