Break even point(BEP)
Download as PPTX, PDF3 likes2,663 views
Okay, let's solve this step-by-step: 1) Capacity = Total Sales / % operated = $375,000 / 75% = $375,000 / 0.75 = $500,000 2) Contribution Margin (CM) = Sales - Variable Costs = $375,000 - $150,000 = $225,000 3) Break Even Point (BEP) in dollars = Fixed Costs / CM = $180,000 / $225,000 = $240,000 So the BEP expressed in dollars of sales for Marconi is $240,000.
Break even point(BEP)
- 1. Linear 5-1 Equations Apps. Applications of Linear Equations ©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved
- 2. 5-2 Linear Equations Apps. Learning Objectives After completing this chapter, you will be able to: LO 1 Graph a linear equation in two variables LO 2 Express a linear equation in the slope-intercept form LO 3 Solve two equations in two unknowns by the graphical method Also ©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved
- 3. 5-3 Linear Learning Objectives Equations Apps. Distinguish between fixed costs and variable costs Perform linear Cost-Volume-Profit and LO 4 LO 5 B break-even analysis employing: - The algebraic approach of solving the cost and revenue functions - A breakeven chart C - The contribution margin approach A ©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved
- 4. 5-4 Linear Equations Apps. LO 1 Step 1 Step 2 Step 3 Graphing a Linear Equation Graph the equation 3x – 2y = 8 over the range x=0 to x=8 Rearrange the equation to solve for y Substitute a few values for x, and calculate the corresponding values for y Plot and connect the points on the xy graph ©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved 3x – 2y =8 – 2y = 8 - 3x y = 8 - 3x -2 y = 1.5x - 4 x y 0 -4 3 0.5 6 5 …continue
- 5. Linear 5-5 Graphing a Linear Equation y = 1.5x - 4 x y 0 -4 3 0.5 6 5 Equations Apps. Step 3 7 6 5 4 3 Y 2 1 0 -1 0 -2 -3 -4 Plot and connect the points on the xy graph y = 1.5x - 4 1 ©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved 2 3 4 5 X 6 7 8 9 10
- 6. 5-6 Linear Graphing a Linear Equation Equations Apps. y = 1.5x - 4 LO 2 This is called the slope–intercept form of this linear equation Where 1.5 is the slope, and -4 is the y-intercept 1 0 -1 Y -2 -3 -4 0 1 ©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved 2 3 4 5 6 7 8 y = 1.5x - 4 X 9 10
- 7. Linear Equations Apps. LO 3 Step 1 5-7 Solving 2 equations in 2 unknowns graphically Find the point of intersection for the equations 3x – 2y = 8 and 4x+2y = 6 Rearrange each equation to solve for y y = 1.5x - 4 y = -2x + 3 Step 2 Step 3 4x+2y = 6 2y = 6- 4x y = 6 – 4x 2 Substitute a few values for x, and calculate the corresponding values for y in each equation Plot and connect the points on the xy graph – the point where the lines cross in the point of intersection, your solution ©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved y = -2x + 3 x y 0 3 3 -3 2 -1
- 8. Linear Equations Apps. 5-8 Solving 2 equations in 2 unknowns graphically Find the point of intersection for the equations 3x – 2y = 8 and 4x+2y = 6 Y 7 6 5 4 3 2 1 0 -1 -2 -3 -4 (2, -1) 0 1 ©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved 2 3x-2y=8 or y= 1.5x - 4 y = -2x + 3 x y 0 3 3 4 5 6 7 8 9 10 3 -3 4x+2y=6 or y = -2x + 3 2 -1
- 9. 5-9 Linear Equations Apps. Cost Analysis ©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved
- 10. 5 - 10 Linear Equations Apps. Terminology LO 4 Fixed Costs Business Costs Business Expenses …do NOT change if sales increase or decrease e.g. rent, property taxes, some forms of depreciation Variable Costs …do change in direct proportion to sales volume e.g. material costs, direct labour costs ©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved
- 11. 5 - 11 Linear Equations Apps. Terminology Break Even Point … is the point at which neither a Profit or Loss is made ©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved
- 12. 5 - 12 Linear Equations Apps. LO 5C Terminology Contribution Margin …is the dollar amount that is found by deducting ALL Variable Costs from Net Sales and ‘contributes’ to meeting Fixed Costs and making a ‘Net Profit’. Contribution Rate …is the dollar amount expressed as a percent (%) of Net Sales A Contribution Margin statement ©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved
