Unit 6 · Web viewCON 170 Fundamentals of Cost and Price Analysis CON 170 Fundamentals of Cost and...

CON 170 Fundamentals of Cost and Price Analysis

Instructor Support Package

CON 170

Fundamentals of Cost and Price Analysis

Unit 2

Quantitative Methods for Contract Pricing

May 2012

CON 170, Unit 2 Quantitative Methods for Contract Pricing 1




Unit 2 – Quantitative Methods for Contract Pricing

OVERVIEW

This lesson consists of material for a guided discussion, several PowerPoint slides, and several quantitative examples for the students to work. The instructor may use information contained in the Contract Pricing Reference Guide, Volume 2, as well as any appropriate FAR and DFARS paragraphs as references.

LESSON DETAILS

Lesson Title Quantitative Methods for Contract Pricing

Terminal Learning Objective

Given a contract pricing scenario, apply the appropriate quantitative method for contract pricing.

Time Required 8.5 hours

Method of Instruction

• Homework reading and research activity

• Instructor-facilitated discussion

• Classroom exercise

Lesson Schedule

Instructor-facilitated Discussion

Classroom Exercise

6.5 hours

1.75 hours

Lesson Summary 15 minutes

References, Supplemental Readings

Contract Pricing Reference Guide (CPRG), Volume 2

Evaluation Method

Student performance will be informally evaluated during class research activities and class exercises.Student performance will be evaluated on Unit 2 Exam.



INSTRUCTOR PREPARATION

Instructional Aids Type Description or Identification

Instructor Slides Unit 2 Instructor Support Package

Student Lesson Materials

• Unit Student Guide

• FAR

• DFARS

• DFARS PGI

• CPRG Vol 2

Whiteboard Yes

Butcher Paper None

Software Internet browserMS ExcelMS PowerPoint

Equipment Computer, Projector, Screen

Other None

Environment Standard classroom setup

Notes to Instructor

None

Student Preparation Prior to Class

Read CPRG Volume 2, and complete Unit 2 Lesson 1.

Estimated Student PreparationTime

1 hour



Lesson Presentation

Overview

IntroductionIn this unit, we will discuss:

Mathematical terminology, symbols and definitions

Terminal Learning Objective2.1 Apply the math, algebra and statistics methods from Unit 2 Lesson 1 in quantitative pricing methods for contract pricing

Enabling Learning ObjectivesAt the conclusion of this unit, you will be able to: Lesson 1 -- Fundamental Quantitative Problems Lesson 2 -- Price Indexing

ELO 2.01 Use Price Indexing to make price adjustments necessary to analyze price and cost information collected over a period of time.

Lesson 3 -- Analyzing Data Shape, Center, Spread and Trend ELO 2.02 Given a set of data, Analyze Data Shape, Center, Spread and Trend characteristics.

Lesson 4 -- Net Present Value ELO 2.03 Given a set of data calculate the Net Present Value of the given data.

Lesson 5 -- Cost Estimating Relationships ELO 2.04 Given Market Research data calculate and identify reasonable Cost Estimating Relationships.

Lesson 6 -- Cost Volume Analysis ELO 2.05 Through Cost-Volume Analysis, recognize the nature of fixed, variable, semi-variable and total costs, and develop a price estimate.ELO 2.06 Through Cost-Volume Analysis, determine a proposed price to be rational or irrational with respect to a “buy-in” seller strategy.

Lesson 7 -- Cost Volume Profit Analysis ELO 2.07 Through Cost-Volume-Profit analysis, recognize the nature of profit, revenue, contribution income, and calculate the contractor’s “break even” point



Lesson 1

Fundamental Quantitative Problems

1. Given the following equations, solve for X:

1a. If a = 6, b = 15, c = 5, solve for X: a(X) = b + c(X) 6(X) = 15 + 5(X) (-5(X)) (-5(X))

X = 151b. If a = 20, b = 70, c = 10, solve for X: a(X) = b + c(X)

20(X) = 70 + 10(X) (-10X) (-10X) 10X = 70

10 10

X = 72. For the equations below, answer the following, and use the graph on the next page:

2a. Graph the following, Y = 4 + 2(X), where X YY= 4 + 2(1) Y = 4 + 2(3) Y = 4 + 2(5) 1 ? 6

Y = 4 + 2 Y = 4 + 6 Y = 4 + 10 3 ? 10 Y = 6 Y = 10 Y = 14 5 ? 14

7 ? 18Y = 4 + 2(7) Y = 4 + 2(9) Y = 4 + 2(11) 9 ? 22Y = 4 + 14 Y = 4 + 18 Y = 4 + 22 11 ? 26Y = 18 Y = 22 Y = 26

2b. On the same graph as 2a, graph the following:Y = 10 + 1(X), where X YY = 10 + 1(0) Y = 10 + 1(2) Y = 10 + 1(4) 0 ? 10Y = 10 + 0 Y = 10 + 2 Y = 10 + 4 2 ? 12Y = 10 Y = 12 Y = 14 4 ? 14

6 ? 16Y = 10 + 1(6) Y = 10 + 1(8) Y = 10 + 1(10) 8 ? 18Y = 10 + 6 Y = 10 + 8 Y = 10 + 10 10 ? 20Y = 16 Y = 18 Y = 20

2c. Look at the graph. At what point do the lines appear to intersect?(6, 16)

Instructor Note: Draw graph on the board. The graph solution is on the next page.2d. Find the value for X which makes the two equations equal

4 + 2(X) = 10 + 1(X) -1(X) -1(X)4 + X = 10

-4 -4 X = 6



2e. How do your responses to 2c and 2d compare?X = 6 in both questions. If you enter the value of X = 6 in either equation you will get a corresponding value of Y = 16. This is the point on the graph where the two equations cross.

Y = 4 + 2(6) Y = 10 + 1(6)Y = 4 + 12 Y = 10 + 6Y = 16 Y = 16

0 2 4 6 8 10 120

5

10

15

20

25

30

Question 2 aQuestion 2 b



3. Given Y = A + BX, and A = 5, and B = 2, calculate Y at the following X coordinates. Note: an equation in this form represents a line, and can be called a “linear equation.”

X Y Y = 5 + 2(0) Y = 5 + 2(1) Y = 5 + 2(2) Y = 5 + 2(4)0 ? 5 Y = 5 + 0 Y = 5 + 2 Y = 5 + 4 Y = 5 + 81 ? 7 Y = 5 Y = 7 Y = 9 Y = 132 ? 94 ? 13

Graph the points. Instructor Note: Graph the answer on the board.

0 0.5 1 1.5 2 2.5 3 3.5 4 4.50

2

4

6

8

10

12

14

Question 3

With respect to the line, what does B represent? B represents the slope of the line. In this equation the slope is 2 or 2 .

1

What does A represent? A represents the Y-intercept, which is the point at which X = 0 and the line crosses or “intercepts” the Y-axis.

Write the equation of this line. Y = 5 + 2(X)



4. Given Y = A + BX, where A = 3 and B = 2, calculate the coordinates and plot the graph for: X Y Y = 3 + 2(O) Y = 3 + 2(1) Y = 3 + 2(2) Y = 3 + 2(3)0 ? 3 Y = 3 + 0 Y = 3 + 2 Y = 3 + 4 Y = 3 + 61 ? 5 Y = 3 Y = 5 Y = 7 Y = 92 ? 73 ? 9

Instructor Notes: Graph the answer on the board.

0 0.5 1 1.5 2 2.5 3 3.50

1

2

3

4

5

6

7

8

9

10

Question 4

Write the equation of this line. Y = 3 + 2(X)

What is the “y-intercept”? 3 (reinforce, this is where X = 0, and the line crosses or “intercepts” the Y-axis.

What is the slope of this line? 2 OR 2 . 1



5. Given the following points, plot the graph.X Y 1 32 43 56 8

Instructor Note: Graph the answer on the board, or show the slide from the Instructor slides.

0 1 2 3 4 5 6 70

1

2

3

4

5

6

7

8

9

Question 5

5a. What is the slope of this line? Hint: slope is “rise over run,” or, the change in y for every change in X. It can be calculated as follows:

Y 2−Y 1

X2−X1

8 - 5 = 3 Thus, the slope of 3 equates to a slope of 16 - 3 3 3

Instructor note: remind students not to solve this like a normal fraction, trying to find a common denominator before doing the subtraction.

5b. What is the y-intercept? Hint: the y-intercept is the value of Y when X = 0. We can calculate the y-intercept with the equation of a line (shown above) by knowing the slope and one other point on the line.

On this line, let’s use the point (6,8), and the slope of 1 to calculate the value of A:From our equation of a line, we can find A by reordering the elements: A = Y - B(X)

A = 8 - 1(6) A = 2

5c. With the slope and the y-intercept, write the equation of this line:From our equation of a line, Y = A + BX, we can write the equation of this line:

Y = 2 + 1X



5d. With the equation of the line, verify the points you plotted earlier fit the line of your graph.Y = 2 + 1X X Y

0 21 32 43 56 8

6. Lester must earn at least a 90% in his agency’s Contracting Officer warrant board course in order to earn his Procuring Contracting Officer (PCO Warrant). Based on his scores, will Lester earn his PCO warrant?

Test 1 84%Test 2 86%Final Exam 96%

In calculating the average (or mean), Lester earned an 88.7% average…not quite up to the standard to earn his PCO warrant.

7. Lester wakes up after a bad dream, and realizes he misread the PCO course syllabus. While he must earn at least a 90% in his Contracting Officer warrant board course to earn his Procuring Contracting Officer (PCO Warrant), his first two tests are worth 25% of his grade, and the final exam is worth 50%. Based on his scores, will Lester earn his PCO warrant?

Test 1 84%Test 2 86%Final Exam 96%

Score Weighting Weighted ScoreTest 1 84 0.25 21Test 2 86 0.25 21.5Final Exam 96 0.5 48

Course grade 90.5

Based on the weighted average of the course, Lester has passed the 90% standard, and earned his PCO warrant!



Lesson 2 -- ELO 2.01 Use Price Indexing to make price adjustments necessary to analyze price and cost information collected over a period of time.

Introduction Price Analysis involves the comparison of the apparent successful quote/proposal to other prices/costs. Sometimes we have to compare the quote/offer to historical prices/costs. The changing value of the dollar over time can complicate comparisons and other analysis using price or cost information collected over time. You can use price indexes to adjust prices/costs to compensate for inflation or deflation and facilitate comparisons and other analysis.

Price Index Number Definition

Probably the most commonly used quantitative measure used in contract pricing is the price index number. Price index numbers measure percentage changes in prices over time.

Any discussion of index numbers in contract pricing normally refers to price indexes. However, other index numbers could be used in contract pricing, particularly measures of productivity.

Simple and Aggregate Price Index Numbers

Price index numbers can indicate price changes for one or several related items or services over a period of time.

Simple index numbers calculate price changes for a single item over time.Index numbers are more accurate if they are constructed using actual prices paid for a single commodity, product or service rather than the more general aggregated index.

Aggregate index numbers calculate price changes for a group of related items over time.Aggregated indexes permit analysis of price changes for the group of related products, such as price changes for apples, oranges, plywood, or nails. An example of an aggregate price index is the Producer Price Index (Bureau of Labor Statistics) that provides information on the changes in the wholesale price of products sold in the United States over a given period of time.



Identifying Situations for Use


You can use price index numbers to:

• Inflate/deflate prices or costs for direct comparisonYou can use price index numbers to estimate/analyze a product’s cost or price today using the cost or price of the same or a similar product in the past.

• Inflate/deflate prices or costs to facilitate trend analysisYou can use index numbers to facilitate trend or time series analysis of costs or prices by eliminating or reducing the effects of inflation so that the analysis can be made in constant-year dollars (dollars free of charges related to inflation/deflation).

• Estimate/project prices or costs over the period of contract performancePrices and costs of future performance are not certain. One effect that you must consider is the changing value of the dollar. You can use index numbers to estimate and negotiate future costs and prices.

• Adjust contract price or cost for inflation/deflationWhen price changes are particularly volatile, you may need to include an economic price adjustment clause in the contract. The use of index numbers is one of the most popular methods used to identify and define price changes for economic price adjustment.

Selecting a Price Index for Analysis

Sources of Published Indexes

You may not have the time or data required to construct the price indexes that you need for price or cost analysis. Fortunately, there are many sources of previously constructed price indexes that you can use to estimate price changes. These sources include:

Bureau of Labor Statistics Other Government agencies Government contracting organizations Commercial forecasting firms Industry Newspapers



Points to Consider in Index Selection

Use published indexes carefully, since a published index will usually not exactly fit the pattern of price changes for the product or service that you are analyzing. The data isn’t usually from a specific contractor or location, but represent national or regional averages. Nevertheless, pre-constructed index numbers offer a practical alternative to the costly and time-consuming task of developing index numbers from basic cost data.

When you use published indexes, choose the index series that best fits your specific analysis effort. Usually, the closer the chosen index series relates to the item that you are pricing, the more useful the number will be in your analysis.

If you are buying a finished good, indexes representing raw materials and purchased components will not necessarily provide an accurate basis for projecting prices because the finished good may also be strongly influenced by trends in direct labor, cost of capital, etc. Accuracy can be improved through the use of a weighted average index, which represents changes in both labor and material elements of price. Many contracting organizations develop weighted average indexes for major products or major groups of products.

Indexes from the Bureau of Labor Statistics

The Government collects and publishes vast amounts of data on prices. The U.S. Department of Labor, Bureau of Labor Statistics (BLS) is the principal fact-finding agency for the Federal Government in the broad field of labor economics and statistics. (See http://www.bls.gov/) Four of the best known sources of index numbers are published by the BLS:

Instructor Note: recommend reviewing these 4 indexes before the lesson. This is an introductory lesson, but you can see from the BLS site, this is a tremendous resource for market research and pricing. For example, take a look at the BLS’ Producer Price Index, “Escalation Guide for Contracting Parties.” (Dude!)

