A firm is considering three capacity alternatives A B and C

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) Which alternative would require the lowest volume of output to generate an annual profit of $50,000?

Solution

Alt A

Alt B

Alt C

Annual fixed cost

100000

120000

80000

Variable cost per unit

22

20

30

Break even quantity = Annual fixed cost / (Price- variable cost per unit)

Break even quantity (A)        = 100,000/ (50-22)

                                                      =3571 units

Break even quantity (B)        = 120,000/ (50-20)

                                                      =4000 units

Break even quantity (C)        = 80,000/ (50-30)

                                                      =4000 units

Alternative A has the lowest break even quantity.

Profit = (price – variable cost per unit) x units to sell - total fixed cost

Profit (A) = (50-22) x 10,000 - 100,000

                   = 180,000

Profit (B) = (50-20) x 10,000 - 120,000

                   = 180,000

Profit (C) = (50-30) x 10,000 - 80,000

                   = 120,000

Alternative A and B has the highest amount of profit at the given quantity of sales units.

Units for target profit = Break even quantity + target profit/ (price – variable cost per unit)

Units for target profit (A) = 3571 + 50,000/(50-22)

                                                        = 5357 units

Units for target profit (B) = 4000 + 50,000/(50-20)

                                                        = 5667 units

Units for target profit (C) = 4000 + 50,000/(50-20)

                                                        = 6500 units

Alternative A will require the lowest volume of output.