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Cost Drivers Learning Event, 2nd November 2005
1
Cost Improvement Curves:Modeling Reuse, Learning,
Amortization and Yield Improvement
Cost Drivers Learning Event, 2nd November 2005
Raymond P. Covert
MCR, LLC2000 Corporate Ridge, Suite 400
McLean, Virginia 22102
(703) 506-4600
www.mcr.com
E-mail: [email protected]
© 2005 MCR, LLC
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Cost Drivers Learning Event, 2nd November 2005
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Agenda
Introduction Cost Improvement Factors The Plant Model Nonrecurring and recurring costs Nonrecurring cost improvement Recurring cost improvement Example hardware cost improvement model Summary Acronym List References
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Introduction
This presentation is intended for an audience with an intermediate understanding of cost analysis methods
We will discuss the phenomenon of “cost improvement”, which is loosely defined as the observed reduction of cost of successive units or projects
0
50
100
150
200
250
300
350
400
0 10 20 30Unit Number
Rec
urr
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$
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Cost Improvement Factors and Learning Cost Improvement is the observed reduction of costs between
successive units or projects Factors affecting cost improvement:
Nonrecurring and recurring accounting standards affect measurement Reuse of existing designs, materials, equipment, effort, or products Learning or gained experience in value added effort Skill Mix changes Process shortcuts that eliminate effort or expenses Yield improvements that reduce cost Production Rate increases allowing for amortization of pooled costs
and greater efficiency Technological advances allowing greater yield and efficiency Inflation which measures the time variable cost of a “basket of goods”
*True “learning” is a subset of cost improvement, so cost improvement is more than learning
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The Plant Model
Can use a plant economic model to show the effects of different factors on cost improvements [Ref. 1, p. 183]
Skills Labor Rates
Engineering 1 2 3 4 5
Manufacturing
Quality and ReliabilityLabor Hours $
Tooling Fee
Testing Labor Overhead G&ALabor
Other + OverheadTravel and Other Direct Costs $ $ Price
Material Prices Total Cost
Material Measures A B C D E Material + Overhead
Pounds G&A
Yards FeeMaterial quantities $
Gallons
Linear Feet Material Overhead
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Cost Drivers Learning Event, 2nd November 2005
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The Plant Model
The plant economic model contains the three classic Elements of Cost: Labor, Materials and Expenses
These costs can be Project related or Pooled (period costs) Direct or Allocable (overhead and fringe) Nonrecurring or Recurring costs
Materials (M) Labor (L) Expenses (E) Total = M+L+E
Direct 105,000.00 2,500,000.00 80,000.00 2,685,000.00 Burden 26,250.00 3,000,000.00 64,000.00 3,090,250.00 Total 131,250.00 5,500,000.00 144,000.00 5,775,250.00 Administration 10,000.00 125,000.00 6,250.00 141,250.00 Distribution 5,000.00 25,000.00 1,250.00 31,250.00 Corporate Transfer 125.00 250,000.00 12,500.00 262,625.00 Marketing 30,000.00 200,000.00 10,000.00 240,000.00 Research 50,000.00 275,000.00 13,750.00 338,750.00 Development 20,000.00 125,000.00 6,250.00 151,250.00 Finance 20,000.00 195,000.00 9,750.00 224,750.00 Total 135,125.00 1,195,000.00 59,750.00 1,389,875.00 Total 266,375.00 6,695,000.00 203,750.00 7,165,125.00
Pooled Costs (Period)
Project Costs
TOTAL COSTS
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Areas of Cost Improvement Cost improvement can be obtained in two areas:
Between subsequent programs Within programs between subsequent production units
Between Programs Nonrecurring cost improvements between successive programs Recurring cost improvements continuing to the subsequent
programs Within programs
Recurring cost improvements
The next step is to define these terms precisely and show how to model them
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Nonrecurring and Recurring Costs Nonrecurring (NR) and recurring (REC) cost definitions
Nonrecurring costs - unique costs of effort, material and expenses tied to a production run rather than a particular unit
Recurring costs – costs of repeated effort, material and expenses repeated for each subsequent unit
Hard to segregate NR and REC in small or single unit production What was recurring work if we only build one unit? What was the theoretical first unit cost (T1)? What if we build a prototype unit and make it the first production
unit? What was the fist prototype unit cost (P1) and T1 cost? What will the theoretical second unit cost (T2) be?
