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Managerial Spreadsheet Modeling -- Prof. Juran 2
Outline
• Sensitivity Analysis• Some fancy Excel functions and graphs
Managerial Spreadsheet Modeling -- Prof. Juran 3
Often our analysis depends on some number whose value is uncertain.
– Inflation rate = 3%? Cost of lost goodwill = ?
What if we aren’t able to reasonably defend our assumption?– SWAG (Simple Wild Guess)– Stratospheric Citation
How critical is the accuracy of the estimated parameter to the business decision under consideration?
– How much would our performance measure change? Would our decision change if we were off by 1%? By 10%? Or wouldn’t it matter?
– Which estimates do we really need to pin down? E.g., for which parameters should we, as managers, devote additional time to estimate more precisely?
Sensitivity Analysis
Managerial Spreadsheet Modeling -- Prof. Juran 4
Base Case: Your initial (best-guess) estimate
Now estimate endpoints for a (non-statistical) confidence interval for your parameter.
– Low & High / Pessimistic & Optimistic / Worst & Best Case estimates
– What do you mean by “Best Case,” exactly?o What’s your Best Case for this evening?o What’s the worst that could have happened to British Petroleum?o However you define it, be consistent.o People generally are overconfident in their forecasting abilities, and
make prediction intervals too small.
Getting More Information
Managerial Spreadsheet Modeling -- Prof. Juran 5
Set all of the parameters to their worst (or best) case values.
– But how representative are these results?
Fit a probability distribution to the three (high / low / most likely) estimates
Use Monte Carlo simulation to generate a distribution for the performance measures you’re interested in.
Characterizing the Effects of Uncertainties
Managerial Spreadsheet Modeling -- Prof. Juran 6
One-at-a-time changes.– Set one parameter to its low and high values, respectively.– Keep all other parameters at the base case values.– Track the changes in the performance measure.
Tornado Graph: Horizontal bar chart– Horizontal axis: performance measure– Vertical axis: Uncertain estimators– Sorted by magnitude of the effect (largest at the top)– Cross axis at base case value
Characterizing the Effects of Uncertainties
($100,000) $0 $100,000 $200,000 $300,000 $400,000 $500,000
Volume Increase
Unit Trinket Cost
Artwork Cost
Base Volume
Managerial Spreadsheet Modeling -- Prof. Juran 7
Base unit sales of kids’ breakfast cereal: 6,500,000 over the next two monthsContribution margin: $1.48 / boxPossible promotion: Add a trinket
– Costs $0.10– Will increase sales by 12%– Artwork cost of $125,000
Should we add the trinket or not?
Example: Cereal Trinket
Managerial Spreadsheet Modeling -- Prof. Juran 8
Initial Calculations
2122
2324252627282930313233343536
E F G H I J K L M N O P Q
Base Volume 6,500,000Contribution Margin $1.48Total Contribution $ 9,620,000
Volume Increase 12%Volume 7,280,000Unit Trinket Cost $0.10Artwork Cost $ 125,000Total Contribution $ 9,921,400
Incremental Contribution $ 301,400
With the Trinket Promotion
Effect of the Trinket Promotion
Without the Trinket Promotion
= H25*H26
= H25*(1 + H30)
= H31*(H26 - H32) - H33
= H34 - H27
Managerial Spreadsheet Modeling -- Prof. Juran 9
• Base volume forecast could by off by ± 2%.• Trinket cost could increase by $0.015 if our supplier can’t
recover from his fire in time.• It’s very difficult to forecast sales response to breakfast
cereal: It could be anywhere between 8% and 14%.• Artwork costs could be 5% lower, or 20% higher, than our
initial estimate.
Uncertainty?
Managerial Spreadsheet Modeling -- Prof. Juran 10
At this point we are able to calculate all the numbers that we’ll need:
– Worst case: Set all 4 numbers to their “Pessimistic” values. (Similarly with the Best case.)
– Tornado graph: Keeping the other three numbers at their base case values, set each of the four estimates to its pessimistic and optimistic values in turn.
Pretty tedious, although straightforward.– We could just Copy, and Home | Paste | Paste Values for
the Incremental Contribution (H36) in each of the 4×2 cases.
