Transcript Cost analysis

COST MANAGEMENT BASICS
COST ANALYSIS
Agenda
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Cost Estimating
Types of Cost
Normalization and Inflation
Risk Assessment
Cost Estimating Methods
Labor Costing
Optimization
Statistical Analysis
Tools
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Cost Estimating
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Cost and Cost Estimating Definition
Cost:
•
The monetary representation of resources used or sacrificed, and
liabilities incurred to achieve an objective
– Example:
 The resources expended in acquiring or producing a good
 The resources expended in performing an activity or service
Cost Estimating:
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The process of collecting and analyzing data and applying quantitative
models, techniques, tools, and databases to estimate the future cost of
an item, product, program, or task
Cost estimating is thought by some to be difficult, but the skills
and knowledge are logical and straightforward.
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Purpose of Cost Estimating
• Enable managers to:
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Make resource-informed decisions
Develop and defend budgets
Identify specific cost drivers
Improve cost controls
• Translate system/functional needs associated
with programs, projects, proposals, or
processes into costs
• Determine and communicate a realistic view of
the probable costs, which will be used to inform
the decision-making process.
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Characteristics of a
Good Cost Estimate
• Well documented
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Includes source data and its significance
Clear and detailed calculations and results
Contains explanations for choosing a particular method or reference
• Comprehensive
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Ensures a level of detail where cost elements are neither omitted nor
double counted
• Accurate
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Avoids bias and overly conservative or optimistic estimates
Bases its assessments on most likely scenarios and assumptions
• Credible
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Discusses any limitations of the analysis deriving from the uncertainty/bias
of the data or assumptions
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Types of Cost
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Sunk Costs
Opportunity Costs
Marginal Costs
Average Costs
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Sunk Costs
• Costs that have already been incurred and
cannot be changed no matter what action is
taken in the future are called Sunk Costs
Example: Paul is assembling his new home theatre system. He has
spent 5 hours thus far and estimates he will complete the assembly
in 2 more hours. Joan informs him he is doing it the hard way and
describes a simpler approach which will take one hour to undo his
work and re-assemble the system.
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Opportunity Costs
• The size of a foregone opportunity of using
a resource is the Opportunity Cost
Example: The opportunity cost of accepting a job is
forgoing the opportunity to do something else with
our time
If our best alternative to working is playing golf the
opportunity cost of working is the forgone
opportunity of playing golf
If the opportunity to play golf has a value greater than
the benefits of working we will choose to play golf
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Marginal Costs
• Marginal Costs are the costs to produce one
more additional unit or output
• The slope of the ‘Total Cost Curve’ at any
given level of production is the marginal
cost for one more unit
• Marginal costs are highest at very low
output rates and at output rates near
capacity
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Marginal Costs
Total cost
C
High marginal costs
Total
(£)
A
B
Lowest marginal costs
High marginal costs
Output
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Average Costs
• Average Cost is calculated by dividing the
total cost by the total units produced
• Average Cost is very high at low levels of
output
Cost Drivers
Organizations perform work activities to
deliver products/services to a stakeholder
 Definition: Factors, activities, or events that cause costs to be incurred
 Usually can be quantified/measured - e.g., number of hours spent on a
task, supported population
 Analyst should identify and focus on the primary cost drivers that affect
total cost
 Helps to ensure the accuracy and reliability of the cost estimate
 Makes it easier to control costs within the organization
 Examples:
 The labor cost associated with assembling a HMMWV at a the factory would
be driven by the quantity of vehicles produced
 Energy consumption at the PX is driven by the square footage of the
building and the operating hours
 The cost of printing budget documents for the Office of Management and
Budget is driven by the number of pages in each set and the number of sets
needed
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Types of Analyses Used in Army
Decision-Making
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Comparative Analyses
Supporting Resource Informed Decision
EA
Economic
Analysis
EA is an OSD MAIS required analysis in support of investment decision at
early IT/ERP program concept phase MS-A with an update at MS-B
decision.
EA is also required by the Army CoE in support of Military construction
decision.
