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## PowerPoint Slideshow about ' Basic Profit Models' - igor-guerra

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### Chapter 3Part 2Break-Even and Cross-Over Analysis

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

Two ingredients combine to make Apple Pies:

Fruit and frozen dough

Step 1: Study the Environment and Frame the

Situation

Critical Decision: Setting the wholesale pie price

Decision Variable: Price of the apple pies (this plus cost parameters will determine profits)

Example 1: Simon Pie

The Pies are then processed and sold to local grocery stores in order to generate a profit.

Follow the three steps of model building.

Step 2: Formulation

Using “Black Box” diagram, specify cost parameters

Model

Pie Price

Exogenous Variables

Unit Cost, Filling

Unit Cost, Dough

Unit Pie Processing Cost

Fixed Cost

An Influence Diagram pictures the connections between the model’s exogenous variables and a performance measure (e.g., profit).

profit

The next step is to develop the relationships inside

the black box.A good way to approach this is to create an Influence Diagram.

start with a performance measure variable.

Decompose this variable into two or more intermediate variables that combine mathematically to define the value of the performance measure.

Further decompose each of the intermediate variables into more related intermediate variables.

Continue this process until an exogenous variable is defined (i.e., until you define an input decision variable or a parameter).

To create an Influence Diagram:

Decompose this variable into the intermediate variables Revenue and Total Cost

Profit

performance

measure

variable

Start here:

Total Cost

Revenue

Profit

Now, further decompose each of these intermediate variables into more related intermediate variables ...

Total Cost

Processing

Cost

Ingredient

Cost

Required

Ingredient

Quantities

Pies Demanded

Unit Pie

Processing Cost

Unit Cost

Filling

Unit Cost

Dough

Pie Price

Fixed Cost

Profit

Revenue

Step 3: Model Construction

Based on the previous Influence Diagram, create the equations relating the variables to be specified in the spreadsheet.

Profit

Total Cost

Processing

Cost

Ingredient

Cost

Total Cost =

Processing Cost + Ingredients Cost + Fixed Cost

Fixed Cost

Profit

Total Cost

Processing

Cost

Processing Cost =

Pies Demanded *

Unit Pie Processing Cost

Pies Demanded

Unit Pie

Processing Cost

Profit

Total Cost

Ingredients Cost =

Qty Filling * Unit Cost Filling + Qty Dough * Unit Cost Dough

Ingredient

Cost

Required

Ingredient

Quantities

Unit Cost

Filling

Unit Cost

Dough

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 ($000’s per week)

$8.00

16

$2.05

$3.48

$0.30

$12

Simon’s Initial Model Input Values

MGS 3100

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.

Basic Relationships

- Profit (π) = 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

Basic Relationships con’t

- By substitution:
- π = (SP x Q) –((VC x Q) + FC)
- π = SP*Q - VC*Q – FC
- π = (SP-VC)*Q - FC

Notice sign reversal when parentheses are removed!

Just a bit of algebraic reorganization…

Contribution Margin

- If Contribution Margin (CM) = SP-VC, then by substitution…
- π = CM*Q – FC
- In case you want to figure the quantity at break-even, you just need to rearrange

Break-Even Quantity

- π = CM*Q – FC
- π + FC = CM*Q
- (π + FC)/CM = (CM*Q)/CM
- (π + FC)/CM = Q
- Q = (π + FC)/CM
- In the case of break-even, where π =0, the formula boils down to:
- Q = FC/CM

Quantity and Profit Example

- Again, Q = (FC + π)/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

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.

Cross-Over Point, con’t

- To find the cross-over point for Plan A and B, set the profit formulas for each plan equal to each other:
- πplanA = πplanB, so
- (CM*Q – FC) planA = (CM*Q – FC)planB
- QAtoB = (FCA - FCB)/(CMA – CMB)

Cross-Over Point, con’t

- So all you need are the fixed costs and contribution margins (selling price and variable cost) to solve.
- For example, here are three plans

Cross-Over Point, con’t

What is the profit at each of these points?

Cross-Over Points

A to B B to C

QCO(150,000-450,000)/(150-250) (450,000-2,850,000)/(250-300)

= 3000 units = 48,000 units

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

πB = CMB*Q - FCB

= 250(48,000) - 450,000

= $11,550,000, or

πC = 300(48,000) - 2,850,000

= $11,550,000

πA = CMA*Q – FCA

= 150(3000) - 150,000

= $300,000, or

πB = 250(3000) - 450,000

= $300,000

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