THE THEORY AND ESTIMATION OF COST

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THE THEORY AND ESTIMATION OF COST
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Cost in Managerial Decisions

• Costs become more important as higher profit
  margins are harder to achieve as a result of
• increasing competition
• changing technology
• customer demand
• Firms look for ways to cut costs in their
  production processes by
• restructuring and downsizing
• outsourcing
• merging and consolidating

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Definition of Cost

• For reporting purposes, cost is defined within
  the domain of the accounting department.
• For decision making purposes, cost is defined
  based on the concept of relevancy.
• A cost is relevant if it is affected by a
  management decision. That is, a relevant cost
  changes as a result of the decision made by the
  management.

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Historical vs Replacement Cost

• E.g. You are holding an inventory of computer
  chips.
• The historical cost of the chips inventory is
  750,000.
• The current market value of the chips is
  1,000,000.
• If you decide to use the chips in production
  today, which cost is relevant?

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• The relevant cost is the current market value
  (the replacement cost).
• If the firm decides to sell the chips inventory
  instead of using it in production, the firm could
  earn 1,000,000 from this sale.
• Hence, by using the chips in production, the firm
  is forgoing the opportunity to receive the
  1,000,000.
• Historical cost of the chips is irrelevant for
  the production decision.

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Opportunity Cost vs Out-of-Pocket Cost

• Opportunity cost is very important in managerial
  decision making because it highlights the
  consequences of making choices under conditions
  of scarcity.
• Opportunity cost is the amount or value forgone
  in choosing one activity over the next best
  alternative.
• It is considered to be an implicit or indirect
  cost.

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• An implicit cost can be contrasted with an
  explicit or direct cost that represents an
  out-of-pocket expense.
• In the example of computer chips, the replacement
  cost of 1,000,000 is the opportunity cost of
  using the chips in production instead of selling
  them in the market.
• If the firm needs additional chips for production
  and purchases them from the market, the expense
  associated with this purchase would be the
  out-of-pocket cost.

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Sunk vs Incremental Cost

• Incremental cost is the cost that varies with the
  range of options available in a decision.
• It is also called the escapable cost. If a
  cost can be avoided when the decision is not
  made, then it is escapable and is an incremental
  cost.
• An incremental cost is incurred only if the
  decision is made and an alternative is chosen.

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Sunk vs Incremental Cost

• Sunk cost is the cost that does not change in
  accordance with the decision alternatives. The
  sunk cost is the same no matter which alternative
  you choose.
• Sunk cost is an inescapable cost.
• It is a cost that is incurred whether or not
  there is any decision to be made about
  alternatives.

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• In the example of computer chips, assume that the
  current market value of the chips is 550,000
  (recall that the historical cost is 750,000).
• If the firm decides to use the chips in
  production, the relevant cost for the firm is
  550,000
• 550,000 is the replacement cost.
• 550,000 is the opportunity cost.
• 550,000 is the incremental cost since depending
  on whether you decide to produce or sell, the
  cost will change.

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• 750,000 - 550,000 200,000 is the sunk cost
  since whether the firm produces or sells, the
  firm has already paid 750,000 for these chips
  and the difference between the replacement value
  and the historical value is a sunk cost.
• 200,000 of sunk cost is an irrelevant cost for
  the decision about production.
• If technology changes and the chips in the
  inventory become obsolete, then the market value
  of the chips will be zero.
• In this case, all of the historical cost of
  750,000 is the sunk cost to the firm.

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Costs and Profits

• The economists concept of profit differs from
  that of the accountant.
• In both cases,
• profit revenues - costs
• Economic cost ? Accounting cost
• Accounting cost out-of-pocket costs
  depreciation
• Economic cost Accounting cost Opportunity cost

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Economic Profit

• E.g. The manager of a small supermarket wants to
  open and operate her own store. She will leave
  her current job and use 50,000 of her savings
  for this business venture. Her current salary is
  45,000 and her 50,000 savings are currently
  earning 10 interest in a savings deposit.

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Accounting and Economic Costs Related to Opening
Her Own Store
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Normal and Economic Profit
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Normal and Economic Profit

• The point of normal profit would be the economic
  break-even for the firm.
• Economic break-even indicates that the firms
  revenue is sufficient to cover both its
  out-of-pocket expense and its opportunity cost.
• A normal profit does not mean no profit.
• Total economic cost includes the opportunity cost
  of all resources used.
• The return on capital is included as a cost since
  it represents the opportunity cost of using the
  capital in the current alternative.

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The Relationship Between Production and Cost

• The cost function is the production function
  expressed in monetary rather than physical units.
• Assumptions about the short-run production
  function also apply to the short-run cost
  function.

