1 Basic Profit Models Chapter 3 Part 1 Influence Diagram
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2 In building spreadsheets for deterministic models, we will
look at: ways to translate the black box representation into a
spreadsheet model. recommendations for good spreadsheet model
design and layout suggestions for documenting your models useful
features of Excel for modeling and analysis
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3 Step 1: Study the Environment and Frame the Situation The
Pies are then processed and sold to local grocery stores in order
to generate a profit. Follow the three steps of model building.
Example 1: Simon Pie Critical Decision: Setting the wholesale pie
price Decision Variable: Price of the apple pies (this plus cost
parameters will determine profits) Two ingredients combine to make
Apple Pies: Fruit and frozen dough
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4 Step 2: Formulation Model Using Black Box diagram, specify
cost parameters The next step is to develop the relationships
inside the black box. A good way to approach this is to create an
Influence Diagram. Pie Price Unit Cost, Filling Unit Cost, Dough
Unit Pie Processing Cost Fixed Cost An Influence Diagram pictures
the connections between the models exogenous variables and a
performance measure (e.g., profit). Exogenous Variables profit
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5 To create an Influence Diagram: start with a performance
measure variable. Further decompose each of the intermediate
variables into more related intermediate variables. Decompose this
variable into two or more intermediate variables that combine
mathematically to define the value of the performance measure.
Continue this process until an exogenous variable is defined (i.e.,
until you define an input decision variable or a parameter).
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6 performance measure variable Profit Start here: Decompose
this variable into the intermediate variables Revenue and Total
Cost
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7 Profit Revenue Total Cost Now, further decompose each of
these intermediate variables into more related intermediate
variables...
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8 Profit Revenue Total Cost Pies Demanded Pie Price Unit Pie
Processing Cost Fixed Cost Processing Cost Ingredient Cost Unit
Cost Filling Unit Cost Dough Required Ingredient Quantities
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9 Step 3: Model Construction Based on the previous Influence
Diagram, create the equations relating the variables to be
specified in the spreadsheet.
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10 Profit Revenue Total Cost Profit = Revenue Total Cost
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11 Profit Revenue Pie Price Pies Demanded Revenue = Pie Price *
Pies Demanded
13 Processing Cost = Pies Demanded * Unit Pie Processing Cost
Processing Cost Total Cost Pies Demanded Unit Pie Processing Cost
Profit
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14 Ingredients Cost = Qty Filling * Unit Cost Filling + Qty
Dough * Unit Cost Dough Ingredient Cost Profit Total Cost Unit Cost
Filling Unit Cost Dough Required Ingredient Quantities
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15 Simons Initial Model Input Values Pie Price Pies Demanded
and sold Unit Pie Processing Cost ($ per pie) Unit Cost, Fruit
Filling ($ per pie) Unit Cost, Dough ($ per pie) Fixed Cost ($000s
per week) $8.00 16 $2.05 $3.48 $0.30 $12
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16 Chapter 3 Part 2 Break-Even and Cross-Over Analysis MGS
3100
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17 Background The Generalized Profit Model: A decision-maker
will break-even when profit is zero. Set the generalized profit
model equal to zero, and then solve for the quantity (Q). For
simplicity, assume that the quantity produced is equal to the
quantity sold. This assumption will be relaxed in the module on
decision analysis.
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18 Basic Relationships Profit () = Revenue (R) - Cost (C)
Revenue (R) = Selling price (SP) x Quantity (Q) Cost (C) =
[Variable cost (VC) x Quantity (Q)] + Fixed Cost (FC) Remember
quantity produced = quantity sold
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19 Basic Relationships cont By substitution: = (SP x Q) ((VC x
Q) + FC) = SP*Q - VC*Q FC = (SP-VC)*Q - FC Notice sign reversal
when parentheses are removed! Just a bit of algebraic
reorganization
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20 Contribution Margin If Contribution Margin (CM) = SP-VC,
then by substitution = CM*Q FC In case you want to figure the
quantity at break-even, you just need to rearrange
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21 Break-Even Quantity = CM*Q FC + FC = CM*Q ( + FC)/CM =
(CM*Q)/CM ( + FC)/CM = Q Q = ( + FC)/CM In the case of break-even,
where =0, the formula boils down to: Q = FC/CM
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22 Quantity and Profit Example Again, Q = (FC + )/CM If fixed
cost is $150,000 per year, selling price per unit (SP) is $400, and
variable cost per unit (VC) is $250, what quantity (Q) will produce
a profit of $300,000? Q = ($150,000+$300,000)/($400-$250) Q =
$450,000/$150 Q = 3000
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23 Cross-Over Point The cross-over point (or indifference
point) is found when we are indifferent between two plans. In other
words, the quantity when profit is the same for each of two
plans.
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24 Cross-Over Point, cont To find the cross-over point for Plan
A and B, set the profit formulas for each plan equal to each other:
planA = planB, so (CM*Q FC) planA = (CM*Q FC) planB Q AtoB = (FC A
- FC B )/(CM A CM B )
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25 Cross-Over Point, cont So all you need are the fixed costs
and contribution margins (selling price and variable cost) to
solve. For example, here are three plans
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26 Cross-Over Point, cont What is the profit at each of these
points? Cross-Over Points A to BB to C Q CO
(150,000-450,000)/(150-250)(450,000-2,850,000)/(250-300) = 3000
units= 48,000 units
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27 Calculating Profit at the Cross-Over After calculating
cross-over, we have a quantity that can be plugged back into the
formula to find profit at the cross-over point B = CM B *Q - FC B =
250(48,000) - 450,000 = $11,550,000, or C = 300(48,000) - 2,850,000
= $11,550,000 A = CM A *Q FC A = 150(3000) - 150,000 = $300,000, or
B = 250(3000) - 450,000 = $300,000