**UNIT 4 **

**Cost Volume Profit (CVP) Analysis **

**4.1 Introduction**

Managers often classify costs as fixed and variable when making decisions that affect the volume of out put. The managers want to know how such decisions will affect costs and revenues. They realize that many factors in addition to the volume of out put will affect costs. Yet, a useful starting point in their decisions process to specify the relation ship between the volume of out put and costs and revenues.

Cost-volume-profit (CVP) analysis is one of the most powerful tool that help managers as they make decisions by facilitating quick estimation of net income at different levels of activity. In other words, it helps them to understand the interrelationship between cost, volume, and profit in an organization by focusing on interactions between the following five elements: prices of products, volume or level of activity, per unit variable costs, total fixed costs, and mix of products sold. Thus, CVP analysis examines the behavior of three different factors: cost-volume-profit and further, the total revenues, and the total costs, and operating income as changes occur in the out put level, selling prices, variable costs, or fixed costs.

Because CVP analysis helps managers understand the interrelationship between cost, volume, and profit, it is a vital tool in many business decisions. These decisions include, for example, what products to manufacture or sell, what pricing policy to follow, what marketing strategy to employ, and what type of productive facilities to acquire.

**4.2. The Basic of CVP Analysis**

The concept is so pervasive in managerial accounting that it touches on virtually every thing that the manager does. Because its wide range of usefulness, CVP analysis undoubtedly the best tool for a manager, who is discovering the untapped profit potential that may exist in an organization. Because CVP analysis helps managers understand the interrelationship between cost, volume, and profit, it is vital tool in many business decisions.

**Contribution Margin Vs Gross Margin**

The form of income statement used in CVP analysis is shown in Exhibit 5.1, i.e., the projected income statement of ABC Merchandising Company for the month ended January 31, 20x6. This income statement is called contribution approach to income statement. The contribution income statement emphasizes the behavior of the costs and there fore is extremely helpful to manager in judging the impact on profits of changes in selling price, cost, or volume.

Exhibit 5.1

In the income statement here above, sales, variable expenses, and contribution margin are expressed on a per unit basis as well as in total. This is commonly done on income statements prepared for management’s own use since it facilitates profitability analysis.

The contribution margin represents the amount remaining from sales revenue after variable expenses have been deducted. Thus, it is the amount available to cover fixed expenses and then to provide profit for the period. Notice the sequence here- contribution margin is used first to cover the fixed expenses, and then whatever remains goes toward profit. In the ABC Merchandising Company income statement shown above, the company has a contribution margin of Br. 40, 000. In this case, the first Br.32, 000 covers fixed expenses; the remaining Br. 8, 000 represents profit.

The per unit contribution margin indicates by how much birrs the contribution margin is increased for each unit sold. ABC Merchandising Company’s contribution margin of Br.4.00 per unit indicates that each unit sold contributes Br.4.00 to covering fixed expenses and providing for a profit. If the firm had sold 5, 000 units, this would cover only Br.20, 000 of their fixed expenses (5, 000 units x Br.4.00 per unit). Therefore, the firm would have a net loss of Br.12, 000.

Contribution margin Br.20, 000

Fixed expenses __32, 000__

Net loss Br__.(12,000)__

If enough units can be sold to generate Br.32, 000 in contribution margin, then all of the fixed costs will be covered and the company will have managed to show neither profit nor loss but just cover all of its cost. To reach this point (called break even point), the company will have to sell 8, 000 units in a month, since each unit sold yield Br. 4.00 in contribution margin.

Total Per Unit

Sales (8, 000 units) Br.160,000 Br.20.00

Variable expenses __128,000__ __16.00__

Contribution margin Br.32, 000 Br__.4.00 __

Fixed expenses __32,000__

Net income Br__. 0 __

Computations of the break-even point are discussed in detail later in this unit. For the moment, note that the break even point can be defined as the point where total sales revenue equals total expenses (variable plus fixed) or as the point where total contribution equals total fixed expenses.

In most cases people confuse the terms contribution margin and gross margin. Gross margin (which is also called 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). It is a widely used concept, particularly in the retailing industry.

