**Operation Management**

**Cost, Volume, and profit analysis**

**(A short term managerial decision making tool)**

__A. Introduction:__Cost-volume-profit (CVP) analysis is one of the most powerful tools that managers at their command. It helps them understand the interrelationship between cost, volume, and profit in an organization by focusing on interaction among the following five elements;

- prices of products
- volume or level of activity
- per unit variable costs
- total fixed costs
- mix of products sold

Because CVP analysis helps managers understand the interrelationships among cost, volume, and profit, it is 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

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__B. Marginal and absorption costing: different rationales__Absorption costing stems from the view that certain necessarily incurred to allow output to occur and should therefore be included in unit costs. In effect, absorption costing is based on a functional classification of costs; that is all out put related (or production costs are attributed to cost units, with non production costs being excluded from unit costs (at least for stock valuation and profit measurement purposes).

Marginal costing, however, is based on a distinction between variable and fixed costs, with the absorption costing being attributed to cost units and the marginal costing being dealt with in total for a particular period. The justification fro this treatment of fixed costs is that, in general, costs such rent rates and insurance relate to a period of time, rather than to volume of out-put and their accounting treatment should reflects this fact. Not only can absorption of fixed costs be viewed as illogical in light of their predominantly time based nature, but it may also cause confusion about their behavior and even amount. Under absorption costing increase/decrease in the volume of out-put will result in increase/decrease in the amount of fixed overhead absorbed, which might give the misleading impression that the amount of the underlying costs incurred is increasing/decreasing in the line with output; that is, that we are dealing with variable costs.

__C. The unit output cost as calculated for each of marginal and absorption costing__

__D. Contribution margin:__Contribution margin is 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 profits for the period.

__E. CVP__**:**

__relationships in Graphic form__The relations among revenue, cost, profit and volume can be expressed graphically by preparing a cost volume profit (CVP) graph. A CVP graph highlights CVP relationships over wide ranges of activity and can give managers a perspective that can be obtained in no other way.

*Preparing the CVP graph:*In a CVP graph (sometimes called a break-even chart), unit volume is commonly represented on the horizontal (X) axis and Taka on the vertical (Y) axis. Preparing a CVP graph involves 3 steps. These steps are keyed to the graph;

- Draw a line parallel to the volume axis to represent total fixed expenses, for example, fixed expenses are TK 35000.
- Choose some volume of sales and plot the point representing total expense (fixed and variable) at the activity level we have selected. For example, choose a volume of 600 units. Total expenses at the activity level would be as follows (where unit price TK 150 per unit)

Fixed expenses TK 35000

Variable expenses (600X150) TK 90000

Total expense TK 125,000

After the point has been plotted, draw a line through it back to the point where the fixed expenses line intersects the Taka axis.

- Again choose some volume of sales and plot the point representing total sales TK at the at the activity level we have selected. Here sales at the activity level total TK 150000. Draw a line through this point back to the origin.

The break-even point is where the total revenue and total expenses lines cross and profit zero.

__F. Contribution margin ratio (CM Ratio):__We explored how CVP relations can be visualized. Now we will look at how the contribution ratio can be used in CVP calculations. According to the previous example contribution income statement may be as follows in which sales revenues, variable expenses, and contribution margin are expressed as percentage of sales;

The CM ratio is extremely useful since it shows how the contribution margin will be affected by change in total sales.

__G. Importance of the contribution margin.__1) CVP analysis can be used to help find the most profitable combination of variable costs, fixed costs, selling price, and sales volume.

2) The size of the unit contribution margin (and the size of the CM ratio) is very important. For example, the greater the unit contribution margin, the greater is the amount that a company will be willing to spend to increase unit sales.

3) In short, the effect on the contribution margin holds the key to many decisions.

__H. Break-even analysis:__CVP analysis is sometimes referred to simply as break even analysis. This is unfortunate because break even analysis is only one element of CVP analysis- although an important element. The break-even point can be computed using either the equation method or the contribution margin method- the two methods are equivalent.

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*The equation method centers on the contribution approach to the income statement. The format of that income statement can be expressed in equation form as follows;*__The equation method:__Profits = (sales - variable expenses) – fixed expenses

Rearranging the equation slightly yields the following equation, which is widely used in CVP analysis;

Sales = variable expenses + fixed expenses + profits

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__Target profit analysis:(suppose our target profit is TK40000; how many units and how much Taka sales needed to attain the target profit)__

__I. The margin of safety:__The margin of safety is the excess of budgeted (or actual) sales over the break-even volume of sales. It states the amount by which sales can drop before losses begin to be incurred. The higher the margin of safety, the lower the risk of not breaking even. The formula for its calculation is;

Margin of safety = total budgeted (or actual) sales – Break even sales

Margin of safety % = Margin of safety in TK ÷ Total budgeted (or actual) sales.

**Note:**Some managers need to know the contribution/sales ratio which is in short CS ratio;

Total contribution

CS ratio = ---------------------------

Total sales revenue

Rearranging, above ratio we can say, Contribution = CS ratio X Sales

At break even point, total contribution = Total Fixed Costs;

So (CS ratio X Sales) = Total Fixed Costs

--------------------------- Md Aminul Islam | maihbd@gmail.com