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

The new product would just break even at the selling price of $246 per unit.

Explanation:

This can be calculated using the formula for calculating the breakeven point in unit as follows:

Breakeven units = Total fixed cost / Contribution margin (1)

Where;

Breakeven units = Annual sales units = 2,500

Total fixed cost = Production fixed costs + Selling fixed costs + Allocated common fixed corporate costs = $50,000 + $75,000 + $55,000 = $180,000

Variable costs per unit = Production variable cost per unit + Selling variable cost per unit = $125 + $49 = $174

Contribution margin = Selling price per unit - Variable costs per unit = Selling price per unit - $174

Let P = Selling price per unit. Substituting the values into equation (1) and solve for P, we have:

2,500 = 180,000 / (P - 174)

2,500(P - 174) = $180,000

2,500P - $435,000 = $180,000

2,500P = $180,000 + $435,000

2,500P = $615,000

P = $615,000 / 2,500

P = $246

Therefore, the new product would just break even at the selling price of $246 per unit.