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CHAPTER 4 Cost-Volume-Profit Analysis

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**Purpose of Budgeting Planning Control Decision making**

How many units of input do I need to support a budgeted output? Control Are operations effective and efficient? Decision making How do we decide on a price, and choose quantity given constraints? Learning objective 1: Identify common cost behavior patterns

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**Common Cost Behavior Patterns**

Variable Costs Costs which change directly in proportion to changes in quantity or activity Fixed Costs Costs which do not change when quantity or activity volume changes Learning objective 1: Identify common cost behavior patterns

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**Common Cost Behavior Patterns**

Mixed Costs Costs that have both variable and fixed elements Step Costs Fixed for a range of output, but increase when upper bound of range is exceeded Learning objective 1: Identify common cost behavior patterns

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Variable Costs Costs that change in proportion to changes in volume or activity An automobile manufacturer will need 400 tires to make 100 cars, but 4,000 tires to make 1,000 cars A bakery will need 2 eggs to make 1 cake and 20 eggs to make 10 cakes If activity increases by 10%, cost increases by 10% Learning objective 1: Identify common cost behavior patterns

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Variable Costs A company has decided that direct labor costs are 100% variable. Last month total direct labor costs were $125,000 and total direct labor hours worked were 10,000. What is the direct labor cost per hour? $125,000 / 10,000 hours = $12.50 per hour Predict labor costs in a month when 12,000 labor hours are worked $12.50 per hour × 12,000 hours = $150,000 Learning objective 1: Identify common cost behavior patterns

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**Variable Costs Total Variable Cost = $91 × Units produced**

Learning objective 1: Identify common cost behavior patterns

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**Fixed Costs Do not change in response to changes in activity level**

Typical fixed costs are depreciation, supervisory salaries, and building maintenance Rent for a bakery will not double if output increases from 100 to 200 cakes Activity increases by 10%, costs remain unchanged Learning objective 1: Identify common cost behavior patterns

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**Fixed Costs Total fixed cost = $94,000**

Learning objective 1: Identify common cost behavior patterns

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**Fixed Costs Discretionary Fixed Costs Committed Fixed Costs**

Management can easily change Advertising, research and development Many companies cut back on these costs when sales drop. This can be shortsighted. Why? Committed Fixed Costs Cannot be easily changed Rent, insurance Learning objective 1: Identify common cost behavior patterns

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**Using Less Water but Paying Higher Rates!**

Fixed Costs LINK TO PRACTICE Using Less Water but Paying Higher Rates! What happens to cost per unit when fixed costs remain the same but volume or activity declines? Can you think of another way to set rates to make ratepayers less angry? Learning objective 1: Identify common cost behavior patterns

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**Mixed Costs Contain both variable and fixed cost elements**

Can separate mixed costs into variable and fixed components Salesperson with base salary (fixed) and commission on sales (variable) Base salary included with fixed costs Commission included with variable costs Learning objective 1: Identify common cost behavior patterns

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**Mixed Costs Total cost = ($91 × Units produced) + $94,000**

Learning objective 1: Identify common cost behavior patterns

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**Step Costs Fixed cost for a specific range**

Increases to higher level when upper bound of range is exceeded Use correct cost when budgeting for a particular relevant range Company adds third production shift, cost increase includes supervisory salary Learning objective 1: Identify common cost behavior patterns

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**Step Costs Total step costs =**

$94,000 for relevant range 0 – 3,000 units produced $144,000 for relevant range 3,001 – 6,000 units $194,000 for relevant range 6,001 – 9,000 units Learning objective 1: Identify common cost behavior patterns

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**Direct Labor Q Is direct labor always a variable cost?**

Are you willing to lay off workers when production declines? What if the decline is temporary? What if the decline is permanent? Does the degree of automation make a difference in whether direct labor is fixed or variable? Learning objective 1: Identify common cost behavior patterns

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**Cost Estimation Methods**

Account Analysis -Classify costs into variable and fixed pools Scattergraphs -Can see cost relationships visually High-Low Method -Linear estimation connects high and low volume observations Regression Analysis -Linear estimation is best fit to observed values Learning objective 2: Estimate the relation between cost and activity using account analysis and the high-low method

