MBA 201A Extra Midterm Practice Problems (With Answers)

Extra Midterm Practice Problems MBA 201A – Professors Davidoff & Hermalin Fall 2004

1. To Enter Or Not To Enter, That Is The Question Your company, Digital Paw, is considering whether to develop and market a new hand- held consumer electronics device, the BearPaw. The BearPaw will utilize the Global Positioning System (GPS) in conjunction with a system of Low Earth Orbit (LEO) communications satellites, allowing communities of customers to track their locations anywhere on the globe in real time. A decision to go ahead will require an up-front commitment of $100 million. Demand for the BearPaw device is uncertain, but early tests indicate that demand will either be “high” or “low” (as described below) with probabilities 0.6 and 0.4 respectively. Digital Paw is risk neutral.

If demand turns out to be high, there is a 25% chance that you will have the market to yourself. In that case, you will earn $200 million of profits (before accounting for the $100 million initial investment.) But with high demand there is a 75% chance that another company will introduce a rival product, in which case you will earn less than $200 million. Your marketing team is uncertain just how much profits will be eroded by the entry of such a rival. Pending further analysis, denote by the variable s (between 0 and 1) the share of the $200 million profits that you will earn if a rival enters. In other words, your profits if demand is high and entry occurs are $200s million. (For example, if s=0.6, your profits facing high demand and rivalry would be $120 million.)

If demand turns out to be low, there is an 80% chance that you will have the market to yourself. In that case, you will earn $50 million of profits (again, before accounting for the $100 million initial investment.) With low demand there is only a 20% chance that another company will introduce a rival product, in which case you will earn less than $50 million. Assume that your profits facing low demand and rivalry would be $50s million, using the same variable s defined in the previous paragraph.

(a) Draw the decision tree facing Digital Paw in this situation.

(b) Solve this decision problem, keeping s as a variable in your analysis. Explain how Digital Paw's optimal choice depends upon s.

(c) What factors affect the level of s? (This is an open-ended question that goes far beyond decision theory, or the fact pattern described in this problem, and foreshadows a number of topics we will cover later in the course.)

(d) [Optional; Food for Thought] How, if at all, would this analysis change if Digital Paw were not sure about the accuracy of the 60% probability for “high” demand? Specifically, how would the analysis change if Digital Paw had conducted one survey predicting that “high” demand would occur with an 80% probability, and another survey indicating that “high” demand would with a 40% probability, and Digital Paw put equal

Page 1 MBA 201A – Extra Midterm Practice Problems (with Answers) weight on each of the two surveys? Would your answer to this question change if Digital Paw were risk averse rather than risk neutral?

2. When to Sell a Depreciating Asset?

You are considering the purchase of a machine that costs $1.7 million. Each year that you run the machine, it produces output worth $500,000 using inputs that cost $100,000 (above and beyond the cost of the machine itself). The machine can be run for no more than four years. If you sell the machine by the end of the first year, you will receive $1 million for it. If you sell the machine by the end of the second year, you will receive $800,000 for it. If you sell the machine by the end of the third year, you will receive $600,000 for it. After that, the machine has no scrap value. The interest rate is zero.

(a) Show the decision tree for this problem.

(b) If you do buy the machine, for how many periods should you operate it?

3. Dober M. N. Pincher

Dober M. N. Pincher has recently recognized a market opportunity that arises from the number of dogs in the Berkeley area. Dober is planning to build a Bed & Biscuit to accommodate dog owners in need of temporary housing for their pets on Telegraph Ave., complete with TV room, massage area, and in touch with Berkeley, an aroma room – scents to be offered are yet to be determined. The choices are to build a small, medium or large dog retreat. Profits will depend on the market demand as outlined below:

Market Demand Bed & Biscuit Size Low Medium High Small 400 400 400 Medium 200 500 500 Large -400 300 800 Profits in thousands of dollars

Dober estimates a 21.75% probability that market demand will be low, a 35.5% probability that it will be medium and a 42.75% probability that it will be high. Assume that Dober is risk-neutral.

