CVP Analysis: Break-Even, Contribution Margin & Target Profit

Learn cost-volume-profit (CVP) analysis from the operating income equation through break-even and target-profit examples. Professor Farhat derives contribution margin per unit, the contribution margin ratio, required sales dollars and the after-tax profit formula for accounting students, CMA candidates and CPA BAR candidates. CORRECTION FOR THE AFTER-TAX EXAMPLE At 18:04–20:56, the recording mixes rounded units and sales amounts. With a $10 price, $6 variable cost, $3,000 fixed cost and a 30% assumed tax rate, earning at least $5,000 after tax requires 2,536 whole units. Selling 2,535 units gives only $4,998 after tax. The consistent calculation appears below. CHAPTERS 00:00 What cost-volume-profit analysis shows 00:55 Fixed, variable and mixed costs in the model 02:05 Derive the operating income equation 04:26 Contribution margin per unit 05:31 Rearrange the formula to solve for units 07:02 Example: units needed for $5,000 profit 08:55 Break-even units and sales dollars 10:29 How contribution margin covers fixed costs 12:47 Contribution margin ratio and break-even sales 14:43 Check break-even with an income statement 15:43 After-tax target profit: gross up first 18:04 Required units: see rounding correction below 18:49 Check the after-tax example: corrected amounts below 21:24 Contribution margin formula review 23:07 Break-even and target-profit shortcuts 24:02 Emma example: required sales dollars 25:17 Read the break-even graph 26:55 After-tax formula recap 27:53 Review and study practice CORE CVP FORMULAS Operating income = (selling price − variable cost per unit) × units sold − fixed cost. Contribution margin per unit = selling price − variable cost per unit. Contribution margin ratio = contribution margin per unit ÷ selling price. Break-even units = fixed cost ÷ contribution margin per unit. Break-even sales dollars = fixed cost ÷ contribution margin ratio. Target-profit units = (fixed cost + target pretax profit) ÷ contribution margin per unit. Target-profit sales dollars = (fixed cost + target pretax profit) ÷ contribution margin ratio. EXAMPLE 1: $10 PRICE, $6 VARIABLE COST, $3,000 FIXED COST Contribution margin is $4 per unit, or 40% of sales. Break-even: $3,000 ÷ $4 = 750 units = $7,500 sales. To earn $5,000 before tax: ($3,000 + $5,000) ÷ $4 = 2,000 units. Each unit's contribution first covers fixed costs; after break-even, additional contribution increases operating profit within the model's assumptions. Contribution margin is not the same measure as gross profit. CORRECTED AFTER-TAX CALCULATION Pretax target = after-tax target ÷ (1 − tax rate). $5,000 ÷ 0.70 = $7,142.857143. Required units = ($3,000 + $7,142.857143) ÷ $4 = 2,535.714286. Round UP to 2,536 if units must be sold whole. Check at 2,536 units: Sales: 2,536 × $10 = $25,360 Variable cost: 2,536 × $6 = $15,216 Pretax profit: $25,360 − $15,216 − $3,000 = $7,144 After-tax profit: $7,144 × 70% = $5,000.80 For comparison, 2,535 units produce $25,350 sales and $7,140 pretax profit, leaving $4,998 after tax. Divide by ONE MINUS the tax rate when grossing up; the result is required pretax profit, not required revenue. The 30% rate is an exercise assumption. EMMA EXAMPLE & GRAPH With $2,000 fixed cost and a 40% contribution margin ratio: Break-even sales = $5,000. Sales for $2,000 pretax profit = $10,000. Sales for $3,000 pretax profit = $12,500. The graph uses a $200 selling price and $120 variable cost, so $80 contribution per unit gives $2,000 ÷ $80 = 25 break-even units, or $5,000 sales. Convert $5,000 sales to units by dividing by $200, not by 25. MODEL ASSUMPTIONS These examples use constant selling price and variable cost per unit, fixed total cost within the relevant range, and one product. A multiple-product model also requires an appropriate sales-mix assumption. The simplified tax example treats operating profit as pretax profit without separate financing or other nonoperating items. Mixed costs must be separated into fixed and variable components to use this model. This lesson does not work high-low, regression, margin-of-safety or multiple-product calculations. CONTINUE STUDYING CVP, Break-Even & Target Profit:    • CVP Analysis Explained: Break-Even, Contri...   Cost-Volume-Profit & After-Tax Income:    • Cost-Volume-Profit Analysis: Break-Even, T...   More lectures and practice: https://farhatlectures.com #CVPAnalysis #CostAccounting #CMAExam