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Cost Behavior and Cost-Volume-Profit Analysis

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## Cost Behavior and Cost-Volume-Profit Analysis

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**19**Cost Behavior and Cost-Volume-Profit Analysis Student Version**1**Classify costs as variable costs, fixed costs, or mixed costs. 19-2**1**Variable Costs Variable costs are costs that vary in proportion to changes in the level of activity.**1**Jason Sound Inc. Jason Sound Inc. produces stereo systems. The parts for the stereo system are purchased from suppliers for $10 per unit (a variable cost) and assembled by Jason Sound Inc.**1**For Model JS-12, the direct materials for the relevant range of 5,000 to 30,000 units of production are shown below.**1**Fixed Costs Fixed costs are costs that remain the same in total dollar amount as the activity base changes.**1**Minton Inc. Minton Inc. manufactures, bottles, and distributes perfume. The production supervisor is Jane Sovissi. She is paid $75,000 per year. The plant produces from 50,000 to 300,000 bottles of La Fleur Perfume.**1**Fixed Versus Variable Cost of Jane Sovissi’s Salary per Bottle of Perfume Salary per Bottle of Perfume Produced Number of Bottles of Perfume Produced Total Salary for Jane Sovissi 50,000 bottles $75,000 $1.500 100,000 75,000 0.750 150,000 75,000 0.500 200,000 75,000 0.375 250,000 75,000 0.300 300,000 75,000 0.250**1**Mixed Costs Mixed costs (sometimes called semivariable or semifixed costs) have characteristics of both a variable and a fixed cost. Over one range of activity, the total mixed cost may remain the same. Over another range of activity, the mixed cost may change in proportion to changes in level of activity.**1**Simpson Inc. Simpson Inc. manufactures sails, using rented equipment. The rental charges are $15,000 per year, plus $1 for each machine hour used over 10,000 hours.**1**High-Low Method The high-low method is a cost estimation method that may be used for separating mixed costs into their fixed and variable components.**$20,250**1 Estimating Variable Cost Using High-Low Production Total (Units) Cost Fill in the formula for difference in cost. June 1,000 $45,550 July 1,500 52,000 August 2,100 61,500 September 1,800 57,500 October 750 41,250 $61,500 41,250 Difference in Total cost $20,250 Variable Cost per Unit = Difference in Production**1**Estimating Variable Cost Using High-Low Production Total (Units) Cost Then, fill in the formula for difference in production. June 1,000 $45,550 July 1,500 52,000 August 2,100 61,500 September 1,800 57,500 October 750 41,250 2,100 750 1,350 Difference in total cost $20,250 Variable Cost per Unit = Difference in Production 1,350**1**Estimating Variable Cost Using High-Low Production Total (Units) Cost June 1,000 $45,550 July 1,500 52,000 August 2,100 61,500 September 1,800 57,500 October 750 41,250 Variable cost per unit is $15 $20,250 = $15 Variable Cost per Unit = 1,350**1**Estimating Fixed Cost Using High-Low The first step in determining fixed cost is to insert the variable cost of $15 into the following formula: Total Cost = (Variable Cost per Unit × Units of Production) + Fixed Cost Total Cost = ($15 × Units of Production) + Fixed Cost**1**Production Total (Units) Cost Using the highest level of production, we insert the total cost and units produced in the formula. June 1,000 $45,550 July 1,500 52,000 August 2,100 61,500 September 1,800 57,500 October 750 41,250 Total Cost = (Variable Cost per Unit × Units of Production) + Fixed Cost $61,500 Total cost = ($15 × Units of Production) + Fixed Cost 2,100 units)**1**$61,500 = ($15 × 2,100 units) + Fixed cost $61,500 = $31,500 + Fixed cost $61,500 – $31,500 = Fixed cost $30,000 = Fixed cost If the lowest level had been chosen, the results of the formula would provide the same fixed cost of $30,000.