Costs
“Cost” is not a simple concept. It is important to
distinguish between four different types - fixed,
variable, average and marginal.
What is the cost of an additional copy of
Windows 2000? Multiply this by the total
number sold. Would Bill Gates recover his
investment at this price? Why not?
Costs & Profits




Profits = Revenues – Costs
Studied how revenues relate to output
Next we study how costs relate to
output.
Then we can decide how profits vary
with output and so what output levels
are most profitable
Cost Structures

First distinction:
(1) fixed costs vs.
(2) variable costs.
Fixed Costs

Independent of output level

examples:
– cost of borrowed money
– rental or mortgage payments on office/factory space
– corporate HQ costs.
Variable Costs

Depend in some way on production levels
within the organization

examples:
– materials
– some labor (depends on the contract)
– power
Note that the line between fixed and
variable costs is not always sharp and
costs may be fixed for one analysis
and variable for another - see the TV
guide case.
TC = total cost, VC = variable cost, AC =
average cost, etc.
TC = FC + VC
VC = VC(N) where N is the level of output
AC = TC/N = FC/N + VC(N)/N
Variable costs linear in output:

VC(N) = N

Then AC = FC/N +  is declining in N

When are variable costs likely to rise
proportionally to output? When more than
proportionally? Less?
Variable cost proportional to output
Average
cost
FC/N +
Large firms have cost
advantage over smaller
ones.

Output
Cost curves & Mergers



Falling average costs can provide impetus
for mergers
Compaq-Hewlett Packard merger may be of
this type, as were mergers of Chase and
Chemical Bank.
Other motives may be in terms of product
complementarity.
Variable costs quadratic in
output:
VC(N) = N + N2
Then AC = FC/N +  + N
This is -shaped as a function of N, falling
for small N and then rising for large N.
Variable cost quadratic in output
Average
cost
FC/N ++N

Output
Next Distinction



Marginal (or incremental) vs.
Average costs.
MC is probably the most import cost
concept
Marginal Costs


MC is change in total cost as result of one
unit change in output, TC(N) - TC(N-1)
Rate of change of total cost with respect to
output:
MC=DTC/DN
=DFC/DN + DVC(N)/DN
=DVC(N)/DN
Marginal Costs


MC depends only on variable costs
Shows cost impact of change in
production – fixed costs have no relevance
to cost consequence of output change
Variable cost proportional to output
Average
cost
FC/N +
Marginal cost
Output

What is the relationship between
average and marginal costs?
If MC < AC, then AC is falling
If MC > AC, then AC is rising
If MC = AC, then AC is constant
Returns to scale




A.k.a. Economies of scale
Increasing returns to scale - AC falls as
output rises.
Decreasing returns - AC rises with output
Constant returns - AC does not change with
output.
Returns to scale & cost structure




Large fixed costs imply increasing returns e.g., autos, telecoms, networks.
Small fixed costs and VCs rising with o/p
imply diminishing returns - e.g farming.
Assembly operations usually show constant
returns.
Large fixed costs - economies of scale make entry of competitors difficult.
Scale economies & competition



Autos - history of consolidation.
Telecom networks prior to fiber optics entry of MCI & Sprint into long distance
after ATT deregulation
Microsoft and Windows
Cost Categories
Fixed Costs
Variable Costs
Average Costs
Yes
Yes
Marginal Costs
No
Yes
Dynamic Changes in
Costs--The Learning Curve


The learning curve measures the impact of
worker’s experience on the costs of
production.
It describes the relationship between a firm’s
cumulative output and amount of inputs
needed to produce a unit of output.
The Learning Curve


The horizontal axis
measures the
cumulative number of
hours of machine tools
the firm has produced
The vertical axis
measures the number of
hours of labor needed to
produce each lot.
Hours of labor
per machine lot
10
8
6
4
2
0
10
20
30
40
50
Dynamic Changes in
Costs--The Learning Curve

Observations
1) New firms may experience a learning
curve, not economies of scale.
2) Older firms have relatively small gains
from learning.
Economies of
Scale Versus Learning
Cost
($ per unit
of output)
Economies of Scale –
reversible.
A
B
AC1
Learning
C
AC2
Output
Dynamic Changes in
Costs--The Learning Curve

The learning curve implies:
1) The labor requirement falls per unit.
2) Costs will be high at first and then will
fall with learning.
The Learning Curve in Practice

The Empirical Findings

Study of 37 chemical products
– Average cost fell 5.5% per year
– For each doubling of plant size, average production
costs fall by 11% (economies of scale)
– For each doubling of cumulative output, the average
cost of production falls by 27% (learning)
The Learning Curve in Practice

Other Empirical Findings
In the semi-conductor industry a study of seven
generations of DRAM semiconductors from
1974-1992 found learning rates averaged 20%.
 In the aircraft industry the learning rates are as
high as 40%.

How do cost concepts relate to
pricing?

Price should never be below marginal costs.

Can it make sense for price to be above
marginal cost but below average costs?


Yes, but do not renew your investment in this
case. This is a situation where you can stay in
the business but it was a mistake to get into it in
the first place.
In this case we cover variable costs but don’t
recover fixed costs.
Breakeven:


Occurs at the output level at which total cost
equals total revenue.
Let P(N) be the price at which N units can
be sold. Then breakeven means:
P(N) . N = FC + VC(N)
Total Cost = FC + VC(N) = FC + bN + c N2
MC = n + 2cN
Costs
Average total cost
AC = FC/N + b + cN
Price
MC
Output
Breakeven
Leverage



Study the elasticity of profits  with
respect to output Q.
Let output change from Q to Q + DQ,
and profits from  to  + D
Intuition - must be greater, the greater
are fixed costs.
The elasticity of profits with respect to
output, denoted E ,Q, is:
E ,Q =
D/
DQ/Q
=
D Q
DQ 
This is the ratio of the proportional change in
profits resulting from an output change to the
proportional change in output causing it. If
this number is 5, for example, it tells us that a
1% change in output leads to a 5% change in
profits
Profit 
 = PQ(revenue) - TC(total cost)
= PQ - FC - VC
Elasticity of  with respect to Q:
E,Q = (d/dQ)(Q/)
d/dQ = P - (dVC/dQ) = P - MC
E,Q = P-MC(Q/)
P - MC = contribution to overhead or
contribution margin
/Q = (PQ - AC*Q)/Q so
(Q/) = 1/(P - AC) so
E,Q = P-MC/P-AC
“Operating leverage”
MC = AC: E,Q = 1
MC < AC: E,Q > 1
MC > AC: E,Q < 1
Applications



Combine operating leverage with income
elasticity of demand.
Firm has Op Lev of 5 and IED for products
of 5. Then 1% rise in consumer income
implies 5% rise in sales and 25% rise in
profits – and vice versa for fall in demand
If Op Lev is 2 and IED is 2 then
corresponding number is 4%.
Windows 95 Facts:



Development costs: $1.1 billion
Promotion costs: $1.2 billion
Variable costs:




zero for OEM use
very low for site licenses
$2-3 for retail sales
Retail price: $50 - $60 (to Microsoft)
Windows 95 Questions:

What is the average cost for various output levels?

What is the marginal cost?

What are the demand elasticities and the income
elasticity?

What is the operating leverage?

What is the nature of competition?

Are there benefits to this product other than sales
revenues?
Sales, M Av Cost
10
20
30
40
50
60
70
80
90
100
230.00
115.00
76.67
57.50
46.00
38.33
32.86
28.75
25.56
23.00
Av Cost
250.00
200.00
150.00
Av Cost
100.00
50.00
0.00
10 20 30 40
50 60 70 80 90 100
Sales, millions
Microsoft needed to sell 65 million units @ $35 to
recover its fixed investment in the development
and promotion of Windows.
At $30, it had to sell 77 million units.
Operating Leverage for Microsoft Windows
Price: averaging over range, let P = 35
Marginal cost: assume MC = 1, a constant
Then for Output level Q, variable cost is VC = Q
Fixed cost is FC = 2.3B (2.3 billion), so
Total cost is TC = FC + VC = 2.3B + Q
Average Cost:
AC = TC/Q = 1 + 2.3B
Q
Compute operating leverage using
formula E,Q = P - MC
P-AC
E,Q =
35
35 - 2.3B
Q
Multiply numerator and denominator by Q/35

Q
Q - 65M
Near the breakeven point, small fluctuations in
output induce large fluctuations in profits.
Thus if Q = 70 million copies, operating leverage is
approximately 17 (a 1% increase in sales leads to a
17% jump in profits)
If output expands to Q = 90 million copies, then
operating leverage is 3.7
A given fluctuation in sales induces a smaller
proportionate increase in profits.
Cost Allocation

How should a multi-divisional company
allocated corporate overhead costs between
its divisions?
PC Computer Company (PCCC) has two operating
divisions
(1) Desk Top (DT)
(2) Lap Top (LT)
PCCC corporate overhead cost = $20m/year
composed of:
- interest on corporate debt
- salaries of the President, CEO, and CFO
- corporate promotional costs
- central office costs (accounting, HR,
management, etc.)
Divisional costs


DT’s division-specific fixed costs are $50m/year
(equipment and fixed labor) and variable costs are
$1,000/machine (components, labor, testing) DT
sells machines for $1,500 each.
LT’s division-specific fixed costs are $50m/year
and variable costs are $1,500 per machine, which
sell for $2,000 each.
Consider the following questions:



At what output level does each division
cover its division specific costs?
How does each division’s contribution to
corporate overheads and profits change with
output once it exceeds the output level
which answers (1)
When does PCCC as a whole make profits?
Answers:




DT will break even at sales of 100,000
relative to divisional costs.
LT will also break even at 100,000.
We will need an extra 40,000 units to cover
corporate overheads of $20m - i.e. a total
sales of 240,000.
The make-up of this 40,000 sales total does
not matter.
The CFO decides to allocate overheads to
DT and LT, $10m/year to each. The CEO
then decides to close down any division
which is not covering division-specific costs
plus its allocated overhead.
Evaluate this policy. What conclusion can
you draw about the appropriate test of a
division’s financial performance?
Answer:


DT and LT now each need to sell 120,000 to
break even, given the allocation of overhead.
Suppose DT sells 121,000 and LT sells
119,000 units. Closing LT will clearly make
the company worse off. Why? Because its
contribution of $19,000X500 = $9.5 m to
corporate overhead will be lost.
Economic & Accounting
Approaches to Costs
Table 2
Income Statement for Product A (1000s)
Sales (40 million lbs. @ 50 cents/lb)
less:
Materials
Direct labour
Manufacturing overhead
Cost of Goods Sold
Gross Margin
less:
Advertising
Promotion
Field Sales
Product Management
Marketing Management
Product Development
Marketing Research
General and Administrative
Total Expenses
Net Profit Before Taxes
$20,000
$8,000
$2,000
$2,200
$12,200
$7,800
$800
$200
$3,200
$50
$300
$300
$150
$1,400
$6,400
$1,400
Table 3
Classifying Product A Costs into Variable and
Fixed (1000s)
Cost Component
Total
Variable
Materials
$8,000
8,000
Direct Labour
2,000
2,000
Manufacturing Overhead 2,200
1,000
Cost of Goods Sold
12,200
11,000
Advertising
800
Promotion
200
Field Sales
3,200
1,000
Product Management
50
Marketing Management
300
Product Development
300
Marketing Research
150
General and Administrative 1,400
Total Expenses
6,400
1,000
Total Costs
18,600
12,000
Fixed
------------1,200
1,200
800
200
2,200
50
300
300
150
1,400
5,400
6,600
Table 4
Reconfigured Income Statement for Product A Using a Variable Budget Format
(1000s)
Sales (40 million lbs. @ 50 cents/lb)
less:
Variable Costs:
Materials
Direct labour
Manufacturing overhead
Sales Commissions
Total Variable Costs
Variable Margin (Profit Contribution)
less:
Fixed Costs:
Advertising
Promotion
Field Sales
Product Management
Marketing Management
Product Development
Marketing Research
Manufacturing Overhead
General and Administrative
Total Fixed Costs
Net Profit Before Taxes
$20,000
8,000
2,000
1,000
1.000
12,000
8,000
800
200
2,200
50
300
300
150
1,200
1,400
6,600
1,400
Important differences between tables 2 and 4
In the typical financial income statement shown in
Table 2, when cost of goods sold is subtracted
from sales, these costs include allocated overhead
that does not vary with the quantity produced.
Fixed costs are combined with variable costs.
Operating Leverage




Average cost = $18,600,000/40,000,000 =
$0.46
MC = AVC = $12,000,000/40,000,000 =
$0.30
(P - MC)/(P - AC) = (50 - 30)/(50 - 46) = 5
So even for this corporation with significant
variable costs leverage is 5.
Other Cost Concepts
Opportunity Cost


Non-cash cost of an alternative foregone
Examples:

a company invests cash reserves internally for return
of 10%. Could have invested externally at 12%.
Accounting cost of the investment is zero, economic
or opportunity cost is 12%

a company owns a building. Uses it for its own
office. Accounting cost is zero. Could have rented it
for $20/ft2 and moved to the suburbs for $12/ft2.
Opportunity cost is $20/ft2 and loss is $8/sq. ft.
Opportunity Costs


In may cases the main cost of continuing a
division will be the human expertise
involved in this.
Example – a skilled manager in a division
barely breaking even may be much better
used in a higher-margin division.
Cost of Frequent Flier Schemes




What does it cost United or American to
provide Frequent Flier schemes?
Dilution and displacement.
What are the gains?
Effect on PED.
Sunk Costs


