ACCT 1064 Cost analysis and applications

ACCT 1064 Cost analysis and applications

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Cost analysis

Cost concepts

1. Opportunity cost:
Opportunity cost refers to the maximum return that could be obtained from an alternative use of resources, but is unavoidable or foregone by employing the resources in their present use. Opportunity Cost is also termed as Implicit Cost. Economic Profit = Earnings or Revenue of Firm - Economic Costs.  For example:

Mr. Subodh has two job opportunities in hand. First job opportunity can help him to earn Rs. 20, 000 per month and the second opportunity can get him Rs. 17, 000 per month. Under normal circumstances Mr. Subodh will opt for the job opportunity which can help him to earn Rs. 20, 000 per month. In the process Subodh rejects the other job opportunity which can help him to earn Rs. 17, 000 per month. In this case Opportunity cost of Mr. Subodh is Rs. 17, 000 per month as this is the income which the can be earn from the next best alternative. In above case Economic Profit or Economic Rent is Rs. 3, 000. This has been obtained after deducting Rs. 17, 000 (opportunity cost) from Rs. 20, 000.

2. Accounting costs and economic costs:
Accounting Cost includes all such business expenses that are recorded in the book of accounts of a business firm as acceptable business expenses. Such expenses include expenses like Cost of Raw Material, Wages and Salaries, Various Direct and Indirect business Overheads, Depreciation, Taxes etc. When such business expenses or accounting expenses are deducted from the Sales income of any firm the accounting profit is obtained. Such Accounting/Business expenses or costs are also termed as Explicit Costs. Accounting Profit = Sales Income - Accounting Cost

Economic Cost on the other hand includes all the accounting expenses as well as the Opportunity cost of a business firm. Economic Cost and Economic Profit is thus calculated as follows: Economic Cost = Accounting Cost (Explicit Costs) + Opportunity Cost Economic Profit = Total Revenues - (Accounting Cost + Opportunity Cost)

3. Direct costs and indirect costs:
Direct costs are directly identifiable and traceable to a particular product or plant or operation. For example in production of shirt, the cost of cloth is easy to identify. Indirect costs are not easy to identify and trace to a particular product or plant or operation. For example, in production of shirt, the cost of electricity used per shirt cannot be identified.

4. Fixed costs and variable costs
Fixed Cost is that cost which does not change (that is either goes up or goes down) irrespective of whether the firm is operating or not. It requires comparatively longer period of time to make change in them. For example, costs like building, land, machinery etc. Variable costs are costs that vary with output. Generally variable costs increase at a constant rate relative to labor and capital. Variable costs may include wages, utilities, materials used in production, etc.

Difference between fixed and variable costs

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Fixed costs
Variable costs
Fixed costs do not vary directly with the level of output
Variable costs are costs that vary directly with output
Examples include the rental costs of buildings, the depreciation of fixed capital etc. Examples of variable costs include the costs of raw materials, the costs of electricity etc.  A change in fixed costs has no effect on marginal costs.  Marginal costs relate only to variable costs.

Fixed costs starts when the firm decides to start a business Variable costs starts only when the actual production takes place.

5. Marginal Cost (MC) & Average Cost (AC)
Total cost is variable cost and fixed cost combined.
TC=VC+FC
Now divide total cost by quantity of output to get average total cost. Average cost or unit cost is equal to total cost divided by the number of goods produced. It is also equal to the sum of average variable costs plus average fixed costs. (AC=AVC+AFC)

AC=TC/Q
Where, AC is average cost, TC is total cost and Q is quantity

AVC= TVC/Q
Where, AVC is average variable cost, TVC is total variable cost and Q is quantity.

AFC=TFC/Q
Where, AFC is average fixed cost, TFC is total fixed cost and Q is quantity

Marginal cost is the change in total cost that arises when the quantity produced changes by one unit. That is, it is the cost of producing one more unit of a good. MC = Change in TC / Change in Q
Where, MC is marginal cost, TC is total cost and Q is quantity

Cost function
Cost function refers to the mathematical relationship between cost of production and the various determinants of costs. C=f (O, S, T, P)
Where, C is cost of output,
O is size of output,
S is size of plant,
T is Time under consideration,
P is prices of factors of production
F is function

Determinants of costs
The various factors that influence the cost are as follows:
1. Size of output:
Cost is affected by the size of output. Whenever the level of output changes the total cost also changes. Average and marginal costs usually falls initially but rises afterwards. 2. Size of plant:

Cost is inversely related with the size of the plant. As the size of the plant increases, costs decline and as the size of the plant decreases, cost rise. Fixed costs of bigger plant are higher than that of the smaller plant.

