Prepared by Debby Bloom-Hill CMA, CFM

Cost-Volume-Profit Analysis Slide 4-2 CHAPTER 4

Management Questions  Planning  What level of profit should be in the budget for the coming year?  Control  Did the manager responsible for production costs do a good job of controlling costs?  Decision making  Should the price be increased? Learning objective 1 : Identify common cost behavior patterns, and estimate the relation between cost and activity using account analysis and the high-low method. Slide 4-3

 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 Common Cost Behavior Patterns Slide 4-4 Learning objective 1 : Identify common cost behavior patterns, and estimate the relation between cost and activity using account analysis and the high-low method.

 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 Common Cost Behavior Patterns Slide 4-5 Learning objective 1 : Identify common cost behavior patterns, and estimate the relation between cost and activity using account analysis and the high-low method.

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 a certain percentage, cost increases by that same percentage Slide 4-6 Learning objective 1 : Identify common cost behavior patterns, and estimate the relation between cost and activity using account analysis and the high-low method.

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, What is the direct labor cost per hour? $125,000 / 10,000 hours = $12.50 per hour 2.Predict labor costs in a month when 12,000 labor hours are worked $12.50 per hour × 12,000 hours = $150,000 Slide 4-7 Learning objective 1 : Identify common cost behavior patterns, and estimate the relation between cost and activity using account analysis and the high-low method.

Variable Costs Total Variable Cost = $91 × Units produced Slide 4-8 Learning objective 1 : Identify common cost behavior patterns, and estimate the relation between cost and activity using account analysis and the high-low method.

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  If activity increases by a certain percentage, costs remain unchanged Slide 4-9 Learning objective 1 : Identify common cost behavior patterns, and estimate the relation between cost and activity using account analysis and the high-low method.

Fixed Costs Total fixed cost = $94,000 Slide 4-10 Learning objective 1 : Identify common cost behavior patterns, and estimate the relation between cost and activity using account analysis and the high-low method.

Fixed Costs  Discretionary fixed costs  Management can easily change, e.g. advertising, research & development  Many companies cut back on these costs when sales drop. This can be shortsighted.  A cut in research & development can have a negative effect on long run profitability  A cut in repair and maintenance can have a negative effect on the life of valuable assets  Committed fixed costs  Cannot be easily changed, e.g. rent, insurance Slide 4-11 Learning objective 1 : Identify common cost behavior patterns, and estimate the relation between cost and activity using account analysis and the high-low method.

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 Slide 4-12 Learning objective 1 : Identify common cost behavior patterns, and estimate the relation between cost and activity using account analysis and the high-low method.

Mixed Costs Total cost = ($91 × Units produced) + $94,000 Slide 4-13 Learning objective 1 : Identify common cost behavior patterns, and estimate the relation between cost and activity using account analysis and the high-low method.

Step Costs  Fixed cost for a specific range of volume  Increases to higher level when upper bound of range is exceeded  At that point, costs again remain fixed until another upper bound is exceeded  Step costs are often classified as either:  Step variable costs, if the range of activity where the cost is fixed is small, or  Step fixed costs, if the range of activity where the cost is fixed is large Slide 4-14 Learning objective 1 : Identify common cost behavior patterns, and estimate the relation between cost and activity using account analysis and the high-low method.

Step Variable Cost Slide 4-15 Learning objective 1 : Identify common cost behavior patterns, and estimate the relation between cost and activity using account analysis and the high-low method.

Step Fixed Cost Slide 4-16 Learning objective 1 : Identify common cost behavior patterns, and estimate the relation between cost and activity using account analysis and the high-low method.

Relevant Range Slide 4-17  The relevant range is the range of activity for which assumptions as to how costs behave are reasonably valid  If it is known that production is going to be within the relevant range, we can use assumptions about the fixed and variable costs  Making assumptions about fixed and variable costs at production levels well above or below this range would not be valid Learning objective 1 : Identify common cost behavior patterns, and estimate the relation between cost and activity using account analysis and the high-low method.

The Relevant Range Total step costs = $7,000 for relevant range 0 – 3,000 units produced $14,000 for relevant range 3,001 – 6,000 units $21,000 for relevant range 6,001 – 9,000 units Slide 4-18 Learning objective 1 : Identify common cost behavior patterns, and estimate the relation between cost and activity using account analysis and the high-low method.

