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Determining How Costs Behave. Chapter 10. Overview. Assumptions Model: Y = a + bX Determinates of Fixed vs. Variable costs Cost Estimation Industrial Engineering Conference Method Account Analysis Quantitative Analysis: H-L & OLS 5) Non-linear cost functions.

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## Determining How Costs Behave

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**Determining HowCosts Behave**Chapter 10**Overview**• Assumptions • Model: Y = a + bX • Determinates of Fixed vs. Variable costs • Cost Estimation Industrial Engineering Conference Method Account Analysis Quantitative Analysis: H-L & OLS 5) Non-linear cost functions**Two assumptions frequently used in cost-behavior estimation**1. Changes in total costs can be explained by changes in the level of a single activity. 2. Cost behavior can adequately be approximated by a linear function of the activity level within the relevant range.**Cost Function**What is a cost function? It is a mathematical expression describing how costs change with changes in the level of an activity.**Cost Function—variable cost**La Playa Hotel offers an airline three alternative cost structures to accommodate its crew overnight: 1. $60 per night per room usage y = $60x The slope of the cost function is $60.**Cost Function—fixed cost**2. $8,000 per month y = $8,000 $8,000 is called a constant or intercept. The slope of the cost function is zero.**Cost Function—mixed cost**3. $3,000 per month plus $24 per room This is an example of a mixed cost. y = $3,000 + $24x y = a + bx**Cost Classificationand Estimation Function**Choice of cost object Time span Relevant range**Choice of Cost Object Example**If the total cost to operate all taxis owned by a taxi company is the cost object, annual taxi registration and license fees would be variable costs (number of taxis). If the cost to operate a particular taxi is the cost object, registration and license fees for that taxi are fixed costs.**Time Span**Whether a cost is variable or fixed with respect to a particular activity depends on the time span. More costs are variable with longer time spans.**Relevant Range**Variable and fixed cost behavior patterns are valid for linear cost functions only within the given relevant range. Costs may behave nonlinear outside the range.**Cost Estimation**What is cost estimation? It is the attempt to measure a past cost relationship between costs and the level of an activity. Past cost-behavior functions can help managers make more accurate cost predictions.**The Cause-and-Effect CriterionIn Choosing Cost Drivers**Physical relationship Contractual agreements Implicitly established by logic**Cost Estimation Approaches**Industrial engineering method Conference method Account analysis method Quantitative analysis methods**Steps In EstimatingA Cost Function**Step 1: Choose the dependent variable. Step 2: Identify the independent variable cost driver(s). Step 3: Collect data on the dependent variable and the cost driver(s).**Steps In Estimating A Cost Function**Step 4: Plot the data. Step 5: Estimate the cost function. Step 6: Evaluate the estimated cost function.**High-Low Method Example(A quantitative analysis method)**High capacity December: 55,000 machine-hours Cost of electricity: $80,450 Low capacity September: 30,000 machine-hours Cost of electricity: $64,200 What is the variable rate?**High-Low Method Example**($80,450 – $64,200) ÷ (55,000 – 30,000) $16,250 ÷ 25,000 = $0.65 What is the fixed cost?**High-Low Method Example**$80,450 = Fixed cost + (55,000 × $0.65) Fixed cost = $80,450 – $35,750 = $44,700 $64,200 = Fixed cost + (30,000 × $0.65) Fixed cost = $64,200 – $19,500 = $44,700 y = a + bx y = $44,700 + ($0.65 × Machine-hours)**Regression Analysis--OLS(A quantitative analysis method)**It is used to measure the average amount of change in a dependent variable, such as electricity, that is associated with unit increases in the amounts of one or more independent variables, such as machine-hours. Regression analysis uses all available data to estimate the cost function.**Regression Analysis**Simple regression analysis estimates the relationship between the dependent variable and one independent variable. Multiple regression analysis estimates the relationship between the dependent variable and multiple independent variables.**Regression Analysis**The regression equation and regression line are derived using the least-squares technique. The objective of least-squares is to develop estimates of the parameters aand b.**Regression Analysis**The vertical difference (residual term) measures the distance between the actual cost and the estimated cost for each observation. The regression method is more accurate than the high-low method.**Criteria to Evaluate andChoose Cost Drivers**Economic plausibility Goodness of fit Slope of the regression line**Goodness of Fit**The coefficient of determination (r2) expresses the extent to which the changes in (x) explain the variation in (y). An (r2) of 0.80 indicates that 80% of the change in the dependent variable can be explained by the change in the independent variable.**Slope of Regression Line**Everything else equal: A relatively steep slope indicates a strong relationship between the cost driver and costs. A relatively flat regression line indicates a weak relationship between the cost driver and costs.**Slope of Regression Line**The closer the value of the correlation coefficient (r) is to ±1, the stronger the statistical relation between the variables.**Excel Regression--results**• Interpret Excel regression output (in class)**Non-linear Cost Functions**A nonlinear cost function is a cost function in which the graph of total costs versus the level of a single activity is not a straight line within the relevant range. Economies of scale Quantity discounts Step cost functions**Concave Cost Functions**Learning versus experience curves**Data Issues**Data problems encountered in estimating cost functions.

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