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 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.
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MBA 201A – Extra Midterm Practice Problems (with Answers)
(a) Draw the decision tree facing Digital Paw in this situation.
No Rival [p=0.25]
100
High Demand [p=0.6] 200
EV=0.25(100)+0.75(200s-100)=150s-50
Rival [p=0.75]
200s-100
Enter 200s
EV=94s-54
-100
No Rival [p=0.8]
-50
Low Demand [p=0.4] 0
EV=0.8*(-50)+0.2*(50s-100)=10s-60
EV=max(94s-54,0)
Rival [p=0.2]
50s-100
50s
Don't Enter
0
(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 BearPaw brand device to the new device, the aggressiveness of the rival’s
efforts to take share away from BearPaw, 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?
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MBA 201A – Extra Midterm Practice Problems (with Answers)
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.
Run in Year Four
-$100
Run in Year Three $400 -$100
$400 $100
Sell in Year Three
Run in Year Two $100
$600 $100
$400 $100
Run in Year One Sell in Year Two
-$100
$400 $100 $800 -$100
Buy in Year One Sell in Year One
-$300
-$1,700 $100 $1,000 -$300
Sell Zero
-$700
$100 $1,000 -$700
Do Not Buy
$0
$0 $0
(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
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MBA 201A – Extra Midterm Practice Problems (with Answers)
Operate for 3 periods.
(c) Should you buy the machine? If you do so, what profit will you earn?
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.
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MBA 201A – Extra Midterm Practice Problems (with Answers)
Low [p=0.2175]
400
400
Small Medium [p=0.355]
400
EV=400 400
High [p=0.4275]
400
400
Low [p=0.2175]
400
400
Medium Medium [p=0.355]
500
EV=400 EV=392.75 500
High [p=0.4275]
300
300
Low [p=0.2175]
-400
-400
Large Medium [p=0.355]
300
EV=361.5 300
High [p=0.4275]
800
800
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.
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MBA 201A – Extra Midterm Practice Problems (with Answers)
(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.
(c) How much is Doris’s information worth to Dober?
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.
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MBA 201A – Extra Midterm Practice Problems (with Answers)
Not a Lemon [p=0.5]
1000
Buy Car 1000
EV=1750
Lemon [p=0.5]
2500
EV=1500 2500
Rental
1500
1500
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.
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MBA 201A – Extra Midterm Practice Problems (with Answers)
Buy
$1,000
Not a Lemon [p=0.5] $1,000
EV=1000
$0
Rent
$1,500
Inspect $1,500
EV=1250
Buy
$2,500
Lemon [p=0.5] $2,500
EV=1500
Rent
$1,500
EV=1250 $1,500
Not a Lemon [p=0.5]
$1,000
Buy $1,000
EV=1750
Lemon [p=0.5]
Don't Inspect $2,500
EV=1500 $2,500
Rent
$1,500
$1,500
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:
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MBA 201A – Extra Midterm Practice Problems (with Answers)
Phase P Fine Revenue per Meter Toll Per
Meter per Hour 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?
As you will soon enough learn, this is one part of the city that runs effectively. BPED
would be ill advised to follow EDS’ recommendation. EDS has extrapolated past
revenues without understanding the behavior behind them. EV maximizing parkers will
always take a chance on a ticket as long as the expected cost (P×$28) is less than the
alternative of paying the meter ($1). This condition held for Phases 1 through 3, but is
violated in the EDS proposal. If implemented, parkers will pay the meter rather than
risking a ticket. Revenues will rise from $0.84 to a cap at $1.00 per meter revenue hour,
rather than the $1.12 projected by EDS. Annual gross parking revenues then increase
from $4,193,280 (=2000 meters ×2496 revenue hours per meter per year × $0.84
revenue per meter per hour) to $4,992,000 (=2000×2496×1). The proposal still
improves BPED’s net revenues, even though it will not enrich the city coffers as much as
EDS projected. Revenues increase by $798,720, costs increase by $500,000, and the city
is ahead by $298,720.
