© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin Cost-Volume-Profit Analysis Chapter 19

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin CVP analysis is used to answer questions such as:  How much must I sell to earn my desired income?  How will income be affected if I reduce selling prices to increase sales volume?  What will happen to profitability if I expand capacity? CVP analysis is used to answer questions such as:  How much must I sell to earn my desired income?  How will income be affected if I reduce selling prices to increase sales volume?  What will happen to profitability if I expand capacity? Questions Addressed by Cost-Volume-Profit Analysis

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin Number of Local Calls Monthly Basic Telephone Bill Total fixed costs remain unchanged when activity changes. Your monthly basic telephone bill probably does not change when you make more local calls. Total Fixed Cost

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin Number of Local Calls Monthly Basic Telephone Bill per Local Call Fixed costs per unit decline as activity increases. Your average cost per local call decreases as more local calls are made. Fixed Cost Per Unit

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin Minutes Talked Total Long Distance Telephone Bill Total variable costs change when activity changes. Your total long distance telephone bill is based on how many minutes you talk. Total Variable Cost

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin Minutes Talked Per Minute Telephone Charge Variable costs per unit do not change as activity increases. The cost per long distance minute talked is constant. For example, 10 cents per minute. Variable Cost Per Unit

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin Cost Behavior Summary

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin Mixed costs contain a fixed portion that is incurred even when facility is unused, and a variable portion that increases with usage. Example: monthly electric utility charge Fixed service fee Variable charge per kilowatt hour used Mixed Costs

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin Variable Utility Charge Activity (Kilowatt Hours) Total Utility Cost Total mixed cost Fixed Monthly Utility Charge Slope is variable cost per unit of activity. Mixed Costs

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin Activity Cost Total cost remains constant within a narrow range of activity. Stair-Step Costs

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin Activity Cost Total cost increases to a new higher cost for the next higher range of activity. Stair-Step Costs

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin Total Cost Relevant Range A straight line closely (constant unit variable cost) approximates a curvilinear variable cost line within the relevant range. Volume of Output Curvilinear Cost Function Curvilinear Costs

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin Let’s extend our knowledge of cost behavior to CVP analysis. Cost-Volume-Profit (CVP) Analysis

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin The break-even point (expressed in units of product or dollars of sales) is the unique sales level at which a company neither earns a profit nor incurs a loss. Computing Break-Even Point

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin Contribution margin is amount by which revenue exceeds the variable costs of producing the revenue. Computing Break-Even Point

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin How much contribution margin must this company have to cover its fixed costs (break even)? Computing Break-Even Point

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin How much contribution margin must this company have to cover its fixed costs (break even)? Answer: $30,000 How much contribution margin must this company have to cover its fixed costs (break even)? Answer: $30,000 Computing Break-Even Point

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin How many units must this company sell to cover its fixed costs (break even)? Computing Break-Even Point

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin How many units must this company sell to cover its fixed costs (break even)? Answer: $30,000 ÷ $20 per unit = 1,500 units How many units must this company sell to cover its fixed costs (break even)? Answer: $30,000 ÷ $20 per unit = 1,500 units Computing Break-Even Point

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin We have just seen one of the basic CVP relationships – the break-even computation. Break-even point in units = Fixed costs Contribution margin per unit Finding the Break-Even Point Unit sales price less unit variable cost ($20 in previous example) Formula for Computing Break-Even Sales (in Units)

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin The break-even formula may also be expressed in sales dollars. Break-even point in dollars = Fixed costs Contribution margin ratio Unit sales price Unit variable cost Formula for Computing Break-Even Sales (in Dollars)

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin ABC Co. sells product XYZ at $5.00 per unit. If fixed costs are $200,000 and variable costs are $3.00 per unit, how many units must be sold to break even? a. 100,000 units b. 40,000 units c. 200,000 units d. 66,667 units ABC Co. sells product XYZ at $5.00 per unit. If fixed costs are $200,000 and variable costs are $3.00 per unit, how many units must be sold to break even? a. 100,000 units b. 40,000 units c. 200,000 units d. 66,667 units Computing Break-Even Sales Question 1

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin ABC Co. sells product XYZ at $5.00 per unit. If fixed costs are $200,000 and variable costs are $3.00 per unit, how many units must be sold to break even? a. 100,000 units b. 40,000 units c. 200,000 units d. 66,667 units ABC Co. sells product XYZ at $5.00 per unit. If fixed costs are $200,000 and variable costs are $3.00 per unit, how many units must be sold to break even? a. 100,000 units b. 40,000 units c. 200,000 units d. 66,667 units Unit contribution = $ $3.00 = $2.00 Fixed costs Unit contribution = $200,000 $2.00 per unit = 100,000 units Computing Break-Even Sales Question 1

