1 Basic Profit Models Chapter 3 Part 1 – Influence Diagram

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

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

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 model’s exogenous variables and a performance measure (e.g., profit). Exogenous Variables profit

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).

6 performance measure variable Profit Start here: Decompose this variable into the intermediate variables Revenue and Total Cost

7 Profit Revenue Total Cost Now, further decompose each of these intermediate variables into more related intermediate variables...

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

9 Step 3: Model Construction Based on the previous Influence Diagram, create the equations relating the variables to be specified in the spreadsheet.

10 Profit Revenue Total Cost Profit = Revenue – Total Cost

11 Profit Revenue Pie Price Pies Demanded Revenue = Pie Price * Pies Demanded

12 Fixed Cost Processing Cost Ingredient Cost Profit Total Cost Total Cost = Processing Cost + Ingredients Cost + Fixed Cost

13 Processing Cost = Pies Demanded * Unit Pie Processing Cost Processing Cost Total Cost Pies Demanded Unit Pie Processing Cost Profit

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

15 Simon’s 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 ($000’s per week) $ $2.05 $3.48 $0.30 $12

16 Chapter 3 Part 2 Break-Even and Cross-Over Analysis MGS 3100

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.

18 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

19 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…

20 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

21 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

22 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

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.

24 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: π planA = π planB, so (CM*Q – FC) planA = (CM*Q – FC) planB Q AtoB = (FC A - FC B )/(CM A – CM B )

25 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

26 Cross-Over Point, con’t What is the profit at each of these points? Cross-Over Points A to BB to C Q CO (150, ,000)/( )(450,000-2,850,000)/( ) = 3000 units= 48,000 units

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 π B = CM B *Q - FC B = 250(48,000) - 450,000 = $11,550,000, or π C = 300(48,000) - 2,850,000 = $11,550,000 π A = CM A *Q – FC A = 150(3000) - 150,000 = $300,000, or π B = 250(3000) - 450,000 = $300,000