3. Prices of input:
Higher the prices of inputs, higher will be the costs of production. Even for the manufacturer getting the raw materials at low cost will help the firm to decide the product price.

4. Period under consideration:
During short period, costs tend to rise sharply as compared to long run period, during which the increase is not that sharp.

5. Technology:
The technology used for producing goods or technology used for packing etc have a great influence on cost of the product. Making the right choice of the technology can increase the costs or decrease the cost to the greatest extent.

6. Level of capacity utilization:
Costs not only depends on the size but also on the efficiency in utilization of capacity, costs, specifically fixed costs, tend to fall with the higher utilization of the capacity.

Short run cost curves
The average total cost curve is constructed to capture the relation between cost per unit of output and the level of output, ceteris paribus. A perfectly competitive and productively efficient firm organizes its factors of production in such a way that the average cost of production is at the lowest point. In the short run, when at least one factor of production is fixed, this occurs at the output level where it has enjoyed all possible average cost gains from increasing production. This is at the minimum point in the diagram below.

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A short-run marginal cost curve graphically represents the relation between marginal (i.e., incremental) cost incurred by a firm in the short-run production of a good or service and the quantity of output produced. This curve is constructed to capture the relation between marginal cost and the level of output, holding other variables, like technology and resource prices, constant. The marginal cost curve is U-shaped. Marginal cost is relatively high at small quantities of output; then as production increases, marginal cost declines, reaches a minimum value, then rises. MC is shown in the diagram below.

The marginal cost curve intersects both the average variable cost curve and (short-run) average total cost curve at their minimum points. When the marginal cost curve is above an average cost curve the average curve is rising. When the marginal costs curve is below an average curve the average curve is falling. This relation holds regardless of whether the marginal curve is rising or falling.

The above table shows the fixed cost of the firm is 50, even if the firm produces 0 units or 11 units. The variable cost keeps changing with every change in the unit produced. It keeps on increasing. As both fixed cost and variable cost increases, even the total cost increases. Total cost is obtained after adding FC and VC column. Marginal cost is the additional cost the firm has to bear on the additional output produced. Here in the total cost column the change is as follows: 1st unit =100-50=50, 2nd unit=128-100=28, 3rd unit =148-128=20 and so on till 11th unit. AFC, AVC and ATC are calculated using the following formulae: AFC=TFC/Q, AVC= TVC/Q, ATC=AVC+AFC.

In the above diagram, the marginal cost curve intersects both the average variable cost curve and (short-run) average total cost curve at their minimum points A and B. In the above table, the AVC decreases till 7th unit of output but after that is starts to rise. Even the ATC also falls till 7th unit and after that it rises. While the MC falls till 4th unit thereafter it rises.

In the short run, the shape of the average total cost curve (ATC) is U-shaped. The, short run average cost curve falls in the beginning, reaches a minimum and then begins to rise. The reasons for the average cost to fall in the beginning of production are that the fixed factors of a firm remain the same. The change only takes place in the variable factors such as raw material, labor, etc.

As the fixed cost gets distributed over the output as production is expanded, the average cost, therefore, begins to fall. When a firm fully utilizes its scale of operation (plant size), the average cost is then at its minimum. The firm is then operating to its optimum capacity. If a firm in the short-run increases its level of output with the same fixed plant; the economies of that scale of production change into diseconomies and the average cost then begins to rise sharply.

Long run cost curves
In the long period a firm can expand his plants and equipments to increase the supply of output to the increased demand. In this period a firm can vary all its inputs. The division of factors into fixed and variable disappears in the long run. All factors become variable as the time period is sufficiently high. Thus the firm who undergoes long-run production function never experiences fixed factors and hence fixed costs. In the long run a firm expands its output fully to the increased demand. All the firms are at liberty to enter or quit the market. Thus in long period a firm can shift from one plant to another. In long run a firm produces output at the minimum point of the long-run average cost curve. A firm only makes normal profit as there is adequate time for the new potential firms to enter the industry and start production. Long run average cost curve is a curve which shows the minimum per unit cost of each quantity of output. The shape of the long run average cost curve is also U-shaped but is flatter than the short run curve as is illustrated in the following diagram:

In the diagram, given above, there are five alternative scales of plant SAC1 SAC2, SAC3, SAC4 and, SAC5. In the long run, the firm will operate the scale of plant which is most profitable to it.

