Question

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 $36,000 for A and $35,000 for B; variable costs per unit would be $7 for A and $11 for B; and revenue per unit would be $20.

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 (or loss)? (Round your answer to the nearest whole amount.)

Profit             units

c. If expected annual demand is 16,000 units, which alternative would yield the higher profit (or the lower loss)?

Higher profit             (Click to select)  A  B

Answer 1

Solution:

(a) Break-even point:

At the breakeven point,

Total costs = Total revenue

Where,

Total costs = Fixed cost + (Variable cost per unit x Number of units)

Total revenue = Revenue per unit x Number of units

Alternative A:

Let the number of units be represented by Q. Therefore, at the breakeven point,

Total costs = Total revenue

Fixed cost + (Variable cost per unit x Number of units) = (Revenue per unit x Number of units)

$36,000 + $7Q = $20Q

Q = 2,769.23 or 2,769 (Rounding off to the nearest whole amount)

​​​​​​​QBEP, A = 2,769 units

Alternative B:

$35,000 + $11Q = $20Q

Q = 3,888.89 or 3,889 (Rounding off to the nearest whole amount)

​​​​​​​QBEP, B = 3,889 units

(b) Profit:

​​​​​​​Profit is calculated as,

Profit = Total revenue - Total cost

Profit for Alternative A = $20Q - ($36,000 + $7Q)

Profit for Alternative B = $20Q - ($35,000 + $11Q)

For Alternative A and Alternative B to have the same profit,

$20Q - ($36,000 + $7Q) = $20Q - ($35,000 + $11Q)

Q = 250 units

Profit (or loss) will be same at 250 units.

(c) Annual demand = 16,000 units

Profit for Alternative A = ($20 x 16,000) - $36,000 - ($7 x 16,000) = $172,000 (Higher)

Profit for Alternative B = ($20 x 16,000) - $35,000 - ($11 x 16,000) = $109,000

Higher profit = Alternative A