Transcript Cost-Volume-Profit Relationships

Chapter 8
Cost-Volume-Profit
Relationships
Introduction
This chapter examines one of the most
basic planning tools available to
managers: cost-volume-profit analysis.
Cost-volume-profit analysis examines the
behaviour of total revenues, total costs,
and operating profit as changes occur in
the output level, selling price, variable
costs per unit, or fixed costs.
Learning Objectives
1 Distinguish between the general case and a special case
of CVP
2 Explain the relationship between operating profit and net
profit
3 Describe the assumptions underlying CVP
4 Demonstrate three methods for determining the
breakeven point and target operating profit
5 Explain how sensitivity analysis can help managers cope
with uncertainty
6 Illustrate how CVP can assist cost planning
7 Describe the effect of revenue mix on operating profit
Learning Objective 1
Distinguish between the
general case and a special
case of CVP
Learning Objective 1(continued)
General versus special case of CVP
Using a general case of profit planning, we
realise that a business has many cost drivers
and revenue streams that are fundamental to its
profitability
In CVP analysis, we assume a much more
simple model, where there are restrictions on
these setting, as outlined in the following slides:
Learning Objective 2
Explain the relationship
between operating profit
and net profit
Learning Objective 1(continued)
Operating profit = Total revenues – Total
costs
Operating profit = Total revenue – Variable
costs - Fixed costs
Net profit = Operating profit (+/-) Nonoperating revenues/costs (such as
interests) – Income taxes
Learning Objective 3
Describe the assumptions
underlying CVP
Learning Objective 1(continued)
• Cost-Volume-Profit Assumptions and
Terminology
1 Changes in the level of revenues and costs arise only
because of changes in the number of product (or
service) units produced and sold.
2 Total costs can be divided into a fixed component and a
component that is variable with respect to the level of
output.
3 When graphed, the behaviour of total revenues and total
costs is linear (straight-line) in relation to output units
within the relevant range (and time period).
4 The unit selling price, unit variable costs, and fixed costs
are known and constant.
Learning Objective 1(continued)
5 The analysis either covers a single product or
assumes that the sales mix when multiple
products are sold will remain constant as the
level of total units sold changes.
6 All revenues and costs can be added and
compared without taking into account the time
value of money.
Learning Objective 3(continued)
Assumptions of Cost-Volume-Profit (CVP)
Analysis
Assume that the shop Dresses by Mary can
purchase dresses for £32 from a local factory;
other variable costs amount to £10 per dress.
Because she plans to sell these dresses
overseas, the local factory allows Mary to return
all unsold dresses and receive a full £32
refund per dress within one year.
Learning Objective 3(continued)
 Mary can use CVP analysis to examine changes in
operating profit as a result of selling different quantities
of dresses.
 Assume that the average selling price per dress is £70
and total fixed costs amount to £84,000.
 How much revenue will she receive if she sells 2,500
dresses?
 2,500 × £70 = £175,000
 How much variable costs will she incur?
 2,500 × £42 = £105,000
 Would she show an operating profit or an operating
loss?
 An operating loss: £175,000 – 105,000 – 84,000 = (£14,000)
Learning Objective 3(continued)
 The only numbers that change are total
revenues and total variable cost.
 Total revenues – total variable costs
=
Contribution margin
 Contribution margin per unit
= selling price – variable cost per unit
 What is Mary’s contribution margin per unit?
£70 – £42 = £28 contribution margin per unit
 What is the total contribution margin when 2,500
dresses are sold?
2,500 × £28 = £70,000
Learning Objective 3(continued)
 Contribution margin percentage (contribution
margin ratio) is the contribution margin per unit
divided by the selling price.
 What is Mary’s contribution margin percentage?
£28 ÷ £70 = 40%
 If Mary sells 3,000 dresses, revenues will be
£210,000 and contribution margin would equal
40% × £210,000 = £84,000.
Learning Objective 4
Demonstrate three methods
for determining the
breakeven point and target
operating profit
Learning Objective 4(continued)
 Breakeven Point ...
– is the sales level at which operating profit is zero.
 At the breakeven point, sales minus variable expenses equals fixed
expenses.
 Total revenues = Total costs
 Abbreviations
 USP = Unit selling price
 UVC = Unit variable costs
 UCM = Unit contribution margin
 CM% = Contribution margin percentage
 FC = Fixed costs
 Q = Quantity of output (units sold or manufactured)
 OP = Operating profit
 TOP = Target operating profit
 TNP = Target net profit
Learning Objective 4(continued)
Methods for Determining Breakeven Point
Breakeven can be computed by using either the
equation method, the contribution margin
method, or the graph method.
