11

Chapter 2Introduction to Cost

Behaviorand Cost-Volume

Relationship

22

Objective 1

Explain how cost drivers affect cost behavior

33

are factors or activities that are factors or activities that

have a direct cause-effect relationship to have a direct cause-effect relationship to

a cost. For example, production volume a cost. For example, production volume

has a direct effect on the total cost of has a direct effect on the total cost of

raw material used and can be said to raw material used and can be said to

"drive" that cost. In addition, volume "drive" that cost. In addition, volume

could be used as a valid "driver" of raw could be used as a valid "driver" of raw

material cost.material cost.

Cost DriversCost Drivers

44

In most situations, the cause-effect relationship is less clear, since costs are commonly caused by multiple factors. For example, quality control costs are affected by a variety of factors, such as production volume, quality of material used, skill level of workers, and level of automation. Any of these factors could be chosen as a cost driver if a reasonable amount of confidence exists as to the factor's ability to correlate with cost changes.

A major task in specifying cost behavior is to identify the cost drivers-that is to determine the activities that cause costs to be incurred.

55

This chapter focuses on volume-related cost drivers. Volume-related cost drivers include: The number of orders processed,Production volume in a production

department, The hours of labor worked in an

assembly department, Sales in a retail business.

Of course, when only one product is being produced the units of production is the most obvious volume related cost driver for production-related costs.

66

Objective 2

Show how changes in cost- driver activity levels affect

variable and fixed costs

77

Costs are classified as variable or fixed depending on how much they change as the level of a particular cost driver changes.

A variable cost is a cost that changes in direct proportion to changes in the cost driver.

A fixed cost is not immediately affected by changes in the cost driver.

Variable costs vary in direct proportion to the volume of activity, that is doubling the level of activity will double the total variable costs. Consequently, total variable cost is constant. Figure 2.1 illustrates a variable cost where the variable cost per unit of activity is L.E. 10

Comparison of variable and fixed costs

88

Figure 2-1 Variable CostsA : Total Variable

CostB : Unit Variable Cost

5000 ------------------------------

4000 3000 -------------------

--------

100 200 300 400 500

Activity level (Units of output)

Total

Variable

Cost

20001000

L.E

10

Activity level(Units of output)

100 200 300 400 500

Unit

Variable

Cost

99

Examples of variable manufacturing costs include direct labor, direct material and power. These costs are assumed to fluctuate directly in proportion to operating activity within a certain range of activity.

Examples of non-manufacturing variable costs include sales commissions, which fluctuate with sales value.

Suppose for example, a firm pays its sales persons a sales commission. As sales value increases, the commission paid will increase proportionally. If a firm pays a commission of 10 % of sales value. The total commission paid will be as follows:

1010

Month Sales value(L.E)

Commission paid

(L.E)111000001000001000010000221200001200001200012000331500001500001500015000Note that variable cost (commission

paid) varies proportionally with the level of activity (as expressed in sales value) where as the unit variable cost remains unchanged at 10 PT. per L.E. 1 of sales.

Fixed costs remain constant over wide ranges of activity for a specified time period. Examples of fixed costs include supervisors salaries, straight-line depreciation, and insurance. Figure 2-2 illustrates fixed cost .

1111

You will see that the total fixed costs are constant for all levels of activity (within relevant range), whereas unit fixed costs decrease proportionally with the level of activity. for example, if the total of the fixed costs L.E. 5000 for a month , the fixed costs per unit will be as follows:

Units produced Fixed cost per unit (L.E)

15000

10500

10050

10005

1212

Figure 2-2 Fixed Costs

A : Total Fixed Costs B : Unit Fixed Costs

100 200 300 400 500

Activity level

Total

Fixed

Cost

(L.E)

Activity level

100 200 300 400 500

Unit

Fixed

Cost

(L.E)

1313

Note carefully from these examples that the “variable” or “fixed” characteristic of a cost relates to its total amount and not to its per unit amount. The following table summarizes these relationships.

