Question

A firm is considering three capacity alternatives: A, B, and C. Alternative A would have an annual fixed cost of $100,000 and variable costs of $22 per unit. Alternative B would have annual fixed costs of $120,000 and variable costs of $20 per unit. Alternative C would have fixed costs of $80,000 and variable costs of $30 per unit. Revenue is expected to be $50 per unit.

A) Which alternative has the lowest break-even quantity?

B) Which alternative will produce the highest profits for an annual output of 10,000 units?

C) At what volumes of output would the company be indifferent between each pair of choices?

Answer 1

A)

break-even quantity for alternative A = Fixed cost/contribution per unit = 100000/(50-22) = 3571.428571

break-even quantity for alternative B = Fixed cost/contribution per unit = 120000/(50-20) = 4000

break-even quantity for alternative A = Fixed cost/contribution per unit = 80000/(50-30) = 4000

Alternative A has the lowest break-even quantity

B)

Profit generated by Alternative A at 10000 units = 10000*50-(100000+22*10000) = 180000

Profit generated by Alternative B at 10000 units = 10000*50-(120000+20*10000) = 180000

Profit generated by Alternative C at 10000 units = 10000*50-(80000+30*10000) = 120000

Alternative A and Alternative B both will produce the highest profits for an annual output of 10,000 units

C)

At point of indifference between each pairs, company will be indifferent between each pair of choices

Point of indifference between A and B = (120000-100000)/(22-20) = 10000
Point of indifference between A and C = (100000-80000)/(30-22) = 2500
Point of indifference between B and C = (120000-80000)/(30-20) = 4000