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 Slide 4-19 Learning objective 1 : Identify common cost behavior patterns, and estimate the relation between cost and activity using account analysis and the high-low method.

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 Slide 4-20 Learning objective 1 : Identify common cost behavior patterns, and estimate the relation between cost and activity using account analysis and the high-low method.

Account Analysis Slide 4-21 Learning objective 1 : Identify common cost behavior patterns, and estimate the relation between cost and activity using account analysis and the high-low method.

Scattergraphs  Utilization of cost information from several previous periods  Weekly, monthly, or quarterly cost reports are useful  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 Slide 4-22 Learning objective 1 : Identify common cost behavior patterns, and estimate the relation between cost and activity using account analysis and the high-low method.

Scattergraphs Is there a relationship between units produced and production costs? Describe the relationship. Slide 4-23 Learning objective 1 : Identify common cost behavior patterns, and estimate the relation between cost and activity using account analysis and the high-low method.

High-Low Method  Utilization of cost information from previous periods  Fits a straight line from lowest activity level to highest activity level  Slope of the line is the estimate of the unit variable cost  The slope measures the change in cost per unit in relation to the change in activity level  Total cost at lowest or highest activity level minus variable cost at that level equals fixed cost Slide 4-24 Learning objective 1 : Identify common cost behavior patterns, and estimate the relation between cost and activity using account analysis and the high-low method.

High-Low Method Slide 4-25 Total cost at high activity level Total cost at low activity level Learning objective 1 : Identify common cost behavior patterns, and estimate the relation between cost and activity using account analysis and the high-low method.

High-Low Method Slide 4-26 Learning objective 1 : Identify common cost behavior patterns, and estimate the relation between cost and activity using account analysis and the high-low method.

Estimate Variable Cost Slide 4-27 Learning objective 1 : Identify common cost behavior patterns, and estimate the relation between cost and activity using account analysis and the high-low method.

Estimate Fixed Cost Slide 4-28 Learning objective 1 : Identify common cost behavior patterns, and estimate the relation between cost and activity using account analysis and the high-low method.

During the past year, Island Air flew 15,000 miles in August (its busiest month) and had total costs of $300,000. In November (its least busy month) the company flew 5,000 miles and had $200,000 of costs. Using the high-low method, estimate variable cost per mile and fixed cost per month. a.$20 of variable cost and $100,000 fixed b.$15 of variable cost and $250,000 fixed c.$10 of variable cost and $150,000 fixed d.$5 of variable cost and $250,000 fixed Answer: c Slide 4-29 Learning objective 1 : Identify common cost behavior patterns, and estimate the relation between cost and activity using account analysis and the high-low method.

Slide 4-30 Learning objective 1 : Identify common cost behavior patterns, and estimate the relation between cost and activity using account analysis and the high-low method.

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  See appendix fox Excel ® example Slide 4-31 Learning objective 1 : Identify common cost behavior patterns, and estimate the relation between cost and activity using account analysis and the high-low method.

The Relevant Range and Cost Estimation  Estimates of fixed and variable costs are valid for only a limited range of activity  Known as the relevant range  Outside the relevant range, estimates of fixed and variable costs may not be useful  Actual costs may behave in a manner that is different from the common cost behavior patterns Slide 4-32 Learning objective 1 : Identify common cost behavior patterns, and estimate the relation between cost and activity using account analysis and the high-low method.

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 2: Perform cost-volume profit analysis for single and multiple products. Slide 4-33

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 $81.50 per unit  Monthly fixed production cost $102,000  Monthly fixed selling and administrative $63,900  Find CodeConnect’s break-even point Slide 4-34 Learning objective 2: Perform cost-volume profit analysis for single and multiple products.

Cost-Volume-Profit Analysis  Break-Even Point $0 = SP(x) – VC(x) – TFC $0 = $ (x) – $81.50(x) – $165,900 $118.50(x) = $165,900 x = 1,400 units  Always round up if the breakeven point is not a whole number Slide 4-35 Learning objective 2: Perform cost-volume profit analysis for single and multiple products.

Break-Even Point Slide 4-36 Learning objective 2: Perform cost-volume profit analysis for single and multiple products.

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. What is the break-even point in number of units? a.200 b.20 c.12 d.100 Answer: b Slide 4-37 Learning objective 2: Perform cost-volume profit analysis for single and multiple products.

