Millstone Company produces only one product. Normal capacity is 20,000 units per year, and the unit sales price is $5. Relevant costs are: (picture attached)

Compute the following:

(1) The break-even point in units of product

(2) The break-even point in dollars of sales

(3) The number of units of product that must be produced and sold to achieve a profit of $10,000

(4) The sales revenue required to achieve a profit of $10,000

Calculation of break-even point in units of product

Fixed Cost = Factory Overhead + Marketing Expenses + Administrative Expenses

Fixed Cost = $15,000 + $5,000 + $6,000

Fixed Cost = $26,000

Selling Price = $5.00

Variable Cost = Materials + Direct Labor + Factory Overhead + Marketing Expense

Variable Cost = $1.00 + $1.20 + $0.50 + $0.30

Variable Cost = $3.00

Contribution Margin Per unit = Selling Price per unit - Variable Cost per unit

Contribution Margin Per unit = $5 - $3

Contribution Margin Per unit = $2

Break-even point (in units) = Fixed Cost / Contribution Margin Per unit

Break-even point (in units) = $26,000 / $2

Break-even point (in units) = 13,000 units

Calculation of the break-even point in dollars of sales

Contribution Margin Ratio = Contribution Margin / Sales

Contribution Margin Ratio = $2 / $5

Contribution Margin Ratio = 0.40

Break-even point (in dollars) = Fixed Cost / Contribution Margin Ratio

Break-even point (in dollars) = $26,000 / 0.40

Break-even point (in dollars) = $65,000

Calculation of number of units of product that must be produced and sold to achieve the profit

Net Income = $10,000

Fixed Cost = $26,000

Net Income = Revenue - Variable Cost - Fixed Cost

Let x = Number of Units

$10,000 = $5x - $3x - $26,000

$2x = $10,000 + $26,000

x = $36,000 / $2

x = 18,000 units

Calculation of the sales revenue required to achieve the profit

Sales Revenue = Sales per unit x Number of units

Sales Revenue = $5 per unit x 18,000 unit

Sales Revenue = $90,000

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(1) 13,000 units

(2) $65,000

(3) 18,000 units

(4) $90,000

Explanation:

(1) Break-even point (in units) = Fixed Cost / Contribution Margin Per unit

Fixed Cost = Factory Overhead + Marketing Expenses + Administrative Expenses

Fixed Cost = $15,000 + $5,000 + $6,000

Fixed Cost = $26,000

Selling Price = $5.00

Variable Cost = Materials + Direct Labor + Factory Overhead + Marketing Expense

Variable Cost = $1.00 + $1.20 + $0.50 + $0.30

Variable Cost = $3.00

Contribution Margin Per unit = Selling Price per unit - Variable Cost per unit

Contribution Margin Per unit = $5 - $3

Contribution Margin Per unit = $2

Break-even point (in units) = $26,000 / $2

Break-even point (in units) = 13,000 units

(2) Break-even point (in dollars) = Fixed Cost / Contribution Margin Ratio

Contribution Margin Ratio = Contribution Margin / Sales

Contribution Margin Ratio = $2 / $5

Contribution Margin Ratio = 0.40

Break-even point (in dollars) = $26,000 / 0.40

Break-even point (in dollars) = $65,000

(3) Net Income = Revenue - Variable Cost - Fixed Cost

Net Income = $10,000

Fixed Cost = $26,000

Let x = Number of Units

$10,000 = $5x - $3x - $26,000

Add $26,000 on both sides we get;

$2x = $10,000 + $26,000

x = $36,000 / $2

x = 18,000 units

(4) Sales Revenue = Sales per unit x Number of units

Sales Revenue = $5 per unit x 18,000 unit

Sales Revenue = $90,000

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