CMA Part 2
Financial Decision Making
Study Unit 8 - CVP Analysis and
Marginal Analysis
Jim Clemons, CMA
Ronald Schmidt, CMA, CFM
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
– Cost-volume-profit analysis is a tool to predict how changes in costs
and sales levels affect income; conventional CVP analysis requires that
all costs must be classified as either fixed or variable with respect to
production or sales volume before CVP analysis can be used.
– 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?
– Cost and revenue relationships are predictable
– Unit selling prices are constant
– Changes in inventory are insignificant
– Fixed costs remain constant over relevant range
(see slide 5 & 6)
– Total variable cost change proportional with
volume (see slide 7 & 8)
Continued
SU- 8.1 – Cost-Volume-Profit (CVP) Analysis Theory
– The revenue (sales) mix is constant
– All costs are either fixed or variable (long-term all
costs are considered as variable)
– Volume is the sole revenue driver and cost driver
– The breakeven point is directly related to costs
and inversely related to the budgeted margin of
safety and the contribution margin
– Time value of money is ignored
SU- 8.1 – Cost-Volume-Profit (CVP)
Analysis – Theory – Fixed Costs
• Fixed Costs
– Total fixed cost remains unchanged in amount when volume of activity
varies from period to period within a relevant range.
– The fixed cost per unit of output decreases as volume increases (and
vice versa).
– When production volume and cost are graphed, units of product are
usually plotted on the Horizontal axis and dollars of cost are plotted on
the vertical axis.
– Fixed cost is represented by a horizontal line with no slope (cost
remains constant at all levels of volume within the relevant range).
– Intersection point of line on cost (vertical) axis is at fixed cost amount.
– Likely that amount of fixed cost will change when outside of relevant
range.
Number of Local Calls
Total fixed costs
remain constant as
activity increases.
Monthly Basic Telephone
Bill per Local Call
SU- 8.1 – Cost-Volume-Profit (CVP) Analysis – Theory
Fixed Costs
Monthly Basic
Telephone Bill
C1
Number of Local Calls
Cost per call
declines as
activity increases.
SU- 8.1 – Cost-Volume-Profit (CVP)
Analysis – Theory – Variable Costs
• Variable Costs
– Total variable cost changes in proportion to changes in
volume of activity.
– Variable cost per unit remains constant but the total
amount of variable cost changes with the level of
production.
– When production volume and cost are graphed
– Variable cost is represented by a straight line starting
at the zero cost level.
– The straight line is upward (positive) sloping. The line
rises as volume increases.
Cost per Minute
SU- 8.1 – Cost-Volume-Profit (CVP) Analysis – Theory
Variable Costs
Total Costs
C1
Minutes Talked
Total variable costs
increase as
activity increases.
Minutes Talked
Cost per Minute
is constant as
activity increases.
SU- 8.1 – Cost-Volume-Profit (CVP)
Analysis – Theory – Mixed Costs
• Mixed Costs
– Include both fixed and variable cost components.
– When volume and cost are graphed,
• Mixed cost is represented by a straight line with an upward
(positive) slope.
• Start of line is at fixed cost point (or amount of total cost
when volume is zero) on cost (vertical) axis. As activity level
increases, mixed cost line increases at an amount equal to
the variable cost per unit.
– Mixed costs are often separated into fixed and
variable components when included in a CVP analysis.
P1
Scatter Diagrams
Draw a line through the plotted data points so that about equal
numbers of points fall above and below the line.
Total Cost in
1,000’s of Dollars
20
* ** *
**
* *
* *
10
Estimated fixed cost = 10,000
0
0
1
2
3
4
5
Activity, 1,000’s of Units Produced
6
P1
Scatter Diagrams
Δ in cost
Δ in units
Unit Variable Cost = Slope =
Total Cost in
1,000’s of Dollars
20
* ** *
**
* *
* *
10
Horizontal distance is the
change in activity.
0
0
1
2
3
4
Activity, 1,000’s of Units Produced
5
6
Vertical
distance is
the change
in cost.
