Question

The accounting department of a garment manufacturing company has estimated that the variable cost will be $21 per unit for a new designer-labeled dress to be introduced for teenage girls. Fixed costs are anticipated to be $1M per year. Forty percent of the business for this garment will be with one preferred customer and will be charged $28 per unit. The remaining 60% of the business will be with several other customers who will be charged $40 per unit. i. Compute a. the breakeven volume for this plant. b. the unit cost if 100,000 units are made per year. c. the annual profit for this quantity. ii. The management wants to know if it should really make this garment if it expects a profit of at least $500,000 per year on this venture.

Answer 1

i.

a. Break-even volume: 70,423 units;

b. Unit cost if 100,000 units are made: $31;

c. Annual profit at 100,000 units made: $420,000.

ii.

The company should make this garment if the company should be able to manufacture and sell 105,634 units per year.

Step-by-step explanation:

i.

a. Break-even volume:

Denote x is the break-even volume, then we have:

1,000,000 = 0.4* X * ( 28 - 21) + 0.6 * X * ( 40 -21) <=> 14.2X = 1,000,000 <=> X = 70,423 units;

b. Unit cost if 100,000 units are made:

Total cost if 100,000 units are made = 1,000,000 + 100,000 * 21 = $3,100,000;

Unit cost = 3,100,000 / 100,000 = $31.

c. Annual profit at 100,000 units made = Total revenue - Total cost = 100,000*0.4*28 + 100,000*0.6*40 - 3,100,000 = 3,520,000 - 3,100,000 = $420,000.

ii.

To meets the minimum expected profit given costs, selling price and sell structure remains the same, the company should be able to manufacture and sell Y units per year, with Y is calculated as below:

0.4 * Y * (28-21) + 0.6 * Y * (40-21) - 1,000,000 = 500,000 <=> 14.2Y - 1,000,000 = 500,000 <=> 14.2Y = 1,500,000 <=> Y = 105,634 units

So, it should make this garment if the company should be able to manufacture and sell 105,634 units per year.