Armando Gonzalez
New Jersey Institute of Technology
Decision Analysis with Quant Modeling
Part 1 Assignment: 3 Case Studies
Case Study 1: The Alset Electric Car
Alset Motors produces a small line of all-electric automobiles ( as opposed to hybrid-electric or
plug-in-hybrid electric). To show customers the benefits of going electric, Alset’s management
decides to market a break-even analysis versus a comparably equipped internal combustion
engine vehicle.
Alset gathers the following information with respect to their leading seller, the Neural, as well as
the leading gas-powered competitor, the BCS-18 which gets an impressive 50 miles per gallon
of gasoline.
Car
List Price ($)
Economy
Energy
Neutral
29,999
0.30 kWH/Mile
0.11 $/kWh
BCS-18
28,999
0.02 gallons/mile
3.50$/gallon
Questions
1. Perform a break-even analysis on buying the Neural Versus buying the BCS-18
2. If the prices of gasoline doubles to $7.00 per gallon, what happens to the break-even point
3. If the price of gasoline crashes to $1.75 per gallon, what happens to the break-even point?
4. Electric cars also don’t need oil, transmission fluid, or ICE car batteries. Prepare a simple one
page marketing flier incorporating these facts along with the data analysis provided.
1.​ To perform a break-even analysis, we need to calculate the total cost of owning each car,
including both the initial purchase price and the ongoing fuel costs.
For the Neural, the total cost is the purchase price plus the cost of electricity per mile times the number of
miles driven. If we let M represent the number of miles driven, the total cost of the Neural is:
$29,999+0.30×0.11×M
For the BCS-18, the total cost is the purchase price plus the cost of gasoline per mile times the number of
miles driven. The total cost of the BCS-18 is: $28,999+0.02×3.50×M
Setting these two equations equal to each other gives the break-even point in terms of miles driven:
$29,999+0.30×0.11×M=$28,999+0.02×3.50×M
Solving this equation for M gives the break-even point: M is approximately 27,027.
This means that after driving about 27,027 miles, the total savings in operating costs would offset the
initial price difference between the electric car and the gas-powered car. After this point, the Neural would
be the more cost-effective option in terms of operating expenses.
2.​ If the price of gasoline rises to $7.00 per gallon, the cost per mile for the BCS-18 will also double.
This causes the break-even point to increase, meaning you would need to drive more miles for
the total cost of the Neural to match the total cost of the BCS-18.
3.​ If the price of gasoline drops to $1.75 per gallon, the cost per mile for the BCS-18 is halved. This
reduces the break-even point, meaning you would need to drive fewer miles for the total cost of
the Neural to equal the total cost of the BCS-18.
4.​ "Ready to make the switch to electric? The Alset Motors Neural is here to help you save money
on fuel and skip the hassle of oil changes, transmission fluid, and replacing traditional car
batteries. With an impressive 0.30 kWh/mile efficiency and just $0.11 per kWh for electricity, the
Neural is a win for both your wallet and the environment. Plus, our break-even analysis shows
that the more you drive, the more you'll save compared to gas-powered cars. Make the smart
choice and go electric with Alset Motors today!"
Case Study 2: WTVX
WTVX, Channel 6, is located in Eugene, Oregon, home of the University of Oregon’s football
team. The station was owned and operated by George Wilcox, a former Duck (university of
Oregon football player). Although there were other television stations in Eugene, WTVX was the
only station that had a weatherperson who was a member of the American Meteorological
Society (AMS). Every night, Joe Hummel would be introduced as the only weatherperson in
Eugene who was a member of the AMS. This was George’s idea, and he believed that this gave
his station the mark of quality and helped with market share.
​
In addition to being a member of AMS, Joe was also the most popular person on any of
the local news programs. Joe was always trying to find innovative ways to make the weather
interesting, and this was especially difficult during the winter months when the weather seemed
to remain the same over long periods of time. Joe’s forecast for next month, for example, was
that there would be a 70% chance of rain every day, and that what happens on one day (rain or
shine) was not in any way dependent on what happened the day before.
