Bates Company currently produces and sells 4,000 units of a product that has a contribution margin of $5 per unit. The company sells the product for a sales price of $20 per unit. Fixed costs are $20,000. The company has recently invested in new technology and expects the variable cost per unit to fall to $12 per unit. The investment is expected to increase fixed costs by $15,000. After the new investment is made, how many units must be sold to break-even

1,875 units.

Explanation:

Break-even is the point where a company neither generate profit not make loss, or we can say that it the sales at which the operating profit will be zero. It can be calculated for sales volume as-well-as dollar sales. Let's prepare a contribution income statement to calculate the break-even sales in quantity. We know that:

               EBIT / Operating Profit = (SP * Q) - (VC * Q) - Fixed Cost

where

SP = Selling Price

Q = Quantity / Units

VC = Variable cost

As it is understood that the operating profit at break-even is zero, simply put it in the above contribution income statements along with other figures given in the question.

⇒ 0 = (20 * Q) - (12 * Q) - 15,000

OR 15,000 / (20 - 12) = Q

⇒ Break-even units = Q = 1,875 units.

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