(a) Construct a decision tree for the problem. What decision will Dober make? What is the expected value of the decision?

Now suppose that Dober’s friend, Doris Labra, tells Dober he and his market research are completely backwards, and that perhaps Dober has been sniffing too many fire hydrants. In particular, she tells Dober that he has overestimated the probability of a good market,

Page 2 MBA 201A – Extra Midterm Practice Problems (with Answers) and that her more informed forecast calls for a 50% probability of low demand, a 20% probability of medium demand, and a 30% probability of high demand.

(b) If Dober believes Doris, does Dober’s decision change? If so, how, and what is the expected value of Dober’s new decision?

4. Wine, Skiing, and Lemons

You are considering buying a car. All the second-year students have told you how useful a car will be for your trips to Napa and Tahoe, although they have been curiously vague about when exactly you might be making such trips. Two options present themselves. First, you can rent a car every time you feel like driving to Calistoga to wallow in the mud baths. Compared to buying a car, this saves a large up-front capital expenditure, but annual operating costs are likely to be higher. Given the number of trips you have planned, you estimate that annual rental costs would be $1500. You are risk neutral.

The second option is to buy a car. You know more about business than about cars, so you worry about buying a lemon. If the car does turn out to be a lemon, it will cost you $2500 each year. This includes repairs, operating costs, and depreciation on the resale price of the car (the interest rate is zero). On the other hand, if the car turns out to be good, it will cost you only $1000 each year. You reckon the chances are exactly even of getting a good car (50%). You only have enough time to purchase one car or rent.

(a) Draw your decision tree. What is your decision (remember you’re risk neutral).

Some second years have studied “thinking outside the box.” They recommend you have a mechanic inspect the car before purchase. You believe that the mechanic can distinguish lemons from good cars with certainty. She has no set fee for inspections, so you must use your new negotiating skills to fix an inspection fee.

(b) Draw your new decision tree. What is the maximum amount you would be willing to pay for an inspection?

5. For Whom the Meter Tolls

The Berkeley Parking Enforcement Department (BPED) is a major provider of city revenues, especially now that the City’s ability to raise taxes has been restricted. BPED recently contracted with the consulting company Extrapolation Data Sciences (EDS) for advice on how to raise revenues further.

EDS examined the historical data (as reflected in Phases 1, 2, and 3 below) and proposed that BPED could dramatically increase revenues if it increased the enforcement rate P, that is the probability that a parking ticket is given to a scofflaw (the technical term for

Page 3 MBA 201A – Extra Midterm Practice Problems (with Answers) one who parks in a metered space but does not pay the meter) from 0.03 to 0.04. Before taking this advice, for each hour of parking there was only a 3% chance that a scofflaw would be ticketed with a fine of $28. One hour on the meter costs $1, and BPED’s enforcement budget was $2.5 million per year. Everyone involved agrees that parkers behave as expected utility maximizers. There are 2000 parking meters in the city, each of which is in operation 6 days a week between 9:00 am and 5:00 pm. You have been in Berkeley long enough to know that no metered parking space is ever vacant. Following EDS’ advice would increase BPED’s costs by 20%. Here are the historical data upon EDS relied:

Phase P Fine Revenue per Meter Toll Meter per Hour Per Hour 1 0.01 $28.00 $0.28 $1.00 2 0.02 $28.00 $0.56 $1.00 3 0.03 $28.00 $0.84 $1.00 EDS Proposal 0.04 $28.00 $1.12 $1.00 (expected)

Note that these data strongly suggest that all revenues so far have been earned from fines rather than the collection of monies paid to meters.

What do you expect to happen if BPED implements EDS’ proposal? Can you offer better advice concerning the best choice for P?

6. If You're Not Happy with Jimmy Beans ... You are considering opening your own restaurant. To do so, you will have to quit your current job, which pays $46k per year, and cash in your life savings of $200k, which have been in a certificate of deposit paying 6% per year. You will need this $200k to purchase equipment for your restaurant operations. You estimate that you will have to spend $4k during the year to maintain the equipment so as to preserve its market value at $200k. Fortunately, you own a building suitable for the restaurant. You currently rent out this building on a month-by-month basis for $2500 per month.

