a) The company's contribution margin ratio is 46.67%.
b) The company's unit break-even in units is 8,572 units.
c) If sales increase by 100 units, the operating income should increase by $3,500.
d) To attain a target operating income of 125,000, the company should sell 12,858 units.
e) The company's margin of safety in dollars is $857,142.86.
f) The degree of operating leverage is 1.75.
g) If the tax rate is 30%, the units that must be sold to attain an after-tax profit of $84,000 is 12,000 units.
Arkadia Corporation
Contribution-format Income Statement
For last month
Sales $1,500,000
Less: variable expenses 800,000
Contribution margin 700,000
Less: fixed expenses 300,000
Operating income $400,000
Units produced and sold = 20,000 units
a) The company's contribution margin ratio = contribution margin/sales:
= 46.67% (700,000/1,500,000)
b) The company's unit break-even can be calculated using the formula: Break-even units = Fixed expenses / Contribution margin per unit.
Contribution margin per unit = $35 (700,000/20,000)
The break-even in units:
= 8,571.43 units. Rounding up, the break-even in units is 8,572 units.
c) If sales increase by 100 units, the operating income should increase by the contribution margin per unit multiplied by the unit increase.
The contribution margin per unit is computed as $35 per unit above.
Therefore, the increase in operating income would be 35 ∗ 100
= $3,500 (35 x 100units)
d) To attain a target operating income of 125,000, the company should sell enough units to cover the fixed expenses and the target income.
The formula to calculate the required units is:
(Fixed expenses + Target income)/Contribution margin per unit
= (300,000 + 125,000)/125,000)/35
= 12,857.14 units.
The company would need to sell 12,858 units to attain the target operating income.
e) The company's margin of safety in dollars is the difference between the budgeted (or actual) sales and the break-even sales.
Margin of safety = Total sales - Break-even sales
= 1,500,000 − (1,500,000 − (300,000 / 0.4667)
= 1,500,000 − 1,500,000 − 642,857.14
= $857,142.86
f) The degree of operating leverage can be calculated as Contribution margin / Operating income.
The degree of operating leverage = 700,000/400,000 = 1.75.
g) Units needed after taxes:
Before-tax profit = After-tax profit / (1 - Tax rate)
Before-tax profit = 84,000/(1 − 0.30)
= 84,000/(1−0.30)
Before−tax profit =84,000 / 0.70
Before-tax profit = $120,000
Now, we can use the before-tax profit to calculate the units needed. The formula to calculate the required units is:
(Fixed expenses + Before-tax profit) / Contribution margin per unit (300,000 + 300,000 + 120,000)/ 35
= 35420,000 / $35
= 12,000 units
Thus, the company would need to sell 12,000 units to attain an after-tax profit of $84,000, given a tax rate of 30%.