Kế toán, kiểm toán - Chapter 6: Cost - Volume - profit relationships

Cost-Volume-Profit RelationshipsChapter 6Learning Objective 1Explain how changes in activity affect contribution margin and net operating income.Basics of Cost-Volume-Profit AnalysisContribution Margin (CM) is the amount remaining from sales revenue after variable expenses have been deducted.The contribution income statement is helpful to managers in judging the impact on profits of changes in selling price, cost, or volume. The emphasis is on cost behavior.Basics of Cost-Volume-Profit AnalysisCM is used first to cover fixed expenses. Any remaining CM contributes to net operating income.The Contribution Approach Sales, variable expenses, and contribution margin can also be expressed on a per unit basis. If Racing sells an additional bicycle, $200 additional CM will be generated to cover fixed expenses and profit.The Contribution ApproachEach month, RBC must generate at least $80,000 in total contribution margin to break-even (which is the level of sales at which profit is zero).The Contribution ApproachIf RBC sells 400 units in a month, it will be operating at the break-even point.The Contribution ApproachIf RBC sells one more bike (401 bikes), net operating income will increase by $200.The Contribution ApproachWe do not need to prepare an income statement to estimate profits at a particular sales volume. Simply multiply the number of units sold above break-even by the contribution margin per unit.If Racing sells 430 bikes, its net operating income will be $6,000.CVP Relationships in Equation FormThe contribution format income statement can be expressed in the following equation:Profit = (Sales – Variable expenses) – Fixed expensesCVP Relationships in Equation FormThis equation can be used to show the profit RBC earns if it sells 401. Notice, the answer of $200 mirrors our earlier solution.Profit = (Sales – Variable expenses) – Fixed expenses401 units × $500401 units × $300$80,000Profit = ($200,500 – Variable expenses) – FixedProfit = ($200,500 – $120,300) – Fixed expensesProfit = ($200,500 – $120,300) – $80,000$200 = ($200,500 – $120,300) – $80,000CVP Relationships in Equation FormWhen a company has only one product we can further refine this equation as shown on this slide. Profit = (Sales – Variable expenses) – Fixed expensesProfit = (P × Q – V × Q) – Fixed expensesCVP Relationships in Equation FormThis equation can also be used to show the $200 profit RBC earns if it sells 401 bikes.Profit = (Sales – Variable expenses) – Fixed expensesProfit = (P × Q – V × Q) – Fixed expensesProfit = ($500 × 401 – $300 × 401) – $80,000$200 = ($500 × 401 – $300 × 401) – $80,000CVP Relationships in Equation FormUnit CM = Selling price per unit – Variable expenses per unitIt is often useful to express the simple profit equation in terms of the unit contribution margin (Unit CM) as follows:Profit = (P × Q – V × Q) – Fixed expensesProfit = (P – V) × Q – Fixed expensesProfit = Unit CM × Q – Fixed expensesUnit CM = P – VCVP Relationships in Equation FormProfit = (P × Q – V × Q) – Fixed expensesProfit = (P – V) × Q – Fixed expensesProfit = Unit CM × Q – Fixed expensesProfit = ($500 – $300) × 401 – $80,000Profit = $200 × 401 – $80,000Profit = $80,200 – $80,000Profit = $200This equation can also be used to compute RBC’s $200 profit if it sells 401 bikes.Learning Objective 2Prepare and interpret a cost-volume-profit (CVP) graph and a profit graph.CVP Relationships in Graphic FormThe relationships among revenue, cost, profit and volume can be expressed graphically by preparing a CVP graph. Racing Bicycle developed contribution margin income statements at 0, 200, 400, and 600 units sold. We will use this information to prepare the CVP graph.Preparing the CVP GraphUnitsDollarsIn a CVP graph, unit volume is usually represented on the horizontal (X) axis and dollars on the vertical (Y) axis. Preparing the CVP GraphUnitsDollarsDraw a line parallel to the volume axis to represent total fixed expenses.Preparing the CVP GraphUnitsDollarsChoose some sales volume, say 400 units, and plot the point representing total expenses (fixed and variable). Draw a line through the data point back to where the fixed expenses line intersects the dollar axis.Preparing the CVP GraphUnitsDollarsChoose some sales volume, say 400 units, and plot the point representing total sales. Draw a line through the data point back to the point of origin.Preparing the CVP GraphBreak-even point(400 units or $200,000 in sales)UnitsDollarsLoss AreaProfit AreaPreparing the CVP GraphProfit = Unit CM × Q – Fixed Costs An even simpler form of the CVP graph is called the profit graph. Preparing the CVP GraphBreak-even point, whereprofit is zero , is 400 units sold.Learning Objective 3Use the contribution margin ratio (CM ratio) to compute changes in contributionmargin and net operating income resulting fromchanges in sales volume.Contribution Margin Ratio (CM Ratio)$100,000 ÷ $250,000 = 40%The CM ratio is calculated by dividing the total contribution margin by total sales.Contribution Margin Ratio (CM Ratio)The contribution margin ratio at Racing Bicycle is:The CM ratio can also be calculated by dividing the contribution margin per unit by the selling price per unit.CM per unitSP per unitCM Ratio = = 40%$200$500=Contribution Margin Ratio (CM Ratio)A $50,000 increase in sales revenue results in a $20,000 increase in CM. ($50,000 × 40% = $20,000)If Racing Bicycle increases sales by $50,000, contributionmargin will increase by $20,000 ($50,000 × 40%).Here is the proof:Quick Check  Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. 2,100 cups are sold each month on average. What is the CM Ratio for Coffee Klatch?a. 1.319b. 0.758c. 0.242d. 4.139 Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. 2,100 cups are sold each month on average. What is the CM Ratio for Coffee Klatch?a. 1.319b. 0.758c. 0.242d. 4.139Quick Check Unit contribution marginUnit selling priceCM Ratio ==($1.49-$0.36)$1.49=$1.13$1.49= 0.758Contribution Margin Ratio (CM Ratio)The relationship between profit and the CM ratio can be expressed using the following equation:Profit = CM ratio × Sales – Fixed expensesProfit = 40% × $250,000 – $80,000Profit = $100,000 – $80,000Profit = $20,000If Racing Bicycle increased its sales volume to 500 bikes, what would management expect profit or net operating income to be?Learning Objective 4Show the effects on contribution margin of changes in variable costs, fixed costs, selling price, and volume.The Variable Expense RatioThe variable expense ratio is the ratio of variable expenses to sales. It can be computed by dividing the total variable expenses by the total sales, or in a single product analysis, it can be computed by dividing the variable expenses per unit by the unit selling price.Changes in Fixed Costs and Sales VolumeWhat is the profit impact if Racing Bicycle can increase unit sales from 500 to 540 by increasing the monthly advertising budget by $10,000?Changes in Fixed Costs and Sales Volume$80,000 + $10,000 advertising = $90,000Sales increased by $20,000, but net operating income decreased by $2,000.Changes in Fixed Costs and Sales VolumeA shortcut solution using incremental analysisChange in Variable Costs and Sales VolumeWhat is the profit impact if Racing Bicycle can use higher quality raw materials, thus increasing variable costs per unit by $10, to generate an increase in unit sales from 500 to 580?Change in Variable Costs and Sales Volume580 units × $310 variable cost/unit = $179,800Sales increase by $40,000, and net operating income increases by $10,200.Change in Fixed Cost, Sales Priceand VolumeWhat is the profit impact if RBC: (1) cuts its selling price $20 per unit, (2) increases its advertising budget by $15,000 per month, and (3) increases sales from 500 to 650 units per month? Sales increase by $62,000, fixed costs increase by $15,000, and net operating income increases by $2,000.Change in Fixed Cost, Sales Priceand Volume650 units × $480 = $312,000Change in Variable Cost, Fixed Costand Sales VolumeWhat is the profit impact if RBC: (1) pays a $15 sales commission per bike sold instead of paying salespersons flat salaries that currently total $6,000 per month, and (2) increases unit sales