Walt’s Woodwork Company makes and sells wooden shelves.
Walt’s carpenters make the shelves in the company’s rented building. Walt has a separate
office at another location that also includes a showroom where customers can view sample shelves
and ask questions of salespeople. The company sells all the shelves it produces each year and keeps
no inventories. The following information pertains to Walt’s Woodwork Company for the past year:
| (a) | Units produced and sold | 50,000 |
| (b) | Sales price per unit | $70 |
| (c) | Carpenter labor to make shelves | $600,000 |
| (d) | Wood to make the shelves | $450,000 |
| (e) | Sales staff salaries | $80,000 |
| (f) | Office and showroom rental expenses | $150,000 |
| (g) | Depreciation on carpentry equipment | $50,000 |
| (h) | Advertising | $200,000 |
| (i) | Sales commissions based on number of units sold | $180,000 |
| (j) | Miscellaneous fixed manufacturing overhead | $150,000 |
| (k) | Rent for the building where the shelves are made | $300,000 |
| (l) | Miscellaneous variable manufacturing overhead | $350,000 |
| (m) | Depreciation for office equipment | $10,000 |
Make appropriate assumptions about cost behavior and assume that direct labor costs vary
directly with the number of units produced.
How many units must the company sell in order to earn a pretax profit of $500,000?
Round up to the nearest unit.
To determine how many units Walt’s Woodwork Company must sell in order to earn a pre-tax profit of $500,000, we need to perform a break-even analysis. This analysis will help us find the level of sales needed to cover all expenses and achieve the desired profit.
First, let’s categorize the expenses into fixed and variable costs:
Fixed Costs
Carpenter labor: $600,000
Office and showroom rental expenses: $150,000
Depreciation on carpentry equipment: $50,000
Advertising: $200,000
Miscellaneous fixed manufacturing overhead: $150,000
Rent for the building where the shelves are made: $300,000
Depreciation for office equipment: $10,000
Variable Costs
Wood to make the shelves: $450,000
Sales staff salaries: $80,000
Sales commissions based on the number of units sold: $180,000
Miscellaneous variable manufacturing overhead: $350,000
Now, let’s calculate the contribution margin per unit. The contribution margin is the difference between the sales price per unit and the variable cost per unit.
Contribution Margin per Unit = Sales Price per Unit – Variable Cost per Unit Contribution Margin per Unit = $70 – (($450,000 + $80,000 + $180,000 + $350,000) / 50,000 units) Contribution Margin per Unit = $70 – ($1,060,000 / 50,000 units) Contribution Margin per Unit = $70 – $21.20 per unit Contribution Margin per Unit = $48.80 per unit
Now, we can use the contribution margin to calculate the number of units needed to earn a pre-tax profit of $500,000. The formula for this is:
Number of Units = (Fixed Costs + Desired Profit) / Contribution Margin per Unit
Number of Units = ($600,000 + $150,000 + $50,000 + $200,000 + $150,000 + $300,000 + $10,000 + $500,000) / $48.80 per unit
Number of Units = $1,860,000 / $48.80 per unit
Number of Units ≈ 38,180 units (rounded up to the nearest unit)
So, Walt’s Woodwork Company must sell approximately 38,180 units to earn a pre-tax profit of $500,000.
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