Without changing any other parameter in the problem, the best choice for P is that which
maximizes BPED's net revenues. This is the P that leaves parkers indifferent between
paying the expected fine and the $1 an hour toll on the meter. Solving for P×$28=$1
yields P=0.0357. Spending to increase P beyond this point is a waste of resources and
decreases net revenues. It also annoys people.
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.
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MBA 201A – Extra Midterm Practice Problems (with Answers)
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?
There are three opportunity costs:
The salary you could earn if you do not quit [$46k]
The interest income your savings could earn if you do not cash in [($200k)(0.06) = $12k]
The rent your building could earn if you do not use it for your restaurant [($2.5k)(12
months) = $30k ]
There are four direct costs:
Maintaining the equipment [$4k]
Food [$50k]
Hiring extra help [$40k]
Utilities and supplies [$14k]
Note that the $200 k cost of the equipment is not an economic cost because it is
essentially reversible. That is, you can always sell the equipment for its current market
value as long as you maintain it. Only the interest you would have earned on the money
tied up in the equipment and the cost to maintain it are economic costs.
Adding up opportunity and direct costs yields $196k. This is the break-even revenue for
first year of operations.
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.
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.
Assuming a constant depreciation rate throughout the machine's lifetime, we have an
average cost of $2m divided by 10 years divided by 100,000t/year, or simply $2/t; plus
labor costs of $2.2/t; for a total of AC=$4.2/t. The profit margin is therefore =$8-
$4.2=$3.8.
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MBA 201A – Extra Midterm Practice Problems (with Answers)
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?
There are two opportunity costs that need to be accounted for. First, by selling tomato
pulp the farmer is foregoing the chance of selling unprocessed tomato. This opportunity
cost amounts to the margin on unprocessed tomato, or $2.1/t. The second opportunity
cost is that of the machine, namely the loss from not selling the machine. Since the
machine is now worth only $1.2m and is still useful for another 8 years, the opportunity
cost per unit is $1.2m divided by 8 years divided by 100,000t/year, or $1.5/t. The new
profit margin, taking into account these two opportunity costs, is
=$6(new price)-$2.2(labor)-$1.5(machine)-$2.1(margin on unprocessed tomato)=$0.2
Since this value is positive, the farmer should continue selling tomato pulp.
An alternative way of stating the same is to compute the margin on tomato pulp with the
correct machine opportunity cost (AC=$6-$2.2-$1.5=$2.3) and compare it to the
unprocessed tomato margin ($2). Since the former is greater than the latter ($2.3>$2.1),
the farmer should stick to tomato pulp.
(c) Suppose that the price of unprocessed tomato is $0.5/t higher than before. Would you
then give a different answer?
By a calculation analogous to the one above, we can conclude that the farmer is better
off by switching to unprocessed tomato.
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
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MBA 201A – Extra Midterm Practice Problems (with Answers)
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:
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?
Economic profit = Revenue – Economic Cost
= Revenue – (Cost of labor + Other direct costs + Cost of cellophane)
Economic profit (Dark Chocolate) = $120 M – ($48 M + $10 M + $1 x 16 M) = $46 M
Economic profit (Mints) = $28 M – ($12 M + $10 M + $1 x 4 M) = $2 M
Economic profit (Nuts) = $55 M – ($24 M + $24 M + $1 x 8 M) = -$1 M
Economic profit (Malts) = $20 M – ($6 M + $10 M + $1 x 2 M) = $2 M
Economic profit (Total) = $223 M – ($90 M + $54 M + $1 x 30) = $49 M
The revenues of both Mints and Malts exceed the operating cost, once the machine
overhead is taken out of the calculation and the packaging is accounted for on a per unit
basis. He should not stop production of these two product lines. Each line has a profit of
$2 mil, so profits would decrease by $4mil if he stopped producing these lines.
(b) Are there any candies that you would tell Willy to stop producing?
Nuts have an operating cost that exceeds their revenue by $1 million, so he should stop
producing Nuts.
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