Producer Price IndexProbably the best known and most frequently used source of price index numbers for material pricing is the Producer Price Indexes (PPI) published monthly by the BLS. These indexes report monthly price changes at the producer/wholesale level for 15 major commodity groups, and over 30 services. The table on the next page includes several of the commodities and services addressed by the PPI, and can be found at http://bls.gov/web/ppi/ppitable06.pdf). A producer price index for an industry is a measure of changes in prices received for the industry’s output sold outside the industry (that is, its net output). Producer price indexes measure the average change in prices received by domestic producers of commodities in all stages of processing. The PPI is an output price index, that is, it measures price changes received by manufacturers of a product. It is neither a buyer's index nor an input price index, that is, it does not measure the cost of producing that item.



PPI data are based on selling prices reported by establishments of all sizes selected by probability sampling, with the probability of selection proportionate to size. Individual items and transaction terms from these firms are also chosen by probability proportionate to size sampling methods. PPIs are based on a monthly sample of about 100,000 quotations, resulting in publication of over 10,000 different indexes each month (for more information, see the BLS’ Producer Price Index, Escalation Guide for Contracting Parties, on the BLS website).

PRODUCER PRICE INDEXES COMMODITY GROUPS

Commodity Code Commodity or Service Description

01 Farm Products03 Textile Products and Apparel04 Hides, Skins, Leather, and Related Products05 Fuels and Related Products and Power06 Chemicals and Allied Products07 Rubber and Plastic Products08 Lumber and Wood Products09 Pulp, Paper, and Allied Products10 Metals and Metal Products11 Machinery and Equipment12 Furniture and Household Durables13 Nonmetallic Mineral Products14 Transportation Equipment30 Transportation Services32 Warehousing Storage Services38 Data Processing and Related Services45 Professional Services (partial, including business,

legal, engineering, IT, logistics consulting)80 Construction (partial)

Indexes from the Bureau of Labor Statistics, (continued)

Consumer Price Index Detailed ReportThe consumer price index (CPI), published monthly in the Consumer Price Index Detailed Report, reports on changes in consumer prices for a fixed mix of goods selected from the following categories: food clothing shelter and fuels transportation medical services



You should normally not use the CPI in adjusting material prices because the CPI reflects retail rather than wholesale price changes. However, the CPI can be of value in pricing services when labor rate increases are linked to changes in the CPI.

Instructor Note: Uses and limitations of PPI and CPI, from the BLS Handbook of Methods, Chapter 14, “Producer Price Index.” For info, Chapter 17 explains the “Consumer Price Index”:

Producer Price Indexes are used for many purposes by government, business, labor, universities, and other kinds of organizations, as well as by members of the general public. From the PPI section, PPI was defined as a measure of changes in prices received for the industry’s output sold outside the industry (that is, its net output). This generally measures prices of goods and services at different stages of production (from raw material or “crude,” to intermediate, to finished). There are a few reasons the PPI and the CPI may not necessarily move together.

PPI measures prices of raw materials and labor to produce goods and services. Through the process and business transactions of transforming raw materials to goods and services, swings in producer prices for foods and other items may be considerably dampened by the time retail prices are measured. For example, suppose that the price of cotton rises sharply. If the price increase is passed through by spinners of cotton yarn, then by weavers of gray cotton fabric, then by producers of finished cotton fabric, and, finally, by shirt manufacturers, where the cotton has finally become a “finished good.” The price of this finished good is shaped not only by the price of cotton, but also by the price swings of all the steps between “cotton” and “finished goods.” Generally, the market price of this finished good is what is measured by the CPI. Thus, prices of raw materials tend to be more volatile than prices of finished goods.

The PPI does not measure changes in prices for imported goods, whereas the CPI includes imports.

The CPI does not capture changes in capital equipment prices, which are captured in the PPI major component of the Finished Goods Price Index.

Monthly Labor ReviewThe Monthly Labor Review is edited and posted by the Bureau of Labor Statistics, and includes analysis of the labor costs, output, productivity, unemployment for different skills and population demographics. The Review also includes selected data from a



number of Government indexes, including: Employment Cost Index Consumer Price Index Producer Price Indexes Export Price Indexes Import Price Indexes

That data and other information presented in the publication can prove useful in conducting market research and for analyzing the price of contracts, such as service contracts, where direct labor is a significant part of contract price.

Employment, Hours, and Earnings Survey

The Employment, Hours, and Earnings Survey presents information on the hours worked and an earnings index for various classes of labor. Like the Monthly Labor Review, the survey can be very useful in market research and for pricing contracts in which direct labor is a significant part of the contract price.

Indexes from Other Government Agencies

Data on contract prices are also available from agencies other than the Bureau of Labor Statistics. The most notable are the Federal Reserve System and the Bureau of Economic Analysis.

* Federal Reserve System.

The Board of Governors publishes the Federal Reserve Bulletin, which includes economic indexes and data on business, commodity prices, construction, labor, manufactures, and wholesale trade. Each bank in the system publishes information each month with special reference to its own Federal Reserve District. (See http://www.federalreserve.gov/pubs/bulletin/default.htm)

* Bureau of Economic Analysis Publications.

The Bureau of Economic Analysis, Department of Commerce, publishes the Survey of Current Business and the Business Conditions Digest. The Survey of Current Business provides general information on trends in industry and the business outlook. It furnishes economic indexes on business, construction, manufactures, and wholesale trade. The Business Conditions Digest presents almost 500 economic indicators in a form convenient for analysis, as well as different approaches to the study of current business conditions and business prospects, including leading economic indicators. (See http://www.bea.doc.gov/)



Indexes from Government Contracting Organizations

Many Government contracting organizations have teams of analysts who develop indexes that are particularly applicable to the organizations’ specific contracting situations. These indexes may be developed from raw price data, or they may be developed as weighted averages of published indexes.

Indexes from Commercial Forecasting Firms

Numerous commercial indexes are available for use in contract price analysis. While most Government indexes only report historical price changes, many commercial indexes also forecast future price movement. In situations where forecasts are necessary, commercial indexes may prove particularly useful. A major source for this information is Global Insight (formerly DRI). Before using such indexes, examine their development and consult with auditors, technical personnel, and other contracting professionals to assure that they are applicable in your analysis situation.

Indexes from Industry

Industry and trade publications frequently provide general forecasts of economic conditions and price changes anticipated in the industry. To identify which publications have economic information relevant to a particular product, ask Government technical personnel. Companies can also assist you in the identification of appropriate publications. However, be sure to verify with Government personnel the appropriateness of sources of information recommended by responders.

Indexes from Newspapers

Publications, such as local, national, and financial newspapers, provide valuable forecasts of price changes in specific industries. The information reported is normally data provided by the Government, economic forecasting firms, or industry groups.

Adjusting Prices/Costs for Analysis




Calculate Relative Price Change Between Two Periods

Index numbers indicate the percentage change in prices relative to the base year. For example, the table below shows that the average product price increased by 23.2 percent between 2006 and 2011.

YEAR PRODUCT INDEX2006 100.02007 105.32008 112.02009 116.52010 119.32011 123.2

Determining Percentage Change Between Two Years

To adjust prices for inflation or deflation, you must be able to do more than determine how prices have changed relative to the base year. You must be able to determine how prices changed between any two time periods.

( NIOI

x 100)−100=Percentage Change

Where:NI = New IndexOI = Old Index(Chronological Indexes)

For example, looking at the table above, how did prices change between 2008 and 2011? To calculate the percentage price change between any two time periods, you must follow the same procedure that you would follow if you had actual price data; you must divide.

NI (2011)OI (2008 )

=123 .2112. 0

=(1 .10 X 100 )– 100 = 10% increase

Based on the price index and this calculation, you could estimate that product prices in 2011 were 1.10 times the prices in 2008 or 10.0 percent more than the prices in 2008.

Estimating Prices/Costs Using Index Numbers

You can use index numbers to adjust prices or costs from any time period for inflation or deflation. For example, the calculation above demonstrated that product prices increased 10.0 percent between 2008 and 2011. If you knew that the price for an equipment item in 2008 was $1,000, you could estimate that the price should be 10.0 percent higher in 2011. That would result in a price estimate of $1,100 for 2011.

Price Adjustment Formula Method. The Price Adjustment Formula is a simplification of the Ratio Method described above.

NIOI

x Old Price (2008 )=Price Estimate

Example:

NI (2011)OI (2008 )

x Old Price (2008)=Price Estimate for 2011

123 .2112 . 0

x $1,000 =Price Estimate for 2011

1 .10 x $1,000=Price Estimate for 2011$1,100=Price Estimate for 2011


Adjusting Prices/Costs for Pricing Comparisons

Introduction You can use price indexes to develop should-pay estimates of current price or cost based on historical information. These should-pay estimates can be used for a variety of purposes including comparison with an offered/quoted price or cost as part of an evaluation of reasonableness.

Steps in Using Price Indexes to Analyze Price/Cost Reasonable-ness

To perform this analysis, follow the steps below:

Step 1. Collect available price/cost data.

Step 2. Select price indexes for adjusting price/cost data.

Step 3. Adjust prices/costs for inflation/deflation.

Step 4. Use adjusted prices/costs for pricing comparisons.

Example of Using Price Indexes to Analyze Price/Cost Reasonable-ness

Consider the problem of analyzing a contractor's proposed price of $23,000 for a turret lathe to be delivered in 2011.

Step 1. Collect Available Price/Cost DataA procurement history file reveals that the same machine tool was purchased in 2008 at a price of $18,500. Determine whether the 2011 proposed price is reasonable.

Step 2. Select An Index Series For Adjusting Price/Cost DataSelect or construct an appropriate index series. In this case, you might select a Machinery and Equipment Index as a reasonable indicator of price movement for a turret lathe. You could extract the data from a publication, such as the PPI, or from a similar commercial index.

YEAR MACHINERY AND EQUIPMENT INDEX

2006 100.02007 103.32008 106.02009 110.82010 115.02011 121.9

Step 3. Adjust Prices/Costs for Inflation/Deflation

After you have selected an index, you can adjust prices to a common dollar value level. In this case, you would normally adjust the historical



2008 price to the 2011 dollar value level. To make the adjustment, you simply use one of the methods already demonstrated.

* Using the Formula Adjustment Method.

NI (2011)OI (2008 )

x OP (2008)=Price Estimate for 2011

121 .9106 . 0

x $18,500 =Price Estimate for 2011

1 .15 x $18,500=Price Estimate for 2011

$21,275=Price Estimate for 2011

Step 4: Make Direct Price ComparisonOnce you have made the adjustment for inflation/deflation, you can compare the offered and historical prices in constant dollars. The offered price/cost is $23,000, but the adjusted historical price/cost is only $21,275. Thus, the offered price/cost is $1,725, or 8.1 percent higher than what you would expect, given the historical data and available price indexes.

Remember: Do not base your determination on price reasonableness based on this type of analysis alone. Consider the entire contracting situation, including: - differences in quantity, quality, delivery requirements; - market changes; - other contract terms that might significantly affect price; - the age of the historical data discovered during market research

Adjusting Prices/Costs for Further Analysis




Introduction Often you will make a series of acquisitions over a period of time. Pricing trends may develop but they may be obscured by inflation/deflation. Adjusting prices for inflation/deflation will make it possible to more accurately identify and track these trends.

Steps in Using Price Indexes to Analyze Price/Cost Reasonableness

Adjustment for further analysis follows four steps similar to those used for data adjustment that are applied in preparation for direct comparison. The major difference is that several elements of cost/price data must be adjusted to a single time period. After adjustment, data is said to be in constant-year dollars.

Step 1. Collect available price/cost data.

Step 2. Select price indexes for adjusting price/cost data.

Step 3. Adjust prices/costs for inflation/deflation.

Step 4. Apply appropriate analysis technique.

Example of Using Price Indexes to Adjust Prices/Costs for Further Analysis

To illustrate this analysis, consider an offer of $22,500 each for five precision presses in 2011.

Instructor Note: Through feedback from the first several offerings, sometimes students miss the purpose of this Example--to determine if the proposed price of $22,500 in 2011 is within a reasonable range.

Step 1. Collect Available Price/Cost Data.The organization has purchased five similar presses each year since 2006. The historical unit prices are shown in Column D of the table below. While purchase quantity changes are not present in this situation, unit prices are used to limit the effect of quantity differences on trend analysis. In this case, the only apparent cost/price trend in the unadjusted data is increasing prices.

Step 2. Select Price Indexes For Adjusting Price/Cost Data.Again, the Machinery and Equipment Index will be used. Annual indexes are presented in Column B of the table below.

Step 3. Adjust Prices/Costs For Inflation/DeflationThe adjustment calculation is presented in Column C of the table below. Each historical price is adjusted to equivalent prices in 2011 dollars.

Instructor Note: have students complete the following table, columns C and E, then move to “Step 4, Apply Appropriate Analysis Technique”

ADJUSTMENT FOR FURTHER ANALYSIS

A B C D E

Year

Machinery and

Equipment Index

Index Adjustment Calculation

Historical Prices

PriceAdjusted to 2011

2006 100.0 121.9 $17,391 $21,200*


Example of Using Price Indexes to Adjust Prices/Costs for Further Analysis, continued

Step 4. Apply Appropriate Analysis Technique

What trends do you observe?Instructor note: Direct students to review column E. After the historical unit prices are adjusted to 2011 dollars, a trend becomes obvious. In 2011 dollars, prices have been dropping $200 each year since 2006. If this trend continues, the price estimate for 2011 is $20,200. That projection is based on the continuation of the historical trend.

What concerns will you address with additional market research?The offer under consideration is $22,500, but based on the adjusted prices in column E, a proposed price in 2011 should be closer to $20,200. Is this reasonable? To find out, we must explain the variance through market research. Analysis based on historical price trends must consider any changes in the contracting situation and their possible affect on contract price. In our case, we are buying the same quantity (5) as in the past, but are we pursuing the same delivery terms, warranty, performance, or another market situation which could cause price changes?

