CVP Analysis

COST-VOLUME-PROFIT ANALYSIS

CHAPTER 3

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GROUP 3 :

Ecleo, D., Ongy E., and A. Tulin

COST-VOLUME-PROFIT ANALYSISCHAPTER 3

Learning Objectives:1. Understand basic cost-volume-profit (CVP) assumptions

2. Explain essential features of CVP analysis

3. Determine the break-even point and output to achieve target operating income

4. Incorporate income tax considerations into CVP analysis

5. Explain the use of CVP analysis in decision making and how sensitivity analysis can help managers cope with uncertainty

6. Use CVP analysis to plan costs

7. Apply CVP analysis to a multiproduct company

8. Adapt CVP analysis to multi cost drivers situations

9. Distinguish between contribution margin and gross margin

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Objective 1

Cost-Volume-Profit Assumptions and Terminology

1. Changes in the level of revenues and costs arise only bec. 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 behavior of total revenues and total costs is linear in relation to output units within the relevant range (and time period).

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Objective 1

4. The unit selling price, unit variable costs, and fixed costs are known and constant.

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 and value of money.

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Objective 1

Operating income = Total revenues – Cost of goods sold andfrom operations and operating costs

(excluding income taxes)

NET INCOME = Operating income – Income taxes

NET INCOME = operating income + nonoperating revenues (such as interest revenue) – nonoperating costs – income taxes

Back to learning objectivesCos

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Objective 2

Essentials of Cost-Volume-Profit Analysis

EXAMPLE:

Mary Frost plans to sell Do-All Software, a home office software package, at a heavily attended two-day computer convention in Chicago. Mary can purchase this software from a computer software wholesaler at $120 per package with the privilege of returning all unsold units and receiving a full $120 refund per package. The units (packages) will be sold at $200 each. She has already paid $2,000 to Computer Conventions, Inc., for the booth rental for the two-day convention. Assume there are no other costs. What profits will Mary make for different quantities of units sold?

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Objective 2

ANALYSIS:

Fixed costs = $2,000 -----booth rental

Variable costs = $120 -----cost of the package

Unit selling price = $200

Mary can use CVP analysis to examine changes in operating income as a result of selling different quantities of software packages.

The only numbers that change in selling different quantities of packages are: (1) total revenues and (2) total variable costs.


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The difference between total revenues and total variable costs is contribution margin. OR

Contribution margin = contribution margin per unit X number of packages sold

Objective 2

The difference between the selling price and the variable cost per unit is the contribution margin per unit.

Contribution margin per unit divided by the selling price is what we call the contribution margin percentage.


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Objective 2

Back to learning objectives

Number of Packages Sold

0 1 5 25 40

Revenues at $200 per package $0 $200 $1,000

$5,000 $8,000

Variable costs at $120 per package 0 120 600 3,000 4,800

Contribution margin at $80 per package 0 80 400 2,000 3,200

Fixed costs 2,000 2,000 2,000 2,000 2,000

Operating income $(2,000)

$(1,920)

$(1,600) $0 $1,200

Contribution Income Statement for Different Quantities for Do-All Software Packages Sold

Spreadsheets computation


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Objective 3

The Break-Even Point

The break-even point is that quantity of output where total revenues equals total costs – that is, where the operating income is zero.

Why would managers be interested in the break-even point?


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Objective 3

Abbreviations used in the subsequent analysis:

USP = Unit selling price

UVC = Unit variable costs

UCM = Unit contribution margin (USP-UVC)

CM% = Contribution margin percentage (UCM/USP)

FC = Fixed costs

Q = Quantity of output units sold (and manufactured)

OI = Operating Income

TOI = Target operating income

TNI = Target net income


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Objective 3

Three methods for determining breakeven point

1. Equation method:

Revenues – Variable costs – Fixed Costs = Operating Income

(USP*Q) – (UVC*Q) – FC = OI

$200Q - $120Q -$2000 = $0

$80Q = $2000

Q = $2000/$80

Q = 25 units

Provides the most general and easy-to-remember approach to any CVP situation.


