2: Interpreting Regression Analysis Output

Appendix 5.2: Interpreting Regression Analysis Output

This appendix expands the discussion in the text to help you understand and interpret regression output.

S TA N D A R D E R R O R S O F T H E C O E F F I C I E N T S A N D t - S TAT I S T I C S

The standard errors of the coefficients give an idea of the confidence we can have in the fixed and variable cost coefficients. The smaller the standard error relative to its coefficient, the more precise the estimate. (Such computational precision does not necessarily indicate that the esti- mating procedure is theoretically correct, however.)

The ratio between an estimated regression coefficient and its standard error is known as the t-value or t-statistic. If the absolute value of the t-statistic is approximately 2 or larger, we can be relatively confident that the actual coefficient differs from zero. 7

If a variable cost coefficient has a small t-statistic, we may conclude that little, if any, relation exists between this particular activity (or independent variable) and changes in costs. If a fixed cost coefficient has a small t-statistic, we may conclude that these costs have little, if any, fixed cost component (which we would expect for operating room supplies or direct materials in manufacturing, for example).

7 Statistics books provide t-tables that make the analysis of t-statistics more precise.

Appendix 5.2: Interpreting Regression Analysis Output 167

Relation between Statistical Significance of Variable Cost Coefficient and R 2

Statistically Significant

Statistically Significant

Variable Cost Coefficient

Variable Cost Coefficient

but Low R 2 but High R 2

R 2 The R 2 attempts to measure how well the line fits the data (that is, how closely the data points

cluster about the fitted line). If all the data points were on the same straight line, the R 2 would be 1.00—a perfect fit. If the data points formed a circle or disk, the R 2 would be zero, indicating that no line passing through the center of the circle or disk fits the data better than any other. Technically, R 2 is a measure of the fraction of the total variance of the dependent variable about its mean that the fitted line explains. An R 2 of 1 means that the regression explains all of the variance; an R 2 of zero means that it explains none of the variance. R 2 is sometimes known as the ‘‘coefficient of determination.’’ Many users of statistical regression analysis believe that a low R 2 indicates a weak relation between total costs (dependent variable) and the activity base (independent variable). A low standard error (or high t-statistic) for the estimated variable cost coefficient signals whether or not the activity base performs well as an explanatory variable for total costs. With a large number of

data observations, both low R 2 and significant regression coefficients can occur. Exhibit 5.15 illustrates this possibility.

CAUTIONSWHENUSINGREGRESSION Computers easily perform statistical estimating techniques but often do not provide the necessary

warnings. We conclude this section by providing several cautionary comments. A relation achieved in a regression analysis does not imply a causal relation; that is, a correlation between two variables does not imply that changes in one will cause changes in the other. An assertion of causality must be based on either a priori knowledge or some analysis other than a regression analysis.

Users of regression analysis should be wary of drawing too many inferences from the results unless they are familiar with such statistical estimation problems as multicollinearity, autocorrelation, and heteroscedasticity and how to deal with them. Statistics books deal with these statistical estimation problems.

Briefly, multicollinearity refers to the problem caused in multiple linear regression (more than one independent variable) when the independent variables are not independent of each other but are correlated. When severe multicollinearity occurs, the regression coefficients are unreliable. For example, direct labor hours worked during a month are likely to be highly correlated with direct labor costs during the month, even when wage rates change over time. If both direct labor hours and direct labor costs are used in a multiple linear regression, we would expect to have a problem of multicollinearity.

Autocorrelation problems arise when the data represent observations over time. Autocorre- lation occurs when a linear regression is fit to data where a nonlinear relation exists between the dependent and independent variables. In such a case, the deviation of one observation from the fitted line can be predicted from the deviation of the prior observation(s). For example, if demand

168 Chapter 5 Cost Drivers and Cost Behavior

for a product is seasonal and production is also seasonal, a month of large total costs will more likely follow another month of large total costs than a month of small total costs. In such a case, we would have autocorrelation in the deviations of the data points from a fitted straight line.

Autocorrelation affects the estimates of standard errors of the regression estimates, and therefore it affects the t-statistics. If autocorrelation exists, the estimates of standard errors may be understated and the t-statistics may be overstated in the regression output.

