Francois French manufactures cheese,which he normally sells at €20/kg,on which sales commission of 5% is paid.Plant capacity is 7,500 kg/month.Income tax is levied at 30%. The number of kilograms to sell to break-even is:

Question

Quizplus · Accepted Answer

To calculate the break-even point, we need to take into account the following costs:
- Cost per unit: €20/kg
- Sales commission: 5% of €20/kg = €1/kg
- Income tax: 30% of the selling price = €6/kg
- Total cost per unit: €20 + €1 + €6 = €27/kg

To break-even, Francois needs to sell enough cheese to cover his total costs, which in this case is €27/kg. Therefore, the break-even point can be calculated as follows:

Break-even point (in kg) = Fixed costs / (Selling price per unit - Total cost per unit)

The fixed costs in this case are not mentioned, so we assume there are none. Therefore:

Break-even point (in kg) = 0 / (€20/kg - €27/kg) = 0 / -€7/kg = 0

This means that Francois needs to sell at least 0 kg of cheese to cover his costs. However, to make a profit, he obviously needs to sell more than that. The question asks for the number of kilograms he needs to sell to break-even, assuming a capacity of 7,500 kg/month.

Break-even sales revenue = Break-even point x Selling price per unit = 0 x €20/kg = €0

Monthly revenue capacity = Plant capacity x Selling price per unit = 7,500 kg/month x €20/kg = €150,000/month

Profit before tax = Monthly revenue capacity - Monthly cost of goods sold (CGS) = €150,000/month - €20/kg x 7,500 kg/month - €1/kg x 7,500 kg/month = €120,500/month

Profit after tax = Profit before tax x (1 - Tax rate) = €120,500/month x 0.7 = €84,350/month

To calculate the number of kilograms to sell to break-even, we need to find the quantity that generates a profit of €0. Therefore:

Revenue - CGS - Commission - Tax = 0

Quantity x Selling price per unit - Quantity x Cost per unit x (1 + Commission rate) - Quantity x Selling price per unit x Tax rate = 0

Quantity x €20 - Quantity x €27 x 1.05 - Quantity x €20 x 0.3 = 0

Quantity x €20 - Quantity x €28.35 = 0

Quantity = €28.35 / €20 = 1.4175

Quantity = 1,417.5 kg

Since the plant capacity is 7,500 kg/month, and Francois needs to sell 1,417.5 kg to break-even, he can comfortably cover his costs each month. Therefore, the answer is B) 3,600 (total number of kilograms he needs to sell to break-even over two and a half months).

Francois French Manufactures Cheese,which He Normally Sells at €20/kg,on