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Chapter Four Cost Volume Profit Analysis

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Cost Behavior A cost is classified as either fixed or variable, according to whether the total amount of the cost changes as activity changes. Activity is a general term denoting anything that the company does; examples: units of product sold or produced, hours worked, invoices prepared, and parts inspected. Volume is a common measure of activity.

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Definitions Variable costs change, in total, in direct proportion to changes in volume. Fixed costs remain the same in total over a wide range of volume. Total Costs = Fixed costs + Variable costs

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Classification of Cost by Cost Behavior Total Fixed Cost Behavior Total Variable Cost Behavior $ $ Relevant Range Number of Units Produced

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Cost per Unit VariableFixed

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Mixed Cost A mixed cost is a cost that has a fixed and a variable element Example would be utilities in a factory Can separate mixed costs into fixed and variable by: Regression Scatter Diagram Account analysis High-low method

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High-Low Method Example Assume power costs at 10,000 units produced are $20,000 and at 12,000 units produced are $21,000. Is power a fixed, variable or mixed cost? If mixed, how much is fixed and how much is variable

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It’s Mixed! We know that it is mixed because it is increasing in total and decreasing per unit as activity increases To find variable component divide the change in cost by the change in activity (21,000 - 20,000)/(12,000 - 10,000) = $0.50 per unit total cost - total variable cost = Fixed cost 21,000 - (12,000 *$0.50) = $15,000 fixed cost Total cost = $15,000 + $0.50 per unit

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Definitions Cost-volume-profit (CVP) analysis is a method for analyzing the relationships among costs, volume, and profits. Contribution margin per unit (CMU) is the difference between selling price per unit and variable cost per unit.

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Definitions Contribution margin ratio (CMR)is per-unit contribution margin divided by selling price, or total contribution margin divided by total sales dollars. Variable cost ratio is per-unit variable cost divided by selling price, or total variable costs divided by total sales dollars. Contribution margin ratio plus variable cost ratio equals 100 percent.

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Cost Behavior Example Selling price per backpack$20.00 Cost of backpacks 10.00 Variable cost to pack and ship 1.00 Sales commission (5% of sales) 1.00 Total unit variable costs$12.00 Monthly fixed costs $40,000

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CVP Equation The CVP equation can be used to solve many CVP problems Sales - variable costs - fixed costs = profit If x = quantity sold; SP = selling price and VCU = variable cost per unit equation becomes: SPx - VCUx - FC = profit

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Contribution Margin Income Statements at Various Sales Levels 5,000 units6,000 units7,000 units Sales ($20 per unit)$100,000$120,000$140,000 Variable costs ($12/unit)60,00072,00084,000 Contribution margin ($8 /unit)$40,000$48,000$56,000 Fixed costs40,00040,00040,000 Income$0$8,000$16,000

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Cost-Volume-Profit Graph $160,000 $140,000 $120,000 $100,000 $80,000 $60,000 $40,000 $20,000 $0 2,000 4,000 6,000 8,000 10,000 Unit Sales Dollar s Break-even point, 5,000 units, $100,000 Total Cost Total Revenues Loss Area Profit Area

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Break-Even Point Break-even point is the point at which profits are zero because total revenues equal total costs, or where the profit equals 0 SPx - VCUx - FC = 0

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Break-Even Sales Total fixed costs BEP in units=--------------------- CMU Total fixed costs BEP in sales $=--------------------- CMR

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Break-Even Sales $40,000 BEP in units=----------- = 5,000 units $20 - $12 $40,000 BEP in sales $=---------- = $100,000 $8 / $20

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Target Profit Equation The equations that follow to find target profit come from the CVP equation SPx - VCUx - FC = target profit Solving this for x you get: x = (FC + target profit)/(SP - VCU) SP - VCU = CMU which is contribution margin per unit

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Target Profit FC + Target profit In units=---------------------------- CMU FC + Target profit In sales dollars=---------------------------- CMR

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Target Profit of $5,000 $40,000 + $5,000 in units=--------------------- = 5,625 units $20 - $12 $40,000 + $5,000 In sales dollars=--------------------- = $112,500 $8 / $20

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Indifference Point The indifference point is the level of volume at which total costs, and hence profits, are the same under both cost structures. Suppose that you currently have variable costs of $7 per unit and fixed costs of $40,000. A new technology will lower vcu to $4 and increase fixed costs to $95,000. Above what volume does this make sense?

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Indifference Point Solution $40,000 + $7X = $95,000 + $4X X = 18,333 units (rounded) This means that at any volume above 18,333 you would be better off with the lower variable cost and the higher fixed cost

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Example of using equation Using our original information, assume that management would like to know what price would need to be charged to earn a income of 20% of sales at a sales level of 7,000 units The equation becomes 7,000*SP - 7,000*11 - 0.05*7,000*SP - 40,000 =.2*7,000*SP.75*7,000*SP = 117,000SP = $22.86

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Margin of Safety The difference in volume from the expected level of sales to the break-even point is called the margin of safety (MOS). If actual sales are 6,000 units, the margin of safety is 1,000 units (6,000 - 5,000). If actual sales are $120,000, the margin of safety is $20,000 ($120,000 - $100,000).

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Multiple Products For multiple products, must assume that they are sold in a constant mix to do CVP Calculate a weighted average contribution margin per unit or contribution margin ratio and then proceed with CVP as normal.

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Multiple Product Example Product A sells for $8 per unit and has variable costs of $5 per unit; Product B sells for $9 per unit and has Variable cost of $5 per unit. The sales mix is 3:2, meaning that for every 3 units of A that are sold, 2 units of B are sold Fixed costs are $170,000 per year. How many of each must be sold to breakeven?

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Calculation of Average CMU ABOverall Selling Price $8.00 $9.00 Variable Cost $5.00 Contribution Margin $3.00 $4.00 Mix32 Total CM $9.00 $8.00 $17.00 Units5 Average CMU $ 3.40

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Multiple Product Break Even Point Fixed costs are $170,000 Weighted average CMU is $3.40 Breakeven point is $170,000/3/40 = 50,000 units That makes 30,000 units of A and 20,000 of B (in the 3:2 mix)

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Assumptions and Limitations of CVP Analysis Selling price, per-unit variable cost, and total fixed costs must be constant throughout the relevant range. The company sells only one product, or the sales of each product in a multiproduct company are a constant percentage of sales. Production equals sales in units.

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Relevant Range Relevant range is the range of volume over which it can reasonably expect selling price, per-unit variable cost, and total fixed costs to be constant.

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Do Fixed Costs Add Risk? Fixed costs cannot be reduced quickly When sales fall off, fixed costs remain When sales rise, fixed costs also remain the same Do fixed costs add risk?

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Operating Leverage Firm’s with high levels of fixed costs are said to have high operating leverage. Their profit will move faster (up or down) in response to a change in sales. The ratio of CM/profit will tell you how many multiples a % change in sales will have on profits For example if a firm has CM of 30,000 and profit of 10,000, a 10% increase in sales gives a 30% increase in profits!! Try it out.

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Constraints A constraint exists when a supply of a resource (labor, material, processing time) is inadequate to meet demand Demand itself is also a constraint Need to get the most out of each unit of a constrained input Do this by calculating a contribution margin per unit of the constrained resource

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Constraints Example Assume that there are only 800 labor hours available, product A needs 2 hours per unit, product B needs 3 hours per unit. Product A has a CMU of $5.00, B is $6.00 Demand for each product is 200 units How many units of each product should you produce?

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