Theory of Cost and Break Even Analysis

Introduction

• We have discussed the input-output relations in terms of physical quantities of input and output. However, business decisions are generally taken on the basis of money values of the inputs and outputs. Inputs multiplied by their respective prices and added together give the money value of the inputs, i.e., the cost of production.

• The cost of production is an important in almost all business analysis and business decision-making, pertaining to a) locating the weak point in production management b) minimizing the cost c) finding the optimum level of output d) determining price and dealers, margin; and e) estimating or projecting the cost of business operation.

Cost Concepts

• The cost concepts that are relevant to business operations and decisions can be grouped on the basis of their nature and purpose under two overlapping categories (i) cost concepts used for accounting purposes and (ii) analytical cost concepts used in economic analysis of business activities.

Accounting Costs• Opportunity Cost : The opportunity cost is the opportunity lost. An

opportunity to make income is lost because of scarcity of resources. Income maximizing resource owners put their scarce resources to their most productive use and thus they forego the income expected from the second best use of the resources. Thus, opportunity cost may be defined as the expected returns from the second best use of the resources that are foregone due to the scarcity of resources. It is also called alternative cost.

• Business Cost and Full costs: Business costs include all the expenses that are incurred to carry out a business. The concept of business costs is similar to the actual or real costs. Business costs “include all the payments and contractual obligations made by the firm together with the book cost of depreciation on plant and equipment”. They are used for calculating business profits and losses and for filing returns for income-tax and also for legal purpose.

• The concept of full cost, includes business costs, opportunity costs and normal profit. Normal profit is a necessary minimum earning in addition to the opportunity cost, which a firm must receive to remain in its present occupation.

Accounting Costs• Actual or Explicit Costs : The actual or Explicit costs are those which are

actually incurred by the firm in payment for labour, material, plant and building, machinery, equipment, travelling and transport, advertisement, etc. The total money expenses, recorded in the books of accounts are, for all practical purpose, the actual costs.

• Implicit Costs: In contrast to explicit costs, there are certain other costs that do not take the form of cash outlays, nor do they appear in the accounting system. Such costs are known as implicit or imputed costs. e.g. opportunity cost.

• Implicit cost are not taken into account while calculating the loss or gains of the business, but they form an important consideration in deciding whether or not to retain a factor in its present use. The explicit and implicit costs together make the economic cost.

Accounting Costs

• Out-of-pocket and Book Costs:The items of expenditure that involve cash payments or cash transfers, both recurring and non-recurring, are known as out-of-pocket costs. All the explicit costs (e.g., wages, rent, interest, cost of materials and maintenance, transport expenditure, electricity and telephone expenses, etc.) fall in this category.

• On the contrary there are certain actual business costs that do not involve cash payments, but a provision is therefore made in the books of account and they are taken into account while finalizing the profit and loss account. Such expenses are known as book costs.

Analytical Cost

• Fixed and Variable Costs: Fixed costs are those that are fixed in volume for a certain quantity of output. In other words, costs that do not vary or are fixed for a certain level of output are known as fixed costs.

• The fixed costs include (i) costs of managerial and administrative staff (ii) depreciation of machinery, building and other fixed assets (iii) maintenance of land etc.

• Variable costs are those which vary with the variation in the total output. It includes cost of raw material, running cost of fixed capital, such as fuel, repairs, routine maintenance expenditure, direct labour wages associated with the level of output and the costs of all other inputs that vary with output.

Analytical Cost

• Total, Average and Marginal Costs: Total cost is the total actual cost incurred on the production of goods and services. It refers to the total outlays of money expenditure both explicit and implicit, on the resources used to produce a given level of output. It includes both fixed and variable costs.

• Average Cost is of statistical nature- it is not actual cost. It is obtained by dividing the total cost by the total output. TC/Q

• Marginal Cost is defined as the addition to the total cost on account of producing one additional unit of the product. MC = TCn – TCn-1

Analytical Cost• Short-run and Long-run Costs: Short-run and long-run cost concepts are

related to variable and fixed costs, respectively.• Short run costs are those that have a short-run implication in the process

of production. Such costs are made once e.g., payment of wages, cost of raw materials etc. From analytical point of view, short run costs are those that vary with the variation in output, the size of the firm remaining the same. Therefore short run costs are treated as variable costs.

• Long run costs are those that have long-run implications in the process of production, i.e., they are used over a long range of output. The costs that are incurred on the fixed factors like plant, building, machinery are known as long-run costs.

