Cost Volume Profit Analysis
Medium Practice Test
Medium Practice Test
Click the “Check Your Answer” box below each question to reveal the correct answer and explanation.
1. A company could never incur a loss that is greater than
a. total sales
b. total fixed costs
c. total costs
d. total contribution margin
Answer
C. Use the formula: Sales – VC = CM – FC = Income/Loss. If sales are 0 than the loss will not be greater than its total costs, FC + VC. Sales of 0 are the lowest sales can go, so the company can’t incur more loss than its total costs.
2. Which of the following is not a major assumption that is used in cost volume profit analysis?
a. all costs are categorized as fixed or variable
b. total contribution margin will change as volume changes
c. variable costs are constant per unit
d. fixed costs are constant per unit
Answer
D. Fixed costs are constant in total and do change per unit. All other answers are assumptions that must hold true for cost volume profit analysis be useful.
3. Management changed the salesperson’s compensation from a fixed salary to only sales commission based on sales dollars. If the company is more profitable, the
a. break even point will increase
b. break even point will decrease
c. operating leverage will decrease
d. contribution margin will increase
Answer
B. A decreasing break even point means that less sales must occur to be profitable. Operating leverage should increase if fixed costs decrease and operating profits increase. Contribution margin per unit will decrease because variable costs are increasing.
4. A company has one product with a break even point of 50,000 units. Fixed costs are $200,000 and the product sells for $10 each. What is the contribution margin ratio?
a. 10 %
b. 20%
c. 40%
d. 50%
Answer
C. At break even fixed cost = contribution margin, so if fixed costs are $200,000, then contribution margin is $200,000 also and for 50,000 units that gives a CM per unit of $4. CM per unit / Sales per unit is the CM ratio. $4 / $10 = 40%
5. When calculating break even, which of the following is true?
a. sales mix remains the same
b. variable costs do not change per unit
c. fixed costs change per unit
d. all of the above
Answer
D. All of the above are assumptions that must hold true when calculating break even.
6. If the sales volume increases and nothing else changes
a. contribution margin per unit will increase
b. margin of safety will increase in units
c. break even will increase in units
d. operating income will decrease
Answer
B. Margin of safety is current sales – breakeven sales and as current sales increases, margin of safety increases also. Since sales and variable costs do not change, the contribution margin per unit does not change and the break even amount does not change either. Operating income will increase as sales increase.
7. A company has variable costs of 60% of sales and wants to increase advertising expenses by $50,000. If sales increase by $100,000, how much will operating income change?
a. $10,000 increase
b. $ 90,000 decrease
c. $ 10,000 decrease
d. $ 40,000 decrease
Answer
C. The CM ratio is calculated by taking Sales – VC, if variable costs are 60%, then the CM ratio is 40%. The CM ratio tells you how much of every additional sales dollar is available to cover fixed costs. For $100,000 increase in sales, there is $40,000 additional contribution margin. The increase in fixed cost of $50,000 is more than the CM that the company will earn from additional sales, and operating income will decrease by $10,000.
8. To maximize profits the company should pay a high sales commission on
a. products with a high variable cost
b. products associated with a low fixed cost
c. products with high contribution margin ratios
d. products with the highest prices
Answer
C. The company should encourage the sales force to sell the products that bring the highest amount of profit for every sales dollar sold, which is the highest contribution margin ratio. High variable costs and high prices do not necessary bring high profit. Products associated with low fixed cost take less sales in units to cover the fixed cost.
9. If fixed costs increase while the sales price and variable costs do not change, the contribution margin will
a. increase
b. decrease
c. remain constant
d. change in direct proportion to the increase in fixed costs
Answer
C. The contribution margins is sales less variable costs. If these do not change then contribution margin will not change also. Contribution margin is not impacted by fixed cost changes.
10. The break even point changes when the company
a. increases fixed costs
b. increases production
c. decreases sales
d. increases sales
Answer
A. The break even formula is: Fixed costs / CM per unit. Sales or production will not impact break-even, so the answer is not b. c. or d. When fixed costs change it requires more/less units sold to cover the fixed costs.
11. Use the information below to answer the following questions, given that each company currently sells the same number of units of one product:
| Company A | Company B | Company C | |
|---|---|---|---|
| Sales | 200 | 200 | 200 |
| – variable costs | 20 | 40 | 60 |
| = contribution margin | 180 | 160 | 140 |
| – fixed costs | 60 | 40 | 20 |
| = operating income | 120 | 120 | 120 |
a. If sales go up by the same amount for each company, which company will have the most increase in operating income?
b. If sales go up by one unit for each, which company will have the most increase in operating income?
c. Which company has the highest margin of safety?
d. Which company has the highest operating leverage?
e. If company B fixed costs increased by 20 % and variable costs went up by 10%, how much would sales dollars have to increase to remain at the same profit amount?
Answer
a. This is determined by using operating leverage which is CM / Income. The company with the highest factor will have the highest increase in profits. Company A has a factor of 180 / 120 = 1.5 which is higher than B at 1.333 and C at 1.1666
Company A will have the highest increase in profits for the sales increase.
b. The company with the highest CM ratio will increase operating income the most.
Company A is .90, B is .80 and C is .70. Company A will benefit the most from and increase in sales of one unit. It will benefit 90% of the sales price compared to the other companies who will benefit 80% and 70% of the sales price.
c. Company C. The company with the lowest fixed costs and similar CM will have the highest margin of safety because it requires less sales to cover the fixed costs and still remain profitable.
d. Company A. Refer to the answer in part 1.
e. Use the target profit formula to solve this and calculate a new CM ratio for company B.
Sales 200
– VC 44
CM 156
CM % 78% (156 / 200)
New FC + Target profit the same / new CM %
(40 + 8) + 120 / .78 = 215.38 less 200 = 15.38 increase
12. Movie Trading Company buys and sells used movies and DVDs. The company has an average sales price of $3.50 each and an average cost to purchase used movies from customers of $1.25 each. The company paid workers $42,980 to service the customer and hours worked varies directly with sales. Workers are paid a sales commission of $0.25 per item sold. Store operating costs for insurance, rent, salaries and other fixed costs totaled $136,000 for the year. Total sales for the year were $$313,397.
Determine:
a. Contribution margin per unit
b. Contribution margin ratio
c. Break – even in units and sales dollars
d. Units and sales dollars to earn before tax profit of $50,000
e. Margin of safety in dollars and units
f. Operating leverage
g. How many more units must be sold to break even if advertising costs increase by $15,000 and management salaries are increased by $22,000 and the cost of purchasing inventory increases 10%?
h. How much more or less will the company earn if the contribution margin decreases by 10% and fixed costs increase by $45,000?
Answer
1st – Identify the sales price as $3.50 per unit and units sold as 89,542
($313,397/$3.50)
2nd – Identify the variable costs as follows:
purchase inventory $1.25
workers $0.48 ($42,980 / 89,542)
sales commission $0.25
total variable $1.98
3rd – Contribution margin per unit is $3.50 sales – $1.98 variable cost = $1.52 per unit
4th – Contribution margin ratio is $1.52 CM / $3.50 sales = 43.4% or .434
5th – Total fixed costs are $136,000
You should follow these steps for all problems.
a. The CM is $1.52 per unit
b. The CM ratio % is 43.4%
c. The break even formula is Total Fixed Costs = units sold to B/E
CM per unit
Plug in the numbers $136,000 = 89,474 to get B/E
$1.52 per unit units
The break even formula is Total Fixed Costs = sales $ sold to B/E
CM %
Plug in the numbers $136,000 = $ 313,364 to get B/E
.434 sales dollars
d. add the desired profit to the break even formula:
The formula is Total Fixed Costs + Desired Profit = units sold
CM per unit
Plug in the numbers $136,000 + $50,000 = 122,369 to earn $50,000
$1.52 per unit units
The formula is Total Fixed Costs + Profit = sales $ sold
CM %
Plug in the numbers $136,000 + $50,000 = $ 428,572 to earn $50,000
.434 sales dollars
e. Margin of Safety formula is
Units Sales $
Current sales 89,542 $313,397
Break-even sales 89,474 $313,364
Margin of Safety 68 $ 33
f. To calculate operating leverage, you must use a contribution margin format.
Reformat the above information.