(MAIS) Major Automated Information System programs
AoA
Analysis of
Alternatives
AoA is an OSD MDAP required analysis in support of acquisition
requirement decision at early program concept phase MS-A with an update
at MS-B decision.
AoA is a formal and elaborate study that in addition to the program life
cycle, often includes an operational model done by TRADOC for the Army
ASARC and OSD DAB decisions.
(MDAP) Major Defense Acquisition Programs
BCA
Business
Case
Analysis
CBA
Cost Benefit
Analysis
BCA is an OSD MDAP required analysis at post production phase in
support of Performance Based Logistics (PBL) Contractor Logistic
Support (CLS) vs. organic O&S decision. Risk analysis is an essential
component of BCA.
BCA term is often synonymous with CBA for non-PBL analysis.
CBA is an Army required analysis for all new and existing initiatives at resource
decision forums with cost of $10M or more.
CBA for Army HQ decision is developed by the initiative advocate and reviewed by
the CBA-RB . AMC and TRADOC also have similar process for their internal
resource decisions.
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Break-Even Point
Cost Reduction = Upfront Investment
Break-Even Point:
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Used when a given alternative has a significant investment
cost but is expected to experience cost reduction in future
years
This is also where (in current dollars):
savings = investment
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Example - Break-Even Point
Summary of Break-Even Point:
- It’s the year where the savings become positive.
- Using inflation indices, constant dollars are converted into current dollars.
- Savings are the difference between cumulative costs.
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Internal Rate of Return (IRR)
• The annualized effective compounded return
rate
• Rate where the present value of cash inflows is
equal to the present value of cash outflows
• IRR = (FV/PV)1/N -1
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Net Present Value
Net Present Value (NPV):
• The difference between the present value of cash inflows
and the present value of cash outflows
– Used to analyze the profitability of an investment
• This works only if values, costs (outflows), and benefits
(inflows) are quantified into monetary terms
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Net Present Value Formula
Net Present Value (NPV):
• The amount of dollars that would have to be invested
during the base year at the assumed discount (interest)
rate to cover the costs, match the revenues, or match
the savings at a specific point in the future
NPV = PV (benefits) – PV (costs)
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Cost Estimating in EA
Must consider the “Economic Life”
• Period of time over which the benefits to be
gained from a project may reasonably be
expected to accrue. Benefits are limited by the
equipment or facility’s physical and technological
life
• Measured against a stipulated level of threat, or
represent a period during which a given mission
or function is required or can be supported
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Total Life Cycle Cost (LCC)
• The sum of all costs required to research,
develop, test, procure, field, operate, sustain,
and dispose a system
• A planning number that often differs from the
sum of budgeted amounts allocated towards or
in support of a particular system
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Investment Multiples/Ratios
• Ratios compare the profits or savings of an
investment cost to illustrate the relativity of cost
and savings
• S/IR = OPERATING COST SAVINGS
COST OF INVESTMENT
• If S/IR > 1, then positive investment
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Business Cases Analysis (BCA):
Key Questions
Is the proposed solution:
1. Financially Viable (Make Economic Sense)
2. Optimal (Best Value or Increased
Effectiveness)
3. Feasible (Assessing Constraints)
4. Implementable (Risks & 2nd/3rd Order Effects)
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Cost Benefit Analysis (CBA)
Within the Department of the Army, one major
process which incorporates cost analysis is
Cost Benefit Analysis (CBA)
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What is a CBA?
Cost-Benefit Analysis:
• Is a structured methodology used to identify alternative
solutions to a problem, determine the costs and benefits of
each alternative, define the appropriate decision criteria,
and select the best alternative
• Produces a strong value proposition – a clear statement
that the benefits outweigh the costs and risks.
• In Basic Terms:
1.
2.
3.
4.
Define a problem or opportunity
Identify alternatives
Determine their costs and benefits
Evaluate and select the best alternative
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Why Do We Need CBAs?
Purpose:
• Supplement (but not replace) professional experience,
subject matter expertise, and military judgment with
rigorous analytical techniques
• Make best possible use of constrained resources
• When making resource decisions:
– Ensure that all decisions are resource-informed
– Treat cost as a consideration from the outset, not as an
afterthought
– Understand how much benefit will be derived
– Identify billpayers
– Consider second- and third-order effects
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CBA and the “Cost Culture”
CBA is part of a high-priority initiative to inculcate
a cost culture throughout the Army.
