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Management Control Systems

on

Cost Volume Profit Analysis as a tool of Managerial Control and Decision making

BySanjay Sinha

IV Semester (PT)Jaipuria Institute of Management

Lucknow

Cost-volume-profit (CVP) analysis

In an expanding market, managers take advantage of fixed costs to generate profitable growth since additional customers do not add much additional costs. In this case, a cost structure dominated by fixed costs is a smart managerial decision.

In an unstable or declining economy, however, a high fixed-cost structure is harmful. Just as adding new customers does not markedly increase costs when a firm has a high fixed cost structure, reducing the number of customers does not lower costs very much. For example, when sales declines profits falls sharply. High fixed cost structures are profitable when sales grow but result in rapid deterioration of profits when sales decline

Cost-volume-profit analysis (CVP), or break-even analysis, is used to compute the volume level at which total revenues are equal to total costs. When total costs and total revenues are equal, the business organization is said to be "breaking even." The analysis is based on a set of linear equations for a straight line and the separation of variable and fixed costs.

Total variable costs are considered to be those costs that vary as the production volume changes. In a factory, production volume is considered to be the number of units produced.

There are a number of costs that vary or change, but if the variation is not due to volume changes, it is not considered to be a variable cost. Examples of variable costs are direct materials and direct labor. Total fixed costs do not vary as volume levels change within the relevant range. Examples of fixed costs are straight-line depreciation and annual insurance charges. Total variable costs can be viewed as a 45o line and total fixed costs as a straight line. The upward slope of line represents the change in variable costs. Variable costs sit on top of fixed costs

It can be seen that it is important to separate variable and fixed costs. Another reason it is important to separate these costs is because variable costs are used to determine the contribution margin, and the contribution margin is used to determine the break-even point. The contribution margin is the difference between the per-unit variable cost and the selling price per

unit. For example, if the per-unit variable cost is Rs.15 and selling price per unit is Rs.20, then the contribution margin is equal to Rs.5.

A CVP analysis is obtained to know:-

What level of sales is necessary to at least cover all expenses?

How many valves should be sold in order to earn a planned profit?

What will happen to profit if we change the selling prices?

How will changes in variable costs or fixed costs impact planned profits?

How would a change in the mix of products sold affect the break-even and target volume and profit potential?

Cost-volume-profit (CVP) analysis helps determine how changes in costs and volume affect a company's profit.

Cost-volume-profit analysis helps the mangers to :-

1. To forecast profit by considering relationship between cost and profit on one hand, and production volume on the other

2. To prepare a flexible budget showing costs at different levels of production

3. To help evaluate a start up operation

4. To evaluate performance for the purpose of benchmarking and control

5. To set pricing policies by projecting the effect of different price structures on cost and profit.

6. It helps in deciding whether the work should be done in house or outsourced.

Important uses of Cost-volume-profit

Cost-volume- profit analysis is an estimating concept that can be used in a variety of pricing situations .You can use the cost-volume relationship for:

Evaluating item price in price analysis: Cost-volume –profit analysis assumes that cost is composed of fixed and variable elements. This assumption can be used to explain price change as well as cost changes . As the volume being acquired increases unit costs decline, the vendor can reduce prices and same make the same profit per unit.

Evaluating direct costs in pricing new contracts: Quantity differences will often affect direct costs—particularly direct material cost. Direct material requirements often include a fixed component for development or production set- up . As that direct cost is spread over an increasing volume unit costs should decline.

Evaluating direct costs in pricing contract changes: How will an increase in contract effort increase contract price? Some costs will increase while others will not The concepts of cost-volume-profit analysis can be an invaluable aid in considering the effect of the change on contract price.

Evaluating indirect costs: The principles of cost-volume – profit analysis can be used in indirect cost analysis. Many indirect costs are fixed or semi-variable. As overall volume increases, indirect cost rates typically decline because fixed costs are spread over an increasing production volume.

The components of Cost-Volume-Profit Analysis are:

Level or volume of activity Unit Selling Prices Variable cost per unit Total fixed costs Sales mix

There are three main tools offered by Cost-Volume-Profit analysis:

Breakeven analysis, which tells the sales volume needed to break even, under different price or cost scenarios

Contribution margin analysis, which compares the profitability of different products, lines, or services

Operating leverage, which examines the degree to which business uses fixed costs, which magnifies profits as sales increase, but also magnifies losses as sales drop.

Basic Assumptions of Cost-Volume-Profit

Should consider only short- term operations. The short term may be defined as a period too short to permit facilities expansion or contraction or other changes that might affect overall pricing relationships.

Assume that a straight line can reasonably be used in analysis ie the constant sales price. While actual price behavior may not follow a straight line, its use can closely approximate actual cost behavior in the short run.