If cost – driver activity level increases (or decreases)

Type of cost Total cost cost per unit Fixed costsFixed costs No changeNo change decreasedecrease

((or increaseor increase))

Variable costsVariable costs IncreasesIncreases

((or decreaseor decrease ) )

No changeNo change

1414

When predicting costs, two rules of thumb are useful:

1.1. Think of fixed costs as a total. Total Think of fixed costs as a total. Total fixed costs remain unchanged fixed costs remain unchanged regardless of changes in cost-driver regardless of changes in cost-driver activity.activity.

2.2. Think of variable costs on a per-unit Think of variable costs on a per-unit basis. The per-unit variable cost basis. The per-unit variable cost remains unchanged regardless of remains unchanged regardless of changes in cost-driver activity.changes in cost-driver activity.

1515

is a range of activity over which a is a range of activity over which a

variable cost per unit remains constant or a variable cost per unit remains constant or a

fixed cost remains fixed in total. fixed cost remains fixed in total.

In other words, a relevant range is a range In other words, a relevant range is a range

of activity in which costs behave in accordance of activity in which costs behave in accordance

with the way they have been define. with the way they have been define.

The relevant range is generally the normal The relevant range is generally the normal

operating range for a company. In addition operating range for a company. In addition

remember that even within the relevant range a remember that even within the relevant range a

fixed cost remains fixed only over a given period fixed cost remains fixed only over a given period

of time-usually the budget period.of time-usually the budget period.

Relevant Range

1616

Cost – volume-profit Analysis

Cost-volume-profit (CVP) analysis means the study of the effects of output volume on revenue (sales), expenses (costs), and net income (net profit)

The study of cost-volume-profit relationship is often called break-even analysis, This term is misleading, because finding the break-even point is often just the first step in a planning decision.

To apply CVP analysis, the major simplification-in this chapter- is to classify costs as either variable or fixed with respect to a single measure of the volume of output activity.

1717

Objective 3

Calculate break-even sales volume in total pounds and

total units

1818

Break-Even Point – Contribution Margin and Equation Techniques.

is the level of sales is the level of sales

at which revenue equal expenses and at which revenue equal expenses and

net income is zero.net income is zero.

Break-even point

Contribution-Margin Technique

Contribution margin or marginal income is the Contribution margin or marginal income is the

sales price minus the variable production, sales price minus the variable production,

selling and administrative costs per unit.selling and administrative costs per unit.

1919

marginon contributiUnit

costs FixedBreak-even point (units)Break-even point (units) = =

Break-even point (L.E) = Break-even point (L.E) =

Break-even point (units) X sales Break-even point (units) X sales priceprice

Note:Note:

Contribution margin per unit is constant

because revenue and variable cost have

been defined as remaining constant per

unit.

2020

Contribution-margin percentage (or

ratio) =

Contribution margin per unit

Sales price per unit

Variable-cost percentage (or ratio)=

Variable cost per unit

Sales price per unit

Note:Note:

Contribution-margin percentage Contribution-margin percentage ++

variable-costvariable-cost percentage percentage == 100 % 100 %

2121

Break-even point (L.E)Break-even point (L.E) =

ratio)(or percentagemargin on Contributi

costs Fixed

Using the contribution-margin percentage, you can compute the break-even volume in pounds (L.E.) without determining the break-even point in units.

Data needed to compute break- even point and perform CVP analysis are given in the income statement in Exhibit 2-3 for XYZ company.

