Cost Behavior Fundamentals
These costs vary in total directly and proportionately with activity but remain constant per unit.
What are variable costs?
The high-low method separates mixed costs into these two components.
Answer: Variable and fixed
Question: What are variable cost component and fixed cost component?
Contribution margin equals revenue minus this.
Variable costs
Break-even occurs when net income equals what?
Answer: Zero
To compute target sales in units, we add target net income to what?
Answer: Fixed costs
Margin of safety equals actual sales minus this.
Answer: Break-even sales
Within this range, cost behavior assumptions (linearity) are valid.
What is the relevant range?
High activity: 50,000 units at $70,000
Low activity: 20,000 units at $40,000
Variable cost per unit = ?
Answer:
($70,000 − $40,000) ÷ (50,000 − 20,000)
= $30,000 ÷ 30,000
= $1 per unit
Selling price = $80
Variable cost = $50
Unit contribution margin = ?
Answer: $30
Fixed costs = $200,000
Unit CM = $50
Break-even units = ?
Answer:
200,000 ÷ 50 = 4,000 units
Fixed costs = $100,000
Target income = $50,000
Unit CM = $25
Required units = ?
Answer:
(100,000 + 50,000) ÷ 25
= 6,000 units
Actual sales = $600,000
Break-even sales = $450,000
MOS in dollars = ?
Answer: $150,000
A company pays $12,000 monthly rent. At 3,000 units, rent per unit is $4.
At 6,000 units, rent per unit is ____.
Answer: $2
What is $12,000 ÷ 6,000?
High activity: 50,000 units at $70,000
Low activity: 20,000 units at $40,000
What are fixed costs?
Answer:
($70,000 − $40,000) ÷ (50,000 − 20,000)
= $30,000 ÷ 30,000
= $1 per unit
Using high point:
$70,000 − (50,000 × $1) = $20,000
Answer: $20,000
Selling price = $80
Variable cost = $50
Fixed costs = $90,000
Units sold = 4,000
Net income = ?
Unit contribution margin = ?
Answer: $30
CM = $30 × 4,000 = 120,000
Net income = 120,000 − 90,000
Answer: $30,000
If CM ratio is 40% and fixed costs are $120,000, break-even sales dollars = ?
120,000 ÷ .40 = $300,000
Fixed costs = $200,000
Target income = $80,000
CM ratio = 40%
Required sales dollars = ?
Answer:
(200,000 + 80,000) ÷ .40
= $700,000
Actual sales = $600,000
Break-even sales = $450,000
MOS ratio = ?
MOS in dollars = ?
Answer: $150,000
150,000 ÷ 600,000
Answer: 25%
Maintenance costs increase from $8,000 at 10,000 units to $11,000 at 20,000 units.
What type of cost is this?
Answer: Mixed cost
Question: What is a mixed cost?
Why might the high-low method produce misleading results?
Because it uses only two data points and ignores the rest.
Contribution margin ratio formula.
Unit contribution margin ÷ Unit selling price
A company sells 10,000 units at BE.
If sales increase to 10,001 units, profit increases by?
Answer: Unit contribution margin
If price increases but variable cost stays constant, what happens to required units to reach same target income?
Answer: Decreases
What does a higher margin of safety indicate?
Answer: Lower operating risk
Explain why fixed cost per unit declines as volume increases, even though total fixed cost remains constant.
Answer: Because fixed costs are spread over more units; denominator increases.
Question: What is cost spreading or operating leverage effect?
Cost equation is:
Total cost = $15,000 + $2.50X
What is total cost at 12,000 units?
Answer:
$15,000 + (2.50 × 12,000)
= $15,000 + 30,000
= $45,000
Why does net income increase by exactly the unit contribution margin for each additional unit sold (within relevant range)?
Because fixed costs do not change; each additional unit contributes full CM to profit.
Explain the difference between break-even in units and break-even in dollars.
Answer:
Units use unit CM; dollars use CM ratio.
Why is CVP analysis highly sensitive to selling price assumptions?
Because CM changes directly with price; small changes significantly impact break-even and target income.
If a company has high fixed costs and low variable costs, what does this imply about operating leverage and risk?
High operating leverage; higher risk but greater profit potential when sales increase.
A company sells product for $120.
Variable cost = $70
Fixed costs = $250,000
Management wants $150,000 profit.
Unit CM = 50
Required units = (250,000 + 150,000) ÷ 50
= 400,000 ÷ 50
= 8,000 units
If actual = 12,000
MOS units = 12,000 − 8,000 = 4,000