• Broadly speaking, ‘the short run costs are those associated with variables in the utilization of fixed plant or other facilities whereas long-run costs are associated with the changes in the size and kind of plant.

Analytical Cost

• Incremental Costs : Incremental costs are closely related to the concept of marginal cost but with a relatively wider connotation. Incremental cost refers to the total additional cost associated with the decisions to expand the output or to add a new variety of product. When firm expands its operations it has to incurred additional costs which is incremental cost.

• Sunk Costs : The sunk costs are those which are made once and for all and cannot be altered, increased or decreased, by varying the rate of output, nor they can be recovered.

Analytical Cost

• Historical Cost & Replacement Cost: Refers to the cost incurred in past on the acquisition of productive assets, e.g. land, building, machinery etc., whereas replacement cost refers to the outlay that has to be made for replacing an old asset.

• The concepts are of significance for the unstable nature of price behavior.

• Historical cost of asset is used for accounting purpose, in the assessment of the net worth of the firm. The replacement cost figures in business decisions regarding renovation of the firm.

Analytical Cost

• Private and Social Costs : The cost concepts that are related to the working of the firm and that are used in the cost-benefit analysis of business decisions. Such costs fall in the category of private costs.

• There are other costs that arise due to the functioning of the firm but do not normally figure in the business decisions and not borne by the firms. Such costs are known as Social Costs. E.g water / air pollution, rivers, lakes, public utility services like roadways, drainage system etc.

COSTS IN THE SHOR RUN

• Fixed Costs : These are costs that do not vary with output. Before a firm actually starts producing, it needs to spend on plant, machinery, fittings, equipments, etc., in fact the firm has to bear these costs even if there is no output. These represent fixed costs. Since such costs do not vary with the level of output, any decision regarding volume of output does not depend upon fixed cost. Hence these are also referred to as subsidiary costs. The shape of the Total Fixed Cost (TFC) is a straight line from the origin, parallel to the quantity axis, indicating that output may increase to any level without causing any change in the fixed cost.

Cost Curves for a Firm

Output

Cost(Rs per

year)

100

200

300

400

0 1 2 3 4 5 6 7 8 9 10 11 12 13

VC

Variable costincreases with production and

the rate varies withincreasing &

decreasing returns.

TC

Total costis the vertical

sum of FC and VC.

FC50

Fixed cost does notvary with output

COSTS IN THE SHOR RUN• Variable Costs: These are the costs that vary with output and are

incurred in getting more and more inputs; variable costs are equal to zero if there is no output.

• TVC curve should be a straight line, but TVS is an inverse S shaped upward sloping curve, starting from origin. This shape is determined by the law of variable proportions.

• This leads to fall in per unit cost in the beginning; if the variable input is increased beyond a certain level, its marginal productivity starts diminishing. Hence, TVC increases at an increasing rate.

• Slope of the TVC curve is less steep in the beginning; as we increase the variable input, with the other input fixed, productivity of the variable input fall because of diminishing rate of technical marginal substitution between two inputs. Hence it is steeper on the upper side.

COSTS IN THE SHOR RUN• Average and Marginal Cost Functions: Average Cost is cost per

unit of output; One can derive Average Fixed Cost AFC, Average Variable Cost AVC and Average Cost AC from total fixed, total variable and total costs respectively. AFC is fixed cost per unit of output and is thus equal to the ratio of TFC and units of output; AC is total cost per unit of output and is thus equal to the ratio of TVC and units of output; AC is total cost per unit of output and is thus equal to the ratio of TC and units of output.

• Marginal Cost is the change in total cost due to a unit change in output. Since the fixed component of cost cannot be altered, MC is virtually the change in variables cost per unit change in output. Therefore it is also known as rate of change in total cost.

COSTS IN THE SHOR RUN• Average and Marginal Cost Curves: AFC can be plotted as a

rectangular hyperbola, asymptotic to the axes. As the number of units of output is increased, Fixed Cost remaining the same, AFC falls steeply at first and then gently.

• AVC curve and the AC curve are both U shaped. This can be explained with the law of variable proportions. Costs decline when there are increasing returns, stabilise with constant returns and increase with diminishing returns.

• AC being the sum of AFC and AVC at each level of output lies above both AFC and AVC curves in. The AC curve is U shaped; initially AC falls with increase in output, reaches a minimum, and then increases.