from 500 to 575 bikes? Change in Variable Cost, Fixed Costand Sales VolumeSales increase by $37,500, fixed expenses decrease by $6,000. Net operating income increases by $12,375.575 units × $315 = $181,125Change in Regular Sales PriceIf RBC has an opportunity to sell 150 bikes to a wholesaler without disturbing sales to other customers or fixed expenses, what price would it quote to the wholesaler if it wants to increase monthly profits by $3,000? Change in Regular Sales PriceLearning Objective 5Determine the level of sales needed to attain a target profit.Target Profit AnalysisWe can compute the number of units that must be sold to attain a target profit using either:Equation methodFormula method.Equation MethodProfit = Unit CM × Q – Fixed expensesOur goal is to solve for the unknown “Q” which represents the quantity of units that must be sold to attain the target profit.Target Profit AnalysisSuppose Racing Bicycle management wants to know how many bikes must be sold to earn a target profit of $100,000.Profit = Unit CM × Q – Fixed expenses$100,000 = $200 × Q – $80,000$200 × Q = $100,000 – $80,000Q = ($100,000 + $80,000) ÷ $200Q = 900The Formula MethodThe formula uses the following equation.Target profit + Fixed expensesCM per unit =Unit sales to attainthe target profitTarget Profit Analysis in Terms of Unit Sales Suppose Racing Bicycle Company wants to know how many bikes must be sold to earn a profit of $100,000.Target profit + Fixed expensesCM per unit =Unit sales to attainthe target profitUnit sales = 900$100,000 + $80,000$200Unit sales = Target Profit AnalysisWe can also compute the target profit in terms of sales dollars using either the equation method or the formula method.EquationMethodFormulaMethodOREquation MethodProfit = CM ratio × Sales – Fixed expensesOur goal is to solve for the unknown “Sales” which represents the dollar amount of sales that must be sold to attain the target profit.Suppose RBC management wants to know the sales volume that must be generated to earn a target profit of $100,000.$100,000 = 40% × Sales – $80,00040% × Sales = $100,000 + $80,000Sales = ($100,000 + $80,000) ÷ 40%Sales = $450,000Formula MethodWe can calculate the dollar sales needed to attain a target profit (net operating profit) of $100,000 at Racing Bicycle.Target profit + Fixed expenses CM ratio=Dollar sales to attainthe target profit Dollar sales = $450,000$100,000 + $80,00040%Dollar sales = Quick Check  Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. Use the formula method to determine how many cups of coffee would have to be sold to attain target profits of $2,500 per month.a. 3,363 cupsb. 2,212 cupsc. 1,150 cupsd. 4,200 cups Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. Use the formula method to determine how many cups of coffee would have to be sold to attain target profits of $2,500 per month.a. 3,363 cupsb. 2,212 cupsc. 1,150 cupsd. 4,200 cupsQuick Check Target profit + Fixed expensesUnit CMUnit salesto attaintarget profit = 3,363 cups=$3,800$1.13$2,500 + $1,300$1.49 - $0.36 ==Quick Check  Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. Use the formula method to determine the sales dollars that must be generated to attain target profits of $2,500 per month.a. $2,550b. $5,011c. $8,458d. $10,555 Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. Use the formula method to determine the sales dollars that must be generated to attain target profits of $2,500 per month.a. $2,550b. $5,011c. $8,458d. $10,555Quick Check Target profit + Fixed expensesCM ratioSales $to attaintarget profit = $5,011=$3,8000.758$2,500 + $1,300($1.49 – 0.36) ÷ $1.49==Learning Objective 6Determine the break-even point.Break-even AnalysisThe equation and formula methods can be used to determine the unit sales and dollar sales needed to achieve a target profit of zero. Let’s us the RBC information to complete the break-even analysis.Break-even in Unit Sales:Equation Method$0 = $200 × Q + $80,000Profits = Unit CM × Q – Fixed expensesSuppose RBC wants to know how many bikes must be sold to break-even (earn a target profit of $0). Profits are zero at the break-even