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin Use the contribution margin ratio formula to determine the amount of sales revenue ABC must have to break even. All information remains unchanged: fixed costs are $200,000; unit sales price is $5.00; and unit variable cost is $3.00. a. $200,000 b. $300,000 c. $400,000 d. $500,000 Use the contribution margin ratio formula to determine the amount of sales revenue ABC must have to break even. All information remains unchanged: fixed costs are $200,000; unit sales price is $5.00; and unit variable cost is $3.00. a. $200,000 b. $300,000 c. $400,000 d. $500,000 Computing Break-Even Sales Question 2

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin Use the contribution margin ratio formula to determine the amount of sales revenue ABC must have to break even. All information remains unchanged: fixed costs are $200,000; unit sales price is $5.00; and unit variable cost is $3.00. a. $200,000 b. $300,000 c. $400,000 d. $500,000 Use the contribution margin ratio formula to determine the amount of sales revenue ABC must have to break even. All information remains unchanged: fixed costs are $200,000; unit sales price is $5.00; and unit variable cost is $3.00. a. $200,000 b. $300,000 c. $400,000 d. $500,000 Unit contribution = $ $3.00 = $2.00 Contribution margin ratio = $2.00 ÷ $5.00 =.40 Break-even revenue = $200,000 ÷.4 = $500,000 Computing Break-Even Sales Question 2

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin Volume in Units Costs and Revenue in Dollars Revenue  Starting at the origin, draw the total revenue line with a slope equal to the unit sales price. Total fixed cost  Total fixed cost extends horizontally from the vertical axis. Preparing a CVP Graph

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin Total cost Volume in Units Costs and Revenue in Dollars Total fixed cost Break- even Point Profit Loss  Draw the total cost line with a slope equal to the unit variable cost. Revenue Preparing a CVP Graph

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin Break-even formulas may be adjusted to show the sales volume needed to earn any amount of operating income. Unit sales = Fixed costs + Target income Contribution margin per unit Dollar sales = Fixed costs + Target income Contribution margin ratio Computing Sales Needed to Achieve Target Operating Income

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin ABC Co. sells product XYZ at $5.00 per unit. If fixed costs are $200,000 and variable costs are $3.00 per unit, how many units must be sold to earn operating income of $40,000? a. 100,000 units b. 120,000 units c. 80,000 units d. 200,000 units ABC Co. sells product XYZ at $5.00 per unit. If fixed costs are $200,000 and variable costs are $3.00 per unit, how many units must be sold to earn operating income of $40,000? a. 100,000 units b. 120,000 units c. 80,000 units d. 200,000 units Computing Sales Needed to Achieve Target Operating Income

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin ABC Co. sells product XYZ at $5.00 per unit. If fixed costs are $200,000 and variable costs are $3.00 per unit, how many units must be sold to earn operating income of $40,000? a. 100,000 units b. 120,000 units c. 80,000 units d. 200,000 units ABC Co. sells product XYZ at $5.00 per unit. If fixed costs are $200,000 and variable costs are $3.00 per unit, how many units must be sold to earn operating income of $40,000? a. 100,000 units b. 120,000 units c. 80,000 units d. 200,000 units = 120,000 units Unit contribution = $ $3.00 = $2.00 Fixed costs + Target income Unit contribution $200,000 + $40,000 $2.00 per unit Computing Sales Needed to Achieve Target Operating Income

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin Margin of safety is the amount by which sales may decline before reaching break-even sales: Margin of safety provides a quick means of estimating operating income at any level of sales: Margin of safety = Actual sales - Break-even sales Operating Margin Contribution Income of safety margin ratio =× What is our Margin of Safety?

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin Oxco’s contribution margin ratio is 40 percent. If sales are $100,000 and break- even sales are $80,000, what is operating income? Operating Margin Contribution Income of safety margin ratio =× Operating Income = $20,000 ×.40 = $8,000 What is our Margin of Safety?

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin Once break-even is reached, every additional dollar of contribution margin becomes operating income: Oxco expects sales to increase by $15,000. How much will operating income increase? Change in operating income = $15,000 ×.40 = $6,000 Change in Change in Contribution operating income sales volume margin ratio =× What Change in Operating Income Do We Anticipate?

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin Business Applications of CVP

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin Consider the following information developed by the accountant at CyclCo, a bicycle retailer: Business Applications of CVP

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin Should CyclCo spend $12,000 on advertising to increase sales by 10 percent? Business Applications of CVP

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin 550 × $300 $80K + $12K No, income is decreased. 550 × $500 Business Applications of CVP Should CyclCo spend $12,000 on advertising to increase sales by 10 percent?

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin Now, in combination with the advertising, CyclCo is considering a 10 percent price reduction that will increase sales by 25 percent. What is the income effect? Business Applications of CVP

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin 625 × $300 $80K + $12K Income is decreased even more. 625 × $450 Now, in combination with the advertising, CyclCo is considering a 10 percent price reduction that will increase sales by 25 percent. What is the income effect? 1.25 × 500 Business Applications of CVP

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin Business Applications of CVP Now, in combination with advertising and a price cut, CyclCo will replace $50,000 in sales salaries with a $25 per bike commission, increasing sales by 50 percent above the original 500 bikes. What is the effect on income?