• When both AFC and AVC fall, AC also falls. AVC soon reaches a minimum and starts rising, while AFC continues to fall.

A Firm’s Short Run Costs

Cost Curves

0 120

20

40

60

80

100

120

Output (units/yr)

Co

st

($/u

nit

) MC

ATC

AVC

AFC

COSTS IN LONG RUN

• All costs are variable in the long run since factors of production, size of plant, machinery and technology are all variable. This in turn implies radical changes in the cost structure of the firm.

• The long run cost function is often referred to as the ‘planning cost function’ and the long run average cost LAC curve is known as ‘planning curve’. As all costs are variable, only the average cost curve is relevant to the firm’s decision making process in the long run.

• The long run consists of many short runs, e.g., a week consists of seven days and a month consists of four weeks and so on. Therefore the long run cost curve is the composite of many short run cost curves.

COSTS IN LONG RUN• Long Run Average Cost: When the plant size and other fixed inputs of the firm

increase in the long run, the short run cost curves shift to the right. • In the long run, the firm operates with different plant sizes and can switch over

to a different plant size, depending on cost considerations. • Thus SAC1 relates to average cost of the firm when its plant size is, say I; when

plant size increases to II, the corresponding SAC curve is SAC2 and so on.• As output increases from a to b in the short run, the firm can continue to

produce along SAC1, utilising its installed capacity of I. Further ahead, at an output level of a, this capacity is overworked.

• Hence, it would be cost effective for the firm to shift to a higher plant size, say II, thus switching over from SAC1 to SAC2. This shift would lower the average cost of the firm.

COSTS IN LONG RUN

COSTS IN LONG RUN• A firm may have multiple alternate plant sizes. So it may have multiple

SACs corresponding to different plant sizes..• LAC function is an envelope of the short run cost function and the LAC

curve envelopes the SAC curves; hence the LAC curve is also known as “envelop curve”.

CONCEPTS OF REVENUE• Total Revenue : TR is the total amount of money received by a firm from

goods sold ( or services provided ) during a certain time period. TR = Q . P

• Average Revenue : AR is the revenue earned per unit of output sold. It is equal to the ratio of TR and output. That means AR is nothing but price.

AR = TR/Q = Q.P / Q = P• Marginal Revenue : MR is the revenue a firm gains in producing one

additional unit of a commodity. It is calculated by determining the difference between the total revenues earned before and after a unit increase in production.

MR = TRq – TRq-1• MR is the slope of TR. When TR is maximum when MR is zero and beyond

which MR becomes negative.• Chart related to Revenue curves

Rules of Profit Maximization• The profit function shows a range of outputs at which the firm

makes positive or supernormal profits. Economists differentiate between normal profit and supernormal profit.

• Normal profit is that amount of return to the entrepreneur which must be earned to keep him/her in that business activity. Anything over and above this is supernormal profit.

• In other words, normal profit is a part of total cost and supernormal profit is the accounting profit that occurs when TR>TC.

• A firm maximizes profit at the point where MR equals MC.• Under the assumption of rationality a firm will continue to produce

till MR is greater than MC and will stop production only when MR is just equal to MC.

Break Even Analysis

• Break Even Analysis examines the relation between total revenue, total costs and total profits of a firm at different levels of output.

• Break Even point is the point where total cost just equals the total revenue; it is the no profit no loss point.

• BE Analysis is about determining profit at various projected levels of sales, identifying the break even point and making a managerial decision regarding the relationship between likely sales, and the breakeven point.

Break Even Analysis : Graphical Method

• Under graphical method the breakeven chart is constructed by plotting firm’s total revenue and total cost on the vertical axes and output on the horizontal axis.

• Break even chart assumes constant AVC for a given range of output. Hence, a firm’s total cost function is given as a straight line.

• The chart would be helpful to find out Breakeven point.• It would also throw light on the profit or loss resulting from

each level of sales by the firm. It can provide valuable information on projected effect of output on costs and profits and firm can ascertain the volume of sales it would need to breakeven.

Break Even Analysis : Graphical Method

• To draw a break even chart following steps need to be followed:• Label the vertical axis ‘revenue and costs in rupees’ and the

horizontal axes ‘output/production units’.• Assuming constant price, plot at least two points from the revenue

data and draw the upward moving TR line starting from the origin.• Draw a horizontal line for total fixed costs starting at the point on

the vertical axis at the level of fixed costs• At the same point on the horizontal axes draw the total costs line.• The point where the revenue line crosses the total costs line is the

break even point.• The gap between the total costs line and revenue line beyond the

breakeven point represents the level of profit or loss.