Expenditures made which cannot be recovered.
Should have no impact on a firm’s decisions.
Example:



A firm is thinking of moving its headquarters. It pays
$500,000 for an option to buy a building for
$5,000,000. The total cost if it buys is the
$5,500,000.
The firm finds a comparable building for $5,250,000.
Which should it buy?
TV Listing Guide
(1) Story Book
(a) common to all editions, 16 pages long
(b) coated paper, color photos
(2) Program Book
(a) specific to each edition
(b) B&W on newsprint
(3) Cover Piece
(a) 4 pages, color on special paper
(b) specific to each edition
Culver City


Increase print run from 126,000 to 146,000. No other
change.
What are the extra costs?
 Binding @ $0.019/copy
 Delivery @ $0.013/copy
 Printing: each copy is
– Cover Piece, 4 color coated pages, 1 sheet/copy @ $0.016
– Program Book, 48 B&W newsprint pages, 12 sheets/copy
@ $0.004/sheet = $0.048/copy
– Story Book, 16 pages color, coated paper. 4 sheets/copy @
$0.012/sheet - $0.048
So, the total incremental cost/copy =
Binding + Delivery + Cover Piece +
Program Book + Story Book =
$0.144
Note: this number does not depend on
the level of sales
Des Moines


Only change: length of Program Book from 16 to
48 pages. Increase of 32 pages = 8 sheets, B&W
newsprint
Costs:




New plates for 32 pages @$108/page = $3456 =
3456/84,000 = $0.041/copy
Printing 8 sheets @ $0.004/sheet = $0.032/copy
So: total incremental cost for constant production of
84,000 per week is $0.073
Note: This number depends on the level of sales
Cheyenne
Circulation = 48,000
Printing costs:
Cover = 4 pages
Story = 16 pages
Program = 48 pages
Printing delivery and binding costs will be same as
in Culver City, = $0.144/copy
What other costs are there in this case?

Add 4 local channels to the d/b @ $1,800
per channel per year = $7,200

Customer service @$6,000/account/year

Plates:



Cover page plates 4 @ $405 = $1620
Story book plates 16 @ $405 = $6480
Program book plates 48 @$108 = $5184
Makes total annual set up costs = $13,200 per
year. To express this per copy divide by
52x48,000 making $0.0053 a copy. Total
weekly setup costs are $13,284. Per copy this
is $0.276
Hence total incremental cost is $0.425 per copy
Rules for Using Cost Data





Don’t use Average Cost, or Average Variable Cost, as a
proxy for Marginal Cost. MC is the appropriate measure
for decisions about the scale of production
A single item of accounting costs can include both fixed
and variable costs. These must be separated to identify
MC
MC should include all relevant opportunity costs, even
those not identified explicitly in firm’s accounts
Ignore sunk costs, even if they are explicit
Concept of asset specificity can be a useful tool when
identifying which costs are truly sunk
Activity - Based Costing:


A method of trying to understand
connections between “overhead costs” and
their drivers in terms of levels of divisional
activity.
To be covered in managerial accounting
course.
Changing Fixed to Variable
Costs




Large fixed costs perceived as risky
Outsourcing a method of transforming fixed
to variable costs
E.G. - computer operations. Outsource to
ADP, EDS, IBM, PWC, etc. Pay on a usage
basis so cost is now variable.
Risk shifted to outsourcer.
Outsourcing as Business Model




Benetton, Liz Claiborne
Subcontract production to third-world
companies
Subcontract distribution to Fedex, UPS, etc.
Benetton franchises retail outlets
What does the corporation do?




Follows market trends
Designs products
Markets products
Assets - intellectual property. Hence
emphasis on intellectual property rights.
Trend Spreading




Compaq, Dell always outsourced component
production.
Cisco has NO production facilities - all
production is outsourced.
Now outsourcing assembly, often to Asia,
Mexico.
Even GM, Ford moving this way.
Motor Industry




GM has sold off components division.
Ford moving this way.
Both looking to suppliers to provide entire
pre-assembled subsystems.
GM has stated publicly that it wants to be
out of manufacturing: to specialize in
designing and marketing cars. Subcontract
manufacturing to third-world countries.
Issues Raised



International mobility of jobs
Labor conditions in third world countries
Environmental issues in third world
countries.
Dematerialization of the
Corporation




Moving to situation where corporate assets
are intellectual property rather than bricks
and mortar.
Quote CFO of GM when Microsoft first
passed GM in market cap:
“Microsoft - hey, their assets could fit in our
executive parking lot!”
complex questions for valuation,
depreciation, etc.