Mathias Corporation manufactures and sells wire rakes. The rakes sell for $20 each. Information about the company's costs is as follows. Variable manufacturing cost per unit $6
Variable selling and administrative cost per unit 2
Fixed manufacturing overhead per month $300,000
Fixed selling and administrative cost per month 600,000

Required:
a. Determine the company's monthly break-even point in units.
b. Determine the sales volume (in dollars) required for a monthly operating income of $1,200,000.
c. Compute the company’s margin of safety if its current monthly sales level is $2,500,000.
d. Estimate the amount by which monthly operating income will increase if the company anticipates a $100,000 increase in monthly sales volume.

a. 75,000 units

b. $1,700,000

c. 0.40 or 40 %

d. $60,000

Explanation:

Break-even point is the level of activity where a firm neither makes a profit nor a loss.

Break-even point (units) = Fixed Costs ÷ Contribution per unit

Where,

Contribution per unit = Unit Selling Price  less Variable Costs per unit

                                   = $20 - $6 - $2

                                   = $12.00

Therefore,

Break-even point (units) = ($300,000 + $600,000) ÷ $12.00

                                        = 75,000 units

Sales (dollars) to reach target profit = (Fixed Costs + Target Profit) ÷ Contribution Margin Ratio

Where,

Contribution Margin Ratio = Contribution ÷ Sales

                                           = $12.00 ÷ $20.00

                                           = 0.60

Therefore,

Sales (dollars) to reach target profit = ($300,000 + $600,000 + 1,200,000) ÷ 0.60

                                                           = $1,700,000

Margin of Safety = (Sales level - Break-even Sales level) ÷ Sales level

                            = ($2,500,000 - $1,500,000) ÷ $2,500,000

                            = 0.40 or 40 %

Calculation of Incremental Monthly Operating Income                          

Incremental Sales                                                    $100,000

Less Incremental Variable Costs (5,000 × $8)      ($40.000)

Incremental Contribution                                         $60,000

Less Incremental Fixed Costs                                           $0

Incremental Operating Income                                $60,000

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