• In any organization, “culture” is the beliefs and principles that guide the
behavior of the people in that organization.
– Example: The Army’s military culture is based on mission accomplishment, selfless
service, valor, and dedication. These concepts establish the foundation for how
Soldiers and Civilians go about their duties.
• In a cost culture:
– Cost is an integral part of every decision
– Soldiers and Civilians strive to find better and more cost effective ways to operate the
Army enterprise
– Leaders at all levels engage in cost control and management activities, which are
supported by talented cost staffs
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Cost Benefit Analysis
CBA – Using analysis to make the case for a project or
proposal:
Weighing the total expected costs against the total expected benefits
over the near, far, and lifecycle timeframes from an Army enterprise perspective
1. Define the Problem/Opportunity
COSTS
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Quantifiable costs
 Direct
 Indirect
 Initial/Start up
 Sustainment
 Procurement
Non-Quantifiable
costs
 Life/Safety/Health
 Perception/Image
 Opportunity
 Risk/Uncertainty
 Political
2. Define the Scope; Formulate Facts and
Assumptions
BENEFITS
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The total of
quantifiable and nonquantifiable benefits
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Quantifiable benefits
 Cost Savings
 Cost Avoidances
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Non-Quantifiable
benefits
 Greater capability
 Faster availability
 Better quality
 Improved morale
 Other?
3. Define Alternatives
4. Develop Cost Estimate for each
Alternative
5. Identify Quantifiable and
Non- Quantifiable Benefits
6. Define Alternative
Selection Criteria
7. Compare Alternatives
8. Report Results and Recommendations
BENEFITS MUST BALANCE OR OUTWEIGH COSTS
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CBA is NOT a Linear Process
Objective
Recommendation
Assumptions
Sensitivity Analysis
Alternatives
Compare
Alternatives
Selection
Criteria
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Benefits
Estimate
Cost
Estimates
At any step in the process, the team’s findings and analysis might
make it necessary to revisit previous steps
Significant findings might require asking the decision maker for
revised guidance
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Normalization and Inflation
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Normalization and Inflation
• Adjusting for inflation is a specific form of normalization,
an adjustment intended to make a given data set
consistent and comparable with other data sets
• A frequent use of simple normalization is to adjust based
on quantities. For example:
– In a manufacturing process, COA 1 produces 17,000 widgets per
year at a total cost of $33,765 and COA 2 produces 14,500
widgets at a total cost of $28,725. It’s difficult to evaluate these
COAs unless we normalize by computing a unit cost, which
shows us that COA 2, with a unit cost of $1.95 per widget, is
preferable to COA 1, which has a unit cost of $1.99.
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What is Inflation?
Definition
• A rise in the general level of prices
• Measure of change in the dollars’ purchasing power
• In other words:
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•
A given dollar amount will have less buying power next year
than it does this year
To maintain consistent buying power, we must adjust this year’s
dollars with the inflation factor from year to year
Common methods for normalization:
• Discounting
• Constant (Base) Year
Of all the topics discussed in cost analysis, none will
be encountered more frequently than inflation
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Inflation Calculation and
Examples
• Basic calculations:
– (Constant Dollars) * (Inflation Factor) = Current (Dollars)
– Inflation is compounded from year to year (i.e., multiplied, not
added).
• Example: A loaf of bread in 1950 cost $0.25. Today, in 2012, it costs
$3.00.
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Example—Current Dollar Calculation
• Data: We’ve calculated the annual cost for a given COA in FY12
constant dollars:
– Civilian personnel: $145,000
– Contract support: $100,000 (paid by OMA appropriation)
• Applicable inflation factors:
– Civilian personnel: 2% per year
– OMA appropriation: 3% per year
• Calculation for the first three years of the life-cycle:
Cost
Element
Const.
Dollar
Cost
Infl.
