Study Unit 8
CVP Analysis and Marginal Analysis
SU- 8.1 – Cost-Volume-Profit (CVP)
Analysis - Theory
• CVP = Break-even analysis
• Allows us to analyze the relationship between revenue and fixed
and variable expenses
• It allows us to study the effects of changes in assumptions about
cost behavior and the relevant ranges (in which those assumption
are valid) may affect the relationships among revenues, variable
costs, and fixed costs at various production levels
• It considers the effects of:
•
•
•
•
Sales volume
Sales price
Product mixes
What else……?
SU- 8.1 – Cost-Volume-Profit (CVP)
Analysis - Theory
• CVP analysis is done with what assumptions? See page 314
“Simplifying assumptions of CVP”
• What is the break-even point and where is it on a graph?
CVP Graph
Break-Even Point
SU- 8.1 – Cost-Volume-Profit (CVP)
Analysis - Theory
• BEP = output level at which Total Rev = Total Exp
• It is also the point at which all fixed cost have been covered and
operating income is zero
Revenue
Var. Cost
Gross Margin
Fixed Cost
Oper. Income
$100,000
$ 80,000
$ 20,000
$ 20,000
$ 0
SU- 8.1 – Cost-Volume-Profit (CVP)
Analysis - Theory
• Other terms and def.
• Margin of safety = excess of “budgeted” sales over BE Sales
• Mixed costs - Costs that have both a fixed and variable component.
For example, the cost of operating an automobile includes some
fixed costs that do not change with the number of miles driven (e.g.,
operating license, insurance, parking, some of the depreciation, etc.)
Other costs vary with the number of miles driven (e.g., gasoline, oil
changes, tire wear, etc.).
• Revenue or sales mix
• Sensitivity analysis – examines the effect on the outcome of not
achieving the original forecast or of changing an assumption. Since
many decisions must be made due to uncertainty, probabilities can
be assigned to different outcomes (“what-if”).
Continued
SU- 8.1 – Cost-Volume-Profit (CVP)
Analysis - Theory
SU- 8.1 – Cost-Volume-Profit (CVP)
Analysis - Theory
• Unit Contribution Margin (UCM) is an important term used
with break-even point or break-even analysis is contribution
margin. In equation format it is defined as follows:
Contribution Margin = Revenues – Variable Expenses
• The contribution margin for one unit of product or one unit of
service is defined as:
Contribution Margin per Unit = Revenues per Unit – Variable
Expenses per Unit
SU- 8.1 – Cost-Volume-Profit (CVP)
Analysis - Theory
• Break-even point in units
Fixed costs
UCM
• Break-even point in dollars
Fixed costs
CMR
SU- 8.1 – Cost-Volume-Profit (CVP)
Analysis – Theory - Question 1
Question 1 - CMA2 Study Unit 8: CVP
Analysis and Marginal Analysis
Cost-volume-profit (CVP) analysis is a key
factor in many decisions, including choice of
product lines, pricing of products, marketing
strategy, and use of productive facilities. A
calculation used in a CVP analysis is the
breakeven point. Once the breakeven point
has been reached, operating income will
increase by the
A.
B.
C.
D.
Gross margin per unit for each additional unit
sold.
Contribution margin per unit for each
additional unit sold.
Fixed costs per unit for each additional unit
sold.
Variable costs per unit for each additional unit
sold.
SU- 8.1 – Cost-Volume-Profit (CVP) Analysis –
Theory – Answer to Question 1
• Correct Answer: B
At the breakeven point, total revenue equals total fixed costs plus
the variable costs incurred at that level of production. Beyond the
breakeven point, each unit sale will increase operating income by
the unit contribution margin (unit sales price – unit variable cost)
because fixed cost will already have been recovered.
Incorrect Answers:
A: The gross margin equals sales price minus cost of goods sold,
including fixed cost.
C: All fixed costs have been covered at the breakeven point.
D: Operating income will increase by the unit contribution margin,
not the unit variable cost.
SU- 8.1 – Cost-Volume-Profit (CVP)
Analysis – Theory - Question 2
Question 2 - CMA2 Study Unit 8: CVP
Analysis and Marginal Analysis
One of the major assumptions limiting
the reliability of breakeven analysis is
that
A.
B.
C.
D.
Efficiency and productivity will
continually increase.
Total variable costs will remain
unchanged over the relevant range.
Total fixed costs will remain unchanged
over the relevant range.
