Operation Management
`Cost-Volume Analysis
Cost–Volume
Analysis
• Cost–volume analysis focuses on
relationships between cost, revenue,
and volume of output.
• The purpose of cost–volume analysis
is to estimate the income of an
organization under different operating
conditions.
• It is particularly useful as a tool for
comparing capacity alternatives.
Cost–Volume
Analysis
• Use of the technique requires identification of all costs related to the
production of a given product.
• These costs are then designated as fixed costs or variable costs.
• Fixed costs tend to remain constant regardless of volume of output.
Examples include rental costs, property taxes, equipment costs, heating
and cooling expenses, and certain administrative costs.
• Variable costs vary directly with volume of output. The major
components of variable costs are generally materials and labor costs.
Total Costs
• The total cost associated with a given
volume of output is equal to the sum of
the fixed cost and the variable cost per
unit times volume:
TC = FC + VC
VC = Q * v
• where v variable cost per unit. Figure
5.6A shows the relationship between
volume of output and fixed costs, total
variable costs, and total (fixed plus
variable) costs.
Total Revenue
• Revenue per unit, like variable cost per unit, is
assumed to be the same regardless of quantity of
output.
• Total revenue will have a linear relationship to
output.
• The total revenue associated with a given quantity
of output, Q, is
TR = R * Q
Break-even point
(BEP)
• The volume at which total cost and total
revenue are equal is referred to as the breakeven point (BEP) .
• When volume is less than the break-even
point, there is a loss; when volume is greater
than the break-even point, there is a profit.
The greater the deviation from this point, the
greater the profit or loss.
• Total profit can be computed using the
formula
P = TR - TC = R * Q - (FC + v * Q)
• Rearranging terms, we have
P = Q(R - v) – FC
Break-even point (BEP)
• The difference between revenue per unit and
variable cost per unit, R v, is known as the
contribution margin.
• The required volume, Q, needed to generate a
specified profit is
Q=
𝑷+𝑭𝑪
𝑹 −𝒗
• A special case of this is the volume of output
needed for total revenue to equal total cost.
• This is the break-even point, computed using the
formula
𝑭𝑪
𝑸𝑩𝑬𝑷 = 𝑹 −𝒗
Indifference
point
• Indifference point : the quantity at
which a decision maker would be
indifferent between two competing
alternatives.
𝑸𝑩𝑬𝑷 =
𝑭𝑪
𝑹 −𝒗
• 𝑄𝐵𝐸𝑃 and FC has Positive relationship.
• 𝑄𝐵𝐸𝑃 and R has Inverse/ negative relationship.
• 𝑄𝐵𝐸𝑃 and contribution margin (V-R) has Inverse/ negative
relationship.
• 𝑄𝐵𝐸𝑃 and V has Positive relationship.
Multiple
Choices
Questions
1. Maximum capacity refers to the upper limit
of:
A. inventories
B. demand
C. supplies
D. rate of output
E. finances
Answer: D
2. At the break-even point:
A. output equals capacity
B. total cost equals total revenue
C. total cost equals profit
D. variable cost equals fixed cost
E. variable cost equals total revenue
Answer: B
3. What is the break-even quantity for the
following situation?
FC = $1,200 per week
VC = $2 per unit
Rev = $6 per unit
A. 100
B. 200
C. 600
D. 1,200
E. 300
Answer: E
4. An alternative will have fixed costs of
$10,000 per month, variable costs of $50 per
unit, and revenue of $70 per unit. The breakeven point volume is:
A. 100
B. 2,000
C. 500
D. 1,000
E. none of these
Answer: C
5. For fixed costs of $2,000, revenue per unit
of $2, and variable cost per unit of $1.60,
the break-even quantity is:
A. 1,000
B. 1,250
C. 2,250
D. 5,000
E. none of these
Answer: D
6. Which of the following are assumptions of
the break-even model?
I. Only one product is involved.
II. Everything that is produced can be sold.
III. The revenue per unit will be the same
regardless of volume.
A. I only
B. I and II only
C. II only
D. II and III only
E. I, II and III
Answer: E
7. If the fixed costs decrease, the 𝑸𝑩𝑬𝑷 will
….
A. Increase
B. Decrease
C. Remain Constant
Answer: B
8. If the Variable costs increase, the
𝑸𝑩𝑬𝑷 will ….
A. Increase
B. Decrease
C. Remain Constant
Answer: A
9. If the revenue decrease, the 𝑸𝑩𝑬𝑷 will ….
A. Increase
B. Decrease
C. Remain Constant
Answer: A
True or False Questions
1.
In cost-volume analysis, costs that vary directly with volume of output are referred to as fixed
costs because they are a fixed percentage of output levels.
FALSE
2.
The break-even quantity can be determined by dividing the fixed costs by the difference between
the revenue per unit and the variable cost per unit.
TRUE
3.
Capacity decisions are usually one-time decisions; once they have been made, we know the
limits of our operations.
FALSE
4.
If the revenue doubled, the 𝑸𝑩𝑬𝑷 will be doubled also
FALSE
5.
There is an inverse relation between the Fixed costs and 𝑸𝑩𝑬𝑷 .
False
6.
There is a negative relation between the variable costs and 𝑸𝑩𝑬𝑷 .
False
7.
There is a positive relation between the Fixed costs and 𝑸𝑩𝑬𝑷 .
True
8.
There is a positive relation between the revenue and 𝑸𝑩𝑬𝑷 .
False
9.
If 𝒇𝒊𝒙𝒆𝒅 𝒄𝒐𝒔𝒕𝒔 𝒊𝒏𝒄𝒓𝒆𝒔𝒆 𝒕𝒉𝒆 𝑸𝑩𝑬𝑷 𝒘𝒊𝒍𝒍 𝒅𝒆𝒄𝒓𝒆𝒂𝒔𝒆 .
False
10. If the revenue increase the 𝑸𝑩𝑬𝑷 𝒘𝒊𝒍𝒍 𝒊𝒏𝒄𝒓𝒆𝒔𝒆 .
False
Mariam Ashraf
Teaching Assistant of Business and
Management, Mansoura
University