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 $38,000 for A and $31,000 for B; variable costs per unit would be $7 for A and $11 for B; and revenue per unit would be $19. a. Determine each alternative’s break-even point in units. (Round your answer to the nearest whole amount.)
QBEP, A units
QBEP, B units
b. At what volume of output would the two alternatives yield the same profit? (Round your answer to the nearest whole amount.)
c. If expected annual demand is 10,000 units, which alternative would yield the higher profit?

Instructions are below.

Explanation:

Giving the following information:

Machine A:

Fixed costs= $38,000

Unitary cost= $7

Machine B:

Fixed costs= $31,000

Unitary cost= $11

Revenue per unit= $19

To calculate the break-even point in units, we need to use the  following formula:

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

Machine A:

Break-even point in units= 38,000 / (19 - 7)

Break-even point in units= 3,167

Machine B:

Break-even point in units= 31,000 / (19 - 11)

Break-even point in units= 3,875

Now, we need to determine the indifference point:

Machine A= 38,000 + 7x

Machine B= 31,000 + 11x

x= number of units

We will equal both formulas and isolate x:

38,000 + 7x = 31,000 + 11x

7,000 = 4x

1,750=x

Indifference point= 1,750 units

Finally, the total cost for 10,000 units:

Machine A= 38,000 + 7*10,000= $108,000

Machine B= 31,000 + 11*10,000= $141,000

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