A small firm intends to increase the capacity of a bottleneck operation by addin

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 $10 for A and $11 for B; and revenue per unit would be $19. a. Determine each alternative's break-even point in units. (Round your answer to the nearest whole amount.) QBEPA units QBEP.B 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 18,000 units, which alternative would yield the higher profit? Higher profit (Click to select)

Explanation / Answer

a.
Let the break even units for A be x
The break-even point is the level of sales where the revenue would be equal to the fixed and variable costs.
Revenue = Fixed costs + variable costs
Therefore, 19x = 36000 + 10x
9x = 36000
x = 4,000 units - A's breakeven units

Following the same process with B,
Let the breakeven units for B be x
19x = 35000 + 11x
8x = 35000
x = 4,375 units - B's breakeven units

b.
For this we are going to use the above formulae to calculate the units they have to sell to yield the same profit
We will check the point where their fixed and variable costs are the same
Here, Costs of A = Costs of B
Thus, 36000 + 10x = 35000 + 11x
11x - 10x = 1000
x = 1000
The alternatives A and B would yield the same profit/loss at the level of 1000 units

c.
Profit = Revenue - fixed - variable costs
In case of A,
= 19*18000 - 36000 - 10*18000
= 342000 - 36000 - 180000
= $118,000
In case of B,
= 19*18000 - 35000 - 11*18000
= 342000 - 35000 - 198000
= $109,000

The alternative A would yield a higher profit

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