Question

Minden Company introduced a new product last year for which it is trying to find an optimal selling price. Marketing studies suggest that the company can increase sales by 5,000 units for each $2 reduction in the selling price. The company’s present selling price is $95 per unit, and variable expenses are $65 per unit. Fixed expenses are $837,600 per year. The present annual sales volume (at the $95 selling price) is 25,900 units.

Required:

1. What is the present yearly net operating income or loss?

2. What is the present break-even point in unit sales and in dollar sales?

3. Assuming that the marketing studies are correct, what is the maximum annual profit that the company can earn? At how many units and at what selling price per unit would the company generate this profit?

4. What would be the break-even point in unit sales and in dollar sales using the selling price you determined in (3) above (e.g., the selling price at the level of maximum profits)?

Answer 1

Contribution margin is computed by subtracting variable cost from sales. Breakeven point defines the point at which the company is able to generate enough sales to service fixed costs. That is at breakeven, there is zero profit or loss.

1.

Net operating income    = Sales – variable expense – fixed costs

                                                = (25,900 X 95 ) – (25,900 X 65) – 837,600

                                                = (60,600)

2.

Break-even point in unit sales     = Fixed expenses/Contribution Margin per unit

                                                                = 837,600 /( 95-65) = 27,920

Break-even point in dollar sales = Break-even point in unit sales*Selling price

                                                                = 27,920 X 95 = $ 2,652,400

3.

Number of Units (a)	25900	30900	35900	40900	45900	50900	55900	60900
Selling Price	95	93	91	89	87	85	83	81
Contribution per unit (b)	30	28	26	24	22	20	18	16
Total Contribution (a X b)	777,000	865,200	933,400	981,600	1,009,800	1,018,000	1,006,200	974,400

As fixed cost remains constant, the maximum contribution margin occurs when the company sells 50,900 units with selling price of $85.

At this price, the maximum annual profit = 1018,000 – 837,600 = $ 180,400

4.

Break-even point in unit sales     = Fixed expenses/Contribution Margin per unit

                                                                = 837,600/20 = 41,880

Break-even point in dollar sales = Break-even point in unit sales*Selling price

                                                                = 41,880 X 85 = $ 3,559,800