Problem #$2($Multiple$-$Product CVP$)$

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A company sells two products: a standard model and a deluxe model.$$ The standard model sells for $$50$ and has a contribution margin ratio of $40\%.$ The deluxe model sells for $$100$ and has a contribution margin ratio of $50\%.$ Last year, the company sold $5000$ standard units and $2500$ deluxe units.

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There is $$200,000$ of cost that is $$fixed$$ in the sense that it does not vary with the number of units produced.$$ However, $$100,000$ of this cost is Direct Fixed Costs that are allocated between products as $80\%$ to the deluxe product, while $20\%$ is allocated to the standard model.$$ The remaining $$100,000$ is Allocated Fixed Costs that are allocated equally between the two products.

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$1.$ In the space below, complete the following segmented income statement to calculate profit by product$-$line and for the overall company.

$$ Standard$$ Deluxe $$ Total$\_\_\_$

Sales$5000*50=250,0002500*100=250,000500,000$

VariableCost$\_\_\_\_\_\_\_\_\_5000*30=150,000\_\_\_\_\_2500*50=125,000\_\_\_\_\_\_\_275,000$

Contribution Margin$5000*20=100,0002500*50=125,000225,000$

Direct Fixed Costs$\_\_\_\_\_20,000\_\_\_\_\_\_\_\_\_\_80,000\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_100,000\_\_$

Segment Margin$80,00045,000125,000$

Allocated Fixed Costs$\_\_50,000\_\_\_\_\_\_\_\_\_\_\_\_\_50,000\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_100,000\_$

Pre$-$Tax Profit$30,000(5,000)25,000$

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$2.$ If the sales mix stays the same as last year, how many standard and deluxe units would have to be sold next year in order to earn $$42,000$ after taxes of $40\%?$

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Sales$250,000(5,000*$ $$50)$

Variable Cost$150,000(5,000*(50*0\mathrm{.}6))$

Contribution Margin $100,000(5,000*(50*0\mathrm{.}4))$

Direct Fixed Costs$20,000(100,000*0\mathrm{.}2)$

Segment Margin $80,000(100,00020,000)$

Fixed Costs $$ Allocated$50,000$

Pre$-$Tax Profit$30,000(80,00050,000)$

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$3.$If the sales mix stays the same as last year, what sales from standard and deluxe models would have to be in order to earn $$42,000$ after taxes of $40\%?$

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$4.$ Assume that the company decided to eliminate the deluxe model with the hope of increasing their profit by $$5,000.$ Once again, they were disappointed to find that their expected results did not materialize.$$ In the space below, compute the effect on profit of eliminating the deluxe model and briefly explain the flaw in the company$$s plan.$$

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