Economic Analysis of Assembly Systems
• Goals of this class
–
–
–
–
understand the basics of economic analysis
unit cost of assembly by different resources
return on investment
particular properties of assembly systems
Econ Analysis
11/18/2004
© Daniel E Whitney
1
Cost and Price Considerations
Development cost
Unit cost
Unit mfr cost:
materials
labor
depreciation
waste, scrap, rework
Production
ramp-up
Marketing
Ongoing support
“Supply curve”
Prod’n volume/yr
Cost
Cost
Loss
Profit
Prod’n volume
Sales volume
3
2
1
Price
Price
“Demand curve”
Sales volume/yr
Econ Analysis
11/18/2004
© Daniel E Whitney
2
“Price Has Nothing to Do with Cost”
•
•
•
•
Price is about value
Value is often perceived and can be influenced
Direct value involves functions and ilities
Perceived value involves or is influenced by
– Marketing
– Perceived quality
– Number of choices available even if most will not be
taken
• Value > Price > Cost, otherwise no sales or no
profit
Econ Analysis
11/18/2004
© Daniel E Whitney
3
Cost Analysis is a Murky Area
• Engineers need to know the basics of cost analysis
for three reasons
– so they can make sound technological choices
– so they can judge the suitability of a supplier’s bid
– so they can argue effectively with accountants
• “Don’t ask us how we do investment justification.
We just fill out a form and after a while an answer
comes back Yes or No.”
• “MAPI means ‘makes a project impossible’”
– MAPI = Manufacturing and Allied Processes Institute
Econ Analysis
11/18/2004
© Daniel E Whitney
4
Kinds of Cost Categories
• Fixed cost = what you pay to set up (usually investment in
facilities)
• Variable cost = what you pay that depends on how many you
make per unit time
–
–
–
–
Labor, both direct and indirect (maintenance, supervisors)
Materials cost: what you buy that you add value to
Expendables: energy, lubricants, tool bits, etc
Scrap, rework • Institutional cost = all other costs of doing business
• In many cases, labor is a fixed cost, due to contracts or the
inability to lay people off for short periods when business
fluctuates
Econ Analysis
11/18/2004
© Daniel E Whitney
5
Cost Distribution in Engine Plants
Image removed for copyright reasons.
Source:
Figure 18-1 in [Whitney 2004] Whitney, D. E. Mechanical Assemblies: Their Design, Manufacture,
and Role in Product Development. New York, NY: Oxford University Press, 2004. ISBN: 0195157826.
Econ Analysis
11/18/2004
© Daniel E Whitney
6
Sources of Cost in the Supply Chain
Image removed for copyright reasons.
Source:
Figure 18-3 in [Whitney 2004] Whitney, D. E. Mechanical Assemblies: Their Design, Manufacture,
and Role in Product Development. New York, NY: Oxford University Press, 2004. ISBN: 0195157826.
Source: Daimler Chrysler via Munro and Associates
Econ Analysis
11/18/2004
© Daniel E Whitney
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A Small Problem
• Fixed costs are usually expended all at once, usually
before production starts
• Variable costs are incurred as production runs
• How should these two kinds of costs be combined to
provide a true picture of the cost per unit?
• The usual method is to allocate the fixed costs to the
units by choosing a time period during which the
investment is “recovered”
• unit cost = variable cost
+ Some_Fct (fixed cost, # of units made in some time period)
Econ Analysis
11/18/2004
© Daniel E Whitney
8
Cash Flows Over Time
Image removed for copyright reasons.
Source:
Figure 18-4 in [Whitney 2004] Whitney, D. E. Mechanical Assemblies: Their Design, Manufacture,
and Role in Product Development. New York, NY: Oxford University Press, 2004. ISBN: 0195157826.
Econ Analysis
11/18/2004
© Daniel E Whitney
9
Payback Period Method
• A payback period P is selected (arbitrarily?)
