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 A or B?

Answer 1

For alternative A

• Fixed cost (FC) = $36000
• Variable cost (VC) = $7

For alternative B

• Fixed cost (FC) = $31000
• Variable cost (VC) = $11

Revenue (R) = $18

a) Break even point for alternative A = FC / (R-VC) = 36000/(18-7) = 36000/11 = 3273 units

Break even point for alternative B = FC/(R-VC) = 31000/(18-11) = 31000/7 = 4429 units

b) Let the volume of output = Q

Profit for alternative A = profit for alternative B

=> Q(R-VC) - FC = Q(R-VC) - FC

=> Q(18-7)- 36000 = Q(18-11) - 31000

=> 11Q - 36000 = 7Q - 31000

=> 11Q - 7Q = - 31000+36000

=> 4Q = 5000

=> Q = 5000/4

=> Q = 1250

So at a volume of output of 1250 units the two alternatives yield the same profit

C) If volume of output (Q) = 15000 units

Profit for alternative A = Q(R-VC) - FC

= 15000(18-7) - 36000

= (15000 x 11) - 36000

= 165000 - 36000

= $129000

Profit for alternative B = Q(R-VC) - FC

= 15000(18-11) - 31000

= (15000 x 7) - 31000

= 105000 - 31000

= $74000

So alternative A would yield the higher profit.