Chapter 24 (Break Even Analysis).pdf

Cost Accounting
Planning and Controlled
Seventh Edition
Matz & Usry

1. Managerial Accounting

Roohullah (M.Com) Lecturer: 0333-8786389 The Standard College Page 1

CHAPTER # 24

Break Even and Cost-Volume-Profit Analysis

Break Even Analysis:
Break even analysis is used to determine the level of sales which are required to just recover
all costs incurred during the period.

Break Even Point
The point at which there is no profit no loss. In other words it is a point where total revenue
equal to total cost.

1. Contribution Margin

CM = Sale price – Variable Cost

2. CM ratio






3. Break Even Point in Units

( )




4. Break Even Point in Sales Revenue

( )




5. Sales Units to Achieve Target Profit






6. Sales Revenue To Achieve Target Profit






7. Margin of Safety

Margin of Safety = Expected or Actual Sale – Break Even Point

8. Margin of Safety (M/S) ratio

M/S ratio

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9. Break Even Point in Percentage of Capacity






Ex # 1

Solution

(i) CM ratio = CM / Sales

CM ratio = $2,700,000 / $4,500,000 = 0.6

CM = Sales – Variable Cost

CM = $4,500,000 - $1,800,000 = $2,700,000

(ii) ( )




R(BEP) = $1,200,000 / 0.6 = $2,000,000

(iii) Contribution Margin = $2,700,000


Ex # 2

(1) ( )




R(BEP) = $84,832 / 0.44 = $192,800

Profit = Sales – Variable cost – Fixed Cost

$31,768 = $265,000 – 148,400 – Fixed Cost

Fixed Cost = $116,600 – 31,768 = $84,832

CM ratio = $265,000 – 148,400 / 265,000 = 0.44

(2) Sales Revenue to Achieve Target Profit of $10,560











R = $216,800

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Ex # 3

Solution

(i) ( )





R(BEP) = $4290 / 0.33 = $13,000


CM ratio = CM / Sale Price = $0.825 / $2.5 = 0.33

CM = $2.5 - $1.675 = $0.825


( )




Q(BEP) = $4,290 / $0.825 = 5200 Units


(ii) Sales Revenue to Achieve Target Profit of $10,560











R = $38,000

Proof

Profit = Sales – Variable cost – Fixed cost

Profit = $13,000 – (5200 × $1.675) - $4,290

Profit = $13,000 - $8,710 - $4,290 = 0

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Ex # 4

R(BEP) = $252,396 / 0.38 = $ 664,200

CM ratio = $342,000 / $900,000 = 0.38

CM = $900,000 - $558,000 = $342,000


Ex # 5

R(BEP) = $4,000 / 0.5 = $8,000

CM ratio = $2.50 / $5 = 0.5

CM = $5 - $2.50 = $2.50


Ex # 6


1. CM ratio = $2,000,000 / $10,000,000 = 0.2

CM = $10,000,000 - $8,000,000 = $2,000,000


2. R(BEP) = $1,000,000 / 0.2 = $5,000,000


3. (a) R(BEP) = $1,100,000 / 0.2 = $5,500,000


(b) Profit = Sales – Variable cost – Fixed cost

Profit = $10,000,000 - $8,000,000 - $1,100,000

Profit = $900,000

4 (a) CM ratio = $2,500,000 / $10,000,000 = 0.25

CM = $10,000,000 - $7,500,000 = $2,500,000

(b) R(BEP) = $1,250,000 / 0.25 = $5,000,000

(c) Profit = Sales – Variable cost – Fixed cost

Profit = $10,000,000 - $7,500,000 - $1,250,000

Profit = $1,250,000

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Ex #7

1. R(BEP) = $46,200 / 0.7 = $66,000

CM = $80,000 - $24,000 = $56,000

CM ratio = $56,000 / $80,000 = 0.7


2. Q(BEP) = $46,200 / 1.4 = 33,000 units

CM per unit = Total CM / Units Sold

CM Per unit = $$56,000 / 40,000 units = $1.4


3. R(BEP) = $48,067 / 0.71 = $67,700

CM = $80,000 - $23,200 = $56,800

CM ratio = $56,800 / $80,000 = 0.71

4. Sales Revenue to Achieve Target profit of $9800











R = $84,300

CM ratio = $55,200 / $80,000 = 0.69

CM = $80,000 - $24,800 = $55,200

Increase in Sales
New Sales needed for $9800 profit $84,300
Budgeting Sales 80,000
Increase in sales $4,300