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. What is the break-even point in number of units? 0 = SP(x) – VC(x) – TFC 0 = (SP – VC)(x) – TFC 0 = ($500 – $200)(x) – $6,000 0 = $300(x) – $6,000 $300(x) = $6,000 x = $6,000 / $300 = 20 cakes to break even Slide 4-38 Learning objective 2: Perform cost-volume profit analysis for single and multiple products.

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 $280,000 and expected sales are $350,000, calculate the margin of safety  The margin of safety is: $350,000 - $280,000= $70,000 Slide 4-39 Learning objective 2: Perform cost-volume profit analysis for single and multiple products.

Margin of Safety Ratio  The margin of safety can also be expressed as a ratio  Called the margin of safety ratio  Equal to the margin of safety divided by expected sales  Shows what percentage sales would have to drop before the product shows a loss Slide 4-40 Learning objective 2: Perform cost-volume profit analysis for single and multiple products.

Contribution Margin  Difference between revenue and variable costs  Contribution margin = total revenue minus total variable costs  Contribution margin per unit = selling price minus variable cost per unit  For CodeConnect’s Model DX375, the contribution margin is the $ selling price less the variable cost of $81.50  $ – $81.50 = $ Slide 4-41 Learning objective 2: Perform cost-volume profit analysis for single and multiple products.

Contribution Margin  The profit equation in terms of the contribution margin Profit = SP(x) – VC(x) – TFC Profit = (SP – VC)(x) – TFC Profit = Contribution margin per unit(x) - TFC Slide 4-42 Learning objective 2: Perform cost-volume profit analysis for single and multiple products.

Contribution Margin  The contribution margin per unit measures the amount of incremental profit generated by selling an additional unit  For CodeConnect, how much incremental profit would be generated by selling 100 more units? Incremental profit = number of units sold * contribution margin per unit Incremental profit = 100 * $ = $11,850 Slide 4-43 Learning objective 2: Perform cost-volume profit analysis for single and multiple products.

Units Needed for Target Profit  Solve the profit equation for the sales quantity in units  Unit sales (x) needed to attain a specified profit = Slide 4-44 Learning objective 2: Perform cost-volume profit analysis for single and multiple products.

Slide 4-45 Learning objective 2: Perform cost-volume profit analysis for single and multiple products.

Contribution Margin Ratio  The unit contribution margin ratio measures the amount of incremental profit generated by an additional dollar of sales  Two methods to calculate the contribution margin ratio 1. Contribution margin divided by sales revenue (Sales – TVC) / Sales 2. Unit contribution margin divided by selling price (SP – VC) / SP Slide 4-46 Learning objective 2: Perform cost-volume profit analysis for single and multiple products.

Contribution Margin Ratio Slide 4-47 Learning objective 2: Perform cost-volume profit analysis for single and multiple products.

Dollar Sales Needed to Achieve Profit Target  Calculate the amount of sales dollars needed to earn a monthly profit of $35,550 Slide 4-48 Learning objective 2: Perform cost-volume profit analysis for single and multiple products.

“What If” Analysis  “What if” analysis examines what will happen if an action is taken  The profit equation can show how profit will be affected by various options under consideration  CodeConnect is selling 3,000 units at $200, with variable cost of $81.50 and fixed cost of $165,900  Management is considering a change to $80.00 variable cost and fixed cost of $215,900 Slide 4-49 Learning objective 2: Perform cost-volume profit analysis for single and multiple products.

“What If” Analysis  Change in fixed and variable costs  Without the change, the profit is $200(3,000) - $81.50(3,000) - $165,900 = $189,600  If the price and quantity stay the same, the profit assuming the alternative is selected would be $200(3,000) - $80(3,000) - $215,900 = $144,100  The alternative would hurt profitability Slide 4-50 Learning objective 2: Perform cost-volume profit analysis for single and multiple products.

“What If” Analysis  Change in selling price  Any one of the variables in the profit equation can be considered  For example, if CodeConnect sells 3,000 units, what selling price is required to earn a profit of $200,000? $200,000 = SP(3,000) - $81.50(3,000) - $165,900 SP(3,000) = $610,400 SP = $ Slide 4-51 Learning objective 2: Perform cost-volume profit analysis for single and multiple products.

