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BA 555 Practical Business Analysis

Midterm Examination #2

Simulation Using @Risk

Agenda

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Key Idea: Use Probability Distributions to Describe Uncertainty/Summarize Experience

Probability Distributions

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Estimated Unit Sales

Summarize your experience/knowledge on unit sales using:

=RiskUniform(0.08, 0.12) =RiskNormal(0.10, 0.02) =RiskNormal(0.10, 0.001) =RiskPert(0.08, 0.10, 0.12)

=RiskTriang(0.08, 0.10, 0.12) =RiskDiscrete({0.08,0.10, 0.12},{0.1, 0.7, 0.2}) =RiskDUniform({0.08, 0.10, 0.12})

or =RiskDUniform( data range )

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NPV: Simulation Results

100100

-150 -100 -50 0 50 100 150 200 250

24.24% 67.82% 7.95% 0 100

Mean=33.08259

Distribution for NPV / Year 0/C19

0.000

0.020

0.040

0.060

0.080

0.100

0.120

0.140

0.160

0.180

0.200

Mean=33.08259

-150 -100 -50 0 50 100 150 200 250

@RISK Student VersionFor Academic Use Only

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Corporate Health Insurance (pp.85-90)

A B C D E F G1 Initial Conditions: Assumptions:2 Number of Covered Employees 18,533 Increasing 2% per month3 Avg. Claim per Employee $250 Increasing 1% per month4 Amt. Contrib. per Employee $125 Constant56 Number of Employee Avg Claim Total Company7 Month Employees Contributions per Employee Claims Cost

8 1 18,904 $2,362,958 $253 $4,773,174 $2,410,2179 2 19,282 $2,410,217 $255 $4,917,324 $2,507,107

10 3 19,667 $2,458,421 $258 $5,065,827 $2,607,40611 4 20,061 $2,507,589 $260 $5,218,815 $2,711,22612 5 20,462 $2,557,741 $263 $5,376,423 $2,818,68213 6 20,871 $2,608,896 $265 $5,538,791 $2,929,89514 7 21,289 $2,661,074 $268 $5,706,063 $3,044,98915 8 21,714 $2,714,295 $271 $5,878,386 $3,164,09116 9 22,149 $2,768,581 $273 $6,055,913 $3,287,33217 10 22,592 $2,823,953 $276 $6,238,802 $3,414,84918 11 23,043 $2,880,432 $279 $6,427,214 $3,546,78219 12 23,504 $2,938,041 $282 $6,621,315 $3,683,275

20 $36,125,850

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“Convenient” Approaches (pp.86-88)

Most-Likely Values Increase in number of employees: 2% per month Increase in average claim size: 1% per month Total cost: $36 million

Best Case Increase in number of employees: -3% per month Increase in average claim size: -5% per month Total cost: $11 million

Worst Case Increase in number of employees: 7% per month Increase in average claim size: 7% per month Total cost: $104 million

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Choosing a Probability Distribution (p.88) Without past observations

With very limited amount of information, try to estimate Max, Min, and Most Likely values and use =RiskPert (or =RiskTriang)

With more information (e.g., percentiles), look for a distribution that reflects the information.

With past observations Click the Define Distributions icon and New Fit. @Risk will find a distribution that fits the data.

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Example 5 Software Development Project (p.97) A software development project consists of 6

activities. What is the expected duration for the entire

project?

AB

C

D

E F1 2 3 4 5A

B

C

D

E F1 2 3 4 5

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Example 3. IRR (p.93)

Is there more than 80% chance that the IRR exceeds the discount rate of 15%?