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 $91 per unit, and variable expenses are $61 per unit. Fixed expenses are $834,600 per year. The present annual sales volume (at the $91 selling price) is 25,800 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

1.
Sales [ 25800 * 91 ]	2347800
Variable cost [ 25800 * 61 ]	1573800
Contribution margin	774000
Fixed cost	834600
Net operating loss	-60600

2.
Contribution margin per unit = Selling price - Variable cost = 91 - 61 =	30
Break-even point in units = Fixed cost / Contribution margin per unit = 834600 / 30 =	27820
Break-even point in dollar sales = Break-even point in units * Selling price per unit = 27820 * 91 =	2531620

3.
Selling price per unit	Number of units	Profit [ Number of units*(Selling price per unit - Variable cost per unit) - Fixed cost ]
91	25800	-60600
89	30800	27800
87	35800	96200
85	40800	144600
83	45800	173000
81	50800	181400
79	55800	169800
77	60800	138200

Maximum annual profit	181400
Number of units	50800
Selling price per unit	81

4.
Contribution margin per unit = Selling price - Variable cost = 81 - 61 =	20
Break-even point in units = Fixed cost / Contribution margin per unit = 834600 / 20 =	41730
Break-even point in dollar sales = Break-even point in units * Selling price per unit = 41730 * 81 =	3380130