A company's fixed operating costs are $420,000, its variable costs are $3.20 per unit, and the product's sales price is $4.65. 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.

units

The volume of sales that will result in a break-even point is 289,655 units

Explanation: For any organization or company to break-even means its total costs is just the same as its total revenue. This means no profit, and no loss either. Or better still, profit/loss equals zero.

The equation to determine the profit or otherwise of an organization is given as Revenue minus Cost. That is, the sales figure should exceed the cost of production, and the excess would be the profit. If on the other hand the cost of production exceeds the sales figure, then the equation would result in a negative figure which simply means a loss has been recorded.

In the question above, the costs have been given as;

Fixed cost = 420000

Variable cost = 3.2y

Total cost = 420000 + 3.2y

Where y is the number of units produced.

Also the revenue has been given as 4.65y

That is, sales price multiplied by number of units produced/sold

The profit is given as revenue minus cost while the break-even point is given as revenue equals cost, that is;

420000 + 3.2y = 4.65y

Collect like terms and you have;

420000 = 4.65y - 3.2y

420000 = 1.45y

Divide both sides by 1.45

289655.172 = y

y ≈ 289,655

Therefore the sales volume that will result in a break even point is 289,655 units

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