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Determine the amount of sales (units) that would be necessary under Break-Even Sales Under Present and Proposed Conditions Darby Company, operating at full capacity, sold 94,500 units at a price of $135 per unit during the current year
Determine the amount of sales (units) that would be necessary under
Break-Even Sales Under Present and Proposed Conditions
Darby Company, operating at full capacity, sold 94,500 units at a price of $135 per unit during the current year. Its income statement for the current year is as follows:
Sales $12,757,500
Cost of goods sold 6,300,000
Gross profit $6,457,500
Expenses:
Selling expenses $3,150,000
Administrative expenses 3,150,000
Total expenses 6,300,000
Income from operations $157,500
The division of costs between fixed and variable is as follows:
Variable
Fixed
Cost of goods sold
70%
30%
Selling expenses
75%
25%
Administrative expenses
50%
50%
Management is considering a plant expansion program that will permit an increase of $1,080,000 in yearly sales. The expansion will increase fixed costs by $108,000, but will not affect the relationship between sales and variable costs.
Required:
1. Determine the total variable costs and the total fixed costs for the current year. Enter the final answers rounded to the nearest dollar.
2. Determine (a) the unit variable cost and (b) the unit contribution margin for the current year. Enter the final answers rounded to two decimal places.
3. Compute the break-even sales (units) for the current year. Enter the final answers rounded to the nearest whole number.
4. Compute the break-even sales (units) under the proposed program for the following year. Enter the final answers rounded to the nearest whole number.
5. Determine the amount of sales (units) that would be necessary under the proposed program to realize the $157,500 of income from operations that was earned in the current year. Enter the final answers rounded to the nearest whole number.
6. Determine the maximum income from operations possible with the expanded plant. Enter the final answer rounded to the nearest dollar.
7. If the proposal is accepted and sales remain at the current level, what will the income or loss from operations be for the following year? Enter the final answer rounded to the nearest dollar.
8. Based on the data given, would you recommend accepting the proposal?
Expert Solution
1). Please see the attachment:
2). Computation of the unit variable cost:-
Unit variable cost = Total variable costs / Total units sold
= $8,347,500 / 94,500
= $88.33 per unit
Computation of the unit contribution margin:-
Unit contribution margin = Sale price per unit - Unit variable cost
= $135 - $88.33
= $46.67
3). Computation of the break-even sales in units:-
Break-even sales in units = Total fixed costs / Unit contribution margin
= $4,252,500 / $46.67
= 91,118 units
4). Computation of the break-even sales in units under the proposed program:-
Break-even sales = Increased fixed cost / Unit contribution margin
= ($4,252,500 + $108,000) / $46.67
= $4,360,500 / $46.67
= 93,432.61 Units Or 93,433 units
5). Computation of the amount of sales units:-
Amount of sales units = ($157,500 + $4,252,500 + $108,000) / $46.67
= $4,518,000 / $46.67
= 96,807.37 units Or 96,807 units
6). Computation of the maximum income from operations possible with the expanded plant:-
Increase in sales units = $1,080,000 / $135
= 8,000 units
Maximum sales units = 94,500 + 8,000
= 102,500 units
Maximum income possible = Sales price - Variable cost - Fixed cost
= (102,500 * $135) - (102,500 * $88.33) - ($4,252,500 + $108,000)
= $13,837,500 - $9,054,166.67 - $4,360,500
= $422,833.33 Or $422,833
7). Computation of the income or loss from operations be for the following year:-
Income = Current income from operations - Additional fixed cost
= $157,500 - $108,000
= $49,500
8). In favor of the proposal because of the possibility of increasing income from operations.
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