**1**With fixed costs and variable costs estimated at $30,000 and $15 per unit, a formula is in place to estimate production at any level. If the company is expected to produce 950 units in November, the estimated total overhead would be calculated as follows: Total Cost = (Variable Cost per Unit × Units of Production) + Fixed cost Total Cost = $15 (950) + $30,000 Total Cost = $44,250**2**Compute the contribution margin, the contribution margin ratio, and the unit contribution margin. 19-19**2**Cost-Volume-Profit Relationships Cost-volume-profit analysis is the examination of the relationships among selling prices, sales and production volume, costs, expenses, and profits.**2**Contribution Margin Thecontribution margin is the excess of sales revenues over variable costs. It is especially useful because it provides insight into the profit potential of a company.**2**Contribution Margin Ratio (in dollars) The contribution margin ratio is most useful when the increase or decrease in sales volume is measured in sales dollars. In this case, the following formula is used to determine change in income from operations. Change in Sales Dollars × Contribution Margin Ratio Change in Income from Operations =**30%**10% Contribution Margin Ratio = Sales – Variable Costs Sales $1,000,000 – $600,000 $1,000,000 Contribution Margin Ratio = 40% Contribution Margin Ratio = 2 Contribution Margin Ratio 100% 60% 40%**Change in Income from Operations**Changes in Sales Units × Unit Contribution Margin = Change in Income from Operations 15,000 × $8 = Change in Income from Operations $120,000 = 2 Using Contribution Margin per Unit as a Shortcut Lambert Inc.’s sales could be increased by 15,000 units from 50,000 to 65,000 units. Lambert’s income from operations would increase by $120,000 (15,000 × $8) as shown below.**3**Determine the break-even point and sales necessary to achieve a target profit. 19-25**Unit selling price $25**Unit variable cost 15 Unit contribution margin $10 3 Baker Corporation’s fixed costs are estimated to be $90,000. The unit contribution margin is calculated as follows:**Fixed Costs**Unit Contribution Margin Break-Even Sales (units) = $90,000 $10 Break-Even Sales (units) = 3 The break-even point (in units) is calculated using the following equation: Break-Even Sales (units) = 9,000 units**Fixed Costs**Contribution Margin Ratio Break-Even Sales (dollars) = $90,000 .40 Break-Even Sales (dollars) = Unit Contribution Margin Unit Selling Price $10 $25 3 The break-even point (in dollars) is calculated using the following equation: Break-Even Sales (dollars) = $225,000**Unit selling price $250**Unit variable cost 145 Unit contribution margin $105 3 Park Co. is evaluating a proposal to pay an additional 2% commission on sales to its salespeople (a variable cost) as an incentive to increase sales. Fixed costs are estimated at $840,000. The unit contribution margin before the additional 2% commission is determined below.**Fixed Costs**Unit Contribution Margin Break-Even in Sales (units) = 8,000 units 8,400 units = = $840,000 $105 Break-Even in Sales (units) = $840,000 $100 Break-Even in Sales (units) = $250 – [$145 + ($250 × 2%)] = $100 3 Without additional 2% commission: With additional 2% commission:**Fixed Costs + Target Profit**Unit Contribution Margin Sales (units) = 3 Target Profit The sales volume required to earn a target profit is determined by modifying the break-even equation.**Fixed Costs + Target Profit**Unit Contribution Margin Sales (units) = 3 Units Required for Target Profit Fixed costs are estimated at $200,000, and the desired profit is $100,000. Unit contribution margin is $30. Unit selling price $75 Unit variable cost 45 Unit contribution margin $30 $200,000 $100,000 $30 Sales (units) =10,000 units**$30**$75 from Slide 32 Contribution Margin Ratio = 40% Contribution Margin Ratio = Fixed Costs + Target Profit Contribution Margin Ratio $200,000 + $100,000 40% Sales (dollars) = Sales (dollars) = Necessary sales to have a $100,000 target profit 3 Target Profit Unit Contribution Margin Unit Selling Price Contribution Margin Ratio = = $750,000**4**Using a cost-volume-profit chart and a profit-volume chart, determine the break-even point and sales necessary to achieve a target profit. 