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 $831,300 per year. The present annual sales volume (at the $95 selling price) is 25,600 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)?

1. Net operating loss is $63,300.

2. break even point in unit is 27,710 units while break even point in dollar sales is $2,632,450.

3. Profit is maximum at $180,700 at 50,600 units and selling price of $85 per unit.

4. Break even point in unit is 41,565 units while break even point in dollar sales is $3,533,025.

Explanation:

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

Total revenue = 25,600 × $95 = $2,432,000  

Total variable expenses =  25,600 × $65 = $1,664,000

Fixed expenses = $831,300

Total expenses = Total variable expenses + Fixed expenses

                          = $1,664,000 + $831,300

Total expenses = $2,495,300

Net operating loss = Total revenue -  Total expenses

                               = $2,432,000  - $2,495,300

Net operating loss = - $63,300

Therefore, net operating loss is $63,300.

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

Break even point in unit = Fixed costs ÷ (Unit selling price - Unit variable cost)

Note that (Unit price - Unit variable cost) refers to contribution per unit. Therefore, we have:

Break even point in unit = $831,300 ÷ ($95 - $65)  = 27,710 units

Break even point in dollar = Break even point in unit × Unit selling price

Break even point in dollar = 27,710 × $95 = $2,632,450.

Therefore, break even point in unit is 27,710 units while break even point in dollar sales is $2,632,450.

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?

Units = 25,600 + (5,000 × n)

Where n denotes number of years.        

Tota revenue = Units × [$95 - (n × $2)]

Total cost = (Units × $65) + $831,300

When n = 3,

Units = 25,600 + (5,000 × 3) = 40,600 units

Total revenue = 40,600 × [$95 - (3 × $2)] = $3,613,400  

Total cost = (40,600 × $65) + $831,300 = $3,470,300

Net profit =  $3,470,300  - $3,470,300 =$143,100

When n = 4,

Units = 25,600 + (5,000 × 4) = 45,600 units

Total revenue = 45,600 × [$95 - (4 × $2)] = $3,967,200  

Total cost = (45,600 × $65) + $831,300 = $3,795,300

Net profit =  $3,967,200  - $3,795,300 =$171,900

When n = 5,

Units = 25,600 + (5,000 × 5) = 50,600 units

Total revenue = 50,600 × [$95 - (5 × $2)] = $4,301,000  

Total cost = (50,600 × $65) + $831,300 = $4,120,300

Net profit =  $4,301,000  - $4,120,300 =$180,700

When n = 6,

Units = 25,600 + (5,000 × 6) = 55,600 units

Total revenue = 55,600 × [$95 - (6 × $2)] = $4,614,800  

Total cost = (55,600 × $65) + $831,300 = $4,445,300

Net profit =  $4,301,000  - $4,120,300 =$169,500

Therefore, profit is maximum at $180,700 at 50,600 units and selling price of $85 per unit.

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)?

Break even point in unit = $831,300 ÷ ($85 - $65)  = 41,565 units

Break even point in dollar sales = 41,565 × $85 = $3,533,025.

Therefore, break even point in unit is 41,565 units while break even point in dollar sales is $3,533,025.

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