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• In addition, for the cost function we assume that
  the firm is a price taker in the input market.
  Therefore, it can use as many or as few inputs as
  it desires as long as it pays the going market
  price for them.
• In the input market, the resources are still
  scarce. However, any given firm is so small in
  comparison with the whole market that the firm
  can use as many units of input as it desires if
  it pays the going market price for inputs.

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An Example Production Process
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• When the total product (Q) increases at an
  increasing rate, total variable cost (TVC)
  increases at a decreasing rate.
• When the total product (Q) increases at a
  decreasing rate, total variable cost (TVC)
  increases at an increasing rate.
• Total variable cost is a mirror image of total
  product.

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• When the firms marginal product is increasing,
  its marginal cost of production is decreasing.
• When the firms marginal product is decreasing
  (when the law of diminishing returns takes
  affect), its marginal cost is increasing.

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Total, Average, and Marginal Cost

• total cost total fixed cost total variable
  cost
• TC TFC TVC
• average cost average fixed cost average
  variable cost
• TC / Q TFC / Q TVC / Q
• AC AFC AVC
• marginal cost marginal fixed cost marginal
  variable cost
• MC ?TFC / ?Q ?TVC / ?Q
• MC MVC

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The Short Run Cost Function

• Two inputs labor (L) and capital (K)
• Short-run production period
• A single product
• A given level of technology
• Price taker for the price of inputs
• The firm is operating most efficiently at all
  levels of output.
• Underlying production function is affected by the
  law of diminishing marginal returns

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TC
TVC
TFC
MC
AC
AVC
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• Average fixed cost declines steadily over the
  range of production.
• Average variable cost declines at first but
  starts to increase after 4 units.
• Average total cost also declines at first but
  starts to increase after 4 units.
• Marginal cost declines and then starts to
  increase once the third unit of output is
  produced.
• When MC lt AVC, AVC is falling.
• When MC gt AVC, AVC is rising.
• When MC AVC, AVC is at its minimum.

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How to Increase Cost Efficiency in the Short Run?

• Since the firm is already operating as
  efficiently as it can, the costs can be reduced
  only if input prices come down.
• In this case, the average variable cost curve
  would shift downward.
• If a fixed cost component becomes cheaper, the
  average fixed cost curve would shift downward.

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/TL
/TL
MC1
MC1
MC2
MC2
AC1
AC1
AC2
AC2
AVC1
AVC1
AVC2
AVC2
Q
Q
When there is a reduction in input prices, AVC
and MC are affected at the same time.
When there is a reduction in input prices, AVC
and MC are affected at the same time.
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/TL
MC1
AC1
AC2
AVC1
Q
When there is a reduction in fixed costs, only AC
is affected and AVC and MC are not affected.
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The Long Run Cost Function

• In the long run, all inputs to a firms
  production function may be changed.
• There are no fixed inputs and thus there are no
  fixed costs.
• Decisions regarding long-run cost of operations
  are considered to be part of the managements
  planning horizon.

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LRMC
LRAC
The long-run cost function exhibits the same
pattern of behavior as the short-run cost
function.
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Similarity Between Short-Run and Long-Run Cost
Functions

• The reason the short-run cost function exhibits
  the decreasing-increasing pattern is the law of
  diminishing marginal returns.
• The reason the long-run cost function exhibits
  the decreasing-increasing pattern is
  increasing-decreasing returns to scale.

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IRTS
CRTS
DRTS
LRTP
LRTC
IRTS
CRTS
DRTS
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Economies of Scale

• If a firms long-run average cost declines as
  output increases, the firm is experiencing
  economies of scale.
• The primary reason for economies of scale is the
  underlying returns to scale in the firms
  long-run production function.
• The returns to scale and economies / diseconomies
  of scale are mirror images of each other.

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/TL
LRAC
Q
economies of scale
constant returns to scale (neither economies
nor diseconomies)
diseconomies of scale
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Possible Reasons for Economies of Scale

• Specialization in the use of labor and capital
• Indivisible nature of many types of capital
  equipment
• Productive capacity of capital equipment rising
  faster than purchase price
• Economies in maintaining inventory of replacement
  parts and maintenance personnel
• Discounts from bulk purchases
• Lower cost of raising capital funds
• Spreading of promotional and research and
  development costs
• Management efficiencies (line and staff)

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Possible Reasons for Diseconomies of Scale

• Disproportionate rise in transportation costs
• Input market imperfections (e.g. wage rates
  driven up)
• Management coordination and control problems
• Disproportionate rise in staff and indirect labor

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The Envelope Curve

• The LRAC curve can be represented as a
  combination of SRAC curves corresponding to each
  level of scale (capacity) along the LRAC.
• This acknowledges the fact that once a firm
  commits itself to a certain level of capacity, it
  must consider at least one of the inputs fixed as
  it varies the rest.

