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 $17. 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 14,000 units, which alternative would yield the higher profit (or the lower loss)? Higher profit rev: 02_06_2019_QC_CS-157424 Next Visit question mapQuestion 2 of 5 Total2 of 5

Answer 1

a) Breakeven units is given as below

BEP = F/(R-V) where F is the fixed costs, R is the revenue and V is the variables costs.

For alternative A, BEP = 36000/(17-7) = 36000/10 = 3600

For alternative B, BEP = 31000/(17-11) = 31000/6 = 5166.67

Hence QBEP, A is 3600 and QBEP, B is 5166.67 units

b) To find the volume where both alternatives gives same profit or loss, we equate the total cost and solve for volume. Total Cost is the sum of fixed cost and total variable cost. Hence we have the below

Total Cost for A = Total Cost for B

36000+7*Volumne = 31000+11*Volume

11*Volumne - 7*Volume = 36000 - 31000 = 5000

4*Volume = 5000

Volume = 5000/4 = 1250 units

Hence at a volume of output = 1250 units the two alternatives yield the same profit (or loss)

c) We know that indifference point is 1250 units from part b. For any quantity above this point, the alternative with the lower variable cost would yield higher profit or lower cost. As Alternative A has lower variable cost, it would yield a higher profit if annual demand is 14000