When we compare the gross margin with the contribution margin:

Gross Margin = Sales price - Cost of goods sold

Contribution margin = Sales price - all variable expenses

In addition to being expressed on a per unit basis, revenue, variable expenses, and contribution margin for ABC Merchandising Company can also be expressed on a percentage basis as shown in the following income statement:

Total **Per Unit** **Percentage**

Sales (10, 000 units) Br.200, 000 Br.20.00 100%

Variable expenses __160, 000__ __16.00__ __80%__

Contribution margin Br.40, 000 Br.__4.00__ __20%__

Fixed expenses __32, 000__

Net income Br__. 8, 000__

The percentage of the contribution margin to total sales is referred to as the contribution margin ratio (CM-ratio). This ratio is computed as follows:

CM-ratio= Contribution Margin / Sales

Contribution margin ratio = 1 – variable cost ratio. The variable-cost ratio or variable-cost percentage is defined as all variable costs divided by sales. Thus, a contribution margin of 20% means that the variable-cost ratio is 80%.

The contribution margin percent or contribution margin ratio, also called profit/volume ratio (p/v ratio) is 20%. This means that for each Birr increase in sales, total contribution margin will increase by 20% .

Once the break-even point has been reached, net income will increase by the unit contribution margin for each additional unit sales. If 8001 units are sold in a month, for example, then we can expect that the ABC Merchandising Company’s net income for the month will be Br. 4, since the company will have sold 1 unit more than the number needed to break even:

Total per Unit

Sales (8, 001 units) Br.160, 020 Br.20.00

Variable expenses __128, 016__ __16.00__

Contribution margin Br.32, 004 __Br.4.00__

Fixed expenses __32,000__

Net income __Br. 4__

**4.3. Break-even Analysis**

The study of cost-volume-profit analysis is usually referred as break-even analysis. The term break-even analysis is interpreted in a narrow as well as broad sense. Using its narrow sense, it is concerned with finding out the break-even profit.

Break even point is the point of out put at which total revenue is equal to total expenses total variable and fixed expenses). In a broad sense the break even analysis means a system of analysis that can be used to determine the probable profit at any level of operations.

In other words break-even point is a point at which the operating income is zero. There are three alternative methods to determine break –even point: equation technique, contribution margin technique, and graphical method.

**Equation Technique:-** It is the most general form of break-even analysis that may be adapted to any conceivable cost-volume-profit situation. This approach is based on the profit equation. Income (or profit) is equal to sales revenue minus expenses. If expenses are separated into variable and fixed expenses, the essence of the income statement is captured by the following equation.

**Profit= Sales revenue-Variable expenses-Fixed expenses**

The above formula can be restated as follows

NI = (P XQ)-(VxQ)-F

Where P=sales price

Q=break-even unit sales

V= variable expenses per unit

F=fixed expenses per period

NI= net income

At break-even point, net income=0 because total revenue equal total expenses.

That is, NI=PQ-VQ-F

0= PQ-VQ-F……………………………………equation (1)

PQ = VQ – FC

Revenue = Total cost

**Contribution-Margin Technique.** This approach centers on the idea that each unit sold provides a certain amount of fixed costs. When enough units have been sold to generate a total contribution margin equal to the total fixed expenses, break-even point (BEP) will be reached.

Thus, one must divide the total fixed costs by the contribution margin being generated by each unit sold to find units sold to break-even.

BEP= Fixed expenses / Unit contribution margin

Given the equation for net income, you can arrive at the above short cut formula for computing break-even sales in units as follows:

NI=PQ-VQ-F

0=Q (P-V)-F because at BEP net income equals zero.

Q (P-V)=F…divide both sides by (p-v)

Q = *F / (P-V)* …………… equation (2) * *

This is a short cut formula that helps to compute the break even sales in units. There is a variation of this method that uses the CM ratio of the unit contribution margin. The result is the break-even point in total sales birrs rather than in total units sold.

BEP (in sales birrs)= Fixed expenses/ CM ratio = F /((P-V)/P)

This approach to break-even analysis is particularly useful in those situations where a company has multiple product lines and wishes to compute a single break-even point for the company as a whole.

**Graphical Method:** The graphical representation of break-even point (cost-volume –profit analysis) is known as break-even chart. Break-even chart is a graph showing the amount of fixed, variable cost and total revenue at different volumes of operations.

In the graphical method we plot the total costs and revenue lines to obtain their point of intersection, which is the breakeven point.

**Total costs line.** This line is the sum of the fixed costs and the variable costs. To plot fixed costs, draw a line parallel to the volume axis. To plot the total cost line, choose some volume of sale and plot the point representing total expenses (fixed and variable) at the activity level you have selected. After the point has been plotted, draw a line through it back to the point where the fixed expense line intersects the Birr axis (the vertical axis).

