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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? Path: p Words:0

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Answer:

A) Alternative A has the lowest preak-even point at 3,572 units

B) Both alternatives A and B will produce the highest profit of $180,000.

C) 10,000 units between A and B

2,500 units between A and C

4,000 units between B and C

Explanation:

The revenue functions for each of the alternatives are:

[tex]R_A = (\$50-\$22)n - \$100,000\\R_B = (\$50-\$20)n - \$120,000\\R_C = (\$50-\$30)n - \$80,000[/tex]

Where 'n' is the annual output, in units produced.

A) At the break-even point, revenue is equal to zero. The break-even outputs for each alternative are:

[tex]0 = (\$50-\$22)n_A - \$100,000\\n_A = 3,572\\0 = (\$50-\$20)n_B - \$120,000\\n_B = 4,000\\0 = (\$50-\$30)n_C - \$80,000\\n_A = 4,000\\[/tex]

Alternative A has the lowest preak-even point at 3,572 units.

B) The revenues for each alternative at n=10,000 units are:

[tex]R_A = (\$50-\$22)10,000 - \$100,000\\R_A = \$180,000R_B = (\$50-\$20)10,000 - \$120,000\\R_B= \$180,000\\R_C = (\$50-\$30)10,000 - \$80,000\\R_C =  \$120,000[/tex]

Both alternatives A and B will produce the highest profit of $180,000.

C) As seen above, for n=10,000 the company would be indifferent between A and B.

Between A and C:

[tex]R_A = R_C\\ (\$50-\$22)n - \$100,000 = (\$50-\$30)n - \$80,000\\n=\frac{100,000-80,000}{28-20} \\n=2,500[/tex]

Between B and C:

[tex]R_B = R_C\\ (\$50-\$20)n - \$120,000 = (\$50-\$30)n - \$80,000\\n=\frac{120,000-80,000}{30-20} \\n=4,000[/tex]

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