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COST MANAGEMENT BASICS. Cost analysis. Agenda. Cost Estimating Types of Cost Normalization and Inflation Risk Assessment Cost Estimating Methods Labor Costing Optimization Statistical Analysis Tools . Cost Estimating. Cost and Cost Estimating Definition. Cost:

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agenda

Agenda

Cost Estimating

Types of Cost

Normalization and Inflation

Risk Assessment

Cost Estimating Methods

Labor Costing

Optimization

Statistical Analysis

Tools

cost and cost estimating definition

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:

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.

purpose of cost estimating

Purpose of Cost Estimating

  • Enable managers to:
    • 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.
characteristics of a good cost estimate

Characteristics of a Good Cost Estimate

Well documented

Includes source data and its significance

Clear and detailed calculations and results

Contains explanations for choosing a particular method or reference

Comprehensive

Ensures a level of detail where cost elements are neither omitted nor double counted

Accurate

Avoids bias and overly conservative or optimistic estimates

Bases its assessments on most likely scenarios and assumptions

Credible

Discusses any limitations of the analysis deriving from the uncertainty/bias of the data or assumptions

types of cost

Types of Cost

  • Sunk Costs
  • Opportunity Costs
  • Marginal Costs
  • Average Costs
sunk costs
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.

7

opportunity costs
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

8

marginal costs
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
marginal costs1

B

Lowest marginal costs

Marginal Costs

Total cost

C

High marginal costs

Total

(£)

A

High marginal costs

Output

10

average costs
Average Costs
  • Average Costis calculated by dividing the total cost by the total units produced
  • Average Cost is very high at low levels of output
cost drivers

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

slide15

Comparative Analyses

Supporting Resource Informed Decision

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 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 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.

break even point

Break-Even Point

Cost Reduction = Upfront Investment

Break-Even Point:

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

example break even point

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.

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

Internal Rate of Return (IRR)
net present value

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
net present value formula
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)

cost estimating in ea
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
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

Total Life Cycle Cost (LCC)
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

Investment Multiples/Ratios
business cases analysis bca key questions
Business Cases Analysis (BCA): Key Questions

Is the proposed solution:

  • Financially Viable (Make Economic Sense)
  • Optimal (Best Value or Increased Effectiveness)
  • Feasible (Assessing Constraints)
  • Implementable (Risks & 2nd/3rd Order Effects)
cost benefit analysis cba

Cost Benefit Analysis (CBA)

Within the Department of the Army, one major process which incorporates cost analysis is Cost Benefit Analysis (CBA)

what is a cba

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:
    • Define a problem or opportunity
    • Identify alternatives
    • Determine their costs and benefits
    • Evaluate and select the best alternative
why do we need cbas

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
cba and the cost culture

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
cost benefit analysis
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 enterpriseperspective

  • BENEFITS
  • The total of quantifiable and non-quantifiable benefits
  • Quantifiable benefits
    • Cost Savings
    • Cost Avoidances
  • Non-Quantifiable benefits
    • Greater capability
    • Faster availability
    • Better quality
    • Improved morale
    • Other?
  • COSTS
  • Quantifiable costs
    • Direct
    • Indirect
    • Initial/Start up
    • Sustainment
    • Procurement
  • Non-Quantifiable costs
    • Life/Safety/Health
    • Perception/Image
    • Opportunity
    • Risk/Uncertainty
    • Political

BENEFITS MUST BALANCE OR OUTWEIGH COSTS

cba is not a linear process

Objective

Recommendation

Assumptions

Sensitivity Analysis

Alternatives

Compare

Alternatives

Cost

Estimates

Benefits

Estimate

Selection

Criteria

CBA is NOT a Linear Process
  • 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
normalization and inflation1

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.
what is inflation

What is Inflation?

Definition

  • A rise in the general level of prices
  • Measure of change in the dollars’ purchasing power
  • In other words:
    • 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

inflation calculation and examples

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.
example current dollar calculation

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:
risk assessment and mitigation

Risk Assessment and Mitigation

The goal of risk assessment is to answer questions like:

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?

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.

types of risks

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 managementchanges

ways to measure address risk

Ways to Measure/Address Risk

  • Methods of measuring and/or addressing risk include, but are not limited to:
    • Effective Mean
    • Cost of Risk Mitigation
effective mean expected value

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.
cost of risk mitigation

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.

cost estimating principles and rules

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
available cost estimating methods

Available Cost Estimating Methods

Available methods:

  • Analogy
  • Parametric
  • Engineering
  • Actual Cost
  • Expert Opinion
  • Learning Curves

Most CBAs utilize all cost estimating methods

cost estimating methods

Cost Estimating Methods

The use of each method is based on the information available to support it.

