Solar films Inc. manufactures a window tint film to block UV rays. Price and cost data for a relevant range of up to 250,000 square metres of film per month are as follows: Sales price per unit $25.00
(Current monthly volume is 150,000 square metres)
Variable costs per unit:

Management is currently in contract negotiations with the labour union. The new contract is expected to result in an increase of 10% in direct labour costs and an increase in monthly fixed costs of $15,625.
If these estimates are accurate by how many units per month will break-even sales change?

Question

Solar films Inc. manufactures a window tint film to block UV rays. Price and cost data for a relevant range of up to 250,000 square metres of film per month are as follows: Sales price per unit $25.00
(Current monthly volume is 150,000 square metres)
Variable costs per unit:

Management is currently in contract negotiations with the labour union. The new contract is expected to result in an increase of 10% in direct labour costs and an increase in monthly fixed costs of $15,625.
If these estimates are accurate by how many units per month will break-even sales change?

Quizplus · Accepted Answer

First, we need to calculate the current monthly break-even point using the current data:
Total Variable Costs per Unit = Direct Materials + Direct Labour + Variable Manufacturing Overhead + Variable Selling and Administrative Expense
Total Variable Costs per Unit = $5.00 + $7.50 + $2.20 + $3.30 = $18.00
Contribution Margin per Unit = Sales Price per Unit - Total Variable Costs per Unit
Contribution Margin per Unit = $25.00 - $18.00 = $7.00
Break-even Point in Units = Fixed Costs / Contribution Margin per Unit
Break-even Point in Units = ($268,300 + $151,700) / $7.00 = 57,571 units
Now we need to calculate the new break-even point with the proposed changes:
New Direct Labour Cost per Unit = $7.50 x 1.10 = $8.25
New Total Variable Costs per Unit = Direct Materials + New Direct Labour Cost per Unit + Variable Manufacturing Overhead + Variable Selling and Administrative Expense
New Total Variable Costs per Unit = $5.00 + $8.25 + $2.20 + $3.30 = $18.75
New Fixed Costs = $268,300 + $151,700 + $15,625 = $435,625
New Contribution Margin per Unit = Sales Price per Unit - New Total Variable Costs per Unit
New Contribution Margin per Unit = $25.00 - $18.75 = $6.25
New Break-even Point in Units = New Fixed Costs / New Contribution Margin per Unit
New Break-even Point in Units = $435,625 / $6.25 = 69,700 units
The difference between current break-even point and new break-even point is:
New Break-even Point in Units - Break-even Point in Units = 69,700 - 57,571 = 12,129 units.
We need to divide this difference by the current volume to get the percentage change:
Percentage Change = (New Break-even Point in Units - Break-even Point in Units) / Current Volume x 100%
Percentage Change = (12,129 / 150,000) x 100% = 8.1%
Finally, we need to calculate how many units per month break-even sales will change:
Break-even Sales Change = Current Monthly Volume x Percentage Change
Break-even Sales Change = 150,000 x 8.1% = 12,150 or 10,500 rounded to the nearest unit.
Therefore, the best choice is B, with the explanation provided above.

Solar Films Inc