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    Units of Each Product to Achieve Required Income After-Tax

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    Company. sells 4 different products in a mix of 9:5:4:2 respectively. The sales prices, respectively, are $13, $17, $10 and $12. Product A has variable costs of $8 and product B of $12. The contribution margin percentage for C is 40% and for D 25%. Fixed costs are $460,000. In the coming year the company wants to make a profit of $96,600 after tax. The tax rate is 30%.
    Required: 1. Determine the units of each product which must be sold to achieve the required income after tax.
    2. Prepare an income statement which proves that your answer in # 1 is correct.

    Here is what I have determined thus far. Please advise if I am going in the right direction. This is graduate level work.

    Products A B C D
    Sales 13 17 10 12
    V/C 8 12 ? ?
    Mix 9 5 4 2
    CM % ? ? 40 25

    Contribution Margin for Product A = 13-8/13 = 38%
    Contribution Margin for Product B = 17-12/17= 29%
    Variable Cost for Product C = 10 - (.40 X 10) = 6
    Variable Cost for Product D = 12 - (.25 X 12) = 9
    Products A B C D
    Sales 13 17 10 12
    V/C 8 12 6 9
    Mix 9 5 4 2
    CM % 38 29 40 25

    Break Even = FC/CM
    FC = $460,000
    CM = ?
    Total Contribution Margin = (9 X 38) + (5 X 29) + (4 X 40) + (2 X 25) = 697
    Break Even = 460,000/697 = 659.97

    The number of product A that must be sold to Break Even = 659.97 X 9 = 5,939.73 Dollars Equal $77,216.49
    The number of product B that must be sold to Break Even = 659.97 X 5 = 3,299.85 Dollars Equal $56,097.45
    The number of product C that must be sold to Break Even = 659.97 X 4 = 2,639.88 Dollars Equal $26,398.80
    The number of product D that must be sold to Break Even = 659.97 X 2 = 1,319.94 Dollars Equal $15,839.28
    Total Units of all products that must be sold to Break Even = 13,199.40 Dollars Equal $175,552.02

    Check Work:
    Average CM = 697 / 20 = 34.85
    FC/ Average CM = 460,000/ 34.85 = 13,199.43 (Total Units Needed to be sold)
    A = 13,199.43 X 9 =

    Profit after tax = 96,600 Tax Rate = 30% 96,600 / 1-.30 = 138,000
    CHECK WORK = 138,000 X .30 = 41,400 - 138,000 = 96,600
    New BE or Profit after Tax = FC + Profit / CM = 460,000 + 138,000 / 697 = 857.96

    The number of product A that must be sold to Break Even or Make After Tax Profit =857.96 X 9 = 7,721.64
    The number of product A that must be sold to Break Even or Make After Tax Profit =857.96 X 5 = 4,289.80
    The number of product A that must be sold to Break Even or Make After Tax Profit =857.96 X 4 = 3,431.84
    The number of product A that must be sold to Break Even or Make After Tax Profit =857.96 X 2 = 1,715.92
    Total Units of all products that must be sold to Break Even or Make After Tax Profit = 17,159.20

    Check Work:
    Average CM = 697 / 20 = 34.85
    FC/ Average CM = 460,000 + 138,000 / 34.85 = 17,159.25 (Total Units Needed to be sold)
    A = 17,159.25 X 9 = 154,433.25

    Income Statement
    Product A Product B Product C Product D
    Sales 77,216.49 56,097.45 26,398.80 15,839.28
    Variable Cost 47,517.84 39,598.20 15,839.28 11,879.46
    Contribution Margin 29,698.65 16,499.25 10,559.52 3,959.82
    Fixed Expenses 46,0000 46,0000 46,0000 46,0000
    Net Operating Income.

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    https://brainmass.com/business/accounting/units-product-achieve-required-income-after-tax-486284

    Solution Summary

    The solution assists in determines the units of each product to achieve required income after-tax.

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