5. Budgeting Profit
Sales (34,000 Units × $2.1) $71,400
Less: Variable cost
Production (71,400 × 23.75%) $16,958
Marketing (71,400 × 6.25%) 4,463 21,421
Contribution Margin 49,979
Less: Fixed Cost
Production $20,000
Marketing 26,200 46,200
Profit $3,779

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Sale price = $80,000 / 40,000 units = $2

New Sale price $2 × 1.05 = $2.1

Variable percentage

Production = $19,000 / $80,000 × 100 = 23.75%

Marketing = $5,000 / $80,000 × 100 = 6.25%

R(BEP) = $46,200 / 0.7 = $66,000

CM ratio = $49,976 / $71,400 = 0.70


Ex # 8

Solution

(i) Direct Costing / Variable costing

Sales (100,000 × $100) $10,000,000
Less: Variable cost (100,000 × $25) 2,500,000
Contribution Margin $7,500,000
Less: Fixed Cost (100,000 × $50) 5,000,000
Profit $2,500,000

(ii)

( )





( )




R(BEP) = $6,666,667




=


= 0.75

(iii)










Margin of safety ratio = 0.3333 or 33.33%

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Ex # 9

Sales $200,000
Less: Variable cost 100,000
Contribution Margin 100,000
Less: Fixed Cost 40,000
Profit $60,000








Ex # 10

(1) ( )









Fixed Cost = $57,600



(2) Sale for the year










= $240,000

(3) CM = Sales – Variable expense

$240,000 × 36% = $240,000 – Variable expense

Variable expense = $240,000 - $86,400 = $153,600

(4)








= 0.3333 or 33.33%

Margin of Safety = Sale – BEP = $240,000 - $160,000 = $80,000

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Ex # 11

Solution

(1) ( )




( )


= $40,500

(2) Actual Sales?
















0.25 Sales = Sales - $40,000

$40,500 = Sales – 0.25 Sales

$40,500 = 0.75 Sales

Sales = $40,000 / 0.75

Sales = $54,000

(3) Profit = CM – Fixed cost

Profit = ($54,000 × 30%) - $12,150

Profit = $16,200 - $12,150

Profit = $4,050


Ex # 12

Solution

(1) Decrease in Sales
Last month sales $220,000
Current month sales 206,250
Decrease in Sales $13,750

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Old ratio New ratio
Sales $220,000 100% 100%
Variable cost 132,000 60 64
CM $88,000 40% 36%





× 100 = $206,250

(2) Break Even Point?

M/S ratio




0.24
– ( )



$49,500 = $206,250 – R(BEP)

R(BEP) = $206,250 - $49,500

R(BEP) = $156,750

(3) Profit = Sales – Variable cost – Fixed cost

Profit = $206,250 - $132,000 - $56,430

Profit = $17,820

R(BEP)




$156,750




Fixed cost = $56,430

Decrease in Fixed Cost
Last month Fixed Cost $61,600
Current Month Fixed Cost 56,430
Decrease in Fixed Cost $5,170


M/S ratio




0.3
( )



$66,000 = $220,000 – R(BEP)

R(BEP) = $220,000 - $66,000

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R(BEP) = $154,000

R(BEP)




$154,000




Fixed Cost = $61,600



Ex # 13

Solution

(1)

( )




( )




Q (BEP) = 50 Units

CM = Sale Price – Variable cost

CM = $10,000 - $5,000 = $5,000











(2) Operating Income
CM ( 5,000 units × 1.25) $6,250
Fixed cost 2,500
Operating Income $3,750


(3) ( )




( )




R(BEP) = $8,400

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Ex # 14

Solution (1)

Profit = Sale – Variable cost – Fixed cost – Advertising

(50,000 units × $6) × 10% = (50,000 × $6) – (50,000 × 3) - $100,000 –
Advertising

$30,000 = $300,000 – 150,000 – 100,000 – Advertising

Advertising = $300,000 – 150,000 – 100,000 – 30,000

Advertising = $20,000


(2) ( )




( )




R(BEP) = $240,000











CM = Sale price – Variable Cost

CM = $6 - $3 = $3


( )




( )




Q (BEP) = 40,000 Units

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Ex # 15

Solution
R( )




R( )




R (BEP) = $2,640,000











CM = Sale price – Variable Cost

CM = $20 - $14 = $6

( )




( )




Q (BEP) = 132,000 Units

(2) Units to be sold to achieve target profit of $60,000

Q




Q




Q = 142,000 Units

(3) Units to be sold to achieve target profit of $90,000 after tax

Q




Q




Q = 157,000 Units

Profit before tax $150,000
Income tax (40%) 60,000
Profit after tax (60%) $90,000

Income tax = 90,000 × 40/60 = $60,000

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(4) Break Even Point in Units if Wages and Salaries increase by 10%

Labor = Variable cost × 50% × 10%
= $14 × 50% × 10% = $0.7

Labor = Fixed × 20% × 10%
= $792,000 × 20% × 10% = $15,840

( )




( )




( )




Q (BEP) = 152,423 Units

CM per unit = Sale price – Variable cost

CM per unit = $20 - $14.7 = $5.3


Ex # 16

Solution

(1)









CM = Sale price – Variable Cost

CM = $1,227,375 – $954,625 = $272,750

(2) R( )




R( )




R (BEP) = $1,260,126


( )




( ) 28,000 days

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CM per unit




CM per unit




(3) M/S ratio =




M/S ratio =




M/S ratio =




(4) R( )




R( )




R (BEP) = $1,575,158

( )




( )




Q (BEP) = 35,000 days


Ex # 17

R( )




R( )




R (BEP) = $300,000

( )




( ) 133,333 units

CM ratio




CM ratio


= 0.4

CM per unit = Sale price – Variable cost

= $2.25 - $1.35 = $0.9

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Break Even Point in Percentage of Capacity









= 66.7%


(2) Margin of Safety = Sale – BEP
= $450,000 - $300,000
= $150,000

M/S ratio




M/S ratio




M/S ratio = 33.33%


(3) R( )




R( )




R (BEP) = $369,231

CM ratio




CM ratio



= 0.325

CM per unit = Sale price – Variable cost

= $2 - $1.35 = $0.65

(4) (i) Sales to achieve target profit of $30,000











R = $375,000






R = $461,538

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(5) ( )




( )




R (BEP) = $250,000

( )




( ) 111,111 units


Break Even Point in Percentage of Capacity









= 55.6%

(6) Budget Profit

(a) (b)
Sales
Less: Variable Cost
Contribution Margin
Less: Fixed Cost
Expected Profit
$450,000
270,000
180,000
120,000
$60,000
$450,000
303,750
146,250
120,000
$26,250


Variable Cost

Units Sold × Variable cost per unit

(a) 200,000 units × $1.35 = $270,000
(b) 225,000 units × $1.35 = $303,750






( )



( )

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Ex # 18

(1)
(a) ( )




( )


= 750 Units

(b) Sales (900 × 100) $90,000
Less: Variable Cost (900 × 60) 54,000
CM 36,000
Less: Fixed Cost 30,000
Profit $6,000
(2)
(a) ( )


= 888 Units

Reduction in variable cost = $60 × 0.25 = $15

Variable Cost = $60 - $15 = $45

CM Per Unit = $90 - $45 = $45

(b) Sales (900 × 90) $81,000
Less: Variable Cost (900 × 45) 40,500
CM 40,500
Less: Fixed Cost 40,000
Profit $ 500


(c) Sales (1000 × 90) $90,000
Less: Variable Cost (1000 × 45) 45,000
CM 45,000
Less: Fixed Cost 40,000
Profit $ 500


(3) Sales (950 × 90) $85,500
Less: Variable Cost (950 × 60) 57,000
CM 28,500
Less: Fixed Cost 30,000
Loss ($1,500)

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Ex # 19

Requirement (1)

Compusite Break Even Point in Dollars

=







Composite CM ratio







Composite CM = Composite Sales price – Composite Variable cost

Composite CM = $112 - $40 = $72

Composite Sales Price

Method of payment Average Daily Rate Patient Mix Weighted Daily
Rate
Self-payment $120 20% $24
Private Insurance 120 25 30
Madicare 110 30 33
Madcaid 100 25 25
Composite Sale Price $112

Composite Variable cost

Method of payment Average Daily Rate Patient Mix Weighted Daily
Rate
Self-payment $40 20% $8
Private Insurance 40 25 10
Madicare 40 30 12
Madcaid 40 25 10
Composite Variable cost $40

Coposite Break Even Point in patient days

=






Requirement (2)

Compusite Break Even Point in Dollars

=







Composite CM ratio







Composite CM = Composite Sales price – Composite Variable cost

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Composite CM = $120 - $40 = $80

Composite Sales Price

Method of payment Average Daily Rate Patient Mix Weighted Daily
Rate
Self-payment $120 50% $60
Private Insurance 120 50 60
Composite Sale Price $120

Composite Variable cost

Method of payment Average Daily Rate Patient Mix Weighted Daily
Rate
Self-payment $40 50% $20
Private Insurance 40 50 20
Composite Variable cost $40

