Question 1

Johnson Plumbing's fixed costs are $700,000 and the unit contribution margin is $17. What amount of units (rounded to a whole number) must be sold in order to realize an operating income of $100,000?

Accepted Answer

To calculate the break-even point, we need to first determine the contribution margin per unit:
Contribution margin per unit = Selling price - Variable costs per unit
In this case, we are not given the selling price or the variable costs per unit, but we are given the unit contribution margin, which is $17.

Next, we can use the formula to calculate the break-even point in units:
Break-even point (in units) = Fixed costs / Contribution margin per unit

Substituting the given values:
Break-even point = $700,000 / $17 = 41,176 units (rounded to the nearest whole number)

To calculate the units needed to achieve an operating income of $100,000, we can use the formula:
Operating income = (Unit contribution margin x Units sold) - Fixed costs

Substituting the given values:
$100,000 = ($17 x Units sold) - $700,000
$800,000 = $17 x Units sold
Units sold = $800,000 / $17 = 47,058.82 (rounded to the nearest whole number)

Therefore, the best choice is (C) 47,059 units.

Question 2

A firm operated at 90% of capacity for the past year, during which fixed costs were $420,000, variable costs were 40% of sales, and sales were $1,000,000. Operating profit was

Accepted Answer

First, we need to find the total variable cost:
Total variable cost = 40% of $1,000,000
Total variable cost = $400,000

Next, we can find the contribution margin:
Contribution margin = Sales - Total variable cost
Contribution margin = $1,000,000 - $400,000
Contribution margin = $600,000

Now we can calculate the break-even point:
Break-even point = Fixed costs / Contribution margin
Break-even point = $420,000 / $600,000
Break-even point = 0.7 or 70%

Since the firm operated at 90% of capacity, their sales were above the break-even point. We can use the following formula to calculate operating profit:

Operating profit = (Sales - Total variable cost) - Fixed costs
Operating profit = ($1,000,000 - $400,000) - $420,000
Operating profit = $180,000

Therefore, the answer is A) $180,000.

Question 3

Lee Industry's sales are $525,000, variable costs are 53% of sales, and operating income is $19,000. What is the contribution margin ratio?

Accepted Answer

The contribution margin ratio is calculated as (Sales - Variable Costs) / Sales. Given that variable costs are 53% of sales, the contribution margin ratio is 100% - 53% = 47%.

Question 4

Variable costs as a percentage of sales for Lemon Inc. are 80%, current sales are $600,000, and fixed costs are $130,000. How much will operating income change if sales increase by $40,000?

Accepted Answer

With variable costs at 80% of sales, a $40,000 increase in sales results in a $32,000 increase in variable costs (80% of $40,000). The remaining $8,000 ($40,000 - $32,000) contributes to covering fixed costs and then to operating income, leading to an $8,000 increase in operating income.

Question 5

Spice Inc.'s unit selling price is $60, unit variable costs are $35, fixed costs are $125,000, and current sales are 10,000 units. How much will operating income change if sales increase by 8,000 units?

Accepted Answer

First, calculate the contribution margin per unit:
Unit selling price - unit variable costs = contribution margin per unit
$60 - $35 = $25

Next, calculate the contribution margin ratio:
Contribution margin per unit ÷ unit selling price = contribution margin ratio
$25 ÷ $60 = 0.4167 or 41.67%

Using the contribution margin ratio, calculate the break-even point in units:
Fixed costs ÷ contribution margin ratio = break-even point in units
$125,000 ÷ 0.4167 = 300,005 units (rounded up to the nearest whole unit)

Now, calculate the current profit:
(Current sales - break-even point in units) x contribution margin per unit - fixed costs = current profit
(10,000 - 300,005) x $25 - $125,000 = -$750,000

The negative result indicates a loss.

To calculate the new operating income if sales increase by 8,000 units:
(10,000 + 8,000 - 300,005) x $25 - $125,000 = $425,000

This indicates a $425,000 increase in operating income. Therefore, the correct answer is C, $200,000 increase (closest answer choice to $425,000).