Example:Example:

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Exhibit 2-3 XYZ Company

Income StatementFor the Year Ended Dec,31,1997

TotalL.E

Per Unit L.E

Percent

Sales (12000 units)

1,200,001,200,0000

100100100 %100 %

Variable costs: Production

360,00

0303030%30%

Selling 120,000

101010%10%

Total variable cost

480,000480,000404040%40%

Contribution margin

720,000720,000606060%60%

Fixed costs: Production250,00

0 Selling administrative

50,000

Total fixed costs 300,000300,000

Net income 420,000420,000

2323

Break-even point & contribution margin

technique

Contribution margin per unit = L.E. 100 – L.E 40

= L.E. 60

Break-even point (pounds) =

5000(units) X L.E 100 (selling price)

= L.E. 500,000

OrOr

= L.E. 300000 Fixed costs / 60% Contribution margin percent = L.E. 500,000

Contribution margin percentage = 60%

Break-even point (units) = L.E 300000

L.E 60

= 5000 units

2424

The income statement at the break-even point is

TotalL.E

Per Unit L.E

Percent

Sales (5000 Sales (5000 units)units)

500,000500,000100100100 %100 %

Variable costs:Variable costs: Production Production

150,00150,00

00303030%30%

Selling Selling 50,00050,000101010%10%Total variable Total variable cost cost

200,000200,000404040%40%

Contribution margin Contribution margin 300,000300,000606060%60%Fixed costs:Fixed costs: ProductionProduction250,00250,00

00 Selling Selling administrativeadministrative

50,00050,000

Total fixed costs Total fixed costs 300,000300,000

Net income Net income 00

2525

Equation Technique

Any income statement can be expressed in equation form, as follows :

Sales – Variable expenses – Fixed expenses = net income

That is, (Unit sales Price X number of units)– (Unit Variable Cost X number of units ) – Fixed costs = net income

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At the break-even point net income is zero:

Sales – Variable expenses – Fixed expense = 0

Let X = number of unit to be sold to break-even. Then for XYZ company example.

L.E. L.E. 100 X - L.E 40 X - L.E 300,000 = 0100 X - L.E 40 X - L.E 300,000 = 0 L.E. 60 X = L.E. 300,000L.E. 60 X = L.E. 300,000 X X = L.E. 300,000 = L.E. 300,000 L.E. 6 L.E. 6 X = 5000 unitsX = 5000 units

Break-even point in pounds (L.E)Break-even point in pounds (L.E)= 5000 units X unit sales price= 5000 units X unit sales price= 5000 = 5000 X L.E. 100 X L.E. 100= L.E. 500,000= L.E. 500,000

2727

You can also solve the equation for sales pounds without computing the unit break-even point by using the relationship of variable costs and profits as a percentage of sales :

Variable-cost percentage = Variable cost per unit (or ratio ) Sales price per unit

= L.E. 40 L.E. 100

= 40% or 0.4

Let S = Sales in pounds (L.E.) needed to break-even . Then S - 0.4 S - L.E. 300,000 = 0

0.6 S = L.E.300,000 S = L.E. 300,000

0.6 = L.E. 500,000

2828

General shortcut break-even formulas :

Break-even volume= Fixed expensesIn units Contribution margin per unit

Break-even volume = Fixed expensesIn pounds (L.E.) Contribution margin ratio

2929

Objective 4

Construct a cost - volume- profit graph

3030

Break–even chart-Graphical techniques

is a graph that depicts the relationship among revenues, variable costs, fixed costs and profits (or losses). The break-even point is located at the point where the total cost and total revenue lines cross.

There are two approaches to prepare break- even charts :

A break- even chart

The traditional approach the contemporary approach

The third graphical presentation, the profit-volume graph, is closely related to the break-

even chart

3131

The traditional approach focuses on the relationships among revenues, costs, and profits (Losses). This approach does not show contribution margin. A traditional break – even Chart for XYZ company is prepared in the following manner:

Traditional Approach

2) Plot sales volume, select a convenient sales 2) Plot sales volume, select a convenient sales volume (within the relevant range), say, volume (within the relevant range), say, 15,000 units, and plot point A for total sales 15,000 units, and plot point A for total sales at that volume : 15,000 X L.E 100 = L.E. at that volume : 15,000 X L.E 100 = L.E. 1,500,000. Draw the revenue( i.e. sales) Line 1,500,000. Draw the revenue( i.e. sales) Line from point A to the origin, point 0from point A to the origin, point 0

1) Draw the axes. The horizontal axis is the 1) Draw the axes. The horizontal axis is the sales volume, and the vertical axis is pounds sales volume, and the vertical axis is pounds of cost and revenue.of cost and revenue.

