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Problem 17

# Chade Corp. is considering a special order brought to it by a new client. If Chade determines the variable cost to be $$\ 9$$ per unit, and the contribution margin of the next best alternative of the facility to be $$\ 5$$ per unit, then if Chade has: a. Full capacity, the company will be profitable at $$\ 4$$ per unit. b. Excess capacity, the company will be profitable at $$\ 6$$ per unit. c. Full capacity, the selling price must be greater than $$\ 5$$ per unit. d. Excess capacity, the selling price must be greater than $$\ 9$$ per unit.

Expert verified
The correct answer is: d. Excess capacity, the selling price must be greater than $$\ 9$$ per unit.
See the step by step solution

## Step 1: Understand the terms

Variable cost is the cost that varies in direct proportion to the number of units produced. Contribution margin is the difference between the selling price and variable cost per unit. It shows how much money the company makes from the sale of one unit, excluding fixed costs. Full capacity means the company is producing at its maximum capacity, while excess capacity means the company has room for producing more.

## Step 2: Analyze each option

a. Full capacity, the company will be profitable at $$\ 4$$ per unit. To determine profitability, we need to compare the potential selling price with the sum of the variable cost and opportunity cost (the contribution margin of the next best alternative): Selling price = Variable cost + Contribution margin of the next best alternative \$4 = \$9 + \$5 This equation doesn't hold, so the company won't be profitable at$4 per unit. This statement is incorrect. b. Excess capacity, the company will be profitable at $$\ 6$$ per unit. In this scenario, Chade has excess capacity, so the opportunity cost of not using the facility for the next best alternative is irrelevant. We just need to compare the selling price with the variable cost, Selling price = Variable cost \$6 = \$9 This equation doesn't hold, so the company won't be profitable at $6 per unit. This statement is incorrect. c. Full capacity, the selling price must be greater than $$\ 5$$ per unit. In this scenario, Chade is at full capacity, so the opportunity cost should be considered. The company would be profitable only if the selling price is greater than the sum of the variable cost and the contribution margin of the next best alternative: Selling price > Variable cost + Contribution margin of the next best alternative Selling price > \$9 + \$5 Selling price > \$14 Here, we only know that the selling price has to be greater than \$5, not greater than the sum of the variable cost and the contribution margin of the next best alternative. So, this statement is incorrect. d. Excess capacity, the selling price must be greater than $$\ 9$$ per unit. In this scenario, Chade has excess capacity so the opportunity cost of not using the facility for the next best alternative is irrelevant. We just need to compare the selling price with the variable cost: Selling price > Variable cost Selling price > \$9 This statement is correct, as the selling price must be greater than the variable cost of \\$9 per unit for Chade to be profitable in a situation with excess capacity.

## Step 3: Conclusion

The correct answer is: d. Excess capacity, the selling price must be greater than $$\ 9$$ per unit.

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