Sensitivity Analysis
Managerial Spreadsheet Modeling -- Prof. Juran 11
Index() function for easier changes
Data tables: Automated “plug and chug”
A couple of advanced Excel functions: Rank(), Match()
Advanced chart features
Admittedly “overkill” for a problem this small.
Application of Advanced Excel
Managerial Spreadsheet Modeling -- Prof. Juran 12
($100,000) $0 $100,000 $200,000 $300,000 $400,000 $500,000
Volume Increase
Unit Trinket Cost
Artwork Cost
Base Volume
Part 1: The Tornado Graph
Managerial Spreadsheet Modeling -- Prof. Juran 13
Easy case: Pessimistic (and Optimistic) values are all positive:
– Series 1: Pessimistic– Series 2: Optimistic – Pessimistic– Turn Series 1 invisible– Don’t delete it!– Set Fill to No Fill and Border Color to No Line
Another easy case: All values are negative:– Series 1: Optimistic– Series 2: Pessimistic – Optimistic– Turn Series 1 invisible
Stacked Bar Chart
Managerial Spreadsheet Modeling -- Prof. Juran 14
More generally, if the base value is positive but at least some pessimistic values are negative:
– Series 1: min{Pessimistic, 0}– Series 2: max{Pessimistic, 0} ← and turn invisible– Series 3: Optimistic – Series 2
If the base value is negative but at lease some optimistic values are positive:
– Series 1: max{Optimistic, 0}– Series 2: min{Optimistic, 0} ← and turn invisible– Series 3: Pessimistic – Series 2
Stacked Bar Chart
Managerial Spreadsheet Modeling -- Prof. Juran 15
Each of the four parameters needs to be set to its pessimistic and optimistic parameter values, while keeping the other three at their base values.
Wouldn’t it be great if there were some way to automatically plug in all 4×2 different combinations of numbers, and record the incremental contribution for each combination?
– Need to specify which parameter (1 – 4) is being changed.– Need to specify what value (2 or 3) it is being changed to.
More generally, wouldn’t it be great if there were some way to automatically “plug and chug” different values for an input parameter (or two) and record the output performance in a table?
Building the Tornado Graph
Managerial Spreadsheet Modeling -- Prof. Juran 16
Open <trinket 1.xlsx> and look at the range T16:V21. Notice that the three columns T, U, and V are in this form:
Series 1 (column T): min{Pessimistic, 0}
Series 2 (column U): max{Pessimistic, 0}
Series 3 (column V): Optimistic – Series 2
Create a stacked bar chart using those three columns.
Depending on your version of Excel, you may need to Switch Row/Column. Your chart should look like this:
($100,000) — $100,000 $200,000 $300,000 $400,000 $500,000 $600,000
1
2
3
4
Neg. Part
Pos. Part
Difference
Managerial Spreadsheet Modeling -- Prof. Juran 17
Eliminate legend, gridlines
Right-Click | Format Axis (Vertical)
Axis option | Categories in reverse order
Axis option | Horizontal axis crosses at maximum category
Axis option | Major tick mark type: None
Axis option | Axis labels: High
Line style | Width: 1.5 pt
Line style | Dash type: - - - -
Font size: 12 pt
Right-Click | Format Axis (Horizontal)
Axis options | Maximum Fixed 500000
Vertical axis crosses: Axis value: 301,400
Font size: 12 pt
Number format: $???,??0; [Red]($???,??0)
Managerial Spreadsheet Modeling -- Prof. Juran 18
Make the middle data series invisible
