Prepared by
Dr.Hassan Sweillam
University of 6th of October, Egypt
7-1
Exercise 1:
Mixed cost function
Machine Hours Maintenance Cost ( Y ) Cost per hour
(X) (b)
1000 $8,000 $8
3000 $12,000 $4
Mixed cost function:
Y=a+bx
Y = Total cost
a = Total fixed cost
b = Variable cost per unit of activity
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x = Number of units of activity
How to analyze mixed costs
into variable and fixed?
Step 1:
Compute the variable rate per unit= difference in cost
difference in hours
= 12,000 – 8,000
3,000 – 1,000
= $ 2 per machine/ hour
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How to analyze mixed costs
into variable and fixed?
Step 2:
Compute the fixed cost element as the difference between total
cost at the particular level and the variable cost at this level
Total cost =
Total fixed cost ( a ) +( b ) Variable cost per unit * (x)Number of
units
y= a + b x
a= y – b x
Fixed cost (a)= $8,000 – ($2 x 1,000) = $ 6,000
Or = $12,000 – ($ 2 x 3,000) = $ 6,000
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Exercise 2:
6th Oct, Company compiled the following financial information in USD $:
Unit sale price $100
Unit variable cost $60
Total fixed cost $120,000
1- Prepare contribution margin income statement for
1,000, 3,000, 5,000, 7000, and 10,000 units of sales.
2- Prepare the contribution margin ratio (CM Ratio)
3- Prepare the Break-even sales dollars
4- Prepare the Break-even units
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Solution:
1- contribution margin income statement
Units of 1,000 3,000 5,000 7,000 10,000
sales
Sales $100,000 $300,000 $500,000 $700,000 $1,000,000
(-)TVC $60,000 $180,000 $300,000 $420,000 $600,000
TCM $40,000 $120,000 $200,000 $280,000 $400,000
(-)TFC $120,000 $120,000 $120,000 $120,000 $120,000
NI(NL) $(80,000) 0 $ 80,000 $160,000 $280,000
TVC: Total variable cost
TCM: Total contribution margin
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TFC: Total fixed cost
NI (NL): Net income (Net loss)
Solution:
2- Contribution margin ratio
Unit sale price $100 100%
(-) Unit variable cost ($60) 60%
Unit contribution margin $40 40%
CM
CM Ratio = ---------------
TS
40,000
CM Ratio = ---------------
100,000
CM Ratio = 40 %
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Solution:
3- Break-even sales dollars
Total fixed cost $120,000
contribution margin ratio 40%
Total fixed expenses
Break-even sales dollars=--------------------------
Contribution margin %
120,000
Break-even sales dollars= -----------------
40%
Break-even sales dollars= $ 300,000
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Solution:
4- Break-even units
Total fixed cost $120,000
Unit contribution margin $40
Total fixed costs (expenses)
Break-even units= ----------------------------------
Unit contribution margin
120,000
Break-even sales dollars= -----------------
40
Break-even units = 3000
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Exercise 3:
The following is the income statement under the contribution
margin approach for the year ended 12/31/2015:
Units of sales 4000 units
Total Sales (Units of sales 4000) $400,000
(-)Total Variable Cost $280,000
Total contribution margin $120,000
(-) Total fixed cost $75,000
Net operating income $45,000
Unit sale price $100 100%
(-) Unit variable cost $70 70%
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Unit contribution margin $30 30%
For the year 2016:
Study the effect of the following cases on the company’s net
operating income next year:
a) Increasing advertising expense by $50,000 which is expected
to increase sales by 10%
b) Increasing unit variable cost by $5 because of using higher
quality materials which is expected to increase sales by 20%
c) Reducing sale price by 10% which is expected to double
sales.
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Solution :
a) Increasing advertising expense by $50,000 which is expected
to increase sales by 10%
Contribution margin income statement for the year 2016
Units of sales 4400 units Percentage Changes
Total Sales $440,000 100 % Increase sales by 10%
(-)Total Variable Cost $308,000 70 % Unit V.C = $ 70
T.V.C = $ 70 x 4400 Units
T.V.C = $ 308,000
Total contribution $132,000 30%
margin
(-) Total fixed cost $125,000 Increasing advertising
expense by $50,000
Net operating income $7,000
Increasing advertising expense by $50,000 and increase sales by
10% will decrease net operating income from $45,000 to $7,000
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Solution :
b) Increasing unit variable cost by $5 because of using higher
quality materials which is expected to increase sales by 20%
Contribution margin income statement for the year 2016
Units of sales 4800 units Percentage Changes
Total Sales $480,000 100 % Increase sales by 20%
(-)Total Variable Cost $360,000 75 % Unit V.C = $ 75
T.V.C = $ 75 x 4800 Units
T.V.C = $ 360,000
Total contribution $120,000 25%
margin
(-) Total fixed cost $75,000
Net operating income $45,000
No change net operating income $45,000
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Solution :
C) Reducing sale price by 10% which is expected to double sales.
Contribution margin income statement for the year 2016
Units of sales 8000 units Percentage Changes
Total Sales $720,000 100 % decrease sales price by 10%
=$90 and increase sales from
4000 units to 8000 units.
8000 units x $90 = $720,000
(-)Total Variable Cost $560,000 77.8 % Unit V.C = $ 70
T.V.C = $ 70 x 8000 Units
T.V.C = $ 560,000
Total contribution $160,000 22.2%
margin
(-) Total fixed cost $75,000
Net operating income $85,000
Net operating income will increase from $45,000 to $85,000
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Exercise 4:
Unit sale price $60
Unit variable cost $36
Total fixed cost $360,000
Compute break-even point in sales dollars
and units of sales :
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Solution:
Step 1- Contribution margin ratio
Unit sale price $60 100%
(-) Unit variable cost ($36) 60%
Unit contribution margin $24 40%
CM unit
CM Ratio = ---------------
SP unit
24
CM Ratio = ---------------
60
CM Ratio = 40 %
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Solution:
Step 2- Break-even sales dollars
Total fixed cost $360,000
contribution margin ratio 40%
Total fixed expenses
Break-even sales dollars=--------------------------
Contribution margin %
360,000
Break-even sales dollars= -----------------
40%
Break-even sales dollars= $ 900,000
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Solution:
3- Break-even units
Total fixed cost $360,000
Unit contribution margin $24
Total fixed costs (expenses)
Break-even units= ----------------------------------
Unit contribution margin
360,000
Break-even sales dollars= -----------------
24
Break-even units = 15000
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