A small firm intends to increase the capacity of a bottleneck operation by adding a new machine. Two alternatives, A and B, have been identified, and the associated costs and revenues have been estimated. Annual fixed costs would be $39,000 for A and $21,000 for B; variable costs per unit would be $10 for A and $11 for B; and revenue per unit would be $15. Required:
a. Determine each alternative's break-even point in units.
b. At what volume of output would the two alternatives yield the same profit?
c. If expected annual demand is 12,000 units, which alternative would yield the higher profit?

Instructions are below.

Explanation:

Giving the following information:

Alternative A:

Fixed costs= 39,000

Unitary variable cost= $10

Selling price per unit= $15

Alternative B:

Fixed costs= 21,000

Unitary variable cost= $11

Selling price per unit= $15

First, we need to calculate the break-even point for each alternative, using the following formula:

Break-even point in units= fixed costs/ contribution margin per unit

Alternative A:

Break-even point in units= 39,000/ (15-10)

Break-even point in units= 7,800 units

Alternative B:

Break-even point in units= 21,000/ (15 - 11)

Break-even point in units= 5,250 units

Now, we need to determine the indifference point:

Alternative A= 5x - 39,000

Alternative B= 4x - 21,000

X= units sold.

We equal both income formulas:

5x - 39,000 = 4x - 21,000

x= 18,000 units

At 18,000 units, both alternatives provide the same profit.

Finally, the best alternative for 12,000 units:

Alternative A= 5*12,000 - 39,000= $21,000

Alternative B= 4*12,000 - 21,000= $27,000

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