Each restaurant would require a capital expenditure of $700,000, plus land acquisition costs of $500,000 for Albuquerque and $1 million for Santa Fe. The company uses the 10% yield on risk-less 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.
C. Assuming that the management of Tex-Mex is risk averse and uses the certainty equivalent method in decision making, which is the more attractive outlet? Why?
P14.8 Decision Trees. Keystone Manufacturing, Inc., is analyzing a new bid to supply the company with electronic control systems. Alpha Corporation has been supplying the systems, and Keystone is satisfied with its performance. However, a bid has just been received from Beta Controls, Ltd., a firm that is aggressively marketing its products. Beta has offered to supply systems for a price of $120,000. The price for the Alpha system is $160,000. In addition to an attractive price, Beta offers a money-back guarantee. That is, if Beta's systems do not match Alpha's quality, Keystone can reject and return them for a full refund. However, if it must reject the machines and return them to Beta, Keystone will suffer a delay costing the firm $60,000.
A. Construct a decision tree for this problem and determine the maximum probability that Keystone could assign to rejection of the Beta system before it would reject that firm's offer, assuming that it decides on the basis of minimizing expected costs.
B. Assume that Keystone assigns a 50% probability of rejection to the Beta Controls. Would Keystone be willing to pay $15,000 for an assurance bond that would pay $60,000 in the event that the Beta Controls fail the quality check? (Use the same objective as in part A.) Explain.
P14.9 Standard Normal Concept. Speedy Business Cards, Inc., supplies customized business cards to commercial and individual customers. The company is preparing a bid to supply cards to the Nationwide Realty Company, a large association of independent real estate agents. Because paper, ink, and other costs cannot be determined precisely, Speedy anticipates that costs will be normally distributed around a mean of $20 per unit (each 500-card order) with a standard deviation of $2 per unit.
A. What is the probability that Speedy will make a profit at a price of $20 per unit?
B. Calculate the unit price necessary to give Speedy a 95% chance of making a profit on the order.
C. If Speedy submits a successful bid of $23 per unit, what is the probability that it will make a profit?
P14.10 Game Theory. Sierra Mountain Bike, Inc., is a producer and wholesaler of rugged bicycles designed for mountain touring. The company is considering an upgrade to its current line by making high-grade chrome alloy frames standard. Of course, the market response to this upgrade in product quality depends on the competitor's reaction, if any. The company's comptroller projects the following annual profits (payoffs) following resolution of the upgrade decision:
States of Nature
Competitor No Competitor
Sierra's Decision Alternatives Upgrade Upgrade
Upgrade $1,000,000 $1,500,000
Do not upgrade 800,000 2,000,000
A. Which decision alternative would Sierra choose given a maximin criterion? Explain.
B. Calculate the opportunity loss or regret matrix.
C. Which decision alternative would Sierra choose given a minimax regret criterion? Explain.
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