• The fixed cost is allocated equally to each unit
made during P:
• unit cost = variable cost
+ fixed cost / (P Q)
where Q = quantity made per year
P = a number of years
Econ Analysis
11/18/2004
© Daniel E Whitney
10
Internal Rate of Return Method
• The payback period is replaced by an investment
horizon H and an interest rate r
• This is equivalent to a mortgage for H years at
interest rate r
• The annual payment A and the annual cost factor
fAC for an initial investment Io are (for zero
salvage value):
A = I0
Econ Analysis
r 1 + rH
1 + rH – 1
11/18/2004
r 1 + rH
fAC = A =
I0
1 + rH – 1
© Daniel E Whitney
11
Unit Cost Based on IRoR
• unit cost = variable cost + fAC *fixed cost /Q
where Q = quantity made per year
fAC = fraction of fixed cost paid per year,
based on:
r = IRoR (ranges from 15% to 35%)
H = investment horizon (ranges from 2 to 5
years or more)
Econ Analysis
11/18/2004
© Daniel E Whitney
12
Annualized Cost Factor vs r
Image removed for copyright reasons.
Source:
Figure 18-5 in [Whitney 2004] Whitney, D. E. Mechanical Assemblies: Their Design, Manufacture,
and Role in Product Development. New York, NY: Oxford University Press, 2004. ISBN: 0195157826.
Econ Analysis
11/18/2004
© Daniel E Whitney
13
Simplified Unit Cost for Manual Assembly
COSTUNIT MANUAL =
# People =
A$
# People
Q
TNQ
2000 * 3600
[largest integer]
Q = annual production volume
T = assembly time per part, sec
N = number of parts per unit
A$ = annual cost of a person
A$ = L H * 2000
L H = labor cos t, $ / hr
2000 = hours per shift year
3600 = sec / hr
(assumes no investment required)
Econ Analysis
11/18/2004
© Daniel E Whitney
14
Simplified Unit Cost for Fixed Automation
f AC N S $
C UNITFIXED =
Q
where Q = annual production volume, units / year
f AC=fraction of machine cost paid for per year
S$ = cost of one station in the machine (assumes one station per part)
(also assumes no people required)
Econ Analysis
11/18/2004
© Daniel E Whitney
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f ACI L$
+
Q
Q
where I = total investment in machines and tools
L$ = annual cost of workers associated with the system
I = # MACHINES * $ / MACHINE + # TOOLS * $ / TOOL
TNQ
2000 * 3600
[
# MACHINES =
]
# TOOLS = N
L$ = w L H # MACHINES * 2000
where w = number of workers / station
Combining the above yields:
C UNIT FLEX =
fAC
L$
# MACHINES * $ /MACHINE + # TOOLS * $ / TOOL +
Q
Q
f $/ MACH IN E T N
f AC $/ TOOL N w T N L H
+
C UNITFLEX - A C
+
3600
Q
2000 * 3600
Econ Analysis
11/18/2004
© Daniel E Whitney
Simplified Unit Cost for Flexible
Automation
C UNITFLEX =
16
Conclusions from Unit Cost Models*
• Cost is linearly proportional to number of parts N
– one reason for fixation on part count reduction
• Cost of flexible automation grows with the “pricetime product”: $/machine * T
– shows that cost and time can be traded
• Other costs grow as part, station, and tool count
grow
– floor space
– support staff
– line downtime (see System Design chapter)
*P. M. Lynch, “Economic-Technological Modeling and Design Criteria for
Programmable Assembly Machines,” MIT ME Dept PhD Thesis, June 1976
Econ Analysis
11/18/2004
© Daniel E Whitney
17
Unit Cost Example
Unit Assembly Cost by Three Methods
2
f AC=0.38
1.8
T=5s
1.6
L H=$15/hr
1.4
S$=50000
$/tool = $10000
Unit Cost
1.2
N = 10 parts/unit
1
w = 0.25 workers/sta
0.8
MANUAL $/UNIT
0.6
FIXED $/UNIT
FLEX $/UNIT
0.4
0.2
0
0
100000
200000
300000
400000
500000
600000
Annual Volume
Econ Analysis
11/18/2004
© Daniel E Whitney
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Unit Cost Example - 2
Image removed for copyright reasons.
Source:
Figure 16-5 in [Whitney 2004] Whitney, D. E. Mechanical Assemblies: Their Design, Manufacture,
and Role in Product Development. New York, NY: Oxford University Press, 2004. ISBN: 0195157826.