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Objective 3

2. Contribution margin method:

It uses the concept of contribution margin to rework the equation method.

By rewriting,

(USP – UVC) * Q = FC + OI

UCM*Q = FC + OI

Q = (FC +OI)/UCM

(USP*Q) – (UVC*Q) – FC = OI

At break-even, OI=0, therefore:

Q = FC /UCM

Break-even no. of units = Fixed costs/Unit contribution margin


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Objective 3

Break-even no. of units = $2000/$80 per unit = 25 units

Substituting,

Break-even no. of units = Fixed costs/Unit contribution margin

Break-even in revenue dollars = Break-even no. of units X USP

Calculating break-even revenues,

= (FC*USP)/UCM

= FC/(UCM/USP)

= FC/CM%Since, CM% = UCM/USP

= $80/$200 = 40% = $2000/40%

Break-even in revenue dollars = $5000

$0.00

$2,000.00

$4,000.00

$6,000.00

$8,000.00

$10,000.00

$12,000.00

$14,000.00

0 5 10 15 20 25 30 35 40 45 50 55 60

Units Sold

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Objective 3

3. Graph method:


Break-even point

Operating Income area

Operating Loss area

Cost-Volume-Profit Graph for Do-All Software

-$3,000.00

-$2,000.00

-$1,000.00

$0.00

$1,000.00

$2,000.00

$3,000.00

$4,000.00

0 5 10 15 20 25 30 35 40 45 50 55 60

Units Sold

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Objective 3

Target Operating Income


Profit-Volume Graph for Do-All Software

Break-even point

Operating Income area

Operating Loss area



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Objective 4

Target Net Income and Income Taxes


Target net income = (Target operating income) – (Target operating income X Tax rate)

Target net income = (Target operating income) (1- Tax rate)

Target operating income = Target net income / (1 – Tax rate)

Substituting, (at tax rate of 40%)

Revenues – Variable costs – Fixed Costs = Target net income / (1 – Tax rate)

$200Q - $120Q -$2000 = $1200/(1-0.40)

$200Q - $120Q -$2000 = $2000

Q = $4000/$80

Q = 25 units


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Objective 5

Using CVP for Making Decisions

Decision to Advertise

Scenario:

Consider again the Do-All Software example. Suppose Mary anticipates selling 40 packages. At this sales level, Mary’s operating income would be $1200. Mary is considering placing an advertisement describing the product and its features in the convention brochure. The advertisement will cost $500. This cost will be fixed because it will stay the same regardless of the number of units Mary sells. She anticipates that advertising will increase sales to 45 packages. Should Mary advertise?


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Objective 5

Cost-Volume-Profit Analysis

40 Packages Sold with No Advertising

45 Packages Sold with

Advertising Difference

(1) (2) (3) = (2)-(1)

Contribution margin ($80 X 40; $80 X 45) $3,200 $3,600 $400

Fixed costs 2,000 2,500 500

Operating income $1,200 $1,100 $ (100)

Operating income decreases by $100, so Mary should not advertise.


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Objective 5

Decision to Reduce Selling Price

Scenario:

Having decided not to advertise, Mary is contemplating whether to reduce the selling price of Do-All Software to $175. At this price she thinks sales will be 50 units. At this quantity, the software wholesaler who supplies Do-All Software will sell the packages to Mary for $115 per package instead of $120. Should Mary reduce the selling price?


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Objective 5

Cost-Volume-Profit Analysis

Contribution margin from lowering price to $175, ($175-$115)*50 units $3,000

Contribution margin from maintaining price to $200, ($200-$120)*40 units $3,200

Increase (Decrease) in contribution margin from lowering price $(200)

Because the fixed costs of $2000 do not change, decreasing the price will lead to $200 lower contribution margin and a $200 lower operating income


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Objective 5

Sensitivity Analysis and Uncertainty

Sensitivity analysis is a “what if” technique that managers use to examine how a result will change if the original predicted data are not achieved or if an underlying assumption changes.

