Question

Aisin Seiki produces an automobile component that has a variable cost of $0.75 per unit; the firm sells this component at a price of $1.25 per unit. The firm’s current volume of production is 50,000 units; the firm incurs fixed costs of $12,000. The firm is planning to expand its production facilities by adding equipment; this expansion will result in the firm incurring additional fixed costs of $5,000; the variable costs incurred would now be $1.00. The firm anticipates that this expansion would enable them to increase their volume of production to 70,000 units.

a) Should Aisin Seiki expand its production facilities by adding equipment (provide detailed calculations to justify your answer)?

b) What are Aisin Seiki’s break-even points (in terms of $ and units) for the above scenarios (provide detailed calculations)?

Answer 1

Answer a:

Sell price= $1.25

Current

Capacity= 50000

Fixed cost= 12,000

Variable cost= 0.75 per unit

Profit= 1.25-0.75= 0.50 per piece

Let the total unit produced be 50000, then the total profit will be

Total profit= Profit per piece*50,000 - Fixed cost

Y= 0.5x - 12000

Y= 25000 – 12000= 13000

For breakeven point, Y=0

Y= 0.5x – 12000

0.5x= 12000

Breakeven point, X= 6000

Expansion cost= 5000, total fixed cost= 12000+5000= 17000

Variable cost now= 1

New capacity= 70000 units

Profit= 1.25-1= 0.25 per piece

Total profit= Profit per piece*70,000 - Fixed cost

Y= 17500 – 17000= 500

For breakeven point, Y=0

Y= 0.25x – 17000

0.25x= 17000

Breakeven point, X= 68000

Answer a: Aisin Seiki should not expand its production facilities by adding equipment, because the total profit before was $13000 but it has been reduced to $500 now

Answer b: Breakeven point (1^st scenario)= 6000

Breakeven point (2nd scenario)= 68000