The cost of production factors varies with
changes in technology.Correct Answer: C
SU- 8.1 – Cost-Volume-Profit (CVP) Analysis –
Theory – Answer to Question 2
Correct Answer: C
One of the inherent simplifying assumptions used in CVP analysis is
that fixed costs remain constant over the relevant range of activity.
Incorrect Answers:
A: Breakeven analysis assumes no changes in efficiency and
productivity.
B: Total variable costs, by definition, change across the relevant
range.
D: The cost of production factors is assumed to be stable; this is
what is meant by relevant range.
SU- 8.1 – Cost-Volume-Profit (CVP)
Analysis – Theory - Question 3
Question 3 - CMA2 Study Unit 8: CVP
Analysis and Marginal Analysis
The margin of safety is a key concept of
CVP analysis. The margin of safety is
the
A.
B.
C.
D.
Contribution margin rate.
Difference between budgeted
contribution margin and breakeven
contribution margin.
Difference between budgeted sales and
breakeven sales.
Difference between the breakeven point
in sales and cash flow breakeven.
SU- 8.1 – Cost-Volume-Profit (CVP) Analysis –
Theory – Answer to Question 3
Correct Answer: C
The margin of safety measures the amount by which sales may decline
before losses occur. It is the excess of budgeted or actual sales over
sales at the BEP.
Incorrect Answers:
A: The contribution margin rate is computed by dividing
contribution margin by sales. The contribution margin equals sales
minus total variable costs.
B: The margin of safety is expressed in revenue or units, not
contribution margin.
D: Cash flow is not relevant.
SU- 8.1 – Cost-Volume-Profit (CVP)
Analysis – Theory - Question 4
Question 4 - CMA2 Study Unit 8: CVP
Analysis and Marginal Analysis
The breakeven point in units increases
when unit costs
A.
Increase and sales price remains
unchanged.
B.
Decrease and sales price remains
unchanged.
C.
D.
Remain unchanged and sales price
increases.
Decrease and sales price increases.
SU- 8.1 – Cost-Volume-Profit (CVP) Analysis –
Theory – Answer to Question 4
Correct Answer: A
The breakeven point in units is calculated by dividing total fixed costs by
the unit contribution margin. If selling price is constant and costs increase,
the unit contribution margin will decline, resulting in an increase of the
breakeven point.
Incorrect Answers:
B: A decrease in costs will cause the unit contribution margin to
increase, lowering the breakeven point.
C: An increase in the selling price will increase the unit contribution
margin, resulting in a lower breakeven point.
D: Both a cost decrease and a sales price increase will increase the unit
contribution margin, resulting in a lower breakeven point.
SU- 8.1 – Cost-Volume-Profit (CVP)
Analysis - Theory
• Review:
• Diff. gross margin and contribution margin
• Effect of an increase in CM
• Effects on BEP by changes in CM
SU – 8.2 CVP Analysis – Basic
Calculations
• CVP Applications
• Target Operating Income
• Multiple products
• Choice of products
• Degree of Operating Leverage (DOL)
• Problems
• 8, 9, 10, 12 & 13 starting on page 330
SU – 8.3 CVP Analysis – Target Income
Calculations
• Target Operating Income
Fixed costs + Target operating income
UCM
• Target Net Income
Fixed costs + Target net income / (1.0 – tax rate)
UCM
• Problem 15, 16 and 18 on page 333
SU – 8.4 CVP Analysis – Multiproduct
Calculations
• Multiple Products (or Services)
S = FC + VC = Calculated Weighted Average Contribution
Margin
• Choice of Product decisions – When resources are limited
companies have to choose which products to produce
• Special Orders
SU- 8.4 CVP Analysis – Multiproduct
Calculations - Question 1
Moorehead Manufacturing Company produces two
products for which the data presented to the right
have been tabulated. Fixed manufacturing cost is
applied at a rate of $1.00 per machine hour. The sales
manager has had a $160,000 increase in the budget
allotment for advertising and wants to apply the
money to the most profitable product. The products
are not substitutes for one another in the eyes of the
company’s customers.
Per Unit
Selling price
Variable manufacturing cost
Fixed manufacturing cost
Variable selling cost
XY-7
BD-4
$4.00
2.00
$3.00
1.50
.75
1.00
.20
1.00
SU- 8.4 – CVP Analysis – Multiproduct
Calculations - Question 1 Continued
Suppose Moorehead has only 100,000 machine
hours that can be made available to produce
additional units of XY-7 and BD-4. If the potential
increase in sales units for either product resulting
from advertising is far in excess of this production
capacity, which product should be advertised and
what is the estimated increase in contribution
margin earned?