Heteroscedasticity refers to the phenomenon that occurs when the average deviation of the dependent variable from the best-fitting linear relation is systematically larger in one part of the range of independent variable(s) than in others. For example, if the firm uses less-reliable equipment and employs less-skilled labor in months of large total production, variation in total costs during months of large total production is likely to be greater than in months of small total production. Heteroscedasticity affects the reliability of the estimates of standard errors of the regression coefficients (and therefore affects the reliability of the t-statistics).

Que stions , Exercis e s , and Problems

REVIEWQUESTIONS

1. Review the meaning of the concepts or terms given in Key Terms and Concepts.

2. Which method of cost estimation does not rely primarily on historical cost data? What are

the drawbacks of this method?

3. Name three methods of cost estimation.

4. The simplifying assumptions on which cost estimations are based include which of the

following?

a. Cost behavior depends on one activity variable (except multiple regression).

b. Cost behavior patterns are not linear within the relevant range.

c. Costs are only fixed.

d. All of the above.

5. (See Appendix 5.2.) R 2

a. measures how well the line fits the data.

b. is a perfect fit when its value is 1.0.

c. is the standard error of the coefficient.

d. a. and b.

6. Multiple regression

a. has one dependent variable.

b. has more than one independent variable.

c. has only one independent variable.

d. a. and b. C R I T I C A L A N A LY S I S A N D D I S C U S S I O N Q U E S T I O N S

7. ‘‘The concepts of short-run costs and long-run costs are relative—short run could mean a day, a month, a year, or even 10 years, depending on what you are looking at.’’ Comment.

8. ‘‘My variable costs are $2 per unit. If I want to increase production from 100,000 units to 150,000 units, my total costs should go up by only $100,000.’’ Comment.

9. What methods of cost estimation rely primarily on historical data? Discuss the problems an

unwary user may encounter with the use of historical cost data.

10. What steps would you take to deal with a supervisor who asks you to falsify the results of

your cost estimation?

11. In what cultures might analysts be more willing to reveal errors they made in estimating

costs?

12. When estimating fixed and variable costs, it is possible to have an equation with a negative intercept. Does this mean that at zero production the company has negative fixed costs?

Questions, Exercises, and Problems 169

13. Refer to the Managerial Application ‘‘United Airlines Uses Regression to Estimate Cost Behavior.’’ What independent variables did the analysts use in the regression? What did the analysts who developed the regression conclude? Based on your experience, do you agree with their conclusions?

14. (See Appendix 5.2.) How is regression used to identify what cost drivers might be used in activity-based costing?

15. (See Appendix 5.1.) Describe the phenomenon that gives rise to learning curves. To what type of costs do learning curves apply?

16. ‘‘Simplification of all costs into only fixed and variable costs distorts the actual cost behavior pattern of a firm. Yet businesses rely on this method of cost classification.’’ Comment.

17. ‘‘The account analysis method uses subjective judgment. So we cannot really consider it a valid method of cost estimation.’’ Comment.

18. Suggest ways that one can compensate for the effects of inflation when preparing cost estimates.

EXERCISES Solutions to even-numbered exercises are at the end of the chapter.

19. Graphs of cost relations. Sketch cost graphs for the following situations:

a. A 30 percent increase in fixed costs will enable Donelan Company to produce up to

75 percent more. Variable costs per unit will remain unchanged.

b. Refer to part a. What if Donelan Company’s variable costs per unit triple for the addi- tional units it intends to produce?

c. Richmond’s variable marketing costs per unit decline as more units are sold.

d. Anderson Paper pays a flat fixed charge per month for electricity plus an additional rate of $0.20 per unit for all consumption over the first 2,000 units.

e. Indirect labor costs at KMD Bank consist only of supervisors’ salaries. The bank needs one supervisor for every 20 clerks.

f. National Plastics currently operates close to capacity. A short-run increase in production would result in increasing unit costs for every additional unit produced.

