Problem 5-4 A small firm intends to increase the capacity of a bottleneck operat
ID: 357580 • Letter: P
Question
Problem 5-4 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 S11 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.) units units b. At what volume of output would the two alternatives yield the same profit? (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? Higher profit (Click to select)Explanation / Answer
a)
alternative A:
fixed cost = 36000
variable cost = 7
revenue = 20
assuming the no. of units manufactured = x
total cost = fixed cost + variable cost
= 36000 + 7*x
revenue = 20*x
for break even point: revenue = total cost
: 20x = 36000 + 7x
13x = 36000
x = 2769.23
x = 2769
alternative B:
fixed cost = 35000
variable cost = 11
revenue = 20
assuming the no. of units manufactured = x
total cost = fixed cost + variable cost
= 35000 + 11*x
revenue = 20*x
for break even point: revenue = total cost
: 20x = 35000 + 11x
9x = 35000
x = 3888.89
x = 3889 units
Break even point for A = 2769
Break even point for B = 3889
b)
let the volume to x
for the profit to be equal, total cost of both alternative should be equal:
cost for alternative A = 36000 + 7x
cost for alternative B = 35000 + 11x
both should be equal: 36000 + 7x = 35000 + 11x
36000 - 35000 = 11x - 7x
1000 = 4x
x = 250
At 250 units, the profit for both alternative would be equal.
c)
demand = 16000.
total profit for alternative A:
revenue - cost
20*16000 - (36000 + 7*16000)
= 320000 - 36000 - 112000
= 172000
total profit for alternative B:
revenue - cost
20*16000 - (35000 + 11*16000)
= 320000 - 35000 - 176000
= 109000
We get higher profit of 172000 in alternative A, hence alternative A to selected.