Factor
Current- Dollar Calculation
Current-Dollar Cost
FY12
FY13
FY14
FY12
FY13
FY14
150,858
Civ per
145,000
2%
145,000
145,000
* 1.02
145 *
1.02^2
145,000
147,900
Contract
100,000
3%
100,000
100,000
* 1.03
100,000
* 1.02^2
100,000
103,000
Total
cost
245,000
245,000
250,900
256,948
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Risk Assessment
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Risk Assessment and Mitigation
The goal of risk assessment is to answer questions like:
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What risks may occur?
What is the likelihood that risks will occur?
Are the source of these risks internal or external?
What causes these risks?
What are the consequences if the risks go unresolved?
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What assets, operations, activities, functions, etc. will be affected as a
result?
How much risk is tolerable?
What should be done to anticipate and limit risks?
Always measure the risk by the potential
adverse impacts on alternatives.
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Types of Risks
Business/Programmatic Risk:
• Affects the budget and viability of a program
Operational Risk:
• Affects the ability to perform a mission
Process Risk:
• Associated with failing to meet standards and performance benchmarks in a
newly established process
Technical Risk:
• Associated with failing to develop or implement technology
Schedule Risk:
• Associated with allocating time to perform and manage tasks
Organizational Risk:
• Associated with management changes
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Ways to Measure/Address Risk
• Methods of measuring and/or addressing risk
include, but are not limited to:
– Effective Mean
– Cost of Risk Mitigation
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Effective Mean (Expected Value)
• The effective mean, or expected value, of a measurable quantity is
the sum of all possible outcomes multiplied by their corresponding
probabilities
• Example: if the cost of a new ground combat vehicle is judged to be
$1.4M with 50% probability, $2M with 25% probability, and $1.2M
with 25% probability, then the effective mean (expected cost) is
$1.4M x 0.5 + $2M x 0.25 + $1.2M x 0.25 = $1.5M.
• Example: if inter-theater transit time for a sustainment brigade is
projected to be 5 days with 90% probability and 4 days with 10%
probability, then the expected transit time is 5 x 0.9 + 4 x 0.1 = 4.9
days.
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Cost of Risk Mitigation
If a cost can be associated
with reducing risk, then
risk can be measured by
that monetary value.
Example: If for $22K
extra, the risk of a
schedule over-run can be
reduced from 15% to 3%,
then $22K can be a
measure for the difference
in risk.
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Cost Estimating Principles and
Rules
• Use authoritative data sources
• Ensure that cost estimates support “apples-to-apples”
comparison among COAs
• Ensure the cost estimate is well-documented,
comprehensive, accurate, and credible
• Constant vs. current dollars
– Use constant (un-inflated) dollars for even comparison for COAs
in CBAs
– Convert estimate to current (inflated) dollars to determine
POM/budget resourcing requirements
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Cost Estimating Methods
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Available Cost Estimating
Methods
Available methods:
• Analogy
• Parametric
• Engineering
• Actual Cost
• Expert Opinion
• Learning Curves
Most CBAs utilize all cost estimating
methods
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Cost Estimating Methods
The use of each method is based on
the information available to support it.
GROSS ESTIMATES
Parametric
DETAILED ESTIMATES
Actual Costs
Engineering
Analogy
Figure 1: A summary of the usual application of each technique.
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Analogy Method
• Estimates the cost, based on historical data, of an
analogous system or subsystem
• Utilizes a current fielded system that is similarly
designed to the proposed system
• Adjusts historical cost of the current system to account
for differences
– Adjustments should be made through parameters/scaling
factors based on quantitative data

These adjustments should show validity of comparison
When is it used?
• When an analogous case (that can be applied to a
subsystem or component level) exists
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Analogy Method Example
Attribute
Old System
New System
Engine:
Thrust:
Cost:
F-100
12,000 lbs
$5.2M
F-200
16,000 lbs
?
Q: What is the unit cost of the F-200?
A: $5.2M * (16,000/12,000) = $6.9M
Warning 1: An
Warning 2: An adjusted
adjusted analogy is
analogy is, by definition,
like a regression, but
estimating outside the
the slope is just a
range of the data.
guess.