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**Account Analysis Most common approach**

Requires professional judgment of management Management classifies costs as fixed, variable, or mixed Total variable costs divided by activity equals variable cost per unit Variable cost per unit and total fixed costs can be used in cost equation Learning objective 2: Estimate the relation between cost and activity using account analysis and the high-low method

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Account Analysis Total cost = ($81.50 Variable cost per unit × Units produced) + $102,000 Fixed costs Expected cost of 2,500 units = ($81.50 × 2,500) + $102,000 = $305,750 Learning objective 2: Estimate the relation between cost and activity using account analysis and the high-low method

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Account Analysis Learning objective 2: Estimate the relation between cost and activity using account analysis and the high-low method

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**Scattergraphs Utilization of cost information from previous periods**

Weekly, monthly, or quarterly cost reports Plot the actual costs at the observed activity levels Look for relationship between cost and activity, linear is ideal Use relationship to predict future costs Learning objective 2: Estimate the relation between cost and activity using account analysis and the high-low method

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Scattergraphs Is there a relationship between units produced and production costs? Describe the relationship. Learning objective 2: Estimate the relation between cost and activity using account analysis and the high-low method

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**High-Low Method Utilization of cost information from previous periods**

Connect straight line from lowest activity level to highest activity level Slope of the line (change in cost divided by change in activity) equals variable cost per unit Total cost at lowest or highest activity level minus variable cost at that level equals fixed cost Learning objective 2: Estimate the relation between cost and activity using account analysis and the high-low method

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**High-Low Method Total cost at high activity level**

Total cost at low activity level Learning objective 2: Estimate the relation between cost and activity using account analysis and the high-low method

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High-Low Method Learning objective 2: Estimate the relation between cost and activity using account analysis and the high-low method

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High-Low Method Learning objective 2: Estimate the relation between cost and activity using account analysis and the high-low method

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**Regression Analysis Statistical technique**

Estimates the slope and intercept of a cost equation Finds the best straight line fit to the observations Typically statistical software packages are utilized Spreadsheet applications like Excel® typically include statistical operations Learning objective 2: Estimate the relation between cost and activity using account analysis and the high-low method

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Regression Analysis Learning objective 2: Estimate the relation between cost and activity using account analysis and the high-low method

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Regression Analysis Input Y range are the costs. Input X range is the production. Learning objective 2: Estimate the relation between cost and activity using account analysis and the high-low method

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Regression Analysis Learning objective 2: Estimate the relation between cost and activity using account analysis and the high-low method

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The Relevant Range Range of activity for which estimates and predictions are expected to be accurate - Accuracy expected only for production levels within range Difficult to assess costs outside the relevant range Learning objective 3: Perform cost-volume profit analysis for single products

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The Relevant Range Learning objective 3: Perform cost-volume profit analysis for single products

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**Cost-Volume-Profit Analysis**

The Profit Equation Profit = SP(x) – VC(x) – TFC Where: x = Quantity of units produced and sold SP = Selling price per unit VC = Variable cost per unit TFC = Total fixed cost Fundamental to CVP analysis Learning objective 3: Perform cost-volume profit analysis for single products

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**Cost-Volume-Profit Analysis**

Break-Even Point Number of units sold that allow the company to neither earn a profit nor incur a loss $0 = SP(x) – VC(x) – TFC CodeConnect has the following cost structure Selling price $ per unit Variable cost $90.83 per unit Total fixed cost $160,285 Find CodeConnect’s break-even point Learning objective 3: Perform cost-volume profit analysis for single products

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**Cost-Volume-Profit Analysis**

Break-Even Point $0 = SP(x) – VC(x) – TFC $0 = [$ (x)] – [$90.83(x)] – $160,285 $0 = [($ – $90.83)(x)] – $160,285 $0 = $109.17(x) – $160,285 $109.17(x) = $160,285 x = $160,285 / $109.17 x = 1, units Break-even point is 1,469 units (always round up) Learning objective 3: Perform cost-volume profit analysis for single products

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Break-Even Point Learning objective 3: Perform cost-volume profit analysis for single products

