Final answer:
Holland Corporation sold 15,534 units last year. The break-even point was 12,500 units. To increase after-tax net income by 20%, they would need to sell 16,141 units given the same selling prices and income tax rate.
Step-by-step explanation:
To calculate the number of units Holland Corporation sold last year, given a net income of $182,000, we must first understand how the selling price per unit contributes to that income. Since the selling price per unit is $130 and $60 of that goes towards fixed costs and net income, we can say the contribution margin per unit is $60. With a fixed cost of $750,000, we can calculate units sold:
Units Sold = (Net Income + Fixed Costs) / Contribution Margin per Unit
Units Sold = ($182,000 + $750,000) / $60
Units Sold = $932,000 / $60
Units Sold = 15,533.33, rounded up to 15,534 units.
For the break-even point in units, it occurs where total revenue equals total fixed costs and variable costs, and there is no net income. Therefore, using the fixed costs and contribution margin per unit:
Break-even Point in Units = Fixed Costs / Contribution Margin Per Unit
Break-even Point = $750,000 / $60
Break-even Point = 12,500 units
To achieve a 20% increase in after-tax net income, the target income can be found by multiplying the current net income by 1.20:
Target Net Income = $182,000 * 1.20 = $218,400
The number of units that must be sold to achieve this can then be calculated in the same way as part a):
Units to be Sold = (Target Net Income After Taxes + Fixed Costs) / Contribution Margin Per Unit
Units to be Sold = ($218,400 + $750,000) / $60
Units to be Sold = $968,400 / $60
Units to be Sold = 16,140, rounded up to 16,141 units.