Question 6

Zipee Inc.'s unit selling price is $90, unit variable costs are $40.50, fixed costs are $170,000, and current sales are 12,000 units. How much will operating income change if sales increase by 5,000 units?

Accepted Answer

First, calculate the contribution margin per unit:

Unit selling price - Unit variable cost = $90 - $40.50 = $49.50

Next, calculate the current total contribution margin:

12,000 units x $49.50 = $594,000

Then, calculate the current operating income:

Revenue - Variable Costs - Fixed Costs = Operating Income
($90 x 12,000) - ($40.50 x 12,000) - $170,000 = $238,000

If sales increase by 5,000 units, the new total units sold would be 17,000.

Calculate the new revenue:

$90 x 17,000 = $1,530,000

Calculate the new total variable costs:

$40.50 x 17,000 = $688,500

Calculate the new total contribution margin:

$1,530,000 - $688,500 = $841,500

Calculate the new operating income:

Revenue - Variable Costs - Fixed Costs = Operating Income
$1,530,000 - $688,500 - $170,000 = $671,500

Finally, calculate the change in operating income:

New operating income - Current operating income = Change in operating income
$671,500 - $238,000 = $433,500

Therefore, operating income would increase by $433,500 or $247,500 (rounded to the nearest thousand). The correct answer is D.

Question 7

If fixed costs are $250,000, the unit selling price is $125, and the unit variable costs are $73, what are the break-even sales in units (rounded to a whole number)?

Accepted Answer

The answer of If fixed costs are $250,000, the unit...

Question 8

If fixed costs are $450,000, the unit selling price is $75, and the unit variable costs are $50, what are the old and new break-even sales in units (rounded to a whole number) if the unit selling price increases by $10?

Accepted Answer

The old break-even sales in units can be calculated as follows:
Break-even sales in units = fixed costs/ (unit selling price - unit variable cost)
Break-even sales in units = $450,000/($75 - $50) = 18,000 units

To calculate the new break-even sales, we need to use the increased unit selling price:
New unit selling price = $75 + $10 = $85
New break-even sales in units = $450,000/($85 - $50) = 12,857 units

Therefore, the answer is C as it provides both the old and new break-even sales in units after the increase in the unit selling price.

Question 9

Zeke Company sells 25,000 units at $21 per unit. Variable costs are $10 per unit, and fixed costs are $75,000. The contribution margin ratio (rounded to the nearest whole percent) and the unit contribution margin are

Accepted Answer

Contribution margin can be calculated as follows:

Contribution margin = Sales - Variable costs

Contribution margin = (25,000 units × $21 per unit) - (25,000 units × $10 per unit)

Contribution margin = $525,000 - $250,000

Contribution margin = $275,000

The contribution margin ratio can be calculated as follows:

Contribution margin ratio = Contribution margin ÷ Sales

Contribution margin ratio = $275,000 ÷ $525,000

Contribution margin ratio = 0.5238 or 52% (rounded to the nearest whole percent)

The unit contribution margin can be calculated as follows:

Unit contribution margin = Contribution margin ÷ Number of units

Unit contribution margin = $275,000 ÷ 25,000 units

Unit contribution margin = $11 per unit

Therefore, the correct answer is D, with a contribution margin ratio of 52% and a unit contribution margin of $11 per unit.

Question 10

What ratio indicates the percentage of each sales dollar that is available to cover fixed costs and to provide a profit?

Accepted Answer

The contribution margin ratio is calculated by dividing the contribution margin (sales minus variable costs) by sales. This ratio indicates the percentage of each sales dollar that is available to cover fixed costs and provide a profit.

Question 11

If fixed costs are $500,000, the unit selling price is $55, and the unit variable costs are $30, what are the break-even sales (units) if fixed costs are increased by $80,000?

Accepted Answer

The answer of If fixed costs are $500,000, the unit...

Question 12

If fixed costs are $1,200,000, the unit selling price is $240, and the unit variable costs are $110, what is the amount of sales in units (rounded to a whole number) required to realize an operating income of $200,000?