Most trends are not so obvious, even after prices have been adjusted to constant-year dollars. Still, techniques such as regression analysis and improvement curve analysis (which we will learn in CON 270) can often be applied to help refine our understanding of variances within historical data.

Identifying Issues and Concerns

Questions to Consider in Analysis

As you perform price/cost analysis, consider the issues and concerns identified in this section, whenever your analysis is based on data collected over time.

* Were prices/costs collected over time adjusted for inflation/deflation?Inflation/deflation can mask underlying price changes. Price indexes should be used to compensate for the effect these general price changes.

* Is it reasonable to use the price index series selected?The price index series selected for making the price/cost adjustment should be as closely related to the item being considered as possible. For example, you should not use the Consumer Price Index to adjust for changes in the price of complex industrial electronic equipment.

* Are adjustments calculated correctly?



Anyone can make a mistake in calculation. Assure that all adjustments are made correctly. This is particularly important when the adjustment is part of a contractor's offer or part of an analysis performed by other Government personnel.

* Is the time period for the adjustment reasonable?When adjusting historical prices for inflation, take care in selecting the period of adjustment. There are two basic methods that are used in adjusting costs/prices, period between acquisition dates and the period between delivery dates. The period between acquisition dates is most commonly used because purchase dates are typically more readily available. However, be careful if delivery schedules are substantially different.

* Is more than one adjustment made for the same inflation/deflation?For example, it is common for offerors to adjust supplier quotes to consider inflation/between the time when the quote was obtained and the date that the product will be required. This is acceptable unless the supplier already considered the inflation/deflation in making the quote.

* How far into the future should you forecast?The farther into the future that you forecast, the greater the risk.

Practice Problems:

You have been asked to analyze changes in prices and costs over the past several years, based on the Producer Price Index for a certain commodity category. Use the following Widget Producer Price Index factors to answer the questions below:

Year Widget PPI2007 100.02008 105.02009 98.02010 106.52011 112.92012 122.0

1. By what percentage did the indexes change between 2008 and 2012? [( 122 / 105 ) X 100 ] - 100 = 16.2%

2. If an item was priced at $5,000 in 2008, estimate the price of the item in 2012. 122 / 105 X $5,000 = $5,809.50

3. An item was priced at $3,000 per unit in 2008. What would you



estimate that the price was in 2009? [(98 / 105) X $3,000] = $2,800

4. It is 2012 and you have just received a proposal from Brown Industries for 1,000 widgets at a price of $850 each. You remember that once before you purchased widgets. You pull the contract file and see that the price of $650 each for 1,500 widgets was determined fair and reasonable in 2010. Based on the Producer Price Index, what would your estimate be for the price in 2012? 122 / 106.5 X $650 = $744.60

Therefore, does the proposed price appear to be fair and reasonable? Defend your determination. Hmm. Based on our Lesson 1 percentage-change lesson, this price is 14% higher than the index data indicate the price should be.

$: $850 proposed - $744.60 estimated = $105.40 higher %: $105.40 / $744.60 = 14.1% over the $744.60 estimate

Thus, before determining the price to be reasonable, we must conduct additional market research or fact-finding to be able to explain the variance. This concept of “analyzing and explaining variance” is emphasized again in the next lesson, and in CON 270.



Lesson 3 -- ELO 2.02 Given a set of data, Analyze Data Shape, Center, Spread and Trend characteristics.

OVERVIEW

In this lesson, the student will be presented with discussion of the techniques of Center, Shape, Spread, and Trend Analysis.

LESSON DETAILS

References, Supplemental Readings

Instructor Support Package Center, Shapes, Spread, and Trend Analysis slides with notes in

note view Student Graphing Handouts and Ruler Contract Pricing Reference Guides:

http://www.acq.osd.mil/dpap/cpf/contract_pricing_reference_guides.html,

Webster’s Online and Free Dictionary

Purpose: Equip buyers to build and use a histogram to analyze market research data as a foundation for contract pricing.

Key terms:

CenterShapeSpreadTrend

Regarding the Center and Shape:AverageArithmetic MeanMedian


http://www.acq.osd.mil/dpap/cpf/contract_pricing_reference_guides.html

http://www.acq.osd.mil/dpap/cpf/contract_pricing_reference_guides.html


INSTRUCTOR PRESENTATION

Overview

Preliminaries

!! This lesson consists of a PowerPoint presentation and interactive student participation.

Instructor Introduction

!! This lesson is a basic overview of how to graphically analyze and display key aspects of how data to determine the best way to describe the middle balance of the data with one point, how much the data points range away from the middle values, and data patterns useful for predictive purposes.

Review of Previous Lessons

N/A

Attention-Gainer

There is an old saying amongst statisticians that if you torture numbers long enough you can get them to confess to anything. The purpose of the lesson, however, is to identify several simple ways of portraying and analyzing a set of numbers to draw conclusions and make predictions about the future.

You may have heard obvious examples of poorly analyzed data – “the average American family has 2.13 children”. This observation doesn’t help plan for the next family to move into your neighborhood because it’s certain the new family will not have 2.13 children. What is more helpful is to find a way to describe the typical family and the level of certainty of expectation that the next family will be typical. In modern language, average has become to mean typical rather than a specific numerical calculation. We will use mean, median, and mode as three different ways to describe typical. We will also look historical patterns to determine is it more or less likely that the next data occurrence will be typical – or in our example, how certain can you be that the next family will have close to the typical number of children.

Fundamental Measures of Centrality

One characteristic of a set of numbers is the middle point of the data. This can be calculated in a couple of different ways:

The Mean is calculated by adding all the numbers together and dividing by the number of values.

The Median is the middle value of the numbers listed in rank order. If there is an even number of values, the median is the mean of the middle two numbers.

Shape of the Data SetPlotting of data may give insight into a characteristic of the data known as shape.

Data with a Normal shape will have the same mean and median. In the normal case, data will be balanced around the middle.



Data might be Skewed either to the right (positive, with the low “tail” pointing to the right) or left (negative, with the low “tail” pointing to the left). In skewed data, a small number of extremely positive or negative values caused the mean to be either higher or lower than the median. When graphed, this produces a tail of data to the right or left.

Instructor Note: draw a normal, skew right (flatter on right side) and skew left (flatter on left side) distribution on the whiteboard.

Data may also be Bi-Modal or Multi-Modal. These means that there is more than one cluster of occurrences of data values along the continuum that when graphed appears as multiple peaks of data.

Instructor Note: draw a bi-modal/multi-modal distribution on the whiteboard. Caution students on the definition of “bi-modal” and “multi-modal.” When analyzing shape, a “bi-modal” or “multi-modal” shape does not necessarily mean the data set includes exactly two (or more) “modes;” but rather, that the shape of the data appears to have two (or more) “humps,” which indicates data elements are clustered near two (or more) general values.

Spread of the data is generally concerned with the range from low to high value and can give indication to the expected extent of the values possible.

Instructor Note: draw a normal distribution with a narrow spread, and a wide spread on the whiteboard.

Data Trends can also be determined. Trends result when a separate influence or variable is determined to influence data. Once the relationship between this separate variable and the data set of interest is established, knowing the value of the separate variable will help determine characteristics of the data set.

As a contracting professional, you should become familiar with the types of scenarios that will be worked in class, as each one describes a unique aspect of data analysis in terms of Center, Shape, Spread, and Trend.

Students should become familiar with the following scenarios that will be worked in class as each describes various characteristics for data analysis in terms of Center, Shape, Spread, and Trend. Instruct students to do each of the examples. Sometimes, student teams may assign each student one of the examples then share answers with each other, rather than having each student working all five. The test bank will include questions from all the examples!



Lesson


For the median, tell students to make a chronological list of numbers; then pick the middle. If there is an even number of elements, take the mean of the middle two.

Instructors should keep the pace moving, get to the exercises quickly where students will best understand these definitions through application

Explain the idea of one data point describing what is typical of all the data (mean and median)

Talk about how the shape can be useful for planning

Highlight how spread is a measure of overall size and breadth of the data

Trends of data will be covered later in greater detail and in CON 270



Walk students through the first scenario. The slides will build as you explain the process.Explain that “normalized” means all variables have been eliminated and the radios being compared are essentially the same.

Students should draw by hand using the graph provided in their student guide.

1. Have students rank order prices high to low

2. Notice the “bins” in the graph. Based on the raw data, we set each bin width at 10. Students should color in a block for each price that occurs in a bin. Stack the colored blocks if there is more than one occurrence in a bin.

3. Mean = sum/7=164

4. Median=middle=164

5. Range=min-max=22

6. Draw a vertical line through the mean and median point



Give students the opportunity to accomplish scenario #2 on their own, using the same format and process as the previous example.

Point out that “typical” is an imprecise data characteristic but has intuitive value. It may mean “if I could only share one value to describe the data…”

Students should draw by hand using the graph provided in their student guide and answer the questions.

Upon completion, go over the rank ordered numbers. Highlight that even though the numbers are different than Scenario #1, the Mean and Median are the same – the “typical” values. The range and shape are not the same. Use this to point out that the wider spread gives less confidence in being able to predict future values. Data in #1 provides greater predictive confidence.



Give students the opportunity to accomplish scenario #3 on their own, using the same format as the previous examples.


Highlight:

1. Skewed Right - a few high values have caused the Mean to be uncharacteristically high

2. Mean > Median

3. Mean occurs in a bin with no occurrences

4. Median occurs in a bin with several occurrences

So…the point is:If this is your market research data, your best estimate would be the median rather than the mean as the most typical price or as a basis to establish a negotiation position, etc. Also, more market research may be necessary to explain the wide range in data.



Give students the opportunity to accomplish scenario #4 on their own.


Highlight:

1. Skewed Left - a few lower values have caused the Mean to be uncharacteristically low

2. Mean < Median

3. Mean occurs in a bin with no occurrences

4. Median occurs in a bin with several occurrences

So…the point is:If this is your market research data, your best estimate would be the median rather than the mean as the most typical price or as a basis to establish a negotiation position, etc. Also, more market research may be needed to explain the wide range in data.



Give students the opportunity to accomplish scenario #5 on their own.


Highlight:

1. Distribution is not normal

2. Mean and Median are close but not useful for forming conclusions

3. Drawing the picture indicates more information is required

So…the point is:If this is your market research data, you should do more analysis or collect more market research data to determine the most typical price or to form a basis to establish a negotiation position, etc.

This could be a case where there are two distinct sets of data rather than just one.


Instructors should close by recapping the basic analysis concepts:

- When the mean and median are close together, this could be a sign the distribution is normal – unless it is a multi-modal distribution.


Give students the opportunity to discuss factors which could be present that might cause the market research to result in a bi-modal distribution.

Some possibilities:- market research data is from two different years, and was not indexed properly.- market research data included two types of radios: for example digital/analogue, ruggedized/simple, touch screen/dials- some other independent variable may still exist that can explain a trend.

So…the point is:- Ask – “did I index correctly”- Am I comparing the same or similar items- Is more market research or analysis required

This discussion should set the stage for Cost Volume Analysis.


- With small data sets, there may or may not be an official “mode” thus graphical analysis is helpful in identifying distribution types.

- Even with equal means and medians under normal distributions, wider distributions (larger ranges) give you less confidence as a predictive tool (Scenario # 1 vs. #2)

- Means and medians may be the same or very close under both normal and multi-modal distributions; but when they are different, the distribution could be skewed one way or the other (e.g. Scenarios #3 and #4).

- With distributions skewed right, the mean is more affected by the extreme values in the tail to the right and will be larger than the median (e.g. Scenario #3).

- With distributions skewed left, the mean is more affected by the extreme values in the tail to the left and will be less than the median.

- The mean often used as the best “average” to typify the data, but this is true when the data are normally distributed (in which case it is close to the median anyway).

- When dealing with skewed data, the median may be the best “average” to use to typify the data.

- In analyzing data which is skewed, multi-modal, or presents a wide range, the price analyst must ensure the data was properly indexed, and appropriately normalized for content, quantity, size, performance, and economics; to ensure the shape, center, spread and trends are based on reasoned analysis.

LESSON SUMMARY

The purpose of this lesson has been to highlight some basic ways of analysis simple sets of data.To recap, key values are easily calculated:

- Mean = Sum of the observations divided by the number of observations.- Median = After rank ordering the observations - the middle value or the average of the middle

two if there is an even number of observations- Range = Subtraction of the Minimum from the Maximum- Distribution of a set of numbers can be described in several different ways:

o The Center can be described by either mean, median, and modeo Shape is commonly categorized into four common distributions: normal, right skew (tail

to the right), left skew (tail to the left), or multi-modalo Spread can be basically described by the range calculating the difference between the

maximum and minimum o Trend: Even with data properly normalized for content, quantity, and economics; certain

size and/or performance attributes may also help explain prices when faced with wider spreads (high range) and/or multi-modal



The objectives of this lesson:- The terminal learning objective for this lesson was to identify techniques for performing data

analysis for center, shape, spread, and trend analysis.- The enabling learning objectives for this lesson were:- Given a set of data, student can describe the measures of central tendency (mean, median, and

mode) and dispersion- Gain understanding of how to graph and interpret simple data sets related to contract pricing- Gain understanding of how to formulate decisions based on fundamental conclusions drawn from

graphing and pictorial data analysis



Lesson 4 -- ELO 2.03 Given a set of data calculate the Net Present Value of the given data.

Instructor Note: For preparation purposes, this lesson was designed to be taught through the slide deck, with minimal additional instruction from the ISP. The red ink in the slides is not in the Student Guides. The intent is for students to complete those areas to apply the instruction. Also note, the slide format changed significantly between October 2011 and January 2012.



To introduce the TVM concept, explain an example of putting $1 in a savings account. Even this simple example may test students’ ability to use a calculator, especially with respect to calculating exponents. Have the students calculate the first PV example, and find the answer of $1.05.