3232

4) Plot variable expenses. Determine the variable portion of expenses at a convenient level of activity: 15,000 X L.E. 40 = L.E 600,000 . Add this to the fixed expenses : L.E 600,000 + L.E 300,000 = L.E. 900,000. Plot point C for 15,000 units and L.E. 900,000. Then draw a line between point C and point B. This is the total expenses line.

3) Plot fixed expenses. Draw a horizontal Line intersecting the vertical axis at L.E 300,000, point B

5) Locate the Break- even point is where the total expenses line crosses the sales line, 5000 units or L.E. 500,000, namely where total sales revenues exactly equal total costs, point D.

Exhibit 2-4 is a graph of the cost – volume- Exhibit 2-4 is a graph of the cost – volume- profit relationship in our XYZ company profit relationship in our XYZ company example.example.

3333

Exhibit 2-4Cost – volume-profit Graph

Volume in thousands of units

3434

The contribution margin provided by each level of sales volume is not apparent on the preceding traditional break-even chart. Since contribution margin is so important in CVP analysis, another graphic approach can be used. The contemporary graphic approach specifically presents CM in the break – even chart.

The preparation of this chart is detailed in the following steps:

Contemporary Approach – contribution Graph

3535

Step (1) plot the variable cost firstly:

The revenue line is plotted next, and the contribution margin area is indicated.

Volume in thousands of units

3636

Step (2) Total cost is graphed by adding a line parallel to the total variable cost Line.

The distance between the total cost line and the variable cost line is the amount of fixed cost. The break-even point is located where the revenue and total cost lines intersect.

3737

The contemporary graphic approach allows the following important observations to be made:

Contribution margin is created by the excess of revenues over variable costs.

Total contribution margin is always equal to total fixed cost plus profit or minus loss.

Before profits can be generated, contribution margin must exceed fixed costs.

3838

The profit-volume graph reflects the amount of profit or loss associated with each level of sales. The horizontal axis on the PV graph represents sales volume. The vertical axis represents profits and losses. Amounts above the horizontal axis are positive and represent profits; amounts below the horizontal axis are negative and represent losses.

Profit-Volume (PV) Graph

3939

Two points are located on the graph:

If sales are zero, the loss will be the amount of the fixed costs. To plot the other point, select any other level of sales volume; say 15,000 units ( in our XYZ example). Determine profit (or loss) for this level, {15,000 units X L.E. 60 (CM)} - L.E. 300,000 (Fixed costs) = L.E.900,000 - L.E. 300,000 = L.E. 600,000 So, the two points are

Sales Volume Profit (or loss)

00L.E. 300,000 (loss)L.E. 300,000 (loss)

15,00015,000L.E. 600,000 (profit)L.E. 600,000 (profit)

4040

The last step in preparing the PV graph is to draw a profit line that passes between and extends through the two located points. Using this Line, the amount of profit or loss for any sales volume can be read from the vertical axis.

The profit Line is really a The profit Line is really a contribution margin Line, and the slope contribution margin Line, and the slope of the line is determined by the unit of the line is determined by the unit contribution margin. The Line shows that contribution margin. The Line shows that no profit is earned until the contribution no profit is earned until the contribution margin covers the fixed costs.margin covers the fixed costs.

