Question

Your uncle is considering investing in a new company that will produce high quality stereo speakers. The sales price would be set at 1.50 times the variable cost per unit; the variable cost per unit is estimated to be $75.00; and fixed costs are estimated at $1,120,000. What sales volume would be required to break even, i.e., to have EBIT = zero?

Answer 1

Answer:

Explanation:

Breakeven point = fixed cost / (sales - variable cost)

0 = $1,120,000 / ($112.50 - $75)

0 = $1,120,000 / $37.5

0 = 29,866.67 units

*sales = $75*1.50 = $112.50

To check:

            Sales                 29,866.67 x 112.50 = 3,360,000

less      variable cost     29,866.67 x 75.00 = 2,240,000

           Gross profit                                            1,120,000

less      fixed cost                                               1,120,000

            Earnings before income tax                        0

Answer 2

Answer:

29,867 units

Explanation:

Variable cost per unit (VC) = $75.00

Sales price (P) = 1.50 * VC = $112.50

Fixed costs (FC) = $1,120,000

Units sold (n) = ?

EBIT is given by:

$EBIT = P*n - VC*n -FC$

Therefore, the number of units sold required to break even is:

$0 = 112.50*n - 75.00*n -1,120,000\\n=\frac{1,120,000}{37.5} \\n=29,866.7$

Round up the value obtained to the next whole unit and the sales volume needed is 29,867 units.