Cost Volume Profit Analysis
Hard Practice Test
Hard Practice Test
Click the “Check Your Answer” box below each question to reveal the correct answer and explanation.
1. Once the volume of sales is higher than the break-even point
a. the contribution margin ratio increases
b. the contribution margin per unit increases
c. total fixed cost per unit will not change
d. total contribution margin will be higher than fixed costs
Answer
D. Use the formula: Sales – VC = CM – FC = Profit. When sales go higher than break-even the profit becomes positive and the contribution margin will be higher than fixed costs since the fixed costs do not increase with volume increases. The contribution margin per unit and ratio do not change with volume because the cost per unit remains the same
2. When a company’s profits do not change as volume changes, it has
a. no fixed costs
b. no variable costs
c. a sales price equal to variable costs
d. fixed costs equal to variable costs
Answer
C. Use the formula: Sales – VC = CM – FC = Profit. When the sales price equals variable costs than there will be no contribution margin. This will hold true as volume changes. Fixed costs do not change with volume changes, therefore, profit will not change either. The contribution margin being 0 is the key.
3. A management team that prefers to have a low operating leverage means that the company most likely
a. expects a strong increase in sales volume
b. expects a decrease in sales volume
c. is very unprofitable
d. has very high fixed costs
Answer
B. The operating leverage indicates how much profits will change as sales change. A company will want to have a low operating leverage when sales are decreasing, because the decrease will lower profits by a lower amount than a high operating leverage. Contribution margin is what most affects the operating leverage, not fixed costs. Operating leverage is not a direct indicator of whether the firm is profitable.
4. When variable costs decrease and all other factors do not change
a. the number of units necessary to be profitable increases
b. the number of units necessary to be profitable decreases
c. the number of units necessary to be profitable does not change
d. none of the above
Answer
B. When variable costs decrease the contribution margin per unit will increase. When you have a higher contribution margin you will need fewer units to be profitable.
5. What must you consider when doing cost volume profit analysis when the company has four different products with four different contribution margin ratios?
a. the per unit contribution margin of each product only
b. that fixed costs will change as the mix changes within the relevant range
c. that the sales mix will impact profitability
d. that as sales increase the variable costs will decrease
Answer
C. The sales mix will impact profits when the company has different products with different contribution margin ratios. You can not only consider the profits individually when doing an analysis for the entire company. As sales increase, variable costs will increase, not decrease.
6. Two companies have a break-even point of 2,000 units. One company has lower fixed costs and higher variable costs than the other company. How will a 10% increase in units sold affect the two companies?
a. the two company’s profits will increase by the same percentage
b. the company with the higher variable cost will be more profitable
c. the company with the higher variable cost will be less profitable
d. can’t determine without additional information
Answer
C. The higher variable cost will give a lower contribution margin ratio and lower contribution dollars from the same increase in sales. Less contribution margin dollars will lead to lower profits.
7. Operating leverage is related to
a. sales and variable costs only
b. sales and fixed costs only
c. sales and fixed costs and variable costs
d. variable costs and contribution margin dollars
Answer
C. Operating leverage works because fixed costs remain constant and as the contribution margin ratio remains constant and sales increase, the company will earn more profits. The formula is CM / Income and income includes all costs.
8. Contribution margin is calculated as
a. one less the variable cost as a percentage of sales
b. sales per unit less variable costs per unit
c. sales less fixed costs less income
d. all of the above
Answer
D. You can calculate the contribution margin in all of the following ways because Sales – VC = CM – FC = Income
9. The break-even point in sales dollars can be calculated using:
a. sales revenue as a percentage of income
b. contribution margin as a percentage of income
c. contribution margin as a percentage of sales
d. fixed costs as a percentage of sales
Answer
C. Break-even in sales dollars is calculated as Fixed Costs / CM % and the CM % is calculated as CM / Sales, therefore it is a percentage of sales
10. As the contribution margin percentage increases, the sales dollars required to break-even will
a. decrease
b. increase
c, remain the same
d. can’t tell unless you know what the contribution margin is currently
Answer
A. The contribution margin percentage is the percentage of every sales dollar that is available to cover fixed costs and when fixed costs are covered is profit. As the percentage increases, less sales will give the same amount of profit.
11. You know the following:
Sales $200,000 Operating Income $24,000
Fixed Costs $ 40,000 Units sold 200
Determine:
a. Contribution margin per unit and contribution margin ratio
b. Break – even in units and sales dollars
c. Units and sales dollars sold to have before tax profit of $50,000
d. Operating leverage
e. The expected income if sales increase 10%
f. How many sales dollars are required to give a $0 profit if variable costs
increase by 10%?