20. Cost behavior in event of capacity change. Slopeside Resort, a lodge located in a fast- growing ski resort, is planning to open its new wing this coming winter, increasing the number of beds by 40 percent. Although variable costs per guest-day will remain unchanged, total fixed costs will increase by 25 percent. Last year’s costs follow:

Variable Costs .....................................................................................................................................................

$50,000

Total Fixed Costs ................................................................................................................................................

30,000

a. Sketch the cost function.

b. Calculate the additional fixed operating costs that Slopeside Resort will incur next year.

21. Cost behavior when costs are semivariable. Data from the shipping department of Brawn Company for the past two months follow:

Number of

Shipping

Packages Shipped

Department Costs

a. Sketch a line describing these costs as a function of the number of packages shipped.

b. What is the apparent variable cost per package shipped?

c. The line should indicate that these shipping costs are semivariable. What is the apparent fixed cost per month of running the shipping department during November and December?

172 Chapter 5 Cost Drivers and Cost Behavior

PROBLEMS

30. Multiple regression. The managers of Peterson’s Catering Company are analyzing the costs involved in providing catering services. Managers have selected the following cost drivers: units of meals produced, total deliveries, number of VIP services, number of new customers, and new products developed. Here are the cost data and levels of cost driver activity for the past 16 months.

Customers Products

a. Using multiple regression, find the cost driver rates for each of the cost drivers. (Note: You must use a computer program such as Microsoft 1 Excel to perform this step.)

b. Management estimates the following levels of cost driver volumes for the next month for the budget. What is the estimated cost for the budget? (Don’t forget to include the intercept of the regression in your estimate.)

12,000 ......................................................................

Meals produced

VIP services

5 ......................................................................

New customers

2 ......................................................................

New products

c. Peterson’s Catering Company is considering outsourcing deliveries. Compared to your answer in requirement b., how much would be saved per month by outsourcing the delivery service (before considering the cost of outsourcing)?

31. Account analysis. Refer to problem 30.

a. Indicate the information in addition to that provided in problem 30 required to perform

account analysis.

b. Now assume that Peterson’s Catering Company had the following breakdown of costs

for the 16 months reported in problem 30:

Total costs of meals produced .................................................................................................................. $334,368 Total costs for delivering ...........................................................................................................................

164,400 Total costs of VIP services ........................................................................................................................

140,352 Total costs of developing new customers ..............................................................................................

154,904 Total costs of developing new products ................................................................................................

18,700 Total facilities-level costs (total for all 16 months) ..........................................................................

159,377 Total costs ..................................................................................................................................................

$972,101

174 Chapter 5 Cost Drivers and Cost Behavior

Number of Water New

Month

Overhead

Produced (hL) Material (kg) Batches

(hL) CIPs Products

a. Using multiple regression, find the cost driver rates for each of the cost drivers. (Note: You must use a computer program such as Microsoft 1 Excel to perform this step.)

b. Assuming the following level of cost driver volume for the next month, what is the estimated cost? (Don’t forget to include the intercept of the regression in your estimate.)

1,650 ...........................................

hL of beer produced

25,500 ..........................................

kg of raw materials consumed

hL of water consumed

New product

c. Brazil Brewery is considering a target for water consumption of 5.0 hL water per hL of beer produced. How much would the company have saved in total over the previous

18 months if it had reached this target in the previous 18 months?

34. Account analysis. Refer to problem 33.

a. Indicate the information in addition to that provided in problem 33 required to perform

account analysis.

b. Now assume that Brazil Brewery had the following breakdown of costs:

Total costs of beer produced ........................................................................................................... $ 292,429.28 Total costs of raw materials consumption ....................................................................................

236,168.40 Total batch-level costs ......................................................................................................................

69,173.19 Total costs of water consumption ..................................................................................................

141,935.36 Total costs of CIPs performed ..........................................................................................................

29,392.65 Total costs of developing new products .......................................................................................

6,204.64 Total facilities-level costs (total for all 18 months) .................................................................

446,233.36 Total costs .........................................................................................................................................

$1,221,536.88

What are the cost driver rates using account analysis?