In the context of CVP analysis, sensitivity analysis answers such questions as, What will operating income be if units sold decreases by 5% from the original prediction? And will operating income be if variable costs per unit increase by 10%?

The widespread use of electronic spreadsheets enables managers to conduct CVP-based sensitivity analyses in a systematic and efficient way.


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Objective 5

Revenues Required at $200 Selling Price to

Earn Operating Income of

Fixed Costs

Variable Costs per

Unit $0 $1,000 $1,500 $2,000

$2,000.00 $100 $4,000 $6,000 $7,000 $8,000

120 5,000 7,500 8,750 10,000

140 6,667 10,000 11,667 13,333

2500 100 5,000 7,000 8,000 9,000

120 6,250 8,750 10,000 11,250

140 8,333 11,667 13,333 15,000

3000 100 6,000 8,000 9,000 10,000

120 7,500 10,000 11,250 12,500

140 10,000 13,333 15,000 16,667

Spreadsheet Analysis of CVP Relationships for Do-All Software



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Objective 5

An aspect of sensitivity analysis is margin of safety, which is the amount of budgeted revenues over and above breakeven revenues.

If expressed in units, margin of safety is the sales quantity minus the breakeven quantity.

The margin of safety answers the “what if “ question: If budgeted revenues are above breakeven and drop, how far can they fall below budget before the breakeven point is reached?


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Objective 5

40 units: budgeted revenues = $8000 ($200*40 units)

Breakeven (25 units): revenues = $5000 ($200*25 units)

Using the given data, for 40 units sold, the margin of safety is $3000 revenues or 15 units if expressed in units

Therefore, margin of safety will be,

$3000 ($8000-$5000) (in terms of revenues)

15 units (40 units – 25 units) (in terms of units)



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Objective 6

Cost Planning and CVP

Alternative Fixed-Cost/Variable-Cost Structures

CVP-based analysis highlights the risks and returns that an existing cost structure holds for a organization. This insight may lead managers to consider alternative cost structures. CVP analysis can help managers evaluate various alternatives.


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Objective 6

Scenario:

Consider again our Do-All Software example. Our original example has Mary paying a $2000 booth rental fee. Suppose, however, Computer Conventions offers Mary three rental alternatives:

Option 1: $2000 fixed fee

Option 2: $800 fixed fee plus 15% of convention revenues

Option 3: 25% of convention revenues with no fixed fee

Mary anticipates selling 40 packages. She is interested in how her choice of a rental agreement will affect the income she earns and the risks she faces.

-$3,000.00

-$2,000.00

-$1,000.00

$0.00

$1,000.00

$2,000.00

$3,000.00

$4,000.00

$5,000.00

$6,000.00

$7,000.00

0 10 20 30 40 50 60 70 80 90 100

Units Sold

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)

Option 1

Option 2

Option 3

Profit-Volume Graph for Alternative Rental Options for Do-All Software

Breakeven point

Breakeven point = 16

Breakeven point = 25


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Objective 6



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Objective 6

If Mary sells 40 packages, each option results in operating income of $1200.

However, if the sales of Mary vary from 40 units, CVP analysis highlights the different risks and returns associated with each option.

margin of safety:

option 1: revenues @ 40 units – revenues @ 25 units = $8000-$5000 = $3000

option 2: revenues @ 40 units – revenues @ 16 units = $8000-$3200 = $4800

option 3: revenues @ 40 units – revenues @ 0 unit = $8000-$0 = $8000


…the downside risk of option 1 comes from its higher fixed cost and hence higher breakeven point and lower margin of safety.


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Objective 6

If the units sold drops to 20, what would be the operating income under each option?

…..Option 1 leads to an operating loss of $400 but options 2 and 3 will continue to produce operating income

However, the higher risk in option 1 must be evaluated against its potential benefits



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Objective 6

Option 1 has the highest UCM because of its low VC. Once FC are recovered at sales of 25 units, each additional unit adds $80 of CM and OI per unit.

At sales 60 units:

Option 1 shows an OI of $2800, greater than the OI under options 2 and 3.

