Question

A digitized music tuner has been a staple in Smooth Sounds' product line for several years. Annual fixed costs of production and administration related to this product in the past have been $643,500. Variable costs of production and sales have been $17 per unit. The selling price in the past has been $28 per unit. Based on the appearance of competing products on the market, management has asked you to do the following:

a. Compute the breakeven point in units and sales dollars for the present product.
b. Compute the breakeven point in units and sales dollars if the variable costs increased by $3 per unit and the fixed costs increased by $14,375 per month.
c. Using the information from (b), an expected additional monthly advertising charge of $10,000, and a monthly sales rate of 15,000 units, compute the competitive selling price that the company must obtain in order to have a profit of $32,000 per month.

Answer 1

a.

Break even point in units = Fixed cost / (Selling price - variable cost)  

= $643,500 / ($28 - $17)

= $643,500 / $11

= 58,500 units

Break even point in sales dollar = Units * Selling price e

= 58,500 * $28

= $1,638,000

b.

New variable cost = $17 + $3

= $20

New fixed cost = $643,500 + ($14,375 * 12)

= $816,000

Break even point in units = Fixed cost / (Selling price - variable cost)

= $816,000 / ($28 - $20)

= 102,000 units

Break even point in sales dollar = Units * Selling price

= 102,000 * $28

= $2,856,000

c.

Fixed cost per month = ($816,000 / 12) + $10,000

= $68,000 + $10,000

= $78,000

Let selling price = x

Estimated sales = (Target profit + fixed cost) / (Selling price - variable cost)

15,000 = ($32,000 + $78,000) / (x - $20)

15,000 = $110,000 / (x - $20)

15,000 (x - $20) = $110,000

15,000 x - $300,000 = $110,000

15,000 x = $410,000

x = $27.33