Question

Parkins Company produces and sells a single product. The company's income statement for the most recent month is given below:             Sales (6,000 units at $40 per unit)............ $240,000 Less variable costs: Direct materials...................................... $48,000 Direct labor (variable)............................ 60,000 Variable manufacturing overhead.......... 12,000 Variable selling and other Expenses 24,000 144,000 Contribution margin.................................. 96,000 Less fixed costs: Fixed manufacturing overheat .............. 30,000 Fixed selling and other expenses........... 42,000    72,000 Net operating income................................ $ 24,000             There are no beginning or ending inventories.                         Required: CLEARLY LABEL AND SHOW ALL OF YOUR WORK. Compute the company's monthly break-even point in units of product. What would the company's monthly net operating income be if sales increased by 25% and there is no change in total fixed expenses? What dollar sales must the company achieve in order to earn a net operating income of $50,000 per month? The company has decided to automate a portion of its operations. The change will reduce direct labor costs per unit by 40 percent, but it will double the costs for fixed factory overhead. Compute the new break-even point in units.

           

            Required: CLEARLY LABEL AND SHOW ALL OF YOUR WORK.

1. Compute the company's monthly break-even point in units of product.
2. What would the company's monthly net operating income be if sales increased by 25% and there is no change in total fixed expenses?
3. What dollar sales must the company achieve in order to earn a net operating income of $50,000 per month?
4. The company has decided to automate a portion of its operations. The change will reduce direct labor costs per unit by 40 percent, but it will double the costs for fixed factory overhead. Compute the new break-even point in units.

Answer 1

Answer a)

Break-Even Point (in units) = Total Fixed Cost / Contribution Margin per unit

Total Fixed Cost = Fixed Manufacturing Overheads + Fixed Selling and Other Expenses

Total Fixed Cost = $30,000 + $42,000

Total Fixed Cost = $72,000

Contribution Margin = $96,000 (Given)

Number of Units Sold = 6,000 (Given)

Contribution Margin per unit = Contribution Margin / Number of Units

Contribution Margin per unit = $96,000 / 6,000

Contribution Margin per unit = $16

Break-even Point (in units) = $72,000 / $16

Break-even Point (in units) = 4,500

Answer b)

Sales increased by 25% (Given)

Sales Revenue (new) = Sales Revenue (old) + 25% of Sales Revenue (old)

= $240,000 + 25% of $240,000

= $240,000 + $60,000

= $300,000

Total Variable Cost (Old) = $144,000 (Given)

Since, sales are increased by 25%. Therefore, Variable Cost will also be increased by 25%

Total Variable Cost (new) = Total Variable Cost (old) + 25% of Total Variable Cost (old)

= $144,000 + 25% of $144,000

= $144,000 + $36,000

= $180,000

Contribution Margin (new) = Sales Revenue (new) - Variable Cost (new)

= $300,000 - $180,000

= $120,000

Total Fixed Cost = $72,000 (Given that Fixed Cost is same)

Net Operating Income = Contribution Margin (new) - Total Fixed Cost

= $120,000 - $72,000

= $48,000

Answer c)

Target Net Operating Income = $50,000 (Given)

Total Fixed Cost = $72,000 (Given)

Contribution Margin Ratio = (Contribution Margin per unit / Sales Price per unit) * 100

= ($16 / $40) * 100

= 0.4 * 100

​​​​​= 40%

Contribution Margin - Total Fixed Cost = Target Net Operating Income

Contribution Margin - $72,000 = $50,000

Contribution Margin = $50,000 + $72,000

= $122,000

Contribution Margin Ratio = Contribution Margin / Sales

40% = $122,000 / Sales

Sales (in $) = $122,000 / 40%

= $305,000

Answer d)

Direct Labor Cost per unit (old) = Direct Labor Cost (old) / Number of Units (old)

= $60,000 / 6,000

= $10

Direct Labor Cost per unit reduced by 40% (Given)

Decrease in Direct Labor Cost per unit = 40% of $10

= $4

Total Variable Cost per unit (old) = Total Variable Cost (old) / Number of Units (old)

= $144,000 / 6,000

= $24

Total Variable Cost per unit (new) = Total Variable Cost per unit (old) - Decrease in Direct Labor Cost per unit

= $24 - $4

= $20

Sales Price per unit = $40

Contribution Margin per unit (new) = Sales Price per unit - Total Variable Cost per unit (new)

= $40 - $20

= $20

Fixed Factory Overhead (new) = 2 * Fixed Factory Overhead (old)

= 2 * $30,000

= $60,000

Fixed Selling and Other Expenses = $42,000

Total Fixed Cost (new) = Fixed Factory Overhead (new) + Fixed Selling and Other Expenses

= $60,000 + $42,000

= $102,000

New Break-even Point (in units) = Total Fixed Cost (new) / Contribution Margin per unit (new)

= $102,000 / $20

= 5,100 units

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