Matthews Consulting expects to work 5,000 hours next month. It has variable costs of $100 per hour and fixed costs of $600,000. What price must the company charge to earn a monthly profit of $900,000? a.$500 b.$350 c.$400 d.$200 Answer: c Slide 4-52 Learning objective 2: Perform cost-volume profit analysis for single and multiple products.

Matthews Consulting expects to work 5,000 hours next month. It has variable costs of $100 per hour and fixed costs of $600,000. What price must the company charge to earn a monthly profit of $900,000? $900,000 = SP(5,000) - $100(5,000) - $600,000 $900,000 = SP(5,000) - $1,100,000 SP(5,000) = $2,000,000 SP = $2,000,000 / 5,000 = $400 Slide 4-53 Learning objective 2: Perform cost-volume profit analysis for single and multiple products.

Multiproduct Analysis  Contribution margin approach  Used if the items sold are similar  Calculate a weighted average contribution margin per unit  Use the weighted average contribution margin in the profit formula to calculate breakeven point and target sales  The relative product mix is then used to calculate the required sales of individual items Slide 4-54 Learning objective 2: Perform cost-volume profit analysis for single and multiple products.

Multiproduct Analysis Slide 4-55  The sales mix is 2:1 Model A, Model B  The company has fixed costs of $3,500,000 Learning objective 2: Perform cost-volume profit analysis for single and multiple products.

Multiproduct Analysis  The 2,500 units is made up of the 2:1 mix, so Rohr must sell 1,667 Model A (2/3 of 2,500) and 833 Model B units (1/3 0f 2,500) Slide 4-56 Learning objective 2: Perform cost-volume profit analysis for single and multiple products.

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  Total company fixed costs (common costs) are not included for contribution margin approach but used for contribution margin ratio approach Slide 4-57 Learning objective 2: Perform cost-volume profit analysis for single and multiple products.

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$484,000 Total common fixed costs$1,120,000 1.Calculate total contribution margin ratio ($6,450,000 – $4,706,000) / $6,450,000 = Calculate total company break-even sales in dollars ($484,000 + $1,120,000) /.2704 = $5,931,953 Slide 4-58 Learning objective 2: Perform cost-volume profit analysis for single and multiple products.

Multiproduct Analysis  Can calculate the contribution margin ratio for each product line  Can also easily calculate the break-even point for the various product lines  Break-even sales for garden tools is $95,000 /.1874 = $506,937  When total company sales increase, each product line’s sales will increase proportionately  Can use the contribution margin ratio to calculate the increase in profit for each product line Slide 4-59 Learning objective 2: Perform cost-volume profit analysis for single and multiple products.

Multiproduct Analysis Slide 4-60 Learning objective 2: Perform cost-volume profit analysis for single and multiple products.

Assumptions in CVP Analysis  Assumptions can affect the validity of the analysis 1. Costs can be separated into fixed and variable components 2. Total fixed cost and unit variable cost do not change over the levels of interest 3. Multiproduct analysis assumes the product mix does not change  Despite assumptions, CVP is useful Slide 4-61 Learning objective 2: Perform cost-volume profit analysis for single and multiple products.

Operating Leverage  Level of fixed versus variable costs in a company  A company with a 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  These companies are seen as more risky  High operating leverage is better when sales are expected to increase Learning objective 3: Discuss the effect of operating leverage, and use the contribution margin per unit of the constraint to analyze situations involving a resource constraint. Slide 4-62

Constraints  Due to shortages of space, equipment or labor there can be constraints on how many items can be produced  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 Slide 4-63 Learning objective 3: Discuss the effect of operating leverage, and use the contribution margin per unit of the constraint to analyze situations involving a resource constraint.

Constraints A company can produce Product A or Product B using the same machinery. Only 1,000 machine hours are available. Slide 4-64 Learning objective 3: Discuss the effect of operating leverage, and use the contribution margin per unit of the constraint to analyze situations involving a resource constraint.

Constraints  With the 1,000 available machine hours,  Product A generates $20,000 of contribution margin  Product B generates $50,000 of contribution margin  Although Product A has the higher contribution margin per unit, Product B has the higher contribution margin per unit of constraint Slide 4-65 Learning objective 3: Discuss the effect of operating leverage, and use the contribution margin per unit of the constraint to analyze situations involving a resource constraint.

CHAPTER 4 Cost-Volume-Profit Analysis Appendix Slide 4-66

Regression Analysis Slide 4-67

Regression Analysis Slide 4-68

Regression Analysis Slide 4-69

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