Question

A firm is considering three capacity alternatives: A, B, and C. Alternative A would have an annual fixed cost of $105000 and variable costs of $24 per unit. Alternative B would have annual fixed costs of $126000 and variable costs of $25 per unit. Alternative C would have fixed costs of $82000 and variable costs of $37 per unit. Revenue is expected to be $52 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?

Answer 1

Solution :

                                      Alternative A          Alternative B            Alternative C

Annual fixed cost          105000                  126000                        82000

Variable fixed cost         24                             25                                  37

a). We have to find out the Break even quantity :

   Break Even quantity for A    $=\frac{\text{annual fixed cost}}{(\text{price - variable cost per unit})}$

                                                $=\frac{105000}{52-24}$

                                                = 3750 units

   Break Even quantity for B    $=\frac{\text{annual fixed cost}}{(\text{price - variable cost per unit})}$

                                                $=\frac{126000}{52-25}$

                                                = 4666 units

   Break Even quantity for C    $=\frac{\text{annual fixed cost}}{(\text{price - variable cost per unit})}$

                                                $=\frac{82000}{52-37}$

                                                = 5466 units

Therefore, Alternate A has the lowest Break Even quantity.

b). Now,

$\text{Profit} = (\text{price - variable cost per unit}) \times \text{units to sell - total fixed cost}$

$\text{Profit of A} = (52 - 24) \times 10000 - 105000$

                = 280,000 - 105,000

                = 175,000

$\text{Profit of B} = (52 - 25) \times 10000 - 126000$

                = 270,000 - 126,000

                = 144,000

$\text{Profit of C} = (52 - 37) \times 10000 - 82000$

                = 150,000 - 105,000

                = 45,000  

Thus, alternate A has the highest amount of profit.

c).

$\text{Units of target profit = break even quantity} + \frac{\text{target profit} }{(\text{price - variable cost per unit })}$

Units of the target profit for A  $=3750 + \frac{50000}{52-24}$

                                                 = 5535 units

Units of the target profit for B  $=4666 + \frac{50000}{52-25}$

                                                 = 6517 units

Units of the target profit for C  $=5466 + \frac{50000}{52-37}$

                                                 = 8799 units

Thus Alternative A will require the lowest volume of the output.