By moving from option 1 to 3, Mary faces less risk when demand is low both because of lower fixed costs and because she losses less CM per unit.



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Objective 6

Operating leverage describes the effects that FC have on changes in OI as changes occur in units sold and hence in CM.

• High FC has high operating leverage

• High operating leverage means small changes in sales will lead to large changes in OI.

sales, OI increases relatively more

sales, OI decline relatively more, leading to a greater risk in losses

Degree of operating leverage equals contribution margin divided by the operating income. ( = CM/OI)

Risk-return trade off measure


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Objective 6

Degree of operating leverage at sales 40 units

Option 1 Option 2 Option 3

Contribution margin per unit $80 $50 $30

Contribution margin (CM) $3,200 $2,000 $1,200

Operating income (OI) $1,200 $1,200 $1,200

Degree of operating leverage(CM/OI) 2.67 1.67 1.00

A sales increase in 50%

From 40 units to 60 units , CM will increase by 50%, then OI increase will be 50% times the degree of operating leverage.

OI increase would then be,

Option 1: 2.67*50% = 133.5% (from $1200 to $2800)

Option 2: 1.67*50% = 83.5% (from $1200 to $2200)

Option 3: 1.00*50% = 50% (from $1200 to $1800)


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Objective 6

Effect of Time Horizon

A critical assumption of CVP analysis is that costs can be classified either variable or fixed.

….This classification is affected by the time period being considered for a decision.

….The shorter the time horizon, the higher the percentage of total costs we may view as fixed.

Example


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Objective 6


Scenario 1:

Suppose a United Airlines plane will depart from its gate in 60 minutes and there are 20 empty seats. A potential passenger arrives bearing a transferable ticket from a competing airline. What are the variable costs to United of placing one more passenger in an otherwise empty seat?

….Variable costs (such as one meal) would be negligible. Virtually, all the costs in this decision situation are fixed.

Scenario 2:

Suppose a United Airlines must decide whether to include another city in its routes.

.....This decision may have a one-year planning horizon. Many more costs would be regarded as variable and fewer as fixed in this decision.


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Objective 7

Effects of Sales Mix on Income

Sales Mix is the relative combination of quantities of products (or services) that constitutes total unit sales.

If the mix changes, the overall unit sales target may still be achieved. However, the effect on operating income depends on how the original proportions of lower or higher contribution margin products have shifted.


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Objective 7

Influencing Cost Structures to Manage the Risk-Return Tradeoff

Building up too many fixed costs can be hazardous to a company’s health. Because fixed costs, unlike variable costs, do not automatically decrease as volumes decline, companies with too many fixed costs can lose a considerable amount of money during lean months.

Manager’s decision influence the mix of fixed and variable costs in a company’s cost structure. In making these decisions, managers use forecasts of the effect on net income at different volume levels to evaluate the risk-return tradeoffs involved in various cost structures.


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Objective 7

Example:

Xerox sells copier machines at lower margins along with maintenance and supplies (for example, paper and toner) contracts a higher margin.

Similarly, Gillette sells razors at low margins and counts on high margins from selling blades. Cellular phone service companies, also, “give away” the cellular phone instrument itself in exchange for higher revenues from using the network.


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Objective 7

Suppose Mary is now budgeting for the next convention. She plans to sell two software products – Do-All and Superword – and budgets the following:

Do-All Superword Total

Units Sold 60 40 100

Revenues, $200 & $100 per unit $ 12,000 $ 4,000 $ 16,000

Variable costs, $120 & $70 per unit 7,200 2,800 10,000

Unit contribution margin (UCM), $80 and $30 $ 4,800 $ 1,200 6,000

Fixed costs4,500

Operating income$ 1,500


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Objective 7

What is the breakeven point?

One possible assumption is that the budgeted sales mix (3 units Do-All sold for every 2 units of Superword sold) will not change at different levels of total unit sales.

