Unformatted text preview: Cost Estimation Cost
Regression analysis Regression Account Analysis HighLow Method What you need to know: What
How to use a data set to run a regression How to interpret the results: significance of How model, coefficients, what that means and how to interpret the coefficients interpret How to use data to identify fixed and variable How costs costs How to forecast costs, sales, etc. When to use the intercept and when to leave it When alone. alone. Cost estimation  Cost behavior Cost
We want to understand is how spending will vary in a variety of decision settings. in Can we separate the fixed and variable costs? Causeeffect relations and costs drivers. When is it important to understand how overhead costs behave? overhead – When making price, production, process and When product design decisions. product – When making bid or make or buy decisions. – When we need to answer “what if” questions. Mixed overhead cost behavior Mixed
Total Power Cost The fixed part: the vertical intercept Total Power Costs The variable part: the slope Production volume or other cost driver Cost behavior: linear function by assumption. by
TC = FC + VC*(level of cost driver) where where TC = total cost TC FC = fixed cost VC = variable cost per unit of the variable cost driver, cost and sometimes the cost driver is and represented by X. represented Overhead Costs Total Cost Curve Volume A B C D What methods are available? What
Engineering estimates Account analysis (e.g., Hilton) Scattergraph and highlow estimates Statistical methods (typically linear regression) Example Example
Suppose management believes that the monthly Suppose overhead cost ($5000) in the factory is mixed. It is believed to be 50% fixed and 50% variable. The variable portion is believed to depend on machine hours, which average 10,000 per month. How would you show this as a linear equation? would TC = $2500 + $.25(machine hours). Look at the data set in your handout. Scattergraph Scattergraph
Suppose you have data on overhead costs and Suppose machine hours for the past 15 months and you believe there is a linear relation between the two. Can you look at the numbers and tell me if there is a relation? relation? Can you easily determine whether the posited Can relationship exists? relationship Plot the data and look for a relationship. Plot of overhead costs vs. Plot machine hours
Scattergram 4000.00 3500.00 3000.00 2500.00 2000.00 1500.00 1000.00 500.00 0.00 0.00 30.00 60.00 90.00 Machine Hours 120.00 150.00 HighLow cost estimation HighLow
Find the variable cost per unit of the cost Find driver (VC): driver VC = Overhead at highest Highest activity  Overhead at lowest activity  Lowest activity activity VC = Rise Run HighLow method: Example continued continued
Look at the data set in your handout. Pick out the month with the highest level of activity; pick out the lowest. What’s O/H? $3,105  $1,896 VC = 142 mhr  50 mhr
$1,209 VC = 92 mhr VC = $13.14/mhr HighLow cost estimation HighLow
Fixed cost = $3,105  ($13.14 * 142 mhr) = $1,239 TC = FC + V overhead cost Estimate the totalC * 115 mhr during a monthC = $1,239 + ($13.14hours will be used: T when 115 machine * 115 mhr) TC = $2,750 Cost estimation using regression Cost
Y = the dependent variable (often, total O/H cost) cost) X = the explanatory variables the Y = α + β ∗X + ε , where X = machine hours and ε = random error. where TC = FC + VC*X + ε . TC Regression fits a line through these data points: these
Scattergram 4000.00 3500.00 3000.00 2500.00 2000.00 1500.00 1000.00 500.00 0.00 0.00 30.00 60.00 90.00 Machine Hours 120.00 150.00 Regression parameter estimates Regression
OLS estimators OLS Desirable properties of estimators Desirable – Unbiased (consistent) – Efficient Assumptions (independent errors, constant Assumptions variance, the expected value of the error is zero, normally distributed, nonstochastic independent variable/s) variable/s) Simple linear regression Simple
One explanatory variable Cost estimation equation Coefficient of correlation (R) Coefficient of determination (R2)
– Goodness of fit – Measure of importance Fstatistic (hypothesis testing) pvalue The F statistic The