​
One of Joe’s most popular features of the weather report was to invite questions during
the actual broadcast. Questions would be phoned in,and they were answered on the spot by
Joe. Once a 10 year old boy asked what caused fog, and Joe did an excellent job of describing
some of the various causes.
Occasionally, Joe would make a mistake. For example, a high school senior asked Joe
what the chances were of getting 15 days of rain in the next month (30 days). Joe made a quick
calculation: (70%) x (15 days/30 days) = (70%)(½) = 35%. Joe quickly found out what it was like
being wrong in a university town. He had over 50 phone calls from scientists, mathematicians,
and other university professors, telling him that he had made a big mistake in computing the
chances of getting 15 days of rain during the next 30 days. Although Joe didn’t understand all of
the formulas the professors mentioned, he was determined to find the correct answer and make
a correction during a future broadcast.
​
Discussion Questions:
1.​ What are the chances of getting 15 days of rain during the next 30 days?
Where:
P(X = k) is the probability of getting exactly k successes (in this case, 15 days of rain).
n is the total number of trials (30 days).
k is the number of successful trials (15 days of rain).
p is the probability of success on a single trial (the chance of rain on any given day).
q is the probability of failure on a single trial (the chance of no rain on any given day).
P(X = k) = C(n, k) * p^k* q^(n-k)
P(X = 15) = C(30, 15) * (0.70)^15 * (0.30)^(30-15)​
C(30, 15) = 30! / (15!(30-15)!) = 15504​
P(X = 15) = 15504 * (0.70)^15* (0.30)^(15)​
P(X = 15) = 15504 * (0.0047475615) * (0.00000000143489070)
P(X = 15) ≈ 0.00000010561684
The chances of getting exactly 15 days of rain during the next 30 days are approximately
0.00000010561684.
2.​ What do you think about Joe’s assumption concerning the weather for the next 30 days?
Joe’s assumption that there's a 70% chance of rain every day and that the weather one day doesn't affect
the next is a bit of an oversimplification. Weather is a lot more complicated and often has patterns that
last a few days or change quickly based on different factors. By assuming each day is independent, Joe’s
approach misses the fact that weather can stick around for a few days or change quickly depending on
the conditions. While his method might give a rough idea, it doesn’t really consider how the weather on
one day might influence the next. Also, Joe's calculation of a 35% chance of getting 15 rainy days was
wrong. A more accurate calculation showed the chance was actually much lower—around 0.0000001.
This highlights how important it is to use the right methods when calculating probabilities, especially in a
place where getting things right matters. Overall, Joe’s assumptions simplify things, but they don’t really
reflect how weather patterns work, and his original calculation was off.
Case Study 3: Internet Case - Drink-At-Home, Inc.
Drink-At-Home, Inc.
Drink-At-Home, Inc. (DAH, Inc.), develops, processes, and markets mixes to be used in
nonalcoholic cocktails and mixed drinks for home consumption. Mrs. Lee, who is in charge of
research and development at DAH, Inc., this morning notified Mr. Dick Jones, the president, that
exciting developments in the research and development section indicate that a new beverage,
an instant pina colada, should be possible because of a new way to process and preserve
coconut. Mrs. Lee is recommending a major program to develop the pina colada. She estimates
that expenditure on the development may be as much as $100,000 and that as much as a
year's work may be required. In the discussion with Mr. Jones, she indicated that she thought
the possibility of her outstanding people successfully developing such a drink now that she'd
done all the really important work was in the neighborhood of 90 percent. She also felt that the
likelihood of a competing company developing a similar product in 12 months was 80 percent.