- 13. 5 - 13 Linear Equations Apps. Terminology A Contribution Margin Statement Net Sales(Price * # Units Sold) Less: Variable Costs Contribution Margin Less: Fixed Costs Net Income ©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved $ x x x x x % 100 x x x x
- 14. 5 - 14 Linear Scenario 1 Equations Apps. Market research for a new product indicates that the product can be sold at $50 per unit. Cost analysis provides the following information: Fixed Costs per period = $8640 Variable Costs = $30 per unit. Production Capacity per period = 900 units uestion: How much does the sale of an additional unit of a firm’s product contribute towards increasing its net income? ©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved
- 15. 5 - 15 Linear Equations Apps. Formulae - To Find - Contribution Margin Contribution Rate *Break Even Point: ...in Units (x) ...in Sales $ ...in % of Capacity CM = SP - VC CR = CM/SP * 100% x = FC / CM $x = (FC / CM)* SP BEPin Units/PC*100 * At Break Even, Net Profit or Loss = 0 Applying ©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved Formulae
- 16. Linear Equations Apps. 5 - 16 Applying the Formulae As in the previous scenario, the new product can be sold at $50 per unit. Costs are as follows: Fixed Costs are $8640 for the period , Variable Costs are $30 per unit, and the Production Capacity is 900 units per period. CM = SP - VC CR = CM/SP * 100% Break Even Point: Units x = FC / CM In $ x = (FC / CM)* SP BEPin units / PC*100 ©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved = $50 - $30 = $20 = $20/$50 * 100 = 40% = $8640/$20 = 432 Units = ($8640/$20)* $50 = $21,600 = 432/ 900*100 = 48% of Capacity
- 17. 5 - 17 Linear Equations Apps. Scenario 2 The Lighting Division of Seneca Electric Co. plans to introduce a new street light based on the following accounting information: FC = $3136 VC = $157 SP= $185 Capacity = 320 units uestion: Calculate the breakeven point (BEP) …in units …in dollars …as a percent of capacity ©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved
- 18. 5 - 18 Linear Equations Apps. Scenario 2 FC = $3136 VC = $157 SP= $185 Capacity = 320 units …in units Break Even Point = FC / CM = $3136/ 28 = 112 Units SP – VC = CM $185 – 157 = $28 …in dollars = (FC / CM)* SP = ($3136/ 28) * $185 = $20720 …as a percent of capacity = BEPin units/PC*100 = 112/320 * 100 = 35% of Capacity ©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved
- 19. 5 - 19 Linear Scenario 2 -1 Equations Apps. FC = $3136 VC = $157 SP= $185 Capacity = 320 units $2688 Determine the BEP as a % of capacity if FC are reduced to $2688. Formula Step 1… Find CM SP = $185 VC = - 157 CM $ 28 ©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved =BEPin units/PC*100 Step 2… Find Step 3… Find BEP in units = FC/CM = $2688/ $28 = 96 Units % of Capacity =BEPin units /PC*100 = 96/320*100 = 30% of Capacity
- 20. 5 - 20 Linear Scenario 2 -2 Equations Apps. FC = $4588 VC = $157 SP= $185 Capacity = 320 units $3136 $148 VC =SP*80% = $148 Determine the BEP as a % of capacity if FC are increased to $4588, and VC reduced to 80% of SP. Formula Step 1… Find CM SP = $185 VC = - 148 CM $ 37 ©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved = BEPin units /PC*100 Step 2… Find Step 3… Find BEP in units = FC/CM = $4588/ $37 = 124 Units % of Capacity =BEPin units /PC*100 = 124/320*100 = 39% of Capacity
- 21. 5 - 21 Linear Scenario 2 -3 Equations Apps. FC = $3136 VC = $157 SP= $185 Capacity = 320 units $171 Determine the BEP as a % of capacity if SP is reduced to $171. Formula Step 1… Find CM SP = $ 171 VC = -157 CM $ 14 ©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved = BEPin units /PC*100 Step 2… Find BEP in units = FC/CM = $3136/ $14 = 224 Units Step 3… Find % of Capacity =BEPin units /PC*100 = 224/320*100 = 70% of Capacity
- 22. 5 - 22 Linear Scenario 2 -4 Equations Apps. FC = $3136 VC = $157 SP= $185 Capacity = 320 units Determine the NI if 134 units are sold! Formula Step 1… Find CM SP = $185 VC = - 157 CM $ 28 CM of $28 per unit ©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved NI = #Units above BEP*CM Step 2… Find BEP in units = FC/CM = $3136/$28 = 112 Units Units Sold 134 BEP 112 Over BEP 22 Company had a NI of 22* $28 = $616.