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/TL
SRAC8
SRAC1
SRAC7
SRAC2
SRAC3
SRAC6
v
v
SRAC4
v
SRAC5
v
v
v
v
Q
Q
economies of scale
diseconomies of scale
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• The firms LRAC curve is the envelope of the
  various SRAC curves.
• Short-run average cost curves for the larger
  plants are positioned to the right of the curves
  for smaller ones.
• Plants with larger capacities are greatly
  influenced by economies or diseconomies of scale.

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• As a result of economies of scale, SRAC2 is
  positioned below and to the right of SRAC1.
• The minimum point of SRAC2 is lower than that for
  SRAC1.
• As a result of diseconomies of scale, SRAC6 is
  positioned above and to the right of SRAC5.
• The minimum point of SRAC6 is higher than that
  for SRAC5.

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• Asterisks mark the minimum points on the SRACs.
• The asterisk for Plant 2s minimum SRAC depicts a
  level above the average cost that would be
  incurred by Plant 3 in the short-run for a
  comparable level of production.
• The envelope curve shows that over certain ranges
  of output, a firm is better off operating a
  larger plant.

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The Learning Curve

• A line showing the relationship between labor
  cost and additional units of output.
• Downward slope of the learning curve indicates
  that the additional cost per unit declines as the
  level of output increases because workers improve
  with practice.
• The reduction in cost from this particular source
  of improvement is referred to as the learning
  curve effect.

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• The learning curve effect is measured by the
  percentage decrease in additional labor cost each
  time the output doubles.
• Learning rate is given by the following formula
• This is the rate at which average cost falls as
  cumulative output doubles.

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unit labor cost
cumulative output over time
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unit labor cost
C
B
A
LRACt
LRACt1
cumulative output over time
Qt
Qt1
From C to B, learning effect From B to A,
economies of scale effect
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Economies of Scope

• The reduction in a firms unit cost that results
  from producing two or more goods jointly rather
  than separately.
• Sharing certain aspects of the production
  process, the firm is able to decrease its unit
  cost.

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COST-VOLUME-PROFIT ANALYSIS
Break-Even Analysis

• Break-even volume is the sales level for which
  total revenue equals total cost.
• After the break-even level, revenues start to
  exceed costs and profits start to build up.
• The critical question is whether the sales volume
  will reach and surpass the break-even level.

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TL/
TC
TR
Q
Q1
Q2
?
There are two break-even sales levels. The
profits are positive between these two
quantities.
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TC
TL/
TR
Q
Q1
Q2
?
There are two break-even sales levels. The
profits are positive between these two
quantities.
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TL/
TR
TC
?
Q
Q
There is a single break-even sales level. The
profits are positive after this quantity.
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Applications of Break-Even Analysis

• BE analysis is very useful when decisions need
  to be made about the price and quantity levels of
  a proposed product.

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TL/
TR2
TR1
TC1
TC2
Q
Q4
Q3
Q2
Q1
Q4 initial break-even volume Q3 break-even
after costs decrease and revenues are constant Q2
break-even after revenues increase and costs
are constant Q1 break-even after revenues
increase and costs decrease
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Algebraic Calculation of Break-Even

• Break-even occurs where total revenues are equal
  to total costs

where CM is the contribution margin.
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In a multi-product firm, each product may be
required to attain a specific profit target to
maintain its place in the product
mix. Break-even analysis can be used to find the
sales volume at which this profit target will be
reached. Since the profit target is a constant
monetary figure in TL or , it can be added to
the fixed-cost figure to represent the total TL
or amount that must be obtained through
contributions from each unit sold.
This calculation will give the sales volume
necessary to cover the fixed costs and to attain
the desired target profit.
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Break-even analysis is useful where a product
may be manufactured under two or more
technologies of production. E.g. A firm is
considering three alternative methods of
manufacturing for a product. The market price
for the product is established at 4.00 per
unit. Alternative 1 FC 20,000 AVC 2.00
/ unit Alternative 2 FC 45,000 AVC 1.00
/ unit Alternative 3 FC 70,000 AVC 0.50
/ unit
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• Assume that the decision makers estimate of
  sales volume exhibit the following distribution

The profitability figures under different sales
scenarios indicate that Alternative 1 is the most
suitable choice since its break-even point is at
the low end of this distribution.
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TL/
TR
TC
Q
Q10
Alternative 1 FC 20,000 AVC 2.00 / unit P
4.00 / unit
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TL/
TR
TC
Q
Q15
Alternative 2 FC 45,000 AVC 1.00 / unit P
4.00 / unit
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TL/
TR
TC
Q
Q20
Alternative 1 FC 70,000 AVC 0.50 / unit P
4.00 / unit