MA1 2007-2008
MANAGEMENT ACCOUNTING
MODULE 4
COST-VOLUME-PROFIT ANALYSIS – KEY FORMULAS
Operating income (before tax):
SPx – VCx – FC = P
Contribution margin:
SP-VC=CM
Contribution margin ratio:
CM
SP
Breakeven in units:
FC =x
CM
Breakeven in sales dollars:
FC
=Y
CM ratio
Unit sales to reach target
before tax operating income:
FC + P =x
CM
Unit sales to reach target
after tax operating income:
PAT
FC + (1-T)
CM
Sales dollars to reach target
before tax operating income:
FC + P =Y
CM ratio
=CM ratio
=x
Cost-volume-profit analysis variables
P
Before tax profits (operating income)
PAT
After tax profits (after tax operating income)
SP
Selling price per unit
VC
Variable cost per unit
FC
Fixed costs
x
Number of units
CM
Contribution margin (SP-VC)
CM ratio
CM/SP
Y
Total sales dollars
T
Tax rate
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MODULE 4
PART 6 Slides 70 – 72: Question 4 December 1992
Omego Enterprises Ltd., has estimated the following costs for producing and selling 8,000 units
of their product.
Direct materials
Direct labour
Variable overhead
Fixed overhead
Variable selling and administrative expenses
Fixed selling and administrative expenses
$ 32,000
40,000
20,000
30,000
24,000
33,000
Omego’s income tax rate is 30%.
REQUIRED:
(a) Given that the selling price of one unit is $35.00, how many units would Omego
have to sell in order to break even?
(b) At a selling price of $37.50 per unit, how many units would Omego have to sell in order to
produce a profit of $22,000 before taxes?
(c) If 7,500 units were produced and sold, what price would Omego have to charge in order to
produce a profit of $28,000 after taxes?
(d) If 9,000 units were produced and sold, what price would Omego have to charge in order to
produce a before-tax profit equal to 30% of sales?
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Question 4 December 1992 Solution
(a)
Variable costs
Direct materials
Direct labour
Variable overhead
Variable selling
Total
32,000/8,000
40,000/8,000
20,000/8,000
24,000/8,000
SP(X) - VC(X) - FC
35(X) - 14.50(X) - 63,000
20.50(X)
X
= 0
= 0
= 63,000
= 3,073.17
Per unit
= 4.00
= 5.00
= 2.50
= 3.00
14.50
=
3,073 units or 3,074 units
Some texts/exams suggest this solution would be 3,073 units. But, by selling 3,073 units or less
you will not break even. SO, tell the marker why you are rounding up.
(b)
37.50(X)
23(X)
-
14.50(X)
-
63,000
= 22,000
= 85,000
= 3,695.65 or 3,696 units
X
(c)
[ 7,500(SP) 7,500(SP)
7,500(SP)
Selling Price
(d)
9,000(SP)
9,000(SP)
6,300(SP)
Selling Price
7,500(14.50)
108,750
-
-
9,000(14.50)
130,500
63,000 ]
63,000
-
-3-
63,000
63,000
= 28,000 /(1-.3)
= 40,000
= 211,750
= $28.23
= .30(9,000SP)
= 2,700(SP)
= 193,500
= $30.71
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MANAGEMENT ACCOUNTING
MODULE 4
PART 6 Slides 73-74: Question 5 December 2005
Warton Ltd. is considering replacing an existing machine with a new and faster machine that will produce
a more reliable product (that is, better tolerances). The switch to a new machine resulting in a superior
product is expected to allow Warton to increase its sales price for the product. The switch will increase
fixed costs, but not the variable costs. The cost and revenue estimates are as follows:
Cost Item
Monthly fixed costs
Variable cost per unit
Sales price per unit
Old Machine
$120,000
14
18
New Machine
$250,000
14
20
Required
a. Determine the break-even point in units for the two machines.
b. Determine the sales level in units at which the new machine will achieve a 10% target profit-tosales ratio (ignore taxes).
c. Determine the sales level at which profits will be the same for either the old or new machine.
d. Which machine represents a lower risk if demand is uncertain? Explain.
Solution
a)
Old machine: BEP units
New machine: BEP units
(b)
20(X)
6X
4X
X
(c)
4(X)
2X
X
-
(d)
If demand is uncertain, the old machine represents less risk because of its lower fixed costs.
In this case, it is not the variable cost per unit that is reduced by the new machine but rather the
selling price per unit which has increased.
14(X)
120,000
–
=
=
120,000/(18 – 14)
250,000/(20 – 14)
250,000
250,000
=
=
=
=
=
=
=
=
=
30,000 units
41,667 units
.10(20X)
2X
250,000
62,500 units
6(X) - 250,000
130,000
65,000 units
However, the effect is the same — the contribution margin per unit is increased with the new
machine at the “Cost” of higher fixed costs. This is an example of operating leverage.
For every unit short of the break-even point, the new machine results in a greater loss per unit,
and for every unit past the break-even point, the new machine results in a greater profit per unit.
Also notice that the break-even point is higher with the new machine than the old machine.
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MODULE 4
PART 7 Slides 76 – 78: Question 3 March 1994
The company you work for as a managerial accountant engages independent agents to sell the
company’s products. These agents are currently being paid a commission of 15% based on sales
price but are asking for an increase to 20% of sales made during the coming year. You had
already prepared the following pro-forma income statement for the company based on the 15%
commission.
Dry Rot Corporation
Pro-forma Income Statement
For the year ending April 30, 1995
Sales
Cost of goods sold (all variable)
Gross profit
Selling and administrative:
Variable (commission only)
Fixed
Income before taxes
Income tax expense (25%)
Net income
$ 1,000,000
600,000
400,000
$ 150,000
10,000
160,000
240,000
60,000
$ 180,000
Management wants to examine the possibility of employing the company’s own sales people.
They believe they will need a sales manager at an annual salary of $60,000 and three salespeople
at an annual salary of $30,000 each plus a commission of 5% of sales. All other fixed costs as
well as the variable cost percentages would remain the same as in the above pro-forma statement.
REQUIRED
a. Based on the pro-forma income statement you have already prepared, what is the breakeven point
in sales dollars for Dry Rot for the year ending April 30, 1995?
b. If Dry Rot employs its own salespeople, what would be the breakeven point in sales dollars for
the year ending April 30, 1995?
c. What would be the volume of sales dollars required for the year ending April 30, 1995 to yield
the same net income as projected in the pro-forma income statement if Dry Rot continues to use
the independent sales agents and agrees to their demand for a 20% sales commission?
d. Compute the estimated sales volume in sales dollars that would generate an identical net income
for the year ending April 30, 1995 regardless of whether Dry Rot employs its own salespeople or
continues to use the independent sales agents and pays them a 20% commission.
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MODULE 4
Question 3 March 1994 Solution
a)
BEP ($)
=
FC/CM ratio =
10,000/.25 =
$40,000
To determine the CM ratio, you must determine the contribution margin first.
Sales =
Var. COGS =
Commissions
Contribution margin
b)
1,000,000
( 600,000)
( 150,000)
250,000
CM ratio = 250,000/1,000,000 = .25
Var. COGS =
Commissions =
60%
Fixed costs = sales manager
5%
3 sales people
65%
admin costs
Contribution margin ratio = 100 – 65 = 35%
BEP ($)
=
160,000/.35
=
= 60,000
= 90,000
= 10,000
160,000
457,142.86 = $457,143
c)
Sales dollars = (FC + NIBT)/CM ratio = (10,000 + 240,000)/.20 = $1,250,000
d)
X = sales volume in dollars where you’d be indifferent
AGENTS
=
OWN sales people
X -.80X + 10,000 = X - .65X + 160,000
.2X
+ 10,000 =
.35X + 160,000
.15X
=
150,000
X
=
$1,000,000
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MANAGEMENT ACCOUNTING
MODULE 4
PART 7 Slides 79 – 80: Question 3 March 2005 (14 marks)
Timeworks Inc. produces two lines of clocks — standard and deluxe. Cost and revenue data are shown
below:
Standard
$ 30
Deluxe
$ 50
9
7
3
2
$9
15
10
5
2
$ 18
Percentage of total unit sales
70%
Total contribution margin
$504,000
Fixed manufacturing costs
(total for both lines of clocks combined)
Administrative
Net income
30%
$432,000
Selling price (per clock)
Variable costs (per clock)
Direct materials
Direct labour
Overhead
Selling
Contribution margin (per clock)
Total expected sales in units (both lines of clocks combined)
Capacity (both lines of clocks combined)
$ 936,000
400,000
325,000
$ 211,000
80,000
100,000
Required
The following three cases are independent, but are based on the above information in the question.
6
a.
The company is considering steps to increase sales, particularly of the deluxe model. It is
considering increasing advertising by $200,000 and increasing the sales commission on
the deluxe clock by $2 per clock. Management believes that these steps will increase total
sales to 95,000 clocks and increase the proportion of deluxe models sold to 40%.
Calculate the new net income if both changes were implemented and the resulting sales
were as predicted.
6
b.
The management of Timeworks is considering purchasing new equipment that will
reduce direct materials and direct labour costs by 20% for both products. The new
equipment would increase fixed manufacturing costs by $175,000, reflecting the
amortization on the new equipment. Calculate the total sales volume that must be
achieved in order for the purchase of the new equipment to have a positive effect on net
income. Assume the mix of sales would be unaffected.
2
c.
A wholly-owned subsidiary of Timeworks purchases standard clocks for use in its own
production process. Sales to the subsidiary do not incur selling expenses. What is the
minimum price that Timeworks should charge the subsidiary for each of its standard
clocks, assuming that Timeworks has sufficient capacity to supply both the outside
demand and the needs of the subsidiary.
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MODULE 4
Question 3 March 2005 Solution
6
a.
Standard model
Contribution margin per clock
$9.00
New sales level
95,000 × 0.6 = 57,000 clocks
New total contribution margin from the standard model (57,000 × $9) =
Deluxe model
New contribution margin per clock $18 – $2 = $16.00
New sales level
95,000 × 0.4 = 38,000 clocks
New total contribution from the deluxe model (38,000 × $16) =
Total contribution margin
Less fixed costs ($400,000 + $325,000 + $200,000) =
New net income
6
b.
$ 513,000
608,000
1,121,000
925,000
$ 196,000
The indifference point for the purchase of the new equipment will be the sales volume at
which the net income with the new equipment equals the net income with the old equipment.
Let the sales volume equal X:
.70X(12.2) + .30X(23) - (400,000 + 325,000 + 175,000)
8.54X + 6.9X
X
X
= 211,000
= 1,111,000
= 71,955.95855
= 71,956 rounded
Calculations:
Standard: 30 – (7.2 + 5.6 + 3 + 2) = 12.2
Deluxe: 50 – (12 + 8 + 5 + 2) = 23
If the total sales volume will be 71,956 units or more in the 70/30 mix, the net income with
the new equipment will be greater than the net income with the old equipment.
2
c.
The minimum price that Timeworks should charge to its wholly-owned subsidiary is simply
the variable costs of production: $9.00 + $7.00 + $3.00 = $19.00.
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MODULE 4
PART 8 Slides 81-82: Question 4 June 2007
Jazz Dance Shoes makes 3 different types of shoes: ballroom shoes, tap shoes, and ballet shoes.
Production data for the month of March indicates the following costs:
Tap Shoes
6,000 pairs
Ballet Shoes
3,000 pairs
$ 30,000
$ 60,000
$ 6,000
$ 72,000
$ 24,000
$ 54,000
$ 5,400
$ 90,000
$ 21,000
$ 33,000
$ 3,300
$ 33,000
Fixed costs:
Fixed factory overhead
$ 200,000
Fixed selling and administration costs $ 50,000
Unit selling prices
$ 120
$ 600,000
$ 50,000
$ 150
$ 350,000
$ 50,000
$ 110
Units produced and sold
Ballroom Shoes
6,000 pairs
Costs for the month of March:
Direct labour
Direct materials
Variable overhead
Variable selling and administration
Required
a. Using the weighted-average contribution margin method, calculate the break-even point for
the company as a whole. Show your calculations. State your answer in pairs of shoes of each
type.
b. How many pairs of each type of shoe would have to be sold to achieve a target after-tax profit
of $1,000,000, assuming the corporate tax rate was 40%?
c. What is the margin of safety in part (b)? State it in terms of each type of shoe sold.
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Question 4 June 2007 Solution
a. Add the costs and revenues for the production of all 3 shoes together.
Units (in pairs)
Ballroom Shoes Tap Shoes Ballet Shoes
6,000
6,000
3,000
Revenue
Total variable costs
Contribution margin
$ 720,000
168,000
$ 900,000
173,400
Fixed costs
$ 250,000 $ 650,000
Total
15,000
Per unit
$ 330,000 $ 1,950,000
90,300
431,700
$ 1,518,300 $101.22
$ 400,000 $ 1,300,000
Weighted-average break-even point:
X = 1,300,000 / 101.22 = 12,844 pairs, of which 6,000 / 15,000 × 12,844 = 5,138 pairs are
ballroom shoes, 5,138 pairs are tap shoes, and [12,844 – (5,138 × 2)] = 2,568 pairs are ballet
shoes.
b. Profit before tax = $1,000,000 / 0.6 = $1,666,667
Weighted-average number of pairs:
X = (1,300,000 + 1,666,667) / 101.22 = 29,310 pairs, of which 6,000 / 15,000 × 29,310 =
11,724 pairs are ballroom shoes, 11,724 pairs are tap shoes, and 5,862 pairs are ballet shoes.
c. Margin of safety is: 29,310 – 12,844 = 16,466 pairs of shoes, of which 6,586 are ballroom
shoes, 6,586 are tap shoes, and 3,293 are ballet shoes.
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MODULE 4
PART 9 Slides 84-86: Multiple Choice Questions - Module 4
Q1.
ABC Manufacturing produces and sells Xenon. During the year 2000, Xenon had sales of
$500,000, a contribution margin of 20%, and a margin of safety of $200,000. What is Xenon’s
fixed cost?
1)
2)
3)
4)
$ 60,000
$100,000
$120,000
$200,000
USE the formulas you have learned based on the information
given in the question.
Total sales - breakeven sales = Margin of Safety
500,000 X
= 200,000
December 1999 exam:
answer 1)
Q2.
Breakeven sales
Variable costs (80%)
Contribution margin
Fixed costs
Net income
=
=
=
=
=
300,000
(240,000)
60,000
(60,000)
0
Upsilon Co., a manufacturer of widgets, had the following data for 2000:
Sales
Sales price
Variable costs
Fixed costs
2,400 units
$40 per unit
$14 per unit
$19,500
If the company wishes to increase its total dollar contribution by 40% in 2001, all other factors
remaining constant, by how much will it need to increase its sales?
1)
2)
3)
4)
$ 17,160
$ 24,960
$ 26,400
$ 38,400
If CM increases 40%, then sales must increase 40%.
Sales will increase: (2,400 x $40) x 40%
= 38,400
June 2000 exam: answer 4)
Q3.
Monthly transportation costs at RFP Ltd. were $18,000 for 16,000 kg transported in July and
$22,500 for 22,000 kg transported in August. If the company plans to transport 18,000 kg in
September, what is the expected shipping cost?
1) $18,500
2) $19,500
3) $20,400
4) $24,000
Use the high low method
Cost = (22,500 – 18,000)=4,500
Weight = (22,000 – 16,000) = 6,000
4,500/6,000=.75 per kg
FC = 22,500 - .75(22,000) = 6,000
Shipping cost = 6,000 + .75(18,000) = 19,500
March 2005 exam: answer 2)
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MODULE 4
PART 9 Slides 84-86: Multiple Choice Questions (continued)
Q4.
Which of the following statements concerning the high-low method of mixed cost analysis is
true?
1) The high-low method of mixed cost analysis provides the best fit for all of the data.
2) The high-low method of mixed cost analysis always shows the fixed cost component of
mixed costs to be zero.
3) The high-low method of mixed cost analysis can be influenced by extreme values or outliers.
4) The cost formula resulting from the high-low method of mixed cost analysis is based on least
squares.
December 2000 exam: answer 3)
Q5.
Chang Company has 2 divisions, True and West. The company’s overall contribution margin
ratio is 40% when combined sales in the 2 divisions total $900,000. If variable costs are $200,000
in Division True, and if Division West’s contribution margin ratio is 20%, what must be the sales
in Division West?
1)
2
$ 200,000
$ 340,000
True
Sales
3)
4)
$ 425,000
$ 700,000
(VC)
CM
December 2000 exam: answer 3)
200,000
(340,000)
.20X
2
Total
900,000
( 540,000)
1
Calculations: JUST fill in what you need.
1
2
900,000 x 60%
= 540,000
540,000 - 200,000
= 340,000
X - 340,000
.80X
X
Q6.
West
X
=
=
=
.20X
340,000
425,000
Dabbler Co. has two divisions, A and B. Dabbler’s overall contribution margin is 30%, and
combined sales in the two divisions total $500,000. If variable expenses in Division A are
$300,000 and Division A’s contribution margin ratio is 25%, then what are sales in Division B?
1)
$ 50,000
2)
3)
4)
$ 100,000
$ 150,000
$ 200,000
Div A
Sales
(VC)
CM
1
400,000 100%
300,000 ( 75%)
25%
March 2005 exam: answer 2)
Div B
X
2
Total
500,000
Calculations: JUST fill in what you need.
1
75%(Sales of Div A)
Sales of Div A
= 300,000
= 400,000
2
Total Sales – Div A Sales = Div B Sales
Div B Sales = 500,000 – 400,000 = 100,000
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MODULE 4
PART 9 Slides 84-86: Multiple Choice Questions (continued)
Q7. Salxom Ltd. had the following results for the year:
Sales
Less: Variable costs
Contribution margin
Less: Fixed costs
Net operating income
$ 45,000
27,000
18,000
12,000
$ 6,000
The average selling price for the units sold was $15 per unit. If sales decrease by 500 units, by how
much will fixed expenses have to be reduced to maintain the current net operating income of
$6,000?
1)
2)
3)
4)
$ 2,000
$ 3,000
$ 3,600
$ 5,000
March 2002 exam:
answer 2)
First we need to determine how many units were sold originally.
$45,000/15 = 3,000 units. Reduction of 500 units means sales of 2,500 units
VC = 27,000/3,000 = $9 per unit
CM = 6 per unit
CM - FC = Net income
6(2,500) - FC = 6,000
Fixed costs = 9,000 THEREFORE, the reduction in FC = 3,000
Q8. Dally Co. has a break-even point of 4,000 units. At that break-even point, variable costs are $4,000
and fixed costs are $2,000. What is the contribution margin of the 401st unit sold?
1)
2)
3)
4)
$ 0.50
$ 1.00
$ 1.50
$ 2.00
It is the same as for all other units! So what is the CM?
BEP (units)
=
4,000
=
March 2002 exam: answer 1)
4,000(SP – 1.00)
SP – 1.00
SP
Fixed Costs
CM per unit
2,000
SP – 1.00
= 2,000
=
.50
= 1.50
Contribution margin per unit = SP – VC
= 1.50 – 1.00 = .50
Q9. Seamless Gutter Co. sells 10-metre sections of gutter for $12.00. Unit variable costs per section are
$8.80. Fixed costs total $4,800. How many sections must be sold to earn an after-tax income of
$4,000 if the tax rate is 40%?
[FC + (after tax inc/(1-tax rate))]/CM
1)
3,000 sections
[$4,800 + (4,000/(1-.4))]/($12-$8.80)
2)
3,300 sections .
3)
3,583 sections
4)
3,800 sections
= 3,583.33
March 2002 exam: answer 3)
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MODULE 4
PART 10 Slides 88-89: Multiple Choice Questions
Q10.
Gorge Mfg. produces two products, X and Y. The following information is presented for both
products:
X
Y
Selling price per unit
$9
$6
Variable cost per unit
7
3
Total fixed costs are $117,000.
What will the breakeven point be for Gorge in units of X and Y if the ratio of sales is expected to
be 3X:1Y?
1)
2)
3)
4)
X = 13,000 units: Y = 13,000 units
X = 26,000 units: Y = 78,000 units
X = 39,000 units: Y = 13,000 units
X = 78,000 units: Y = 26,000 units
June 2003 exam: answer 3)
Q11.
X = number of units of Y to breakeven
3X = number of units of X to breakeven
3X ($2) + X ($3) - 117,000 = 0
9X
= 117,000
X ( # units of Y ) = 13,000 units
3X ( # units of X ) = 39,000 units
June 2002 exam: Parts (a) and (b) refer to the following information:
Belton Company operated at normal capacity during the current year, producing 50,000 units of
its single product. Sales totalled 40,000 units at an average price of $20 per unit. Variable
manufacturing costs were $8 per unit, and variable marketing costs were $4 per unit sold. Fixed
costs were incurred uniformly throughout the year and amounted to $188,000 for manufacturing
and $64,000 for marketing. There was no year-end work in process inventory.
(a) What is Belton’s break-even point in sales dollars for the current year?
1)
2)
3)
4)
$ 420,000
$ 470,000
$ 630,000
$ 732,000
SP =
VC =
CM
BEP $
answer 3)
20
(12)
8
100%
( 60)
40%
= Fixed Costs / CM ratio
= 252,000 / 40% = 630,000
(b) If Belton’s variable manufacturing costs unexpectedly increase by 10%, what is the new unit
selling price that would yield the same contribution margin ratio as before the cost increase
(rounded to the nearest cent)?
1)
2)
3)
4)
$ 20.00
$ 20.67
$ 21.00
$ 21.33
Only the variable manufacturing costs increase.
New VC = (8 x 1.10) + 4.00 = 12.80
SP
(12.80)
CM
answer 4)
=
100%
60%
40%
New selling price: 60% (SP) = 12.80
SP
= $ 21.33
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MODULE 4
PART 10 Slides 88-89: Multiple Choice Questions (continued)
Q12.
Ceta Ltd. manufactures top-quality lacrosse sticks. The selling price per stick is $160 and the
variable cost per stick is $95. The sales volume of $1,552,000 is necessary to produce a net
income of $201,500 before taxes. What are Ceta’s total fixed costs?
1)
2)
3)
4)
$201,500
$429,000
$535,000
$635,500
June 2003 exam: answer 2)
Q13.
SP(X)
- VC(X)
- FC
1,552,000 - 95(9,700) - FC
1,552,000
- 921,500 - FC
Fixed Costs
NIBT
201,500
201,500
429,000
To calculate the number of units: 1,552,000/160 = 9,700
If fixed expenses were to double and contribution margin ratio per unit were to double, what
would the effect be on the break-even point?
1)
2)
3)
4)
The break-even point would be reduced to half. USE NUMBERS – don’t guess!
The break-even point would not change.
BEP = FC/Contrib margin per unit
The break-even point would double.
= 10,000/(20 – 10)
The break-even point would quadruple.
= 1,000 units
December 2004 exam: answer 2)
Q14.
=
=
=
=
Double it….
BEP = 20,000/(40 – 20) = 1,000 units
June 2004 exam: Parts (a) and (b) refer to the following information:
The following data is for the Liu Company, a manufacturer of ball-point pens:
Income tax rate
40%
Selling price per unit
$2.75
Variable cost per unit
$2.20
Total fixed costs
$115,000
(a) How many units must Liu Co. sell to earn an after-tax income of $30,000?
1)
2)
3)
4)
30,000 units
55,000 units
155,000 units
300,000 units
[FC + (after tax inc/(1-tax rate))]/CM
[115,000 + (30,000/(1-.4))]/(2.75-2.2)
.
= 300,000 units
answer: 4)
(b) If total fixed costs doubled and contribution margin per unit was cut in half, what would happen
to the break-even point?
1)
2)
3)
4)
It would decrease by half.
It would double.
It would triple.
It would quadruple.
Fixed Costs
CM/unit
BEP
answer: 4)
-15-
Now
100
10
Change
200
5
100/10
= 10
200/5
= 40
ma1_mod4_handout1.doc