MBA 201A Extra Midterm Practice Problems (With Answers)

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

Extra Midterm Practice Problems (with Answers)

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 BearPawâ. The BearPawâ 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 BearPawâ 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.

The expected profits when demand is high are (0.25)×200 + (0.75)×200s - 100. The expected profits when demand is low demand are 50×(0.8+0.2s)-100. Since there is a 0.6 chance that demand will be high and a 0.4 chance that it will be low, the expected profit after entering the business will be 0.6×(200×(0.25+0.75s)-100) + (0.4)×(50×(0.8+0.2s)-100) which can be simplified to 94s-54. Investment is worthwhile so long as s > 54/94 = 0.57.

(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.)

Some general factors to consider include the degree to which consumers prefer the original BearPawâ brand device to the new device, the aggressiveness of the rival’s efforts to take share away from BearPawâ, and the Digital Paw’s willingness to accommodate or fight for share after the entrant arrives.

(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 weight on each of the two surveys? Would your answer to this question change if Digital Paw were risk averse rather than risk neutral?

Remember that the probability estimates we use are always best estimates given the available information. Uncertainty about these estimates is present in all realistic cases where the underlying probability is subjective (a matter of judgement) rather than objective. So, whether Digital Paw is risk averse or risk neutral, adding further uncertainty about the probabilities has no effect on the decision analysis, so long as the best estimate taking into account all sources of information remains that "high" demand will occur with probability 0.6.

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?

The payoff from operating through one, two, three or four periods is as follows:

One period = $1,000,000 + $500,000 - $100,000 - $1,700,000= -$300,000

Two periods = $800,000 + 2 × ($500,000 - $100,000) - $1,700,000=-$100,000

Three periods = $600,000 + 3 × ($500,000 - $100,000) - $1,700,000=$100,000

Four periods = 4 × ($500,000 - $100,000) - $1,700,000=-$100,000

Þ Operate for 3 periods.

Yes, you should buy the machine and operate it for 3 years then sell it, yielding you a net profit on your investment of $100,000. The depreciation in the fourth year exceeds the operating profits.

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?

See figure 3. The expected profit from a small B&B is (0.2175)(400)+ (0.355)(400)+ (0.4275)(400)=400 or $400,000. The expected profit from a medium B&B is (0.2175)(200)+(0.355)(500)+(.4275)(500)=434.75 or $434,750. The expected profit from a large B&B is (0.2175)(-400)+(0.355)(300)+(0.4275)(800)=361.50 or $361, 500. Dober should clearly build a medium B&B.

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, 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?

If Doris is correct, the expected profit from a small B&B is (0.5)(400)+ (0.2)(400)+ (0.3)(400)= 400 or $400,000. The expected profit from a medium B&B is (0.5)(200)+(0.2)(500)+(0.3)(500)=350 or $350,000. The expected profit from a large B&B is (0.5)(-400)+(0.2)(300)+(0.3)(800)=100 or $100,000. Now, Dober should build the small B&B.

The value of Doris’s information should equal the difference in the expected profits Dober realizes with and without the information. If Doris is correct, and Dober does not acquire her information, he will erroneously choose to build a medium B&B based on his calculus from part (a). But instead of earning the expected profit of $434,750, he will earn an expected profit of $350,000 because of his misperceptions about the probabilities. If he acquires Doris’s information, he will earn an expected profit of $400,000, which is $50,000 greater than without the information. The information is therefore worth $50,000 to him.

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).

See figure 4(a). The expected cost of buying a car is 0.5×1000+×0.5×2500=1750. Since the cost of renting a car, $1500, is less than the expected value of owning a car, $1,750, you should rent a car.

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?

The inspection gives you information about whether you will face an expense of $1,000 or $2,500. Since the cost of the car if it turns out to be good will be less than the cost of renting, knowing whether it is a good car or a lemon is useful information. Redrawing your decision tree with this new information, we get the figure for problem 4(b). The figure shows that if the inspector tells you it is a good car your optimal choice is to buy a car which will have a cost of $1,000. If the inspector tells you that the car is a lemon, your optimal choice is to rent, which will cost you $1,500. Since your prior beliefs regarding the type of report the inspector will give are that fifty percent of the time she will report that the car is a lemon and fifty percent of the time she will report that the cars is good, your expected cost with inspection is 0.5×1000+0.5×1500=1250.

Since without the inspection you would have rented a car for $1,500, you would be willing to pay up to 1500-1250 = 250 for the 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 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: