PROBLEM
1. Dance Unlimited plans to sell 10,000 ballet shoes at $50 each in the coming year. Unit variable cost
is $30 and total fixed cost equals $65,000.
Required:
A.) Calculate the break-even in ballet shoes.
B.) Calculate the break-even in sales dollars.
2. Shamrock Inc. plans to sell 3,000 Irish sweaters for $200 each in the coming year. Product costs
include:
Direct materials per sweater
$40
Direct labor per sweater
10
Variable overhead per sweater
15
Total fixed factory overhead
20,000
Variable selling expenses are $5 per sweater and fixed selling and administrative expenses total
$12,000.
Required:
A.) Calculate the total variable cost per unit.
B.) Calculate the total fixed expenses for the year.
C.) Prepare a contribution margin income statement for Shamrock Inc. for the coming year.
3. Newman Company expects to produce and sell 2,000 units next month. Data on costs follows:
Per unit costs:
Selling price
Variable manufacturing costs
Variable selling costs
Total costs:
Fixed manufacturing costs
Fixed selling costs
Required:
A.
What is the variable cost per unit?
B.
What is contribution margin per unit?
C.
What is the variable cost ratio?
D.
What is the contribution margin ratio?
A.
Variable cost per unit = $10 + $6 = $16
Contribution margin per unit = $40 − $16 = $24
C.
Variable cost ratio = $16/$40 = 0.4 or 40%
D.
Contribution margin ratio = $24/$40 = 0.6 or 60%
4. McCallen Company expects to produce and sell 500 units next month. Data on costs follows:
Per unit costs:
Selling price
Variable manufacturing costs
Variable selling costs
Total costs:
Fixed manufacturing costs
Fixed selling costs
Required:
A.
What is the variable cost per unit?
B.
What is contribution margin per unit?
C.
What is the variable cost ratio?
D.
What is the contribution margin ratio?
5.
Fry Company
Projected Income Statement
For the Current Year Ending December 31
Sales (12,000 units)
$240,000
Less variable costs:
Variable manufacturing costs
$60,000
Variable selling costs
36,000
Total variable costs
96,000
Contribution margin
$144,000
Less fixed costs:
Fixed manufacturing costs
$85,000
Fixed selling and administrative costs
35,000
Total fixed costs
120,000
Operating income
$ 24,000
Required:
A.
Determine the break-even point in sales dollars.
B.
The sales manager believed the company could increase sales by 1,000 units if
advertising expenditures were increased by $15,000. By how much will operating
income increase or decrease if the advertising is increased as suggested?
C.
What is the maximum amount the company could pay for advertising if the advertising
would increase sales by 1,000 units?
$120,000/($20 − $8) = 10,000 units x $20 = $200,000
(1,000 $12) − $15,000 = $3,000 decrease
1,000 $12 = $12,000
A.
Variable cost per unit = $2.75 + $0.25 = $3
Contribution margin per unit = $8 − $3 = $5
C.
Variable cost ratio = $3/$8 = 0.375 or 37.5%
D.
Contribution margin ratio = $5/$8 = 0.625 or 62.5%
6. Music Now plans to sell 6,000 MP3 players at $60 each in the coming year. Variable cost per unit is
$12 and total fixed cost is $24,000.
Required:
A.) Calculate the variable cost ratio.
B.) Calculate the contribution margin ratio.
C.) Calculate the break-even point in sales dollars.
D.) If Music Now has a target profit of $90,000, how many MP3 players will they have to sell?
7. A company provided the following information:
Sales
Variable costs
Fixed costs
Required:
A.
What is the contribution margin ratio?
B.
What is the level of sales in dollars necessary to generate a profit of $40,000?
C.
What is the contribution margin ratio if the sales price is increased by 10%?
D.
Using the information in part C, what level of sales in dollars is necessary to generate a
profit of $40,000?
($500,000 − $100,000)/$500,000 = 80%
B.
($200,000 + $40,000)/80% = $300,000
($500,000 1.1) = $550,000
($550,000 − $100,000)/$550,000 = 81.82%
D.
($200,000 + $40,000)/81.82% = $293,327 rounded
8. Aaron Company provided the following data for next month:
Selling price per unit
Variable manufacturing costs per unit
Fixed manufacturing costs per unit
Variable selling costs per unit
Fixed selling costs per unit
Expected production and sales
Required:
A.
What is contribution margin per unit?
B.
What is the contribution margin ratio?
C.
What is the break-even point in units?
D.
What are the sales in dollars needed to obtain an operating income of $20,000?
$400 − ($100 + $60) = $240
$400 − ($100 + $60) = $240
$240/$400 = 0.60 or 60%
$400 − ($100 + $60) = $240
Fixed costs = ($80 + $40) 1,800 = $216,000
$216,000/$240 per unit = 900 units
D.
($216,000 + $20,000)/60% = $393,333 rounded
9. Thomas Corporation developed the following income statement using a contribution margin approach:
Thomas Corporation
Projected Income Statement
For the Current Year Ending December 31
Sales
$750,000
Less variable costs:
Variable manufacturing costs
$280,000
Variable selling costs
120,000
Total variable costs
$400,000
Contribution margin
$350,000
Less fixed costs:
Fixed manufacturing costs
$130,000
Fixed selling and administrative costs
80,000
Total fixed costs
$210,000
Operating income
$140,000
The projected income statement was based on sales of 100,000 units. Thomas has the capacity to
produce 120,000 units during the year.
Required:
A.
Determine the break-even point in units.
B.
The sales manager believes the company could increase sales by 8,000 units if
advertising expenditures were increased by $22,000. By how much will income
increase or decrease if this plan is put into effect?
C.
What is the maximum amount the company could pay for advertising if the sales
would really increase by 8,000 units?
10. The following information was extracted from the accounting records of MVP Corporation:
Selling price per unit
Variable cost per unit
Total fixed costs
Required:
A.
What is MVP’s break-even point in units?
B.
How many units must be sold to earn operating income of $80,000?
C.
What is MVP’s break-even point in units if the selling price increases by 20% and the
variable costs decrease by 20%?
D.
Using the information in part C, what sales level in dollars is needed to earn an
operating income of $80,000?
$480,000/($60 per unit − $20 per unit) = 12,000 units
($480,000 + $80,000)/($60 − $20) = 14,000 units
($60 1.2) = $72 new sales price
($20 .8) = $16 new variable cost
$210,000/($7.50 − $4.00) = 60,000 units
(8,000 $3.50) − $22,000 = $6,000 increase
8,000 $3.50 = $28,000
($72 − $16) = $56 new contribution margin
$480,000/$56 = 8,572 units (rounded)
($480,000 + $80,000)/$56 = 10,000 units
(10,000 $72) = $720,000
11. Information for Crisby Company is as follows:
Sales
Variable costs
Fixed costs
Required:
A.
What is the break-even point in sales dollars?
B.
What sales (in dollars) are needed to generate operating income of $40,000?
($500,000 − $100,000)/$500,000 = 80%
$200,000/80% = $250,000
($500,000 − $100,000)/$500,000 = 80%
($200,000 + $40,000)/0.80 = $300,000
12. The Noble Company manufactures two products. Information about the two products are as follows:
Selling price per unit
Variable costs per unit
Contribution margin per unit
The company expects fixed costs to be $189,000. The firm expects 60% of its sales (in units) to be
Product A (a sales mix of 3:2).
Required:
A.
Calculate the contribution margin per package.
B.
Determine the break-even point in units for Products A and B.
C.
Determine the level of sales (in dollars) necessary to generate operating income of
$135,000.
13. Travel On Inc. sells luggage. They sell a duffle bag, a carry-on suitcase and a deluxe suitcase. The
price and variable cost for each type of luggage is listed below.
Price
Variable Cost
Duffle bag
$100
$25
Carry-on
$180
$40
Deluxe
$300
$120
The total fixed costs for Travel On Inc. equals $60,000. For every 8 duffle bags Travel On Inc sells it
sells 3 carry-on suitcases and 1 deluxe suitcase.
Required:
A.) Calculate the package contribution margin.
B.) Calculate the break-even point in units for duffle bags, carry-on suitcases and deluxe suitcases.
C.) If Travel On Inc. has a target income for the coming year of $300,000, how many packages will
company have to sell?
D.) Based on your answer in Part C, prepare a contribution margin income statement for the coming
year.
E.) What is the company’s margin of safety in packages?
Duffle bag
14. The Lauren Company manufactures two products. Information about the two product lines for the year
is as follows:
Selling price per unit
Variable costs per unit
Contribution margin per unit
The company expects fixed costs to be $144,000. The firm expects 60% of its sales (in units) to be
Product X.
Required: Determine the break-even point in units for both Product X and Product Y.
15. The Young Manufacturing Company produces the following three products:
Saws
Selling price per unit
$50
Variable costs per unit
$30
Contribution per unit
$20
Fixed costs are $76,000 per year.
50% of all sales in units are hammers, 30% are screwdrivers, and 20% are saws.
Required: Calculate the following values:
A.
break-even point in total units.
B.
Number of hammers that will be sold at break-even.
C.
Total sales in units to obtain a target income of $19,000.
Ave. CM/unit = ($12 0.5) + ($4 0.3) + ($20 0.2) = $11.20
$76,000/$11.20 = 6,786 packages of hammers, screwdrivers, and saws
6,786 0.5 = 3,393 hammers
($76,000 + $19,000)/$11.20 = 8,482 packages
16. Income statements for two different companies in the same industry are as follows:
Sales
Less: Variable costs
Contribution margin
Less: Fixed costs
Operating income
Required:
A.
Calculate the degree of operating leverage for each firm.
B.
Calculate the margin of safety in dollars for each firm.
C.
Determine the operating income for each firm if sales increase by 20%.
17. Newman Company expects to produce and sell 2,000 units next month. Data on costs follows:
Per unit costs:
Selling price
Variable manufacturing costs
Variable selling costs
Total costs:
Fixed manufacturing costs
Fixed selling costs
Required:
A.
What is the break-even point in units?
B.
What is the break-even point in sales dollars?
C.
What is the expected operating income for next month?
D.
What is the margin of safety in dollars?
A.
break-even units = ($16,000 + $8,000)/$24 = 1,000 units
A.
Company A: $100,000/$50,000 = 2
Company B: $200,000/$50,000 = 4
B.
Company A:
break-even sales = $50,000/($100,000/$400,000) = $200,000
Margin of safety = $400,000 − $200,000 = $200,000
Company B:
break-even sales = $150,000/($200,000/$400,000) = $300,000
C.
Company A:
Increase in net income = (.20 2) $50,000 = $20,000
Net income = $50,000 + $20,000 = $70,000
Company B:
Increase in net income = (.20 4) $50,000 = $40,000
Net income = $50,000 + $40,000 = $90,000
break-even sales dollars = 1,000 $40 = $40,000
OR
break-even sales dollars = $24,000/0.6 = $40,000
Expected operating income = $80,000 − $32,000 − $24,000 = $24,000
Margin of safety = $80,000 − $40,000 = $40,000
18. McCallen Company expects to produce and sell 500 units next month. Data on costs follows:
Per unit costs:
Selling price
Variable manufacturing costs
Variable selling costs
Total costs:
Fixed manufacturing costs
Fixed selling costs
Required:
A.
What is the break-even point in units?
B.
What is the break-even point in sales dollars?
C.
What is the expected operating income for next month?
D.
What is the margin of safety in dollars?
E.
What is the break-even point in units if fixed manufacturing costs increase by $500?
F.
What is the break-even point in units if variable manufacturing costs decrease by
$0.75?
A.
break-even units = $1,125/$5 = 225 units
break-even sales dollars = $8 225 = $1,800
OR
break-even sales dollars = $1,125/0.625 = $1,800
Expected operating income = $4,000 − $1,500 − $1,125 = $1,375
Margin of safety in dollars = $4,000 − $1,800 = $2,200
E.
($1,000 + $500 + $125)/$5 = 325 units
($1,000 + $125)/($8 − $2 − $.25) = $1,125/$5.75 = 196 units (rounded)
19. At a monthly sales volume of $25,000, a company incurs variable costs of $19,000 and fixed costs of
$6,000.
Required: Determine each of the following values:
A.
Variable cost ratio
B.
Contribution margin ratio
C.
Monthly break-even dollar sales volume
D.
Monthly margin of safety in dollars
C.
D.
20. Arnold Corporation has the following information for the current year:
Selling price per unit
Variable costs per unit
Fixed costs
Required: Prepare a cost-volume-profit graph identifying the following items:
A.
Total costs line
B.
Total fixed costs line
C.
Total variable costs line
D.
Total revenues line
E.
break-even point in sales dollars, indicate the amount
F.
break-even point in units, indicate the amount
G.
Profit area
H.
Loss area
21. The following information has been provided for Walsh Corporation:
Sales price per unit
$20
Variable costs per
unit
$10
Fixed costs
$500
Required: Prepare a cost-volume-profit graph identifying the following items:
A.) Total cost line
B.) Total fixed cost line
C.) Total variable cost line
D.) Total revenue line
E.) Loss area
F.) Profit area
G.) Compute the break-even point in units
H.) Compute the break-even point in sales dollars
22. Place Corporation had the following income statement for the current year:
Sales
Variable expenses
Contribution margin
Fixed expenses
Operating income
Required:
A.
Calculate the operating leverage ratio.
B.
If sales increase by 20%, what will be the percentage change in income?
C.
If sales increase by $15,000, how much will income increase?
$10,000/$6,000 = 1.6667
1.6667 0.2 = 0.33333, or 33.33% increase
$15,000 .4 = $6,000
ESSAY
1. Explain why cost-volume-profit analysis can be useful to managers.
2. What are the assumptions underlying cost-volume-profit analysis?
3. How can a multi-product firm determine its break-even point?
4. As a cost accountant at A&E Company you have been given a set of data and have been asked to
perform a break-even analysis as well as a sensitivity analysis. Why are these analyses important?