- 23. 5 - 23 Linear Scenario 2 -5 Equations Apps. FC = $3136 VC = $157 SP= $185 Capacity = 320 units What unit sales will generate NI of $2000? Formula Step 1… Find CM SP = $185 VC = - 157 CM $ 28 CM of $28 per unit ©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved #Units above BEP = NI/CM Step 2… Find BEP in units = FC/CM = $3136/$28 = 112 Units NI/CM = $2000/$28 per Unit = 72 Units above Break Even 72 Units + 112 BEP Units = Total Sales Units = 184
- 24. 5 - 24 Linear Scenario 2 -6 Equations Apps. FC = $3136 VC = $157 SP= $185 Capacity = 320 units What are the unit sales if there is a Net Loss of $336? Formula Step 1… Find CM SP = $185 VC = - 157 CM $ 28 CM of $28 per unit ©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved # Units below BEP = (NI)/CM Step 2… Find BEP in units = FC/CM = $3136/$28 = 112 Units (NI)/CM = ($336)/$28 per Unit = 12 Units below Break Even 112 BEP - 12 Units Below = Total Sales Units = 100
- 25. 5 - 25 Linear Scenario 2 -7 Equations Apps. FC = $3136 VC = $157 SP= $185 Capacity = 320 units The company operates at 85% capacity. Find the Profit or Loss. Step 1… Find CM SP = $185 VC = - 157 CM $ 28 Step 2… Find BEP in units = FC/CM = $3136/$28 = 112 Units CM of $28 per unit Formula 320*.85 = 272 Units Production 272 BEP 112 Over BEP 160 # units above BEP *CM = NI 160 Units * $28 = Profit $4480 ©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved
- 26. 5 - 26 Linear Case Equations Apps. The Marconi Co. year end operating results were as follows: Total Sales of $375000 Operated at 75% of capacity Total Variable Costs were $150000 Total Fixed Costs were $180000 What was Marconi’s BEP expressed in dollars of sales? ©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved
- 27. 5 - 27 Linear Equations Apps. Case The Marconi Co. year end operating results were as follows: Total Sales of $375000 Operated at 75% of capacity Total Variable Costs were $150000 Total Fixed Costs were $180000 What was Marconi’s BEP expressed in dollars of sales? What information is needed to calculate the $BEP? 1. Number of Units sold ©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved 2. VC per Unit 3. CM 4. BEP in $
- 28. 5 - 28 Linear Case Equations Apps. The Marconi Co. year end operating results were as follows: Total Sales of $375000 Operated at 75% of capacity Total Variable Costs were $150000 Total Fixed Costs were $180000 What was Marchoni’s BEP expressed in dollars of sales? 1. Number of Units sold Let SP = $1 and X be the Number of $1 Units sold Sales of $375 000 = 375000 Total Units sold 2. VC per Unit Total VC = Total Unit Sales 3. CM ©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved SP $1.00 VC .40 CM $ .60 $150000 375000 = $0.40perunit
- 29. 5 - 29 Linear Case Equations Apps. The Marconi Co. year end operating results were as follows: Total Sales of $375000 Operated at 75% of capacity Total Variable Costs were $150000 Total Fixed Costs were $180000 What was Marchoni’s BEP expressed in dollars of sales? 4. BEP in $ $BEP = (FC/CM)*SP = ($180000/0.60)*$1.00 # Of Units = (300000)*1.00 = $300 000 $BEP ©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved
- 30. 5 - 30 Linear Equations Apps. This completes Chapter 5 ©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved