1. University of 6th of October, Egypt
Prepared by
Dr.Hassan Sweillam
University of 6th of October, Egypt

2. Exercise 1: Mixed cost function Mixed cost function: Y = a + b x
Machine Hours
(X)
Maintenance Cost ( Y )
Cost per hour
( b )
1000
$8,000
$ 8
3000
$12,000
$ 4
Mixed cost function:
Y = a + b x
Y = Total cost a = Total fixed cost b = Variable cost per unit of activity x = Number of units of activity

3. 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

4. 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 4

5. Exercise 2: Unit sale price $100 Unit variable cost $60
6th Oct, Company compiled the following financial information in USD $:
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
Unit sale price $100
Unit variable cost $60
Total fixed cost $120,000

6. 1- contribution margin income statement
Solution:
1- contribution margin income statement
Units of sales
1,000
3,000
5,000
7,000
10,000
Sales
$100,000
$300,000
$500,000
$700,000
$1,000,000
(-)TVC
$60,000
$180,000
$420,000
$600,000
TCM
$40,000
$120,000
$200,000
$280,000
$400,000
(-)TFC
NI(NL)
$(80,000)
$ 80,000
$160,000
TVC: Total variable cost
TCM: Total contribution margin
TFC: Total fixed cost
NI (NL): Net income (Net loss)

7. 2- Contribution margin ratio
Solution:
2- Contribution margin ratio CM
CM Ratio = TS
40,000
100,000
CM Ratio = 40 %
Unit sale price $ %
(-) Unit variable cost ($60) %
Unit contribution margin $ %

8. 3- Break-even sales dollars
Solution:
3- Break-even sales dollars
Total fixed cost $120,000
contribution margin ratio %
Total fixed expenses
Break-even sales dollars=
Contribution margin %
120,000
Break-even sales dollars=
40%
Break-even sales dollars= $ 300,000

9. 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

10. Exercise 3: Unit sale price $100 100% (-) Unit variable cost $70 70%
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 $ %
(-) Unit variable cost $ %
Unit contribution margin $ %

11. For the year 2016:
Study the effect of the following cases on the company’s net operating income next year:
Increasing advertising expense by $50,000 which is expected to increase sales by 10%
Increasing unit variable cost by $5 because of using higher quality materials which is expected to increase sales by 20%
Reducing sale price by 10% which is expected to double sales.

12. Contribution margin income statement for the year 2016
Solution :
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 margin
$132,000
30%
(-) 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

13. Contribution margin income statement for the year 2016
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 margin
$120,000
25%
(-) Total fixed cost
$75,000
Net operating income
$45,000
No change net operating income $45,000

14. 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 margin
$160,000
22.2%
(-) Total fixed cost
$75,000
Net operating income
$85,000
Net operating income will increase from $45,000 to $85,000

15. 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 :

16. Step 1- Contribution margin ratio
Solution:
Step 1- Contribution margin ratio
CM unit
CM Ratio =
SP unit 24 60
CM Ratio = 40 %
Unit sale price $ %
(-) Unit variable cost ($36) %
Unit contribution margin $ %

17. Step 2- Break-even sales dollars
Solution:
Step 2- Break-even sales dollars
Total fixed cost $360,000
contribution margin ratio %
Total fixed expenses
Break-even sales dollars=
Contribution margin %
360,000
Break-even sales dollars=
40%
Break-even sales dollars= $ 900,000

18. 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