point.Break-even in Unit Sales:Equation Method$0 = $200 × Q + $80,000$200 × Q = $80,000Q = 400 bikesProfits = Unit CM × Q – Fixed expensesBreak-even in Unit Sales:Formula Method Let’s apply the formula method to solve for the break-even point.Unit sales = 400$80,000$200Unit sales = Fixed expensesCM per unit =Unit sales to break evenBreak-even in Dollar Sales:Equation MethodSuppose Racing Bicycle wants to compute the sales dollars required to break-even (earn a target profit of $0). Let’s use the equation method to solve this problem.Profit = CM ratio × Sales – Fixed expensesSolve for the unknown “Sales.”Break-even in Dollar Sales:Equation MethodProfit = CM ratio × Sales – Fixed expenses$ 0 = 40% × Sales – $80,00040% × Sales = $80,000Sales = $80,000 ÷ 40%Sales = $200,000Break-even in Dollar Sales:Formula MethodNow, let’s use the formula method to calculate the dollar sales at the break-even point.Dollar sales = $200,000$80,00040%Dollar sales = Fixed expenses CM ratio=Dollar sales tobreak evenQuick Check Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. 2,100 cups are sold each month on average. What is the break-even sales dollars?a. $1,300b. $1,715c. $1,788d. $3,129 Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. 2,100 cups are sold each month on average. What is the break-even sales dollars? a. $1,300 b. $1,715 c. $1,788 d. $3,129Quick Check Fixed expensesCM RatioBreak-evensales $1,3000.758= $1,715==Quick Check Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. 2,100 cups are sold each month on average. What is the break-even sales in units? a. 872 cups b. 3,611 cups c. 1,200 cups d. 1,150 cups Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. 2,100 cups are sold each month on average. What is the break-even sales in units?a. 872 cupsb. 3,611 cupsc. 1,200 cupsd. 1,150 cupsQuick Check Fixed expensesCM per UnitBreak-even =$1,300$1.49/cup - $0.36/cup=$1,300$1.13/cup= 1,150 cups=Learning Objective 7Compute the margin of safety and explain its significance.The Margin of Safety in DollarsThe margin of safety in dollars is the excess of budgeted (or actual) sales over the break-even volume of sales.Margin of safety in dollars = Total sales - Break-even salesLet’s look at Racing Bicycle Company and determine the margin of safety.The Margin of Safety in DollarsIf we assume that RBC has actual sales of $250,000, given that we have already determined the break-even sales to be $200,000, the margin of safety is $50,000 as shown.The Margin of Safety PercentageRBC’s margin of safety can be expressed as 20% of sales.($50,000 ÷ $250,000)The Margin of SafetyThe margin of safety can be expressed in terms of the number of units sold. The margin of safety at RBC is $50,000, and each bike sells for $500; hence, RBC’s margin of safety is 100 bikes.Margin ofSafety in units== 100 bikes$50,000$500Quick Check  Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. 2,100 cups are sold each month on average. What is the margin of safety expressed in cups?a. 3,250 cupsb. 950 cupsc. 1,150 cupsd. 2,100 cups Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. 2,100 cups are sold each month on average. What is the margin of safety expressed in cups?a. 3,250 cupsb. 950 cupsc. 1,150 cupsd. 2,100 cupsQuick Check Margin of safety = Total sales – Break-even sales= 950 cups= 2,100 cups – 1,150 cupsCost Structure and Profit StabilityCost structure refers to the relative proportion of fixed and variable costs in an organization. Managers often have some latitude in determining their organization’s cost structure.Cost Structure and Profit StabilityThere are advantages and disadvantages to high fixed cost (or low variable cost) and low fixed cost (or high variable cost) structures.An advantage of a high fixedcost structure is that incomewill be higher in good yearscompared to companieswith lower proportion offixed costs.A disadvantage of a high fixedcost structure is that incomewill be lower in bad yearscompared to companieswith lower proportion offixed costs.Companies with low fixed cost structures enjoy greater stability in income across good and bad years.Learning Objective 8Compute