8 – Cost Analysis

Introduction

An important factor in making decisions is the cost that a company incurs when producing its goods and services. Total cost plus total revenue are the two factors that determine a company’s profit level. A company strives to increase revenue while decreasing costs to maximise profits. Managers strive to produce optimal levels of output, use the lowest-cost combination of production factors, increase factor productivity, and improve organisational efficiency.

8.1 Cost Concepts

Costs are very important in managerial decisions that involve choosing between alternative courses of action. It aids in the quantitative specification of various alternatives. The type of cost to be used in a specific situation is determined by the business decisions to be made. Costs factor into almost every business decision, and it is critical to conduct a proper cost analysis. As a result, it is critical to comprehend what these various cost concepts are, as well as how they can be defined and operationalized. This necessitates an understanding of two concepts: (i) that conventional financial accounting cost estimates are not appropriate for all managerial uses, and

(ii) that different business problems necessitate different types of costs.

Future and Past Costs

All business decisions must consider the future. Future costs are time-adjusted past or present costs that are reasonably expected to be incurred in some future period. Their actual incurrence is a projection, and their management is a guess. Past costs are actual expenses incurred in the past and are always included in income statements. Their measurement is primarily a record-keeping activity.

Sunk and Incremental Costs

Incremental costs are defined as the change in overall costs caused by specific decisions. Fixed and variable costs can both be included in incremental costs. In the short term, incremental costs will consist of variable costs—costs of additional labour, additional raw materials, power, fuel, and so on—incurred as a result of the firm’s new decision. Because these costs can be avoided by not changing the activity, they are also known as avoidable costs or escapable costs. They are also referred to as differential costs.

Sunk costs are those that are unaffected or altered by changes in the level or nature of business activity. Whatever the level of activity, it will remain the same.

Example: The most common type of sunk cost is the amortisation of past expenses, such as depreciation.

Out-of-Pocket and Book Costs

Out-of-pocket costs are those that require immediate payments to third parties, as opposed to book costs, which do not necessitate immediate cash expenditure.

Wages and salaries paid to employees, for example, are out-of-pocket expenses, whereas the owner’s salary is not.

It is a book cost if not paid. Other examples of book costs include the interest cost of the owner’s fund and the cost of depreciation. By selling assets and leasing them back from the buyer, book costs can be converted into out-of-pocket costs.

Historical and Replacement Costs

The historical cost of an asset is the cost of plant, equipment, and materials at the original purchase price, whereas the replacement cost is the cost that the firm would have to incur if it wanted to replace or acquire the same asset now.

For example, if the price of bronze at the time of purchase, say, in 1974, was 15 per kg and the current price is 18 per kg, the original cost of 15 is the historical cost and the current price of 18 is the replacement cost. The price that would have to be paid today to acquire the same plant is referred to as the replacement cost.

Explicit Costs and Implicit or Imputed Costs (Accounting Concept of Cost and
Economic Concept of Cost)

Explicit costs are those expenses that are actually paid for by the company (paid-out costs). These expenses are recorded in the firm’s accounting records. Implicit costs, on the other hand, are theoretical costs in the sense that they are not recognised by the accounting system. These costs can be defined as the earnings from the employed resources that belong to the owner.

Actual costs and opportunity costs

Actual costs are the actual expenses incurred in the acquisition or production of a good or service. These are the costs that are generally recorded in books of account, such as actual wages paid, materials purchased, interest paid, and so on.

Direct (or Separable or Traceable) Costs and Indirect (or Common or Non-traceable) Costs

Some costs are directly related to the production of a single unit of a given product. These are direct costs that can be easily separated, calculated, and assigned to a unit of output. This is because these costs vary depending on the output units. Other costs, however, cannot be separated and attributed to individual units of production. As a result, these costs are classified as indirect costs in the accounting process.

Shut-down and Abandonment Costs

Shut-down costs must be incurred when production operations are suspended and are not required if production operations continue. When a plant is permanently shut down, some costs must be incurred to dispose of the fixed assets. These are known as abandonment costs.

