Question

Help ASAP Please! Accounting class! Lorge Corporation has collected the following information after its first year of sales. Sales were $1,575,000 on 105,000 units; selling expenses $250,000 (40% variable and 60% fixed); direct materials $606,100; direct labor $250,000; administrative expenses $270,000 (20% variable and 80% fixed); and manufacturing overhead $357,000 (70% variable and 30% fixed). Top management has asked you to do a CVP analysis so that it can make plans for the coming year. It has projected that unit sales will increase by 10% next year.

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Answer 1

The contribution margin for the current year is $111,900, and for the projected year, it is $269,400. The fixed costs for the current year are $943,100. The break-even point is 88,265 units or $1,320,750. The required sales for the target net income of $190,000 are $1,060,000. The margin of safety ratio is 16.1%. If the company implements proposed changes, the new contribution margin is $518,900, and the break-even point increases to $2,870,732.

(1) Contribution Margin for Current Year:

The contribution margin is calculated as the sales revenue minus the variable expenses.

`\[ \text{Contribution Margin} = \text{Sales} - \text{Variable Expenses} \]`

For the current year:

`\[ \text{Contribution Margin} = \$1,575,000 - (\$250,000 + \$606,100 + \$250,000 + \$357,000) \]\[ \text{Contribution Margin} = \$1,575,000 - \$1,463,100 \]\[ \text{Contribution Margin} = \$111,900 \]`

For the projected year (with a 10% increase in unit sales):

`\[ \text{Projected Sales} = \$1,575,000 * 1.10 = \$1,732,500 \]\[ \text{Projected Contribution Margin} = \$1,732,500 - (\$250,000 + \$606,100 + \$250,000 + \$357,000) \]\[ \text{Projected Contribution Margin} = \$1,732,500 - \$1,463,100 \]\[ \text{Projected Contribution Margin} = \$269,400 \]`

(2) Fixed Costs for Current Year:

Fixed costs can be calculated by subtracting total variable costs from total costs.

`\[ \text{Fixed Costs} = \text{Total Costs} - \text{Total Variable Costs} \]\[ \text{Fixed Costs} = (\$250,000 + \$606,100 + \$250,000 + \$357,000) - (\$250,000 + \$270,000) \]\[ \text{Fixed Costs} = \$1,463,100 - \$520,000 \]\[ \text{Fixed Costs} = \$943,100 \]`

3. Break-Even Point

To calculate the break-even point:

`\[ \text{Break-Even Point (in units)} = \frac{\text{Fixed Costs}}{\text{Contribution Margin per Unit}} \]\[ \text{Break-Even Point (in units)} = (\$943,100)/((\$111,900)/(105,000)) \]\[ \text{Break-Even Point (in units)} \approx (\$943,100)/(1.0667) \]\[ \text{Break-Even Point (in units)} \approx 88265 \]`

To find the break-even point in sales dollars:

`\[ \text{Break-Even Point (in dollars)} = \text{Break-Even Point (in units)} * \text{Selling Price per Unit} \]\[ \text{Break-Even Point (in dollars)} \approx 88265 * (\$1,575,000)/(105,000) \]\[ \text{Break-Even Point (in dollars)} \approx \$1,320,750 \]`

4. Sales Dollars for Target Net Income

The required sales in dollars to meet the target net income of
`\$190,000` can be calculated:

`\[ \text{Required Sales Dollars} = \frac{\text{Fixed Costs} + \text{Target Net Income}}{\text{Contribution Margin Ratio}} \]\[ \text{Required Sales Dollars} = (\$943,100 + \$190,000)/((\$111,900)/(\$1,575,000)) \]\[ \text{Required Sales Dollars} \approx (\$1,133,100)/(1.0667) \]\[ \text{Required Sales Dollars} \approx \$1,060,000 \]`

5. Margin of Safety Ratio

The margin of safety ratio is calculated as the difference between actual or projected sales and break-even sales, divided by actual or projected sales.

`\[ \text{Margin of Safety Ratio} = \frac{\text{Actual or Projected Sales} - \text{Break-Even Sales}}{\text{Actual or Projected Sales}} \]`

For the current year (with actual sales of
`\$1,575,000`)

`\[ \text{Margin of Safety Ratio} = (\$1,575,000 - \$1,320,750)/(\$1,575,000) \]\[ \text{Margin of Safety Ratio} \approx 0.161 \]`

6. New Contribution Margin and Break-Even Point in Sales Dollars:

With the proposed changes, the new contribution margin can be calculated using the adjusted variable and fixed costs. The contribution margin ratio is then used to find the break-even point in sales dollars.

`\[ \text{New Contribution Margin} = \text{Sales} - \text{Adjusted Variable Costs} \]\[ \text{New Contribution Margin} = \$1,575,000 - (\$250,000 + \$606,100 + \$110,000 + \$90,000) \]\[ \text{New Contribution Margin} = \$1,575,000 - \$1,056,100 \]\[ \text{New Contribution Margin} = \$518,900 \]`

`\[ \text{Contribution Margin Ratio} = \frac{\text{New Contribution Margin}}{\text{Sales}} \]\[ \text{Contribution Margin Ratio} = (\$518,900)/(\$1,575,000) \approx 0.329 \]`

`\[ \text{New Break-Even Point (in dollars)} = \frac{\text{Fixed Costs}}{\text{Contribution Margin Ratio}} \]\[ \text{New Break-Even Point (in dollars)} \approx (\$943,100)/(0.329) \]\[ \text{New Break-Even Point (in dollars)} \approx \$2,870,732 \]`

Therefore, the answers are

Contribution Margin

- Current Year:
`\$111,900`

- Projected Year:
`\$269,400`

Fixed Costs for Current Year

-
`\$943,100`

Break-Even Point

- In Units:
`88,265` units

- In Dollars:
`\$1,320,750`

Sales Dollars for Target Net Income

-
`\$1,060,000`

Margin of Safety Ratio

-
`16.1\%`

New Contribution Margin and Break-Even Point in Sales Dollars

- New Contribution Margin:
`\$518,900`

- New Contribution Margin Ratio:
`32.9\%`

- New Break-Even Point:
`\$2,870,732`

Answer 2

Lorge Corporation

Contribution margin for the current year

= $315,000 ($3 per unit)

Contribution margin for the proposed year = $346,500

Fixed costs for the current year = $473,100

Break-even units = 157,700 units

Break-even sales dollars = $2,365,500

Step-by-step explanation:

a) Data and Calculations:

Sales revenue = $1,575,000

Sales units = 105,000 units

Sales price per unit = $15 ($1,575,000/105,000)

Total Variable Fixed

Selling expenses = $250,000 $100,000 (40%) $150,000 (60%)

Direct materials $606,100 606,100

Direct labor $250,000 250,000

Administrative expenses $270,000 54,000 (20%) 216,000 (80%)

Manufacturing overhead $357,000 249,900 (70%) 107,100 (30%)

Total costs $1,733,100 $1,260,000 $473,100

Contribution margin for the current year = $315,000 ($1,575,000 - $1,260,000)

= $3 per unit

Unit sales = 115,500 (105,000 * 1.1)

Sales revenue = $1,732,500

Variable costs 1,386,000 ($15 - $3)

Contribution margin for the proposed year = $346,500 ($3 * 115,500)

Fixed costs for the current year = $473,100

Break-even units = $473,100/$3 = 157,700 units

Break-even sales dollars = $473,100/0.2 = $2,365,500