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin The combination of advertising, a price cut, and change in compensation increases income. 750 × $325 $92K - $50K 750 × $450 Business Applications of CVP Now, in combination with advertising and a price cut, CyclCo will replace $50,000 in sales salaries with a $25 per bike commission, increasing sales by 50 percent above the original 500 bikes. What is the effect on income? 1.5 × 500

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin  Different products with different contribution margins.  Determining semivariable cost elements.  Complying with the assumptions of CVP analysis. Additional Considerations in CVP

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin Sales mix is the relative combination in which a company’s different products are sold. Different products have different selling prices, costs, and contribution margins. If CyclCo sells bikes and carts, how will we deal with break-even analysis? Sales mix is the relative combination in which a company’s different products are sold. Different products have different selling prices, costs, and contribution margins. If CyclCo sells bikes and carts, how will we deal with break-even analysis? CVP Analysis When a Company Sells Many Products

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin CyclCo provides us with the following information: CVP Analysis When a Company Sells Many Products

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin The overall contribution margin ratio is: $265,000 $550,000 = 48% (rounded) CVP Analysis When a Company Sells Many Products

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin Break-even in sales dollars is: $170, = $354,167 (rounded) CVP Analysis When a Company Sells Many Products

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin OwlCo recorded the following production activity and maintenance costs for two months: Using these two levels of activity, compute:  the variable cost per unit.  the total fixed cost.  total cost formula. The High-Low Method

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin  Unit variable cost = = = $0.90 per unit   in cost  in units $3,600 4,000 The High-Low Method

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin  Unit variable cost = = = $0.90 per unit  Fixed cost = Total cost – Total variable cost   in cost  in units $3,600 4,000 The High-Low Method

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin  Unit variable cost = = = $0.90 per unit  Fixed cost = Total cost – Total variable cost Fixed cost = $9,700 – ($0.90 per unit × 9,000 units) Fixed cost = $9,700 – $8,100 = $1,600   in cost  in units $3,600 4,000 The High-Low Method

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin  Unit variable cost = = = $0.90 per unit  Fixed cost = Total cost – Total variable cost Fixed cost = $9,700 – ($0.90 per unit × 9,000 units) Fixed cost = $9,700 – $8,100 = $1,600  Total cost = $1,600 + $.90 per unit   in cost  in units $3,600 4,000 The High-Low Method

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin If sales commissions are $10,000 when 80,000 units are sold and $14,000 when 120,000 units are sold, what is the variable portion of sales commission per unit sold? a. $.08 per unit b. $.10 per unit c. $.12 per unit d. $.125 per unit If sales commissions are $10,000 when 80,000 units are sold and $14,000 when 120,000 units are sold, what is the variable portion of sales commission per unit sold? a. $.08 per unit b. $.10 per unit c. $.12 per unit d. $.125 per unit The High-Low Method Question 1

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin If sales commissions are $10,000 when 80,000 units are sold and $14,000 when 120,000 units are sold, what is the variable portion of sales commission per unit sold? a. $.08 per unit b. $.10 per unit c. $.12 per unit d. $.125 per unit If sales commissions are $10,000 when 80,000 units are sold and $14,000 when 120,000 units are sold, what is the variable portion of sales commission per unit sold? a. $.08 per unit b. $.10 per unit c. $.12 per unit d. $.125 per unit $4,000 ÷ 40,000 units = $.10 per unit The High-Low Method Question 1

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin If sales commissions are $10,000 when 80,000 units are sold and $14,000 when 120,000 units are sold, what is the fixed portion of the sales commission? a. $ 2,000 b. $ 4,000 c. $10,000 d. $12,000 If sales commissions are $10,000 when 80,000 units are sold and $14,000 when 120,000 units are sold, what is the fixed portion of the sales commission? a. $ 2,000 b. $ 4,000 c. $10,000 d. $12,000 The High-Low Method Question 2

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin If sales commissions are $10,000 when 80,000 units are sold and $14,000 when 120,000 units are sold, what is the fixed portion of the sales commission? a. $ 2,000 b. $ 4,000 c. $10,000 d. $12,000 If sales commissions are $10,000 when 80,000 units are sold and $14,000 when 120,000 units are sold, what is the fixed portion of the sales commission? a. $ 2,000 b. $ 4,000 c. $10,000 d. $12,000 The High-Low Method Question 2

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin  A limited range of activity, called the relevant range, where CVP relationships are linear.  Unit selling price remains constant.  Unit variable costs remain constant.  Total fixed costs remain constant.  Sales mix remains constant.  Production = sales (no inventory changes). Assumptions Underlying CVP Analysis

© The McGraw-Hill Companies, Inc., 2002 McGraw-Hill/Irwin End of Chapter 19