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Parametric Method
• Uses regression or other statistical methods to develop a
cost estimating relationship based on observed patterns
of how specific parameters influence total cost
• Utilizes:
• High-level ‘Work Breakdown Structure’ (top down approach)
• A database from elements of one or more systems
When is it used?
• Historical data is available but not detailed
• In earlier stages of the system or project life cycle
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Parametric Method Example
High Mobility Wheeled Vehicles Database
Vehicle
M274
M561
M656
M520
Cost of
First Unit
$ 9,585
50,002
93,262
147,889
Gross
Weight
1,770
8,363
24,785
36,590
Curb
Weight
970
5,363
14,785
10,500
Cubic Ft
Shipping
81.6
732.3
1,227
2,368
Net
Horsepower
12.5
93
183
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Is ‘Cubic Ft Shipping’ a good predictor of cost?
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Parametric Method Example
(Cont’d)
Cost of First Unit vs. Shipping Capacity
Cost of First Unit ($K)
200000
150000
100000
50000
0
0
500
1000
1500
Cubic Feet of Shipping
2000
2500
Cost of First Unit = 60.992 * (Cubic
Shipping Feet) + 7,957.2
We can estimate the cost of any vehicle given the
shipping capacity using the above equation.
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Engineering Method
• Breaks down the system of interest into lower level
components, each of which is estimated separately
– Work Breakdown Structure
• Uses algebraic equations (bottom up approach)
– Most detailed of all techniques
• Requires extensive knowledge of a system’s
characteristics and the respective detailed data
• Is expensive and time consuming
When is it used?
• All potential costs can be assumed or estimated
Types of Army data sources (AMCOS Lite, MILCON,
SRM, historical ,execution, travel, etc.)
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Developing the WBS
• What the WBS does:
– Ensures that all component elements are identified so that all costs are
counted only once
– Provides a systematic, standardized way to collect data
• Decompose to as many levels as needed
• Example: The airplane cockpit can be decomposed into its
subelements:
– Instrument panel
• Primary flight instruments
–
–
–
–
Directional gyro
Turn and bank indicator
Altimeter
Airspeed indicator
• Avionics controls
– Communications
– Navigation
– Radar
– Flight control systems
• Rudder pedals
• Steering yoke
• Trim tab controls
– Seats
• Seat and shoulder belts
• Cushions
• Head rest
… and so on
A well-decomposed process flowchart that defines/describes
the COA is a useful tool in developing the WBS
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WBS – Another Example
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Actual Cost Method
• If historical costs from experience or trends from
prototypes, engineering development models, and early
production items are available, they can be used to cost
current goods or services
• Extracts costs that were actually incurred on same
system during an earlier period
– Obtaining access to these actual costs may be difficult
When is it used?
• The actual data from the same system is present
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Actual Cost Method Example
a. The development process is nearing completion
b. The materials have all been procured at a cost of
$20M
c. The labor cost to date is $30M
d. According to earned value cost performance
reports (CPRs), the estimated cost at completion
for the remainder of the labor is another $20M
Cost = $20M + $30M + $20M = $70M
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Expert Opinion Method
• Obtains opinions from experienced individuals or a
group
– Documents the source of opinions
– Lists attributes of the sources
When is it used?
• When availability of data is limited.
Delphi Technique
1. Query expert opinion from group
2. Seek expert opinion from each group, and then summarize
results to send in reports
3. Gather another opinion and summarize those results
4. Continue process until experts reach a consensus
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Expert Opinion Method Example
Scenario: Three software engineers are
recognized experts in ERP software
development
1. You hold interviews to explain the Stakeholders’ needs,
sizing level, and development process for your new
system
2. Each member of the group submits his/her opinion of
the final cost
3. If all expert opinions converge to, or hover around the
same figure, that may be taken as a good cost estimate
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Forecasting: What is Forecasting?
•
Process of predicting a
future event
•
Underlying basis
of all business
decisions
•
Production
•
Inventory
•
Personnel
•
Facilities
??
