Question

A small firm intends to increase the capaclty of a bottleneck operation by adding a new machine. Two alternatives, A and B. have been identified, and the assoclated costs and revenues have been estimated. Annual fixed costs would be $54,000 for A and $27,000 for B : variable costs per unit would be $9 for A and $11 for B; and revenue per unit would be $16

a. Determine each alternative's break-even point in units.
b. At what volume of output would the two alternatives yleld the same profit (or loss)?
c. If expected annual demand is 13,000 units, which alternative would yield the higher profit

Answer 1

A small firm evaluating two alternatives for a new machine will find that Alternative A has a break-even point of 6,000 units, while Alternative B's break-even point is 5,400 units. They yield the same profit at a volume of 13,500 units. However, with an expected annual demand of 13,000 units, Alternative A offers higher profits.

Step-by-step explanation:

The break-even point for alternative A is calculated by dividing the annual fixed costs by the difference between revenue per unit and variable costs per unit. For Alternative A: Break-even point = $54,000 / ($16 - $9) = 6,000 units. For Alternative B, it would be: Break-even point = $27,000 / ($16 - $11) = 5,400 units.

To find the volume at which both alternatives would yield the same profit, set the total profit equations equal to each other and solve for the quantity of units (Q):
54,000 + 9Q = 27,000 + 11Q, which simplifies to Q = 13,500 units.

Given an expected annual demand of 13,000 units, Alternative A would yield a higher profit because it has lower variable costs per unit which becomes significant at higher volumes.

The profit for Alternative A would be: (13,000 units * $16/unit) - $54,000 - (13,000 units * $9/unit).

The profit for Alternative B would be: (13,000 units * $16/unit) - $27,000 - (13,000 units * $11/unit).

After performing the calculations, Alternative A offers a higher profit.