Coposite Break Even Point in patient days

=








Ex # 20





Sales
Variable cost:
Manufacturing
Nonmanufacturing
Total Var. Cost
Contribution Margin
Increase in annual
program fixed cost
Manufacturing
Nonmanufacturing

Contribution to other
fixed costs & Income
before income tax
Current Operation
(50,000 Units
(a)
Low Elasticity
(52,000 Units
(b)
High Elasticity
(80,000 Units)
Per Unit
$10.00

$5.00
1.00
$6.00
$4.00
Total
$500,000

$250,000
50,000
$300,000
$200,000







$200,000
Per Unit
$9

$5.00
.90
$5.90
$3.10
Total
$468,000

$260,000
46,800
$306,000
$161,200







$161,200
Per Unit
$9

$5.00
.90
$5.90
$3.10
Total
$720,000

$400,000
72,000
$472,000
$248,000

$5,000
1,000
$6,000



$242,000

The low elasticity sales level can be anticipated to result in a contribution margin reduction of
$38,800 ($200,000 - $161,200)

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The high elasticity sales level can be anticipated to result in a contribution marging increase
of $42,000 ($242,000 -$200,000)


Ex # 21 (1)

Abite Belite
(a) Profit per dollar of sales (profit ÷ Sales) $ 0.20 $ 0.15
(b) Contribution margin per unit (Sale price – Variable cost) $7.00 $3.75
(c) C/M ratio (CM ÷ Sale price) 0.47 0.56
(d) Contribution Margin per hour (CM per unit × Units per hour) $70.00 $93.75
(e) Profit per hour (Profit per unit × Units per hour) $30.00 $25.00

(2) Belite is more profitable because of its greater contribution margin per hour.


PROBLEMS
P # 1

(1) ( )




( )




Q(BEP) = 275,000 boxes

(2) Current




Current










( )








0.4 Sale price = Sale price - $2.7

$2.7 = Sale price – 0.4 Sale price

$2.7 = 0.6 Sale price






Sales price = $4.5

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(3) Sale to achieve target profit $184,000 ($110,400 × 100/60)












R = $1,920,000







P # 2

Solution

(1) Projected income after tax for 19A

Income Statement – Direct Costing

Sales
Less: Variable cost
Contribution Margin
Less: Fixed Cost
Operating income
Less: Tax ($90,000 × 40%)
Profit after tax
$500,000
275,000
225,000
135,000
90,000
36,000
$54,000


(2) ( )




( )




Q (BEP) = 12,000 units

CM per unit = Sale price – variable cost

CM per unit = $25 - $13.75 = $11.25

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(3) Net Income 19B

Sales
Less: Variable cost
Contribution Margin
Less: Fixed Cost
Operating income
Less: Tax ($90,000 × 40%)
Profit after tax
$550,000
302,500
247,500
146,250
101,250
40,500
$60,500

(4)
( )




( )


= $325,000









= 0.45

(5) Sale to achieve profit of $90,000 after advertising of $11,250










= $525,000

(6) Advertising expense

Sales – Variable cost – Fixed cost – Advertising = profit

$550,000 – 302,500 – 135,000 – Advertising = $100,000

$112,500 – Advertising = $100,000

$112,500 - $100,000 = Advertising

Advertising = $12,500

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P # 3

Solution

(1) ( )




( )




R (BEP) = $723,065


Composite CM ratio




Composite CM ratio


= 0.2766

Composite CM = Composite Sale price – Composite variable cost

Composite CM = $141 - $102 = $39

Composite Sale Price
A ($10 × 4) $40
B ($8 × 3) 24
C ($11 × 7) 77
$141

Composite Variable Cost
A ($6 × 4) $24
B ($5 × 3) 15
C ($9 × 7) 63
$102


Break Even Point by Dollars








( )





(2) ( )




Product Units Sale Price BEP in Dollars
A (5128 × 4) 20,512 $10 $205,120
B (5128 × 3) 15,384 8 123,072
C (5128 × 7) 35,896 11 394,856

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( )


= $646,512









= 0.3094

Composite CM = Composite Sale price – Composite Variable cost

Composite CM = $139 - $96 = $43

Composite Sale Price
A ($10 × 6) $60
B ($8 × 3) 24
C ($11 × 5) 55
$139

Composite Variable Cost
A ($6 × 6) $36
B ($5 × 3) 15
C ($9 × 5) 45
$96


( )


= 4,651 packages

Break Even Point by Dollars









Product Units Sale Price BEP in Dollars
A (4651 × 6) 27,906 $10 $279,060
B (4651 × 3) 13,953 8 111,624
C (4651 × 5) 23,255 11 255,805