You anticipate that you will spend $50k for food, $40k for extra help, and $14k for utilities and supplies during the first year of operations. There are no other costs involved in this business.

What are the economic costs of operating the restaurant during the first year? In other words, what level of revenues will you need to achieve in the first year to make the first year profitable in an economic sense?

7. Old McDonald goes industrial

2002 was a turning point for Old McDonald's farm. Until then, the farm produced exclusively unprocessed tomato, selling its 100,000t for a profit margin of $2.1/t. In January 2002, however, Old McDonald decided to start exporting processed tomato (tomato pulp) to Europe. At that time, the price of tomato pulp was $8/t.

Page 4 MBA 201A – Extra Midterm Practice Problems (with Answers)

In order to produce tomato pulp, Old McDonald bought a machine capable of processing 100,000t per year. The machine cost $2m and is expected to last for 10 years. In addition to the machine cost, there is a $2.2/t harvesting and processing cost (mostly labor cost).

(a) Determine Old McDonald's average cost and profit margin in the production of tomato pulp. Assume that Old McDonald expects to produce for the next 10 years.

Things turned bad for Old McDonald in 2003. Increased tariff barriers by the European Union implied that the net price received by American exporters is now only $6/t. It is not expected that this price will change in the future. One accountant consulting for Old McDonald stated that as margins were cut in half the farmer had better sell the machine and go back to producing unprocessed tomato. Old McDonald investigated this possibility and concluded that used tomato-processing machines sell for $1.2m if two- years old, the price then declining proportionally to age.

(b) What would you advise the farmer to do?

8. Willy & the Chocolate Factory

Five years ago, Willy’s grandfather, owner of a famous chocolate factory, gave Willy some cash to start a business. Not surprisingly, Willy figured his core competence was chocolate, and so he purchased a candy-making machine for $300 million. The machine makes 4 kinds of candies: dark chocolate bars, chocolate mints, chocolate covered nuts, and malted milk balls. The machine is highly specialized to Willy’s candy- making technique, and so has no resale value in the market for candy machines. The machine is capable of making all kinds of candy at once, or making any combination of the four at the same time. However, making less of one kind of candy does not mean that you can make more of any other kind of candy (think of the machine as having 4 dedicated slots that are not interchangeable).

Willy also employs several experienced candy-makers. They spend a small fraction of their time combining the ingredients for each type of candy and putting them in the machine and spend most of their time wrapping each candy as it comes off the machine with cellophane paper in Willy’s trademark orange and black colors. Packaging any candy bar, regardless of whether it is a bar, mint, nut or malt, requires exactly the same amount of time and materials.

Although Willy benefits from a long family history in the chocolate business, he has little formal training in economics. Willy is considering whether or not he should stop making one or more of the types of candy bars. Willy thinks that the accounting numbers for his business are as follows:

Page 5 MBA 201A – Extra Midterm Practice Problems (with Answers)

DarkChoc Mints Nuts Malts Total Bars # Sold 16 4 8 2 30 Revenue $120 $28 $55 $20 $223 Labor hours 8 2 4 1 15 Cost of labor (@$6/ hour) $48 $12 $24 $6 $90 Other direct costs $10 $10 $24 $10 $54 Overhead* $15 $15 $15 $15 $60 Profit $47 ($9) ($8) ($11) $19 [All figures in millions, except as noted. Numbers in parentheses represent negative amounts.] *Total overhead includes the total cost of cellophane paper ($30 million) and the depreciated cost of the machine ($30 million) using straight-line depreciation over 10 years.

(a) Willy is considering halting the production of Mints and Malts this year, since they are the biggest money losers based on his calculations. What would you advise him about this? Why? If he does stop producing Mints and Malts, by how much would his profits change?

(b) Are there any candies that you would tell Willy to stop producing?

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