Goodness of fit hypothesis testing Compute a statistic from regression results Compute the associated pvalue, or Look up a critical Fvalue and compare after Look matching on matching
– 1 numerator degree of freedom – (n2) denominator degrees of freedom – alpha = .05 The F test: The
The null hypothesis is: The slope coefficient The is zero or that F is really 1. This means there is no relation between the y and the x measures, so the mean is just as good as our regression predicted value. regression The Fstatistic measures the loss of fit that The results when we impose the restriction that the slope coefficient is zero. the If F is large, the null hypothesis is rejected. The pvalue The
This is the probability that the statistic we This computed could have come from the population implied by our null hypothesis. implied Suppose we hypothesize that the slope Suppose coefficient is zero. coefficient If the pvalue associated with the Fstatistic is If small, chances are the slope coefficient is not zero. zero. Regression Plot 3750 3500 3250 New O/H Cost 3000 2750 2500 2250 2000 1750 1500 1250 40 50 60 70 80 90 100 110 120 130 140 150 Machine Hours Y = 2782.765  3.047 * X; R^2 = .026 Y = 2504  0 * X; R^2 = .0 Re gression Summary Overhea d Costs vs. Machine Hours Co unt Nu m. Missing R R Squared Adjusted R Squared RMS Residu al 15 0 .896 .802 .787 182.244 Regression result interpretation interpretation
Mean Square 1753772.049 33212.714 FValue 52.804 PValue <.0001 ANOVA Table Overhea d Costs vs. Machine Hours DF Re gression Re sidual Total 1 13 14 Sum of Squares 1753772.049 431765.285 2185537.333 Re gression Coefficients Overhea d Costs vs. Machine Hours Co efficient Intercept Machine Hours 1334.293 12.373 Std. Error 162.913 1.703 Std. Coeff. 1334.293 .896 tValue 8.190 7.267 PValue <.0001 <.0001 Simple linear regression Simple
Scattergram 4000.00 3500.00 3000.00 2500.00 2000.00 1500.00 1000.00 500.00 0.00 0.00 30.00 60.00 90.00 Machine Hours 120.00 150.00 O/H = 2468 + 0 * Machine Hours Overhead Costs = 1334.293 + 12.373 * Machine Hours; R^2 = .802 Re gression Summary Overhea d Costs vs. Direct Materials Cost Co unt Nu m. Missing R R Squared Adjusted R Squared RMS Residu al 15 0 .960 .921 .915 115.087 Results using DM$ DM$
Mean Square 2013351.144 13245.091 FValue 152.007 PValue <.0001 ANOVA Table Overhea d Costs vs. Direct Materials Cost DF Re gression Re sidual Total 1 13 14 Sum of Squares 2013351.144 172186.189 2185537.333 Re gression Coefficients Overhea d Costs vs. Direct Materials Cost Co efficient Intercept Di rect Ma terials Cost 1456.586 .356 Std. Error 87.225 .029 Std. Coeff. 1456.586 .960 tValue 16.699 12.329 PValue <.0001 <.0001 Regression Summary Overhead Costs vs. 2 Independents Count Num. Missing R R Squared Adjusted R Squared RMS Residual 15 0 .976 .952 .944 93.658 Multiple regression regression
Ne assum w ption: No de grading m ulticoline arity
Mean Square 1040137.401 8771.878 FValue 118.576 PValue <.0001 ANOVA Table Overhead Costs vs. 2 Independents DF Regression Residual Total 2 12 14 Sum of Squares 2080274.802 105262.531 2185537.333 Regression Coefficients Overhead Costs vs. 2 Independents Coefficient Intercept Machine Hours Direct Materials Cost 1333.960 4.359 .258 Std. Error 83.724 1.578 .042 Std. Coeff. 1333.960 .316 .697 tValue 15.933 2.762 6.101 PValue <.0001 .0172 <.0001 Forecasting overhead Forecasting
Predict monthly overhead when machine Predict hours are expected to be 62 and direct materials costs are expected to be $1,900. materials Recall
− α = $1,333.96 $1,333.96 – Coefficient for mhrs = $4.359 – Coefficient for DM$ = $.258 Overhead = $1,333.96 + $4.359 * mhrs + $.258 * DM$ Predicted overhead Predicted Overhead = $1,333.96 + $4.359(62) + $.258($1,900) = $2,094.42 Putting together a bid Putting
Calculate a minimum bid for a contract Calculate that would use 22 machine hours and $900 of direct materials. This would be a onetimeonly job. onetimeonly What if there is no idle capacity? Would your bid change if there were Would potential for repeated business? potential The end! The ...
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 Spring '08
 Atkison,S
 Regression Analysis, overhead costs

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