Econ Analysis
11/18/2004
© Daniel E Whitney
19
More Detailed Cost Model
Image removed for copyright reasons.
Source:
Figure 18-9 in [Whitney 2004] Whitney, D. E. Mechanical Assemblies: Their Design, Manufacture,
and Role in Product Development. New York, NY: Oxford University Press, 2004. ISBN: 0195157826.
Econ Analysis
11/18/2004
© Daniel E Whitney
20
Caveats About Examples
• If T = 2 s, then Q = 3.6 million, or else the line
runs only part of one shift
• If # people > # of parts or operations, then extra
people are needed for one shift operation
• If Q > 7.2 Million / T, then a 2nd or 3rd shift is
needed
Econ Analysis
11/18/2004
© Daniel E Whitney
21
Discounted Cash Flow Analysis
• AKA net present value calculation
• More detailed and sophisticated than unit cost
comparisons
• Seeks to determine if an investment is “good”
• Based on comparing return on investment
– a base case is compared to an alternate
– the alternate requires upfront investment
– it creates a saving stream over time, which is
discounted to “present value”
– do the savings justify the investment?
Econ Analysis
11/18/2004
© Daniel E Whitney
22
Discounting Future Cash Flows
Money is a two-dimensional quantity ($,t)
$
Its value now
1
(1 + DF) i
e- ρ t
ρ = DF = discount factor
Its value if delayed
until t
t
Econ Analysis
11/18/2004
© Daniel E Whitney
Time
23
Two Cash Flow Formulas
Takeaway:
Takeaway:The
Theearly
earlycash
cashflows
flowscontribute
contributethe
themost.
most.
10
Sum of future
cash flows
without
discounting
9
8
7
present value of
sum of future
cash flows
6
5
CF/ ( 1+DF)^ i
Σ ( CF/ ( 1+DF) ^ i)
4
e^ -DF t
( 1-e^ -DF t ) / DF
3
2
DF = 0.1
1
present value of
future cash flows
0
1
3
Econ Analysis
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11/18/2004
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© Daniel E Whitney
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Comparison Analysis
• Base case
• Alternate case
– fixed costs
– labor costs
– material costs
– fixed costs
– labor costs
– material costs
Comparison:
What discount rate makes the discounted sum of future
savings in labor and material costs greater than or equal
to the difference in fixed cost between base and alternate?
H
Net savingsi / 1 + DF .
Investment alt – Investment base = iΣ
=1
i
Alternatively: set discount rate = cost of borrowing
Choose the alternate investment if NPV > 0
Econ Analysis
11/18/2004
© Daniel E Whitney
25
Discounted Cash Flow (DCF) and Economic Value Added (EVA)
• EVA is very similar to DCF. The discount rate used in EVA is the weighted average cost of capital (WACC)
– Cost of capital includes interest rate on debt plus expected rate of
return on stock (not easy to compute)
• EVA is usually used to value the whole company but is
being used more and more to value individual investments
• See http://www.pitt.edu/~roztocki/abc/abc.htm
• See Econ DEMO-Stanley Hammer.xls on MIT Server.
