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

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

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

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

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

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)

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

3- Break-even sales dollars 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

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

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 $100 100% (-) Unit variable cost $70 70% 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: 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.

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

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

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

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 :

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 $60 100% (-) Unit variable cost ($36) 60% Unit contribution margin $24 40%

Step 2- Break-even sales dollars 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

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