Sinclair Company's single product has a selling price of $25 per unit.Last year the company reported a profit of $20,000 and variable expenses totaling $180,000.The product has a 40% contribution margin ratio.Because of competition,Sinclair Company will be forced in the current year to reduce its selling price by $2 per unit.How many units must be sold in the current year to earn the same profit as was earned last year?

Question

Quizplus · Accepted Answer

CM ratio = 1 - Variable expense ratio
CM ratio = 1 - Variable expenses F1F1F1S1F1F1F10 Sales
0.40 = 1 - ($180,000 F1F1F1S1F1F1F10 Sales)
$180,000 F1F1F1S1F1F1F10 Sales = 1 - 0.40
Sales = $180,000 F1F1F1S1F1F1F10 (1 - 0.40)= $180,000 F1F1F1S1F1F1F10 0.60 = $300,000
Sales = Selling price per unit F1F1F1S1F1F1F10 Quantity sold
$300,000 = $25 per unit F1F1F1S1F1F1F10 Quantity sold
Quantity sold = $300,000 F1F1F1S1F1F1F10 $25 per unit = 12,000 units
Variable expense per unit = Variable expenses F1F1F1S1F1F1F10 Quantity sold
= $180,000 F1F1F1S1F1F1F10 12,000 units = $15 per unit
Profit = (Sales - Variable expenses)- Fixed expenses
$20,000 = ($300,000 - $180,000)- Fixed expenses
Fixed expenses = ($300,000 - $180,000)- $20,000 = $120,000 - $20,000 = $100,000
New unit selling price = $25 per unit - $2 per unit = $23 per unit
New unit contribution margin = $23 per unit - $15 per unit = $8 per unit
Unit sales to attain a target profit = (Target profit + Fixed expenses)F1F1F1S1F1F1F10 Unit CM
= ($20,000 + $100,000)F1F1F1S1F1F1F10 $8 per unit = 15,000 units

Sinclair Company's Single Product Has a Selling Price of $25