**Total Revenue Line.** Again choose some volume of sales to construct the revenue line and plot the point representing total sales birrs at the activity you have selected. Then draw a line through this point back to the origin.

The break-even point is where the total revenues line and the total costs line intersect. This is where total revenues just equal total costs.

**4.4 Applying CVP Analysis**

** 4.4.1 Overview**

To apply cvp analysis, managers usually resort to some simplifying assumptions. The major simplification is to classify costs either as variable or fixed with respect to a single measure of the volume of out put or activity. The study of the effect of out put volume on revenues (sales) expenses, ( costs) and net income is a critical activity in a decision making process for the management of a company.

** 4.4.2 Sensitivity “What If” Analysis **

Sensitivity analysis is a “what if” technique that 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, sensitivity analysis answers such questions as, what will operating income be if the out put level decreases by a given percentage from the original reduction? And what will be operating income if variable costs per unit increase? The sensitivity analysis to various possible outcomes broadens managers’ perspectives as to what might actually occur despite their well-laid plans.

**4.4.3 Target Net Profit Analysis**

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

The method used for computing desired or targeted sales volume in units to meet the desired or targeted net income is the same as was used in our earlier breakeven computation.

**4.4.4** **The Margin of Safety **

The margin of safety is the excess of budgeted (or actual) sales over the breakeven volume of sales. It states the amount by which sales can drop before losses begin to be incurred. In other words, it is the amount of sales revenue that could be lost before the company’s profit would be reduced to zero. The formula for its calculations follows:

Total sales - Break even Sales = Margin of safety

The margin of safety can also be expressed in percentage form. This percentage is obtained by dividing the margin of safety in birr terms by total sales as follows:

Margin of safety in birrs = Margin of safety ratio x Total sales

**4.5 The Impact of Income Tax CVP Analysis**

Thus far we have ignored income taxes. However, profit-seeking enterprises must pay income taxes on their profits. A firm’s net income after tax, the amount of income remaining after subtracting the firm’s income- tax expense, is less than its before- tax income. This fact is expressed in the following formula:

NIAT = NIBT (1 – tax rate)

Where NIAT = net income after taxes

NIBT=net income before taxes

The requirement that companies pay income taxes affects their CVP relationships. To earn a particular after-tax net income will require greater before-tax income than if there were no tax.

**4.6 CVP Analysis with Multiple Products**

** 4.6.1 Overview**

With multiple product cvp analysis, a managerial accountant can investigate the impact on profit change in:

. Sales volume

. Price

. Variable cost

. Fixed cost

. The sales mix

** 4.6.2 Definition of sales mix**

The term **sales mix** (also called revenue mix) is defined as the relative proportions or combinations of **quantities** of products that comprise total sales. If the proportions of the mix change, the CVP relationships also change. Thus, managers try to achieve the combination, or mix, that will yield the greatest amount of profit.

A shift in sales-mix from high-margin items to low-margin items can cause total profits to decrease even though total sales may increase. Conversely, a shift in the sales mix from low margin items to high-margin items can cause the reverse effect-total profit may increase even though total sales decrease.

**4.6.3 Sales Mix and CVP Analysis**

The concept of CVP analysis had been developed in the context of a single product firm. Since single product firms are virtually non-existent this section of the unit examines the usefulness of CVP technique for firms that deal with several products. In such a case the cvp equation can be expanded as follows:

P1Q1 + P2Q2+...+PnQn – V1Q1 – V2Q2-...VnQn-FC = NI

where Pi = Selling price per unit of product i

Qi = Number units of i produced and sold

Vi = Unit variable cost of product i

FC = Fixed Cost Per Period

NI = Net Income

In a multi product firm, break-even analysis is somewhat more complex. The reason is that different products will have different selling prices, different costs, and different contribution margins.

Using contribution margin approach, the computation of the break-even point (BEP) in multi product firm follows:

BEP (in units) = __Total fixed expenses__

Weighted average CM

BEP (in birrs) = __Total Fixed Expenses__

CM – ratio

Weighted average unit contribution margin is the average of the several products’ unit contribution margins, weighted by the relative sales proportion of each product.

For a company manufacturing and selling three products (X, Y and Z), with sales of mix of n1,n2 and n3, respectively, the break even point may be given by the following short cut formula:

BEP (in units) = __Total fixed costs __

__cm1n1 + cm2n2 + cm3n3 __

n1 + n2 + n3

Where cmi = Unit contribution margin for product i.

