Question

A company produces and sells 2408 products per month for a turnover of 102337€. For this volume of products its total variable costs are 54647€ and its fixed costs are 29167€, of which 4 workers with a cost of 3750€ each one. One worker can produce a maximum of 750 products per month. The company is now considering a new hypothesis: to pay its workers by piecework at a cost of 5€ per product. By how much would the monthly break-even in Euro decrease with the new hypothesis?

Answer 1

To calculate the monthly break-even with the new hypothesis of paying workers by piecework, the number of products the company needs to sell to cover the total costs must be determined. The equivalent fixed costs of paying workers by piecework can be calculated by multiplying the number of workers, the maximum number of products per month, and the cost per product. By solving for the break-even point with the new total costs, the decrease in break-even in Euro can be determined.

Step-by-step explanation:

To calculate the break-even point, we need to compare the total costs with the total revenue. With the current payment system, the company's total costs per month are the sum of variable costs and fixed costs, which is 54647€ + 29167€ = 83814€. The monthly break-even point is when the total revenue is equal to the total costs. So, to calculate the break-even point with the new payment system, we need to determine the number of products the company needs to sell to cover the total costs of 83814€.
With the new hypothesis, workers are paid 5€ per product. Now, we can calculate the equivalent fixed costs of paying workers by piecework. Since each worker can produce a maximum of 750 products per month, the equivalent fixed costs would be 4 workers x 750 products x 5€/product = 15000€. Therefore, the new total costs per month with the piecework system would be the sum of variable costs (54647€) and equivalent fixed costs (15000€), which is 69647€.

To find the break-even point, we can set the total revenue equal to the new total costs of 69647€ and solve for the number of products:

Total revenue = Total costs

4€ x Number of products = 69647€

Number of products = 69647€ / 4€ = 17411.75

Therefore, the monthly break-even point with the new hypothesis would be approximately 17412 products. To calculate the decrease in break-even in Euro, we subtract the new break-even point from the old break-even point: 2408 products - 17412 products = -14996 products. So, the monthly break-even point would decrease by 14996 products with the new hypothesis.