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

Averagecost

Output

FC/N +

Large firms have costadvantage over smallerones.

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.

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 costs quadratic in output:

Variable cost quadratic in output

Averagecost

Output

FC/N +N

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=TC/N FC/N + VC(N)/N

VC(N)/N

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

Averagecost

Output

FC/N +

Marginal cost

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

Average Costs Marginal CostsFixed Costs Yes NoVariable Costs Yes Yes

Dynamic Changes inCosts--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

Hours of laborper machine lot

10 20 30 40 500

2

4

6

8

10

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.

Observations

1) New firms may experience a learning curve, not economies of scale.

2) Older firms have relatively small gains from learning.

Dynamic Changes inCosts--The Learning Curve

Economies ofScale Versus Learning

Output

Cost($ per unitof output)

Economies of Scale – reversible.

AC1

BA

AC2

Learning C

The learning curve implies:

1) The labor requirement falls per unit.

2) Costs will be high at first and then will fall with learning.

Dynamic Changes inCosts--The Learning Curve

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%.

The Learning Curve in Practice

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)

Average total costAC = FC/N + b + cN

Price

Breakeven

Costs

Total Cost = FC + VC(N) = FC + bN + c N2

MC = n + 2cN

MCOutput

Study the elasticity of profits with respect to output Q.

Let output change from Q to Q + Q, and profits from to +

Intuition - must be greater, the greater are fixed costs.

Leverage

The elasticity of profits with respect to output, denoted E ,Q, is:

E ,Q = /

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

Q/Q=

QQ

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

10 230.0020 115.0030 76.6740 57.5050 46.0060 38.3370 32.8680 28.7590 25.56

100 23.00

Av Cost

0.00

50.00

100.00

150.00

200.00

250.00

10 20 30 40 50 60 70 80 90 100

Sales, millions

Av Cost

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 +

Compute operating leverage using

formula E,Q =

E,Q =

Q Q - 65M

2.3B Q

P - MCP-AC

3535 - 2.3B Q

Multiply numerator and denominator by Q/35

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 3.7A 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$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$50m/year (equipment and fixed labor) and variable costs are $1,000/machine$1,000/machine (components, labor, testing) DT sells machines for $1,500$1,500 each.

LT’s division-specific fixed costs are $50m/year$50m/year and variable costs are $1,500$1,500 per machine, which sell for $2,000$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 2Income Statement for Product A (1000s)

Sales (40 million lbs. @ 50 cents/lb) $20,000less:

Materials $8,000Direct labour $2,000Manufacturing overhead $2,200

Cost of Goods Sold $12,200Gross Margin $7,800less:

Advertising $800Promotion $200Field Sales $3,200Product Management $50Marketing Management $300Product Development $300Marketing Research $150General and Administrative $1,400

Total Expenses $6,400Net Profit Before Taxes $1,400

Table 3Classifying Product A Costs into Variable and

Fixed (1000s) Cost Component Total Variable Fixed

Materials $8,000 8,000 ------- Direct Labour 2,000 2,000 ------- Manufacturing Overhead 2,200 1,000 1,200Cost of Goods Sold 12,200 11,000 1,200 Advertising 800 800 Promotion 200 200 Field Sales 3,200 1,000 2,200 Product Management 50 50 Marketing Management 300 300 Product Development 300 300 Marketing Research 150 150 General and Administrative 1,400 1,400Total Expenses 6,400 1,000 5,400Total Costs 18,600 12,000 6,600

Table 4Reconfigured Income Statement for Product A Using a Variable Budget Format

(1000s)Sales (40 million lbs. @ 50 cents/lb) $20,000less:Variable Costs:

Materials 8,000Direct labour 2,000Manufacturing overhead 1,000Sales Commissions 1.000

Total Variable Costs 12,000Variable Margin (Profit Contribution) 8,000less:Fixed Costs:

Advertising 800Promotion 200Field Sales 2,200Product Management 50Marketing Management 300Product Development 300Marketing Research 150Manufacturing Overhead 1,200General and Administrative 1,400

Total Fixed Costs 6,600Net Profit Before Taxes 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 = 48,000Printing costs:

Cover = 4 pagesStory = 16 pagesProgram = 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.