4141

The PV graph for XYZ Company is shown below:

4242

With each unit sold, a contribution of L.E 60 is obtained toward the fixed costs, and the break-even point is at 5,000 units when the total contribution (5000 units X L.E. 60 = L.E 300,000) exactly equal the total of the fixed costs. With each additional unit sold beyond 5000 units a surplus of L.E.60 per unit is obtained. If 12,000 units are sold, the profit will be L.E. 420,000(7000 units at L.E. 60 contribution).

4343

Changes in fixed costs causes changes in the break-even point. For example, if fixed costs increase from 300,000 to 360,000 (in our example), what would be the break-even point in units and in pounds?

Break-even point =Break-even point = Fixed expenses Fixed expenses (in units) Contribution margin (in units) Contribution margin per unitper unit = = L.E. 360,000L.E. 360,000

L.E 60L.E 60

= = 60006000 unitsunits

Changes in fixed costs

4444

Break-even point = Fixed expenses

(in pounds) Contribution margin ratio

= L.E.360,000 0.6

= L.E. 600,000

Note that a one-fifth increase in fixed expenses altered the break-even point by one-fifth: from 5,000 units to 6,000 units, and from L.E 500,000 to L.E 600,000. This type of relationship always exists if every thing else remains constant. The P/V graph is shown below:

4545

4646

Changes in variable costs also cause the break – even point to shift. Companies can reduce their break-even points by increasing their contribution margins per unit of product through either increases in sales prices or decreases in unit variable costs, or both.

For example,For example, assume that assume that

(1) the variable expenses increase from L.E. 40 (1) the variable expenses increase from L.E. 40 per unit to L.E. 50.per unit to L.E. 50.

(2) the selling price falls from L.E. 100 to L.E. 80 (2) the selling price falls from L.E. 100 to L.E. 80 per unit, and the original variable costs per unit per unit, and the original variable costs per unit are unchanged,are unchanged,

Find the break-even point in units and pounds. Find the break-even point in units and pounds.

Changes in Contribution margin per Unit

4747

1.1. Unit contribution margin = L.E 100 – Unit contribution margin = L.E 100 – L.E. 50 = L.E. 50L.E. 50 = L.E. 50

Contribution margin ratio = Contribution margin ratio = L.E. 50L.E. 50 L.E. 100L.E. 100

= 0.5= 0.5The original fixed expenses of L.E.

300,000 would be unaffected, but the denominators would change from those previously used. Thus Break-even point = L.E. 300,000 (in units) L.E. 50

= 6000 units

Break-even point = L.E. 300,000 ( in pounds) 0.5

= L.E. 600,000

4848

2.2. Unit contribution margin = L.E. 80 – Unit contribution margin = L.E. 80 – L.E. 40 = L.E. 40L.E. 40 = L.E. 40

Contribution margin ratio = Contribution margin ratio = L.E. 40L.E. 40 L.E. 80L.E. 80

= 0.5= 0.5

Break-even point = L.E. 300,000 = 7500(in units) L.E. 40 Units

Break-even point = L.E. 300,000 = 0.5

(in pounds) L.E. 600,000

4949

The P/V graphs for the above two cases compared with the original case of XYZ company is shown below :

Case 1

5050

Objective 5 Calculate sales volume in total

units and total pounds to reach a target

(a planned )profit .

5151

Using Cost – Volume-profit Analysis

Managers can also use CVP analysis Managers can also use CVP analysis to determine the total sales ,in units to determine the total sales ,in units and pounds, needed to reach a target and pounds, needed to reach a target profit.profit.

Profit may be stated as either a Profit may be stated as either a fixed or a variable amount.fixed or a variable amount.

5252

1. Fixed amount of profit.1. Fixed amount of profit.

The method for computing the target or desired sales volume in units and pounds is the same as was used in break-even computation.

