Session 7 Managerial Spreadsheet Modeling -- Prof. Juran1

Session 7

Managerial Spreadsheet Modeling -- Prof. Juran 1


Outline

• Sensitivity Analysis• Some fancy Excel functions and graphs


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


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


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


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


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


Initial Calculations

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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


• 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?


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.



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


($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


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


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


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


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


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)


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


($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


Part 2a: INDEX and OFFSET23456789101112

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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


For the labels, use OFFSET:

N18=OFFSET($D$11,V7,0)

And copy down to rows 19:21.

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3


Pessimistic


Index #

Para

m. #



=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


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



3


Pessimistic


Index #Pa

ram

. #



= INDEX(R$7:R$10, $V7)


Now use these formulas to create the three series.

T18= MIN(R18, 0)

U18= MAX(R18, 0)

V18= S18 - U18

And copy down

13141516171819202122



Pessimistic



= MIN(R18, 0)

= MAX(R18, 0)

= S18 - U18


Part 2b: IFNew template file: <trinket 2b.xlsx>

Built-in DataTable in Q6:S10 -- leave that range alone

2345678910111213141516171819202122


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


Index #Pa

ram

. #


Base VolumeVolume IncreaseUnit Trinket CostArtwork Cost


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



Pessimistic

Sensitivity Analysis Data Table for Incremental Contribution

Index #

Para

m. #


Keeps all assumptions at their “base case” value by default

Allows one assumption to be optimistic or pessimistic


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


Volume Increase 12%Volume 7,425,600Unit Trinket Cost $0.10Artwork Cost $ 125,000Total Contribution $10,122,328






($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.


2345678910111213141516171819202122232425262728293031323334353637



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


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 Increase 12%Volume 7,425,600Unit Trinket Cost $0.10Artwork Cost $ 125,000Total Contribution $10,122,328






Pessimistic


Index #

Para

m. #


($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.


Part 2c: DataTableNew template file: <trinket 2c.xlsx>

234567891011

O P Q R S T U V W


3


Index #

Para

m. #

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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


Index #

Para

m. #


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)


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


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


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


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:

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3


Index #

Para

m. #


Two-way Data Table

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13141516171819



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


Set parameter # 1To index # 1


Index #

Para

m. #


=TABLE(J18,J17)

=H36

= IF($J$17 = C12, $J$18, 1)


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


3


Index #

Para

m. #

The #3 ranked parameter is in the 4th row

Parameter 1 is ranked #4


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.

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O P Q R S T U V W


3


Index #

Para

m. #


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


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)


The Index Function: Example

C3 = "Scenario: " & Index(C10:C12, B3)

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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

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Session 7 Managerial Spreadsheet Modeling -- Prof. Juran1