Question

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 117,450 units at a price of $120 per unit during the current year. Its income statement for the current year is as follows: Sales $14,094,000 Cost of goods sold 6,960,000 Gross profit $7,134,000 Expenses: Selling expenses $3,480,000 Administrative expenses 3,480,000 Total expenses 6,960,000 Income from operations $174,000 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 $1,320,000 in yearly sales. The expansion will increase fixed costs by $132,000, 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. Total variable costs $ Total fixed costs $ 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. Unit variable cost $ Unit contribution margin $ 3. Compute the break-even sales (units) for the current year. Enter the final answers rounded to the nearest whole number. units 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. units 5. Determine the amount of sales (units) that would be necessary under the proposed program to realize the $174,000 of income from operations that was earned in the current year. Enter the final answers rounded to the nearest whole number. units 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? In favor of the proposal because of the reduction in break-even point. In favor of the proposal because of the possibility of increasing income from operations. In favor of the proposal because of the increase in break-even point. Reject the proposal because if future sales remain at the current level, the income from operations will increase. Reject the proposal because the sales necessary to maintain the current income from operations would be below the current year sales. Choose the correct answer.

Answer 1

Solution

Darby Company

Determination of total variable costs and the costs that tend to remain the same in amount regardless of variations in the level of activity:

Total variable costs –

Cost of goods sold       70% x 6,960,000 = $4,872,000

Selling expenses          75% x 3,480,000 = $2,610,000

Administrative expenses 50% x 3,480,000 = $1,740,000

Total variable expenses = $9,222,000

Total fixed costs –

Cost of goods sold       30% x 6,960,000 = $2,088,000

Selling expenses          25% x 3,480,000 = $870,000

Administrative expenses 50% x 3,480,000 = $1,740,000

Total fixed cost = $4,698,000

Unit Variable cost = total variable cost/units sold

= $9,222,000/117,450 units

= $78.52 per unit

Unit Contribution margin = unit selling price – unit variable cost

= $120 – 78.52 = $41.48

Determination of the break-even unit sales for current year:

Break-even unit sales = total fixed cost/contribution margin per unit

= $4,698,000/$41.48 = 113,255 units

Determination of the break-even unit sales under the proposed program for the following year:

Proposed program –

Increase in yearly sales = $1,320,000

Increase in fixed cost = 132,000

Revised sales = $14,094,000 + $1,320,000 = $15,414,000

Percent increase in sales = 1,320,000/14,094,0400 = 9.4%

Increased variable cost = 9,222,000 + 9.40% x 866,868 = $10,088,868

Increased fixed cost = $4,698,000 +132,000 = $4,830,000

Contribution margin = sales – variable cost

= 15,414,000 – 10,088,868 = $5,325,132

Sales units = $15,414,000/$120 = 128,450 units

Contribution margin per unit = $5,325,132/128,450 units = $41.50

Break-even sales units under the proposed program = $4,830,000/$41.50 = 116,507 units

Determination of the amount of sales needed to realize $174,000 income from operations under the proposed program:

Desired sales = (target income + fixed cost)/contribution margin

Target income = $174,000

Fixed cost –

Original fixed cost       $4,698,000

Add: increase              $132,000

Total fixed cost           $4,830,000

Contribution margin = $41.50

Desired sales = (174,000 + 4,830,000)/$19.70 = 120,704 units

Determination of maximum income possible from expanded plant:

Revised Sales              $15,414,000

Less: Variable costs     $10,088,868

Contribution margin   $5,325,132

Less: Fixed cost           $4,830,000

Net operating income $495,132

If proposal accepted and sales remain at current level, determination of net income:

Sales                            $14,094,000

Variable cost               $9,222,000

Contribution margin   $4,872,000

Fixed cost                    $4,830,000

Net operating income $42,000

Based on the given data, the proposed program could be accepted –

In favour of the proposal because of the possibility of increasing income from operations.

The income from operations under the proposed program would be $495,132. Hence, the proposed program would increase income from operations by $321,132 (495,132 – 174,000)

In favour of proposal because of the possibility of increasing the income from operations.