After they finish the first PV example, to ensure students understand the concept and can use their calculator, ask them what the Future Value of $150 would be after 3 years at 5% interest. Perhaps on the whiteboard, write:

FV = $150 X (1 + .05) 3 yrs

FV = $173.64



A great way to introduce this lesson AND get students to dive in to the CPRG is to start with the example in the CPRG, Vol 2, Ch 9. Have the students turn to/click to paragraph 9.0 in this CPRG reference and review:

- If a car dealer offers to sell you a car for $21,000 cash, or offers “free financing” for $21,000 due in 1 year, which is a more attractive offer?

- Certainly, you’d prefer to pay the $21,000 later, so you could invest the money for 1 year and earn interest.

- Then, one dealer offers to sell you the car for $20,000 cash on delivery (now) or for $21,000 if you pay the entire amount in 1 year. Which deal is best?

- Hmmm. Offer 1 has a PV of $20,000, for it will be paid “now.”- But Offer 2 has a future value of $21,000. What is its present value?- You check with your bank, and the interest rate for a one-year car loan is 5%.- Thus, the PV of $21,000 would be calculated as follows:

PV = $21,000 X (1 / (1 + .05) 1) = $21,000 X .9524 = $20,000Here, we see these two offers are essentially identical.

After introducing the concept of “present value” in the previous slide, have the students calculate the following example.

Help students understand the time value of money is an important aspect of net present value. Ask them, “If you are comparing two proposals, both worth $10,000. One requires a two $5,000 payments after 6 and 12 months, while the other requires full payment in 12 months. Do they have the same present value?

- No, due to the time value of money, we’d generally prefer to keep money longer, and pay later



Students should recognize the terms PV and NPV are sometimes used synonymously, but it is important to recognize NPV Analysis includes calculating the PV of both inflows and outflows.

Here’s the first example where we illustrate both a cash outflow and a cash inflow. Students should understand the PV of the $10,000 purchase is already at “present value,” for its being made in the present. If they’d like to figure it out mathematically, remind them that at the present time, t = 0; and any factor raised to the “0” power (where the exponent is “0”) is 1.



Important—help put students at ease with the title slide: “Selecting the Discount Rate,” for there is no “calculating” at this point.

Definition of 'Nominal Interest Rate’Nominal interest rates refer the real rate of interest, plus inflation (actual or expected) and risk premium.



Read more: http://www.investopedia.com/terms/n/nominal-interest-rate.asp#ixzz1g3iDKWjX

Investopedia explains 'Nominal Interest Rate'Nominal Interest Rate = Real Interest Rate + Inflation Premium + Risk PremiumIn practice, the inflation premium is often assumed to be the expected inflation rate and the risk premium is ignored. Unless the economy is experiencing a deflationary period, the nominal rate will be higher than the real rate.

Read more: http://www.investopedia.com/terms/n/nominal-interest-rate.asp#ixzz1g3iKz3gk

Definition of 'Real Interest Rate'An interest rate that has been adjusted to remove the effects of inflation to reflect the real cost of funds to the borrower, and the real yield to the lender. The real interest rate of an investment is calculated as the amount by which the nominal interest rate is higher than the inflation rate.

Real Interest Rate = Nominal Interest Rate - Inflation (Expected or Actual)Read more: http://www.investopedia.com/terms/r/realinterestrate.asp#ixzz1g3iguv8m

Investopedia explains 'Real Interest Rate'The real interest rate is the growth rate of purchasing power derived from an investment. By adjusting the nominal interest rate to compensate for inflation, you are keeping the purchasing power of a given level of capital constant over time.

For example, if you are earning 4% interest per year on the savings in your bank account, and inflation is currently 3% per year, then the real interest rate you are receiving is 1% (4% - 3% = 1%). The real value of your savings will only increase by 1% per year, when purchasing power is taken into consideration.

Read more: http://www.investopedia.com/terms/r/realinterestrate.asp#ixzz1g3iuGGiy



Here’s a quick look comparison of the Real Discount Rate and the Nominal Discount Rate.Remember, per FAR 32.205(c)(4), we must use the nominal discount rate in our assessments.

Instructor Note: The slides above and below highlight the formula to get a Present Value and then to get an overall Net Present Value when given a Discount Factor. We will walk the students through getting the interest rate and calculating the Discount Factor, but this is the simple version of the formula to give them an idea of where we are going. Then we will show them how to get the individual elements and how those tie into this formula.



A common use for PV calculations: DCAA, DCMA, and PCOs analyzing the area of deferred compensation.

Instructor Note: Help students understand their goal is to find the PV of that future payment with a Future Value of $5,000. For additional learning, ask them to verify the values of “t” and “i.” They can



do so by reviewing the previous OMB Discount Factors slide. After completing the calculations, they should be able to figure out the “This means” statement at the bottom.

With a fundamental understanding of NPV, Example 2 illustrates:- how two proposals with the same face value can have different present values based on the

timing of cash outflows;- the difference between the “end of year” factor and the “mid-year” factor;- the “5-step process” for calculating PV and NPV, per the CPRG, Vol 2, Ch 9



For all NPV problems, the first step is to determine the maximum timeframe. Thus, after reviewing the slide above, drive students to figure out what the maximum timeframe is for Offeror A and B scenarios.



Then have students select the right discount rate based on that maximum timeframe. Note, Offeror A’s timeframe is only two years; however, the OMB site does not break out two years as a separate rate.

Step 2 drives buyers and PCOs to understand all aspects of the proposal, the timing of the cash flows, and the overall period of performance. In addition, it is critical to identify any unique elements of each proposal, to ensure we are comparing realistic NPVs. The most common example is selecting a “purchase” over a “lease,” but then later realizing we did not include annual maintenance or disposal costs in our NPV calculations.



In Step 3 students can either calculate the “discount factor,” or simply look it up on the OMB discount rate slide, included earlier in this lesson. Either way, students must still figure out the timing of the cash inflows and outflows, and select the correct interest/discount rate.



This slide depicts and allows comparison of the cash flows of Offeror A and B.

Specifically point out on the graph:- Offeror A (above the timeline): Offeror A proposes the annual payments, beginning at contract

award. By now, students should understand this will require 3 PV calculations…one for each year, then the sum will equal the PV.

- Offeror B (below the timeline): Quick comparison. We see Offeror B proposes monthly payments. Ask students, “How many of you would like to calculate the PV of each monthly payment? That would be 36 calculations. Then you could add them all up for the total PV for Offer B (hear crickets chirping). This could be tedious! Is it necessary? We will learn a simpler way to calculate such payment schedules with a tool called a ‘mid-year factor’ in this lesson!”



Remember the quick comparison between Offeror A and B? Here’s where we find the appropriate, and sometimes simpler method for calculating the PV.



Emphasis: there is essentially no difference between the end of one year, and the very beginning of the subsequent year. This is explained in CPRG Vol 2, Ch 9, para 9.4 (specifically 9.4.1)

Discount Factors. The discount factor that you use in net present value analysis will depend on the discount rate that you use and the timing of the cash flow. In defining the timing of the cash flow, you must identify the year and the timing during the year. There are two commonly used assumptions about when during the year the payment occurs:

End-of-year payment -- use this assumption when a single payment is made at the end of the year or the beginning of the year.

A payment that is due immediately is not discounted. A payment that is due at the beginning of Year t is evaluated as a payment due at the end

of Year t-1. For example, payments due at the beginning of Year 2 and Year 3 will be treated as if they are due at the end of Year 1 and Year 2.

Mid-year payment -- use this assumption when a single payment will be made mid-year or payments will be made at regular intervals throughout the year.

9.4.1 - Discount Factors For End-Of-Year PaymentWhen to Use End-of-Year Discount Factors. Use end-of-year discount factors when payments are due at the end of the year or the beginning of the year. Remember, that a payment due at the beginning of Year 3 is the same as a payment due at the end of Year 2.



Again, from the CPRG, Vol 2, Ch 9:

9.4.2 - Discount Factors For Mid-Year PaymentWhen to Use Mid-Year Discount Factors. Use mid-year discount factors when a single payment will be made mid-year or payments will be made at regular intervals (e.g., monthly or quarterly) throughout the year.Mid-Year Discount Factor Calculation. The discount factor formula for mid-year cash flow (payment/receipt) is written:

In examining the slide below, ask students, “Look at payment plans 1, 2, and 3. Are any of these like offeror A?” (no)

Are any similar to Offeror B? (students should see payment plan 1 is like Offeror B’s monthly payment plan)



Following these descriptions of the end-of-year and mid-year factors, refer students back to the scenario, and ask, “Based on what we just reviewed, let’s review our scenario. Review the proposed cash flows of Offeror A and B and figure out whether we use end-of-year factors, or mid-year factors.”

Hint: there is one of each kind in this scenario!The goal is for them to understand Offeror A’s payment plan is like the end-of-year plan, while Offeror B’s payment plan fits the description of a mid-year plan.





With an overall understanding of the timing of the cash flows, and an understanding of how to set each Offeror’s “t” value through the end-of-year or mid-year factor, we can summarize a comparison of the offers as follows.



The key to this part of the lesson is to help students understand, once they have selected the interest/discount rate, and understand the timing of the cash flows, they must determine the discount factor.



They may either calculate the DF (above), or select the DF from the OMB DF data, presented in the table in the following slides. In both methods, students must know how to select the “t” and the “I” for each cash flow. For Offeror A, students must figure out the DF for the third payment.



After successfully figuring out a DF for Offeror A, students must figure out all three DF’s for Offeror B’s proposed payment plan. If they intend to select the DF from the OMB data, have them refer back to their slide in the SG (at/near the 12th slide, entitled, “Discount Factors, per OMB Circular A-94’s 3 and 5-year Discount Rates”



In this step, students calculate the PV of each cash flow by multiplying the cash flow amount by the discount factor, then sum the cash flows to get the NPV. From our scenario, here is the NPV of Offeror A. Though all cash flows are “outflows,” it is still acceptable to consider this NPV, rather than simply PV.

Next, students do the same for Offeror B.



Finally, we compare the two Offerors’ NPVs, and select the most advantageous one.





Having worked through the previous examples, instruct students to take about 10-15 minutes to accomplish this exercise. Students should review the 5-step process, and refer to previous examples. The only new element in this exercise is one offer’s proposal includes a cash inflow, which must be considered in the NPV analysis.

For info, in case the students need incentive to remain engaged, this exercise is similar to an NPV test question!





Discussion point: in reviewing this scenario, raise the issue of a newly discovered cost in one of the offers. For example, if you discover annual maintenance costs in the purchase offer, you would have to add that to the list of Offeror B annual cash flows, and calculate the PV for each.

For information, in the next update of CON 170, the NPV class exercise will include unique factors which must be accounted for, as well as specific elements in BOTH offers which are the same price, and can generally be ignored (example: insurance costs for both leased and owned vehicles).

Instructor Note: NPV does not determine fair and reasonable. Rather it enables us to normalize historical or proposed data to compare values in ‘Constant Dollars.”







Lesson 5 -- ELO 2.04 Given Market Research data calculate and identify reasonable Cost Estimating Relationships.

Definition of Cost Estimating Relationship (CER), per CPRG Vol 2, Chapter 4, Para 4.0As the name implies, a cost estimating relationship (CER) is a technique used to estimate a particular cost or price by using an established relationship with an independent variable. If you can identify an independent variable (driver) that demonstrates a measurable relationship with contract cost or price, you can develop a CER. That CER may be mathematically simple in nature (e.g., a simple ratio) or it may involve a complex equation.

Link to FAR 15.404-1(b)(2)

Instructor note: Lead the students through a discussion of the FAR reference, and emphasize where CERs fit in price analysis.

Price analysis for commercial and non-commercial items.(1) Price analysis is the process of examining and evaluating a proposed price without evaluating its separate cost elements and proposed profit. Unless an exception from the requirement to obtain certified cost or pricing data applies under 15.403-1(b)(1) or (b)(2), at a minimum, the contracting officer shall obtain appropriate data, without certification, on the prices at which the same or similar items have previously been sold and determine if the data is adequate for evaluating the reasonableness of the price. Price analysis may include evaluating data other than certified cost or pricing data obtained from the offeror or contractor when there is no other means for determining a fair and reasonable price. Contracting officers shall obtain data other than certified cost or pricing data from the offeror or contractor for all acquisitions (including commercial item acquisitions), if that is the contracting officer’s only means to determine the price to be fair and reasonable. (2) The Government may use various price analysis techniques and procedures to ensure a fair and reasonable price. Examples of such techniques include, but are not limited to the following:(i) Comparison of proposed prices received in response to the solicitation. Normally, adequate price competition establishes a fair and reasonable price (see 15.403-1(c)(1)).(ii) Comparison of proposed prices to historical prices paid, whether by the Government or other than the Government, for the same or similar items. This method may be used for commercial items including those “of a type” or requiring minor modifications.

(A) The prior price must be a valid basis for comparison. If there has been a significant time lapse between the last acquisition and the present one, if the terms and conditions of the acquisition are significantly different, or if the reasonableness of the prior price is uncertain, then the prior price may not be a valid basis for comparison.

(B) The prior price must be adjusted to account for materially differing terms and conditions, quantities and market and economic factors. For similar items, the contracting officer must also adjust the prior price to account for material differences between the similar item and the item being procured.

(C) Expert technical advice should be obtained when analyzing similar items, or commercial items that are “of a type” or requiring minor modifications, to ascertain the magnitude of changes required and to assist in pricing the required changes.(iii) Use of parametric estimating methods/application of rough yardsticks (such as dollars per pound or per horsepower, or other units) to highlight significant inconsistencies that warrant additional pricing inquiry.


http://farsite.hill.af.mil/reghtml/regs/far2afmcfars/fardfars/far/15.htm#P352_59737



(iv) Comparison with competitive published price lists, published market prices of commodities, similar indexes, and discount or rebate arrangements.(v) Comparison of proposed prices with independent Government cost estimates.(vi) Comparison of proposed prices with prices obtained through market research for the same or similar items.(vii) Analysis of data other than certified cost or pricing data (as defined at 2.101) provided by the offeror.(3) The first two techniques at 15.404-1(b)(2) are the preferred techniques. However, if the contracting officer determines that information on competitive proposed prices or previous contract prices is not available or is insufficient to determine that the price is fair and reasonable, the contracting officer may use any of the remaining techniques as appropriate to the circumstances applicable to the acquisition.(4) Value analysis can give insight into the relative worth of a product and the Government may use it in conjunction with the price analysis techniques listed in paragraph (b)(2) of this section.]

