Predicting Cost Behavior Chapter 2, Appendix 2A ACCTG 404 A2A-1

Build a model to predict life expectancy: What factors would you collect? How would you use data to build predictive model? A2A-2

Predictive Output from Regression Models Volunteer to use the model… Height / Weight Medical history Alcohol / Tobacco / Drug (!) use A2A-3

Our Application of Predictive Models There are many applications for predictive analysis throughout accounting and finance. In this course we will focus on using regression analysis and other techniques to estimate future (fixed and variable) costs. – Pay attention to the basic principles – Focus on understanding the outputs A2A-4

Plot of Actual Observations A2A-5

Which Line Best Estimates Total Cost? A2A-6

1) Variable cost = $2,400 ÷ 3,000 units = $0.80 per unit 2) Fixed cost = Total cost – Total variable cost Fixed cost = $9,800 – ($0.80 per unit × 8,000 units) Fixed cost = $9,800 – $6,400 = $3,400 3) Total cost = Fixed cost + Variable cost (Y = a + bX) Y = $3,400 + $0.80X 1) Variable cost = $2,400 ÷ 3,000 units = $0.80 per unit 2) Fixed cost = Total cost – Total variable cost Fixed cost = $9,800 – ($0.80 per unit × 8,000 units) Fixed cost = $9,800 – $6,400 = $3,400 3) Total cost = Fixed cost + Variable cost (Y = a + bX) Y = $3,400 + $0.80X The High-Low Method A2A-7

Sales salaries and commissions are $10,000 when 80,000 units are sold, and $14,000 when 120,000 units are sold. Using the high-low method, what is the variable portion of sales salaries and commission? a. $0.08 per unit b. $0.10 per unit c. $0.12 per unit d. $0.125 per unit Sales salaries and commissions are $10,000 when 80,000 units are sold, and $14,000 when 120,000 units are sold. Using the high-low method, what is the variable portion of sales salaries and commission? a. $0.08 per unit b. $0.10 per unit c. $0.12 per unit d. $0.125 per unit Quick Check $4,000 ÷ 40,000 units = $0.10 per unit Sales salaries and commissions are $10,000 when 80,000 units are sold, and $14,000 when 120,000 units are sold. Using the high-low method, what is the variable portion of sales salaries and commission? a. $0.08 per unit b. $0.10 per unit c. $0.12 per unit d. $0.125 per unit Sales salaries and commissions are $10,000 when 80,000 units are sold, and $14,000 when 120,000 units are sold. Using the high-low method, what is the variable portion of sales salaries and commission? a. $0.08 per unit b. $0.10 per unit c. $0.12 per unit d. $0.125 per unit A2A-8

Sales salaries and commissions are $10,000 when 80,000 units are sold, and $14,000 when 120,000 units are sold. Using the high-low method, what is the fixed portion of sales salaries and commissions? a. $ 2,000 b. $ 4,000 c. $10,000 d. $12,000 Sales salaries and commissions are $10,000 when 80,000 units are sold, and $14,000 when 120,000 units are sold. Using the high-low method, what is the fixed portion of sales salaries and commissions? a. $ 2,000 b. $ 4,000 c. $10,000 d. $12,000 Sales salaries and commissions are $10,000 when 80,000 units are sold, and $14,000 when 120,000 units are sold. Using the high-low method, what is the fixed portion of sales salaries and commissions? a. $ 2,000 b. $ 4,000 c. $10,000 d. $12,000 Sales salaries and commissions are $10,000 when 80,000 units are sold, and $14,000 when 120,000 units are sold. Using the high-low method, what is the fixed portion of sales salaries and commissions? a. $ 2,000 b. $ 4,000 c. $10,000 d. $12,000 Quick Check A2A-9

Pitfalls to High-Low Method High level of activity may not coincide with high level of cost and vice-versa Utilizes only two data points Unusually high or low levels of activity (outliers) may produce inaccurate results A2A-10

Regression Analysis Regression analysis is a statistical method that measures the average amount of change in the dependent variable (i.e., y variable) associated with a unit change in one or more independent variables (i.e., x variable or variables) It is more accurate than the High-Low method because the regression equation estimates costs using information from all observations; the High- Low method uses only two observations A2A-11

Which Line Best Estimates Total Cost? A2A-12 High-Low Method Regression Analysis

Simple Regression Analysis Example Qdoba wants to know its average fixed cost and variable cost per unit. Using the data to the right, let’s see how to do a regression using Excel. Qdoba wants to know its average fixed cost and variable cost per unit. Using the data to the right, let’s see how to do a regression using Excel. A2A-13

We will need three pieces of information from your regression analysis: We will need three pieces of information from your regression analysis: 1.Estimated Variable Cost per Unit (line slope) 2.Estimated Fixed Costs (line intercept) 3.Goodness of fit, or R 2 We will need three pieces of information from your regression analysis: We will need three pieces of information from your regression analysis: 1.Estimated Variable Cost per Unit (line slope) 2.Estimated Fixed Costs (line intercept) 3.Goodness of fit, or R 2 Simple Regression Analysis Example A2A-14

Mac Users: Data Analysis ToolPak Mac users: n/products/statplusmacle/dow nload.phtml n/products/statplusmacle/dow nload.phtml PC users: n-us/magazine/ff aspx n-us/magazine/ff aspx A2A-15

Regression Analysis in Excel A2A-16

Regression Analysis in Excel A2A-17

Regression Analysis in Excel A2A-18

Regression Analysis in Excel: Intercept Intercept (constant): amount of Y when X is 0. In this regression it can be interpreted as the fixed costs. A2A-19

Regression Analysis in Excel: Slope Slope (coefficient on independent variable): the increase in Y (cost) for each unit increase in X (cost driver). A2A-20 so, expected monthly total costs = $2,618 + $2.76x

“R-Square” measures the explanatory power of the regression. It ranges from 0 to 1. More reliable (better fit) if closer to 1. “R-Square” measures the explanatory power of the regression. It ranges from 0 to 1. More reliable (better fit) if closer to 1. Regression Analysis in Excel: R 2 A2A-21

Regression Analysis in Excel: t-Stat t-value (t-stat): Coefficient ÷ SE Degree to which variable has a valid, stable, long-term relationship with the dependent variable. Generally look for t-values > |2|. t-value (t-stat): Coefficient ÷ SE Degree to which variable has a valid, stable, long-term relationship with the dependent variable. Generally look for t-values > |2|. A2A-22

Regression Analysis in Excel: p-value p-value: risk that independent variable has only a small chance of relationship to dependent variable. As a general guide p-values less than.05 or.01 are generally representative of a relationship. p-value: risk that independent variable has only a small chance of relationship to dependent variable. As a general guide p-values less than.05 or.01 are generally representative of a relationship. A2A-23

Regression Analysis in Excel In formal statistics, we would normally calculate the desired CI from Z table for specific intervals. In this course we concentrate on two approximations. 67% CI Z value ~ 1 then 67% C. I. = M ± (1 × SE) 95% CI Z value ~ 2 then 95% C. I. = M ± (2 × SE) In formal statistics, we would normally calculate the desired CI from Z table for specific intervals. In this course we concentrate on two approximations. 67% CI Z value ~ 1 then 67% C. I. = M ± (1 × SE) 95% CI Z value ~ 2 then 95% C. I. = M ± (2 × SE) A2A-24

Regression Analysis in Excel Confidence interval (CI): range around the regression coefficient within which the user can be confident that the predicted cost will fall. Calculate 95% Confidence Interval for the variable cost per meal. 95% C. I. = M ± (2 × SE) 95% C. I. = ± (2 ×.1988) 95% C. I. = ± (.3976) 95% confidence that costs range from to Confidence interval (CI): range around the regression coefficient within which the user can be confident that the predicted cost will fall. Calculate 95% Confidence Interval for the variable cost per meal. 95% C. I. = M ± (2 × SE) 95% C. I. = ± (2 ×.1988) 95% C. I. = ± (.3976) 95% confidence that costs range from to A2A-25

Regression Analysis in Excel Calculate 95% Confidence Interval for the total cost assuming 1,500 meals (1500×2.768) = (1500×2.768) = % C. I. = M ± (2 × SE) 95% C. I. = ± (2 × ) 95% C. I. = ± (1,176.61) 95% confidence that costs range from 5, to 7, Calculate 95% Confidence Interval for the total cost assuming 1,500 meals (1500×2.768) = (1500×2.768) = % C. I. = M ± (2 × SE) 95% C. I. = ± (2 × ) 95% C. I. = ± (1,176.61) 95% confidence that costs range from 5, to 7, A2A-26

Types of Regression Simple: estimates the relationship between the dependent variable and one independent variable Multiple: estimates the relationship between the dependent variable and two or more independent variables A2A-27

The Ideal Database 1.The database should contain numerous reliably-measured observations of the cost driver and the costs 2.In relation to the cost driver, the database should consider many values spanning a wide range A2A-28

Potential Data Issues The relationship between the cost driver and the cost is not stationary – Inflation has affected costs, the driver, or both Outliers in the data – Hurricane Sandy in NJ/NY: you should exclude from national Qdoba forecast – Data errors Non-linearity – Economies of Scale – Quantity Discounts – Step Cost Functions: resources increase in “lot-sizes,” not individual units A2A-29

In Class Problem As part of his job as cost analyst, Max Thompson collected the following information concerning the operations of the Machining Department: ObservationMachine-hoursTotal Operating Costs January4,000$45,000 February4,60049,500 March3,80045,750 April4,40048,000 May4,50049,800 a. Use the high-low method to determine the estimating cost function with machine- hours as the cost driver. b. If June's estimated machine-hours total 4,200, what are the total estimated costs of the Machining Department? As part of his job as cost analyst, Max Thompson collected the following information concerning the operations of the Machining Department: ObservationMachine-hoursTotal Operating Costs January4,000$45,000 February4,60049,500 March3,80045,750 April4,40048,000 May4,50049,800 a. Use the high-low method to determine the estimating cost function with machine- hours as the cost driver. b. If June's estimated machine-hours total 4,200, what are the total estimated costs of the Machining Department? a. Slope coefficient = ($49,500 - $45,750)÷(4, ,800) = $ per machine-hour Constant = $49,500 - ($ × 4,600) = $27, Estimating equation = $27, $4.6875X b. June's estimated costs = $27, $ × 4,200 = $47,625 A2A-30

In Class Problem a.What is linear regression estimate? Y = X b.What is the the predicted GPA for someone with a SAT_SCORE of 1200? a.What is linear regression estimate? Y = X b.What is the the predicted GPA for someone with a SAT_SCORE of 1200? A2A-31

In Class Problem c.What is the 95% confidence interval for the coefficient SAT_SCORE? d.What is the 95% confidence interval around the predicted GPA for someone with a SAT_SCORE of 1200? c.What is the 95% confidence interval for the coefficient SAT_SCORE? d.What is the 95% confidence interval around the predicted GPA for someone with a SAT_SCORE of 1200? A2A-32