Question

An apparel manufacturing plant has estimated the variable cost to be $2.40 per unit. Fixed costs are $2,000,000 per year. Forty percent of its business is with one preferred customer and the customer is charged at cost. The remaining 60% of the business is with several different customers who are charged $50 per unit. Find :

(a) The break even volume for this job.
(b) The unit cost if 100,000 units are made per year.
(c) The annual profit for this quantity(100,000 units)

Answer 1

To solve for break-even volume, we consider the proportion of business charged at $50 per unit and the fixed and variable costs. The unit cost at 100,000 units is found by dividing total costs by the number of units. Annual profit is calculated by subtracting total costs from total revenue for 100,000 units, considering the pricing strategy for the preferred customer and other customers.

Step-by-step explanation:

The apparel manufacturing plant question involves calculating the break-even volume, the unit cost at a specific production level, and the annual profit for producing 100,000 units. To find the break-even volume, we need to set up the equation where total revenue equals total costs (fixed costs + variable costs). The fixed costs are $2,000,000 per year, and the variable cost per unit is $2.40. Since 60% of the business is charged $50 per unit, the revenue per unit for that portion of the business would be $50. So we have $2,000,000 = ($50 - $2.40) ×X for the 60% segment, where X represents the break-even volume for 60% of the business.

The unit cost if 100,000 units are made per year is found by adding the total fixed cost and total variable costs and then dividing by the total number of units produced. So, Unit Cost = ($2,000,000 + $2.40 ×100,000) / 100,000.

The annual profit is calculated by subtracting the total costs from the total revenue for 100,000 units. The total revenue for 100,000 units considering that 40% are sold at cost and 60% are sold at $50 per unit would be $50 * 60,000. The total costs would be the fixed costs plus the variable costs for 100,000 units. So, Annual Profit = Total Revenue - Total Costs.

Answer 2

BEP units: 42,017

BEP dollars: 2,100,850

unit cost at 100,000 units produced: 22.40 dollars

operating profit : 1,656,000

Step-by-step explanation:

`Sales \: Revenue - Variable \: Cost = Contribution \: Margin`

50 - 2.4 = 47.6 contirbution margin per unit

`(Fixed\:Cost)/(Contribution \:Margin) = Break\: Even\: Point_(units)`

2,000,000/47.6 = 42.016,80 BEP units

BEP units x sales price = BEP dollars

42,017 x 50 = 2,100,850

(B)

fixed cosy/ units produced = fixed cost per unit

2,000,000/ 100,000 = 20 fixed cost per unit

fixed cost + variable cost = total cost

20 + 2.40 = 22.4

(C)

There are 40% units sold at the preferred customer at cost

So we sale at gain only 60% of the units:

100,000 units x 60% x 50 = 3,000,000

100,000 units x 40% x 22.40 = 896,000

Total revenue 3,896,000

Cost: 100,000 x 22.40 (2,240,000)

operating profit 1,656,000