Instructor note:- Specifically, we see in paragraph 15.404-1(b)(2)(iii) the indication for use of CERs;- The techniques described in 15.404-1(b)(2)(ii) emphasize how comparing similar items,

ensuring a valid comparison, and seeking the advice of experts contribute to effective price analysis;

- Thus, as we consider use of CERs in estimating future prices, we must follow the guidance in 15.404-1(b).

Discussion. - By definition, contract pricing with CERs requires us to know the independent variables, or “drivers” for every requirement. What are the “drivers” for cost or design in the following areas:

Category Independent Variable (“driver”)General supplies Quantity, rush deliveryShipping Distance, weight, speedSecurity service Number of guards required, location, environmentRoofing Square feetAircraft Distance, speed, weight, rangeConstruction Square feet, number of rooms, land, locationEngineering service Hours required, specific qualificationsSheet metal quality, scrap rate

Instructor note: To help figure out the independent variables (the drivers) for each requirement, we might ask:

Q: “In market research, will I find two security service contracts exactly the same?” A: No, but it may be feasible to compare the number of guards, location, or security

environment--those are drivers in the price of security contracts.





Q: “In market research, will I find two construction projects exactly the same?” A: Probably not, but if may be feasible to compare the square footage of enclosed

space, the number of rooms, the acreage or location--those are drivers in the design and price of construction contracts.

Developing a CER, per CPRG Vol 2 Ch 4Steps for Developing a Cost Estimating Relationship. Strictly speaking, a CER is not a quantitative technique. It is a framework for using appropriate quantitative techniques to quantify a relationship between an independent variable and contract cost or price. In a sense, CERs are relationships we can use to compare prices of similar items, then estimate prices of similar items when it is not possible to compare the same items. In developing CERs, the CPRG recommends the following six step process.

Step 1. Define the dependent variable (e.g., cost dollars, hours, and so forth) Define what the CER will estimate. Will the CER be used to estimate price, cost dollars, labor hours, material cost, or some other measure of cost? Will the CER be used to estimate total product cost or estimate the cost of one or more components? The better the definition of the dependent variable, the easier it will be to gather comparable data for CER development.

Step 2. Select independent variables to be tested for developing estimates of the dependent variable. In selecting potential independent variables for CER development: • Draw on personnel experience, the experience of others, and published sources of

information. When developing a CER for a new state-of-the-art item, consult experts experienced with the appropriate technology and production methods. • Consider the following factors:

o Variables should be quantitatively measurable. Parameters such as maintainability are difficult to use in estimating because they are difficult to measure quantitatively.

o Data availability is also important. If you cannot obtain historical data, it will be impossible to analyze and use the variable as a predictive tool. For example, an independent variable such as physical dimensions or parts count would be of little value during the conceptual phase of system development when the values of the independent variables are not known. Be especially wary of any CER based on 2 or 3 data observations.

o If there is a choice between developing a CER based on performance or physical characteristics, performance characteristics are generally the better choice, because performance characteristics are usually known before design characteristics.

Step 3. Collect data concerning the relationship between the dependent and independent variables. Collecting data is usually the most difficult and time-consuming element of CER development. It is essential that all data be checked and double checked to ensure that all observations are relevant, comparable, relatively free of unusual costs.



Step 4. Explore the relationship between the dependent and independent variables. During this step, you must determine the strength of the relationship between the independent and dependent variables. This phase of CER development can involve a variety of analytical techniques from simple graphic analysis to complex mathematical analysis. Simple ratio analysis, moving averages, and linear regression are some of the more commonly used quantitative techniques used in analysis.

Step 5. Select the relationship that best predicts the dependent variable. After exploring a variety of relationships, you must select the one that can best be used in predicting the dependent variable. Normally, this will be the relationship that best predicts the values of the dependent variable. A high correlation (relationship) between a potential independent variable and the dependent variable often indicates that the independent variable will be a good predictive tool. However, you must assure that the value of the independent variable is available in order for you to make timely estimates. If it is not, you may need to consider other alternatives.

Step 6. Document your findings. CER documentation is essential to permit others involved in the estimating process to trace the steps involved in developing the relationship. Documentation should involve the independent variables tested, the data gathered, sources of data, time period of the data, and any adjustments made to the data.

Additional Guidance: - Some CERs may be simple, linear ratios, while others may be more complex, non-linear

relationships.- The CPRG cautions buyers to beware of data samples of only 2 or 3 data observations (Vol

2 Ch 4, Para 4.0, Step 2). In such cases, seek additional data points, as well as expert advice.

- When developing CERs, do other subject matter experts agree that your independent variables are drivers?



Example 1. (class discussion, whiteboard exercise)What would be a reasonable CER for buying a residential house? (Review CPRG, Vol 2, Ch 4, Sections 4.0 through 4.4)Step 1. Define the dependent variable. Price, taxes. Our objective is to estimate the price.Step 2. Select independent variables to be tested for developing estimates of the dependent variable. Have students review factors in the CPRG, Vol 2, Ch 4, Section 4.0, under “Step 2”. Responses should include # of bedrooms, square footage, acreageStep 3. Collect data concerning the relationship between the dependent and independent variables.

Market Research Data:

House Price #BR $ / BR Acres $ / Acre Sq ft $ / Sq ft

1 $350K 4 $87.5K .5 $700K 3500 $100

2 $297K 3 $99K 2 $149K 3000 $99

3 $409K 4 $102.25K .5 $818K 3900 $105

4 $307K 3 $102.33K 1 $307K 3200 $96

5 $303K 4 $75.75K 5 $60.6K 3000 $101

6 $306K 3 $102K .5 $612K 3100 $99

Range $26.55K $757.4K $9

Step 4. Explore the relationship between the dependent and independent variables. Instructor Note: the Student Guides include the graphs below, which depict the relationship between the dependent and independent variables. As students compare the graphs, lead a discussion through the following points.

Notice the range of differences among the three different CER candidates. $ per acre had the widest range, and # of BR also had a significantly wide range. However, the $ per sq foot is a fairly narrow range. A simple way to assess how “narrow” the range is, is to compare the range to the average:

The $ per BR avg is $95K. The range of $26,600 is 28% of the avg.The $ per Acre avg is $441K. The range of $756K is 170% of the avg!The $ per Sq Ft avg is $100. The range of $9 is 9% of the avg, and thus is the best of these three measures to serve as a CER.

Note: this is a simple way to analyze a set of data. From our histogram lesson, here we are essentially comparing the “spread” and “trend” of a few data points. A more precise method (linear regression and analysis of variance) will be taught in CON 270. As a foundation, if time



permits, have the students plot the independent variable on the x-axis, and the dependent variable (price) on the y-axis. Just looking at the graphs, note the position of the data points without the trend line. Is a clear pattern or line evident? Of the three, the $ per sq foot presents the most linear trend. Thus, we would expect $ per sq foot to yield the most accurate predictive assessment. When we add the trend line (which students will do in CON 270, via Microsoft Excel), we see the data points are either on or very close to the trendline, to a greater extent than the other two CER candidates. Finally, if we add the “R squared” calculation for this data (which students will do in CON 270, via Microsoft Excel), we see the $ per sq foot offers the best estimating relationship. FYI, for the trend lines of the data sets below, the “R squared” values are as follows: $/BR, .40; $/Acre, .20; $/Sq Foot, .97



Step 5. Select the relationship that best predicts the dependent variable. Based on the relatively narrow range of $ per sq foot variability among these houses, the $ per sq foot appears to be the best CER for us to use to estimate the price we can expect to pay for a house in this area, during this timeframe in the house buying market.

Step 6. Document your findings. In addition to documenting your market research as a home buyer, notice how realtors and banks look at “comps.” This is a CER which gives realtors, buyers and lenders data to base their decisions regarding buying prices, selling prices, and lending risks.

Example 2 - Security Guard ServicesWhat would be a reasonable CER for buying security guard services? Step 1. Define the dependent variable. PriceStep 2. Select independent variables to be tested for developing estimates of the dependent variable. # of guards, # of hours, # of gates, location, environmentStep 3. Collect data concerning the relationship between the dependent and independent variables. See table above.

Market Research Data:

Contract Price Gates $ per Gate Hours $ per hr

1 $2,080,000 6 $346,667 208,000 $10

2 $1,575,000 1 $1,575,000 150,000 $10.50



3 $3,800,000 10 $380,000 400,000 $9.50

Range $1,228,333 $1.00

Step 4. Explore the relationship between the dependent and independent variables. While graphing the $ per Gate and $ per Hr, and calculating the relative percentages could make the students answer more precise, students should be able to see $ per gate has a wider relative range compared to the narrower relative range of $ per hr. It is likely that if a contract requires security at only 1 gate, it is a huge entry control point. Perhaps the contract to secure 10 gates are all smaller entry control points, or only manned a few hours each day.

The $ per Gate avg is $767K. The range of $1.2M is 200% of the avg.The $ per Hr avg is $10. The range of $1 is 10% of the avg!

Step 5. Considering the following graphs, select the relationship that best predicts the dependent variable ($ per gate, or $ per hour). With its narrow range of responses, the $ per hr CER appears to be a reasonable estimating tool for estimating future prices.Step 6. Document your findings. Market Research indicated location and security environment were drivers in the $ per hour cost. Thus, Market Research focused on finding historical prcies for security contracts in similar locations under similar security conditions. Within this framework, the $ per hr metric appeared to be the best CER for estimating the price of our next security service contract.

For info, the following graphs reinforce the conclusion that $ per hr is a more accurate CER than $ per gate. The “R squared” for $ per Gate is .78; for $ per Hr is .91.

Market Research Data for Security Guard Services

Price per Gate6 3466671 1575000

10 380000

0200000400000600000800000

10000001200000140000016000001800000

0 5 10 15

Pric

e pe

r Gat

e

Security Guard Services

No. of Gates



Price per Hour208000 10150000 10.5400000 9.5

9.4

9.6

9.8

10

10.2

10.4

10.6

0 100000 200000 300000 400000 500000

Pric

e Pe

r Hou

r

Hours

Security Guard Services



Lesson 6 -- ELO 2.05 and 2.06 Cost Volume Analysis (CVA)

Purpose: ELO 2.05 Through Cost-Volume Analysis, recognize the nature of fixed, variable, semi-variable and total costs, and develop a price estimate.

ELO 2.06 Through Cost-Volume Analysis, determine a proposed price to be rational or irrational with respect to a “buy-in” seller strategy

Background and Assumptions

When you acquire supplies or services, you expect to pay a lower price per unit as the purchase quantity increases. You expect contractors to have lower costs per unit as production quantity increases. This general expectation remains the same whether you are buying items specifically built for the Government, or items that are mass-produced for a variety of commercial and Government customers. Cost-volume analysis can be used to analyze the natural relationship between cost and volume in pricing decisions.

Assumptions: In cost-volume analysis, you consider only short-term operations. The short term may be defined as a period too short to permit facilities expansion or contraction, or other changes that might affect overall pricing relationships.

The CVA technique also assumes use of a straight line relationship between cost and volume. While actual price behavior may not follow a straight line, its use can closely approximate actual cost behavior in the short run. If purchase volume moves outside the relevant range of the available data, the straight-line assumption and the accuracy of estimates becomes questionable.

Finally, the CVA technique assumes the terms “cost” and “price” are the same. The “cost” data points in CVA could refer to either “prices” discovered through market research, or could refer to actual “costs” to produce the good or service. The important point is to avoid mixing “cost” and “price” data points into the same data set. In CON 170, the data points used in the CVA examples refer to prices paid for goods or services.

Instructor note: we can teach this with the slides provided on Blackboard, but I believe a better method is to walk the students through this problem, with lots of interaction, engaging the students and drawing the graph(s) on the class whiteboard. Let the students know you expect them to draw the same graphs on their given graph paper, and that there is a test question very similar to these exercises.

This lesson gets the students engaged by understanding the cost-volume analysis concept first. Thus, we introduce CV analysis by drawing a picture (less intimidating than “graphing a data set”). After grasping the concept with graphs, we’ll step up to learning the math relationships behind the graphs. For info, the math is the same as CON 120; but in 170, we added the graphical analysis to begin the lesson.



Exercise 1 -- Wiring HarnessesGiven market research data for commercial grade wiring harnesses, estimate the price for an upcoming purchase of 18 harnesses.

Data Set 1--Commercial Grade Wiring HarnessesQuantity Total Cost Unit Cost

5 $150.00 $30.0010 $200.00 $20.0015 $250.00 $16.6720 $300.00 $15.008 $180.00 $22.50

12 $220.00 $18.3317 $270.00 $15.8825 $350.00 $14.00

Step 1: Plot data on graph paper.

0 5 10 15 20 25 300

50

100

150

200

250

300

350

400

Wiring Harnesses

Instructor note: after looking at the data set together, explain to the students the scale and axis labels for the graph before they begin plotting data. Our goal is for all the graphs to look the same to ensure we can learn the process and minimize confusion

Step 2: Establish a “trendline” or estimating line by connecting the data pointsInstructor note: for CON 170, the data sets reflect a perfectly linear relationship. This lets students see what a trendline is in the simplest form, and gives them a foundation for the “least squares best fit” line in CON 270.



Step 3: Based on the graph and estimating line, what is your estimate for the price of 18?Instructor note: if we were able to get all students on the same scale, it will be apparent the graph estimates should be under 300, but over 250

From this data set and estimating line, could you estimate the price of 50 harnesses? How about 200?Yes for both, but recognize:

- those estimates would be outside the relevant range of your data set;- we would have to extend our trendline to give an estimate;- LEARNING POINT: we would likely need to continue our market research to find data

on purchases of larger quantities.