Private and Social Costs

Economic costs can be calculated at two different levels: micro and macro. The micro-level economic costs are related to the operation of a firm as a production unit, whereas the macro-level economic costs are those generated by the firm’s decisions but borne by society rather than the firm. Private costs are those that a person or business actually pays for or incurs during the course of its operations. The social cost, on the other hand, is the total cost to society of producing a good. As a result, the economic costs include both private and public costs.

8.2 Fixed and Variable Costs

Some inputs or factors can be adjusted in response to changes in output level. As a result, if a company needs to increase output, it can easily hire more workers. Similarly, if it needs to expand production, it can obtain and use more raw materials and chemicals with little delay. Thus, labour, raw materials, and chemicals are the factors that can be easily changed as output changes. These are known as variable factors. On the other hand, some factors, such as capital equipment, buildings, and top management personnel, cannot be easily changed—it takes a long time to make changes to them. Fixed factors are factors that cannot be easily changed and take a long time to adjust. Examples include capital equipment and buildings. As a result, fixed costs are those that are independent of output, i.e., they do not change as output changes. Regardless of whether the output is small or large, a firm must pay these “fixed” costs in the short term. Fixed costs, also known as overhead costs, include contractual rent, insurance fees, maintenance costs, property taxes, interest on capital invested, and minimum administrative expenses such as manager’s salary, watchman’s wages, and so on. Thus, fixed costs are those incurred in hiring the fixed factors of production, the amount of which cannot be changed in the short run.

Variable costs, on the other hand, are those incurred as a result of the use of variable factors of production, the amount of which can be changed in the short run. As a result, in the short run, the total variable costs vary with changes in output. These costs include payments such as labour wages, the cost of raw materials, fuel and power used, transportation expenses, and so on. Variable costs are also referred to as prime costs. A company’s total cost is the sum of its total variable and total fixed costs. As a result, TC = TFC+TVC.

Figure depicts output on the X-axis and cost on the Y-axis. The total fixed cost curve (TFC) is parallel to the X-axis because the total fixed cost remains constant regardless of output level. This curve begins on the Y-axis, implying that the total fixed cost will be incurred even if the output is zero. The total variable cost curve (TVC), on the other hand, rises upward, indicating that as output increases, so do total variable costs. The total variable cost (TVC) begins at zero, indicating that when output is zero, variable costs are also zero. It should be noted that total cost is proportional to total output; the higher the output, the higher the total cost. TC = f(q)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Because total cost is a sum of total fixed cost and total variable cost, the total cost curve (TC) was obtained by adding the total fixed cost curve and total variable cost curve ‘vertically.’ Because there is a similar vertical distance between the two curves, the total cost curve (TC) and the total variable cost curve (TVC) have the same shape.

8.3 Short Run and Long Run Costs

The short run is a time period during which output can be increased or decreased by changing only the number of variable factors such as labour, raw materials, chemicals, and so on. In the short term, the company cannot build a new plant or close an old one. If the company wants to increase output in the short run, it can only do so by employing more workers and purchasing more raw materials. It cannot increase output in the short run by expanding the capacity of its existing plant or constructing a new plant with a larger capacity. The long run, on the other hand, is defined as the period of time during which all factors’ quantities can be varied. Because all factors are variable in the long run, the dichotomy of fixed and variable factors holds only in the short run. In other words, it is the time period during which all adjustments and changes are possible.

Short-run costs are those that vary with the degree of plant utilisation and other fixed factors. In other words, these costs are related to output variation given plant capacity. Short-run costs are thus classified into two types: fixed costs and variable costs. Fixed costs remain constant in the short run, while variable costs fluctuate with output. Long-run costs, on the other hand, can vary with the size of the plant and other facilities that are normally regarded as fixed in the short run. There are no fixed inputs and thus no fixed costs in the long run, implying that all costs are variable.

8.3.1 Average Costs and Output in the Short Run

8.3.2 Short Run Marginal Cost (MC) and Output

The marginal cost is the cost added to the total cost of producing one more unit of output. In other words, marginal cost is the cost of producing n units rather than n-1 units added to the total cost.

