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## Cost-Volume-Profit Analysis

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**Cost-Volume-Profit Analysis**Cost-Volume-Profit (CVP) Analysis - the study of the interrelationships between costs and volume and how they impact profit. I can’t make a good marketing decision without understanding the CVP relationships.**setting prices for products and services.**introducing a new product or service. replacing a piece of equipment. deciding whether a given product or service should be made within the firm or purchased outside the firm. performing strategic “what if?” analyses. Cost-Volume-Profit Analysis CVP aids management in . . .**Cost-Volume-Profit Analysis**Profit = Revenues - Total Costs or Revenues = Fixed Costs + Variable Costs + Profits or (Units sold × Price) =Fixed Cost + (Units sold × Unit Variable Cost) + Profit**Cost-Volume-Profit Analysis**Q = units sold v = unit variable cost f = total fixed cost p = unit selling price N = operating profit The CVP Model: (p × Q) = f + (v × Q) + N**The total contribution marginis the unit contribution margin**multiplied by the number of units sold. The Contribution Margin andContribution Income Statement The unit contribution margin is the difference between unit sales price and unit variable cost, and is a measure of the increase in profit for a unit increase in sales. p – v = Unit contribution margin**Fixed cost $5,000 $60,000**Desired operating profit $4,000 $48,000 Price $37,500 $450,000 $75 Variable cost $17,500 $210,000 $35 Planned production 250 units 3,000 units Planned Sales 250 units 3,000 units The Contribution Margin andContribution Income Statement Household Furnishings, Inc. Per Monthly Annual Unit**The Contribution Margin andContribution Income Statement**Household Furnishings, Inc. 2,400 units × $75 = $180,000**The Contribution Margin andContribution Income Statement**Household Furnishings, Inc. $15,000 × 53.33% = $8,000**What if the expected level of profit at a give sales volume?**What additional amount of sales is needed to achieve a desired level of profit? What will be the effect on profits of a given increase in sales? What is the required funding level for a governmental agency, given desired service level? Is the forecast for sales consistent with forecasted profits? What additional profit would be obtained from a given percentage of reduction in unit variable costs? Strategic Role of CVP Analysis**CVP Analysis forBreakeven Planning**The Equation Method:Break-Even in Units $75 × Q = $5,000 + ($35 × Q) Selling priceper unit Total fixed cost Variable costper unit**CVP Analysis forBreakeven Planning**The Equation Method:Break-Even in Units $75 × Q = $5,000 + ($35 × Q) ($75 - $35) × Q = $5,000 Q = $5,000 ÷ $40 Q = 125 units per month**CVP Analysis forBreakeven Planning**The Equation Method:Break-Even in Dollars Y = (v ÷ p) × Y + f + N**CVP Analysis forBreakeven Planning**The Equation Method:Break-Even in Dollars Y = (.4667) × Y + f + N $210,000 ÷ $450,000**CVP Analysis forBreakeven Planning**The Equation Method:Break-Even in Dollars Y = (.4667) × Y + f + N Y = .4467 × Y + $5,000 + 0 Y = $9,375 per month**CVP Analysis forBreakeven Planning**Contribution Margin Method f p -v Q = $5,000 $75 - $35 Q = Q = 125 units per month**The CVP Graph**Total Revenue Total Revenue Total Cost Cost or Revenue Total Cost 0 (5,000) Output Volume Q = 125 Breakeven Point**Profit-Volume Graph**Profits Profits Total Cost 0 Output Volume Q = 125 Losses 25,000 50,000 75,000**CVP Analysis forBreakeven Planning**Contribution Margin Method f (p - v) ÷ p p × Q = $5,000 ($75 - $35) ÷ $75 p × Q = p × Q = $9,375 per month**f + N**(p – v) f + N (p – v) ÷ p Revenue Planning Management wants to know the sales volume necessary to achieve $48,000 in annual profit. Breakeven in units = Breakeven in dollars =**$60,000 + $48,000$75 – $35**Breakeven in units = Revenue Planning Management wants to know the sales volume necessary to achieve $48,000 in annual profit. f + N (p – v) Breakeven in units = Breakeven in units = 2,700 units per year**Trade-offs BetweenFixed and Variable Costs**Management is considering a new piece of equipment that will reduce variable costs but also increase fixed costs by $2,500 per month. Annual sales are currently 2,700 units. How much will unit variable cost have to fall to maintain the current level of profit, assuming sales volume and other factors remain the same? Q = 2,700 unitsp = $75v = unknownf = ($5,000 + $2,250)×12 = $87,000N = $48,000**(f + N)Q**v = p – ($87,000 + $48,000)2,700 v = $75 – = $25 Trade-offs BetweenFixed and Variable Costs Management is considering a new piece of equipment that will reduce variable costs but also increase fixed costs by $2,500 per month. Annual sales are currently 2,700 units. How much will unit variable cost have to fall to maintain the current level of profit, assuming sales volume and other factors remain the same?