If the anticipated rate of output is 200 units per unit of time, the firm will choose the smallest plant. It will build the scale of plant given by SAC1 and operate it at point A. This is because of the fact that at the output of 200 units, the cost per unit is lowest with the plant size 1 which is the smallest of all the four plants.

In case, the volume of sales expands to 400, units, the size of the plant will be increased and the desired output will be attained by the scale of plant represented by SAC2 at point B.

If the anticipated output rate is 600 units, the firm will build the size of plant given by SAC3 and operate it at point C where the average cost is $26 and also the lowest. The optimum output of the firm is obtained at point C on the medium size plant SAC3.

If the anticipated output rate is 1000 per unit of time the firm would build the scale of plant given by SAC5 and operate it at point E. If we draw a tangent to each of the short run cost curves, we get the long average cost (LAC) curve. The LAC is U-shaped but is flatter than tile short run cost curves. Mathematically expressed, the long-run average cost curve is the envelope of the SAC curves.

In this figure, the long-run average cost curve of the firm is lowest at point C. CM is the minimum cost at which optimum output OM can be, obtained.

Major components of cost
1. Prime costs
Prime cost refers to all such expenses which are directly related with the production of a commodity. It consists of costs of direct material, direct labour and direct expense specifically identifiable to the product. This is also known as flat, direct or basic cost.

2. Production overhead:
It refers to the costs which are not easy to identify with the commodity. It includes costs of indirect material, indirect labour and indirect expense. These costs are generally spread over all the units of the products. It is also called factory overheads.

3. Production cost:
It comprises of prime cost and production overheads. This cost is also known as factory cost, production cost or manufacturing cost.

4. Total cost:
It is the sum of production cost and costs related to other departments.

5. Costs related to other functions:
It includes administrative overheads such as rent, salaries of managers etc., Selling overheads such as salesmen salaries, showroom’s rent etc., distribution overheads such as warehouse rent, insurance of godowns etc.

Break-even analysis (BEA)
Meaning of BEA
Break-even analysis is the summary of the operating costs of the whole part of the activities of an undertaking for a specific period.

Meaning of Break-even chart:
Break-even chart is a convenient way of demonstrating the profitability of an undertaking at various levels of activity.

Meaning of Break-even point
Break-even point in the break-even chart indicates the point at which the profit or loss to a firm is zero. It is also called no-profit-no loss point. It is a point of sale where total revenue is equal to total cost.

In the above diagram, on OX axis output is measured and on OY axis cost and revenue is measured. Total fixed cost is a horizontal line parallel to OX axis and total cost includes fixed cost and variable cost. Total revenue is represented by sales revenue line. Total revenue is calculated by multiplying the number units sold with the price per unit. The break-even point, P, occurs when the sales revenue line and total cost line intersect with each other. The area below the intersection is the loss area and above the intersection is called profit area. BEP is the no profit no loss point.

BEP is calculated with the help of following formula:

Contribution per unit = selling price per unit – variable cost per unit 
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Assumptions of BEP
1. The total cost can be divided as fixed cost and variable costs. 2. The behavior of the fixed cost and variable cost remains same or constant. 3. Selling price remains constant as output level changes.

4. There is one product or in the case of multiple products, the present sales mix continues. 5. Volume of the production is the only factor that influences the cost. 6. Management policies do not change as the production changes. 7. Efficiency level remains same.

Advantages or usefulness or merits of BEP:
Break even analysis enables a business organization to:
1. BEP helps to measure profit and loss at different levels of production and sales. 2. It helps to predict the effect of changes in price of sales. 3. BEP helps to analysis the relationship between fixed cost and variable cost. 4. It helps to predict the effect on profitability if changes in cost and efficiency are made. 5. Safety margin can be calculated with the help of BEP and can safeguard the firm from making losses. IT is calculated as follows:

6. It is useful in determining the target for the sales man which helps in determining profits for the firm. It is calculated as follows:

Limitation of BEP
1. BEP assumes that sales prices are constant at all levels of output which is not true as it may vary due to many factors. 2. It assumes production and sales are the same but due to competitors or to increase profits the firm can make changes in them and the calculate BEP also changes. 3. Break even charts may be time consuming to prepare.

4. It can only apply to a single product or single mix of products. 5. The assumption that the costs can be divided as fixed and variable is difficult, as some costs can fall in the category of semi fixed or semi variable costs. 6. Its scope is limited to short period.

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