Break Even Analysis : Graphical Method

• chart

• Super Computers Ltd. Sells personal computers, laptops and peripherals. The following information (in Rs. Crores) was obtained from the chief Accountant of Super at the end of March 2006. It was also assumed that wages are fixed cost, since the company did not lay off any worker and also that 20% of the overheads are variable. Consider yourself to be a managerial economist and analyse the information, especially the BEP.

PCs Laptops PeripheralsSales 2,500,000 600, 000 120,000Materials 2,300,000 300,000 100,000Wages 55,000 300,000 60,000Overheads 50,000 50,000 20,000Profit/Loss 95,000 50,000 60,000

• From the assumptions, the modified information is presented in below table:

PCs Laptops PeripheralsSales 2,500,000 600, 000 120,000Variable cost2,310,000 310,000 104,000Contribution 1,90,000 290,000 16,000Fixed Cost 95,000 340,000 76,000Profit/Loss 95,000 -50,000 -60,000PV Ratio 0.076 0.483 0.133BEP 1,250,000 704,000 570,000Contribution = Sales – Variable CostPV ratio = Contribution / Sales

BEP = FC / PV Ratio

Break Even Analysis : PV Ratio

• Profit volume ratio is the ratio of contribution margin and sales. It is also defined as the ratio of marginal change in profit and marginal change in sales.

• PV Ratio = Contribution / Sales• Using PV Ratio also, we can calculate BEP as:

BEP = FC / PV Ratio

Economies of Scale• “Economies” refer to lower costs; hence economies of

scale would mean lowering of costs of production by way of producing in bulk.

• Economies of scale refers to the efficiencies associated with large scale operations; it is a situation in which the long run average costs of producing a good or service decrease with increase in the level of output.

• Firms are often concerned about a minimum efficient level of production, which is nothing but the amount of production that spreads setup costs sufficiently for firms to undertake production profitably.

Economies of Scale• There are two types of economies of scale: Internal

economies (in which cost per unit depends upon the size of firm)External economies (in which cost per unit depends upon the size of industry)

• Internal Economies:• Specialization• Greater efficiency of machines• Managerial Economies• Financial Economies• Production in stages

Economies of Scale• External Economies: As an industry grows in size, it would create

various economies for the firms in the industry.• Technological advancement• Easier access to cheaper raw materials• Financial institutions in proximity• Pool of skilled workers• Diseconomies of Scale : Refers to decrease in productivity when

there are equal increases of all inputs, assuming that no input is fixed.

• If some cost of a business rises with an increase in size by a greater proportion than the increase in size of operations, it is known as a diseconomy of scale.

Economies of Scale

• Diseconomies may arise if the size of operations becomes unwieldy by size; coordination among different work groups and units may become complex; too much specialization may lead to boredom and monotony among workers; management may become less effective and thus indirectly impose costs.

• Economies of scope refer to a situation in which average costs of manufacturing a product are lowered when two complementary products are produced by a single firm, than when they are produced separately.

• It is applicable to firms that produce more than one product and obtain production or cost advantages.

Learning Curves• LAC declines as the scale of production increases to a certain level and

beyond this level of production, LAC begins to rise. Economies of scale provide the reasoning why LAC decreases with increasing scale of production and diseconomies of scale provide reason for increase in LAC beyond minimum point.

• Economists and business analysts have discovered another factor that causes a continuous decrease in average cost of production over a large scale of production. The factor is called learning by doing or learning by experience.

• Firms engaged in the production of a commodity or service over a long period of time gain experience. They learn by performing the same activity repeatedly.

• Along with that factors like technological know-how, mgnt style, organizational behaviour help firms in getting work done at least cost.

Learning Curves

• Thus, firm’s average cost of production continues to fall with increase in production, though the rate of fall in average cost goes on declining. The curve that represents the declining trend in long-run average cost of production is called the learning curve.

Learning Curves• The learning curve is widely used by business

managers, economists and engineers to foresee the possible trend in long run average cost of production and plan production accordingly.

• Learning curve is different from the conventional LAC curve. While LAC give the average cost of plant-wise production, learning curve gives the average cost of cumulative output, i.e., the total output right from the beginning of production of a commodity or service.