**Sales Commissions and Salaries**Management finds that $1,000 of the $5,000 monthly fixedcosts is sales salaries, and that $7.50 of the $35 variablecost is sales commissions. If salaries are increased to $1,450, how much would sales commission rate need to be decreasedto keep profits the same? v = r × $75 + $27.50 Original $35 - $7.50 (10% of $75)**Sales Commissions and Salaries**Management finds that $1,000 of the $5,000 monthly fixedcosts is sales salaries, and that $7.50 of the $35 variablecost is sales commissions. If salaries are increased to $1,450, how much would sales commission rate need to be decreasedto keep profits the same? v = r × $75 + $27.50 Fixed costs will increase by $450 per month and variable costs will decrease. f = $5,000 + $450 = $5,450**Sales Commissions and Salaries**Managers would have to reduce the commission rate from 10% to 7.33% to keep profits the same if the salespeople’s salaries are increased by $450. $65,400 - $48,000 2,700 r × $75 + $27.50 = $75 – r = .0733**N**(1 - t ) f + p - v Q = $48,000/(1 - .2) $75 - $35 Including Income Taxesin CVP Analysis t = tax rate If the company is subject to a 20% tax rate. Q = $60,000 + Q = 3,000 units per year**Sensitivity Analysis of CVP Results**What-if Sensitivity Analysis Management may look at changes in unit variable cost, total fixed costs or unit selling price on profits. Look at the analysis below:**Margin of Safety =**Planned Sales - Breakeven Sales Margin of Safety = 3,000 units - 1,500 units Margin of Safety = 1,500 units Sensitivity Analysis of CVP Results Margin of Safety**CVP Graph for a Firm with Relatively High Fixed Costs**$1.5 $.5 Total Revenue Losses @ 25,000 units = – 25,000 x $10 = – $250,000 Cost or Revenue(in millions) Total Cost Fixed cost/yr. $500,000 Variable cost/ unit $2 Price $12 Contribution margin $10 25,000 50,000 75,000 Output in Units**CVP Graph for a Firm with Relatively High Fixed Costs**Profits @ 75,000 units = 25,000 x $10 = $250,000 $1.5 $.5 Total Revenue Cost or Revenue(in millions) Total Cost Fixed cost/yr. $500,000 Variable cost/ unit $2 Price $12 Contribution margin $10 25,000 50,000 75,000 Output in Units**CVP Graph of a Firm withRelatively Low Fixed Costs**$1.5 $.5 Total Revenue Total Cost Losses @ 25,000 units = -25,000 x $3 = -$75,000 $1.0 Cost or Revenue(in millions) Fixed cost/yr. $150,000 Variable cost/ unit $9 Price $12 Contribution margin $3 $ .l5 Output in Units 25,000 50,000 75,000**CVP Graph of a Firm withRelatively Low Fixed Costs**$1.5 $.5 Profits @ 75,000 units = 25,000 x 3 = $75,000 Total Revenue Total Cost $1.0 Cost or Revenue(in millions) Fixed cost/yr. $150,000 Variable cost/ unit $9 Price $12 Contribution margin $3 $ .l5 Output in Units 25,000 50,000 75,000**CVP Analysiswith Multiple Products**Here is information about two surfboard models manufactured:**CVP Analysiswith Multiple Products**• Assume a Constant Sales Mix The product mix inunits sold is 1.5 Pro : 1 Hang Ten**Hang Ten 1.0 × $62.50 = $62.50**Pro 1.5 × $150.00 = 225.00 Total contribution $287.50 $38,750.00 $287.50 X = = 135 packages(rounded) CVP Analysiswith Multiple Products • Assume a Constant Sales Mix**135 packages(rounded)**X = CVP Analysiswith Multiple Products • Assume a Constant Sales Mix Nose-to-Toes uses a weighted-average product mix to calculate break-even.**CVP Analysiswith Multiple Products**Here is the calculation of Nose-to-Toes’ average contribution margin . . . 1.0 ÷ 2.5 = 40% 40% × $62.50 = $25.00**$38,750**$115 = 337 boards(rounded) X = CVP Analysiswith Multiple Products We find the break-even point as follows . . .**CVP Analysis withStep Cost Behavior**Revenues, Total Costs Total Revenue Total Cost $100,000 Losses Output in Units 10,000 20,000 25,000 30,000**CVP Analysis withStep Cost Behavior**There is no breakeven below the 10,000 unit level of output. Revenues, Total Costs Total Revenue $100,000 Losses Output in Units 10,000 20,000 25,000 30,000**Assumptions and Limitationsof CVP Analysis**• Linearity and the Relevant Range • Identifying Fixed and Variable Cost for CVP Analysis