If purchase volume moves outside the relevant range of available data , the straight-tine assumption and the accuracy of estimates become questionable.

The time value of money (interest) is ignored

Units sold equals units produced.

Types of Cost :

In the short run , costs can be of three general types:

Fixed Cost: Total fixed costs remain constant as volume in the relevant range of production Fixed cost per unit decreases as the cost is spread over an increasing number of units.Examples include: Insurance , depreciation, facility rent and property taxes.

Variable Cost: Variable cost per unit remains constant no matter how many unit are made in the relevant rang of production . Total variable cost increases the number of units increases.

Examples include :Production, material and labor.

Semi – variable cost: Semi – variable costs include both fixed and variable cost elements. Costs may increase in steps or increase relatively smoothly from a fixed base.Examples include: Electricity, and telephone.

Analyzing The Cost – Volume Relationship

Algebraic Analysis

Total Cost = Fixed +Variable Cost

Using symbols:

C= F + VWhere:

C = Total cost F = Fixed cost V = Variable cost

Total variable cost depends on two elements:

Variable Cost = Variable Cost per Unit * Quantity Produced

Using symbols: V = Vu (Q)

Where: Vu = Variable cost per unit Q= Quantity produced substituting this variable cost information into the basic total cost equation, we have the equation used in cost- volume analysis:

C =F + Vu * Q

Example of Calculating Total Cost of production. If you know that fixed costs are Rs.500 , variable cost per unit is Rs. 10 , and the volume produced is 1, 000 units, you can calculate the total cost of production.

C = F+ Vu (Q) = Rs.500 + Rs.10 (1,000)= Rs.500 + Rs.10,000=Rs.10,500

Example of Calculating Variable Cost. Given total cost and volume for two different levels of production , and using the straight- line assumption , you can calculate variable cost per unit:

Vu = Change in Total Cost Change in Volume or

= C2-C1 Q2-Q1

Where: C1 = Total cost for Quantity 1

C2 = Total cost for Quantity 2 Q1 = Quantity 1 Q2 = Quantity 2

You are analyzing an offer or a cost proposal . As part of the proposal the offer or shows that a supplier offer or 5,000 units of a key part for Rs.60,000. The same quote offered 4,000 Rs.50,000 . What is the apparent variable cost per unit?

Vu = C2-C1 Q2-Q1 =Rs.60,000- Rs.50,000 5,000-4,000

= Rs.10,000 1,000 = Rs.10

Example of Calculating fixed Cost. If you know total cost and variable cost per unit for any quantity, you can calculate fixed cost per unit the basic total cost equation .

You are analyzing an offer or cost proposal . As part of the proposal the offer of shows that a supplier offered 5,000 unit of a key part for Rs.60,000. The apparent variable cost is Rs.10 per unit .

What is the apparent fixed cost ?

C =F + Vu (Q)

Rs.60,000=F+Rs.10(5,000)Rs.60,000=F+Rs.50,000Rs.60,000-Rs.50,000= FRs.10,000

Developing an Estimating Equation. Now that you know that Vu is Rs.10 and F is Rs.10,000 you can substitute the values into the general total cost equation.

C = F +Vu(Q) =Rs. 10,000 + Rs.10 (Q)

You can use this equation to estimate the total cost of any volume in the relevant range between 4,000 and 5,000 units.

Using the Estimating Equation. Using the estimating equation for the relevant range, estimate the total cost of 4,400 units.

C= Rs.10,000 + Rs.10(Q) = Rs.10,000+Rs.10 (4,400) = Rs.10,000+ Rs.44,000 = Rs.54,000

Graphic Analysis

Introduction to Graphic Analysis.

When you only have two data points , you must generally assume a linear relationship .When you get more data , you can examine the data to determine if there is truly a linear relationship .

You should always graph the data before performing an algebraic analysis.

Graphic analysis is the best way of developing an overall view of cost – volume relationship.

Graphic analysis is useful in analyzing cost –volume relationships, particularly, when the cost and volume numbers involved are relatively small.

Even when actual analysis is performed algebraically you can use graphs to cost – volume analysis to others.

Example of Graphic analysis . The four steps of cost – volume – profit analysis can be used to graph and analyze any cost- volume relationship. Assume that you have been asked to estimate the cost of 400 units given the following data:

Units Cost200 Rs.100500 Rs.175600 Rs.200

Steps of Graphic Analysis:

There are four steps in using graph paper to analyze cost – volume relationships:

Step 1. Determine the scale that you will use: Volume is considered the independent variable and will be graphed on the horizontal axis. Cost is considered the dependent variable and will be graphed on the vertical axis . The scales on the two axis do not have to be the same . However, on each axis one block of the same size on that axis . Each sale should be large enough to permit analysis – and small enough to permit the graphing of all available data and anticipated data estimates.

