Question

Stellar manufactures and sells swimsuits for $40.00 each. The estimated income statement for 2017 is as follows:

Sales: $2,000,000, Variable costs: 1,090,000, contribution margin: 910,000. Fixed costs: 765,000. Pretax earnings: 145,000

1.Compute the contribution margin per swimsuit and the number of swimsuits that must be sold to break even. (Round contribution margin per swimsuit to 2 decimal places, e.g. 15.25 and break even swimsuits to 0 decimal places, e.g. 125.)

2.What is the margin of safety in the number of swimsuits?
3.Compute the contribution margin ratio and the breakeven point in revenues. (Round contribution margin ratio to 3 decimal places, e.g. 0.256 and breakeven point to 0 decimal places, e.g. 125.)

4.What is the margin of safety in revenues? (Round answer to 0 decimal places, e.g. 125.)

5.Suppose next year’s revenue estimate is $200,000 higher. What would be the estimated pretax earnings?

6.Assume a tax rate of 30%. How many swimsuits must be sold to earn after-tax earnings of $180,000? (Round answer to 0 decimal places, e.g. 125.)

Answer 1

Solution 1:

Units sold = $2,000,000 / $40 = 50000 units

Contribution margin per Swimsuit= $910,000 / 50000 = $18.20

Swimsuits that must be sold to break even = Fixed Costs / Contribution margin per unit = $765000 / $18.20 = 42,033 units

Solution 2:

Margin of safety in the number of swimsuits = Units sold - Break even units = 50000 - 42033 = 7,967 units

Solution 3:

Contribution margin ratio = Contribution margin per Swimsuit / Selling price per swimsuit = $18.20 / $40 = 45.5%

Breakeven point in revenues = Fixed Costs / Contribution margin ratio = $765000 /45.5% = $1,681,319

Solution 4:

Margin of safety in revenue = $2,000,000 - $1,681,319 = $318,681

Solution 5:

Next years estimated revenue = $2,000,000 + $200,000 = $2,200,000

Contribution margin = $2,200,000*45.5% = $1,001,000

Estimated Pretax Earnings = $1,001,000 - $765,000 = $236,000

Solution 6:

After tax earnings = $180,000

tax rate = 30%

Pretax earnings = $180,000 / (100%-30%) = $180,000 / 70% = $257,142.86

Swimsuits to be sold = (Pretax earnings + Fixed Costs) / Contribution margin per unit

= ($257,142.86 + $765,000) / $18.20 = 56,162 units