178 Chapter 5 Cost Drivers and Cost Behavior

a. The total overhead cost for an estimated activity level of 20,000 direct labor hours

would be (1) $55,000

(2) $64,000 (3) $82,000 (4) $119,000 (5) Some other amount

b. What is the expected contribution margin per unit to be earned during the first year on 100,000 units of the new product? (Assume all marketing and administrative costs are fixed.)

(1) $4.38 (2) $4.89 (3) $3.83 (4) $5.10 (5) Some other amount

c. How much is the variable manufacturing cost per unit, using the variable overhead estimated by the regression (and assuming direct materials and direct labor are variable costs)?

(1) $1.30 (2) $1.11 (3) $1.62 (4) $3.00 (5) Some other amount

d. What is the manufacturing cost equation implied by these results, where x refers to units

produced? (1) TC ¼ $80,000 þ $1.11x (2) TC ¼ $55,000 þ $1.62x (3) TC ¼ $185,000 þ $3.20x (4) Some other equation

e. (Answer if Appendix 5.2 was assigned reading.) What percentage of the variation in

overhead costs is explained by the independent variable? (1) 90.8 percent

(2) 42 percent (3) 48.8 percent (4) 95.3 percent (5) Some other amount

40. Interpreting multiple regression results (Appendix 5.2). To select the most appropriate activity base for allocating overhead, KenLee Manufacturing ran a multiple regression of several independent variables against its nonmaintenance overhead cost. The results were as follows for 24 observations:

Variable Name

Coefficient

Standard Error t -Statistic

Direct labor hours ....................................................................

0.876

2.686 0.326

Units of output ........................................................................

10.218

5.378 1.900

Maintenance costs ...................................................................

$(12.786)

$1.113 (11.488)

Cost of utilities ........................................................................

R 2 for the multiple regression ¼ 0.90

Discuss the appropriateness of each of these variables for use as an activity base. Which would you recommend selecting? Why?

180 Chapter 5 Cost Drivers and Cost Behavior

Fixed overhead ..........................................................................................

50 percent of direct labor dollars

Variable overhead .....................................................................................

100 percent of direct labor dollars

Factory overhead rate ..............................................................................

150 percent of direct labor dollars

b Assembly labor consists of hourly production workers. c Factory overhead is applied to products on a direct labor dollar basis. Variable overhead costs vary closely with direct labor dollars. General and administrative overhead is applied at 10 percent of the total cost of material (or components), assembly labor, and

factory overhead.

a. Was the analysis prepared by the engineering, manufacturing, and accounting depart- ments of Nippon Company and the recommendation to continue purchasing the pumps that followed from the analysis correct? Explain your answer and include any supportive calculations you consider necessary.

b. Assume Nippon Company could experience labor cost improvements on the pump assembly consistent with an 80 percent learning curve. An assembly run of 10,000 units represents the initial lot or batch for measurement purposes. Should Nippon produce the 80,000 pumps in this situation? Explain your answer.

S ug ge ste d S olutions to Even -Numb ere d Exercis e s

20. Cost behavior in event of capacity change.

a.

Total Costs

Guest Days

Current Capacity

b. Additional fixed operating costs ¼ 0.25($30,000) ¼ $7,500

22. Identifying cost behavior. Plotting the data, these costs appear to be semivariable. The fixed-cost component estimate is $1,500, and the variable cost component is $1 per package up to 2,000 packages [$1 ¼ ($3,500 – $1,500)/2,000 packages]. With only four data points, you should view these estimates skeptically, however.

Suggested Solutions to Even-Numbered Exercises 181

Number of Packages Shipped

24. Learning curve.

Cumulative Number of

Average Labor

Units Produced

Costs per Unit

26. Repair cost behavior. The most likely explanation for the inverse relation between pro- duction and repair costs is that the firm schedules repair work during slow, rather than busy, times. So repair costs increase when volume decreases.

28. Interpreting regression data. This problem frequently arises when applying analytical techniques to certain costs. Quite often the advertising expenditures result in sales being generated in the following month or later. In addition, many companies increase their advertising when sales are declining and cut back on advertising when manufacturing is at capacity. A better model might relate this month’s sales to last month’s advertising.

Similar problems exist for repair and maintenance costs because routine repairs and maintenance usually occur during low volume periods.