Econ Analysis
11/18/2004
© Daniel E Whitney
26
Zero or Net Present Value Calculations
• Comparing two investments, the savings Sv are
considered income
• You pay taxes on the income at tax rate Tx, yielding
your net income Ni
• You can claim depreciation Dp on your investment,
decreasing your taxable income and lowering your
taxes
• The IRS specifies how much you can claim in
depreciation each year
– the net income is: Ni = Sv - Tx(Sv - Dp)
• “present value analysis” spreadsheet on MIT Server
finds the discount rate that gives NPV = 0
•Econ
Can
be used
to find© Daniel
NPV
for any discount rate
27
11/18/2004
Analysis
E Whitney
Zero Present Value Analysis
ZERO PRESENT WORTH CASH FLOW ANALYSIS
7 YEARS ECONOMIC LIFE
0% SALVAGE VALUE % OF COST AT END OF ECONOMIC LIFE
EXPENSE FORECAST
YEAR
0
1
2
3
4
5
6
7
8
RATIO
100.00%
INCOME FORECAST
TAX RATE
34.00%
DEPRECIABLE
66.67%
SAVINGS
DEPRECIATION
$100
$181
$198
$150
TOTAL INVESTMENT
DEPRECIABLE INVESTMENT
INTERNAL RATE OF RETURN
TAX RATE
CREDIT
14.29%
24.49%
17.49%
12.49%
8.92%
8.92%
8.92%
4.46%
34.00%
34.00%
34.00%
34.00%
34.00%
SUM OF UNUSED YRS
DEPR=
31.22%
USED FOR SALVAGE VALUE
OF REMAINING DEPRECIABLE INVESTMENT
$400
$267
18.41%
GOAL SEEK
ON CELL G38 = 0
TAX CREDIT IN YR 0 0N
UNDEPRECIATED INVESTMENT
RESULT OF
PRO FORMA CASH FLOW
YEAR
INCOME
0
($400)
1
$100
2
$181
3
$198
4
$150
4
$83
SALVAGE VALUE
IN YEAR 4
DEPRECIATION
TAXES
$38
$65
$47
$33
$0
($45)
$21
$39
$51
$40
$0
CREDITS
$0
$0
$0
$0
$0
$0
NET
($355)
$79
$142
$147
$110
$83
DISC NET
($355)
$67
$101
$88
$56
$42
$355
GROSS INCOME
$713
$183
$152
$0
$561
NET INCOME
$313
$183
$106
$0
$206
Econ Analysis
11/18/2004
© Daniel E Whitney
SUM OF UNDISC INC
$79
$221
$368
$478
$561
UNDISC PAYBA
FOR EX IN FIG
($0)
28
How to Use this Spreadsheet
•
•
•
•
•
Enter savings, tax rate, depreciation rate
Goal seek to get zero NPV
Or
Put in various discount rates and observe NPV
NPV > 0 is desired
Econ Analysis
11/18/2004
© Daniel E Whitney
29
Aircraft Development Cost Quandry
Aircraft Product Development Cost Recovery
PD Investment = $3.5B
all taken in year 0
Depreciated over 7 years MACRS
$1.2B tax credit in year 0
First plane sold in year 2
2500
2000
1500
IRoR = 7.11%
Cost Recovery
1000
Undiscounted Cumulative
Income After Taxes and
Depreciation
500
0
-500
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17
Discounted Cumulative Income
After Taxes and Depreciation
Annual Gross Income Before
Taxes and Depreciation
-1000
-1500
-2000
-2500
-3000
Year
Econ Analysis
11/18/2004
© Daniel E Whitney
aircraft pd investment analysis.xls
30
A380 Business Case
A380
Cost and Income
PD Development cost $10.5B
14000
660 planes sold, price $200M ea
10000
$Millions
8000
6000
4000
First planes sold
12000
Avg profit/plane = $50M
IROR = 11.5%
Net Income Before
Depreciation and Taxes
Net Income After Taxes
and Depreciation
Sum of Undiscounted Net
Cash Flows
2000
0
-2000 0
10
20
30
Sum of Discounted Net
Cash Flows
-4000
-6000
Years
Econ Analysis
11/18/2004
© Daniel E Whitney
31
NPV vs Discount Rate for A380
NPV VS DISC RATE
FOR A380
5000
4000
NPV, $M
3000
2000
NPV
1000
0
-1000 0
5
10
15
20
25
-2000
DISC RATE, %
Econ Analysis
11/18/2004
© Daniel E Whitney
32
Critiques of DCF
• Target IROR is arbitrary
• The calculations can be gamed
• “Cost” is a slippery quantity
– People know their expenditures and assume that they
know their costs, but these are different even if they add
up to the same amount
– Overheads are allocated arbitrarily and can distort the
calculations
– Activity-based costing is intended to overcome this
– Robert Kaplan is an EE!
Econ Analysis
11/18/2004
© Daniel E Whitney
33
Summary of Economic-Technical Analysis
Image removed for copyright reasons.
Source:
Figure 18-14 in [Whitney 2004] Whitney, D. E. Mechanical Assemblies: Their Design, Manufacture,
and Role in Product Development. New York, NY: Oxford University Press, 2004. ISBN: 0195157826.
Econ Analysis
11/18/2004
© Daniel E Whitney
34