MC_n is equal to TC_n–TC_n–1.

In symbols, marginal cost is defined as the rate of change in total cost in relation to a unit change in output, i.e., MC= d(TC)/dQ, where d in the numerator and denominator represents the change in TC and Q, respectively.

It is important to note that the marginal cost is independent of the fixed cost. Because fixed costs do not change with output, when output increases in the short run, there are no marginal fixed costs. In the short run, only the variable costs vary with output. As a result, marginal costs are caused by changes in variable costs.

MC = d(TVC/dQ)

The marginal cost’s independence from the fixed cost can be demonstrated algebraically as follows:

MC_n = TC_n – TC_n–1 = (TVC_n + TFC) – (TVC_n–1 + TFC) = TVC_n + TFC – TVC_n–1 – TFC = TVC_n – TVC_n–1 – TFC = TVC_n – TVC_n–1

As a result, marginal cost is the addition to total variable costs when output is increased from n-1 to n units. As a result, the marginal cost is independent of the amount of fixed costs.

The slope of the TC curve is denoted by MC in Table 8.1. Because the TC curve rises at first at a decreasing rate and then at an increasing rate, the MC curve will also first decline and then rise.

The benefit of TC is that it calculates the firm’s break-even profit.

AC has the advantage of calculating a firm’s per unit profit.

The benefit of MC is that it allows a company to determine whether or not it needs to expand.

The laws that govern costs are the same as the laws that govern productivity. In the short run, increasing output can only be accomplished by increasing the variable input. However, as more variable inputs are added to a fixed input, the law of diminishing marginal productivity kicks in. Productivity, both marginal and average, is declining.

8.3.3 Costs in the Long Run

The long run is a time period in which the firm can vary all of its inputs. None of the factors are fixed, and they can all be changed to increase output. Long run is a period of time long enough to allow changes in the plant, such as capital equipment, machinery, land, and so on, to expand or contract output. The long run cost of production is the lowest possible cost of producing any given level of output when all inputs, including plant size, are variable. There is no fixed factor of production and thus no fixed cost in the long run.

If Q = f(L, K), then TC = L.PL + K.PK.

Given factor prices and a specific production function, one can draw an expansion path that minimises the costs associated with various levels of output, yielding the long run total cost schedule/curve. LTC grows as a function of output. Unless the qualitative relationship is quantified, the rates of change in these two variables are unknown. If one recalls the concept of returns to scale and assumes fixed factor prices, three things can be seen:

1. When returns to scale increase, inputs increase less than output increases in proportion. As a result, total cost must increase less than in proportion to output. Figure depicts this relationship (a).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2. When returns to scale are decreasing, total cost rises faster than output. Figure depicts this relationship (b).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

3. When the returns to scale are constant, total cost and output both move in the same direction and the same proportion. Figure depicts this as well (c).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Thus, given factor prices, there will be a relationship between LTC and output, depending on the nature of returns to scale. Most industries and firms experience increasing returns to scale at first, followed by constant returns to scale, which eventually give way to decreasing returns to scale. As shown in Figure, the long run total cost function would first increase at a decreasing rate and then increase at an increasing rate. A U-shaped long run average cost function would be associated with such a total cost function.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Q	LTC	LAC	LMC
0	0	–	–
5	25	5.00	5
10	45	4.50	4
15	60	4.00	3
20	85	4.25	5
25	120	4.85	7
30	180	6.00	12

When all production factors are variable, the LTC curve gives the lowest total cost for various levels of output. Its shape is such that, when viewed from the output axis, the curve is first concave and then convex. As seen above, its shape is determined by the operations of the varying degrees of scale returns given the factor prices.

The relationship between LAC and LMC is derived from the LTC curve. LAC and LMC are both U-shaped. Furthermore, the following relationships are valid:

1. LMC takes the smallest value at the point of inflection on the LTC curve (A).

2. At the point of kink in the LTC curve (B), where the slope of the straight line from the origin to the LTC curve is the smallest, LAC takes the smallest value.

