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## Cost-Volume-Profit Analysis

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**Chapter19**Cost-Volume-Profit Analysis**CVP analysis is used to answer questionssuch as:**How much must I sell to earn my desired income? How will income be affectedif I reduce selling prices toincrease sales volume? What will happen toprofitability if I expandcapacity? Questions Addressed byCost-Volume-Profit Analysis**Total Fixed Cost**Total fixed costs remain unchangedwhen activity changes. Monthly Basic Telephone Bill Your monthly basictelephone bill probablydoes not change whenyou make more local calls. Number of Local Calls**Fixed costs per unit declineas activity increases.**Fixed Cost Per Unit Monthly Basic Telephone Bill per Local Call Your average cost perlocal call decreases asmore local calls are made. Number of Local Calls**Total Variable Cost**• Total variable costs changewhen activity changes. Total Long DistanceTelephone Bill Your total long distancetelephone bill is basedon how many minutesyou talk. Minutes Talked**Variable costs per unit do not changeas activity**increases. Variable Cost Per Unit Per MinuteTelephone Charge The cost per long distanceminute talked is constant.For example, 10cents per minute. Minutes Talked**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 perkilowatt hour used Mixed Costs**Mixed Costs**Slope isvariable costper unitof activity. Total mixed cost Variable Utility Charge Total Utility Cost Fixed MonthlyUtility Charge Activity (Kilowatt Hours)**Stair-Step Costs**Total cost remainsconstant within anarrow range ofactivity. Cost Activity**Stair-Step Costs**Total cost increases to a new higher cost for the next higher range of activity. Cost Activity**Relevant Range**Curvilinear Costs CurvilinearCost Function A straight line closely (constant unit variable cost)approximates acurvilinear variablecost line withinthe relevant range. Total Cost Volume of Output**Cost-Volume-Profit(CVP) Analysis**Let’s extend ourknowledge ofcost behavior to CVP analysis.**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**Computing Break-Even Point**Contribution margin is amount by which revenue exceeds the variable costs of producing the revenue.**Computing Break-Even Point**How much contribution margin must this company have to cover its fixed costs (break even)?**Computing Break-Even Point**How much contribution margin must this company have to cover its fixed costs (break even)? Answer: $30,000**Computing Break-Even Point**How many units must this company sell to cover its fixed costs (break even)?**Computing Break-Even Point**How many units must this company sell to cover its fixed costs (break even)? Answer: $30,000 ÷ $20 per unit = 1,500 units**We have just seen one of the basic CVP relationships –**thebreak-evencomputation. Fixed costs Break-even point in units = Contribution margin per unit Formula for ComputingBreak-Even Sales (in Units) Finding the Break-Even Point Unit sales price less unit variable cost($20 in previous example)**Unit sales price Unit variable cost**Formula for ComputingBreak-Even Sales (in Dollars) The break-even formula may also be expressed in sales dollars. Fixed costs Break-even point in dollars = Contribution margin ratio**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 SalesQuestion 1**Computing Break-Even SalesQuestion 1**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 = $5.00 - $3.00 = $2.00 Fixed costsUnit contribution $200,000$2.00 per unit = = 100,000 units**Computing Break-Even SalesQuestion 2**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 SalesQuestion 2**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 = $5.00 - $3.00 = $2.00 Contribution margin ratio = $2.00 ÷ $5.00 = .40 Break-even revenue = $200,000 ÷ .4 = $500,000**Total fixed costextends horizontallyfrom the vertical axis.**Total fixed cost Preparing a CVP Graph • Starting at the origin, draw the total revenueline with a slope equal to the unit sales price. Revenue Costs and Revenuein Dollars Volume in Units**Preparing a CVP Graph**• Draw the total cost line with a slopeequal to the unit variable cost. Revenue Break-even Point Profit Costs and Revenuein Dollars Total cost Loss Total fixed cost Volume in Units**Break-even formulas may be adjusted to show the sales**volume needed to earnany amount of operating income. Computing Sales Needed to Achieve Target Operating Income Fixed costs + Target income Unit sales = Contribution margin per unit Fixed costs + Target income Dollar sales = Contribution margin ratio**Computing Sales Needed to Achieve Target Operating Income**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**Unit contribution = $5.00 - $3.00 = $2.00**Fixed costs + Target income Unit contribution $200,000 + $40,000 $2.00 per unit = 120,000 units Computing Sales Needed to Achieve Target Operating Income 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**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?**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?**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 Change in Contributionoperating income sales volume margin ratio = × Change in operating income = $15,000 × .40 = $6,000 What Change in Operating Income Do We Anticipate?**Consider the following information developed by the**accountant at CyclCo, a bicycle retailer: Business Applications of CVP**Should CyclCo spend $12,000 on advertising to increase**sales by 10 percent? Business Applications of CVP**$80K + $12K**Business Applications of CVP Should CyclCo spend $12,000 on advertising to increase sales by 10 percent? 550 × $500 550 × $300 No, income is decreased.**Business Applications of CVP**Now, in combination with the advertising, CyclCo is considering a 10 percent price reduction that willincrease sales by 25 percent. What is the income effect?**$80K + $12K**Business Applications of CVP Now, in combination with the advertising, CyclCo is considering a 10 percent price reduction that willincrease sales by 25 percent. What is the income effect? 1.25 × 500 625 × $450 625 × $300 Income is decreased even more.**Business Applications of CVP**Now, in combination with advertising and a price cut, CyclCowill 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?**$92K - $50K**Business Applications of CVP Now, in combination with advertising and a price cut, CyclCowill 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 × 500 750 × $450 750 × $325 The combination of advertising, a price cut,and change in compensation increases income.**Different products with different contribution margins.**• Determining semivariablecost elements. • Complying with theassumptions of CVP analysis. Additional Considerations in CVP**Sales mix is the relative combination in whicha company’s**different products are sold. Different products have different selling prices, costs, and contribution margins. If CyclCo sells bikes and carts, howwill we deal with break-even analysis? CVP Analysis When a Company Sells Many Products**CyclCo provides us with the following information:**CVP Analysis When a Company Sells Many Products**The overall contribution margin ratio is:**CVP Analysis When a Company Sells Many Products $265,000 $550,000 = 48% (rounded)**Break-even in sales dollars is:**CVP Analysis When a Company Sells Many Products $170,000 .48 = $354,167 (rounded)**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 High-Low Method**$3,600 4,000 in costin units • Unit variable cost = = = $0.90 per unit**The High-Low Method**$3,600 4,000 in costin units • Unit variable cost = = = $0.90 per unit • Fixed cost = Total cost – Total variable cost**The High-Low Method**$3,600 4,000 in costin units • 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