Math

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Stan's Cans, Inc. expects to earn $150,000 next year after taxes on sales of $2,200,000. Stan's manufactures only one size of garbage can and is located in the small, but beautiful, town of Mount Dora, Florida. Stan sells his cans for $8 a piece and they have a variable cost of $2.40 a piece. Stan's tax rate is currently 34%.


a. What are the firm's expected fixed costs for next year?



b. What is the break-even point in units?

  • Math -

    after-tax revenue = 66% of 2,200,000 = 1452000

    revenue from n cans = 8n
    cost for n cans is f + 2.4n
    where f is the fixed cost.
    after-tax income = 8n*.66 = 5.28n
    earnings = income less expenses

    2200000/8 = 275000 cans
    150000 = 1452000 - f - 2.4(275000)
    150000 = 792000 - f
    f = 642000

    So, earnings = 5.28n - f - 2.4n
    = 2.88n - 642000

    at breakeven, earnings = 0, so

    0 = 2.88n - 642000
    n = 222916.6, or 222917

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