La imagen-actitud

When a firm has been carrying out activities for some time and expects future activities to be similar to those of the past, the firm can analyze the historical data to estimate the variable and fixed components of total cost and to estimate likely future costs. The procedure for analyzing historical cost data requires two steps:

1. Make an estimate of the past relation.

2. Update this estimate so that it is appropriate for the present or future period for which management wants the estimate. This step requires adjusting costs for inflation and for changes that have occurred in the relation between costs and activity. For example, if a firm expects the production process to be more capital-intensive in the future, the accountant should reduce variable costs and increase fixed costs.

Before developing cost estimates from historical data, analysts should take the following pre- liminary steps.

P

RELIMINARY

S

TE P S IN

A

NALY ZING

H

IS TORIC AL

C

OS T

D

ATA

Data analysts use the term garbage in, garbage out to indicate that the results of an analysis cannot be better than the input data. Before using cost estimates, the analyst should be confident that the estimates make sense and result from valid assumptions.

Keep in mind that we are trying to find fixed costs per period, F, and variable cost per unit, V, of some activity variable, X, in the relation

TC¼ F þ VX:

Historical data comprise numerous observations. An observation is the total cost amount for a period and for the level of activity carried out during that period. Thus we may have total labor costs by month (the dependent variable) and the number of units produced during each of the months (the independent variable). Exhibit 5.8 shows 12 observations, one for each month, for the suite of operating rooms at Chicago Hospital.

EXHIBIT 5.8 CHICAGO HOSPITAL

Operating Room Overhead Cost Data by Month

Month Total Overhead O.R. Hoursa

January... $ 558,000 590 February ... 433,000 460 March ... 408,000 440 April ... 283,000 290 May... 245,500 230 June ... 308,000 320 July ... 358,000 390 August ... 445,500 480 September... 533,000 560 October... 658,000 700 November... 558,000 590 December ... 693,000 740 Total... $5,481,000 5,790 a_{An operating room hour is one hour that one operating room is being used for surgery.}

We should take the following steps in analyzing cost data:

1. Review alternative cost drivers (independent variables). A cost driver ideally measures the activity that causes costs. The cost drivers, if not the sole cause of costs, should directly influence costs. Operating room hours is an example of a cost driver in a hospital; machine hours is an example in a manufacturing firm; labor hours is an example in a service firm. 2. Plot the data. One simple procedure involves plotting each of the observations of total costs

against cost-driver activity levels. Plotting the data may make it clear that either no relation or only a nonlinear relation exists between the chosen cost driver and actual costs.

3. Examine the data and method of accumulation. Do the time periods for the cost data and the activity correspond? Occasionally, accounting systems will record costs actually incurred late on a given day as occurring on the following day. Observations collected by the month may smooth over meaningful variations of the cost driver’s activity level and cost that would appear if the accountant collected weekly data.

Be aware that a number of common recording procedures can make data appear to exhibit incorrect cost behavior patterns. Accounting systems often charge fixed overhead to production on a unit-by-unit basis. This ‘‘unitizing’’ of fixed costs makes fixed costs appear to be variable when they are not.

Sometimes an inverse relation seems to appear between activity and particular costs—when activity is high, costs are low; when activity is low, costs are high. An excellent example is maintenance. Firms sometimes purposefully do maintenance only when activity is slow. High maintenance levels often occur during plant shutdowns for automobile model changes, for example. The analyst would be naive to infer that low activity levels cause high maintenance costs.

These examples are a few of the data-recording methods that could lead the analyst astray. In general, we should investigate cost allocations, accruals, correcting and reversing entries, and relations between costs and activity levels to ensure that costs match activities in the appropriate time period for estimating costs.2Invalid relations between activity and costs will invalidate the analysis.

