Question

Flying Cloud Co. has the following operating data for its manufacturing operations:

Unit selling price $200
Unit variable cost 120
Total fixed costs 772,000
The company has decided to increase the wages of hourly workers which will increase the unit variable cost by 10%. Increases in the salaries of factory supervisors and property taxes for the factory will increase fixed costs by 4%. If sales prices are held constant, the next break-even point for Flying Cloud Co. will be (rounded to a whole number)
a. increased by 1,726 units
b. decreased by 2,157 units
c. increased by 2,157 units
d. increased by 2,588 units

Answer 1

The new break-even point for Flying Cloud Co., after a 10% increase in unit variable cost and a 4% increase in fixed costs, is increased by approximately 2,157 units.

Step-by-step explanation:

First, let's calculate the new unit variable cost and the new total fixed costs after the increases:

• New unit variable cost = $120 + (10% of $120) = $132
• New total fixed costs = $772,000 + (4% of $772,000) = $802,880

Next, we determine the old and new break-even points. The break-even point is the number of units that must be sold to cover both variable and fixed costs, with no profit or loss. The formula is:

Break-even point (units) = Total Fixed Costs / (Selling Price per Unit - Variable Cost per Unit)

Old break-even point = $772,000 / ($200 - $120) = 772,000 / 80 = 9,650 units

New break-even point = $802,880 / ($200 - $132) = 802,880 / 68 ≈ 11,806 units (rounded to the nearest whole number)

The increase in the break-even point is 11,806 units - 9,650 units = 2,156 units.

Since the new break-even point is increased by 2,156 units, and options require a rounded whole number, the closest correct option is:

c. increased by 2,157 units

Answer 2

the break-even point has increased by approximately 2,157 units. This is how we arrive at the conclusion that the new break-even point for Flying Cloud Co. is increased by 2,157 units when sales prices are held constant. Therefore, option C is correct

a detailed step-by-step calculation to determine the new break-even point for Flying Cloud Co. after cost changes:

Step 1: Original Contribution Margin per Unit

The contribution margin per unit is calculated by subtracting the unit variable cost from the unit selling price.

Original Contribution Margin per Unit:

`\[ \$200 - \$120 = \$80 \]`

Step 2: New Unit Variable Cost

The new unit variable cost is found by increasing the original unit variable cost by 10%.

New Unit Variable Cost:

`\[ \$120 * 1.10 = \$132 \]`

Step 3: New Total Fixed Costs

The new total fixed costs are calculated by increasing the original total fixed costs by 4%.

New Total Fixed Costs:

`\[ \$772,000 * 1.04 = \$802,880 \]`

Step 4: New Contribution Margin per Unit

The new contribution margin per unit is the unit selling price minus the new unit variable cost.

New Contribution Margin per Unit:

`\[ \$200 - \$132 = \$68 \]`

Step 5: New Break-Even Point in Units

The break-even point in units is the point where total sales equal total costs (both fixed and variable), resulting in zero profit. The new break-even point is found by dividing the new total fixed costs by the new contribution margin per unit.

New Break-Even Point in Units:

`\[ (\$802,880)/(\$68) \approx 11,807 \text{ units} \]`

Step 6: Difference Between New and Original Break-Even Points

To find how much the break-even point has increased, subtract the original break-even point from the new one.

Difference in Break-Even Points:

`\[ \approx 11,807 \text{ units} - 9,650 \text{ units} \approx 2,157 \text{ units} \]`

So, the break-even point has increased by approximately 2,157 units. This is how we arrive at the conclusion that the new break-even point for Flying Cloud Co. is increased by 2,157 units when sales prices are held constant.