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Cost-Volume-Profit Relationships

Cost-Volume-Profit Relationships. Cost Definitions. Fixed Costs: Costs incurred when there is no production. Marginal cost: cost of producing (and selling) one more unit = variable costs after the initial production stage Average cost: Total costs divided by number of units produced.

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Cost-Volume-Profit Relationships

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  1. Cost-Volume-Profit Relationships

  2. Cost Definitions Fixed Costs: Costs incurred when there is no production. Marginal cost: cost of producing (and selling) one more unit = variable costs after the initial production stage Average cost: Total costs divided by number of units produced Mugan 2007

  3. Cost Definitions TC = FC + (VC Q)for Q in relevant range Total costs (TC) are a linear function of quantity (Q) produced over a relevant range. Variable Cost (VC): Cost to produce one more unit. Variable cost is a linear approximation of marginal opportunity costs. Fixed Cost (FC): Predicted total costs with no production (Q=0). Relevant Range: Range of production quantity (Q) where a constant variable cost is a reasonable approximation of opportunity cost. Mugan 2007

  4. Y X Cost Curve Total Cost –Mixed Cost Variable Cost per unit or marginal cost Total Cost Average Cost Fixed Cost Mugan 2007

  5. Cost Drivers • Cost driver: units of physical activity most highly associated with total costs in an activity center Examples of cost drivers: • Quantity produced • Direct labor hours • Number of set-ups • Number of orders processed • Different activity drivers might be used for different decisions • Costs could be fixed, variable, or mixed in different situations Mugan 2007

  6. Cost Estimation Example • In each month, Exclusive Billiards produces between 4 to 10 pool tables. The plant operates on 40-hr shift to produce up to seven tables. Producing more than seven tables requires the craftsmen to work overtime. Overtime work is paid at a higher hourly wage. The plant can add overtime hours and produce up to 10 tables per month. The following table contains the total cost of producing between 4 and 10 pool tables. • Required: a. compute average cost per pool table for 4 to 10 tables • Estimate fixed costs per month. Mugan 2007

  7. Format of Income Statement Financial Accounting (traditional – required for financial statements and tax ) Sales Revenue - Cost of goods sold (product costs) = Gross profit - General, selling, administrative, and taxes (period costs) = Net income Decision Making( useful for managers – internal oriented) Revenue - Variable costs (product and selling and administration) = Contribution margin - Fixed costs and taxes( product and selling and administration) = Net income Mugan 2007

  8. Income Statement Example Mugan 2007

  9. Income Statement Example Mugan 2007

  10. CVP definitions Cost-Volume-Profit (C-V-P) analysis is very useful for production and marketing decisions. Contribution margin equals price per unit minus variable cost per unit: CM = (P – VC). Total contribution margin equals total revenue minus total variable costs: (CM Q) = (P - VC) Q. Mugan 2007

  11. COST VOLUME PROFIT ANALYSIS • HELPFUL TO UNDERSTAND THE RELATIONSHIP AMONG VARIABLE COSTS, FIXED COSTS AND PROFIT • BASIC ASSUMPTIONS: • SELLING PRICE IS CONSTANT • COSTS ARE LINEAR AND CAN BE DIVIDED INTO FIXED AND VARIABLE • FIXED ELEMENT CONSTANT OVER THE RELEVANT RANGE • UNIT VARIABLE COST CONSTANT OVER THE RELEVANT RANGE • SALES MIX IS CONSTANT • INVENTORIES STAY AT THE SAME LEVEL Mugan 2007

  12. Basics of Cost-Volume-Profit Analysis CM is used first to cover fixed expenses. Any remaining CM contributes to net operating income. Mugan 2007

  13. The Contribution Approach Sales, variable expenses, and contribution margin can also be expressed on a per unit basis. If FM sells an additional gadget, TL 175 additional CM will be generated to cover fixed expenses and profit. Mugan 2007

  14. The Contribution Approach Each month FM must generate at least TL 665.000 in total CM to break even. Mugan 2007

  15. The Contribution Approach If F sells 3800 unitsin a quarter, it will be operating at the break-even point. Mugan 2007

  16. The Contribution Approach If Racing sells one more bike (3801 gadgets), net operating income will increase by TL 175. Mugan 2007

  17. The Contribution Approach We do not need to prepare an income statement to estimate profits at a particular sales volume. Simply multiply the number of units sold above break-even by the contribution margin per unit. If Racing sells 4000 gadgets, its net income will be 35.000 TL. Mugan 2007

  18. Development of CVP graph Mugan 2007

  19. The Contribution Approach If Racing sells 400 unitsin a month, it will be operating at the break-even point. Mugan 2007

  20. CVP Relationships in Graphic Form The relationship among revenue, cost, profit and volume can be expressed graphically by preparing a CVP graph. Racing developed contribution margin income statements at 300, 400, and 500 units sold. We will use this information to prepare the CVP graph. Mugan 2007

  21. CVP Graph Dollars In a CVP graph, unit volume is usually represented on the horizontal (X) axis and dollars on the vertical (Y) axis. Units Mugan 2007

  22. Fixed Expenses CVP Graph Dollars Units Mugan 2007

  23. Total Expenses Fixed Expenses CVP Graph Dollars Units Mugan 2007

  24. Total Sales Total Expenses Fixed Expenses CVP Graph Dollars Units Mugan 2007

  25. Break-even point(400 units or $200,000 in sales) CVP Graph Profit Area Dollars Loss Area Units Mugan 2007

  26. Total CM Total sales CM Ratio = $80,000 $200,000 = 40% Contribution Margin Ratio The contribution margin ratio is:For Racing Bicycle Company the ratio is: Each $1.00 increase in sales results in a total contribution margin increase of 40¢. Mugan 2007