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Units Produced

Cost

Step 2. Plot the available cost – volume data: Find the volume given for one of the data points on the horizontal axis. Draw an imaginary vertical line from that point . Find the related cost on the vertical axis and draw an imaginary horizontal line from that point . The point where the two lines intersect represents the cost for the given volume .(If you not feel comfortable with imaginary lines you may draw dotted lines to locate the intersection .) Repeat this step for each data point .

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Step 3. Fit a straight line to the data : In this section of text, all data points will fall on a straight line . All that you have to do to fit a straight line is connect the data points . Most analysts use regression analysis to fit a straight line when all points do not fall on the line.

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Step 4. Estimate the cost for a given volume : draw an imaginary vertical line from the given volume to the point where it intersects the straight line that you fit to the data points . Then move horizontally until you intersect the cost for the given volume of he item.

From the graph , you can estimate that the total cost of 400 units will be Rs.150.

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Fixed CostLine

Variable CostLine

Break even Point

Cost

Units Produced

Graphic representation of Break Even Point

Breakeven Point

The breakeven point can be defined as the point at which sales revenue is adequate to cover all costs to manufacture and sell the product, but no profit is earned

Operating income = (Selling price-Variable cost per unit) × Quantity -Total fixed costs =0

(Selling price-Variable cost per unit) × Quantity = Total fixed costs

Breakeven number of units ＝ Fixed costs (Selling price-Variable cost per unit)

= Fixed CostContribution margin per unit

Breakeven revenues ＝ Fixed costs (Profit-volume ratio)Contribution margin %

Breakeven point in Contribution margin per unitterms of revenues Selling Price

The relationship between contribution margin and sales in percentage terms

= 1 －(Variable cost per unit / selling price)

Quantity of output units = Fixed costs +Target operating incomerequired to be sold Contribution margin per unit

Example:

Selling price = 8% × Rs. 1,000 = Rs. 80 per ticketVariable cost per unit = Rs. 35 per ticketContribution margin per unit = Rs.80 –Rs.35 = Rs.45 per ticketFixed costs = Rs. 22,000 a month

Answer:

Breakeven (units) ＝ Fixed costs ＝ 22,000 ＝489 ticketsContribution margin per unit 45

Quantity of output units requiredto be sold ＝ (22,000＋10,000) ＝712 tickets

45

Example

1.a Operating income = [Units sold (Selling price –Variable costs)] –Fixed costs

[5,000,000 (Rs.0.50 –Rs.0.30)] –Rs. 900,000 = Rs.100,000

1.b Breakeven units = Fixed costs ÷ Contribution margin per unit

Rs.900,000 ÷[(Rs.0.50 –Rs.0.30)] = 4,500,000 units

Breakeven revenues = Breakeven units ×Selling price4,500,000 units × Rs.0.50 per unit = Rs.2,250,000

Breakeven revenues= Fixed costs ÷ Contribution margin ratio (0.5-0.3) ÷ 0.5＝ 0.4

Rs.900,000 ÷ 0.40 = Rs. 2,250,000

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

Target Operating income ＝ (Target Net income)

(1－Tax rate)

Quantity of output units = Fixed Cost ＝ (Target Net income)

required to be sold (1－Tax rate)

Contribution margin per unit

Margin of Safety

The margin of safety (MOS) is the difference between the total sales and the breakeven sales. It may be expressed in monetary terms or as a percentage ie. The margin of safety in relation to total sales. It indicates the amount that sales can decrease before the company will suffer a loss. It is an extremely valuable guide for the management to check the strength of business.

Margin of safety ＝ Actual Sales －Breakeven sales

Margin of Safety in Rupees = ProfitP/V ratio

Margin of Safety in Units = Profit Contribution per unit

Example

Current Sales are 20000 units paSelling Price Rs. 6 per unitPrime Cost Rs. 3 per unitVariable overheads Rs. 1 per unit

Fixed Cost Rs. 30,000Answer

Margin of Safety StatementOutput 20000

unitsPer Unit

Total

Sales 6 120,000Less: Marginal CostPrime cost 3Variable cost 1 80,000

4Contribution 2 40,000Less Fixed Cost 30,000Profit 10,000

P/V ratio = Contribution x 100 = 40,000 x 100 = 33.33% Sales 1,20,000

BEP = Fixed cost = 30,000 x 100 = 90,000 P/V Ratio 33.33

BEP in Units Fixed Cost = 30,000 = 15,000 units Cost per unit 2

Margin of Safety = Actual sales – BEP

1,20,000 – 90,000 = Rs. 30,000

OR

Margin of Safety = Profit = 10,000 x 100 = Rs.30,000 P/V ratio 33.33