Let 3Ss = number of units of Do-All to breakevenThen 2S = number of units of Superword to breakeven

Revenues – Variable costs – Fixed costs = Operating income[$200(3S) + $100(2S)] – [$120(3S) + $70(2S)] - $4,500 =0

$300s = $4,500S = 15

No. of units of Do-All to breakeven = 3 x 15 = 45 unitsNo. of units of Superword to breakeven = 2 x 15 = 30 units


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Objective 7

The breakeven point is 75 units when the sales mix is 45 units of Do-All and 30 units of Superword, which maintains the ratio of 3 units of Do-All for 2 units of Superword.

At this mix, the total contribution margin of $4,500 (Do-All $80 x 45 units = $3,000 + Superword $30 x 30 = $900) equals the fixed costs of $4,500.

Units Sold

Revenues, $200 & $100 per unit

Variable costs, $120 & $70 per unit

Unit contribution margin (UCM), $80 and $30

Fixed costs

Operating income


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Objective 7

We can also calculate the breakeven point in revenues for the multiple product situation using the weighted-average contribution margin percentage.

Weighted-average contribution margin percentage

Total contribution margin

Total revenues=

=$6,000

$16,000= 0.375 or 37.5%


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Objective 7

Total revenues required to break even

Fixed costs

Weighted-average contribution margin percentage

=

=$4,500

0.375= $12,000


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Objective 7

The $16,000 of revenues are in the ratio of 3:1 ($12,000 : $4,000) or 75% :25%. Hence the breakeven revenues of $12,000 should be apportioned in the ratio of 75% ; 25%. This amounts to breakeven revenue dollars of $9,000 (75% x $12,000) of Do-All and $3,000 (25% x $12,000) of Superword. At a selling price of $200 for Do-All and $100 for Superword, this equals 45 units ($9,000 / $200) of Do-All and 30 units ($3,000 / $100) of Superword.

Units Sold

Revenues, $200 & $100 per unit

Variable costs, $120 & $70 per unit

Unit contribution margin (UCM), $80 and $30

Fixed costs

Operating income


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Objective 7

CVP Analysis in Service and Non-Profit Organizations

CVP can also be applied readily to decisions by manufacturing , service, and nonprofit organizations . The key to applying CVP analysis in service and nonprofit organizations is measuring their output. Examples of output measures in various service and nonprofit industries follow.

Industry Measure of Output

Airlines Passenger-miles

Hotels/motels Room-nights occupied

Hospitals Patient-days

Universities Student-credit hours


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Objective 7

Consider a social welfare agency of the government with a budget appropriation (revenue) for year 2000 of $900,000. This nonprofit agency’s major purpose is to assist handicapped people who are seeking employment. On average, the agency supplements each person’s income by $5,000 annually. The agency’s fixed costs are $270,000. It has no other costs. The agency manager wants to know how many people could be assisted in 2000. We can use CVP analysis here by setting operating income to zero. Let Q be the number handicapped people to be assisted:


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Objective 7

Revenues – Variable costs – Fixed costs = $0$900,000 - $5,000Q - $270,000 = $0

$5,000Q = $900,000 - $270,000$5,000Q = $630,000

Q = $630,000 / $5,000 per personQ = 126 people


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Objective 7

Suppose the manager is concerned that the total budget appropriation for 2001 will be reduced by 15% to a new amount of $900,000 x (1 – 0.15) = $765,000. The manager wants to know how many handicapped people could now be assisted. Assume the same amount of monetary assistance per person.

Revenues – Variable costs – Fixed costs = $0$765,000 - $5,000Q - $270,000 = $0

$5,000Q = $765,000 - $270,000$5,000Q = $495,000

Q = $495,000 / $5,000 per personQ = 99 people


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Objective 7

Note the following two characteristics of the CVP relationships in this nonprofit situation:

1. The percentage drop in service, (126 – 99) / 126, or 21.4%, is more than the 15% reduction in the budget appropriation. Why? Because the existence of $270,000 in fixed costs means that the percentage drop in service exceeds the percentage drop in budget appropriation.

