Questions Addressed by Cost-Volume-Profit Analysis
CVP analysis is used to answer questions such 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?

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Cost-Volume-Profit AnalysisChapter19 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 AnalysisNumber of Local CallsMonthly Basic Telephone BillTotal fixed costs remain unchangedwhen activity changes.Your monthly basictelephone bill probablydoes not change whenyou make more local calls.Total Fixed CostNumber of Local Calls Monthly Basic Telephone Bill per Local CallFixed costs per unit declineas activity increases.Your average cost perlocal call decreases asmore local calls are made.Fixed Cost Per UnitMinutes TalkedTotal Long DistanceTelephone BillTotal variable costs changewhen activity changes.Your total long distancetelephone bill is basedon how many minutesyou talk.Total Variable CostMinutes TalkedPer MinuteTelephone Charge Variable costs per unit do not changeas activity increases. The cost per long distanceminute talked is constant.For example, 10cents per minute.Variable Cost Per UnitCost Behavior Summary 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 chargeFixed service feeVariable charge perkilowatt hour used Mixed CostsVariable Utility ChargeActivity (Kilowatt Hours) Total Utility CostTotal mixed costFixed MonthlyUtility ChargeSlope isvariable costper unitof activity.Mixed CostsActivityCostTotal cost remainsconstant within anarrow range ofactivity.Stair-Step CostsActivityCostTotal cost increases to a new higher cost for the next higher range of activity. Stair-Step CostsTotal CostRelevant RangeA straight line closely (constant unit variable cost)approximates acurvilinear variablecost line withinthe relevant range. Volume of OutputCurvilinearCost FunctionCurvilinear CostsLet’s extend ourknowledge ofcost behavior to CVP analysis.Cost-Volume-Profit(CVP) AnalysisThe 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 PointContribution margin is amount by which revenue exceeds the variable costs of producing the revenue.Computing Break-Even PointHow much contribution margin must this company have to cover its fixed costs (break even)?Computing Break-Even PointHow much contribution margin must this company have to cover its fixed costs (break even)?Answer: $30,000Computing Break-Even PointHow many units must this company sell to cover its fixed costs (break even)?Computing Break-Even PointHow many units must this company sell to cover its fixed costs (break even)?Answer: $30,000 ÷ $20 per unit = 1,500 unitsComputing Break-Even PointWe have just seen one of the basic CVP relationships – the break-even computation.Break-even point in units = Fixed costsContribution margin per unitFinding the Break-Even PointUnit sales price less unit variable cost($20 in previous example)Formula for ComputingBreak-Even Sales (in Units)The break-even formula may also be expressed in sales dollars.Break-even point in dollars = Fixed costsContribution margin ratio Unit sales price Unit variable costFormula for ComputingBreak-Even Sales (in Dollars)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 1ABC 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 unitsComputing Break-Even SalesQuestion 1 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 = $2.00Contribution margin ratio = $2.00 ÷ $5.00 = .40Break-even revenue = $200,000 ÷ .4 = $500,000Computing Break-Even SalesQuestion 2Volume in UnitsCosts and Revenuein DollarsRevenue Starting at the origin, draw the total revenueline with a slope equal to the unit sales price.Total fixed cost Total fixed costextends horizontallyfrom the vertical axis.Preparing a CVP GraphTotal costVolume in UnitsCosts and Revenuein DollarsTotal fixed costBreak-even PointProfitLoss Draw the total cost line with a slopeequal to the unit variable cost.RevenuePreparing a CVP Graph Break-even formulas may be adjusted to show the sales volume needed to earnany amount of operating income. Unit sales = Fixed costs + Target incomeContribution margin per unit Dollar sales = Fixed costs + Target incomeContribution margin ratioComputing 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 Computing Sales Needed to Achieve Target Operating IncomeABC 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 unitsUnit contribution = $5.00 - $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 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 salesOperating 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 = $8,000What 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 operating income = $15,000 × .40 = $6,000 Change in Change in Contributionoperating income sales volume margin ratio=×What Change in Operating Income Do We Anticipate?Business Applications of CVP 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 CVP550 × $300$80K + $12KNo, income is decreased.550 × $500Business Applications of CVP Should CyclCo spend $12,000 on advertising to increase sales by 10 percent? 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?Business Applications of CVP625 × $300$80K + $12KIncome is decreased even more.625 × $450Now, 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 × 500Business Applications of CVPBusiness Applications of CVPNow, 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? The combination of advertising, a price cut,and change in compensation increases income.750 × $325$92K - $50K750 × $450Business Applications of CVPNow, 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 Different products with different contribution margins. Determining semivariablecost elements. Complying with theassumptions of CVP analysis.Additional Considerations in CVPSales 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 ProductsCyclCo provides us with the following information:CVP Analysis When a Company Sells Many ProductsThe overall contribution margin ratio is: $265,000 $550,000= 48% (rounded)CVP Analysis When a Company Sells Many ProductsBreak-even in sales dollars is: $170,000 .48= $354,167 (rounded)CVP Analysis When a Company Sells Many ProductsOwlCo 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 Unit variable cost = = = $0.90 per unitin costin units$3,600 4,000The High-Low Method Unit variable cost = = = $0.90 per unit Fixed cost = Total cost – Total variable cost in costin units$3,600 4,000The High-Low Method 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 costin units$3,600 4,000The High-Low Method 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 costin units$3,600 4,000The High-Low MethodIf 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 MethodQuestion 1If 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 unitThe High-Low MethodQuestion 1If 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 MethodQuestion 2If 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 MethodQuestion 2 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 AnalysisEnd of Chapter 19