  27. Unit CM Unit selling price CM Ratio = $200 $500 = 40% Contribution Margin Ratio Or, in terms of units, the contribution margin ratiois:For Racing Bicycle Company the ratio is: Mugan 2007

  28. A $50,000 increase in sales revenue results in a $20,000 increase in CM. ($50,000 × 40% = $20,000) Contribution Margin Ratio Mugan 2007

  29. CONTRIBUTION MARGIN RATIO CMR= CONTRIBUTION MARGIN RATIO = CM / SALES OR cmu/p VCR = VARIABLE COST RATIO = VC/SALES OR vcu/p CMR +VCR= 1 EFFECT OF CHANGE IN FIXED COSTS? EFFECT OF CHANGE IN VARIABLE COSTS? EFFECT OF CHANGE IN SELLING PRICE? Mugan 2007

  30. Quick Check  Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. 2,100 cups are sold each month on average. What is the CM Ratio for Coffee Klatch? a. 1.319 b. 0.758 c. 0.242 d. 4.139 Mugan 2007

  31. Unit contribution margin Unit selling price CM Ratio = ($1.49-$0.36) $1.49 = $1.13 $1.49 = = 0.758 Quick Check  Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. 2,100 cups are sold each month on average. What is the CM Ratio for Coffee Klatch? a. 1.319 b. 0.758 c. 0.242 d. 4.139 Mugan 2007

  32. Changes in Fixed Costs and Sales Volume What is the profit impact if Racing can increase unit sales from 500 to 540 by increasing the monthly advertising budget by $10,000? Mugan 2007

  33. $80,000 + $10,000 advertising = $90,000 Changes in Fixed Costs and Sales Volume Sales increased by $20,000, but net operating income decreased by $2,000. Mugan 2007

  34. Changes in Fixed Costs and Sales Volume The Shortcut Solution Mugan 2007

  35. Change in Variable Costs and Sales Volume What is the profit impact if Racing can use higher quality raw materials, thus increasing variable costs per unit by $10, to generate an increase in unit sales from 500 to 580? Mugan 2007

  36. 580 units × $310 variable cost/unit = $179,800 Change in Variable Costs and Sales Volume Sales increase by $40,000, and net operating income increases by $10,200. Mugan 2007

  37. Change in Fixed Cost, Sales Price and Volume What is the profit impact if Racing (1) cuts its selling price $20 per unit, (2) increases its advertising budget by $15,000 per month, and (3) increases unit sales from 500 to 650 units per month? Mugan 2007

  38. Change in Fixed Cost, Sales Price and Volume Sales increase by $62,000, fixed costs increase by $15,000, and net operating income increases by $2,000. Mugan 2007

  39. Change in Variable Cost, Fixed Cost and Sales Volume What is the profit impact if Racing (1) pays a $15 sales commission per bike sold instead of paying salespersons flat salaries that currently total $6,000 per month, and (2) increases unit sales from 500 to 575 bikes? Mugan 2007

  40. Change in Variable Cost, Fixed Cost and Sales Volume Sales increase by $37,500, variable costs increase by $31,125, but fixed expenses decrease by $6,000. Mugan 2007

  41. Change in Regular Sales Price If Racing has an opportunity to sell 150 bikes to a wholesaler without disturbing sales to other customers or fixed expenses, what price would it quote to the wholesaler if it wants to increase monthly profits by $3,000? Mugan 2007

  42. Change in Regular Sales Price Mugan 2007

  43. Break-Even Analysis Break-even analysis can be approached in two ways: • Equation method • Contribution margin method Mugan 2007

  44. At the break-even point profits equal zero Equation Method Profits = (Sales – Variable expenses) – Fixed expenses OR Sales = Variable expenses + Fixed expenses + Profits Mugan 2007

  45. Break-Even Analysis Here is the information from Racing Bicycle Company: Mugan 2007

  46. Equation Method • We calculate the break-even point as follows: Sales = Variable expenses + Fixed expenses + Profits $500Q = $300Q + $80,000 +$0 Where: Q = Number of bikes sold $500 = Unit selling price $300 = Unit variable expense $80,000 = Total fixed expense Mugan 2007

  47. Equation Method • We calculate the break-even point as follows: Sales = Variable expenses + Fixed expenses + Profits $500Q = $300Q + $80,000 + $0 $200Q = $80,000 Q = $80,000 ÷ $200 per bike Q = 400 bikes Mugan 2007

  48. Equation Method • The equation can be modified to calculate the break-even point in sales dollars. Sales = Variable expenses + Fixed expenses + Profits X = 0.60X + $80,000 +$0 Where: X = Total sales dollars 0.60 = Variable expenses as a % of sales $80,000 = Total fixed expenses Mugan 2007

  49. Equation Method • The equation can be modified to calculate the break-even point in sales dollars. Sales = Variable expenses + Fixed expenses + Profits X = 0.60X + $80,000 + $0 0.40X = $80,000 X = $80,000 ÷ 0.40 X = $200,000 Mugan 2007

  50. Break-even point in units sold Fixed expenses Unit contribution margin = Break-even point in total sales dollars Fixed expenses CM ratio = Contribution Margin Method The contribution margin method has two key equations. Mugan 2007

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