Ferkil Corporation manufacturers a single product that has a selling price of $100 per unit. Fixed expenses total $225,000 per year, and the company must sell 5,000 units to break even. If the company has a target profit of $67,500, sales in units must be:

Question

Quizplus · Accepted Answer

Firstly, let's calculate the contribution margin per unit:

Contribution margin per unit = Selling price per unit - Variable expenses per unit 
We are not given the variable expenses per unit, but we do know that the company must sell 5,000 units to break even. This means that at the break-even point, total revenues equals total expenses (including variable expenses).

Total revenues at the break-even point = Total expenses at the break-even point 
$100 x 5,000 units = Fixed expenses + Variable expenses x 5,000 units 
$500,000 = $225,000 + Variable expenses x 5,000 units 
Variable expenses per unit = ($500,000 - $225,000)/5,000 units = $55 per unit

Therefore, the contribution margin per unit is: 
Contribution margin per unit = Selling price per unit - Variable expenses per unit 
= $100 - $55 = $45

Now we can use the contribution margin ratio to calculate the sales in units required to meet the target profit of $67,500:

Contribution margin ratio = Contribution margin per unit/Selling price per unit 
= $45/$100 
= 0.45 or 45%

We know that the company wants to make $67,500 in profit, and we know the contribution margin ratio is 45%. Therefore:

Profit = (Contribution margin ratio x Sales in units x Selling price per unit) - Fixed expenses 
$67,500 = (0.45 x Sales in units x $100) - $225,000 
0.45 x Sales in units x $100 = $292,500 
Sales in units = $292,500/(0.45 x $100) 
Sales in units = 6500

Therefore, the company must sell 6,500 units to achieve a target profit of $67,500. The correct answer is D.

Ferkil Corporation Manufacturers a Single Product That Has a Selling