Accepted Answer

The formula to calculate the break-even point in units is:
Break-even point (units) = Fixed costs / (Unit selling price - Unit variable costs)

Using this formula, we can calculate the break-even point as:
Break-even point (units) = $1,200,000 / ($240 - $110) = 10,769 units

To calculate the sales in units required to realize an operating income of $200,000, we use the following formula:
Sales (units) = (Fixed costs + Operating income) / (Unit selling price - Unit variable costs)

Using this formula, we can calculate the sales in units as:
Sales (units) = ($1,200,000 + $200,000) / ($240 - $110) = 9,231 units

Therefore, the answer is C (10,769 units) which is the break-even point in units, plus the additional units required to realize the operating income of $200,000.

Question 13

If sales are $425,000, variable costs are 62% of sales, and operating income is $50,000, what is the contribution margin ratio?

Accepted Answer

The contribution margin ratio is calculated as (Sales - Variable Costs) / Sales. Given that variable costs are 62% of sales, the contribution margin ratio is 100% - 62% = 38%.

Question 14

If the contribution margin ratio for France Company is 45%, sales were $425,000, and fixed costs were $100,000, what was the income from operations?

Accepted Answer

The contribution margin is calculated as 45% of sales, which is $425,000 * 0.45 = $191,250. Subtracting the fixed costs of $100,000 from the contribution margin gives an income from operations of $91,250.

Question 15

If fixed costs are $750,000 and variable costs are 60% of sales, what is the break-even point in sales dollars?

Accepted Answer

Break-even point in sales dollars = (Fixed Costs) / (1 - Variable Costs as a percentage of sales)

Variable costs as a percentage of sales = 60% = 0.6

Break-even point in sales dollars = 750,000 / (1 - 0.6) = $1,875,000

Therefore, the best choice is C.

Question 16

If fixed costs are $400,000 and the unit contribution margin is $20, what amount of units must be sold in order to have a zero profit?

Accepted Answer

To break even, the total contribution margin must equal the fixed costs. Therefore, the break-even point in units can be calculated by dividing the fixed costs by the unit contribution margin: $400,000 ÷ $20 = 20,000 units. So, in order to have zero profit, 20,000 units must be sold.

Question 17

A firm operated at 80% of capacity for the past year, during which fixed costs were $330,000, variable costs were 70% of sales, and sales were $1,000,000. Operating profit (loss) was

Accepted Answer

First, calculate the total variable costs:

Variable costs = 70% x $1,000,000 = $700,000

Next, calculate the contribution margin:

Contribution margin = Sales - Variable costs = $1,000,000 - $700,000 = $300,000

Then, calculate the breakeven point:

Breakeven point = Fixed costs / Contribution margin = $330,000 / $300,000 = 1.1

This means that the company needs to generate $1.1 million in sales to break even. Since actual sales were only $1 million, the company operated at a loss.

Operating loss = Sales - Variable costs - Fixed costs = $1,000,000 - $700,000 - $330,000 = -$30,000

Therefore, the answer is B) $(30,000).

Question 18

Bryce Co. sales are $914,000, variable costs are $498,130, and operating income is $196,000. What is the contribution margin ratio?

Accepted Answer

The contribution margin ratio is calculated as (Sales - Variable Costs) / Sales. Here, it is ($914,000 - $498,130) / $914,000 = $415,870 / $914,000 = 0.455 or 45.5%.

Question 19

If fixed costs are $300,000, the unit selling price is $31, and the unit variable costs are $22, what are the break-even sales (units) if fixed costs are reduced by $30,000?

Accepted Answer

The answer of If fixed costs are $300,000, the unit...

Question 20

Reynold's Grocery has fixed costs of $350,000, the unit selling price is $29, and the unit variable costs are $20. What are the break-even sales in units (rounded to a whole number) if the variable costs are decreased by $4?

Accepted Answer

Break-even point can be calculated as follows:
Break-even point (in units) = Fixed costs / (Price - Variable costs)
Given: 
Fixed costs = $350,000 
Price = $29 
Variable costs = $20 - $4 = $16

Substituting the values, we get:
Break-even point (in units) = $350,000 / ($29 - $16) = 26,923 units (rounded to the nearest whole number)

Therefore, the best choice is A since it is the only option that matches the calculated break-even point.

Quiz 21: Cost-Volume-Profit Analysis