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Personnel Costing
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Personnel Costing
• Labor is expensive and typically accounts for the
majority of costs incurred
• Example: when you get your car repaired, labor
typically accounts for 70-85% of the bill
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AMCOS
• AMCOS is the principal tool cost analysts use for
labor costing and it can be found at:
https://www.osmisweb.army.mil/amcos/app/home.
aspx
• Costs are shown for military, government
civilian, and private sector civilian workers
• Costs are most detailed for military, and the
least detailed for private sector civilians
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AMCOS
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AMCOS
AMCOS ApplicationsAMCOS lite
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GFEBS Payroll vs. Labor
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Optimization
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What is optimization?
• Optimization is about achieving the maximum or
minimum possible result
• Example: If you have 20ft of fence to make a
rectangular garden, what is the maximum sized
garden you can make? The answer is a square
with each length measuring 5ft.
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Example: Finding Optimal
Solutions
• U.S. Army Central Command has secured $198M for the
procurement of two different models of the “HIMARS 2”
multiple rocket launcher—class X and class Y—for
deployment to Afghanistan.
• The class Y HIMARS 2 costs $9M each and weighs
27,000 pounds.
• The class X HIMARS 2 costs $11M and weighs 12,000
pounds.
• After procurement, all the HIMARS 2 will be transported
to Afghanistan by a fleet of C-130 Hercules aircraft, each
with a total maximum payload of 405,000 pounds.
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Example: Finding Optimal
Solutions
1. How do you maximize the total number of
HIMARS procured?
2. If you buy only Class X, you can afford 18.
3. If you buy only Class Y, you can carry 15.
4. So is “buy 18 Class X HIMARS” the optimal
solution?
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Example: Finding Optimal Solutions
COA 2
COA 3
COA 4
COA 1 (Status Quo)
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Example: Finding Optimal
Solutions
• You can procure 9 Class X and 11 Class Y
HIMARS, for a total of 20.
• Moral of the exercise: analysis is sometimes
necessary to determine the optimal solution.
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Statistical Analysis
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Statistical Analysis
Area under curve
between a and b
is 99.74%
a
m
Mean
Time
Beta distribution
b
3σ
a
3σ
m
Mean
Time
b
Normal distribution
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Statistic Analysis Applications
• Statistics is the study of the collection,
organization, analysis, interpretation and
presentation of data
• One application of statistics is the U.S. Census.
It seeks to understand some details (such as
income, gender, marital status) of people living
in the country
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Statistical Analysis Standard Terms
• Probability: likelihood of an event occurring
(expressed as a value between 0 and 1, e.g.
0.63)
• Average/mean: the sum of a list of numbers
divided by the size (amount of numbers) of the
list
• Mode: the most frequent appearing or most
likely to be drawn quantity
• Variance: (1/N)*∑(xi-average)2
• Standard deviation: square root of variance
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Statistical Analysis Example
• A data set consists of the values 6.5, 6.5, 0.2,
4.0
• The mean is (6.5+6.5+0.2+4.0)/4=4.3
• The mode is 6.5
• The variance is (1/4)*((4.3-6.5)2+ (4.3-6.5)2+
(4.3-0.2)2+ (4.3-4.0)2)=6.6
• The standard deviation is sqrt (6.6)=2.6
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Understanding likelihood of
occurrence
• How likely an event is to occur is expressed in probability
– Example: if you roll a fair die, you have a 1/6 chance of getting a
particular number since the die is 6-sided
• In the case of dice, there are 6 possible outcomes (which
is finite). Sometimes there may be infinite outcomes
• What is the likelihood of leaving work at exactly 5pm?
(not being even one billionth of a second over or under)
• For cases like this in which there are infinite outcomes
(i.e. you may leave one millisecond over, two
milliseconds over, 5 microseconds under, etc.) you need
to use probability densities
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Quantifying Cost Risk
• Statistics can be used to quantify risk associated
with costs
• We may ask, what are the odds of the costs
being significantly under or above the target?
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Cost Risk and Schedule Example
• Example: Let’s say the cost to construct a building is
expected to be approximately $3,000,000 if completed
on time and every month delay in completion adds
$23,000 to the cost, and every month the building is
completed in advance saves $23,000.
