A painting operation is performed by a production worker at a labor cost of $1.40 per unit. A robot spray-painting machine, costing $15,000, would reduce the labor cost to $.20 per unit. If the device would be valueless at the end of 3 years, what is the minimum number of units that would have to have been painted each year to justify the purchase of the robot machine

4,166.66 units per year

Explanation:

Break-even is defined as the production volume at which the cost incurred in the production process is equal to the revenue earned.

Production above this point will result in positive revenue for the company.

The formula for break-even is

Break-even= Fixed cost ÷ (Difference in cost of labour per unit)

Difference in labour cost is the gain from this process. When it involves sales the denominator is Sales price less variable cost.

Break-even = 15,000 ÷ (1.4 - 0.2)

Break-even = 12,500 units

Production will have to exceed 12,500 units to justify purchase of the robot for 3 years.

Units produced per year will be

12,500 ÷ 3 = 4,166.66 units per year

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