3. When LMC = LAC, LAC is the smallest.

4. When LMC LAC, the LAC curve falls.

5. When LMC > LAC, the LAC curve rises.

8.4 Total Cost, Average Cost and Marginal Cost

1. Total Cost (TC):

Definition: Total Cost is the overall expense incurred by a firm in producing a given quantity of output. It comprises both fixed costs (costs that do not vary with the level of output) and variable costs (costs that change with the level of output).

Formula:

TC: Total Cost

TFC: Total Fixed Cost

TVC: Total Variable Cost

Example: If a bakery has a fixed cost of $1,000 (rent, insurance) and variable cost of $2 per cake (flour, labor), the total cost to produce 100 cakes would be $TC=1,000+(2\times 100)=1,200$.

Average Cost (AC) or Average Total Cost (ATC):

Definition: Average Cost is the cost per unit of output and is calculated by dividing the total cost by the quantity of output produced.

Formula:

$\mathrm{AC}=\frac{\mathrm{TC}}{Q}$

where:

AC: Average Cost

TC: Total Cost

Q: Quantity of Output

Example: Using the previous example, if the bakery produces 100 cakes, the average cost per cake would be

$\mathrm{AC}=\frac{1,200}{100}=12$

dollars.

Marginal Cost (MC):

Definition: Marginal Cost is the additional cost incurred by producing one more unit of output. It helps determine the impact on total cost when the level of production changes by one unit.

Formula:

$\mathrm{MC}=\frac{\mathrm{\Delta }\mathrm{TC}}{\mathrm{\Delta }Q}$

​ where:

MC: Marginal Cost

ΔTC: Change in Total Cost

ΔQ: Change in Quantity of Output

Example: If producing the 101st cake increases the total cost to $1,220, the marginal cost of the 101st cake is MC

$=\frac{1,220-1,200}{101-100}=20$

dollars.

In summary, Total Cost is the overall expense, Average Cost is the cost per unit, and Marginal Cost is the additional cost of producing one more unit. Each serves a crucial role in understanding a firm’s production and cost structure.

In the long run, a larger plant will result in lower per-unit costs. However, after a certain point, larger plants will result in higher average costs. Why the long run ATC curve is U-shaped requires more explanation.

It should be noted, first and foremost, that the law of diminishing returns does not apply here because it assumes that one resource is fixed in supply and that resource prices are variable in the long run. In addition, we assume that in the short run, resource prices are constant. Thus, the U-shaped long run average cost curve can be explained in terms of large-scale production “economies and diseconomies.”

The behaviour of the average cost curve as the plant size is increased is the subject of economies and diseconomies of scale. The down sloping portion of the long run AC curve is explained by economies of scale. LAC typically decreases over some range of output as the size of the plant increases for a variety of reasons. The most important is that as the scale of output grows, the potential for specialisation of productive factors grows. This is most noticeable in terms of labour, but it may also apply to other factors. Other factors that contribute to declining LAC include the ability to use more advanced technologies and sophisticated capital equipment, managerial specialisation, the ability to take advantage of lower costs for some inputs by purchasing larger quantities, effective by-product utilisation, and so on.

However, after a while, increasing a firm’s output may result in diseconomies and, as a result, a higher per unit cost. Further expansion of output beyond a reasonable level may result in issues such as overcrowding of labour, managerial inefficiencies, and so on, raising per unit cost.

These are all illustrations of internal economies and scale diseconomies brought about by the firm’s own growth. External economies and diseconomies of scale, according to Marshall, may arise as a result of industry’s overall expansion.

For example, improved infrastructure facilities as a result of industrial expansion may result in lower per-unit production costs across all firms in an industry.

8.6 Economies of Scope

According to the concept of economies of scale, cost advantages result from an increase in production volume, also known as the scale of output. Such cost advantages may result from a variety of output–product diversification within the given scale of plant, according to the concept of economies of scope. If the same plant can produce multiple products, there is the potential for significant cost savings due to the shared use of inputs. Product diversification allows manufacturers to take advantage of scope economies through broad banding policy.

For example, Escorts manufactures four-wheelers from the same plant that manufactures two-wheelers with minor modifications.