High-low method
• The following is not in this Study Unit, but it is
important to know and be able to calculate.
The High-Low Method
The following relationships between units
produced and total cost are observed:
Using these two levels of activity, compute:
 the variable cost per unit.
 the total fixed cost.
The High-Low Method
High activity level - December
Low activity level - January
Change in activity
Units
67,500
17,500
50,000
Cost
$ 29,000
20,500
$ 8,500
 Variable cost per unit is determined as follows:
 Fixed costs are determined as follows:
Total cost = $17,525 + $0.17 per unit produced
Contribution Margin and its
Measures
Sales Revenue (2,000 units)
Less: Variable costs
Contribution margin
Less: Fixed costs
Net income
Total
$ 200,000
140,000
$ 60,000
24,000
$ 36,000
Unit
$ 100
70
$ 30
Contribution margin is the amount by which revenue
exceeds the variable costs of producing the revenue.
Total contribution margin is $60,000 and the
contribution margin per unit sold is $30.
SU- 8.1 – Cost-Volume-Profit (CVP) Analysis
- Theory
• Breakeven point def. – Level of output where
total revenues equals total expenses; the
point at which all fixed costs have been
covered and operating income is zero.
– What is the break-even point and where is it on a
graph on the next page?
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 – (See slide 11) 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 is the composition of total revenues in terms of various
products
– Sensitivity analysis – (See slide 12) 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”).
C1
SU- 8.1 – Cost-Volume-Profit (CVP) Analysis – Theory
Mixed Costs
Total Utility Cost
Mixed costs contain a fixed portion that is incurred even when the
facility is unused, and a variable portion that increases with
usage. Utilities typically behave in this manner.
Variable
Cost per KW
Activity (Kilowatt Hours)
Fixed Monthly
Utility Charge
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 (Sales price) – Variable
Expenses per Unit
Expressed in either percentage of the selling price (contribution margin ratio) or
dollar amount
Slope of total cost curve plotted so that volume is on the x-axis and dollar value is
on the y-axis
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
A1
Contribution Margin Ratio
Sales Revenue (2,000 units)
Less: Variable costs
Contribution margin
Less: Fixed costs
Net income
Contribution
margin ratio
Contribution
margin ratio
Total
$ 200,000
140,000
$ 60,000
24,000
$ 36,000
Unit
$ 100
70
$ 30
=
Contribution margin per unit
Sales price per unit
=
$30 per unit
$100 per unit
=
30%
P2
Computing the Break-Even Point
Sales Revenue (2,000 units)
Less: Variable costs
Contribution margin
Less: Fixed costs
Net income
Total
$ 200,000
140,000
$
60,000
24,000
$
36,000
Unit
$ 100
70
$ 30
How much contribution margin must Rydell Company
have to cover its fixed costs (break-even)?
Answer: $24,000
How many units must Rydell sell to cover its fixed
costs (break-even)?
Answer: $24,000 ÷ $30 per unit = 800 units
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.
Remember
Computing the Break-Even Point
We have just seen one of the basic CVP relationships
– the break-even computation.
Fixed costs
Break-even point in units =
Contribution margin per unit
Unit sales price less unit variable cost
($30 in previous example)
REMEMBER
COMPUTING THE BREAK-EVEN POINT
The break-even formula may also be
expressed in sales dollars.
Break-even point in dollars =
Fixed costs
Contribution margin ratio
Unit contribution margin
Unit sales price
SU- 8.1 – Cost-Volume-Profit (CVP) Analysis Theory
• Review:
– What is the difference between 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 8.2 – Practice Question 1
Which of the following would decrease unit a contribution margin the most?
A.
A 15% decrease in selling price.
B.
A 15% increase in variable expenses.
C.
A 15% decrease in variable expenses.
D.
A 15% decrease in fixed expenses.
SU 8.2 – Practice Question 1 Answer
• Correct Answer: A
Unit contribution margin (UCM) equals unit
selling price minus unit variable costs. It can be
decreased by either lowering the price or raising
the variable costs. As long as UCM is positive, a
given percentage change in selling price must
have a greater effect than an equal but opposite
percentage change in variable cost. The example
below demonstrates this point.
Continued
SU 8.2 – Practice Question 1 Answer
Original:
UCM = SP – UVC
= $100 – $50
= $50
Lower Selling Price:
UCM = (SP × .85) – UVC
= $85 – $50
= $35
Higher Variable Cost:
UCM = SP – (UVC × 1.15)
= $100 – $57.50
= $42.50
Since $35 < $42.50, the lower selling price has
the greater effect.
SU 8.2 – Practice Question 2
The breakeven point in units sold for Tierson Corporation is
44,000. If fixed costs for Tierson are equal to $880,000 annually
and variable costs are $10 per unit, what is the contribution
margin per unit for Tierson Corporation?
A.
$0.05
B.
$20.00
C.
$44.00
D.
$88.00
SU 8.2 – Practice Question 2 Answer
Correct Answer: B
The breakeven point in units is equal to the fixed
costs divided by the contribution margin per
unit. Thus, the UCM is $20.00 ($880,000 ÷
44,000 units).
SU 8.2 – Practice Question 3
A manufacturer contemplates a change in technology that would
reduce fixed costs from $800,000 to $700,000. However, the
ratio of variable costs to sales will increase from 68% to 80%.
What will happen to breakeven level of revenues?
A.
Decrease by $301,470.50.
B.
Decrease by $500,000.
C.
Decrease by $1,812,500.
D.
Increase by $1,000,000.
SU 8.2 – Practice Question 3 Answer
Correct Answer: D
The original breakeven level was:
Breakeven point = Fixed costs ÷ Contribution margin ratio
= $800,000 ÷ (1.0 – .68)
= $2,500,000
Continued
SU 8.2 – Practice Question 3 Answer
The new level is:
Breakeven point = Fixed costs ÷ Contribution margin ratio
= $700,000 ÷ (1.0 – .80)
= $3,500,000
Thus, there is an increase of $1,000,000 ($3,500,000 –
$2,500,000).
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
Computing Sales (Dollars) for a
Target Net Income
To convert target net income to before-tax
income, use the following formula:
Target net income
Before-tax income =
1 - tax rate
SU 8.3 – Practice Question 1
The data below pertain to the forecasts of XYZ Company for the upcoming year.
Total Cost
Sales (40,000 units)
Unit Cost
$1,000,000
$25
Raw materials
160,000
4
Direct labor
280,000
7
80,000
2
Factory overhead:
Variable
Fixed
Selling and general expenses:
360,000
Variable
120,000
Fixed
225,000
3
Continued
SU 8.3 – Practice Question 1
How many units does XYZ Company need to produce and sell to make a before-tax
profit of 10% of sales?
A.
65,000 units.
B.
36,562 units.
C.
90,000 units.
D.
25,000 units.
SU 8.3 – Practice Question 1 Answer
Correct Answer: C
Revenue minus variable and fixed expenses equals net income.
If X equals unit sales, revenue equals $25X, total variable expenses
equal $16X ($4 + $7 + $2 + $3), total fixed expenses equal $585,000
($360,000 + $225,000), and net income equals 10% of revenue. Hence, X
equals 90,000 units.
$25X – $16X – $585,000
=
$25X × 10%
6.5X
=
$585,000
X
=
90,000 units
SU 8.3 – Practice Question 2
The data below pertain to the forecasts of XYZ Company for the upcoming year.
Total Cost
Sales (40,000 units)
Unit Cost
$1,000,000
$25
Raw materials
160,000
4
Direct labor
280,000
7
80,000
2
Factory overhead:
Variable
Fixed
Selling and general expenses:
360,000
Variable
120,000
Fixed
225,000
3
Continued
SU 8.3 – Practice Question 2
Assuming that XYZ Company sells 80,000 units, what is the maximum that can be paid
for an advertising campaign while still breaking even?
A.
$135,000
B.
$1,015,000
C.
$535,000
D.