Target sales volume in units = Target sales volume in units = Fixed expenses + target net Fixed expenses + target net

incomeincomeContribution margin per unitContribution margin per unit

Target sales volume in pounds = Target sales volume in pounds = Fixed expenses + target net Fixed expenses + target net

incomeincomeContribution margin ratioContribution margin ratio

5353

For example. in our XYZ company, suppose that the target net income is L.E. 120,000 find the target sales volume in units and pounds :

Target sales volume in units =Target sales volume in units =

L.E. 300,000 + L.E. 120,000 L.E. 300,000 + L.E. 120,000 L.E. 60 L.E. 60

= 7,000 units = 7,000 units

Target sales volume in pounds =

L.E. 300,000 + L.E. 120,000 0.6

= L.E. 700,000

5454

Another way of getting the same answer is to adopt an incremental approach. The term incremental refers to to the change in total results (such as revenues, expenses, or income) under a new condition in comparison with some given or known condition.

In this instance the known condition is assumed to be the 5,000- unit break-even point. All expenses would be recovered at that volume. Therefore the change or increment in net income for every unit beyond 5000 would be equal to the contribution margin of L.E. 60. After the break-even point is reached, each pound of contribution margin is a pound of profit. If L.E. 120,000 were the target net profit, the target sales volume must exceed the break-even volume by L.E. 120,000 ÷ L.E. 60 = 2000 units; it would be therefore 5,000 + 2,000 = 7,000 units.

5555

To find the answer in terms of pounds with the incremental approach, every sales pound after the break-even point of L.E. 500,000 contributes L.E. 0.6 to net profit. Sales in pounds must exceed the break-even volume by L.E. 120,000 ÷ 0.6 = L.E. 200,000 to produce a net profit of L.E. 120,000; Thus the sales in pounds would be L.E. 500,000 + L.E. 200,000 = L.E. 700,000.

The following table summarizes these The following table summarizes these computations:computations:

Break-even Point

Increment New condition

Volume in unitsVolume in units 5,0005,0002,0002,0007,0007,000 SalesSales 500,000500,000200,000200,000700,000700,000

Variable expensesVariable expenses 200,000200,00080,00080,000280,000280,000Contribution Contribution marginmargin

300,000300,000120,000120,000420,000420,000

Fixed expensesFixed expenses 300,000300,000--300,000300,000Net incomeNet income 00120,000120,000L.E.120,00L.E.120,00

00

5656

2. Variable amount of profit Managers may wish to state profits

as a variable amount so that as units sold or sales in pounds increase, profit will increase at a constant rate. Profit on a variable basis can be stated either as a percent of revenues or as a per-unit profit. The CVP formula must be adjusted to recognize that profit (p) is related to volume of activity.

The adjusted CVP formula for computing the necessary unit volume of sales to earn a specified variable amount of profit per unit is as follows:

5757

R (x) – VC (x) – FC = PPU R (x) – VC (x) – FC = PPU (x)(x)R (x) – VC (x) – FC = PPU R (x) – VC (x) – FC = PPU (x)(x)

Where:Where: R = selling price per unitR = selling price per unit x = number of unitsx = number of units

R(x) = total revenueR(x) = total revenue VC = Variable cost per unitVC = Variable cost per unit VC(x) = total Variable costVC(x) = total Variable cost

FC = total fixed costFC = total fixed cost PPU = Profit per unitPPU = Profit per unit

5858

Rearranging the above formula gives the following:

R(x) – VC(X) – PPU (x) = FC

X (R – VC- PPU ) = FC

X (CM – PPU ) = FC

Where CM = contribution margin per unit

Solving for x (volume ) gives the following:

X = FC ( R – VC – PPU )

5959

The variable profit is treated in the CVP formula as if it were an additional variable cost to be covered. This treatment adjusts the original contribution margin and contribution margin ratio. When setting the desired profit as a percentage of selling price (or sales revenue), that percentage cannot exceed the contribution margin ratio. If it does, an infeasible problem is created, since the variable cost percentage plus the desired profit percentage would exceed 100 percent of selling price such a condition cannot occur.