Format Data Series | Fill No fill
Format Data Series | Border color No line
Format the other two series
Format Data Series | Series Options | Gap Width = 50%
Format Data Series | Fill | Gradient
Type = Linear; Angle = 90°
Stop 1 (0%) and Stop 3 (100%): Same dark tone
Stop 2 (50%): Light tone
Managerial Spreadsheet Modeling -- Prof. Juran 19
($100,000) $0 $100,000 $200,000 $300,000 $400,000 $500,000
Volume Increase
Unit Trinket Cost
Artwork Cost
Base Volume
• Volume Increase assumption has the biggest potential effect
• Widest range, and could lead to a negative outcome
• Decision maker would be wise to invest time and effort into refining this specific input value
Managerial Spreadsheet Modeling -- Prof. Juran 20
Part 2a: INDEX and OFFSET23456789101112
1314151617181920
2122
M N O P Q R S T U V W
2 3 Difference Rank Sequence1 $284,344 $309,928 $ 25,584 4 22 ($ 57,400) $480,800 $538,200 1 33 $192,200 $301,400 $109,200 2 44 $276,400 $307,650 $ 31,250 3 1
3
PositivePessimistic Optimistic Neg. Part Pos. Part Difference($ 57,400) $480,800 ($ 57,400) — $480,800$192,200 $301,400 — $192,200 $109,200$276,400 $307,650 — $276,400 $ 31,250$284,344 $309,928 — $284,344 $ 25,584
Pessimistic
Data Table for Incremental Contribution
Index #
Para
m. #
Sorted Data for Incremental Contribution
Volume IncreaseUnit Trinket CostArtwork CostBase Volume
1. OFFSET for the assumption labels
2. INDEX for optimistic and pessimistic
3. Formulas to create the series for the graph
Managerial Spreadsheet Modeling -- Prof. Juran 21
For the labels, use OFFSET:
N18=OFFSET($D$11,V7,0)
And copy down to rows 19:21.
2345678910111213141516171819202122
M N O P Q R S T U V W
2 3 Difference Rank Sequence1 $284,344 $309,928 $ 25,584 4 22 ($ 57,400) $480,800 $538,200 1 33 $192,200 $301,400 $109,200 2 44 $276,400 $307,650 $ 31,250 3 1
3
PositivePessimistic Optimistic Neg. Part Pos. Part Difference($ 57,400) $480,800 ($ 57,400) — $480,800$192,200 $301,400 — $192,200 $109,200$276,400 $307,650 — $276,400 $ 31,250$284,344 $309,928 — $284,344 $ 25,584
Pessimistic
Data Table for Incremental Contribution
Index #
Para
m. #
Sorted Data for Incremental Contribution
Volume IncreaseUnit Trinket CostArtwork CostBase Volume
=OFFSET($D$11,V7,0)
Looks to see what is 2 rows down and 0 columns to the right of D11 (because V7 is a 2)There’s nothing in D11; it’s just a reference point for the OFFSET
Managerial Spreadsheet Modeling -- Prof. Juran 22
Use INDEX to get the pessimistic and optimistic numbers:
R18= INDEX(R$7:R$10, $V7)
S18= INDEX(S$7:S$10, $V7)
And copy down2345678910111213141516171819202122
M N O P Q R S T U V W
2 3 Difference Rank Sequence1 $284,344 $309,928 $ 25,584 4 22 ($ 57,400) $480,800 $538,200 1 33 $192,200 $301,400 $109,200 2 44 $276,400 $307,650 $ 31,250 3 1
3
PositivePessimistic Optimistic Neg. Part Pos. Part Difference($ 57,400) $480,800 ($ 57,400) — $480,800$192,200 $301,400 — $192,200 $109,200$276,400 $307,650 — $276,400 $ 31,250$284,344 $309,928 — $284,344 $ 25,584
Pessimistic
Data Table for Incremental Contribution
Index #Pa
ram
. #
Sorted Data for Incremental Contribution
Volume IncreaseUnit Trinket CostArtwork CostBase Volume
= INDEX(R$7:R$10, $V7)
Managerial Spreadsheet Modeling -- Prof. Juran 23
Now use these formulas to create the three series.