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Exercise 1 Gabby’s Wedding Cakes creates elaborate wedding cakes. Each cake sells for $500. The variable cost of baking the cakes is $200 and the fixed cost per month is $6,000 Calculate the break-even point in units $6,000 / ($500 - $200) = 20 cakes 2. How many cakes must be sold to earn a profit of $9,000? ($9,000 + $6,000) / ($500 - $200) = 50 cakes Learning objective 3: Perform cost-volume profit analysis for single products

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Margin of Safety The margin of safety is the difference between the expected level of sales and break-even sales If breakeven sales for Model DX375 is $293,600 and expected sales are $350,000, calculate the margin of safety. The margin of safety is: $350,000 - $293,600 = $56,400. Learning objective 3: Perform cost-volume profit analysis for single products

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Review 1 At Winford Corp., the selling price per lawn mower is $120, variable cost per lawn mower is $55. Fixed costs are $130,000. Expected sales are 4,200 units. The Margin of Safety is? $264,000 $384,000 $143,000 $121,000 Answer a: Expected sales = 4,200 units X $120 = $504,000 Break even sales = 2,000 units X $120 = $240,000 Margin of safety = $504,000 – $240,000 = $264,000 Learning objective 3: Perform cost-volume profit analysis for single products 40

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Review 2 At Winford Corp., the selling price per lawn mower is $120, variable cost per lawn mower is $55. Fixed costs are $130,000. Expected sales are 4,200 units. What is profit expected to be? Answer here: _________________ Margin of safety in units = 4,200 – 2,000 = 2,200 2,200 units × $65 unit CM = $143,000 $143,000 Learning objective 3: Perform cost-volume profit analysis for single products 41

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**Contribution Margin Difference between revenue and variable costs**

Total revenue minus total variable costs Unit contribution margin = Selling price minus variable cost per unit - The unit contribution margin measures the amount of incremental profit generated by selling an additional unit Learning objective 3: Perform cost-volume profit analysis for single products

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**Contribution Margin Ratio**

The contribution margin ratio measures the amount of incremental profit generated by an additional dollar of sales Two methods to calculate the contribution margin ratio Contribution margin divided by sales revenue (Sales – TVC) / Sales Unit contribution margin divided by selling price (SP – VC) / SP Learning objective 3: Perform cost-volume profit analysis for single products

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Exercise 2 Rhetorix, Inc. produces stereo speakers. The selling price per pair of speakers is $800. The variable cost of production is $300 and the fixed cost per month is $50,000. Calculate the unit contribution margin associated with a pair of speakers $800 – $300 = $500 Calculate the contribution margin ratio for Rhetorix associated with a pair of speakers ($800 – $300) / $800 = 0.625 Learning objective 3: Perform cost-volume profit analysis for single products

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Contribution Margin Using the contribution margin and the contribution margin ratio SP = $200.00, VC = $90.83, CM = 200 – = $109.17, TFC = 160,285, profit = $40,000 Units to produce = (Profit + TFC) / Unit contribution margin ($40,000 + $160,285) / = 1,835 units Sales required (in dollars) = (Profit + TFC) / Contribution margin ratio CM ratio = $ / $ = ($40,000 + $160,285) / = $366,890 Learning objective 3: Perform cost-volume profit analysis for single products

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Exercise 3 Rhetorix, Inc. produces stereo speakers. The selling price per pair of speakers is $800. The variable cost of production is $300 and the fixed cost per month is $50,000. If the company sells five more speakers than planned, what is the expected effect on profit of selling the additional speakers? 5 speakers × $500 unit CM = $2,500 profit If the company has sales that are $5,000 higher than expected, what is the expected effect on profit? $5,000 × = $3,125 Learning objective 3: Perform cost-volume profit analysis for single products

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Review 3 At Winford Corp., the selling price per lawn mower is $120, variable cost per lawn mower is $55. Fixed costs are $130,000. Contribution Margin per unit is? $65 $75 $175 $30 Answer a: $120 – $55 = $65 Learning objective 3: Perform cost-volume profit analysis for single products 47

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Review 4 At Winford Corp., the selling price per lawn mower is $120, variable cost per lawn mower is $55. Fixed costs are $130,000. Break-Even Point in units is? 1,000 units 1,083 units 2,000 units None of these Answer c: $130,000 / ($120 – $55) = 2,000 units Learning objective 3: Perform cost-volume profit analysis for single products 48