$695,000
SU 8.3 – Practice Question 2 Answer
Correct Answer: A
The company will break even when net income equals zero. Net income is equal to
revenue minus variable expenses and fixed expenses, including advertising. Thus, if X
equals advertising cost, the equation is
80,000)($25) – (80,000)($16) – $585,000 – X
=
0
$2,000,000 – $1,280,000 – $585,000 – X
=
0
X
=
$135,000
SU 8.3 – Practice Question 3
For one of its divisions, Buona Fortuna Company has fixed costs of $300,000
and a variable-cost percentage equal to 60% of its $10 per unit selling price. It
would like to earn a pre-tax income of $90,000 per year from the division.
How many units will Buona Fortuna have to sell to earn a pre-tax
income of $90,000 per year?
A.
65,000 units.
B.
75,000 units.
C.
77,250 units.
D.
97,500 units.
SU 8.3 – Practice Question 3 Answer
Correct Answer: D
Buona Fortuna’s unit contribution margin is $4 ($10 unit price – $6 unit variable cost).
By treating desired profit as an additional fixed cost, the target unit sales can be
calculated as follows:
Target unit sales = (Fixed costs + Target operating income)
÷ UCM
= ($300,000 + $90,000) ÷ $4
= 97,500
Computing a Multiproduct
Break-Even Point
The CVP formulas can be modified for use
when a company sells more than one product.
– The unit contribution margin is replaced with the
contribution margin for a composite unit.
– A composite unit is composed of specific numbers
of each product in proportion to the product sales
mix.
– Sales mix is the ratio of the volumes of the various
products.
SU – 8.4 CVP Analysis – Multiproduct
Calculations
• Multiple Products (or Services)
S = FC + VC = Calculated Weighted Average Contribution Margin
See example page 318
SU – 8.4 CVP Analysis – Choice of
Product Calculations
• Choice of Product decisions – When resources are
limited companies have to choose which products to
produce
• A breakeven analysis of the point where the same
operating income or loss will result
See example page 318
SU – 8.4 CVP Analysis – Special Order
Calculations
• Special Orders (usually lower price than std.)
– The assumption are that idle capacity is sufficient
to manufacture extra units of a special order.
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 5speeds, 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 5speeds, 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 5speeds, 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 - A market structure in which a
very large number of firms sell a standardized
product into which entry is very easy in which the
individual seller has no control over the product
price and in which there is no nonprice competition;
a market characterized by a very large number of
buyers and sellers.
Examples : Agricultural products such as potatoes and wheat
SU 8.6 Short-run Profit Maximization
•
Monopoly - A market structure in which one firm sells a unique product into which
entry is blocked in which the single firm has considerable control over product
price and in which non-price competition may or may not be found.
Examples / Importance
1. Public utilities: gas, electric, water, cable TV, and local telephone service
companies, are often pure monopolies.
2. First Data Resources (Western Union), Wham-O (Frisbees), and the DeBeers
diamond syndicate are examples of "near" monopolies. (See Last Word.)
3. Manufacturing monopolies are virtually nonexistent in nationwide U.S.
manufacturing industries.
4. Professional sports leagues grant team monopolies to cities.
5. Monopolies may be geographic. A small town may have only one airline, bank,
etc.
SU 8.6 Short-run Profit Maximization
• Monopolistic Competition - A market
structure in which many firms sell a
differentiated product into which entry is
relatively easy in which the firm has some
control over its product price and in which
there is considerable non-price competition.
Examples are grocery stores and gas stations
SU 8.6 Short-run Profit Maximization
• Oligopoly - A market structure in which a few
firms sell either a standardized or
differentiated product into which entry is
difficult in which the firm has limited control
over product price because of mutual
interdependence (except when there is
collusion among firms) and in which there is
typically non-price competition.
SU 8.6 Short-run Profit Maximization
• Law of Demand - Law of demand states that ' all
other things remaining unchanged, people
demand (buy) more of any good / service if the
price of that good / service falls and demand
(buy) less if the price increases. The law of
demand is usually represented by a negativelysloped demand curve which slows that the
quatity demanded (quantity of a particular good
people intending to buy) declines as price rises
and increases as price rises.
