CHAPTER 4 Cost-Volume-Profit Analysis

Common Cost Behavior Patterns Variable Costs Fixed Costs Mixed Costs Step Costs

Variable Costs Costs that change in proportion to changes in volume or activity At restaurants, food costs vary with the number of customers served For airlines, fuel costs vary with the number of miles flown Example Activity increases by 10% Cost increases by 10%

Variable Costs

Fixed Costs Do not change in response to changes in activity level Typical fixed costs are depreciation, supervisory salaries, and building maintentance Example Activity increases by 10% Costs remain unchanged

Fixed Costs

Fixed Costs Discretionary Fixed Costs Committed Fixed Costs Management can easily change Advertising, Research and Development Committed Fixed Costs Cannot be easily changed Rent, Insurance

Fixed Costs

Mixed Costs Contain variable and fixed cost elements Example Salesperson with base salary (fixed) Receives commission on sales (variable)

Mixed Costs

Step Costs Fixed cost for a specific range Increases to higher level when upper bound of range is exceeded Example Company adds third production shift Costs increase to include supervisory costs

Step Costs

Direct Labor

Cost Estimation Methods Account Analysis Scattergraphs High-Low Method Regression Analysis

Account Analysis Most common approach Requires professional judgment of management Management classifies costs as fixed and variable

Account Analysis Costs are then estimated Variable cost per unit Total fixed costs

Account Analysis Estimates used to find total production costs at various production levels

Scattergraphs Utilization of cost information from previous periods Weekly, monthly, or quarterly cost reports Plot the costs at specific activity levels

Scattergraphs

High-Low Method Utilization of cost information from previous periods Connect straight line from lowest activity level to highest activity level

High-Low Method

High-Low Method Cost Estimations Variable cost equals the slope of the line Fixed cost equals the intercept of cost axis Estimates used to find total production costs at various production levels

Regression Analysis Statistical technique Estimates the slope and intercept of a cost equation Typically spreadsheet programs are utilized

Regression Analysis

The Relevant Range Limitation of estimates Accuracy expected only for production levels within range Difficult to assess costs outside the relevant range

The Relevant Range

Cost-Volume-Profit Analysis Equation Abbreviations x = Quantity of units produced and sold SP = Selling price per unit VC = Variable cost per unit TFC = Total fixed cost

Cost-Volume-Profit Analysis The Profit Equation Profit = SP(x) – VC(x) – TFC Fundamental to CVP analysis

Cost-Volume-Profit Analysis Break-Even Point Number of units sold that allow the company to neither a profit nor a loss $0 = SP(x) – VC(x) – TFC Margin of Safety Difference between expected sales and break-even sales

Break-Even Point

Cost-Volume-Profit Analysis Contribution Margin (CM) Difference between selling price and variable cost per unit Profit = (SP – VC)(x) – TFC OR Profit = CM per unit(x) - TFC

Cost-Volume-Profit Analysis Contribution Margin Ratio Contribution of every sales dollar to covering fixed cost CM Ratio = SP – VC SP Profit Equation (utilizing CM Ratio) Sales($) = Profit + TFC CM Ratio

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

Cost-Volume-Profit Analysis Taxes in CVP Analysis Profit Formula without Tax Considerations Before Tax Profit = SP(x) – VC(x) – TFC Profit Formula with Tax Considerations After Tax Profit = [SP(x) – VC(x) – TFC](1-t)

Break-Even

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 for a month. How many cakes must be sold to earn a monthly profit of $9,000?

Solution Break-Even Point What if monthly profit is $9,000? x = (Profit + TFC) / CM per Unit x = ($0 + $6,000) / $300 x = 20 cakes What if monthly profit is $9,000? x = ($9,000 + $6,000) / $300 x = 50 cakes

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

Multiproduct Analysis Contribution Margin Ratio Approach Products are substantially different Identify dollar amount of sales needed to break even Calculate total CM Ratio and use to determine break-even point

Assumptions in CVP Analysis Costs can be accurately separated into fixed and variable components Fixed costs remain fixed Variable costs per unit do not change

Operating Leverage Level of fixed versus variable costs in a company High level of fixed costs has a high operating leverage Typically have large fluctuations in profit when sales fluctuate

Outsourcing

Constraints Constraints on how many items can be produced Shortage of space, equipment, or labor Utilize contribution margin per unit to analyze situations

Decisions that Increase Sales or Production

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 contribution margin associated with a pair of speakers. Calculate the contribution margin ratio for Rhetorix associated with a pair of speakers.

Solution Contribution Margin CM = SP – VC CM = $800 - $300 CM = $500 If the company sells five more speakers than planned, what is the expected effect on profit of selling the additional speakers? Expected Effect = $500 * 5 units = $2,500

Solution Contribution Margin Ratio CM Ratio = (SP – VC)/SP = ($800 - $300)/$800 = 62.5% If the company has sales that are $5,000 higher than expected, what is the expected effect on profit? Expected Effect = 62.5% * $5,000 = $3,125

Review 1 At Winford Corp., the selling price per unit for lawn mowers is $120, variable cost per unit is $55. Fixed costs are $130,000. Contribution Margin per unit is? $65 $75 $175 $30

Review 1 At Winford Corp., the selling price per unit for lawn mowers is $120, variable cost per unit is $55. Fixed costs are $130,000. Contribution margin per unit is? $65 $75 $175 $30

Review 2 At Winford Corp., the selling price per unit for lawn mowers is $120, variable cost per unit is $55. Fixed costs are $130,000. Break-Even Point is? 1,000 units 1,083 units 2,000 units None of these

Review 2 At Winford Corp., the selling price per unit for lawn mowers is $120, variable cost per unit is $55. Fixed costs are $130,000. Break-Even Point is? 1,000 units 1,083 units 2,000 units None of these

Review 3 At Winford Corp., the selling price per unit for lawn mowers is $120, variable cost per unit 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

Review 3 At Winford Corp., the selling price per unit for lawn mowers is $120, variable cost per unit 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

Review 4 At Winford Corp., the selling price per unit for lawn mowers is $120, variable cost per unit is $55. Fixed costs are $130,000. Expected sales are 4,200 units. What is profit expected to be? Answer here: _________________

Review 4 At Winford Corp., the selling price per unit for lawn mowers is $120, variable cost per unit is $55. Fixed costs are $130,000. Expected sales are 4,200 units. What is profit expected to be? Answer here: $143,000

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