Equation Method
With the equation approach, breakeven sales
in units is calculated as follows:
(Unit sales price × Units sold) – (Variable unit
cost × units sold) – Fixed expenses =
Operating profit
Learning Objective 4(continued)
Using the equation approach, compute the
breakeven for Dresses by Mary.
£70Q – £42Q – £84,000 = 0
£28Q = £84,000
Q = £84,000 ÷ £28
Q = 3,000 units
Learning Objective 4(continued)
Contribution Margin Method
With the contribution margin method,
breakeven is calculated by using the following
relationship:
(USP – UVC) × Q = FC + OP
UCM × Q = FC + OP
Q = (FC + OP) ÷ UCM
£84,000 ÷ £28 = 3,000 units
Using the contribution margin percentage, what
is the breakeven point for Dresses by Mary?
£84,000 ÷ 40% = £210,000
Learning Objective 4(continued)
Graph Method
In this method, we plot a line for total revenues
and total costs.
The breakeven point is the point at which the
total revenue line intersects the total cost line.
The area between the two lines to the right of
the breakeven point is the operating profit area.
Learning Objective 4(continued)
Graph Method (Dresses by Mary)
£ (000)
Revenue
245
Breakeven
Total expenses
231
210
84
3000
3500
Units
Learning Objective 4(continued)
• Target Operating Profit ...
– can be determined by using any of three methods:
1 The equation method
2 The contribution margin method
3 The graph method
Insert the target operating profit in the formula and solve
for target sales either in pounds or units.
(Fixed costs + Target operating profit) divided either by
Contribution margin percentage or Contribution margin
per unit
Learning Objective 4(continued)
Assume that Mary wants to have an
operating profit of £14,000.
How many dresses must she sell?
(£84,000 + £14,000) ÷ £28 = 3,500
What £ sales are needed to achieve this
profit?
(£84,000 + £14,000) ÷ 40% = £245,000
Learning Objective 5
Explain how sensitivity
analysis can help
managers cope with
uncertainty
Learning Objective 5(continued)
Using CVP Analysis
Suppose the management of Dresses by Mary
anticipates selling 3,200 dresses.
Management is considering an advertising
campaign that would cost £10,000.
It is anticipated that the advertising will increase
sales to 4,000 dresses.
Should Mary advertise?
Learning Objective 5(continued)
 3,200 dresses sold with no advertising:
Contribution margin
Fixed costs
Operating profit
£89,600
84,000
£ 5,600
 4,000 dresses sold with advertising:
Contribution margin
Fixed costs
Operating profit
£112,000
94,000
£ 18,000

Mary should advertise.
 Operating profit increases by £12,400.
 The £10,000 increase in fixed costs is offset by
the £22,400 increase in the contribution margin.
Learning Objective 5(continued)
Instead of advertising, management is
considering reducing the selling price to
£61 per dress.
It is anticipated that this will increase sales
to 4,500 dresses.
Should Mary decrease the selling price per
dress to £61?
Learning Objective 5(continued)
3,200 dresses sold with no change in the selling price:
Operating profit
£ 5,600
4,500 dresses sold at a reduced selling price:
Contribution margin: (4,500 × £19) £85,500
Fixed costs
84,000
Operating profit
£ 1,500
 The selling price should not be reduced to £61.
 Operating profit decreases from £5,600 to
£1,500.
Learning Objective 5(continued)
 Sensitivity Analysis and Uncertainty
Sensitivity analysis is a “what if” technique that examines
how a result will change if the original predicted data are
not achieved or if an underlying assumption changes.
 Assume that Dresses by Mary can sell 4,000
dresses.
Fixed costs are £84,000.
Contribution margin ratio is 40%.
At the present time Dresses by Mary cannot handle
more than 3,500 dresses.
To satisfy a demand for 4,000 dresses, management
must acquire additional space for £6,000.
 Should the additional space be acquired?
Learning Objective 5(continued)
 Revenues at breakeven with existing space are
£84,000 ÷ 0.40 = £210,000.
 Revenues at breakeven with additional space are
£90,000 ÷ 0.40 = £225,000.
 Operating profit at £245,000 revenues with existing
space = (£245,000 × 0.40) – £84,000 = £14,000.
 (3,500 dresses × £28) – £84,000 = £14,000
 Operating profit at £280,000 revenues with additional
space = (£280,000 × 0.40) – £90,000 = £22,000.
