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Math  /  Data & Statistics

QuestionManagement is considering a plant expansion program for the following year that will permit an increase of $11,160,000\$ 11,160,000 in yearly sales. The expansion will increase fixed costs by $3,500,000\$ 3,500,000 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.
Total variable costs $86,000,000✓\$ \mathbf{8 6 , 0 0 0 , 0 0 0} \checkmark Total fixed costs $38,400,000\$ 38,400,000
2. Determine (a) the unit variable cost and (b) the unit contribution margin for the current year.
Unit variable cost \86Unitcontributionmargin$100<br/>3.Computethebreak−evensales(units)forthecurrentyear. 86 Unit contribution margin \$ 100<br />3. Compute the break-even sales (units) for the current year. 384,000 \checkmark$ units
4. Compute the break-even sales (units) under the proposed program for the following year.
419,000 ✓\checkmark units
5. Determine the amount of sales (units) that would be necessary under the proposed program to realize the $61,600,000\$ 61,600,000 of operating income that was earned in the current year. 1,035,000✓1,035,000 \checkmark units
6. Determine the maximum operating income possible with the expanded plant. \ \square$

Studdy Solution

STEP 1

1. The current year's total variable costs are \$86,000,000.
2. The current year's total fixed costs are \$38,400,000.
3. The unit variable cost is \$86.
4. The unit contribution margin is \$100.
5. The break-even sales for the current year are 384,000 units.
6. The proposed program increases fixed costs by \$3,500,000.
7. The proposed program's break-even sales are 419,000 units.
8. The operating income for the current year is \$61,600,000.
9. The increase in sales due to the expansion is \$11,160,000.

STEP 2

1. Calculate the maximum operating income possible with the expanded plant.

STEP 3

Calculate the total contribution margin for the expanded sales. The increase in sales is \$11,160,000, and the unit contribution margin is \$100. Therefore, the increase in units sold is:
Increase in units=$11,160,000$100=111,600 units\text{Increase in units} = \frac{\$11,160,000}{\$100} = 111,600 \text{ units}

STEP 4

Calculate the total contribution margin for the increased units:
Total contribution margin=111,600×$100=$11,160,000\text{Total contribution margin} = 111,600 \times \$100 = \$11,160,000

STEP 5

Calculate the increase in operating income by subtracting the increase in fixed costs from the total contribution margin:
Increase in operating income=$11,160,000−$3,500,000=$7,660,000\text{Increase in operating income} = \$11,160,000 - \$3,500,000 = \$7,660,000

STEP 6

Calculate the maximum operating income possible with the expanded plant by adding the increase in operating income to the current operating income:
Maximum operating income=$61,600,000+$7,660,000=$69,260,000\text{Maximum operating income} = \$61,600,000 + \$7,660,000 = \$69,260,000
The maximum operating income possible with the expanded plant is:
$69,260,000\boxed{\$69,260,000}

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