GROSS ESTIMATES

DETAILED ESTIMATES

Parametric

Actual Costs

Engineering

Analogy

Figure 1: A summary of the usual application of each technique.

analogy method
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
analogy method example
Attribute Old System New System

Engine: F-100 F-200

Thrust: 12,000 lbs 16,000 lbs

Cost: $5.2M ?

Q: What is the unit cost of the F-200?

A: $5.2M * (16,000/12,000) = $6.9M

Analogy Method Example

Warning 2: An adjusted analogy is, by definition, estimating outside the range of the data.

Warning 1: An adjusted analogy is like a regression, but the slope is just a guess.

parametric method
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
parametric method example
Parametric Method Example

High Mobility Wheeled Vehicles Database

Is ‘Cubic Ft Shipping’ a good predictor of cost?

Cost of Gross Curb Cubic Ft Net

VehicleFirst UnitWeightWeightShippingHorsepower

M274 $ 9,585 1,770 970 81.6 12.5

M561 50,002 8,363 5,363 732.3 93

M656 93,262 24,785 14,785 1,227 183

M520 147,889 36,590 10,500 2,368 176

parametric method example cont d
Parametric Method Example (Cont’d)

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.

engineering method
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.)

developing the wbs

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

actual cost method
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
actual cost method example
Actual Cost Method Example
  • The development process is nearing completion
  • The materials have all been procured at a cost of $20M
  • The labor cost to date is $30M
  • 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

expert opinion method

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

  • Query expert opinion from group
  • Seek expert opinion from each group, and then summarize results to send in reports
  • Gather another opinion and summarize those results
  • Continue process until experts reach a consensus
expert opinion method example

Expert Opinion Method Example

Scenario: Three software engineers are recognized experts in ERP software development

  • You hold interviews to explain the Stakeholders’ needs, sizing level, and development process for your new system
  • Each member of the group submits his/her opinion of the final cost
  • If all expert opinions converge to, or hover around the same figure, that may be taken as a good cost estimate
forecasting what is forecasting

??

Forecasting: What is Forecasting?
  • Process of predicting a future event
  • Underlying basis of all business decisions
    • Production
    • Inventory
    • Personnel
    • Facilities

62

personnel costing1
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
amcos
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
amcos2

AMCOS

AMCOS ApplicationsAMCOSlite

what is optimization
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.
example finding optimal solutions

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.
example finding optimal solutions1

Example: Finding Optimal Solutions

  • How do you maximize the total number of HIMARS procured?
  • If you buy only Class X, you can afford 18.
  • If you buy only Class Y, you can carry 15.
  • So is “buy 18 Class X HIMARS” the optimal solution?
example finding optimal solutions2

Example: Finding Optimal Solutions

COA 2

COA 3

COA 4

COA 1 (Status Quo)

example finding optimal solutions3

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.
statistical analysis1

Area under curve between a and b is 99.74%

a

m

Mean

b

Time

Beta distribution

a

m

b

Mean

Time

Normal distribution

Statistical Analysis

78

statistic analysis applications
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
statistical analysis standard t erms
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

80

statistical analysis example
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

81

understanding likelihood of occurrence
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

82

quantifying cost risk
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?
cost risk and schedule example
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?
solution to example
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%
the normal gaussian bell curve distribution

Normal distribution:

Mean = 69 weeks;

σ = 3.45 weeks

Probability of meeting the schedule is 0.8078

Probability of exceeding 72 weeks is 0.1922

69 72

Project duration (weeks)

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
  • A probability density function shows the likelihood of an event occurring.
  • The height of the curve corresponds to the likelihood of an event occurring.
  • Perhaps the most commonly used probability distribution is the normal distribution.
  • Given two points on the x-axis, the area 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 x-coordinate corresponding to the curve’s peak.

86

variances
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

variances1
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
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
Variance Analysis
  • VAR (X) = E [(X - µ)2]
  • Continuous random variable
  • Discrete random variable
  • Normal distribution

89

available tools and models for cost data
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.

Access links through the “Resources” tab in the CBA Portal at:

https://cpp.army.mil

overhead variances
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