Managerial Decision Analysis

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Case Study - Ski Right

After retiring as a physician, Bob Guthrie became an avid downhill skier on the steep slopes

of the Utah Rocky Mountains. As an amateur inventor, Bob was always looking for

something new. With the recent deaths of several celebrity skiers, Bob knew he could use his

creative mind to make skiing safer and his bank account larger. He knew that many deaths on

the slopes were caused by head injuries. Although ski helmets have been on the market for

some time, most skiers considered them boring and basically ugly. As a physician, Bob knew

that some type of new ski helmet was the answer.

Bob’s biggest challenge was to invent a helmet that was attractive, safe, and fun to wear.

Multiple colors, using the latest fashion designs would be a must. After years of skiing, Bob

knew that many skiers believed that how you looked on the slopes was more important than

how you skied. His helmets would have to look good and fit in with current fashion trends.

But attractive helmets were not enough. Bob had to make the helmets fun and useful. The

name of the new ski helmet, Ski Right, was sure to be a winner. If Bob could come up with a

good idea, he believed that there was a 20% chance that the market for the Ski Right Helmet

would be excellent. The chance of a good market should be 40%. Bob also knew that the

market for his helmet could be only average (30% chance) or even poor (10% chance).

The idea of how to make ski helmets fun and useful came to Bob on a gondola ride to the top

of a mountain. A busy executive on the gondola ride was on his cell phone trying to complete

a complicated merger. When the executive got off of the gondola, he dropped the phone and it

was crushed by the gondola mechanism. Bob decided that his new ski helmet would have a

built-in cell phone and an AM/FM Stereo radio. All of the electronics could be operated by a

control pad worn on a skier’s arm or leg.

Bob decided to try a small pilot project for Ski Right. He enjoyed being retired and didn’t

want a failure to cause him to go back to work. After some research, Bob found Progressive

Products (PP). The company was willing to be a partner in developing the Ski Right and

sharing any profits. If the market were excellent, Bob would net $5,000. With a good market,

Bob would net $2,000. An average market would result in a loss of $2,000, and a poor market

would mean Bob would be out $5,000.

Another option for Bob was to have Leadville Barts (LB) make the helmet. The company had

extensive experience in making bicycle helmets. Progressive would then take the helmets

made by Leadville Barts and do the rest. Bob had a greater risk. He estimated that he could

lose $10,000 in a poor market or $4,000 in an average market. A good market for Ski Right

would result in a $6,000 profit for Bob, while an excellent market would mean a $12,000

profit. A third option for Bob was to use TalRad TR, a radio company in Tallahassee, Florida.

TalRad had extensive experience in making military radios. Leadville Barts could make the

helmets, and Progressive Products could do the rest. Again, Bob would be taking on greater

risk. A poor market would mean a $15,000 loss, while an average market would mean a

$10,000 loss. A good market would result in a net profit of $7,000 for Bob. An excellent

market would return $13,000.

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Bob could also have Celestial Cellular (CC) develop the cell phones. Thus, another option

was to have Celestial make the phones and have Progressive do the rest of the production and

distribution. Because the cell phone was the most expensive component of the helmet, Bob

could lose $30,000 in a poor market. He could lose $20,000 in an average market. If the

market were good or excellent, Bob would see a net profit of $10,000 or $30,000,

respectively.

Bob’s final option was to forget about Progressive Products entirely. He could use Leadville

Barts to make the helmets, Celestial Cellular to make the phones, and TalRad to make the

AM/FM stereo radios. Bob could then hire some friends to assemble everything and market

the finished Ski Right helmets. With this final alternative, Bob could realize a net profit of

$55,000 in an excellent market. Even if the market were just good, Bob would net $20,000.

An average market, however, would mean a loss of $35,000. If the market were poor, Bob

would lose $60,000.

Answer the following questions.

1. Construct the Decision Tree and based on the analysis what do you

recommend?

2. What is the opportunity loss for this problem?

3. Compute the expected value of perfect information.

4. Was Bob completely logical in how he approached this decision problem?

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1. Based on the analysis what do you recommend?

I think the best decision could be to have LB make the helmets and have

PP make rest of them (2nd option).

Expected value = $2,600

However the option of not using Progressive (I mean using LB & CC &

TR) was very close with an expected value of $2500.

EMVPP = (-5000*0.1) + (-2000*0.3) + (2000*0.4) + (5000*0.2) =700

EMVLP & PP =

(-10000*0.1) + (-4000*0.3) + (6000*0.4) + (12000*0.2) =2600

EMVTR&PP = (-15000*0.1) + (-10000*0.3) + (7000*0.4) + (13000*0.2)

=900

EMVCC&PP = (-30000*0.1PP) + (-20000*0.3) + (10000*0.4) +

(30000*0.2) =1000

EMVLB&CC&TR = (-60000*0.1) + (-35000*0.3) + (20000*0.4) +

(55000*0.2) =2500

Options Poor Average Good Excellent EMV

1-PP -5,000 -2,000 2,000 5,000 700

2-LP & PP -10,000 -4,000 6,000 12,000 2,600

3-TR & PP -15,000 -10,000 7,000 13,000 900

4-CC & PP -30,000 -20,000 10,000 30,000 1,000

5-LB & CC & TR -60,000 -35,000 20,000 55,000 2,500

PROBABILITY 0.1 0.3 0.4 0.2

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2. What is the opportunity loss for this problem?

3. Compute the expected value of perfect information.

(2 & 3) At this place we have to calculate the opportunity loss and EVPI. They

are as follows:

Perfect Information

Poor Average Good Excellent

Perfect

Information

-5,000 -2,000 20,000 55,000

Probabilities 0.1 0.3 0.4 0.2

Expected Value WITH Perfect Information

= (-5000*0.1) + (-2000*0.3) + (20000*0.4) + (55000*0.2) =17900

EVwPI =17900

Best Expected Monetary Value as we calculated before is:

EMVLP & PP =

(-10000*0.1) + (-4000*0.3) + (6000*0.4) + (12000*0.2) =2600

EMV =2600

Expected Value OF Perfect Information

EVPI = EVwPI- EMV

EVPI =17900-2600=15300

The maximum EMV is 2,600 given at Option 2.

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For this choice the EVPI is $15300. (The minimum EOL is $15,300)

Outcomes

Alternatives Poor Average Good Excellent EOL Choice

PP 0 0 18,000 50,000 17,200

LB & PP 5,000 2,000 14,000 43,000 15,300

TR & PP 10,000 8,000 13,000 42,000 17,000

CC & PP 25,000 18,000 10,000 25,000 16,900

LB& CC& TR 55,000 33,000 0 0 15,400

Probability 0.1 0.3 0.4 0.2

4. Was Bob completely logical in how he approached this decision

problem?

Yes. In my opinion he clearly made a logical decision, since there are a number

of options that Bob did not consider, because they were wrong based on his

information and calculations.