Sales (120,000 units) $7,500,000 Less: variable expenses $3,450,000 Contribution

Question

Sales (120,000 units)    $7,500,000

Less: variable expenses $3,450,000

Contribution margin       $ 4,050,000

Less: fixed expenses        $3,375,000

Operating income             $ 675,000

Calculate contribution mark per unit, and the break even point per unit

Contribution mark per unit=

Break even point per unit =

Compute the contribution margin ratio and calculate break-even point in sales dollars.

Contribution ration=

Break even in sales=

Using the original information, if sales revenue increased by $540,000. How much would profits increase?

How many units must be sold to earn an after tax profit of $1,254,000? Assume a tax rate is 34%

Compute the margin of safety in dollars based on the given income statement.

Explanation / Answer

Contribution margin per unit = Total contribution margin / Number of units sold = 4,050,000 / 120,000 = $ 33.75

Break-even point in units = Fixed expenses / Contribution margin per unit = $ 3,375,000 / $ 33.75 = 100,000 units

Contribution margin ratio = Contribution margin / Sales x 100 = $ 4,050,000 / $ 7,500,000 x 100 = 54%

Break-even point in sales dollars = Fixed expenses / Contribution margin ratio = $ 3,375,000 / 54% = $ 6,250,000

If sales revenue increased by $ 540,000, profit would increase by 540,000 x 54% = $ 291,600

If after-tax profit is $ 1,254,000, and the tax rate is 34%, pre-tax profit would be 1,254,000/ ( 1 - 0.34) = $ 1,900,000

Number of units to be sold to earn a pre-tax profit of $ 1,900,000 = (Fixed expenses + Target profit) / Contribution margin per unit = $ ( 3,375,000 + 1,900,000) / $ 33.75 = $ 5,275,000 / $ 33.75 = 156,297 units

Margin of safety = Actual sales - Break-even sales = (120,000 - 100,000) x 62.50 = $ 1,250,000

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