Question

A company's fixed operating costs are $430,000, its variable costs are $2.10 per unit, and the product's sales price is $6.00. What is the company's break-even point; that is, at what unit sales volume will its income equal its costs? Round your answer to the nearest whole number.

Answer 1

110,257 units.

Step-by-step explanation:

Fixed operating costs (FC) = $430,000

Variable costs (VC) = $2.10 per unit,

Sales price (P) = $6.00 per unit.

The revenue, as a function of 'n' units produced, for this company is given by:

`R(n)= (P-VC)n -FC\\R(n)= (6.00-2.10)n -430,000`

The break-even point occurs when revenue is zero. The break-even point is:

`0= (6.00-2.10)n -430,000\\n=(430,000)/(3.90) \\n=110,256.41`

Rounding it up to the next whole unit, the sales volume needed to reach the break-even point is 110,257 units.