T18= MIN(R18, 0)
U18= MAX(R18, 0)
V18= S18 - U18
And copy down
13141516171819202122
M N O P Q R S T U V W
PositivePessimistic Optimistic Neg. Part Pos. Part Difference($ 57,400) $480,800 ($ 57,400) — $480,800$192,200 $301,400 — $192,200 $109,200$276,400 $307,650 — $276,400 $ 31,250$284,344 $309,928 — $284,344 $ 25,584
Pessimistic
Sorted Data for Incremental Contribution
Volume IncreaseUnit Trinket CostArtwork CostBase Volume
= MIN(R18, 0)
= MAX(R18, 0)
= S18 - U18
Managerial Spreadsheet Modeling -- Prof. Juran 24
Part 2b: IFNew template file: <trinket 2b.xlsx>
Built-in DataTable in Q6:S10 -- leave that range alone
2345678910111213141516171819202122
M N O P Q R S T U V W
2 3 Difference Rank Sequence1 $499,166 $499,166 — 1 12 $499,166 $499,166 — 2 23 $499,166 $499,166 — 3 34 $499,166 $499,166 — 4 4
3
PositivePessimistic Optimistic Neg. Part Pos. Part Difference$499,166 $499,166 — $499,166 —$499,166 $499,166 — $499,166 —$499,166 $499,166 — $499,166 —$499,166 $499,166 — $499,166 —
Pessimistic
Data Table for Incremental Contribution
Index #Pa
ram
. #
Sorted Data for Incremental Contribution
Base VolumeVolume IncreaseUnit Trinket CostArtwork Cost
Managerial Spreadsheet Modeling -- Prof. Juran 25
J12 = IF($J$17 = C12, $J$18, 1) and copy down to rows 13:15.
2345678910111213141516171819202122
B C D E F G H I J K L M N O P Q R S T U V W
1 2 3Base Case Pessimistic Optimistic 2 3 Difference Rank Sequence
1 Base Volume 6,500,000 – 2% + 2% 1 $292,872 $309,928 $ 17,056 4 24 Artwork Cost $125,000 +20% – 5% 2 ($ 57,400) $480,800 $538,200 1 3
3 $192,200 $301,400 $109,200 2 41 2 3 Index 4 $276,400 $307,650 $ 31,250 3 1
Base Case Pessimistic Optimistic Used 31 Base Volume 6,500,000 6,370,000 6,630,000 32 Volume Increase 12% 8% 14% 13 Unit Trinket Cost $0.10 $0.115 $0.10 14 Artwork Cost $125,000 $150,000 $118,750 1
PositiveSet parameter # 1 Pessimistic Optimistic Neg. Part Pos. Part DifferenceTo index # 3 ($ 57,400) $480,800 ($ 57,400) — $480,800
$192,200 $301,400 — $192,200 $109,200$276,400 $307,650 — $276,400 $ 31,250$292,872 $309,928 — $292,872 $ 17,056
Volume IncreaseUnit Trinket CostArtwork CostBase Volume
Effect of the Trinket Promotion
Pessimistic
Sensitivity Analysis Data Table for Incremental Contribution
Index #
Para
m. #
Sorted Data for Incremental Contribution
Keeps all assumptions at their “base case” value by default
Allows one assumption to be optimistic or pessimistic
Managerial Spreadsheet Modeling -- Prof. Juran 26
2345678910111213141516171819202122232425262728293031323334353637
B C D E F G H I J K
1 2 3Base Case Pessimistic Optimistic
1 Base Volume 6,500,000 – 2% + 2%4 Artwork Cost $125,000 +20% – 5%
1 2 3 IndexBase Case Pessimistic Optimistic Used
1 Base Volume 6,500,000 6,370,000 6,630,000 32 Volume Increase 12% 8% 14% 13 Unit Trinket Cost $0.10 $0.115 $0.10 14 Artwork Cost $125,000 $150,000 $118,750 1
Set parameter # 1To index # 3
Base Volume 6,630,000Contribution Margin $1.48Total Contribution $ 9,812,400
Volume Increase 12%Volume 7,425,600Unit Trinket Cost $0.10Artwork Cost $ 125,000Total Contribution $10,122,328
Incremental Contribution $ 309,928
With the Trinket Promotion
Effect of the Trinket Promotion
Without the Trinket Promotion
Sensitivity Analysis
($100,000)
Note INDEX used in the table below.
The four assumptions are linked to J12:J15, which are controlled by J17:J18.
Try different combinations for J17:J18 and watch what happens in cell H36.