Mr. Jones is strictly a bottom line guy and is concerned about the sales volume of such a
beverage. Consequently, Mr. Jones talked to Mr. Besnette, his market research manager, whose
specialty is new product evaluation, and was advised that a market existed for an instant pina
colada, but was somewhat dependent on acceptance by both grocery stores and retail liquor
stores. Mr. Besnette also indicated that the sales reports indicate that other firms are
considering a line of tropical drinks. If other firms should develop a competing beverage the
market would, of course, be split among them. Mr. Jones pressed Mr. Besnette to make future
sales estimates for various possibilities and to indicate the present (discounted value of future
profits) value. Mr. Besnette provided Table 1.
Mr. Besnette's figures did not include (1) cost of research and development, (2) cost of new
production equipment, or (3) cost of introducing the pina colada. The cost of the new production
equipment is expected to be $ 100,000 because of the special way the coconut needs to be
handled, and the cost of introducing the new product is expected to be about $150,000 because
of the point-of purchase displays that would be necessary to introduce the new product.
Mrs. Lee has indicated that she does have alternative development proposals, which are:
1.​ A reduced research program to see someone else comes out with the product first and if
not, then proceed with a crash program. The reduced program for the first eight months
would cost $10,000 per month. One advantage of this is that if the effort was
unsuccessful, then development costs would be held to the eight-month figure (8 months
X $ 10,000 = $80,000). The likelihood of success under this approach is the same as the
more orderly development. (The likelihood of a competing company developing a
product in 8 months is 60 percent.) The crash development program would take place in
months 9 through 12 and would cost an additional $60,000. It would proceed only if the
eight-month study guaranteed a success.
2.​ Use a reduced research program and maintain an awareness of industry developments
to see if someone else develops a product. If someone else has developed a product at
the end of six months, it would cost only an additional $30,000 to analyze their product
and duplicate it. The reduced development program would cost $10,000 per month.
Mr. Besnette, being the great marketer that he is, is of course reluctant to be second on the
market with a new product. He says that the first product on the market will usually obtain a
greater share of the market, and it will be difficult to win those customers back. Consequently,
he indicates that only about 50 percent of the sales that he indicated in Table 1 could be
expected if Drink-at-Home waited until competing brands were already on the market. Moreover,
he suspects that there is only a 50/50 chance that the competitor will be out with a product
within the next six months. There are four options: (1) orderly development of the pina colada,
(2) modest development effort followed by the crash program, (3) a modest development effort
for the first six months to see if a competitive product comes on the market, and (4) do nothing.
TABLE 1 Sales and Profit Potentials
Consumer Acceptance (Sales Potential) Probability Present Values (Discounted Value of Future
Profits) Substantial 0.10 $800,000 Moderate 0.60 $600,000 Low 0.30 $500,000
Consumer Acceptance
(Sales Potential) Probability
Present Values
(Discounted Value of Future
Profits)
Substantial
0.10
$800,000
Moderate
0.60
$600,000
Low
0.30
$500,000
1. What do you recommend?
Modest Development Effort for the First 6 Months
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Reduced research cost (first 6 months): 6 months * $10,000 = $60,000
Analysis and duplication cost (if a competitor enters the market): $30,000
Total development cost: $60,000 + $30,000 = $90,000
Timeframe: 6 months (if no competitor enters the market in this time)
Probability of competitor entering the market within 6 months: 50%
Sales potential if first to market: $800,000 (10% probability), $600,000 (60% probability),
$500,000 (30% probability)
This is recommended for several reasons. First, it offers a lower upfront cost of $90,000, making it a more
financially conservative option that aligns with a risk-averse approach. By monitoring industry
developments and competitor activity for the first six months, the company can assess whether further
investment is necessary based on competitors' actions. Additionally, if Drink-At-Home is first to market,
there is significant sales potential, with the possibility of earning up to $800,000 if successful, making the
initial investment worthwhile. Moreover, Option 3 provides flexibility, allowing the company to adapt its
strategy based on market conditions. If a competitor enters within the first six months, the company can
analyze their product and replicate it at a lower cost of $30,000. However, it is crucial for Drink-At-Home
to stay vigilant in monitoring the market and competitor activity to make informed decisions about
continuing the development program.