How can we sharpen our cost estimate?With the tools from Lesson 1, we can determine the mathematical expression for the estimating line we drew in the first part of this lesson. First, we must understand the estimating building blocks: variable costs, fixed costs, and the total cost.

Types of Costs: In the short run, costs can be of three general types:

Fixed Cost (symbol is “F”). Total fixed costs remain constant as volume varies in the relevant range of production. Fixed cost per unit decreases as the cost is spread over an increasing number of units.

Examples include: Fire insurance, depreciation, facility rent, and property taxes.

Variable Cost (symbol is “Vu”). Variable cost per unit remains constant no matter how many units are made in the relevant range of production. Total variable cost increases as the number of units increases.

Examples include: Production material and labor. If no units are made, neither cost is necessary or incurred. However, each unit produced requires production material and labor.



Semi-variable Cost (symbol is “SVu”). Semi-variable costs include both fixed and variable cost elements. Costs may increase in steps or increase relatively smoothly from a fixed base.

Examples include: Supervision and utilities, such as electricity, gas, and telephone. Supervision costs tend to increase in steps as a supervisor's span of control is reached. Utilities typically have a minimum service fee, with costs increasing relatively smoothly as more of the utility is used.

Graphic Depiction of Cost Behavior

Total Cost (symbol is “C”). The sum of fixed and variable costs. Examples include: the total cost for production includes the cost to build the factory (fixed cost), plus the cost of utilities and labor (variable costs). Total cost can be considered a “semi-variable” cost because it contains both fixed and variable cost elements.

The following four graphs illustrate the different types of cost behavior described above:




Situations for Use

Cost-volume analysis is an estimating concept that can be used in a variety of pricing situations. You can use the cost-volume relationship for:

* Evaluating item price in price analysis.Cost-volume analysis assumes that total cost is composed of fixed and variable elements. This assumption can be used to explain price changes as well as cost changes. As the volume being acquired increases unit costs decline. As unit costs



decline, the vendor can reduce prices and still make the same profit per unit.

* Evaluating direct costs in pricing new contracts.Quantity differences will often affect direct costs -- particularly direct material cost. Direct material requirements often include a fixed component for development or production operation set-up. As that direct cost is spread over an increasing volume unit costs should decline.

* Evaluating direct costs in pricing contract changes.How will an increase in contract effort increase contract price? Some costs will increase others will not. The concepts of cost-volume analysis can be an invaluable aid in considering the effect of the change on contract price.

* Evaluating indirect costs.The principles of cost-volume analysis can be used in indirect cost analysis. Many indirect costs are fixed or semi-variable. As overall volume increases, indirect cost rates decline because fixed costs are spread over an increasing production volume.

Analyzing the Cost-Volume Relationship

Key Assumption

The assumption of linear cost behavior permits use of straight-line graphs and simple linear algebra in cost-volume analysis. This lesson will begin with the graphical analysis, and then presents the algebraic analysis.

Calculating Total Cost Algebraically

Total cost is a semi-variable cost—some costs are fixed, some costs are variable, and others are semi-variable. In analysis, the fixed component of a semi-variable cost can be treated like any other fixed cost. The variable component can be treated like any other variable cost. As a result, we can say that:

Total Cost = Fixed Cost + Variable Cost

Using symbols:

C = F + V where: C = Total Cost F = Fixed Cost

V = Variable Cost

Total variable cost depends on two elements:1. Variable Cost per Unit 2. Quantity Produced



V = VU(Q) where: VU = Variable Cost per unitQ = Quantity Produced

Substituting this information into the basic Total Cost Equation, we have the equation used in cost-volume analysis:

C = F + VU (Q)

Example of Calculating Total CostAlgebraically

If you know that Fixed Costs are $500, Variable Cost per Unit is $10, and the Volume produced is 1,000 units, you can calculate the Total Cost of production.

C = F + VU(Q)

C = $500 + $10 (1,000)

C = $500 + $10,000

C = $10,500

Instructor Note: walk the students through the next two examples, using the next three slides. The SG slides do not contain the answers.

Examples of Calculating Total Cost:



Instructor note: in teaching the next section, “how to develop a cost estimate with CVA,” the SG covers the 4 steps. The slides offer the same information but are not in the SG.

Steps to Develop a Cost Estimate with CVA

There are 4 steps to estimating the cost for a given quantity using historical data:

Step 1. Calculate the variable element.Step 2. Calculate the fixed element.Step 3. Develop the Estimating Equation.Step 4. Estimate the cost for a given quantity.

Example of Calculating Variable Cost Algebraically

Step 1. Calculate the variable element.

Given Total Cost and Volume for two different levels of production, and the straight-line assumption, you can calculate Variable Cost per Unit.

Remember that:



1. Fixed Costs do NOT change no matter what the volume, as long as we are in the relevant range of production. Any change in total cost is the result of a change in total Variable Cost.

2. Variable Cost per Unit does NOT change in the relevant range of production.

As a result, we can calculate Variable Cost per unit (VU) by:

V u=Change in Total CostChange in Quantity

V u=Total Cost at Point 2 - Total Cost at Point 1

Quantity at Point 2 - Quantity at Point 1

¿ V u=C2 - C1Q2 - Q1

Example of Calculating Variable Cost Algebraically, continued

You are analyzing an offeror's cost proposal. As part of the proposal, the offeror shows that a supplier offered 5,000 units of a key part for $60,000. The same offer contained 4,000 units for $50,000. What is the apparent variable cost per unit?

V u=C2 - C1Q2 - Q1

V u=$60,000−$50,0005,000−4,000

V u=$10,0001,000

V u=$10



Calculating Fixed Cost Algebraically

Step 2. Calculate the fixed element.

If you know Total Cost and Variable Cost per Unit for any Quantity, you can calculate Fixed Cost using the basic Total Cost equation.

Example of Calculating Fixed Cost Algebraically

In the previous section, we calculated Variable Cost per Unit given information on two data points. Using the Total Cost for 5,000 units, $60,000; the calculated Variable Cost per Unit, $10; and the Total Cost equation; we can calculate fixed cost.

Remember, Total Cost is expressed as C = F + Vu(Q)To calculate Fixed Cost, we can rewrite as F = C - VU(Q)

where:C = $60,000VU = $10Q = 5,000

F=$ 60000−$10(5 ,000 )F=$ 10000



Developing an Estimating Equation

Step 3. Develop the Estimating Equation.

Now that you know that Vu is $10 and F is $10,000 you can substitute the values into the general Total Cost Equation.

C = F + Vu(Q) C = $10,000 + $10(Q)

The result is an equation that can be used to estimate the total cost of any volume in the relevant range between 4,000 and 5,000 units.

Using the Estimating Equation

Step 4. Estimate the cost for a given quantity.

Estimate the total cost of 4,400 units.



C = $10,000 + $10(Q)C = $10,000 + $10(4,400)C = $10,000 + $44,000C = $54,000

Now, try an example on your own!

Now, back to our customer who needs an price estimate for 18 wiring harnesses! We’ll need:



- Our graph- The market research data (data set 1, below)- The 4-step process stated above.

Data Set 1--Commercial Grade Wiring HarnessesQuantity Total Cost Unit Cost

5 $150.00 $30.0010 $200.00 $20.0015 $250.00 $16.6720 $300.00 $15.008 $180.00 $22.50

12 $220.00 $18.3317 $270.00 $15.88

25 $350.00 $14.00

0 5 10 15 20 25 300

50

100

150

200

250

300

350

400

Wiring Harnesses

From the graph, notice the estimating line slopes up to the right. This means for every additional unit produced, the total cost increases. This is called a positive slope—it moves up and to the right with each additional unit purchased. The increase in total cost with the purchase of an additional unit is the variable cost. Thus, the “slope” of the estimating line is the variable cost.

Instructor note: some students may ask, “I thought costs were supposed to decrease as more units were produced.” This brings up a good learning point for later—the difference between unit cost and total cost. Unit cost generally will decrease as more units are produced, because it allows the producer to spread fixed costs over more units. Total cost is different. In our examples, with variable cost remaining constant, and fixed price remaining fixed, total cost will increase as more units are produced.

1. Based on data set 1, calculate the variable cost for a wiring harness:



From our data set, the variable costs is calculated as $200 - $150 = $10 per unit 10 units – 5 units

This means, for every additional unit we purchase, the contractor’s cost is an additional $10.

2. Now, using data set 1 and the variable cost, calculate the fixed cost element.

The fixed cost is calculated by taking the Total Cost equation and isolating the fixed cost (F). Thus, if total cost is $150 for 5 units, the fixed costs is calculated as: F = $150 - ($10) X 5 units F = $100

3. With both the fixed and variable costs, you can build the estimating line’s equation!

Total Cost = $100 + ($10) X (Quantity)

4. Based on this estimating equation, hypothetically, what is the cost to produce zero wiring harnesses?- Point: this exercise illustrates the contractor must pay its fixed costs even if zero units

are produced.- Another point to emphasize: in the first part of this lesson, if we extended the estimating

line all the way to the y-axis, it would reveal a good estimate for contractor’s fixed costs. Here, we’ve reinforced what the initial graph suggested in a simple manner.

5. Now, estimate what the customer asked us for…the price of 18 units: Total Cost = $100 + ($10) X (18 units) Total Cost = $280

6. Does this appear to be close to the estimate we figured simply by looking at the graph? Yes! Should be pretty close.

Instructor Note: Part of the learning point here is to show how the math (which so many folks are nervous about) helps us do even tighter estimates from what we can “eyeball” on a simple graph of market research data. This math is exactly the same as CON 120, but also requires students to graph the line. The graphing establishes a foundation for linear regression in CON 270.


V U =C 2 - C1Q2 - Q1

F = C - V U (Q )

C = F + V U (Q)


EXERCISE 2 – Tracked Vehicle Ball-Bearing Sets (similar scenario is a test question)Given a data set, use graphical analysis and Cost Volume Analysis to estimate the price for 130 ball bearing sets.

Instructor note: some students will want to jump to Excel, but drive them to draw the graph, draw the estimating line, and state their estimate based on their written graph.

Data Set -- Tracked Vehicle Ball-bearing SetsQuantity Total Cost Unit Cost

20 $7,500.00 $375.0040 $10,000.00 $250.0060 $12,500.00 $208.3380 $15,000.00 $187.50

100 $17,500.00 $175.00120 $20,000.00 $166.67140 $22,500.00 $160.71160 $25,000.00 $156.25

1. Graph the data of Quantity in relation to Total Cost.

0 20 40 60 80 100 120 140 160 180$0.00

$5,000.00

$10,000.00

$15,000.00

$20,000.00

$25,000.00

$30,000.00

Bearing Sets

2. Calculate the variable cost:

$10000 - $7500 = $125 per unit40 units - 20 units

3. Now, using the data set and the variable cost, calculate the fixed cost element.F = C - Vu(Q)F = $10000 - ($125) (40)F = $5000


V U =C 2 - C1Q 2 - Q1


4. With both the fixed and variable costs, you can build the estimating line’s equation!C = F + Vu(Q)C = $5000 + $125 (Quantity)

5. Finally, the customer asked for a price estimate for 130 ball bearing sets:C = $5000 + $125(130)C = $21,250

6. How about the estimated price for 200 sets?C = $5000 + $125 (200)C = $30,000

7. Based on your market research, what is the lowest price you would reasonably expect to pay?

Good discussion question. Given market research data, you would expect contractors to charge a price which would enable them to cover all of their fixed costs, variable costs, and earn a reasonable profit. Thus, the first unit produced would be at least $5,125, plus profit. We would expect 10 units to be $6,125 plus profit. We recognize our market research data is not perfect; but based on the historical data, if a proposed price is significantly lower than the data indicates, we must:

Be cautious about determining “fair and reasonable” Conduct additional market research and fact-finding before considering the offer

to be unreasonably low—avoid the temptation not to award because the offer initially appears to be “too low,” a “low-ball,” or a “buy-in”

Conduct additional market research and fact-finding, considering the guidelines set by TINA and FAR 15.402 and 15.403, as discussed in Unit 1 Lesson 2.



8a. After a recent, city-wide tradeshow, a small business representative visits your office, and says he can deliver 130 units for $16,500. Based on your market research data, and your cost-volume analysis, do you believe this is a reasonable offer?

Instructor note: See graph below, with this “Tradeshow Price” of 130 Units at Price of $16,500. Drive students to realize this is significantly lower than the market research data; but, is it reasonable? Learning point is, we would probably have to do some fact-finding through additional market research. Good news for us here is, there is not a solicitation published yet, so fact-finding is much simpler!

Estimated price analysis: As we calculated above, our estimated total cost for 130 units is $21,250. His offer of $16,500 is well below (about 22% less than) our estimate. How would we discern if this is a rational offer, rather than a “get the foot in the door,”

low-ball, irrational offer? After all, this offeror may have implemented newer, more efficient processes! Thus, some questions to ask:

o Have you sold at this price before? At a similar quantity, quality and delivery schedule? May I see records of previous sales history? Will it be valid next year? Such questions follow the “order of preference” from our TINA lesson!

o My market research indicates that could be an attractive price. Can you help me understand the risk to the Government--are you able to cover your fixed and variable costs?



8b. The offeror responds to your question, “I’m in a business cycle where I have all of my fixed costs covered for the rest of this year due to more orders than I expected on other contracts. Thus, I can offer you a better price than normal.” What do you think?

- By our estimating equation, if this offeror has the fixed costs covered through other contracts, his total costs will be $5,000 less than we’d normally expect: 130 units X $125 per unit = $16,250. At his proposed price of $16,500, the offeror is covering his variable costs, has all fixed costs covered, and is still earning $50 in profit.

- If the offeror can make the case he can cover his fixed and variable costs, the price can still be considered rational.

- If the offeror is not covering at least his variable costs, it may be an irrational, low-ball “buy-in” offer. Remember, it is seldom a good idea to award a contract knowing the contractor is losing money! Such a scenario typically presents more risk than benefit.

Students will likely engage in discussion, “What if the offeror is deliberately planning to lose money, with hopes of getting his foot in the door?”

Discussion should emphasize that contractors may do this, but that our job is to recognize those situations through this type of analysis, rather than simply going by “gut feel” of an offer that “appears to be too low.” This is a good lead-in to Contribution Income…coming up next!



Lesson 7 -- ELO 2.07 Using Cost-Volume Profit Analysis for Contract Pricing

Purpose: Through Cost-Volume-Profit analysis, and recognize the nature of profit, revenue, contribution income, and calculate the contractor’s “break even” point.

Instructor Note: This lesson begins by walking students through an example of CVP, all the way through contribution income and break-even. Next, on page 100 in the ISP, there is a current slide deck which can be used to teach this lesson, and provides another example of CVP, contribution income, and break-even, which we can walk students through. If you choose to use the slides, recommend skipping to page 100 in the ISP, and students skip forward to the slides which are included in the SG on/near page 90. Finally, there are two Exercises at the end of the lesson, which should reinforce what has been taught through the text and the slides.

Cost-Volume-Profit Equation

Until now, we have only looked at the cost-volume relationship. Now, we are going to expand that relationship to consider the relationship between cost, volume, and profit.

The revenue taken in by a firm is equal to cost plus profit.That can be written:

Revenue = Total Cost + Profit

We have already seen that total cost (C) is:

C = F + VU (Q)

Using this information, we can rewrite the Revenue equation as:

Revenue = F + VU (Q) + Profit

In the cost-volume-profit equation, profit can be positive, negative, or zero. If profit is negative, we normally refer to it as a loss. If profit is zero, the firm is breaking even, no profit or loss. If we let P stand for profit, we can write the equation:

Revenue = F + VU (Q) + P

Revenue is equal to selling price per unit (RU) multiplied by volume.

Revenue = RU (Q)

If we assume that the firm makes all the units that it sells, and sells all the units that it makes, we can complete the cost-volume-profit equation:

Ru (Q)= F + VU(Q) + P



Application of the Cost-Volume-Profit Equation

This equation and limited knowledge of a contractor's cost structure can provide you with extremely valuable information on the effect purchase decisions can have on a firm's profitability.

Using the Cost-Volume-Profit Equation to Estimate Selling Price

Given the following product information, a firm prepared an offer for an indefinite quantity contract with the Government for a new product developed by the firm. There are no other customers for the product. In developing the unit price estimate (RU), the firm used its estimated costs and its best estimate of the quantity that it would sell under the contract.

Fixed Cost = $10,000Variable Cost per Unit = $20Contract Minimum Quantity = 4,000 unitsContract Maximum Quantity = 6,000 unitsFirm’s Best Estimate of Quantity = 5,000 unitsTarget Profit = $7,500

Ru (Q)=F+V u (Q)+PRu (5,000)=$10,000+$20(5,000)+$7,500Ru (5,000)=$10,000+$100,000+$7,500Ru (5,000)=$117,500Ru(5,000 )5000

=$117,5005,000

Ru=$23 . 50

Using the Cost-Volume-Profit Equation to Estimate Profit

Managers' of the firm wanted to know how profits would be affected if it actually sold the maximum quantity (6000 units) at $23.50 per unit.

Ru(Q)=F+V u (Q)+P$23 .50 (6,000)=$10,000+$20(6,000 )+P$141,000=$10,000+$120,000+P$141,000=$130,000+P$11,000=P

If the firm sells 6,000 at $23.50 per unit, profit will be $11,000. That is a $3,500 increase from the original $7,500 target profit, or an increase of 47 percent. Note that the firm’s profit would increase solely because sales were higher than estimated.

Managers were even more concerned about how profits would be affected if they only sold the minimum quantity (4000 units) at $23.50



per unit.

Ru (Q)=F+V u (Q)+P$23 .50 (4,000 )=$10,000+$20( 4,000)+P$94,000=$10,000+$80,000+P$94,000=$90,000+P$4,000=P

If the firm sells 4,000 at $23.50 per unit, profit will be $4,000. That is $3,500 less than the original $7,500 target profit, or 47 percent of the original estimate. Note that the firm’s profit would decrease solely because sales were lower than estimated.

Using the Cost-Volume-Profit Equation to Estimate Required Sales

In a final effort to analyze the risk to the firm under the proposed indefinite delivery contract, managers wanted to know the level of sales that would be required for the firm to break even (zero profit).

Ru(Q )=F+V u(Q )+P$23.50(Q )=$10,000+$20(Q )+0($23 .50−$20 )Q=$10,000$3. 50(Q )=$10,000Q=2857 .14 units

The calculations show that the firm would break even at 2857.14 units. Assuming that the firm could not sell .14 units, the firm must sell 2,858 units to assure that all costs are covered. Selling 2857 units would still result in a $0.50 loss.

Contribution Income

The difference between revenue and variable cost is contribution income (CI). The term contribution income comes from the contribution made to covering fixed costs and profit. If contribution income is positive, increasing sales will increase profits or reduce losses. If contribution income is negative, increasing sales will reduce profits or create greater losses.

Contribution Income = Revenue - Variable Cost

CI = RU (Q) - VU (Q) or CI = (RU - VU ) Q

Knowledge of a contractor's cost structure and contribution income can be valuable in analysis of proposed costs.



Contribution Income Example

In evaluating an offeror's proposal for 500 units at $900 each, your analysis reveals the following cost structure:

Fixed Cost = $100,000 Variable Cost per Unit = $1,000

How would this affect your analysis of contract risk?

CI = (RU - VU) QCI = ($900 - $1,000) (500)CI = (-$100) (500)CI = -$50,000

The contribution income from the sale is a negative $50,000. The firm would be substantially worse off for having made the sale. Unless the firm can offer a positive rationale for such a pricing decision, such as fixed cost has already been covered under a previous contract, you must consider pricing as an important factor as you analyze the risk of contract performance.

Identifying Issues and Concerns

Questions to Consider in Analysis

As you perform price/cost analysis, consider the issues and concerns identified in this section, whenever you use cost-volume-profit analysis concepts.

• Has the contractor’s cost structure changed substantially?Application of cost-volume-profit analysis assumes that the period covered by the analysis is too short to permit facilities expansion or contraction or other changes that might affect overall pricing relationships. If the contractor has substantially changed its cost structure, your ability to use cost-volume-profit analysis may be limited. Examples of possible changes include: Downsizing to reduce fixed costs. Increased investment in automated equipment to reduce

variable costs of labor and material.

• Is the straight-line assumption reasonable?The cost-volume-profit relationship is not usually a straight- line relationship. Instead, it is a curvilinear relationship. A straight-line analysis works as long as the straight line is a good approximation of the cost-volume-profit relationship. Most computer programs designed to fit a straight-line to a set of data provide measures of how well the line fits the data. For example, a regression program will usually provide the coefficient of determination (r2).



Instructor note: this is an important reference for students—CON 170 assumes a straight-line relationship among data points. However, “real life data” (as we may recall from our CER lesson with the relationships between $ per sq foot, $ per acre, and $ per bedroom) is not usually perfectly linear. CON 270 will teach how to analyze data when the relationship cannot be depicted by a perfectly straight line and help us understand how to analyze and explain variance. There is a test question regarding us making this “straight-line assumption.”

• Are current volume estimates within the relevant range of available data?

If the current business volume is substantially higher or lower than the volumes used to develop the cost-volume-profit equation, the results may be quite unreliable. The contractor should be expected to change the way it does business and its cost structure if volume increases or decreases substantially.

Instructor Note: this module can be taught with the slide deck provided on Blackboard, which walk instructors and students through the learning points and calculations one step at a time.





Instructor Note: the slide deck breaks the calculation down step-by-step over several slides. The previous problem asks to find the selling price, so a logical process is to solve for Ru. The next problem asks us to find a change in profit, so a logical process is to use the same CVP formula, but this time, set the equation up to solve for P.

Instructor Note: The slide deck gets the students started, but does not give the students the answer until the next slide. Thus, let students work the calculations with the same process as the previous example.



Because the problem asks us to find the effect on PROFIT, recommend using the “Profit” equation from the earlier slide. However, if students prefer, they could use the same Ru(Q) equation from the last problem. The variables are the same, and the answer will be the same.

The last question of the previous slide, “what assumptions did we make?” Focus discussions on assuming variable costs remained the same even during a production run “outside” the planned production window of 6,000 to 7,000 units.Outside the planned production levels, it’s likely the firm would face:

- Need for overtime or additional employees- Unplanned equipment maintenance or calibration, additional utility expenses- Additional warehousing/workspace (could increase fixed or variable costs)- Premium shipping or ordering terms from their suppliers- Additional service/sales technicians- All these would be examples that would increase the variable cost per unit.

Instructor Note: as we noted before, students may prefer to set the CVP equation up as follows. The formula and variables are the same, and the answer is the same.

Ru (Q) = F + Vu (Q) + P($33.08)(4,700) = $15,000 + $30 (4,700) + P $155,476 = $15,000 + $141,000 + P $155,476 = $156,000 + P - $524 = P





Instructor note: teach the break-even point one line at a time:- Remember, at the break-even point, sales revenue (point to the line) is equal to the

total cost (point to the “Variable Cost + Fixed Cost” line), and profit = $0- From the previous slide, the Break-even Point is Ru(Q) = F + Vu(Q); where:

o Ru(Q) is the selling price X the quantity of units soldo F is the fixed costso Vu(Q) is the variable cost per unit X the quantity of units sold

- Thus, in explaining the graph:o Green Sales Revenue line represents Ru(Q): the unit selling price X

quantityo Red Total Cost line represents F + Vu(Q): fixed cost + (variable cost X

quantity) o These two lines intersect where Ru(Q) = F + Vu(Q), which is the break-

even point!

Check for understanding:- On the graph, where would profit be depicted?

o The “wedge” in the upper right: to the right of the breakeven point, under the green sales revenue line, but over the red total cost line. This makes sense, right? No profit will be earned until we’ve passed the breakeven point, where sales revenues begin to exceed total costs.



- If an item has a low fixed cost, a low variable cost, and a high selling price, where on the graph would the breakeven point be…lower left or bottom right?

o lower left…with low fixed and variable, but a high selling price, the producer would reach the breakeven point after selling only a few units (perhaps like an iPod or a “beanie baby” during their first year of sales)

- Comparing the total cost line of two different commodities, which would have a steeper slope:

o One with a higher variable cost, or lower variable cost? Higher variable cost would drive a steeper slope.

- Comparing the total cost lines again, with identical variable costs, which would reach their breakeven point quicker?

o One with higher fixed cost, or lower fixed cost? Not quite enough information, but help students consider: Firm 1 and 2

produce ball-bearing sets. Firm 1 invests in the latest, most efficient production equipment. Firm 2 invests in used, less-efficient equipment which is less expensive than the newest and best. As a rule, Firm 1 will have higher fixed costs, but will most likely be able to produce at a lower variable cost. The decision on investing in fixed costs is closely tied to seller strategies, production capacities, profit goals and break even points. This will be discussed more specifically in the Unit 4 “Apex/Baker” example.



With an understanding of the break-even point, it is also important to understand how the contractor’s break-even point compares to its overall production capacity. We can accomplish this through a simple estimating ratio:

Break-even Capacity = Break-even Quantity / Maximum Production Quantity



Check for understanding: - What is the ratio for calculating “break-even capacity?”

o Break-even capacity = Break-even Quant / Max Production Quant

- What is the purpose of understanding the break-even capacity?o Indicates how much of the contractor’s capacity is dedicated to simply breaking

even…recognizing profit is not earned until the contractor is passed the break-even point.

- Compare the risk of offers with the following break-even capacities:

o Offer 1’s break-even capacity is 30% Low risk, plenty of margin compared to max capacity

o Offer 2’s break-even capacity is 99% High risk, for the contractor is almost at max capacity just to break even)

o Offer 3’s break-even capacity is 120% Probably unacceptably high risk, for the contractor is beyond its current

capacity just to break even!





Goal is to understand the basis of the proposal (responsible, responsive) before determining fair/reasonable, and making award.

1. Contact the offeror seeking clarification, to ensure the price is correct.2. If there is no sensible explanation (such as a typo or misunderstanding of the

solicitation), and their proposed, low-price stands, then more questions are warranted.3. Keep them in the competitive range. Then ask them a few questions about their price,

such as:



- verify they understand the requirement;- assess if they recognize this price is lower than normal, and discern if price is

due to “normal business cycle” (all fixed costs covered—only charging Gov’t the variable costs)

- or if the price is lower than normal due to good/beneficial relationship w/subs who provided their parts at an alarmingly low price due to “normal business cycles” or some reason that significantly lowered their fixed or variable costs.

- or perhaps they have some other rational explanation regarding their fixed and variable costs to produce at such a low price.

4. Answers that may not give confidence to award to this “low offeror:”- no rational or detailed answers; perhaps offeror gives general marketing

statements when asked about this price compared to previous prices- admission they are operating at a loss (cannot cover fixed or variable costs) to

“buy-in” to the future market—this adds much risk, especially when things do not go well

- admission they have no certain terms or commitments with subs or suppliers, but that they will be getting a “better than ever” deal.

- Emphasize: if the firm cannot cover their fixed and variable costs, the strategy should be considered IRRATIONAL. Sometimes, an offeror will have an adequate business base to cover all of its fixed costs; however, if they are not also covering variable costs, they’re either not paying them or pulling from another area (banks, income from other areas). A negative CI is generally an indicator of an IRRATIONAL offer, for which a CO should NOT make award without careful risk assessment.

Even though this scenario drives students/buyers to dig for and analyze historical cost information, certified cost and pricing data cannot be obtained because there is adequate price competition. Through this process, we must abide by the “order of preference” in requesting data other than cost or pricing data (Unit 1 Lesson 2 “TINA” lesson). Our goal is to understand their proposal, and make a compelling conclusion that the offer is within a reasonable range.

Discussion Question: if this offer is irrational, what is the lowest price you would be willing to pay?