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**Cost-Volume-Profit Analysis**

“What If” Analysis Utilize profit equation to determine impact of managerial decisions Change in Fixed and Variable Costs Change in Selling Price Taxes in CVP Analysis After tax profit = [SP(x) – VC(x) – TFC](1 – t) Learning objective 3: Perform cost-volume profit analysis for single products

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**Multiproduct Analysis**

Contribution Margin Approach Used if products are similar Identify number of units needed to be sold to break even Calculate weighted average contribution margin based on expected units sold and product mix Assume product mix to calculate break-even point and target profit Learning objective 3: Perform cost-volume profit analysis for single products

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**Multiproduct Analysis**

Rohr Watch Company Model A Model B Total Selling price $2,000 $3,000 Variable cost 800 1,200 Contribution margin $1,200 $1,800 Units produced and sold 4,000 2,000 6,000 Weight ,000 / 6, ,000 / 6,000 Weighted average contribution margin is [(2 × $1,200) + (1 × $1,800)]/3 = $1,400 per unit Break-even is $3,500,000 / $1,400 = 2,500 units Break-even is 2,500 × (4,000 / 6,000) = 1,667 Model A units (Whole units.) Break-even is 2,500 × (2,000 / 6,000) = 834 Model B units (Whole units.) Learning objective 4: Perform cost-volume profit analysis for multiple products

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**Multiproduct Analysis**

Contribution Margin Ratio Approach - Products are substantially different Calculate total company contribution margin ratio Use total company contribution margin ratio to compute required sales in dollars Learning objective 4: Perform cost-volume profit analysis for multiple products

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**Multiproduct Analysis**

A company with 4 divisions has the following information available: Total sales $6,450,000 Total variable costs $4,706,000 Total direct fixed costs $1,260,000 Total common fixed costs $1,120,000 Calculate total company contribution margin ($6,450,000 – $4,706,000) / $6,450,000 = .2704 Calculate total company break-even sales in dollars. ($1,260,000 + $1,120,000) / = $8,801,775 Learning objective 4: Perform cost-volume profit analysis for multiple products

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**Assumptions in CVP Analysis**

Assumptions can affect the validity of the analysis Costs can be separated into fixed and variable components Total fixed cost and unit variable cost do not change over the levels of interest Multiproduct analysis assumes the product mix does not change Despite assumptions, CVP is useful Learning objective 4: Perform cost-volume profit analysis for multiple products

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**Operating Leverage Level of fixed versus variable costs in a company**

High level of fixed costs has a high operating leverage - Companies with high operating leverage have large fluctuations in profit when sales increase or decrease Learning objective 5: Discuss the effect of operating leverage

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**Fixed vs. Variable Costs**

LINK TO PRACTICE Fixed Costs Too High—Make Them Variable! Can you think of any ways other than incentive compensation and outsourcing to turn fixed costs into variable costs? Would you rather have fixed or variable costs when revenues are increasing? When revenues are decreasing? Learning objective 5: Discuss the effect of operating leverage

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**Constraints Constraints on how many items can be produced**

Shortage of space, equipment, or labor Utilize contribution margin per unit to analyze situations - Calculate contribution margin per unit of constraint Produce product with highest contribution margin per unit of constraint Linear programming can solve multiple constraints Learning objective 6: Use the cost per unit of the constraint to analyze situations involving a resource constraint

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Constraints A company can produce Product A or Product B using the same machinery. Only 1,000 machine hours are available Product A has the higher contribution margin, but Product B has the higher contribution margin per machine hour Learning objective 6: Use the cost per unit of the constraint to analyze situations involving a resource constraint

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Copyright © 2010 John Wiley & Sons, Inc. All rights reserved. Reproduction or translation of this work beyond that permitted in Section 117 of the 1976 United States Copyright Act without the express written permission of the copyright owner is unlawful. Request for further information should be addressed to the Permissions Department, John Wiley & Sons, Inc. The purchaser may make back-up copies for his/her own use only and not for distribution or resale. The Publisher assumes no responsibility for errors, omissions, or damages, caused by the use of these programs or from the use of the information contained herein.

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