Instead of increasing the scale of production of an existing product, the company can now add new and newer products if the plant’s size and type allow for this. Firms will benefit from scope economies rather than scale economies as a result of this process. In certain processes, the firm can wisely plan to exploit both types of economies at the same time.

8.7 Types of Revenue Curves and their Applications

In the previous unit, we discussed the shapes of the revenue curves. We’ll define the terms again just to refresh your memory.

Total revenue (TR) is the total amount of money received from the sale of any given quantity of output over a given time period. (TR= P Q, where P is the unit price and Q is the total number of units sold)

Average revenue (AR) is calculated by dividing total sales receipts by the number of units sold, i.e., AR= TR/Q. It is very important in determining a company’s profit. A company’s ‘per unit profit’ is calculated by dividing average revenue by average (total) cost. In general, a firm seeks to maximise profit by producing the greatest amount of output possible. (We’ll go over this in more detail in later units.)

The revenue associated with one additional unit of production is referred to as marginal revenue. MR_n = TR_n-TR_n-1 is the formula for calculating marginal revenue.

Analysis of Break-even Points

Many of the planning activities that occur within a company are based on the expected level of output. Cost-volume profit analysis, also known as break-even analysis, is the study of the interrelationship between a firm’s sales, costs, and operating profits at various output levels. Business executives frequently use this analysis to determine the sales volume required to break even as well as total profits and losses at various output levels. To demonstrate the breakeven analysis. As shown in Figure, it is assumed that the cost and revenue curves are non-linear. Total revenue is calculated by multiplying the number of units of output sold by the price per unit. The concave shape of the revenue curve implies that the firm can only sell more units of output by lowering the price. The total cost curve is based on the traditional approach of a short-run relationship between cost and output.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

At any level of output, the difference between total revenue and total cost represents the total profit or loss that will be realised. The vertical distance between the total revenue (TR) and total cost (TC) curves gives the total profit (TP) at any level of output. When total revenue equals total cost, a break-even situation (zero profit) occurs. The breakeven condition is shown in Figure at two different output levels, Y1 and Y3. TR TC will cause Y1 losses below a certain output level. Profits will be obtained between Y1 and Y3 because TR > TC. When the output level exceeds Y3, losses will occur again because of TR TC. Total profit is maximised between Y1 and Y3, where the vertical distance between the TR and TC curves is greatest, corresponding to an output level of Y2.

The non-linear revenue output and cost output relationship of economic theory is generally replaced by linear functions for practical decision making. Figure  depicts a breakeven analysis based on a linear function.

Break-even Analysis by using Linear TC and TR Curves

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

TR is a straight line in this case, assuming firms change a constant selling price P per unit of output. In the case of a cost curve, total cost is calculated as the sum of fixed costs that are independent of output level and variable costs that increase at a constant rate per unit of output. The breakeven analysis occurs in this case at point Yb in Figure 8.7, where TR and TC intersect. If a firm’s output level falls below this breakeven point, i.e. If TR TC, it suffers operating losses. If the firm’s output level exceeds this breakeven point, or if TR > TC, it realises operating profits. Algebraically, it is defined as: Total revenue equals selling price per unit multiplied by output level.

TR = P x Y

Total cost equals fixed cost-plus variable cost, with variable cost equalling the product of variable cost per unit multiplied by output level.

TFC + AVC x QY = TC

Now, the break-even output level is the point at which profit is zero.

TC = TR

P x Y = TFC + AVC x Y

P x Y – AVC x Y = TFC

Y (P – AVC) = TFC

Y= TFC/(P – AVC)

Changes In Break- Even Point Due To Price, Fixed Cost And Variable Cost:

 

 

 

 

 

 

 

 

 

 

 

The X-axis in the diagram represents output, while the Y-axis represents cost and revenue. The initial TR (Total Revenue) and TC (Total Cost) curves intersect at the initial break-even point, denoted as B, with the initial break-even quantity as OQ.