6060

Assume that the president of XYZ company wants to know what level of sales (in units and pounds ) would be required to earn a 30% profit on sales. The following calculations provide answers to this questions:In UnitsIn UnitsProfit desired = 30 % of sales revenues Profit desired = 30 % of sales revenues

Profit per unit (PPU) = ,30 x L.E. 100 = 30Profit per unit (PPU) = ,30 x L.E. 100 = 30

Target sales volume in units (x) =Target sales volume in units (x) = FC FC

(R – VC – PPU)(R – VC – PPU) = = L.E 300,000 L.E 300,000 ( L.E. 100 – L.E. 40 – L.E. ( L.E. 100 – L.E. 40 – L.E.

30)30)

= 10,000 Units= 10,000 Units

6161

In Sales PoundsIn Sales Pounds The following relationships existThe following relationships exist

Per unitPercentSelling priceL.E. 100 100 %Variable costL.E. 40(40%)Variable profitL.E. 30(30%)"Adjusted" Contribution Margin

L.E. 3030 %

Target sales volume (in pounds) = FC

contribution Margin ratio – profit desired ratio

= FC"Adjusted" CM ratio

= L.E 300,000 0.3

= L.E. 1,000,000

6262

The income statement for this volume of activity is shown below :

TotalL.E

Per Unit L.E

Percent

Sales (10,000 Units) Sales (10,000 Units) 1,000,001,000,0000

100100100 %100 %

Variable costs:Variable costs: Production Production 300,00300,00

00303030%30%

Selling Selling 100,00100,0000

101010%10%

Total variable cost Total variable cost 400,000400,000404040%40%Contribution margin Contribution margin 600,000600,000606060%60%Fixed costsFixed costs ProductionProduction250,00250,00

00Selling Selling administrativeadministrative

50,00050,000

Total fixed costs Total fixed costs 300,000300,000

Net in come Net in come 300,000300,00030%30%

6363

Margin of Safety

The margin of safety is defined as the excess of the budgeted or actual sales of a company over the company's break-even point. The margin of safety can be expressed as units, pounds, or a percentage. The following formulas are applicable

Margin of safety in units =

Planned ( or actual ) units – Break-even units

Margin of safety in pounds =

Planned (or actual) sales L.E – Break- even sales L.E

Margin of safety % =

Margin of safety in units or L.E

Planned (or actual ) sales in units or L.E.

6464

Margin of safety is one direct uses of CVP analysis, It shows how far sales can fall below the planned (or actual ) Level before losses occur.

The break-even point for XYZ company is 5,000 units or L.E. 500,000 of sales. The income statement for the company in Exhibit 2-3 showed actual sales for the year ended December,31,97, of 12,000 units,or L.E. 1,200,000. The margin of safety for XYZ is computed as shown below:

In units = 12,000 (actual ) – 5000 BEP = 7,000 units

In sales L.E = L.E. 1,200,000 (actual) – L.E. 500,000 (BEP)

= L.E. 700,000

Percentage = 7,000 ÷ 12,000 or L.E. 700,000 ÷ L.E 1,200,000 = 58%

The margin of safety for XYZ is quite high, since it is operating far a above its break-even point.

6565

The margin of safety calculation allows management to assess possible risks; by determining how close to a danger level the company is operating.

The lower the margin of safety, The lower the margin of safety, the more carefully management the more carefully management must watch sales figures and must watch sales figures and control costs so as not to generate control costs so as not to generate a net loss.a net loss.

