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 $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.) OBEPA units OBEPB 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 15,000 units, which alternative would yield the higher profit? Higher profit A

Explanation / Answer

Answer to question a :

Breakeven point = Fixed cost / ( Price/ unit – Variable cost / unit )

Breakeven point for alternative A = 36000 / ( 18 – 7 ) = 36000/11 =3272.72 ( 3273 rounded to nearest whole number )

Breakeven point for alternative B = 31000/ ( 18 – 11 ) = 31000/ 7 = 4428.57 ( 4429 rounded to nearest whole number )

Answer to question b :

Since price and therefore revenue under both alternatives are same, total cost for both options also should be same to yield the same profit.

Let the corresponding volume = N

Total cost = Fixed cost + Variable cost / unit x Number of units

Total cost under option A = $36000 + $7.N

Total cost under option B = $31000 + $11.N

Therefore,

36000 + 7.N = 31000 + 11.N

Or, 4.N = 5000

Or, N = 1250

REQUIRED VOLUME OUTPUT = 1250 UNITS

Answer to question c:

Total cost under option A for annual output of 15000 units

= $ 36000 + $ 7 x 15000

= $36000 + $105000

= $141000

Total cost under option B for annual output of 15000 units

= $31000 + $11 x 15000

= $31000 + $165000

= $196,000

Since total cost under alternative A is less , it would yield higher profit

ALTERNATIVE A WILL YILED HIGHER PROFIT

REQUIRED VOLUME OUTPUT = 1250 UNITS

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