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 $40,000 for A and $30,000 for B; variable costs per unit would be $10 for A and $12 for B; and revenue per unit would be $15 for A and $16 for B. 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?

Results are below.

Explanation:

Giving the following information:

Alternative A:

Fixed costs= $40,000

Variable cost per unti= $10

Revenue per unit= $15

Alternative B:

Fixed costs= $30,000

Variable cost per unti= $12

Revenue per unit= $16

First, we need to calculate the break-even point in units using the following formula:

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

Alternative A= 40,000 / (15 - 10)

Alternative A= 8,000

Alternative B= 30,000 / (16 - 12)

Alternative B= 7,500  

To calculate the indifference point in units, we need to determine the net income equations:

Alternativa A= 5*x - 40,000

Alternative B= 4*x - 30,000

x= number of units

We equal both formulas and isolate x:

5x - 40,000 = 4x - 30,000

x = 10,000

The indifference point is 10,000 units.

Finally, the higher income for 12,000 units:

Alternativa A= 5*12,000 - 40,000= $20,000

Alternative B= 4*12,000 - 30,000= $18,000

For 12,000 units the best option is alternative A.

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