ScholarPak Company produced and sold 70,000 backpacks during the year just ended at an average price of $30 per unit. Variable manufacturing costs were $12 per unit, and variable marketing costs were $6 per unit sold. Fixed costs amounted to $540,000 for manufacturing and $216,000 for marketing. There was no year-end work-in-process inventory. (Ignore income taxes.)
Required:
1. Compute ScholarPak’s break-even point in sales dollars for the year.
2. Compute the number of sales units required to earn a net income of $540,000 during the year.
3. ScholarPak’s variable manufacturing costs are expected to increase by 10 percent in the coming year. Compute the firm’s break-even point in sales dollars for the coming year.
4. If ScholarPak’s variable manufacturing costs do increase by 10 percent, compute the selling price that would yield the same contribution-margin ratio in the coming year.
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To calculate the break-even point in sales dollars, we need to determine the total fixed costs and the contribution margin per unit.
1. Total fixed costs:
Manufacturing fixed costs: $540,000
Marketing fixed costs: $216,000
Total fixed costs = $540,000 + $216,000 = $756,000
2. Contribution margin per unit:
Selling price per unit - Variable costs per unit
= $30 - ($12 + $6)
= $12
3. Break-even point in sales dollars:
Break-even point = Total fixed costs / Contribution margin per unit
= $756,000 / $12
= $63,000
Therefore, ScholarPak's break-even point in sales dollars for the year is $63,000.
To calculate the number of sales units required to earn a net income of $540,000 during the year, we need to consider the net income, the contribution margin per unit, and the fixed costs.
2. Number of sales units:
Target net income = Fixed costs + (Number of sales units × Contribution margin per unit)
$540,000 = $756,000 + (Number of sales units × $12)
Number of sales units = ($540,000 - $756,000) / $12
Number of sales units = - $216,000 / $12
Number of sales units = -18,000 units
To achieve a net income of $540,000 during the year, ScholarPak would need to sell an additional 18,000 units.
4. To calculate the break-even point in sales dollars for the coming year, assuming a 10% increase in variable manufacturing costs, we need to adjust the variable manufacturing cost per unit and the fixed manufacturing costs.
Variable manufacturing costs per unit = $12 × 1.10
= $13.20
Total fixed costs:
Manufacturing fixed costs = $540,000
Break-even point in sales dollars = (Total fixed costs + Fixed manufacturing costs) / Contribution margin per unit
Break-even point = ($756,000 + $540,000) / ($30 - $13.20)
Break-even point = $1,296,000 / $16.80
Break-even point = $77,143
Therefore, ScholarPak's break-even point in sales dollars for the coming year, considering the 10% increase in variable manufacturing costs, is $77,143.
5. To calculate the selling price that would yield the same contribution-margin ratio in the coming year, assuming a 10% increase in variable manufacturing costs, we need to adjust the variable manufacturing cost per unit and calculate the new selling price.
Variable manufacturing costs per unit = $12 × 1.10
= $13.20
Contribution margin ratio = (Selling price per unit - Variable costs per unit) / Selling price per unit
Contribution margin ratio = ($30 - $13.20) / $30
Contribution margin ratio = $16.80 / $30
Contribution margin ratio = 0.56
Let X be the new selling price.
(X - $13.20) / X = 0.56
X - $13.20 = 0.56X
0.44X = $13.20
X = $13.20 / 0.44
X ≈ $30
Therefore, to maintain the same contribution-margin ratio in the coming year with a 10% increase in variable manufacturing costs, ScholarPak should set the selling price at approximately $30.
To answer these questions, we need to understand some basic concepts of cost-volume-profit analysis.
1. Break-even point in sales dollars:
The break-even point is the level of sales at which a company neither makes a profit nor incurs a loss. It is calculated by dividing the fixed costs by the contribution margin ratio. The contribution margin ratio is the difference between the selling price and the variable costs, expressed as a percentage.
In this case, the fixed costs for manufacturing are $540,000, and the fixed costs for marketing are $216,000. The variable manufacturing costs are $12 per unit, and the variable marketing costs are $6 per unit sold. The selling price per unit is $30.
To calculate the break-even point, we need to find the contribution margin ratio. The contribution margin ratio can be calculated as follows:
Contribution Margin Ratio = (Selling Price per unit - Variable Costs per unit) / Selling Price per unit
Contribution Margin Ratio = ($30 - $12 - $6) / $30 = $12 / $30 = 0.4 or 40%
Now we can calculate the break-even point in sales dollars:
Break-even Point = Fixed Costs / Contribution Margin Ratio
Break-even Point = ($540,000 + $216,000) / 0.4 = $756,000 / 0.4 = $1,890,000
Therefore, ScholarPak's break-even point in sales dollars for the year is $1,890,000.
2. Number of sales units required to earn a net income of $540,000:
To calculate the number of sales units required to earn a net income, we need to consider the fixed costs, variable costs, and the desired net income.
Fixed costs for manufacturing are $540,000, and fixed costs for marketing are $216,000. Desired net income is $540,000.
Net Income = (Selling Price per unit - Variable Costs per unit) * Number of sales units - Fixed Costs
Number of sales units = (Fixed Costs + Desired Net Income) / (Selling Price per unit - Variable Costs per unit)
Number of sales units = ($540,000 + $216,000 + $540,000) / ($30 - $12 - $6) = $1,296,000 / $12 = 108,000 units
Therefore, ScholarPak would need to sell 108,000 units to earn a net income of $540,000 during the year.
3. Break-even point in sales dollars for the coming year with a 10% increase in variable manufacturing costs:
With a 10% increase in variable manufacturing costs, we need to calculate the new contribution margin ratio and then determine the break-even point.
Variable manufacturing costs increase by 10%, so the new variable manufacturing cost per unit is $12 + ($12 * 0.1) = $13.20.
New Contribution Margin Ratio = (Selling Price per unit - New Variable Manufacturing Costs per unit - Variable Marketing Costs per unit) / Selling Price per unit
New Contribution Margin Ratio = ($30 - $13.20 - $6) / $30 = $10.80 / $30 = 0.36 or 36%
New Break-even Point = Fixed Costs / New Contribution Margin Ratio
New Break-even Point = ($540,000 + $216,000) / 0.36 = $756,000 / 0.36 = $2,100,000
Therefore, ScholarPak's break-even point in sales dollars for the coming year, with a 10% increase in variable manufacturing costs, is $2,100,000.
4. Selling price that would yield the same contribution-margin ratio in the coming year with a 10% increase in variable manufacturing costs:
To calculate the selling price that would yield the same contribution-margin ratio, we need to find the new selling price that would result in a contribution margin ratio of 36%.
New Selling Price per unit = New Variable Manufacturing Costs per unit + Variable Marketing Costs per unit + (Contribution Margin Ratio * New Selling Price per unit)
$30 = $13.20 + $6 + (0.36 * New Selling Price per unit)
Solving for New Selling Price per unit:
New Selling Price per unit = ($30 - $13.20 - $6) / 0.36 = $10.8 / 0.36 = $30
Therefore, if ScholarPak's variable manufacturing costs increase by 10%, the selling price that would yield the same contribution-margin ratio in the coming year is $30 per unit.