S

TATIS TIC AL

R

E GRE S S ION

A

NALYS IS

Having taken the preliminary steps to analyze the historical data, we now discuss the use of statistical analysis—specifically, a method called regression analysis. We discuss a simple estima- tion of variable and fixed overhead for the Chicago Hospital operating room suite. The Chicago Hospital operating room suite has 12 operating rooms used for a variety of surgeries ranging from simple vasectomies to major brain surgeries. This example discusses estimating overhead costs only—not costs of surgeons, nurses, or medical supplies—that can be directly traced to a particular surgery. (Each surgery is a ‘‘job’’ in cost language.) We assume that all data have been adjusted for the effects of inflation to make amounts from different time periods comparable to each other.

Because of inflation, one dollar in the year 2001 has a greater purchasing power than one dollar in the year 2007. Analysts should adjust all amounts so they have the same purchasing power. For example, if inflation between 2001 and 2007 has been 10%, then one could multiply the 2001 dollars by 1.10 to make them equivalent to 2007 dollars.

The task is to estimate the relation between total overhead costs and the activities that cause or at least are closely associated with those costs. For now, assume that, of the possible activity bases, the number of operating room hours during the month is the primary cause of overhead costs. Exhibit 5.8 shows total overhead costs and operating room hours each month for the past 12 months, adjusted for inflation. That is, the amounts presented are expressed in current dollars.

The cost equation to be estimated is Total Overhead Costs per Month ¼ Fixed Costs per Month þ Variable Overhead Costs per Operating Room Hour
Operating Room Hours Used during Month 0 B B @ 1 C C A TC ¼ F þ VX:

Although the estimate is done by computer, it may be helpful to think about regression as fitting a line to the data points on a graph. Regression analysis ‘‘fits’’ this line to the data by the

2

For an extended discussion of these remarks, see W. E. Wecker and R. L. Weil, ‘‘Statistical Estimation of Incremental Costs from Accounting Data,’’ Chapter 43 in R. L. Weil et al., eds., Litigation Services Handbook, 2nd ed. (New York: John Wiley & Sons, 1995).

method of least squares. Least squares fits the data points to the line to minimize the sum of the squares of the vertical distances between the observation points and the regression line. The statistical regression locates the line that best fits the data points using the least-squares criterion. So think of regression analysis as giving you the best ‘‘fit’’ of the line to the data, although it might not be a perfect fit.

In our example, an observed actual value of total overhead cost is TC, and the line we fit by the least-squares regression will be of the form

c

TC ¼ bFþ bV X,

where the ˆ on cTC , bF , and bV indicates that we have estimated the value of TC, F, and V. The V in this cost equation is the cost driver rate. A cost driver rate is the rate at which the cost driver ‘‘drives’’ or causes costs. The cost driver rate in this example will be the rate at which the operating rooms incur costs for each hour of operating room usage.

Standard terminology designates the vertical distance between the actual and the fitted values, TC cTC , as the residual. The method of least squares fits a line to the data to minimize the sum of all the squared residuals, which makes the line the ‘‘best fit’’ to the data.

Virtually every computer system and spreadsheet software package for personal computers can execute regression analysis. Be aware, however, that one needs entire books to understand these methods fully.

Running the data for TC and X in Exhibit 5.8 through a least-squares regression computer program gives the following results:3

Estimated Total

Overhead ¼ $18,600 þ ð$908
Operating Room Hours Used per MonthÞ Costs per Month

We interpret the $18,600 and $908 amounts as follows. The first—the intercept—estimates the fixed overhead cost per month to be $18,600. The second—the coefficient on the independent variable, or cost driver, estimates the variable overhead cost per unit to be $908. In this example, the units are operating room hours used per month.