Managerial Spreadsheet Modeling -- Prof. Juran 27
2345678910111213141516171819202122232425262728293031323334353637
B C D E F G H I J K L M N O P Q R S T U V W
1 2 3Base Case Pessimistic Optimistic 2 3 Difference Rank Sequence
1 Base Volume 6,500,000 – 2% + 2% 1 $292,872 $309,928 $ 17,056 4 24 Artwork Cost $125,000 +20% – 5% 2 ($ 57,400) $480,800 $538,200 1 3
3 $192,200 $301,400 $109,200 2 41 2 3 Index 4 $276,400 $307,650 $ 31,250 3 1
Base Case Pessimistic Optimistic Used 31 Base Volume 6,500,000 6,370,000 6,630,000 32 Volume Increase 12% 8% 14% 13 Unit Trinket Cost $0.10 $0.115 $0.10 14 Artwork Cost $125,000 $150,000 $118,750 1
PositiveSet parameter # 1 Pessimistic Optimistic Neg. Part Pos. Part DifferenceTo index # 3 ($ 57,400) $480,800 ($ 57,400) — $480,800
$192,200 $301,400 — $192,200 $109,200$276,400 $307,650 — $276,400 $ 31,250$292,872 $309,928 — $292,872 $ 17,056
Base Volume 6,630,000Contribution Margin $1.48Total Contribution $ 9,812,400
Volume Increase 12%Volume 7,425,600Unit Trinket Cost $0.10Artwork Cost $ 125,000Total Contribution $10,122,328
Incremental Contribution $ 309,928
With the Trinket Promotion
Volume IncreaseUnit Trinket CostArtwork CostBase Volume
Effect of the Trinket Promotion
Without the Trinket Promotion
Pessimistic
Sensitivity Analysis Data Table for Incremental Contribution
Index #
Para
m. #
Sorted Data for Incremental Contribution
($100,000) $0 $100,000 $200,000 $300,000 $400,000 $500,000
Volume Increase
Unit Trinket Cost
Artwork Cost
Base Volume
Notice that the DataTable in Q6:S10 contains all of the combinations.
Managerial Spreadsheet Modeling -- Prof. Juran 28
Part 2c: DataTableNew template file: <trinket 2c.xlsx>
234567891011
O P Q R S T U V W
2 3 Difference Rank Sequence1 $292,872 $309,928 $ 17,056 4 22 ($ 57,400) $480,800 $538,200 1 33 $192,200 $301,400 $109,200 2 44 $276,400 $307,650 $ 31,250 3 1
3
Data Table for Incremental Contribution
Index #
Para
m. #
234567891011
O P Q R S T U V W
Difference Rank Sequence— 1 #N/A— 2 #N/A— 3 #N/A— 4 #N/A
3
Data Table for Incremental Contribution
Index #
Para
m. #
Managerial Spreadsheet Modeling -- Prof. Juran 29
Automated “plug and chug.”
More generally, a slick way to automatically check the consequences of adjusting one or two input parameters.
Data Tables: Enumerate, Don’t Optimize
key output(s)
key input parameters (1 or 2)
Managerial Spreadsheet Modeling -- Prof. Juran 30
Components of data tables– List(s) of values– Cell(s) which will assume these values– Performance measure to be tracked
Two-input data table– Two input parameters change at once– Only one performance measure can be tracked
One-input data table– Only one input parameter changes– Any number of performance measures can be tracked
Data Tables
Managerial Spreadsheet Modeling -- Prof. Juran 31
Only one parameter to enumerate, but multiple performance measure recorded for each value.
Tip: Make the performance measurement cells invisible across the top. Double secret tip: Use custom number formatting to replace these values with their labels.
One-way Data Table
Values for the Column input cell
Formulas for multiple outputsNot
used
Managerial Spreadsheet Modeling -- Prof. Juran 32
Start by building a table containing the values for the two variables you want to enumerate, across the top and down the left.
Put the equation for the (one) performance measure in the top left corner.
Two-way Data Table
Values for the Column input cell
Values for the Row input cell
Formula for one output
Managerial Spreadsheet Modeling -- Prof. Juran 33
Q6=H36
Type Scenario numbers 2 and 3 in R6:S6.