A.
Product XY-7 should be produced, yielding a
contribution margin of $75,000.
B.
Product XY-7 should be produced, yielding a
contribution margin of $133,333.
C.
Product BD-4 should be produced, yielding a
contribution margin of $187,500.
D.
Product BD-4 should be produced, yielding a
contribution margin of $250,000.
SU- 8.4 CVP Analysis – Multiproduct
Calculations – Answer to Question 1
Correct Answer: D
The machine hours are a scarce resource that must be allocated to the product(s) in a proportion
that maximizes the total CM. Given that potential additional sales of either product are in excess of
production capacity, only the product with the greater CM per unit of scarce resource should be
produced. XY-7 requires .75 hours; BD-4 requires .2 hours of machine time (given fixed
manufacturing cost applied at $1 per machine hour of $.75 for XY-7 and $.20 for BD-4). XY-7 has a
CM of $1.33 per machine hour ($1 UCM ÷ .75 hours), and BD-4 has a CM of $2.50 per machine hour
($.50 ÷ .2 hours). Thus, only BD-4 should be produced, yielding a CM of $250,000 (100,000 × $2.50).
The key to the analysis is CM per unit of scarce resource.
Incorrect Answers:
A: Product XY-7 actually has a CM of $133,333, which is lower than the $250,000 CM for product
BD-4.
B: Product BD-4 has a higher CM at $250,000.
C: Product BD-4 has a CM of $250,000.
SU- 8.4 CVP Analysis – Multiproduct
Calculations - Question 2
Question 2 - CMA2 Study Unit 8: CVP
Analysis and Marginal Analysis
Product A accounts for 75% of a
company’s total sales revenue and has a
variable cost equal to 60% of its selling
price. Product B accounts for 25% of total
sales revenue and has a variable cost
equal to 85% of its selling price. What is
the breakeven point given fixed costs of
$150,000?
A.
B.
C.
D.
$375,000
$444,444
$500,000
$545,455
SU- 8.4 CVP Analysis – Multiproduct
Calculations – Answer to Question 2
Correct Answer: B
Using the relationship: sales = total
variable costs + total fixed costs, the
combined breakeven point can be
calculated as follows:
S
=
0.75S(0.60) + 0.25S(0.85) + $150,000
S
=
0.45S + 0.2125S + $150,000
S – 0.6625S
=
$150,000
0.3375S
S
=
=
$150,000
$444,444
Incorrect Answers: A: This amount is
based on the contribution margin of
Product A only rather than a weighted
average. C: This amount is based on
half of the required sales at B’s
contribution margin. D: This amount is
based on an unweighted average of the
two contribution margins.
SU- 8.4 CVP Analysis – Multiproduct
Calculations - Question 3
Question 3 - CMA2 Study Unit 8: CVP Analysis and Marginal
Analysis
Von Stutgatt International’s breakeven point is 8,000 racing
bicycles and 12,000 5-speed bicycles. If the selling price and
variable costs are $570 and $200 for a racer, and $180 and $90
for a 5-speed respectively, what is the weighted-average
contribution margin?
A.
B.
C.
D.
$100
$145
$179
$202
SU- 8.4 CVP Analysis – Multiproduct
Calculations – Answer to Question 3
Correct Answer: D
Contribution margin
equals selling price
minus variable costs.
The product contribution margins are:
Racer:
$570 – $200
=
$370
5-Speed:
$180 – $90
=
$90
Racer:
8,000 ÷ (8,000 + 12,000) =
40%
5-Speed:
12,000 ÷ (8,000 +
12,000)
60%
The sales mix is:
Multiply the CM by the sales mix for each product,
and add the results.
Weighted-average CM = ($370 × 40%) + ($90 ×
60%)
= $148 + $54
= $202
=
SU- 8.4 CVP Analysis – Multiproduct
Calculations – Answer to Question 3
Incorrect Answers:
A: The sales mix dictates how much of the total CM will come from
sales of each product. Unit sales are attributable 40% to racers and
60% to 5-speeds, so 40% of the UCM for racers must be added to 60%
of the UCM for 5-speeds to get the weighted-average CM.
B: The sales mix dictates how much of the total CM will come from
sales of each product. Unit sales are attributable 40% to racers and
60% to 5-speeds, so 40% of the UCM for racers must be added to 60%
of the UCM for 5-speeds to get the weighted-average CM.
C: The sales mix dictates how much of the total CM will come from
sales of each product. Unit sales are attributable 40% to racers and
60% to 5-speeds, so 40% of the UCM for racers must be added to 60%
of the UCM for 5-speeds to get the weighted-average CM.