2. If the relationships were graphed, the budget appropriation amount would be a straight horizontal line of $765,000. The manager could adjust operations to stay within this reduced appropriations in one or more three basic ways: (a) Reduce the no. of people assisted, (b) reduce the variable costs (the assistance per person), or (c) reduce the total fixed costs.



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Objective 8

Multiple Cost Drivers

From the previous topics we have assumed that the number of output units is the only revenue and cost driver. In this section we relax this important assumption and describe how some aspects of CVP analysis can be adapted to the more general case of multiple cost drivers.


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Objective 8

Let us consider again the single product Do-All Software example. Suppose that Mary Will incur a variable cost of $10 for preparing documents and invoices associated with the sale of Do-All Software. These documents and invoices will need to be prepared for each customer that buys Do-All Software. That is, the cost driver of document-and-invoice-preparation costs is the number of different customers that buy Do-All Software. Mary’s operating income can then be expressed as:

Operating Income

= Revenues - (Costs of each Do-All Software package

X Number of packages sold)

- (Cost of preparing each document and invoice

X Number of documents and invoices)

- Fixed costs


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Objective 8

Assuming that Mary sells 40 packages to 15 customers, then :

Operating = ($200x40) – ($120x40) – ($10x15) - $2,000income

= $8,000 - $4,800 - $150 - $2,000= $1,050

If instead Mary sells 40 packages to 40 customers, then:

Operating = ($200x40) – ($120x40) – ($10x40) - $2,000income

= $8,000 - $4,800 - $400 - $2,000= $800


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Objective 8

Note that the number of packages sold is not the only determinant of Mary’s operating income. For a given number of packages sold, Mary’s operating income will be lower if Mary sells Do-All Software to more customers. Mary’s cost structure depends on two cost drivers – the number of packages sold and the number of customers.

There is no unique breakeven point when there are multiple cost drivers, just as in the case of multiple products.



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Objective 9

Contribution Margin Versus Gross Margin

Gross Margin = Revenues – Cost of goods sold

Contribution margin = Revenues – All variable costs


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Objective 9

Merchandising Sector

Contribution margin is computed by deducting all variable costs from revenues, whereas gross margin is computed by deducting only cost of goods sold from revenues.

Contribution Income StatementEmphasizing Contribution Margin

Revenues $ 1,000Variable manufacturing costs $ 120Variable non-manufacturing costs 43 163

Contribution margin 37Fixed manufacturing costsFixed non-manufacturing costs 19Operating income $ 18


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Objective 9

Merchandising Sector

Contribution margin is computed by deducting all variable costs from revenues, whereas gross margin is computed by deducting only cost of goods sold from revenues.

Financial Accounting Income StatementEmphasizing Gross Margin

Revenues $ 1,000Cost of goods sold 120Gross margin 80

Operating costs ($43 + $19) 62Operating income $ 18


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Objective 9

Manufacturing Sector

The two areas of difference between contribution margin and gross margin for companies in the manufacturing sector are fixed manufacturing costs and variable non-manufacturing costs.

Contribution Income StatementEmphasizing Contribution Margin

Revenues $ 1,000Variable manufacturing costs $ 250Variable non-manufacturing costs 270 520

Contribution margin 480Fixed manufacturing costs 160Fixed non-manufacturing costs 138 298Operating income $ 182


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Objective 9

Manufacturing Sector

The two areas of difference between contribution margin and gross margin for companies in the manufacturing sector are fixed manufacturing costs and variable non-manufacturing costs.

Financial Accounting Income StatementEmphasizing Gross Margin

Revenues $ 1,000Cost of goods sold ($250 + $160) 410Gross margin 590 Non-manufacturing costs ($270 + $138) 408Operating income $ 182


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Objective 9

Fixed manufacturing costs are not deducted from revenues when computing contribution margin but are deducted when computing gross margin. Cost of goods sold in manufacturing company includes all manufacturing costs. Variable non-manufacturing costs are deducted from revenues when computing contribution margin but are not deducted when computing gross margin.


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Documents

CVP Analysis