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NR/T1 Factors for Space Programs
NR/T1 is the ratio of NR costs to T1 costs Analysis of NR/T1 Ratios of 100 programs from the
NAFCOM database* provide the following results:
TYPERocket Engine
Earth Orbiting
Launch Vehicle Manned Planetary
NUMBER 4 61 10 8 17MIN 27.65 0.00 2.61 1.29 2.38MAX 202.24 7.59 39.78 11.56 18.35MEDIAN 128.83 2.02 16.00 3.48 6.18MEAN 121.89 2.35 16.93 4.44 6.52
min ML mean (average) max
ML = most likely = 3 * mean - (min + max)
* NASA / Air Force Cost Model (NAFCOM) Includes subsystem hardware, systems engineering, program management, integration, assembly and test, ground test equipment, launch and orbital operations support
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New Design and Reuse*
The amount of new design on a program and reuse from previous programs is a key factor in determining NR/T1 Reuse = 1 – New Design Assumes all have some prototype development Almost never have 0% redesign or 100% redesign Use table to estimate NR/T1 cost ratio from % new design
% New Design Description NR/T1
0.0 Off the Shelf 0.10.1 0.20.2 0.30.3 0.50.4 0.80.5 1.30.6 1.70.7 2.10.8 2.50.9 2.81.0 3.0New Design
Tech Maturity
Min Mods
Moderate Mods
Major Mods
NR/T1 vs. % New Design
0.00.51.01.52.02.53.03.5
0.0 0.2 0.4 0.6 0.8 1.0
% New Design
NR
/T1
* For earth orbiting spacecraft
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Modeling NR Costs Using Reuse
Use our plant economic model to build-up the T1 costs
Use T1 costs and reuse (or percent new design) to determine NR costs
Look at effect of reuse on NR cost How does this affect total cost improvement?
Total acquisition costs = NR+ REC costs
Not really interesting until we look at other cost improvement factors like learning and amortization
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The Learning Curve
(Wright) Cumulative Average Learning Curve Based on accumulated experience and ability to do the
same task with less labor (time)
Cumulative Average Unit Cost =
Cost of ith Unit = Where:
T1 = Theoretical 1st unit cost N = number of units i = unit number LCS = learning curve slope ln = natural log
)2ln(
)ln(
1_ *$LCS
AveCum NT
)2ln(
)ln(1
)2ln(
)ln(1
1_ )1()(*$LCSLCS
iUnit iiT
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0.20
0.40
0.60
0.80
1.00
1.20
0 2 4 6 8 10 12
Units
Co
st,
$
Cumulative average
Unit
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Observations on Learning Can be measured in hours and dollars (Euros and Pounds are
OK as well!) This implies that it covers the same work content
Accounting standards need to include NR and REC cost definitions True learning should be independent of other factors such as:
Reuse of existing designs, materials, equipment, effort, or products Skill Mix changes Process shortcuts that eliminate effort or expenses Yield improvements that reduce cost Production Rate increases allowing for amortization of pooled
costs and greater efficiency Technological advances allowing greater yield and efficiency Inflation which measures the time variable cost of a “basket of
goods”
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0.0
0.2
0.4
0.6
0.8
1.0
1.2
0 2 4 6 8 10 12
Units
Co
st,
$
Unit Cost
The Production Rate Curve Production Rate Curve
Division of labor and overheads with number (N) of units produced over a period of time
Strongly influenced by amortization of period and fixed costs Unit cost =
“Bath tub” shape due to added capital equipment and labor when production capacity is exceeded
Niablefixed
Unitvar$$
$
Max capacity
Increase fixed costs
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Yield
"Yield" is the fraction of units that meet specifications Unit cost =
Process Screening
Fail = Does Not Meet Specifications
Pass = MeetsSpecifications
N Units Started
yieldNiablefixed
unit *
$$$ var
MeetsSpecifications
Does Not Meet Specifications
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0.0 0.2 0.4 0.6 0.8 1.0
Yield
Un
it C
os
t, $
Unit Cost
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Sensitivity Analysis What affects cost improvement the most?
Reuse? Amortization (production rate)? Yield?