Answer
You have to do the income statement and plug to find total variable costs:
You cannot do cost volume profit analysis without knowing variable costs and the contribution margin.
| Sales | $200,000 | |
| Variable costs | $136,000 | 2nd plug working up |
| 2nd plug working up | $ 64,000 | 1st plug working up |
| Fixed costs | $ 40,000 | |
| Operating Income | $ 24,000 |
1st – Identify the sales price as $1000 per unit ($200,000 / 200 units given)
2nd – Identify the variable costs as $680 per unit: ($136,000 / 200 units given)
3rd – Contribution margin per unit is $1000 sales – $680 variable cost = $320 per unit
4th – Contribution margin ratio is $320 CM / $1000 sales = 32% or .32
5th – Total fixed costs are $40,000
You should follow these 5 steps first for all problems.
a. The CM is $320 per unit and the CM ratio % is 32%
b. The break-even formula is
Total Fixed Costs = units sold to B/E
CM per unit
$40,000 = 125 units to get B/E
$320 per unit
b. The break-even formula is
Total Fixed Costs = sales $ sold to B/E
CM %
$40,000 = $125,000 to get B/E
.32
For c., add the desired profit to the break-even formula:
c. The formula is
Total Fixed Costs + Desired Profit = units sold
CM per unit
$40,000 + $50,000 = 281.25 to earn $50,000
$320 per unit
c. The formula is
Total Fixed Costs + Profit = sales $ sold
CM %
$40,000 + $50,000 = $281,250 to earn $50,000
.32
d. The operating leverage formula is
Contribution Margin
Income
64,000 / 24,000 = 2.667 factor
e. To get the % income is expected to increase is sales increase do the following:
Sales % increase 10%
x operating leverage factor 2.667
= % income will increase 26.67%
Use the % income will increase to determine the income if sales go up 10%
Current Income $24,000
x % income will increase .2667
= Added income $ 6,401
+ current income $24,000
= income if sales + 20% $30,401
f. A zero profit is just another way of saying break-even. Use the break-even formula with the new contribution margin after the 10% increase in variable costs.
Sales $200,000
New variable costs $149,600 ($136,000 x 1.1)
New Contribution margin $ 50,400
New CM ratio 25.2% ($50,400 / $200,000)
Fixed Costs $40,000 = $158.730
CM ratio .252
to break-even if variable costs increase
12. The company had sales of $1,000,000 and units sales of 50,000 and incurred the following costs:
| Rent at the manufacturing plant |
$89,000
|
|
| Utilities at the manufacturing plant |
$32,000
|
|
| General business insurance |
$12,000
|
|
| Direct Materials |
$288,000
|
|
| Plant manager’s salary |
$56,000
|
|
| Direct labor |
$156,000
|
|
| Glue used to put together every product |
$6,000
|
|
| Total advertising paid at a weekly rate |
$28,000
|
|
| Sales commissions |
$10,000
|
|
| Salesman travel that is planned each year |
$39,000
|
|
| Executive and administrative salaries |
$162,000
|
Determine:
a. Contribution margin per unit and contribution margin ratio
b. Break – even in units and sales dollars
c. Operating leverage and expected income if sales increase 10%
Answer
You have to do a contribution margin income statement which requires you to determine which costs are variable costs and which are fixed costs
Sales $1,000,000
Less variable costs:
Utilities at the manufacturing plant $ 32,000
Direct materials $288,000
Direct labor $156,000
Glue used to put together every product $ 6,000
Sales commissions $ 10,000
Total variable costs $492,000
Contribution Margin $508,000
Less fixed costs:
Rent at the manufacturing plant $ 89,000
General business insurance $ 12,000
Plant manager’s salary $ 56,000
Total advertising paid at a weekly rate $ 28,000
Salesman travel that is planned each year $ 39,000
Executive and administrative Salaries $162,000
Total fixed costs $386,000
Operating Income $122,000
Then:
1st – Identify the sales price as $20 per unit ($1,000,000 / 50,000 units)
2nd – Identify the variable costs as $9.84 per unit: ($492,000 / 50,000 units)
3rd – Contribution margin per unit is $20 sales – $9.84 variable cost = $10.16 per unit
4th – Contribution margin ratio is $10.16 CM / $20 sales = 50.8% or .508
5th – Total fixed costs are $386,000 You should follow these 5 steps first for all problems.
a. The CM is $10.16 per unit and the CM ratio % is 50.8%
b.
$386,000 = 37,993 to get B/E
$10.16 per unit units
b.
$386,000 = $759,843 to get B/E
.508
c.
508,000 / 122,000 = 4.164 factor
e. To get the % income is expected to increase if sales increase do the following:
Sales % increase 10%
x operating leverage factor 4.164
= % income will increase 41.64%
Use the % income will increase to determine the income if sales go up 10%
Current Income $122,000
x % income will increase .4164
= Added income $ 50,801
+ current income $122,000
= income if sales + 20% $172,801
Total fixed costs are $2,000,000 per year. Considering the current sales mix, calculate the following:
1. The total company break-even point in units
2. The total company break-even point in sales dollars
3. Unit sales required to earn $500,000 in operating income
Answer
Y Z
1. Sales $1,000 $500
- Variable Cost 400 100
= CM $ 600 $400
units sold (3/8) .375 (5/8) .625 average CM
Average CM $ 225 $250 = $475 per product
FC / CM per unit = $2,000,000 / $475 = 4,211 units
2. Weighted average sales price is:
Y Z
Sales $1,000 $500
% .375 .625
$375 + $312.50 = $687.50
W.A. CM / W.A. Sales = $475 / $687.50 = .6909
Fixed cost / CM % = $2,000,000 / .6909 = $2,894,775
3. Fixed cost + profit / CM per unit
$2,000,000 + $500,000 / $475 = 5,263