Question

Key Corporation is considering the addition of a new product. The expected cost and revenue data for the new product are as follows: Annual sales 2,500 units Selling price per unit $ 304 Variable costs per unit: Production $ 125 Selling $ 49 Avoidable fixed costs per year: Production $ 50,000 Selling $ 75,000 Allocated common fixed corporate costs per year $ 55,000 If the new product is added, the combined contribution margin of the other, existing products is expected to drop $65,000 per year. Total common fixed corporate costs would be unaffected by the decision of whether to add the new product. At what selling price would the new product be just breaking even

Answer 1

The break-even selling price for Key Corporation's new product is calculated by summing the total variable costs and avoidable fixed costs and then subtracting the decrease in contribution margin from other products. This total cost is then divided by the number of units to find the break-even price per unit, which is $198.

Step-by-step explanation:

To determine the break-even selling price for Key Corporation's new product, we should not consider allocated common fixed corporate costs as they are unaffected by the decision to add the new product. To calculate the break-even selling price, we take into account the variable costs, avoidable fixed costs, and the decrease in contribution margin from other products. The break-even point is where total revenue equals total costs.

Firstly, calculate the total variable cost per unit by adding the production and selling variable costs:
$125 (production) + $49 (selling) = $174 per unit.

To find the annual total variable costs, multiply the total variable costs per unit by the annual sales units:
2,500 units × $174 = $435,000.

Add the annual avoidable fixed costs to find total costs:
$435,000 (total variable costs) + $50,000 (production fixed costs) + $75,000 (selling fixed costs) - $65,000 (drop in other products' contribution) = $495,000.

To break even, total revenue from the new product must equal $495,000. Hence, divide the total costs by the number of units to find the break-even selling price:
$495,000 ÷ 2,500 units = $198 per unit.

Thus, the break-even selling price for the new product is $198 per unit.