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 $31,000 for B; variable costs per unit would be $7 for A and $11 for B; and revenue per unit would be $18.

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 15,000 units, which alternative would yield the higher profit (or the lower loss)?

Higher profit             (Click to select)  A  B

Answer 1

a. Determine each alternative’s break-even point in units.

Alternative A	Alternative B
Fixed cost = 36,000 Variable cost per unit = 7 Revenue (Price) per unit = 18 Contribution per unit = Sales price – Variable cost Contribution = 18 – 7 = 11 Breakeven point in units = FC/Contribution per unit BEP = 36,000/11 = 3272.72 units BEP = 3273 units	Fixed cost = 31,000 Variable cost per unit = 11 Revenue (Price) per unit = 18 Contribution per unit = Sales price – Variable cost Contribution = 18 – 11 = 7 Breakeven point in units = FC/Contribution per unit BEP = 31,000/7 = 4428.57 units BEP = 4429 units

b. At what volume of output would the two alternatives yield the same profit (or loss)?

Profit                     = Quantity (Price – VC) – FC

Profit A                 = Profit B

Quantity (Price – VC) – FC = Quantity (Price – VC) – FC

Q (18-7) - 36,000 = Q (18-11) - 31,000

Q (11) - 36,000        = Q (7) - 31,000

                      Q      =1250 units (5000/4)

In this case there will not be any profit and the loss will be same in both the alternatives.

Profit (loss) = Quantity (Price – VC) – FC

Alternative A = 1250 (18 – 7) – 36000 = -22250

Alternative A = 1250 (18 – 11) – 31000 = -22250

c. If expected annual demand is 15,000 units, which alternative would yield the higher profit (or the lower loss)?

Alternative A

Profit A = Quantity (Price – VC) – FC

Profit A = 15000 (18 – 7) – 36000

Profit A = 15,000 (11) - 36,000

Profit A = 129000

Alternaitve B

Profit B = Quantity (Price – VC) – FC

Profit B = 15000 (18 – 11) – 31000

Profit B = 15,000 (7) - 31,000

Profit B = 74000

Higher profit – Alternative A