• There is a 20% chance the building is completed on
time, a 20% chance of being one month late, a 20%
chance being two months late, a 20% chance being one
month early, and a 20% chance being two months early.
• What is the likelihood of paying no more than $2,977,000
for the building?
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Solution to Example
• $2,977,000 is the amount paid if the building is
one month early. Thus, if we seek to pay no
more than this, we must finish the building one
month ahead of schedule (at the latest). In other
words, we can finish one or two months early.
• There is a 20% chance of being one month
ahead of schedule, and another 20% chance of
being two months ahead of schedule, so the
answer is 20%+20%=40%
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The “normal/Gaussian/bell-curve”
distribution
•
•
•
•
•
•
Consider the normal curve below:
– The x-axis shows project duration in weeks.
– The peak of the curve occurs at week 69. Week 69 is also the average project duration
(which is intuitive due to the symmetry of the curve).
– The purple shaded area represents the probability of having project duration of at least 72
weeks.
– The blue shaded area represent the probability of having a project duration less than 72
weeks.
•
Probability distributions, especially probability densities, are often used to quantify risk in cost
estimating and in other fields
Normal distribution:
Mean = 69 weeks;
A probability density function shows the
σ = 3.45 weeks
likelihood of an event occurring.
The height of the curve corresponds to
the likelihood of an event occurring.
Perhaps the most commonly used
Probability
Probability of
probability distribution is the normal
of meeting
exceeding 72
distribution.
the schedule
weeks is
is
0.8078
Given two points on the x-axis, the area
0.1922
under the curve bounded by these points
is equal to the probability that a value
within those bounds will occur
The average and mode are given by the
69 72
x-coordinate corresponding to the
Project duration (weeks)
curve’s peak.
86
Variances
• Statistically, how far a set of numbers is spread
out or distributed
• In the context of budgeting or cost estimation, a
variance is the difference between an actual and
an expected (budgeted) amount.
87
Variances
• Further analysis decomposes (breaks down) the
variance analysis into progressively smaller
components answers: “How much were we off?”
• Examination of variance into progressively
more-detailed levels of analysis answers:
“Where and why were we off?”
90
Variances Basic Concepts
• Static-Budget Variance (Level 0): the difference
between the actual result and the corresponding
static budget amount
• Favorable Variance (F): has the effect of
increasing operating income relative to the budget
amount
• Unfavorable Variance (U): has the effect of
decreasing operating income relative to the budget
amount
88
Variance Analysis
• VAR (X) = E [(X - µ)2]
• Continuous random variable
• Discrete random variable
• Normal distribution
89
Tools
85
Available Tools and Models for
Cost Data
Some of the websites listed here require user accounts. In most cases, anyone with a dot mil address can
obtain an account. You are encouraged to scan these sites and request an account to any site that you
think will be useful to you. This will save time when you need to use any sites to support a CBA or other
projects.
Tool/Model
URL
Purpose
FORCES Cost Models
https://www.osmisweb.army.mil/forces/login.aspx
Suite of models that provides quick
and reasonable unit cost estimates
to a wide variety of users
Army Military-Civilian
Cost System (AMCOS)
https://www.osmisweb.army.mil/amcos/app/home.
aspx
Personnel costs for military, civilian,
and/or contractor
ASA(FM&C) Website
http://asafm.army.mil/Documents/OfficeDocument
s/CostEconomics/rates/indices.xls
Inflation indices
Capabilities Knowledge
Base
http://asafm.army.mil/Documents/officedocuments
/costeconomics/guidances/ckb-ui.pdf
http://asafm.army.mil/offices/CE/Ckb.aspx?Office
Code=1400
Research, development, and
acquisition costing for major
weapon/material systems
Operating and Support
Management
Information System
(OSMIS)
https://www.osmisweb.army.mil/osmisrdb/login.as
px
Operating and support information
for major weapon/material systems
Access links through the “Resources” tab in the CBA Portal at:
https://cpp.army.mil
86
Conclusion
87
Overhead Variances
• Overhead is the most difficult cost to manage, and is the
least understood
• Overhead variances involve taking differences between
equations as the analysis moves back and forth between
actual results and budgeted amounts
88