Exam 16: Risk Analysis

Game Theory. Catskill Mountain Bike, Inc. is a producer and wholesaler of rugged bicycles designed for mountain touring. The company is considering upgrading its current line by making standard high-grade Chromalloy frames. Of course, the market response to this upgrade in product quality would depend on the competitor response, if any. The company's comptroller projects the following annual profits (payoffs) following resolution of the upgrade decision. A. Which decision alternative represents Catskill's secure strategy? Explain. B. Calculate the opportunity cost (or regret) matrix. C. Which decision alternative would Catskill choose if the company seeks to minimize opportunity cost? Explain.

The maximin criterion involves:

Probability Analysis. The Medical Centre is considering taking on a new lease for additional office space in alternative suburban shopping areas. Alternative 1 requires a current investment outlay of $50,000; alternative 2 requires an outlay of $75,000. The following cash flows will be generated each year over an initial five-year lease period. A. Calculate the expected cash flow for each investment alternative. B. Calculate the standard deviation and coefficient of variation of cash flows (risk) for each investment alternative. C. The firm will use a discount rate of 15% for the cash flows with higher degree of dispersion and a 12% rate for the less risky cash flows, calculate the expected net present value for each investment. Which alternative should be chosen?

Probability Analysis. WD-50, Inc. has just completed development of a new spray lubricant. Preliminary market research indicates two feasible marketing strategies: developing general consumer acceptance through media advertising, or developing distributor acceptance through intensive personal selling by company representatives. The marketing manager has developed the following estimates for sales under each alternative:

The amount of a bet is irrational when it:

The minimax regret criterion directs the decision maker to select the alternative that:

Expected Return Analysis. Dr. John Carter offers health seminars to local PTA groups. On average, Carter expects 2% of seminar participants to become patients of his HMO organization at a gross billing of $2,500 per patient per year. A. Calculate Carter's expected net return per dollar of gross patient billings if attendance averages fifty persons per seminar, and a first-year net return of $100 must be earned to justify Carter's time and effort per seminar.

A probability distribution for total profit is a list of:

Expected Return Analysis. Alex P. Keaton has just accepted a job as a broker at a major NYSE member firm, and has been asked to develop a list of customers by telephoning medical doctors and other professionals located in the metropolitan area. On average, Keaton expects 1% of those called to purchase $15,000 each in mutual fund investments, and 3% to purchase $10,000 each in stocks and bonds. Keaton earns a 2% net commission on mutual funds and 1% on stocks and bonds. A. Calculate Keaton's expected net commissions if he calls an average of twenty-five persons per day.

Certainty Equivalent Method. Saddie Hawkins, a management analyst with Mobile Telephone Services, Inc., has collected the following information about three investment projects undertaken by the firm during the past six month period. Hawkins wishes to use this information as a backdrop against which to evaluate the attractiveness of a recent investment proposal put forth by the quality control department. In that proposal, dubbed Project X, the quality control department proposes to spend $100,000 to modify transmission equipment at the Colorado Springs, Colorado facility. Annual expected cost savings of $25,000 per year over the 10-year 2005-2014 period have been projected, and verified as reasonable by Hawkins. A. Calculate the present value of anticipated cost savings using an 8% discount rate as a reasonable estimate of the risk-free cost of capital. B. In light of the $100,000 investment required for each of these projects, and the discounted present value of future benefits, calculate the certainty equivalent adjustment factor a implicit in the decision to fund each of these investment projects. C. Assume that the a's implicit in the decisions to fund projects Y and Z represent the upper limits for investment projects of this type. Would a decision to fund project X be consistent or inconsistent with the firm's decision to fund projects Y and Z?

Decision Trees. Atlanta Corporation has been supplying Raleigh Manufacturing, Inc. with electronic control systems, and Raleigh is satisfied with their performance. However, Raleigh has just received a competing bid from Brahmin, Inc., a firm that is aggressively marketing its products. Brahmin has offered to supply systems for a price of $237,500, or $12,500 below the $250,000 price for the Atlanta system. In addition to an attractive price, Brahmin offers a money-back guarantee. That is, if Brahmin's systems do not match Atlanta's quality, Raleigh can reject them and return them for a full refund. However, if it must reject the machines and return them to Brahmin, Raleigh will suffer a manufacturing delay costing the firm $50,000. A. Construct a decision tree for this problem and determine the maximum probability Raleigh can assign to rejection of the Brahmin system before it would reject the offer, assuming it decides on the basis of minimizing expected costs. B. Assume that Raleigh assigns a 40% probability of rejection of the Brahmin controls. Would Raleigh be willing to pay $5,000 for an assurance bond that would cover manufacturing delay costs if the Brahmin controls fail the quality check? (Use the same objective as in part A above.) Explain.

Game Theory. F&M Manufacturing, Inc., a diversified manufacturer of packaging products, is considering upgrading its current line by making available a new line of coated paper products. Of course, the market response to this upgrade in product quality would depend on the competitor response, if any. The company's comptroller projects the following annual profits (payoffs) following resolution of the upgrade decision. A. Which decision alternative would F&M choose given a secure strategy criterion? Explain. B. Calculate the opportunity loss or regret matrix. C. Which decision alternative would F&M choose if the company seeks to minimize opportunity cost? Explain.

The minimum expected opportunity loss associated with a decision equals the:

Following an increase in the risk-free rate, the certainty equivalent adjustment factor a will:

Certainty Equivalents. Pier-4, Inc. is a rapidly growing chain of sea-food restaurants. The company has a limited amount of capital for expansion, and must carefully weigh available alternatives. Currently, the company is considering opening restaurants in Providence, Rhode Island and/or Gloucester, Massachusetts. Projections for the two potential outlets are: Each restaurant would involve a capital expenditure of $2.5 million, and the company uses the 10% yield on risk-free U.S. Treasury bills to calculate the risk-free annual opportunity cost of investment capital. A. Calculate the expected value, standard deviation, and coefficient of variation for each outlet's profit contribution. B. Calculate the minimum certainty equivalent adjustment factor for each restaurant's cash flows that would justify investment in each outlet.

Probability Analysis. Ceramic Tile, Inc. wishes to adopt one of two feasible marketing strategies: developing general consumer acceptance through media advertising, or developing distributor acceptance through intensive personal selling by company representatives. The marketing manager has developed the following estimates for sales under each alternative:

If profits are normally distributed with a mean of $12 and a standard deviation of $4, there is a 50/50 chance actual profits will exceed:

If you are indifferent between $1 and a lottery ticket that gives you a 0.001 chance of winning $1,000 you are:

Standard Normal. University Savings, Inc offers personal checking accounts to commercial and individual customers. Although unit costs cannot be determined precisely, University anticipates that monthly costs will be normally distributed around a mean of $5 per unit with a standard deviation of $1 per unit. A. What is the probability that University would make a profit at a checking price of $5 per unit? B. Calculate the unit price necessary to give University a 90% chance of making a profit on an individual checking account. C. If University offers its accounts at a price of $6, what is the probability that it will make a profit?

When the dispersion of possible returns is irrelevant, the decision maker is said to be: