Identifying And Using Rules Of Thumb

      Identifying Rules of Thumb . As you perform your market analysis, you should be on the lookout for cost estimating rules of thumb that are commonly used in the product marketplace. For example, when we compare the prices of houses, we typically do so in price per square foot. Using this rule of thumb, we can compare the cost of different houses or the same house in different parts of the country. There may be ways to develop more accurate estimates, but this rule of thumb is widely accepted, relatively easy to calculate, and it provides reasonably accurate results for many purposes. The same statement can probably be made about most rules of thumb. You may be able to develop better cost estimating relationships, but given the time available and the dollars involved, rules of thumb often provide useful tools for contract pricing. Validate a Rule of Thumb Before Using . Like any CER, a rule of thumb can be based on another cost, performance characteristic, or physical characteristic of the item being priced. Unlike other CERs, rules of thumb typically have not been validated for use in specific estimating situations. Validation has come from acceptable results produced in a variety of situations over a number of years. Before you use a rule of thumb, consider the 6-step CER development process and ask the following questions: • Can the rule of thumb reasonably be used to estimate what you are trying to estimate (e.g., cost, hours, or price)? • Are there other rules of thumb that can be used to estimate the same cost, hours, or price? • Are the data required to use this rule of thumb readily available? • Does the rule of thumb provide reasonably accurate results? • If more than one rule of thumb is available, which one appears to produce the most accurate estimate? • Have technical experts or other buyers documented the results obtained from using the rule of thumb? Example of Rule of Thumb Validation. You just received two offers for 500 laboratory tables. Each table is 4' x 6' (24 square feet of surface area), with an oak frame and legs. The work surface is a unique composite material developed to meet Government requirements. The low offer is $425; that offer is $175 less than the second low offer and $180 less than the Government estimate. As a result, you are concerned that the price may be unreasonably low. You have no acquisition history for this item and there are no similar items on the commercial market. As a result, you have been looking for a CER that you can use in your pricing decision. Another buyer, who has acquired similar tables, tells you that he has used a rule of thumb in pricing similar tables -- $19 per square feet of surface area. You want to know the answers to the following questions before you use it in making your own pricing decisions. • Can the rule of thumb reasonably be used to estimate what you are trying to estimate (e.g., cost dollars, hours, or product price)? The answer appears to be yes. The buyer who recommended the CER has used it successfully. Additional information shows that he learned of the CER from the scientists who developed the table-top material. • Are there other rules of thumb that can be used to estimate the same cost or price? You have asked several "experts" and have been unable to identify any other rules of thumb for estimating the price of these unique tables. • Are the data required to use this rule of thumb readily available? Yes, you already know the table surface area. • Does the rule of thumb provide reasonably accurate results? You have identified four recent acquisitions of similar tables and recorded the following information comparing the estimates made using the rule of thumb and the actual prices paid: Sq Ft Estimate Actual Price Percentage Difference 15 $285 $310 + 8.8% 18 $342 $335 - 2.0% 32 $608 $580 - 4.6% This sample size is too small to perform an effective statistical analysis, but you can still subjectively evaluate rule of thumb estimate accuracy. All estimates are within 8.8 percent of the actual price. For a rule of thumb, this appears reasonably accurate, especially since our evaluation did not consider other acquisition situation differences (e.g., the number of tables on each contract). • If more than one rule of thumb is available, which one appears to produce the most accurate estimates? In this example, there is only one known rule of thumb to consider. • Have technical experts or other buyers documented the results obtained from using the rule of thumb? In this case, the buyer documented every contract file when the rule of thumb was used. Such documentation is not only valuable in supporting the contracting officer's decision on price reasonableness; it provides valuable information to any contracting officer considering rule of thumb use in the future. Example of Using a Rule of Thumb in Estimate Development . Once you have determined that a rule of thumb is acceptable for estimate development, you must apply it to the available data. Using this rule of thumb, your estimate would be $456 (24 x $19). That estimate is about 7.3 percent higher than the low offer. Based on the rule of thumb, the price does not seem unreasonable. 4.3 - Developing And Using Estimating Factors Situations for Using Estimating Factors . An estimating rate or factor is a simple ratio, used to estimate cost or price. The rule of thumb used to develop table price estimates in the previous section is an example -- $19 per square foot. As the size of the table top increases, the price estimate increases in direct proportion. Most rules of thumb are simple factors. Many CERs developed by Government or industry are also simple factors. They are relatively easy to develop, easy to understand, and in many cases quite accurate. Development and use of estimating rates and factors involves two important implicit assumptions. • There is no significant element of the cost or price being estimated that is not related to the independent variable (i.e., there is no "fixed cost" that is not associated with the independent variable). • The relationship between the independent variable and the cost being estimated is linear. If you believe that there are significant costs that cannot be explained by the relationship or that the relationship is not linear, you should either try to develop an equation that better tracks the true relationship or limit your use of the estimating factor to the range of the data used in developing the factor. Example of Estimating Factor Development . Assume that you are negotiating a guard service contract for your facility and you want to develop a CER to assist you in estimating a should-pay contract price. Development should follow the 6-step CER process. Step 1. Define the dependent variable. The objective is to develop an estimate of the price that the Government should expect to pay for this contract. Step 2. Select independent variables to be tested for developing estimates of the dependent variable. Logically, the major driver of price in a guard service contract is the wages paid the security guards manning the various posts identified in the contract. Step 3. Collect data concerning the relationship between the dependent and independent variables. You have collected information on prices, minimum manning requirements, and service contract wage-rate determinations for the guard service contract at your facility for the last three years. The minimum manning requirement for the current contract totals 75,000 (Guard II) hours. The Service Contract Act (SCA) wage rate for the current year is $10.00 per hour. The estimated direct labor cost for each year (Column D) is calculated by multiplying estimated direct labor hours (Column B) by the Service Contract Act wage rate (Column C). A B C D E Year Estimated Direct SCA Minimum Estimated Direct Contract Price Labor Hours Wage Rate Labor Cost 1 87,600 $9.15 $801,540 $1,346,585 2 78,840 $9.45 $745,038 $1,244,215 3 70,040 $9.50 $665,380 $1,124,490 Current 75,000 $10.00 $750,000 Step 4. Explore the relationship between the dependent and independent variables. The following table demonstrates calculation of the Price to Direct Labor Cost Ratio. The ratio (Column F) is calculated by dividing the contract price (Column E) by the estimated direct labor cost (Column D). In Year 1 for example, price was 1.68 times the estimated direct labor cost. A B C D E F Year Estimated Direct Labor Hours SCA Minimum Labor Rate Estimated Direct Labor Cost Contract Price Price to Direct Labor Cost Ratio 1 87,600 $9.15 $801,540 $1,346,585 1.68 2 78,840 $9.45 $745,038 $1,244,215 1.67 3 70,040 $9.50 $665,380 $1,124,490 1.69 Current 75,000 $10.00 $750,000 Step 5. Select the relationship that best predicts the dependent variable. It appears from the information above, that there is a relationship between contract price and the estimated direct labor cost. The price is between 1.67 and 1.69 times the estimated direct labor cost. The average ratio is 1.68. Average Ratio = (1.68 + 1.67 + 1.69) / 3 = 1.68 You can now use this ratio to estimate the price of similar contracts. Step 6. Document your findings. Your documentation of CER development should include the information from the 6-step process above. Exact documentation requirements will vary with the analysis involved. Using an Estimating Factor in Estimated Development . Once you calculate an estimating factor, you can use it to estimate should-pay price for similar products. Using the 1.68 factor from the guard contract example, you can calculate a should-pay price for the current year. Using this factor, the best estimate of a reasonable price would be $1,260,000, as shown in the table below: A B C D E F Year Estimated Direct Labor Hours SCA Minimum Labor Rate Estimated Direct Labor Cost Contract Price Price to Direct Labor Cost Ratio Current 75,000 $10.00 $750,000 $1,260,000 1.68 Given the data above, you should be reasonably confident of your estimate, because the range of ratios is only from 1.67 to 1.69. Even without statistical analysis, that range might be useful in establishing a range of reasonable prices. High side: 1.69 x $750,000 = $1,267,500 Mean: 1.68 x $750,000 = $1,260,000 Low side: 1.67 x $750,000 = $1,252,500 4.4 - Developing And Using Estimating Equations Situations for Using Estimating Equations . Not all estimating relationships lend themselves to the use of simple estimating factors. If there is a substantial element of the cost or price being estimated that is not related to the independent variable (i.e., there is a "fixed cost" that is not associated with the independent variable), you should consider using a linear estimating equation. If the relationship is not linear, consider a nonlinear estimating equation. Example of Estimating Equation Development . Assume that you are analyzing the costs proposed for the construction of a new house and decide to develop a CER to support your analysis. Development should follow the 6-step CER process described in the chapter Introduction Step 1. Define the dependent variable. The objective is to estimate the cost of a new base housing model. Step 2. Select independent variables to be tested for developing estimates of the dependent variable. A variety of house characteristics could be used to estimate cost. These include such characteristics as square feet of living area, exterior wall surface area, number of baths, and others. Step 3. Collect data concerning the relationship between the dependent and independent variables. Base Housing Model Unit Cost Baths Sq. Ft. Living Area Sq. Ft. Exterior Wall Surface Burger $166,500 2.5 2,800 2,170 Metro $165,000 2.0 2,700 2,250 Suburban $168,000 3.0 2,860 2,190 Executive $160,500 2.0 2,440 1,990 Ambassador $157,000 2.0 1,600 1,400 New Home 2.5 2,600 2,100 Step 4. Explore the relationship between the dependent and independent variables. Analysis of the relationship between the independent variable and house price could be performed using many different techniques. In this situation most analysts would use regression analysis. However, here we will use graphic analysis to demonstrate the thought process involved. Three independent variables will be tested: number of baths, living area, and exterior wall surface area. • Price and the Number Of Baths. This graph appears to demonstrate that the number of baths is not a good estimating tool, because three houses with a nearly $8,000 price difference have the same number of baths. • Price and Square Feet Of Living Area. This graph appears to depict a relationship. • Price and Exterior Wall Surface Area. This graph also appears to depict a relationship. Step 5. Select the relationship that best predicts the dependent variable. Based on the initial analysis, it appears that square feet of living area and exterior wall surface have the most potential for development of a CER. The two graphs below depict efforts to fit a straight line through the observed values. Note that both graphs demonstrate efforts to fit a line with and without using the data from the Ambassador model. • Price and Living Area. • Price and Exterior Wall Surface Area. Consider Analysis Results and Other Data. Viewing both of these relationships, we might question whether the Ambassador model data should be included in developing our CER. In developing a CER, you need not use all available data if all data is not comparable. However, you should not eliminate data just to get a better looking relationship. After further analysis, we find that the Ambassador's size is substantially different from the other houses for which we have data and the house for which we are estimating. This substantial difference in size might logically affect relative construction cost. Based on this information, you might decide not to consider the Ambassador data in CER development. Final Analysis. If you exclude the Ambassador data, you find that the fit of a straight-line relationship of cost to the exterior wall surface is improved. The relationship between cost and square feet of living area is even closer, almost a straight line. If you had to choose one relationship, you would probably select living area over exterior wall surface because living area has so much less variance from the trend line. Since the relationship between living area and price is so close, we can reasonably use it for our CER. If the analysis of these relationships did not reveal a useful predictive relationship, you might consider combining two or more of the relationships already explored or exploring new relationships. Step 6. Document your findings. In documenting our findings, we can relate the process involved in selecting living area for price estimation. We may then present the following graph developed as an estimating tool. We might also convert the graphic relationship to an equation. The cost estimating relationship (CER) would be: Y = $117,750 + ($17.50 x Sq Ft of Living Area) Using an Estimating Equation to Estimate Cost. Once developed, you can use an estimating equation to contract cost or price in similar circumstances. For example : Applying our new CER to the estimation of cost for our new 2,600 square-foot house, we would estimate: Y = $117,750 + ($17.50 x Sq Ft of Living Area) = $117,750 + ($17.50 x 2,600) = $117,750 + $45,500 = $163,250 estimated price CERs, like most other tools of cost analysis, MUST be used with judgment. Judgment is required to evaluate the historical relationships in the light of new technology, new design, and other similar factors. Therefore, knowledge of the factors involved in CER development is essential to proper application of the CER. 4.5 Identifying Issues And Concerns Questions to Consider in Analysis . As you perform price or cost analysis, consider the issues and concerns identified in this section as you consider use of a cost estimating relationship. • Does the available information verify the existence and accuracy of the proposed relationship? Technical personnel can be helpful in analyzing the technical validity of the relationship. Audit personnel can be helpful in verifying the accuracy of any contractor data and analysis. • Is there a trend in the relationship? For example, the cost of rework is commonly estimated as a factor of production labor. As production continues, the production effort should become more efficient and produce fewer defective units which require repair. The factor should decrease over time. You should also consider the following related questions: Is the rate distorted by one bad run? What is being done to control the rate? What else can be done? • Is the CER used consistently? If an offeror uses a CER to propose an element of cost, it should be used in all similar proposals. Since the CER can be used to estimate the average value, some jobs should be expected to cost more and others less. With a valid CER, you assume the variances will be minor and will average out across all contracts. To use a CER in some cases and a discrete estimate in others destroys it usefulness by over or understating costs across all proposals (e.g., using the average unless a discrete estimate is lower/higher negates the averaging out of cost across all contracts and is clearly unfair to one of the contracting parties). • Has the CER been consistently accurate in the past? No matter how extensive the price/cost information or how sophisticated the analysis technique, if a CER does not do a good job of accurately projecting cost, then it is not a useful tool. • How current is the CER? Even the most accurate CER needs to be reviewed and updated. While the time interval between updates will differ with CER sensitivity to change, in general a CER should be reviewed and updated at least annually. A CER based on a moving average should be updated whenever new data become available. • Would another independent variable be better for developing and applying a CER? If another independent variable would consistently provide a more accurate estimate, then it should be considered. However, remember that the CER may be applicable to other proposals, not just yours. It is possible that a relationship which works well on your contract would not work well across the entire contract population. When assessing CER validity, you should consider all affected contracts. • Is the CER a self-fulfilling prophecy? A CER is intended to project future cost. If the CER simply "backs into" a rate that will spread the cost of the existing capacity across the affected contracts, then the CER is not fulfilling its principle function. If you suspect that a CER is being misused as a method of carrying existing resources, you should consider a should-cost type review on the functions represented by the CER. • Would use of a detailed estimate or direct comparison with actual cost from a prior effort produce more accurate results? Development of a detailed estimate can be time consuming and costly but the application of the engineering principles required is particularly valuable in estimating cost of efficient and effective contract performance. • 5.0 - Chapter Introduction • 5.1 - Identifying Situations For Use • 5.2 - Developing And Using A Simple Regression Equation • 5.3 - Analyzing Variation In The Regression Model • 5.4 - Measuring How Well The Regression Equation Fits The Data • 5.5 - Calculating And Using A Prediction Interval • 5.6 - Identifying The Need For Advanced Regression Analysis • 5.7 - Identifying Issues And Concerns 5.0 - Chapter Introduction In this chapter, you will learn to use regression analysis in developing cost estimating relationships and other analyses based on a straight-line relationship even when the data points do not fall on a straight line. Line-of-Best-Fit . The straight-line is one of the most commonly used and most valuable tools in both price and cost analysis. It is primarily used to develop cost estimating relationships and to project economic trends. Unfortunately, in contract pricing the data points that are used in analysis do not usually fall exactly on a straight line. Much of the variation in a dependent variable may be explained by a linear relationship with an independent variable, but there are usually random variations that cannot be explained by the line. The goal in establishing a line-ofbest-fit is to develop a predictive relationship that minimizes the random variations. This can be done visually with a graph and a ruler, but the visual line-of-best-fit is an inexact technique and has limited value in cost or price analysis. Regression analysis is commonly used to analyze more complex relationships and provide more accurate results. This chapter will focus on simple regression (2-variable linear regression); in which a single independent variable (X) is used to predict the value of a single dependent variable (Y). The dependent variable will normally be either price or cost (e.g., dollars or labor hours), the independent variable will be a measure related to the product (supply or service) being acquired. It may be a physical characteristic of the product, a performance characteristic of the product, or an element of cost to provide the product. In some situations, you may need regression analysis tools that are more powerful than simple regression. Multiple regression (multivariate linear regression) and curvilinear regression are variations of simple regression that you may find useful. The general characteristics of both will be addressed later in the chapter. 5.1 - Identifying Situations For Use Cost Estimating Relationship Development and Analysis . Regression analysis is one of the techniques most commonly used to establish cost estimating relationships (CERs) between independent variables and cost or price. If you can use regression analysis to quantify a CER, you can then use that CER to develop and analyze estimates of product cost or price. Indirect Cost Rate Analysis ( FAR 31.203 ). Indirect costs are costs that are not directly identified with a single final cost objective (e.g., a contract), i.e., indirect costs are identified with two or more final cost objectives or an intermediate cost objective(s). Minor direct costs may be treated as indirect costs if the treatment is consistently applied to all final cost objectives and the allocation produces substantially the same results as treating the cost as a direct cost. FAR 31.203 requires that indirect costs be accumulated into logical cost pools and allocated to final cost objectives on the basis of the benefits accruing to the various cost objectives. Regression analysis is commonly used to quantify the relationship between the indirect cost allocation base and expense pool over time. If you can quantify the relationship, you can then use that relationship to develop or analyze indirect cost rate estimates. Time-Series Analysis . You can use regression analysis to analyze trends that appear to be related to time. It is particularly useful when you can identify and adjust for other factors that affect costs or prices (e.g., quantity changes) to isolate the effect of inflation/deflation for analysis. The most common applications of this type are forecasting future wage rates, material costs, and product prices. In time-series analysis, cost or price data are collected over time for analysis. An estimating equation is developed using time as the independent variable. The time periods are normally weeks, months, quarters, or years. Each time period is assigned a number (e.g., the first month is 1, the fourth month is 4, etc.). All time periods during the analysis must be considered, whether or not data were collected during that period. Time does not cause costs or prices to change. Changes are caused by a variety of economic factors. Do not use time-series analysis when you can identify and effectively measure the factors that are driving costs or prices. If you can identify and measure one or more key factors, you should be able to develop a better predictive model than by simply analyzing cost or price changes over time. However, if you cannot practically identify or measure such factors, you can often make useful predictions by using regression analysis to analyze cost or price trends over time. Just remember that regression analysis will not automatically identify changes in a trend (i.e., it cannot predict a period of price deflation when the available data trace a trend of increasing prices). As a result, regression analysis is particularly useful in short-term analysis. The further you predict into the future, the greater the risk. 5.2 - Developing And Using A Simple Regression Equation Simple Regression Model . The simple regression model is based on the equation for a straight line: Yc = A + BX Where: Yc = The calculated or estimated value for the dependent (response) variable A = The Y intercept, the theoretical value of Y when X = 0 X = The independent (explanatory) variable B = The slope of the line (the change in Y divided by the change in X, i.e., the value by which Y changes when X changes by one). For a given data set, A and B are constants. They do not change as the value of the independent variable changes. Yc is a function of X. Specifically, the functional relationship between Yc and X is that Yc is equal to A plus the product of B times X. The following figure graphically depicts the regression line: Steps for Developing a 2-Variable Linear Regression Equation . To develop a regression equation for a particular set of data, use the following 5-step least-squares-best-fit (LSBF) process: Step 1. Collect the historical data required for analysis. Identify the X and Y values for each observation. X = Independent variable Y = Dependent variable Step 2. Put the data in tabular form. Step 3. Compute and . Where: = Sample mean for observations the independent variable = Sample mean for observations the dependent variable = Summation of all the variables that follow the symbol (e.g., X represents the sum of all X values) X = Observation value for the independent variable Y = Observation value for the dependent variable n = Total number of observations in the sample Step 4. Compute the slope (B) and the Y intercept (A). Step 5. Formulate the estimating equation. 2-Variable Linear Regression Equation Development Example . Assume a relationship between a firm's direct labor hours and manufacturing overhead cost based on the use of direct labor hours as the allocation base for manufacturing overhead. Develop an estimating equation using direct labor hours as the independent variable and manufacturing overhead cost as the dependent variable. Estimate the indirect cost pool assuming that 2,100 manufacturing direct labor hours will be needed to meet 20X8 production requirements. Step 1. Collect the Historical Data Required for Analysis. Historical Data Year Manufacturing Direct Labor Hours Manufacturing Overhead 20X2 1,200 $ 73,000 20X3 1,500 $ 97,000 20X4 2,300 $128,000 20X5 2,700 $155,000 20X6 3,300 $175,000 20X7 3,400 $218,000 20X8 2,100 (Est) Step 2. Put The Data In Tabular Form. X = Manufacturing direct labor hours in hundreds of hours (00s) Y = Manufacturing overhead in thousands of dollars ($000s) Tabular Presentation X Y XY X 2 Y 2 12 73 876 144 5,329 15 97 1,455 225 9,409 23 128 2,944 529 16,384 27 155 4,185 729 24,025 33 175 5,775 1,089 30,625 34 218 7,412 1,156 47,524 Column Totals 144 846 22,647 3,872 133,296 Step 3. Compute and . Step 4. Compute the slope (B) and the intercept (A). Step 5. Formulate the estimating equation. Substitute the calculated values for A and B into the equation: Y C = A + BX Y C = 5.8272 + 5.6322X Where: Yc = Manufacturing overhead ($000's) X = Manufacturing direct labor hours (00's) Example of Estimate Using Simple Regression Equation . Estimate manufacturing overhead given an estimate for manufacturing direct labor hours of 2,100: Y C = 5.8272 + 5.622X = 5.8272 + 5.622(21) = 5.8272 + 118.2762 = 124.1034 thousand dollars Rounded to the nearest dollar, the estimate would be $124,103.