SU- 8.4 CVP Analysis – Multiproduct
Calculations - Question 4
Question 4 - CMA2 Study Unit 8: CVP
Analysis and Marginal Analysis
Catfur Company has fixed costs of $300,000.
It produces two products, X and Y. Product X
has a variable cost percentage equal to 60%
of its $10 per unit selling price. Product Y
has a variable cost percentage equal to 70%
of its $30 selling price. For the past several
years, sales of Product X have averaged 66%
of the sales of Product Y. That ratio is not
expected to change.
What is Catfur’s breakeven point in dollars?
A.
B.
C.
D.
$300,000
$750,000
$857,142
$942,857
SU- 8.4 CVP Analysis – Multiproduct
Calculations – Answer to Question 4
Correct Answer: D
A helpful approach in a multiproduct situation is to make calculations
based on the composite unit, i.e., 2 units of Product X and 3 units of
Product Y (a 66% ratio). The selling price of this composite unit is $110 [(2
× $10) + (3 × $30)]. The UCM of the composite unit is $35 {[2 × ($10 – $6)]
+ [3 × ($30 – $21)]}. Consequently, the breakeven point in composite units
is 8,571.43 ($300,000 FC ÷ $35 UCM), and the breakeven point in sales
dollars is $942,857 (8,571.43 × $110).
Incorrect Answers:
A: This amount equals the fixed costs.
B: This amount assumes a 40% contribution margin ratio.
C: This amount assumes a 35% contribution margin ratio.
SU 8.5 – Marginal Analysis
• Accounting Costs vs. Economic Costs
• Accounting Costs = The total amount of money or goods expended in an
endeavor. It is money paid out at some time in the past and recorded in
journal entries and ledgers.
• Economic Costs = The economic cost of a decision depends on both the
cost of the alternative chosen and the benefit that the best alternative
would have provided if chosen. Economic cost differs from accounting
cost because it includes opportunity cost.
As an example, consider the economic cost of attending college. The accounting cost
of attending college includes tuition, room and board, books, food, and other
incidental expenditures while there. The opportunity cost of college also includes the
salary or wage that otherwise could be earning during the period. So for the two to
four years an individual spends in school, the opportunity cost includes the money
that one could have been making at the best possible job. The economic cost of
college is the accounting cost plus the opportunity cost.
Thus, if attending college has a direct cost of $20,000 dollars a year for four years, and
the lost wages from not working during that period equals $25,000 dollars a year,
then the total economic cost of going to college would be $180,000 dollars ($20,000 x
4 years + the interest of $20,000 for 4 years + $25,000 x 4 years).
SU 8.5 – Marginal Analysis
• Explicit vs. Implicit Costs
• Implicit Costs = implicit cost, also called an imputed cost, implied
cost, or notional cost, is the opportunity cost equal to what a firm
must give up in order to use factors which it neither purchases
nor hires.
• Explicit Costs = An explicit cost is a direct payment made to
others in the course of running a business, such as wage, rent and
materials.
SU 8.5 – Marginal Analysis
• Accounting vs. Economic Profit
• See Utorial at http://www.khanacademy.org/economics-finance-domain/microeconomics/firmeconomic-profit/economic-profit-tutorial/v/economic-profit-vs-accounting-profit
• Accounting Profit = book income exceeds book expenses
• Economic Profit = includes Accounting Profit + Implicit costs
SU 8.5 – Marginal Analysis
• Marginal Revenue and Marginal Cost
• Marginal Revenue is the additional or incremental revenue of one
additional unit of output. See page 321
• See that Marginal Revenue is $540 between generating 4 vs. 5 units
of output.
• Marginal Cost is the additional or incremental cost incurred of
one additional unit of output.
• Note that while cost decrease over some range they will at some
point begin to increase due to the process becoming lest efficient.
• Profit Maximization is where MR = MC (see page 322)
SU 8.5 – Marginal Analysis
• Short-Run Cost Relationship – See graph on page 323
• Other considerations/applications of CVP
• Make-or-Buy
• Capacity Constraints and Product Mix
• Disinvestments
• Sell-or-Process further
SU 8.6 Short-run Profit Maximization
• Pure Competition
• Monopoly
• Monopolistic Competition
• Oligopoly
• Law of Demand
• Calculating Price elasticity of demand
• Def.
•
•
•
•
•
Greater than one
Equal to one
Less than one
Infinite or perfectly elastic
Equal to zero or perfectly inelastic