U

S ING

R

E GRES S ION TO

E

S TIMATE

C

OS T

D

RIVE R

R

ATE S

Using the least-squares regression equation,

TC¼ $18,600 þ ð$908
Operating Room Hours per MonthÞ,

assume a hospital administrator is attempting to estimate the overhead costs of the operating room suite for next month for budgeting purposes. To make that estimate, the administrator must estimate the volume of activity—operating room hours—for the month. Then she would insert the volume of activity into the cost equation that we just estimated using simple regression. If the administrator estimates the number of operating room hours to be 600 hours next month, then she estimates the operating suite’s overhead costs to be $563,400 as follows:

TC¼ $18,600 þ ð$908
Operating Room Hours per MonthÞ ¼ $18,600 þ ð$908
600 hoursÞ

¼ $563,400:

Warning

We should be wary of predicting total costs for operating room hours worked outside the range of observations. Any activity less than about 200 hours per month or more than about 800 hours per month is outside the range of observations. We should also be wary of our estimate of fixed costs because, at zero operating room hours per month, it is also outside the range of observations.

M

ULTIP LE

R

E GRE S S ION

The preceding discussion dealt with only one independent variable. Multiple regression has more than one independent variable. We use Chicago Hospital data to illustrate multiple regression analysis with multiple cost drivers.

3

We obtained these results using the Regression option for Data Analysis in the Tools menu in Microsoft1Excel.

Assume that administrators at Chicago Hospital want to better understand the causes of costs. If they know the cost drivers, they can take actions to manage those costs better, thus reducing costs to HMOs which (should) reduce costs to members of the HMOs. After many interviews with the staff who work in the operating room suite, the administrators identified the following major cost drivers:

 Operating room hours (as used in the preceding simple regression analysis).

 Operating room setup hours. These are the hours used to clean the operating room after a surgery and prepare it for the next surgery.

 Number of VIP patients. VIP stands for ‘‘Very Important Person,’’ such as a City of Chicago councilperson, a member of the Chicago Bulls basketball team, or the owner of a very good restaurant. VIPs get special care, including extra staff on call during surgery and the highest-quality drugs.

 Number of different operating rooms used. Each operating room has to be heated, lit, cleaned by maintenance personnel at the end of the day, and otherwise maintained. The more operating rooms used in a day, the more overhead costs. (That is, it would be less expensive to use one operating room for 10 surgeries scheduled sequentially than to use 10 operating rooms, one per surgery.)

 _{Number of special surgeries. Special surgeries include organ transplants, major cancer} surgeries, and brain surgeries. Such major surgeries require greater overhead costs than more minor surgeries, all other things equal.

Exhibit 5.9 shows the cost driver volumes for the new cost drivers as well as the monthly costs and operating room hours that were presented in Exhibit 5.8.

The output for the multiple regression gives the following results: TC¼ $90,592 þ ð$175
Operating Room HoursÞ þ

ð$257
Operating Room Setup HoursÞ þ ð$3,839
Number of VIP patientsÞ þ ð$2,043
Number of Operating RoomsÞ þ ð$6,050
Number of Special SurgeriesÞ

Now suppose the operating room administrator estimates the following level of activity for next month. What do you estimate the costs to be?

EXHIBIT 5.9 CHICAGO HOSPITAL

Multiple Cost Drivers

Cost Driver Volumes

Total Overhead Costs Incurred during Month Operating Room Hours Used during Month Operating Room Setup Hours Used during Month Number of VIP Patients during Month Average Number of Operating Rooms Used per Day Number of Special Surgeries during Month January... $ 558,000 590 279 6 8 42 February ... 433,000 460 235 3 8 29 March ... 408,000 440 172 3 7 28 April ... 283,000 290 126 1 4 16 May... 245,500 230 103 0 4 13 June ... 308,000 320 115 1 4 20 July ... 358,000 390 183 2 5 22 August ... 445,500 480 217 3 6 32 September... 533,000 560 265 5 8 40 October... 658,000 700 355 7 9 51 November... 558,000 590 312 5 8 41 December ... 693,000 740 354 7 10 55 Total... $5,481,000 5,790 2,716 43 81 389

Estimated activity:

Operating room hours... 600 hours Operating room setup hours ... 280 hours Number of VIP patients... 6 patients Average number of operating rooms used per day... 8 rooms Number of special surgeries... 40 surgeries Given these estimates of activities, the administrator now estimates the overhead cost of the operating room suite for next month as shown in the last column of Panel A in the spreadsheet in Exhibit 5.10. Note that the estimated cost using multiple regression is different from the estimated cost obtained from simple regression. Without belaboring the point with discussion that is best left to statistics courses and textbooks, we simply note that models with different variables will give different results. It is likely that the multiple regression results are more accurate if (emphasize if ) the cost drivers in the multiple regression model are appropriate. (Note that there is good reason for calling this process cost estimation, not cost truth.)