19-34**4**The cost-volume-profit chart inSlides 36to 48is based on Exhibit 5. Exhibit 5 was constructed using the following data: Unit selling price $ 50 Unit variable cost 30 Unit contribution margin $ 20 Total fixed costs $100,000**Exhibit 5**Dollar amounts are indicated along the vertical axis. 4 Cost-Volume-Profit Chart $500 $450 $400 $350 $300 $250 $200 $150 $100 $ 50 Sales and Costs (in thousands) 0 1 2 3 4 5 6 7 8 9 10 Units of Sales (in thousands) Volume is shown on the horizontal axis. (continued)**4**Using maximum sales of $500,000 and knowing that each unit sells for $50, we can find the values of the two axis. Where the horizontal sales and costs line intersects the vertical 10,000 unit of sales line is Point A in Slide 38.**Exhibit 5**4 Cost-Volume-Profit Chart (continued) Point A $500 $450 $400 $350 $300 $250 $200 $150 $100 $ 50 Sales and Costs (in thousands) 0 1 2 3 4 5 6 7 8 9 10 Units of Sales (in thousands) Point A could have been plotted at any sales level because linearity is assumed.**Exhibit 5**4 Cost-Volume-Profit Chart (continued) Point A $500 $450 $400 $350 $300 $250 $200 $150 $100 $ 50 Sales and Costs (in thousands) 0 1 2 3 4 5 6 7 8 9 10 Units of Sales (in thousands) Beginning at zero on the left corner of the graph, connect a straight line to the dot (Point A).**Exhibit 5**4 Cost-Volume-Profit Chart (continued) $500 $450 $400 $350 $300 $250 $200 $150 $100 $ 50 Sales and Costs (in thousands) 0 1 2 3 4 5 6 7 8 9 10 Units of Sales (in thousands) Fixed cost of $100,000 is a horizontal line.**4**A point on the chart is needed to establish the revenue line. An arbitrary sales amount is picked of 10,000 units. At this sales level, the cost should be $400,000, calculated as follows: [(10,000 × $30) + $100,000] = $400,000.**Exhibit 5**4 Cost-Volume-Profit Chart (continued) $500 $450 $400 $350 $300 $250 $200 $150 $100 $ 50 Sales and Costs (in thousands) 0 1 2 3 4 5 6 7 8 9 10 Units of Sales (in thousands) A line is drawn between fixed cost ($100,000) and the point.**4**The line would be the same if another point had been picked. For example, assume that 8,000 units had been chosen. At this sales level, the cost should be $400,000 [(8,000 × $30) + $100,000 = $340,000].**Exhibit 5**Break-Even Point 4 Cost-Volume-Profit Chart (continued) $500 $450 $400 $350 $300 $250 $200 $150 $100 $ 50 Sales and Costs (in thousands) 0 1 2 3 4 5 6 7 8 9 10 Units of Sales (in thousands)**Exhibit 5**Break-Even Point 4 Cost-Volume-Profit Chart (continued) $500 $450 $400 $350 $300 $250 $200 $150 $100 $ 50 Sales and Costs (in thousands) 0 1 2 3 4 5 6 7 8 9 10 Units of Sales (in thousands) Break-even is sales of 5,000 units or $250,000.**Exhibit 5**4 Cost-Volume-Profit Chart (continued) $500 $450 $400 $350 $300 $250 $200 $150 $100 $ 50 Operating Loss Area Sales and Costs (in thousands) 0 1 2 3 4 5 6 7 8 9 10 Units of Sales (in thousands)**Exhibit 5**4 Cost-Volume-Profit Chart (continued) $500 $450 $400 $350 $300 $250 $200 $150 $100 $ 50 Sales and Costs (in thousands) Operating Profit Area 0 1 2 3 4 5 6 7 8 9 10 Units of Sales (in thousands)**Exhibit 5**4 Cost-Volume-Profit Chart (concluded)**Exhibit 6**4 Revised Cost-Volume-Profit Chart Break-even in sales would be reduced from $250,000 to $200,000 (5,000 to 4,000 in units).**Maximum Profit**4 The maximum operating loss is equal to the fixed costs of $100,000. Assuming that the maximum unit sales within the relevant range is 10,000 units, the maximum operating profit is $100,000, computed as follows: Sales (10,000 units × $50) $500,000 Variable costs (10,000 units × $30) 300,000 Contribution margin (10,000 units × $20) $200,000 Fixed costs 100,000 Operating profit $100,000