• If the fixed cost increases, the TFC (Total Fixed Cost) curve shifts upward to TFC1, causing the TC curve to shift upward to TC1. This results in a new break-even point at a higher level, marked as B1, and an increased break-even quantity from OQ to OQ1.
• Conversely, if the TFC falls, the TFC curve shifts downward to TFC2, leading to a downward shift of the TC curve to TC2. The new break-even point becomes B2, and the break-even quantity decreases from OQ to OQ2.

3. Changes in Variable Cost per Unit: Using the same mathematical example, if we keep the price and fixed cost constant and alter the variable cost per unit, there is a change in break-even quantity.

• If the average variable cost per unit increases to Rs. 10, the break-even quantity is:
  $\mathrm{QB}=\frac{\mathrm{FC}}{P-\mathrm{AVC}}=\frac{4000}{15-10}=\frac{4000}{5}=800\text{ units}$ 
• If the variable cost per unit falls to Rs. 5, the break-even quantity is:
  $\mathrm{QB}=\frac{\mathrm{FC}}{P-\mathrm{AVC}}=\frac{4000}{15-5}=\frac{4000}{10}=400\text{ units<span style="font-family: Georgia, 'Times New Roman', 'Bitstream Charter', Times, serif;"> </span>}$ 

This demonstrates that an increase in per-unit variable cost leads to an increase in break-even quantity, while a decrease in average variable cost results in a decrease in break-even quantity.

The effects of these changes are depicted in the accompanying diagram.

 

 

 

 

 

 

 

 

 

 

 

 

In the provided diagram, the X-axis represents output, and the Y-axis represents cost and revenue. The initial break-even point is denoted as C, where the Total Revenue (TR) and Total Cost (TC) curves intersect. The initial break-even quantity is indicated as OQ.

Effects of Changes in Variable Cost:

• With an increase in Total Variable Cost (TVC), the TVC curve shifts to TVC1, consequently shifting the TC curve to TC1. Both TVC1 and TC are parallel to each other. As a result, the new break-even point shifts upward to C1 and the break-even quantity increases from OQ to OQ1.
• Conversely, with a decrease in TVC, the TVC curve shifts to TVC2, leading to a downward shift of the TC curve to TC2. The new break-even point also shifts down to C2, and again, TVC2 and TC2 are parallel to each other. The break-even quantity falls from OQ to OQ2.

Application of Break-Even Analysis:

Businesses utilize break-even analysis to determine the output level at which the firm covers all its costs and begins making a profit. This analysis serves various purposes in business:

1. Targeting Profits: Break-even analysis helps set short-term and long-term profit targets by identifying the point where the firm starts generating profits.

2. Cost Recovery: At the break-even point, the firm covers its entire production cost (fixed and variable). Understanding this allows for effective cost management strategies.

3. Production Technique Decision: Break-even analysis aids in deciding on the most efficient and cost-effective production techniques.

4. Effects of Changes: Changes in pricing, marketing, and other policies impact revenue, costs, and, consequently, the break-even point. This analysis helps anticipate these effects on profitability.

5. Sales and Marketing Policies: Businesses can lower the break-even point through innovative marketing strategies, but it requires careful consideration of associated cost implications.

6. Capacity Utilization: Efficiently using full capacity reduces average costs, minimizes wastages, and accelerates the journey to the break-even point.

7. Capital Raising Capacity: Achieving the break-even point enhances a firm’s ability to secure capital for future expansion, as financial institutions are more willing to provide loans to profitable ventures.

Limitations of Break-Even Analysis:

Break-even analysis has several limitations:

1. Misleading Profit Impression: Linear Total Revenue (TR) and Total Cost (TC) curves may wrongly imply that all output beyond the break-even point is profitable, which may not be the case.

2. Limited Applicability to Multiple Products: Break-even analysis is suitable for single product units, but for businesses with multiple or joint products, determining costs for each product becomes challenging.

3. Reliance on Historical Data: Break-even analysis relies on historical data for costs, prices, etc. If historical data is not indicative of future costs and prices, the analysis may not be applicable.

4. Fixed and Variable Cost Classification Difficulty: The effectiveness of break-even analysis is contingent on the clear classification of costs as fixed or variable. However, in some cases, this classification may not be straightforward.