Answer: Generally, the selling price should be at least equal to or greater than the variable unit cost. Under this pricing strategy, the offeror should still provide some explanation for how he is covering his fixed costs (adequate business base for this business cycle, a grant, or some other unexpected, windfall profits which contributed to paying all of the fixed costs). Even if the proposed unit price does not earn much profit, an offeror should be able to explain how both fixed and variable costs are covered. Otherwise, an offer should be considered irrational.



EXERCISE 1As a 13-year old, Lester has a goal to earn enough money to attend college. His goal is to earn $1250 of profit each summer until he graduates from high school. After some practice, he has developed skill in mowing lawns. With some guidance from his dad, Lester purchased a lawn-mower, a trimmer, and a broom for a total of $250. With gas and expendables, his variable cost per lawn is $10. After doing market research on the prices of lawn service, he intends to charge $30 per lawn.

1. How many lawns would he have to mow in order to earn this year’s goal of $1250?

Instructor note: slides are available to walk students through the calculations step by step, which can save time over writing on the whiteboard.

Here are the necessary elements for solving this problem:Fixed costs (F): $250Variable costs, Vu(Q): $10 per lawnProfit Goal (P): $1250Selling price or Revenue per lawn, Ru(Q): $30Needs to mow ____________ lawns to earn the Profit Goal?

In our last example of “wiz-bangs,” we were given the estimated production quantity and the profit objective, and had to calculate the selling price. In this problem, we are given the selling price and are solving for Q, what is the “quantity” of lawns that needs to be mowed?

Revenue = Fixed Costs + Variable Costs + Profit Ru(Q) = $250 + $10 (Q) + $1250 ($30)(Q) = $250 + $10 (Q) + $1250 $30Q = $1500 + $10(Q) $20Q = $1500 Q = 75 lawns



2. Assuming the weather permits 15 weeks of lawn-mowing per year, and Lester can mow a maximum of 6 lawns per week. At what capacity is Lester operating in order to earn his profit goal? How much mowing risk do you believe Lester is managing to achieve his goal?

- Lester must mow 75 lawns to achieve goal and can mow 15 X 6 = 90 lawns per year.- To earn his goal, he will operate at 75 / 90 = .833, or about 83% of capacity- Students should relate the 75 lawns to the maximum capacity of 90 lawns. He can

achieve his goal within his maximum capacity. If he gets sick, faces unusually hazardous weather, or has unplanned equipment failure, he may have to adjust his prices, his mowing schedule, or even hire a buddy to help adjust his production to achieve his goal. This appears to be within reasonable risk.

3. What if he needed to mow 90 lawns to earn his profit goal?- With his maximum capacity at 90 lawns, achieving his goal is probably too risky; would

expect to see a backup plan or an alternative lawn mowing seller strategy, with different pricing, another lawn mowing crew, or move to an area with a longer mowing season.

4. Under his pricing arrangement, what is the “Contribution Income”? CI = (Ru - Vu) X (Q) CI = ($30 - $10) X 75 units CI = ($20) X (75) CI = $1500 have been contributed to his fixed costs and profit. Notice, this is enough to cover his fixed costs of $250 and ‘contribute’ $1250 to profit. Through this equation, we see the “contribution income” is $20 per lawn, which means every time Lester mows a lawn and gets paid, he can contribute $20 toward his fixed costs. When his fixed costs are paid, the $20 can be contributed to profit.



5. Given Lester’s fixed and variable costs, and his anticipated sales revenue, draw a graph to estimate the number of lawns Lester must mow to “break even.” (The revenue line is already given in the graph below)

- Instructor Note (see data table and graph solution below). The intent is to estimate the break-even point based on the graph, then actually calculate the break-even point in the next question.):

o Start by graphing the sales revenue line: Sales Revenue = $30(Q).o Then, graph the total cost line. C = Fixed Cost + Variable Cost(Q). For

additional understanding, make sure students understand the total cost line is the sum of the fixed costs and the variable costs, as depicted on the “Break-even Point” graph, earlier in this lesson.

o The lines intersect at the breakeven point, total cost = total revenue, and profit = 0.

o The intersection point of the total cost and total revenue lines should be shown at about 12 or 13 lawns.

Number of lawns mowedFixed Costs

Variable Costs

Total Cost

Sales Revenue

0 250 0 250 05 250 50 300 150

10 250 100 350 30015 250 150 400 45020 250 200 450 60025 250 250 500 750



6. Given Lester’s fixed and variable costs, and his anticipated sales revenue, calculate the breakeven point. Is your calculation consistent with your graph above? Break-even point: R = Total Cost + Profit Ru(Q) = F + Vu(Q) + $0 $30(Q) = $250 + $10(Q) + $0 $20(Q) = $250 Q = 12.5 lawns. Thus, Lester will break-even after mowing his 13 th lawn! Remember…students MUST round the fraction up to 13 lawns! The test question is similar.

7. Assuming the weather permits 15 weeks of lawn-mowing, Lester can mow a maximum of 6 lawns per week. At what capacity is Lester operating at his breakeven point? Does this appear to be a risky venture?

- Max Capacity: 15 weeks X 6 lawns per week = 90 lawns.- Breakeven at 13 lawns- To break even, he will operate at 13 / 90 = .144, or about 14% of capacity.- This appears to be a LOW RISK venture, for to break even, he is well within his

maximum capacity!-



EXERCISE 2Jill has figured out how to build her own version of an iPodTM player which also dispenses PezTM candy. Her goal is to earn $25,000. She believes she can build and sell 5,000 units. Her fixed costs are $60,000, variable cost are $20 per unit.

1. How much must she charge for each unit, assuming she sells all she makes?

Ru(Q) = Fixed Costs + Variable Costs + Profit Ru(Q) = Fixed Costs + Vu(Q) + Profit Ru(5000) = $60,000 + $20(5000) + $25,000 Ru(5000) = $60,000 + $125,000 Ru(5000) = $185,000 Ru = $37.00

Ms. Jill Blackson must sell each unit for $37.00 and sell all 5000 units to cover her fixed and variable costs, and earn her goal of

$25,000 profit.

2. Under this pricing arrangement, what is Jill’s contribution income? CI = (Ru - Vu) X (Q) CI = ($37.00 - $20) X 5000 units CI = ($17.00) X (5000) CI = $85,000 total

CI per unit = $85,000 / 5000 units = and $17.00 per unit

3. As she assesses what type of equipment to buy within the fixed costs, she believes her maximum capacity will be 6,000 units. At what capacity will she be producing to earn her profit goal?



- She’ll build and sell 5,000 units, with a maximum capacity of 6,000 units. Thus, she will be operating at 5000 / 6000 = .8333, or 83% capacity.

- She can achieve her profit goal within her maximum capacity; however, because she is approaching her maximum capacity, a prudent investor may inquire about her strategy for managing risk.

4. Given her fixed and variable costs, and her anticipated sales revenue, draw a graph in the space below to estimate the number of units she must sell “break even.” Remember: - Total cost line is graphed with C = F + Vu(Q); - Sales revenue is graphed with R = Ru(Q)

- Start by graphing the “number of iPodsTM” on the x-axis, and “Sales Revenue” on the y-axis. This is the “Sales Revenue” line, Ru(Q).

- Then, graph the “number of iPodsTM” on the x-axis, and the “Total Cost” on the y-axis. This is the Total Cost line. C = F + Vu(Q)

Ms. Jill Blackson Example: Variable $20 Fixed: $60,000Goal: Earn Profit of $25,000

Number of iPods fixed costs Variable Costs Total Cost Sales Revenue0 $60,000 $0 $60,000 $0

1000 $60,000 $20,000 $80,000 $37,0002000 $60,000 $40,000 $100,000 $74,0003000 $60,000 $60,000 $120,000 $111,0004000 $60,000 $80,000 $140,000 $148,0005000 $60,000 $100,000 $160,000 $185,0006000 $60,000 $120,000 $180,000 $222,000

This slide is the solution, and is not in the student guide.

0 1000 2000 3000 4000 5000 6000 70000

50,000

100,000

150,000

200,000

250,000

Total CostSales Revenue



- At the breakeven point, total cost = total revenue, and profit = 0.o Based on the graph, the intersection point of the total cost and total revenue

lines can be estimated at/above 3500 units.

5. Under this pricing arrangement, calculate Jill’s breakeven point. Is your calculated answer consistent with your estimate from the graph?

Break-even point: R = Total Cost + Profit Ru(Q) = F + Vu(Q) + $0 $37.00(Q) = $60,000 + $20(Q) + $0 $17(Q) = $60,000 Q = 3529.41 units sold to break even.

= Which means 3530 units sold is the breakeven point!!

Ensure students’ graphs are reasonably close to their calculation.

Re-emphasize, because Ms. Jill Blackson cannot build and sell “.41” units, we MUST round our breakeven quantity up to 3530 units. If she only sells 3529, she does not breakeven! A similar scenario IS A TEST QUESTION, in which the student must “round up” in order to get credit. Some students may say, “I thought I’m supposed to round “down” if the remainder is less than 0.5.” This is normally true, but not with respect to break-even calculation.

6. At what capacity is she producing at the break-even point? - Break-even quantity / max production quantity - 3530 / 6000 - .588 - Which is about a 59% capacity

7. At Jill’s birthday party, she announces to her guests that she will sell this initial production run of 5,000 units for $24 per unit. Is she off her rocker? (i.e., is this a rational strategy, or irrational?). How will you find out?

Instructor Note: Facilitate discussion w/students to re-emphasize contribution income, sales revenue, and how a business must cover its fixed and variables costs to stay in business. As Government buyers, we must be assured a contractor’s proposed price will cover fixed and variable costs. Otherwise, we may be facing additional performance risk. This new unit price is significantly lower than her original selling price. Is it a “low-ball,” irrational price?

To determine if this new price is rational, start by calculating the CI, and determine how much of the fixed and variable costs she can pay for at this new price. CI = (Ru - Vu) X (Q) CI = ($24 - $20) X 5000 units CI = $20,000

- At $24 per unit, she is covering her variable costs, but does not contribute enough over 5000 units to cover her $60,000 in fixed costs and still earn her goal of $25,000 profit. Thus, so far, her pricing strategy of $24 per unit appears to be irrational.



- To find out if she has a rational plan, students must ask/investigate if she’s offered this price before, if she’s covering her fixed and variable costs, lowered her profit goal, or changed her business strategy. This is market research!

When students catch on to having to ask/investigate, give them this response: “She responds, “For my birthday, a venture capitalist paid my $60,000 in fixed costs. With less risk, I was willing to lower my profit goal to $20,000.”

8. Given this new information, does she have a rational strategy?- Yes. At that selling price, she will earn $20,000 in contribution income. With her fixed

costs paid for, she can keep the $20,000 for profit, and achieve her revised profit goal.

- Have students place themselves in a buyer’s position, where they determined a proposed price to be “too low,” and subsequently eliminated the offer from the competitive range. During the debriefing, or protest, the offeror explains he was able to offer the unusually low price for a reason similar to Ms. Jill Blackson’s reason, or due to an unusually healthy business cycle which virtually eliminated Fixed Costs for our order. Could be defend our decision for eliminating them?

- The point of this example is to re-enforce that Government buyers cannot simply discard an offer because it appears to be “too low.” There may be rational reasons for a contractor to offer us a “better than ever” price, or a “one time good deal.” Normal business cycles can provide unexpected windfalls for contractors, which enable them to offer the Government unusually low prices. It is our responsibility to explore and understand the prices before awarding…or not awarding.



Additional Example (looking ahead to CON 270)

Instructor Note: this is an optional example to reinforce previous lessons and give students a glimpse of the linear regression tools to be taught in CON 270. This example can be covered in 10 minutes, but could also take an hour if students dig deep and ask questions. Thus, if time appears to be limited, recommend directing students to review this example on their own, in preparation for CON 270.

Consider the following. Our maintenance customer asked us to acquire 200 widgets. We’ve worked together to accomplish market research.

In building the price estimate, we plotted the data with Microsoft Excel on a scatterplot, added the trendline and the estimating equation, and estimated the price for 200 units to be $637,200.



Instructor note: This graph introduces students to the concept of linear regression analysis, which is taught in CON 270. Notice the data does not fall on a straight line (not a perfectly “linear relationship”) like the other CON 170 examples. This is more realistic to what we might find in conducting and plotting market research data. We will learn how to account for such variance in CON 270. Building this graph is not testable in CON 170, but provides an introduction and transition for their next level of training.

During a pre-proposal conference, one firm indicates they will sell us 200 units for $925 each, for a total price of $185,000. Through the discussion, it is clear the firm understands the requirement, and is considering terms and conditions similar to previous purchases. Clearly, this price is significantly lower than we would expect.



1. What should you do to determine if this is a rational offer under a market penetration type strategy, or an irrational offer under a “buy-in” strategy?

- Based on your price history, and the estimating line:-- What are the fixed costs: $486,000-- What are the variable costs: $756-- Selling price: $925

- What is the contribution income:-- CI = (Ru - Vu) (Q)-- CI = ($925 - $756) (200 units)-- CI = $33,800



At this selling price for 200 units, the offeror is covering variable costs of $756 per unit. However, at this selling price, can the offeror cover all fixed costs, and still earn a profit? Or, is the offeror simply “buying-in” with a low-ball price? Through fact-finding, we should try to find out how he pays for his fixed costs in the short term.



Instructor note:

- Highlight the market research points on the graph do not fall on a perfectly straight line. CON 170 examples assume a perfectly linear relationship.

- This example’s “trend line” was plotted by Excel, but a student can infer the trendline by looking at the pattern of data points on the graph. Students will see it follows a similar pattern to their previous examples of a trend line, and that the trend line can be represented by an equation which includes fixed and variable cost elements.

- Lead a discussion based upon the same questions and learning points from the “Bearing Sets” example in Unit 2 Lesson 6, and Ms. Jill Blackson’s example in Lesson 7, for the considerations a buyer must take before making a decision to award, or not award.

- Another take-away: market research should give the contracting officer an understanding of a reasonable range of pricing, including how “low” of a selling price the Gov’t should reasonably expect to pay.


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