Q = __ FC __ …………….. equation (1)

__Cm1n1 + Cm2n2 + Cm3n3 __

n1 + n2 + n3

Here in equation (1), the denominator, __Cm1n1 + Cm2n2 + Cm3n3__ , is the n1 + n2 + n3

weighted average contribution margin.

Similarly, the company’s break-even sales in birrs would be calculated as

BEP (in birrs) = __Fixed expenses__

CM – ratio

= __Fixed expenses__

__Average CM __

Average Sales Price

= __Fixed expenses __

__ Cm1n1 + Cm2n2 + Cm3n3__

n1 + n2 + n3

__P1n1 + P2n2 + P3n3 __

n1 + n2 + n3

BEP (in birrs) = __Fixed expenses __ …………….. equation (2)

__Cm1n1 + Cm2n2 + Cm3n3__

p1n1 + p2 n2 + p3n3

Here in equation (2), the denominator represents the contribution margin ratio.

**4.7 Underlying Assumptions in CVP Analysis**

For any CVP analysis to be valid, the following important assumptions must be reasonably satisfied within the relevant range.

1. The behavior of total revenue is linear (straight-line). This implies that the price of the product or service will not change as sales volume varies within the relevant range

2. The behavior of total expense is linear over the relevant range. This implies the following more specific assumptions:

- Expenses can be categorized as fixed, variable, or semi variable costs. Total fixed costs remain constant as activity changes and unit variable expenses remain constant as activity varies.
- The efficiency and productivity of the production process and the workers remain constant.

3. Total variable cost vary with the volume output but prices of variable costs such as wage rate, price of materials, and supplies will be unchanged.

4. Multi product companies, the sales mix remains constant over the relevant range.

5. In Manufacturing firms, inventories do not change, i.e., the inventory levels at the beginning and end of the period are the same. This implies that the number units produced during the period equals the number of units sold.

6. The value of a birr received today is the same as the value of a birr received in any future year.

**4.8 Cost Structure and Operating Leverage**

** 4.8.1 Overview**

Costs are associated with all types of organizations- business, non-business, services, retail, …etc. Generally, the kinds of costs that are incurred and the way in which theses costs are classified will depend on the type of organization involved. Thus, cost items variable or fixed are analyzed and grouped according to their common characteristics and the effect of each on the operating leverage of the particular company.

** 4.8.2 Cost Structure and Profit Stability**

**Cost structure** refers to the relative proportion of fixed and variable costs in an organization. Highly leveraged companies are characterized by high fixed cost and low variable costs. In the contrary, low leveraged companies are characterized by lower fixed costs and higher variable costs, which cost structure is better-high variable costs and low fixed costs, or the opposite? No categorical answer to this question is possible: we can simply note that there may be advantages either way, depending on the specific circumstances involved.

**4.8.3 Operating Leverage**

To the scientist, leverage explains how one is able to move a large object with a small force. To the manager, leverage explains how one is able to achieve a large increase in profits with only a small increase in sales and/or assets. One type of leverage that the manager uses to do this is known as operating leverage.

**Operating leverage** is a measure of the extent to which fixed costs are being used in an organization. It is greatest in companies that have a high proportion of fixed cost in relation to variable costs. Conversely, operating leverage is lowest in companies that have a low proportion of fixed costs in relation to variable costs. If a company has high operating leverage (that is, a high proportion of fixed costs in relation to variable costs), then profits will be very sensitive to changes in sales. Just a small percentage increase (or decrease) in sales can yield a large percentage increase (or decrease) in profits.

The degree of operating leverage at a given level of sales is computed by the following formula.

__Contribution margin__ = Degree of operating leverage (DOL)

Net income

**4.9 Summary**

An understanding of cost-volume-profit relation ships is necessary for successful management of any enterprise. CVP analysis provides a sweeping overview of the effects on profit of all kinds of changes in sales volume, expenses, product mix, and sales prices.

Cost-volume-profit relation ships are important enough to operating managers that some firms prepare a contribution income statement. This income statement format separates fixed and variable expenses, and helps managers concern on profits from changes in volume. The contribution income statement also discloses an organization’s cost structure, which is relatively proportion of fixed and variable costs. The cost structure of organizations defines its operating leverage, which determines the impact on profit of changes in the sales volume.