Type Parameter numbers 1, 2, 3, 4 in Q7:Q10
Now select the range Q6:S10, and select Data | What If Analysis | DataTable
Fill in the dialog box as shown:
234567891011
O P Q R S T U V W
2 3 Difference Rank Sequence1 $292,872 $309,928 $ 17,056 4 22 ($ 57,400) $480,800 $538,200 1 33 $192,200 $301,400 $109,200 2 44 $276,400 $307,650 $ 31,250 3 1
3
Data Table for Incremental Contribution
Index #
Para
m. #
Managerial Spreadsheet Modeling -- Prof. Juran 34
Two-way Data Table
3456789101112
13141516171819
B C D E F G H I J K L M N O P Q R S T U V W
1 2 3Base Case Pessimistic Optimistic 2 3 Difference Rank Sequence
1 Base Volume 6,500,000 – 2% + 2% 1 $292,872 $309,9284 Artwork Cost $125,000 +20% – 5% 2 ($ 57,400) $480,800
3 $192,200 $301,4001 2 3 Index 4 $276,400 $307,650
Base Case Pessimistic Optimistic Used 31 Base Volume 6,500,000 6,370,000 6,630,000 12 Volume Increase 12% 8% 14% 13 Unit Trinket Cost $0.10 $0.115 $0.10 14 Artwork Cost $125,000 $150,000 $118,750 1
Set parameter # 1To index # 1
Sensitivity Analysis Data Table for Incremental Contribution
Index #
Para
m. #
Sorted Data for Incremental Contribution
=TABLE(J18,J17)
=H36
= IF($J$17 = C12, $J$18, 1)
Managerial Spreadsheet Modeling -- Prof. Juran 35
Automatic SortingT7 = S7 – R7
U7 = Rank(T7, $T$7:$T$10)
U8 = Rank(T8, $T$7:$T$10) + CountIf($T$7:T7, T8 )
(Breaks ties in the rankings, otherwise use the formula for U7.)
V7 = Match(Q7, $U$7:$U$10, 0)234567891011
O P Q R S T U V W
2 3 Difference Rank Sequence1 $292,872 $309,928 $ 17,056 4 22 ($ 57,400) $480,800 $538,200 1 33 $192,200 $301,400 $109,200 2 44 $276,400 $307,650 $ 31,250 3 1
3
Data Table for Incremental Contribution
Index #
Para
m. #
The #3 ranked parameter is in the 4th row
Parameter 1 is ranked #4
Managerial Spreadsheet Modeling -- Prof. Juran 36
The DataTable lists all $ contributions that would result from each assumption taking on its optimistic and pessimistic values – holding the other assumptions at base case values, which we then use to generate the data for the tornado graph.
234567891011
O P Q R S T U V W
2 3 Difference Rank Sequence1 $292,872 $309,928 $ 17,056 4 22 ($ 57,400) $480,800 $538,200 1 33 $192,200 $301,400 $109,200 2 44 $276,400 $307,650 $ 31,250 3 1
3
Data Table for Incremental Contribution
Index #
Para
m. #
Managerial Spreadsheet Modeling -- Prof. Juran 37
Sensitivity analysis (and tornado graphs) indicate which variables generate the largest effect on the performance measure.
– Useful after prototyping, to see where to invest to get more accurate data.
– Useful before Monte Carlo simulation.
Some advanced Excel tools– The incredibly useful Index() function– Data tables– Rank() and Match() functions to automate sorting– Advanced chart settings
Take-aways
Managerial Spreadsheet Modeling -- Prof. Juran 38
Index(array, num)– Returns the num item in a one-dimensional array– The array can be either horizontal or vertical.
Index(range, row_num, col_num)– Returns the value from a two-dimension range.
Appendix: The Index Function
12345678
A B C D E F G
1 2 3 411 12 13 1421 22 23 24
Horizontal 13Vertical 22Two-dimensional 14
=INDEX(B3:E3,3)
=INDEX(C2:C4,3)
=INDEX(B2:E4,2,4)
Managerial Spreadsheet Modeling -- Prof. Juran 39
The Index Function: Example
C3 = "Scenario: " & Index(C10:C12, B3)
123456789
101112
B C D E F G
3
Return on Investment 14.0%Inflation Rate 2.5%Real ROI 11.2%
ScenarioBase Case 10.0%Double Dip Recession 3.0%Strong Recovery 14.0%
Scenario: Strong Recovery
=INDEX(D10:D12,B3)
=(1+D5)/(1+D6)-1