the degree of operating leverage at a particular level of sales and explain how it can be used to predict changes in net operating income.Operating Leverage Operating leverage is a measure of how sensitive net operating income is to percentage changes in sales. It is a measure, at any given level of sales, of how a percentage change in sales volume will affect profits. Contribution marginNet operating incomeDegree ofoperating leverage=Operating Leverage$100,000 $20,000= 5Degree ofOperatingLeverage=To illustrate, let’s revisit the contribution income statement for RBC. Operating LeverageWith an operating leverage of 5, if RBC increases its sales by 10%, net operating income would increase by 50%.Here’s the verification!Operating Leverage10% increase in sales from$250,000 to $275,000 . . .. . . results in a 50% increase inincome from $20,000 to $30,000.Quick Check  Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. 2,100 cups are sold each month on average. What is the operating leverage?a. 2.21b. 0.45c. 0.34d. 2.92 Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. 2,100 cups are sold each month on average. What is the operating leverage?a. 2.21b. 0.45c. 0.34d. 2.92Quick Check Contribution marginNet operating incomeOperating leverage =$2,373$1,073== 2.21Quick Check At Coffee Klatch the average selling price of a cup of coffee is $1.49, the average variable expense per cup is $0.36, the average fixed expense per month is $1,300 and an average of 2,100 cups are sold each month.If sales increase by 20%, by how much should net operating income increase?a. 30.0%b. 20.0%c. 22.1%d. 44.2%At Coffee Klatch the average selling price of a cup of coffee is $1.49, the average variable expense per cup is $0.36, the average fixed expense per month is $1,300 and an average of 2,100 cups are sold each month.If sales increase by 20%, by how much should net operating income increase?a. 30.0%b. 20.0%c. 22.1%d. 44.2%Quick Check Verify Increase in ProfitStructuring Sales CommissionsCompanies generally compensate salespeople by paying them either a commission based on sales or a salary plus a sales commission. Commissions based on sales dollars can lead to lower profits in a company.Let’s look at an example.Structuring Sales CommissionsPipeline Unlimited produces two types of surfboards, the XR7 and the Turbo. The XR7 sells for $100 and generates a contribution margin per unit of $25. The Turbo sells for $150 and earns a contribution margin per unit of $18.The sales force at Pipeline Unlimited is compensated based on sales commissions.Structuring Sales CommissionsIf you were on the sales force at Pipeline, you would push hard to sell the Turbo even though the XR7 earns a higher contribution margin per unit.To eliminate this type of conflict, commissions can be based on contribution margin rather than on selling price alone.Learning Objective 9Compute the break-even point for a multiproduct company and explain the effects of shifts in the sales mix on contribution margin and the break-even point.The Concept of Sales MixSales mix is the relative proportion in which a company’s products are sold.Different products have different selling prices, cost structures, and contribution margins.When a company sells more than one product, break-even analysis becomes more complex as the following example illustrates. Let’s assume Racing Bicycle Company sells bikes and carts and that the sales mix between the two products remains the same.Multi-Product Break-Even AnalysisBikes comprise 45% of RBC’s total sales revenue and the carts comprise the remaining 55%. RBC provides the following information:$265,000 $550,000= 48.2% (rounded)Multi-Product Break-Even AnalysisFixed expenses CM ratio=Dollar sales to break evenDollar sales tobreak even$170,00048.2%== $352,697Key Assumptions of CVP Analysis Selling price is constant. Costs are linear and can be accurately divided into variable (constant per unit) and fixed (constant in total) elements. In multiproduct companies, the sales mix is constant. In manufacturing companies, inventories do not change (units produced = units sold).End of Chapter 6