A certain processing center has the capacity to assemble 650,000 units per year.

Question

A certain processing center has the capacity to assemble 650,000 units per year. At present, it is operating at 65% of capacity. The annual income is $416,000. Annual fixed cost is $192,000 and the variable cost is $0.38 per unit assembled. a) What is the annual profit or loss attributable to the center? b) At what volume of output does the center break even? c) What will be the profit or loss at 70%, 80% and 90% of capacity on the basis of constant income per unit and constant variable cost per unit?

Explanation / Answer

A certain processing center has the capacity to assemble 650,000 units per year. At present, it is operating at 65% of capacity. So it is producing .65 X 650,000=422,500 (quantity is 422,500) The annual income is $416,000. Annual fixed cost is $192,000 and the variable cost is $0.38 per unit assembled. a) What is the annual profit or loss attributable to the center? Profit=Income-FixedCost-VariableCost Profit=416,000-192,000-.38(422,500) Profit=416,000-192,000-160,550=$63,450 b) At what volume of output does the center break even? Assuming constant income per unit, income per unit=416,000/422,500=$.9846 So, profit will be zero where 0=.9846(Q)-192,000-.38(Q) 192,000=.6046(Q) Q=317,565 The percentage of capacity is 317,565/650,000=49% capacity c) What will be the profit or loss at 70%, 80% and 90% of capacity on the basis of constant income per unit and constant variable cost per unit? 70% of 650,000 is .7 x 650,000=455,000 which is Q income per unit from above is $.9846 which is P Profit=PQ-FC-VC Profit=.9846(455,000)-192,000-.38(455,000) Profit@ 70% =$83,093 80% of 650,000 is .8 x 650,000=520,000 which is Q income per unit from above is $.9846 which is P Profit=PQ-FC-VC Profit=.9846(520,000)-192,000-.38(520,000) Profit@ 80% =$122,392 90% of 650,000 is .9 x 650,000=585,000 which is Q income per unit from above is $.9846 which is P Profit=PQ-FC-VC Profit=.9846(585,000)-192,000-.38(585,000) Profit@ 90% =$161,691 Please let me know if you have any questions.

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