Sales $313,397
– all VC $177,293 ($1.98 x 89,542)
= CM $136,104 ($1.52 x 89,542)
– all FC $ 136,000
= Income $ 104
The operating leverage formula is Contribution Margin
Income
Plug in the numbers: 136,104 / 104 = 1309 factor
g. You must calculate a new contribution margin and use the new CM in the break even formula:
Sales $3.50
– variable costs
purchase inventory $1.375 ($1.25 x 1.10)
workers $0.48 ($42,980 / 89,542)
sales commission $0.25
total variable $2.105
CM per unit $1.395
Prior fixed costs $136,000
+ additional fixed costs 37,000
Total fixed costs $173,000
The break even formula is Total Fixed Costs = units sold to B/E
CM per unit
Plug in the numbers $173,000 = 124,014 to get B/E
$1.395 per unit
Break even Now 124,014
Previous break even 89,474
Increase in units 34,540
h. The prior CM was $1.52 and a decrease of 10% will take it to $1.368 per unit
You can also calculate the new CM by taking total CM x 90%
$136,104 x 90% = $122,494 revised CM
$136,000 + $45,000 = $181,000 revised FC
$ (58,506) revised income
$ 104 previous income
$ 58,610 less income
13. Log Cabin Builders built 19 houses and had the following results for the current year:
Sales $2,565,000
Cost of Goods sold:
Variable production costs 1,216,000
Fixed production costs 246,000
Gross Profit 1,103,000
Administrative costs:
Fixed: 398,000
Variable: 57,000
Selling costs
Fixed: 248,000
Variable: 114,000
Income before tax 286,000
Determine:
a. Contribution margin per unit and the contribution margin ratio
b. Break – even in units and sales dollars
c. Operating leverage
d. How many more houses must be sold to earn $300,000 if fixed selling costs
increase by $75,000 and fixed administrative costs are increased by$100,000?
e. How much more or will the company earn if the sales price of a house increases by 10% and variable costs increase 12%?
Answer
1st – Identify the sales price as $135,000 per unit ($2,565,000 / 19)
2nd – Identify the variable costs as follows:
total variable production $64,000 ($1,216,000 / 19)
total variable admin $ 3,000 ($57,000 / 19 )
total variable selling $ 6,000 ($114,000 / 19)
total variable $73,000 per house
3rd – Contribution margin per unit is $135,000 sales – $73,000 variable
cost = $62,000 per unit
4th – Contribution margin ratio is $62,000 CM / $135,000 sales = 45.9%
5th – Total fixed costs are $246,000 + $398,000 + $248,000 = $892,000
You should follow these steps for all problems.
a. The CM is $62,000 per unit and the CM ratio % is 45.9%
b. The break even formula is Total Fixed Costs = units sold to B/E
CM per unit
Plug in the numbers $892,000 = 14.4 or 15 to get B/E
$62,000 per unit units
The break even formula is Total Fixed Costs = sales $ sold to B/E
CM %
Plug in the numbers $892,000 = $ 1,943,355 to get B/E
.459
c.To calculate operating leverage, you must use a contribution margin format. Reformat the above information.
Sales $2,565,000
– all VC $1,387,000
= CM $1,178,000
– all FC $ 892,000
= Income $ 286,000
The operating leverage formula is Contribution Margin
Income
Plug in the numbers: 1,178,000 / 286,000 = 4.12 factor
d. Add the desired profit to the break even formula with the increased fixed cost:
The formula is Total Fixed Costs + Desired Profit = units sold
CM per unit
Plug in the numbers $892,000 + $175,000 + $300,000 = 22 to earn $300,000
$62,000 per unit units
22 less the current 19 = 3 more houses if FC increase to earn $300,000
e. Current sales dollars are $135,000 per house, a 10% increase makes the
sales $148,500 per house, and increase of $13,500.
The variable cost per house is $73,000 per house and a 12% increase will make
variable cost per house $87,760, an increase of $8,760.
Added sales revenue per house $13,500
– added variable cost per house ($ 8,760)
Increase in CM per house $ 4,740
x number of houses 19___
Increase in total CM $90,060
Increase in Fixed costs $ 0__
Increase in profits $90,060
14. How do changes in volume change the break-even point?
Answer
Changes in volume do not change the break even point because the break-even point is based primarily on the level of fixed costs which do not change and a contribution margin per unit which also does not change as volume changes.
15. What information does the margin of safety calculation provide to management?
Answer
Margin of safety tells how much sales can drop and the company still remain at 0 profit, or not incur a loss.