 (4,000 dresses × £28 contribution margin) – £90,000 =
£22,000
Learning Objective 6
Illustrate how CVP can
assist cost planning
Learning Objective 6(continued)
Alternative Fixed/Variable
Cost Structures
Suppose that the factory Dresses by Mary uses
to obtain the merchandise offers Mary the
following:
Decrease the price they charge Mary from £32
to £25 and charge an annual administrative fee
of £30,000.
What is the new contribution margin?
Learning Objective 6(continued)
£70 – (£25 + £10) = £35
Contribution margin increases from £28 to
£35.
What is the contribution margin
percentage?
£35 ÷ £70 = 50%
What are the new fixed costs?
£84,000 + £30,000 = £114,000
Learning Objective 6(continued)
 Management questions what sales volume would yield
an identical operating profit regardless of the
arrangement.
 28X – 84,000 = 35X – 114,000
 114,000 – 84,000 = 35X – 28X
 7X = 30,000
 X = 4,286 dresses
 Cost with existing arrangement = Cost with new
arrangement
 .60X + 84,000 = 0.50X + 114,000
 0.10X = £30,000
 X = £300,000
 (£300,000 × 0.40) – £ 84,000 = £36,000
 (£300,000 × 0.50) – £114,000 = £36,000
Learning Objective 6(continued)
 Operating Leverage ...
– measures the relationship between a company’s variable
and fixed expenses.
 It is greatest in organisations that have high fixed
expenses and low per unit variable expenses.
 The degree of operating leverage shows how a
percentage change in sales volume affects profit.
Degree of operating leverage = Contribution margin ÷
Operating profit
 What is the degree of operating leverage of
Dresses by Mary at the 3,500 sales level under
both arrangements?
Learning Objective 6(continued)
Existing arrangement:
3,500 × £28 = £98,000 contribution margin
£98,000 contribution margin – £84,000 fixed
costs = £14,000 operating profit
£98,000 ÷ £14,000 = 7.0
New arrangement:
3,500 × £35 = £122,500 contribution margin
£122,500 contribution margin – £114,000 fixed
costs = £8,500
£122,500 ÷ £8,500 = 14.4
Learning Objective 7
Describe the effect of
revenue mix on operating
profit
Learning Objective 7(continued)
Effects of Revenue Mix on Profit
Revenue mix (or Sales mix) is the combination
of product that a business sells.
Assume that Dresses by Mary is
considering selling blouses.
This will not require any additional fixed costs.
It expects to sell 2 blouses at £20 each for
every dress it sells.
The variable cost per blouse is £9.
What is the new breakeven point?
Learning Objective 7(continued)
The contribution margin per dress is £28 (£70 selling
price – £42 variable cost).
The contribution margin per blouse is
£20 – £9 = £11.
The contribution margin of the mix is
£28 + (2 × £11) = £28 + £22 = £50.
£84,000 fixed costs ÷ £50 = 1,680 packages
1,680 × 2 = 3,360 blouses
1,680 × 1 = 1,680 dresses
Total units = 5,040
 What is the breakeven in £?
Learning Objective 7(continued)
1,680 × 2 = 3,360 blouses × £20 = £ 67,200
1,680 × 1 = 1,680 dresses × £70 = 117,600
£184,800
 What is the weighted average budgeted
contribution margin?
Dresses
Blouses
1 × £28 + 2 × £11 = £50 ÷ 3 = £16.667
Breakeven point for the two products is: £84,000 ÷
£16.667 = 5,040 units
5,040 × 1/3 = 1,680 dresses
5,040 × 2/3 = 3,360 blouses
Learning Objective 7(continued)
Revenue mix can be stated in sales £:
Dresses
Sales price
£70
Variable costs
42
Contribution margin
£28
Contribution margin ratio
40%
Blouses
£40
18
£22
55%
 Assume the revenue mix in £ is 63.6% dresses
and 36.4% blouses.
Weighted contribution would be:
40% × 63.6% = 25.44% dresses
55% × 36.4% = 20.02% blouses
45.46%
Learning Objective 7(continued)
Breakeven sales £ is £84,000 ÷ 45.46% =
£184,778 (rounding).
£184,778 × 63.6% = £117,519 dress sales
£184,778 × 36.4% = £67,259 blouse sales
Learning Objective 7(continued)
CVP Analysis in Service and Non-profit
Organisations
CVP can also be applied to decisions by
manufacturing, service, and non-profit
organisations.
The key to applying CVP analysis in service
and non-profit organisations is measuring their
output.