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Financial Modeling for Short-Term Decision-Making

Learning Objectives

1. Describe the use of financial modeling for

5. Explain how to use sales dollars as the

profit-planning purposes.

measure of volume.

2. Explain how to perform cost-volume-profit

6. Explain the effect of taxes on financial

(CVP) analysis.

modeling.

3. Describe the use of spreadsheets in financial

7. Describe the use of financial modeling in a

modeling.

multiple-product setting.

4. Identify the effects of cost structure and 8. Explain financial modeling with multiple cost operating leverage on the sensitivity of profit

drivers.

to changes in volume.

Financial modeling, a simple but appealing tool, can provide a sweeping overview of an organi- zation’s financial activities or can help managers make specific decisions.

Suppose that a student club wants to show movies on campus. The club can rent a particular movie for one weekend for $1,000. Rent for an auditorium, salaries to the ticket-takers and other personnel, and other fixed costs would total $800 for the weekend. The organization would sell tickets for $4 per person. In addition, it estimates that profits from the sale of soft drinks, popcorn, and candy are $1 per ticket holder. How many people would have to buy tickets for the club to break even and therefore justify renting the movie? (The answer is 360.)

The analysis relies on concepts of fixed and variable cost behavior that we first discussed in Chapter 1 and just covered in Chapter 5. This chapter presents the concept of financial modeling, more specifically a particular type of financial model, and demonstrates how managers can use it in a number of decision-making situations.

After reading this chapter, you should understand how to use financial modeling to project profits (or losses) and how to use the resulting information to make short-term decisions.

184 Chapter 6 Financial Modeling for Short-Term Decision-Making

What Is Fin ancial Mo delin g ?

A model represents reality. You likely have seen models over the years, such as model airplanes, models of commercial buildings created by architects, or dolls and action figures. Another example is a simulator used to train airplane pilots. The simulator allows one to test skills under different conditions in an effort to study reactions of the pilot.

A financial model, which works in much the same fashion as a simulator, enables analysts to test the interaction of economic variables in a variety of settings. These models require that analysts develop a set of equations that represent a company’s operating and financial relations. For example, these relations may include that of contribution margin to selling price, numbers of sales, inventory turnover ratios, and the relative proportion of various products sold (called product mix). They can include any financial relation that would help managers make decisions. The analyst then embeds the model in software, often a spreadsheet, allowing a user to compute the effect that changes to variables such as sales price or volume or costs might have on operating profits of the business. For example, a company may want to know the impact on cash flow, sales, and profitability of credit tightening proposed by one of its divisions. An analyst can construct an appropriate financial model and, in a matter of seconds, predict the outcome of various scenarios. (We explore this technique later in the chapter.)

Financial models offer several benefits to users. Once developed, analysts can use the model for business purposes without becoming overwhelmed by the related number crunching. Like the simulators just discussed, many models allow an organization to study the impact of a possible business action by reviewing the potential results before taking that action. The models help managers identify a bad project or decision ahead of time, before it negatively impacts the company involved.

Be warned about GIGO—garbage in, garbage out. Using financial models can present problems. Sound models do not automatically improve decision making. A model is only as good as the assumptions it uses. Faulty assumptions or bad data result in faulty output—sometimes worse than useless because it sends managers off in wrong directions.

The Cost-Volume - Prof|t Mo del

One basic financial model, the cost-volume-profit (CVP) model, summarizes the effects of volume changes on an organization’s costs, revenue, and income. Users can extend such analysis to include the impact on profit of changes in selling prices, service fees, costs, income-tax rates, and the organization’s mix of products or services. For example,

What effect on profit can General Motors expect if it builds a larger sport utility vehicle? How will NBC’s profit change if the ratings increase for its evening news program? How many online subscribers must AOL obtain to break even for the year? What happens if AOL reduces fees charged to its customers—will profits increase with an increase in subscribers?

Each of these questions concerns the effects on profits when some activity changes, and the CVP model can aid the analysis.

Although the word profit appears in its title, the cost-volume-profit model applies as well to not-for-profit enterprises. Managers in nonprofit organizations also routinely use CVP analysis to examine the effects of activity and other short-run changes on revenue and costs.