SU 8.6 Short-run Profit Maximization
• Elasticity of demand measures how responsive a
products demand is to changes in its price level.
When we have inelastic demand, a consumer will pay
almost any price for the good.
Elastic demand therefore means that demand for the
product will vary when its price changes. Generally
goods which have elastic demand tend to have many
substitutes, so if the price of one good increases too
much I will substitute out towards a similar good which
is cheaper.
SU 8.6 Short-run Profit Maximization
•
Calculating Price elasticity of demand
–
Price elasticity of demand is calculated as the percentage change in quantity demanded divided by
the percentage change in price.
–
There are a number of factors that can determine the price elasticity of demand for a good or
service.
For example, the demand for luxury items tend to be more elastic than the demand for necessities.
For items that are essential, you tend to be less responsive to changes in price. An example of this
would be the demand for diamonds tends to be more price elastic than the demand for electricity.
Price elasticity of demand is also affected how large a percentage of your total income an item is. We
tend to be more elastic in regards to price changes for items that make up a larger percentage of our
incomes. For example, if the price of a pack of gum goes up by 10%, I probably wouldn't even notice.
On the other hand, if the price of a car I'm considering purchasing goes up by 10%, I would definitely
notice and I would probably reconsider the purchase.
A third factor that influences the price elasticity of demand is the time frame allowed for response.
We tend to be more responsive to changes in price in the long run than in the short run. For
example, if the price of gas were to go up overnight to $10/gallon I would still have to put gas in my
car tomorrow morning because I have to go to work and I have to go to school. But if the price of gas
were to stay at $10/gallon for a year, then I have more options. I could move closer to work, start
carpooling, or trade in my car for a hybrid with better gas mileage so that I don't have to buy as much
gas. So in the long run, demand tends to be more elastic than in the short run.
SU 8.6 Short-run Profit Maximization
Price elasticity example
Antoinette has a beauty salon. She services 100
customers per day. Her usual fee is $50. She
wants to expand her business. If she lowers her
price (gives everyone a coupon for $10 off), she
expects to get an extra 10 customers per day.
Calculate the price elasticity of demand. Did she
make the correct decision?
SU 8.6 Short-run Profit Maximization
Price elasticity example
• A) Percentage change in quantity demanded = 10% (100 customers
increased to 110 customers)
B) Percentage change in price = -20% ($50 reduced to $40)
A/B = 10%/-20% = -0.5
The price elasticity of demand for this service is -0.5, and a price elasticity
of demand less than 1 means that a good is inelastic, meaning that
quantity demanded is relatively unresponsive to a change in price.
So you could argue that she made the wrong decision, as the price
decrease did not greatly affect demand. She might have been better
choosing another strategy, such as better advertising or her services.
You could also argue that she is reducing the price by 20% in return for a
10% increase in volume.
SU 8.6 Short-run Profit Maximization
Price elasticity defined
A product with elasticity of 1.2 has elastic demand. What this means is that
for every 1% rise in the price, demand will fall by 1.2% (similarly, a 1% fall in
the price will lead to a 1.2% rise in demand).
The rule is:
Elasticity > 1 : elastic (% change in demand is greater than % change in price e.g. luxury
goods such as cars etc.)
Elasticity < 1 : inelastic (% change in demand is less than % change in price e.g. essential
goods such as food)
Elasticity = 1 : unitary elastic (% change in demand is equal to the % change in price)
Basically a firm producing an inelastic good can increase revenue by raising the price, as the
fall in demand is more than offset by the increased revenue on the remaining demand.
SU 8.6 Short-run Profit Maximization
Price elasticity defined
• Infinite or perfectly elastic - If it were “perfectly” elastic,
demand would be infinite at all prices less than $3. A perfectly
elastic demand graph is a vertical line. And, when the price is
at $3, you can not tell from the graph what the demand is
since the line is vertical. The demand could be at any value.
• Perfectly price inelastic - means that the quantity demanded
will not change when price changes. Vertical demand curve
Also, perfectly price elastic means if price changes, quantity
demanded changes totally, Horizontal Demand Curve