Depends on the scenario (looked at 5 scenarios) Small quantity satellite production Medium quantity satellite production Large quantity satellite production Electronic box production Integrated circuit production
Use plant model with uniform distributions of quantity, reuse, amortization and yield to show sensitivity
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The Plant Model Equations Start with parameters we wish to vary:
Total number of projects over which non-pooled costs will be amortized Learning curve slope (LCS) Yield parameters (start quantity, yield, final quantity) Percent reuse for nonrecurring costs Pooled rate factor (factor for adjusting pooled / period costs)
Determine Direct costs T1 costs are constants
T1(labor) = 100, T1(material) = 20, T1(expenses) = 12 NR costs = f(T1, Reuse) from reuse table Recurring Costs from learning curve Total direct costs = NR + Rec costs
Add indirect costs to direct costs using these factors Materials (5%), Labor (150%), Expenses (70%)
Add period costs (constants adjusted by pooled rate factor)
MIN MAX BASE1 2 Total Projects 1
0.999 1 LCS 1800 1200 FinalQuantity 1000
Start Quantity 20000.2 0.7 Yield 0.50.2 0.8 Reuse 0.8
1 3 Pooled Rate Factor 2
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Small Quantity Satellite Production
Most sensitive to new designMIN MAX BASE
1 2 Total Projects 10.9 1 LCS 1
1 3 FinalQuantity 2Start Quantity 2
0.99 1 Yield 10.2 0.7 Reuse 0.5
250 400 Pooled Rate Factor 300
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Medium Quantity Satellite Production
Most sensitive to: New Design Learning curve slope
MIN MAX BASE1 2 Total Projects 1
0.9 1 LCS 14 10 FinalQuantity 5
Start Quantity 50.99 1 Yield 1
0.2 0.7 Reuse 0.5250 400 Pooled Rate Factor 300
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Large Quantity Satellite Production
Most sensitive to: Learning curve slope
MIN MAX BASE1 2 Total Projects 1
0.98 1 LCS 120 40 FinalQuantity 30
Start Quantity 300.99 1 Yield 1
0.2 0.7 Reuse 0.5250 400 Pooled Rate Factor 300
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Electronic Box Production
Most sensitive to: Period costs (amortization)
MIN MAX BASE1 2 Total Projects 1
0.98 1 LCS 120 80 FinalQuantity 50
Start Quantity 630.5 0.8 Yield 0.80.2 0.8 Reuse 0.810 30 Pooled Rate Factor 20
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Integrated Circuit Production Most sensitive to yield MIN MAX BASE
1 2 Total Projects 10.999 1 LCS 1
800 1200 FinalQuantity 1000Start Quantity 2000
0.2 0.7 Yield 0.50.2 0.8 Reuse 0.8
1 3 Pooled Rate Factor 2
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Results of Scenarios Model results tell us what we probably already know
In small quantity production, reuse is the most important cost improvement factor
In large quantity, labor intensive production, learning is the most important factor
In large quantity electronic box production, production rate is the most important factor
In very large quantity, automated processes, yield is the most important factor
Scenario Quantities Primary Cost Improvement Factor:Small quantity satellite production 1-3 Reuse (New design)Medium quantity satellite production 4-10 Reuse & Learing curve slopeLarge quantity satellite production 20-40 Learning curve slopeElectronic box production 20-80 Amortization (production rate)Integrated circuit production 800-1200 Yield
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Summary
Many factors affect cost improvement Cost improvement can be obtained between
subsequent programs or subsequent production units Use plant model to show sensitivities of these factors We chose reuse, learning, amortization (production
rate) and yield Effects are scenario dependent
Depends on quantity of production and production volumes Also depends on amount of process automation and
external factors such as plant amortization
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Acronym List NR = Nonrecurring cost T1 = Theoretical first unit recurring cost T2 = Theoretical second unit [recurring] cost P1 = Theoretical first prototype unit cost REC = Recurring cost LCS = Learning curve slope ML = Most likely NR/T1 = Ratio of NR to T1 costs N = number of units i = unit number ln = natural log
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References1. Stewart, R. and Wyskida, R., “Cost Estimator’s Reference Manual”, 1997, John Wiley and
Sons, New York.
2. “Pricing Handbook: Cost Accounting Standards”, Federal Aviation Administration, http://fast.faa.gov/archive/v1198/pguide/98-30C14.htm