Question

Fern Corporation manufacturers a single product that has a selling price of $20.00 per unit. Fixed expenses total $48,000 per year, and the company must sell 6,000 units to break even. If the company has a target profit of $14,000, sales in units must be:

Answer 1

7750 units

Step-by-step explanation:

The BEP which is the break even point is the point where the company's sales or revenue generated is equal to the cost incurred. As such, the BEP is the number of units that must be sold for the company to make neither a profit nor a loss.

Both sales and variable cost are dependent on the number of units sold.

The sales less the variable cost gives the contribution margin. The contribution margin less the fixed cost gives the net operating income.

As such, the net operating income/loss is the difference between the sales and the total costs.

Let the variable cost per unit be v

20 * 6000 - 6000v = 48000

120,000 - 48,000 = 6000v

6,000v = 72,000

v = $12

To achieve a set profit of $14,000, let the sales in unit be u

u(20 - 12) - 48,000 = 14,000

8u = 62,000

u = 62,000/8

= 7750 units

Answer 2

Break-even point in units= 7,750 units

Step-by-step explanation:

Giving the following information:

Selling price= $20.00 per unit.

Fixed expenses total $48,000 per year

The company must sell 6,000 units to break even.

Desired profit= $14,000

First, we need to calculate the unitary contribution margin:

Break-even point in units= fixed costs/ contribution margin per unit

6,000= 48,000/ (20 - X)

120,000 - 6,000X= 48,000

12= unitary variable cost

Unitary contribution margin= (20 - 12)= 8

Now, we need to incorporate to the break-even point formula the desired profit:

Break-even point in units= (fixed costs + desired profit)/ contribution margin per unit

Break-even point in units= (48,000 + 14,000)/8

Break-even point in units= 7,750 units