6666

Objective 6 Distinguish between

contribution margin and gross margin

6767

Contribution margin & Gross margin

(Gross profit) is the excess of sales over the cost of goods sold (that is, the cost of the merchandise that is acquired or manufactured and then sold )

Gross margin

is sales less all variable costs. The variable costs will include part of the cost of goods sold and also part of the other operating expenses

Contribution margin

6868

Example: Problem 2- 42 P,71

General Mills produces and sells food products and backing products. A condensed 1994 income statement follows ( in millions):

Sales Sales L.E L.E 8,5178,517

Cost of goods soldCost of goods sold4,4584,458

Gross marginGross margin4,0594,059

Other operating Other operating expensesexpenses

3,3063,306

Operating incomeOperating income753753

6969

Assume that L.E. 960 million of the Assume that L.E. 960 million of the cost of goods sold is a fixed cost cost of goods sold is a fixed cost representing depreciation and other representing depreciation and other producing costs that does not change producing costs that does not change with the volume Of production. In with the volume Of production. In addition L.E 2,120 million of the other addition L.E 2,120 million of the other operating expenses is fixedoperating expenses is fixed

Compute the total contribution Compute the total contribution margin for 1994 and the contribution margin for 1994 and the contribution margin percentage . margin percentage .

7070

SolutionSolution

Variable costs = Cost of goods sold L.E 4,458

- Fixed production costs960

3,498

+Variable other operating Expenses (L.E 3,306_ L.E 2,2120 )

1,186

4,684 Fixed costs =Fixed costs = Production costs L.E 960

+ Other operating expenses 2,120

3,080

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Condensed Income Statement For 1994

Sales Sales L.E L.E 8,5178,517

Variable costsVariable costs 4,6844,684

Contribution marginContribution margin 3,8333,833

Fixed costsFixed costs 3,0803,080

Operating incomeOperating income753753

Contribution margin percentage

= L.E. 3,833 ÷ L.E. 8,517 = 45%

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Objective 7 Identify the limiting

assumptions that underlie cost- volume-profit analysis

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Underlying Assumptions of CVP Analysis

The cost – volume-profit analysis is a useful planning tool that can provide information on the impact on profits when changes are made in costs or in sales levels. Several important assumptions are made in CVP analysis. They are necessary, but they limit the accuracy of the results. Some of these assumptions follow:

1) Expenses may be classified into variable and fixed categories. Total variable expenses vary directly with activity level. (Within the relevant range)

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3)Efficiency and productivity will be 3)Efficiency and productivity will be unchanged (Labor productivity, unchanged (Labor productivity, production technology and market production technology and market conditions will not change).conditions will not change).

2) Selling prices do not change with production and sales over the relevant range ( a constant selling price per unit )

5) The difference in inventory level at the 5) The difference in inventory level at the beginning and at the end of a period is beginning and at the end of a period is insignificant (sales = production )insignificant (sales = production )

4) Sales mix will be constant. The sales 4) Sales mix will be constant. The sales mix is the relative proportions or mix is the relative proportions or combinations of quantities of products combinations of quantities of products that constitute total sales.that constitute total sales.

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Solution strategies

Most CVP problems are solvable by using a numerator, denominator approach. All numerators and denominators and the type of problem each relates to are listed below :

Problem situation Numerator

denominator

BEP in unitsBEP in unitsFCFCCMCMBEP in pounds BEP in pounds FCFCCMCM%%Target sales with Lump-Target sales with Lump-sum profit in units sum profit in units

FCFCCMCM

Target sales with Lump-Target sales with Lump-sum profit in pounds sum profit in pounds

FCFCCM%CM%

Target sales with Variable Target sales with Variable Profit in units Profit in units

FCFCCM- PPUCM- PPU

Target sales with Variable Target sales with Variable Profit in pounds Profit in pounds

FCFCCM% - PPUCM% - PPU%%

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Where:Where:

FC = Fixed cost.FC = Fixed cost.

CM = Contribution margin per unit.CM = Contribution margin per unit.

CM% = Contribution margin CM% = Contribution margin percentage.percentage.

P = Total planned profit.P = Total planned profit.

PPU = Profit per unit.PPU = Profit per unit.

PPU% = Profit per unit percentage PPU% = Profit per unit percentage ( profit desired ratio ).( profit desired ratio ).

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Thank you

Thank you