Prepared by Diane Tanner University of North Florida ACG Multi-Product CVP 4-4

Product Profitability Considerations If customers prefer to buy one product unit and do not care which one they buy 2 2  Focus on profitability per unit of product  ‘Push’ the product with the higher contribution margin per unit Goal = To generate the largest profit If customers prefer to spend a fixed sum of money and do not care which products they buy  Focus on profitability per sales dollar  Push the product with the higher contribution margin ratio (i.e., the highest profit out of each sales dollar)

Sales Mix BucketsPails Units2,0008,000 Sales$4,000$6,000 Expenses$1,600$3,500 Profit$2,400$2,500  What is sales mix?  The relative proportion in which a company’s products are sold  Based on the premise that different products have different selling prices, cost structures, and contribution margins  Two ways to express 3 Revenue sales mix 4000 : : 3 Unit sales mix 2000 : : 4

Approaches to Multiproduct CVP 4  Weighted average approach  Also known as the contribution approach  Based on the weighted average contribution margin for all products combined  Bundle approach  Based on the unit contribution margins of each product weighted by the sales mix Both can be used to calculate units or sales revenue at breakeven or target profit

Weighted Average Approach Breakeven in Units 5  Calculate the weighted average contribution margin (WACM) per unit Total CM / total units  Use the WACM per unit in the profit equation to calculate breakeven point in units  This breakeven point is for all products  Calculate the unit sales mix  Multiply the sales mix proportion (a fraction) by the unit breakeven point for each product  Round up to nearest full unit Both are based on units

Weighted Average Approach Breakeven in Revenue Dollars 6  Calculate the weighted average contribution margin (WACM) ratio Total CM / Total sales revenue  Use the WACM ratio in the profit equation to calculate the breakeven point in sales revenue  This is the sales revenue breakeven point for all products  Calculate the revenue sales mix  Multiply the sales mix proportion (a fraction) by the revenue breakeven point for each product Both are based on sales revenue

Weighted Average Approach Breakeven in Units 7 DonutsBagelsTotal 4,5005,50010,000 Sales$6,750100%$11,000100%$17,750100% Variable costs3,24048%4,62042%7,86052% Contribution margin$3,51052%$6,38058%9,89048% Fixed costs5,450 Profit$4,440 How many units of each product must be sold to break even? Weighted-average CM per unit = $9,890/10,000 = $0.989 per unit BEP in units = SPx – VCx – TFC = Profit CMx - TFC = Profit 0.989x – 5,450 = 0 X = 5, total units Donuts: 9/20 × 5, = 2, = 2,480 units Bagels: 11/20 × 5, = 3, = 3,031 units Donuts: 9/20 × 5, = 2, = 2,480 units Bagels: 11/20 × 5, = 3, = 3,031 units Unit sales mix = 4,500 : 5,500  9 : 11

Weighted Average Approach Breakeven in Revenue Dollars 8 DonutsBagelsTotal 4,5005,50010,000 Sales$6,750100%$11,000100%$17,750100% Variable costs3,24048%4,62042%7,86052% Contribution margin$3,51052%$6,38058%9,89048% Fixed costs5,450 Profit$4,440 How much is revenue for each product at break even? Weighted-average CM ratio = $9,890/17,750 = % BEP in revenue = SPx – VCx – TFC = Profit CMx - TFC = Profit x – 5,450 = 0 X = $9, Donuts: 27/71 × $9, = $3, = $3,720 Bagels: 44/71 × $9, = $6, = $6,062 Donuts: 27/71 × $9, = $3, = $3,720 Bagels: 44/71 × $9, = $6, = $6,062 Revenue sales mix = 6,750 : 11,000  27 : 44

Bundle Approach  Determine the unit contribution margin for each product  Determine the unit sales mix  Set up a profit equation that uses these components of each product: (CM1)(SM1)x + (CM2)(SM2)x – TFC = profit * Where CM = contribution margin, and SM = sales mix *Assumes two products  The answer is a ‘bundle’ amount. Multiply the sales mix (whole number) for each product separately by the ‘bundle’ amount.  To determine breakeven in sales dollars, multiply the BE units by the selling price per unit 9

Bundle Approach-Breakeven BeefPork Unit selling price$5.50$4.00 Unit variable costs Total allocated fixed costs12,00011,200 Los Foodo produces two varieties of tacos, beef and pork. The company currently sells 3 beef to every 5 pork tacos and predicts its sales mix to remain steady. Information regarding these products for May follows: CM per unit–Beef = $ $3.08 = $2.42 CM per unit–Pork = $ $2.08 = $1.92 How many units of each product must be sold to break even? Beef = 4,129 × $5.50 = $22,710 Pork = 6,881 × $4.00 = $27,524 Units Sales Revenue (Dollars) Sales mix in units 3 : 5 Sales mix in units 3 : 5 (2.42x)(3) + (1.92x)(5) – 23,200 = 0 X = 1, bundles Beef = 3 × 1, = 4, = 4,129 beef tacos Pork = 5 × 1, = 6, = 6,881 pork tacos

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