F

INANCIAL

P

L ANNING

The spreadsheet in Exhibit 5.10 becomes a financial planning model and basis for decision making. For example, suppose the hospital administrator is appalled at the overhead associated with VIP patients and decides to eliminate special treatment for all but benefactors who give large sums to the hospital. In so doing, she reduces the number of VIP patients in Exhibit 5.10 to 1 by simply replacing the 6 in the spreadsheet with 1. You can verify that the costs in the spreadsheet change to $3,839 for VIP patient overhead and to $529,735 for the total for next month.

C

US TOME R

P

ROF ITAB ILIT Y

A

NALYS IS

Suppose the administrator is toying with the idea of becoming the surgery vendor for knee and hip replacements for other hospitals in the Chicago region. One health maintenance organization (HMO) has contacted Chicago Hospital about the possibility of doing its knee and hip replacements

EXHIBIT 5.10 CHICAGO HOSPITAL

Cost Estimation Using Multiple Regression Results

Cost Driver

Cost Driver Rate (given in text)

Estimated Activity (given in text)

Estimated Costa

Panel A: Cost estimation for next month

Intercept... $ 90,592 Operating room hours... $ 175 600 105,000 Operating room setup hours ... 257 280 71,960 Number of VIP patients... 3,839 6 23,034 Average number of operating rooms used per day... 2,043 8 16,344 Number of special surgeries... 6,050 40 242,000 Total estimated overhead for next month... $548,930 Panel B: Cost estimate for new customers

Operating room hours... $ 175 100 $ 17,500 Operating room setup hours ... 257 40 10,280 Number of VIP patients... 3,839 0 0 Average number of operating rooms used per day... 2,043 1 2,043 Number of special surgeries... 6,050 0 0 Total estimated overhead for new customer... $ 29,823 a_{Except for the intercept, which was estimated in the cost equation in the text, the estimated costs equal the cost driver rate times the estimated activity.}

for a set monthly fee. The administrator for Chicago Hospital believes that three overhead cost drivers will be affected:

 Operating room hours will increase by 100 hours per month.  Operating room setup hours will increase by 40 hours per month.  The average number of operating rooms used will increase by 1 per day.

The administrator believes that no other overhead cost driver will be affected, nor will the intercept in the regression equation change. If so, the overhead cost increase is shown in Panel B of Exhibit 5.10 to be $29,823. The administrator can use this information to ascertain whether to take the HMO’s offer.

In practice, analysts and managers use such estimates derived from cost estimation for thousands of applications, including cost management, standard setting, planning, all sorts of decision making, and many others. Keep in mind that such applications are only as good as the quality of the data and initial cost estimates.

A

CCOUNT

A

NALYS IS

Now we turn to another method of estimating cost drivers. Using the account analysis method, analysts review each cost account and classify it according to its relation to a cost driver. Continuing the Chicago Hospital example, the administrator would classify each overhead cost for the operating room suite according to its cost driver. For example, the wages paid to staff who clean up operating rooms between surgeries would be assigned to the activity ‘‘operating room setup.’’ Exhibit 5.11 shows the overhead costs assigned to the activities in the top row, ‘‘Costs.’’ These amounts were summed over the same 12 months that were used in the previous regression analysis. We show only the totals for the 12-month period because the totals are the minimum data required to estimate the cost drivers. (We could have shown you the amounts for each month, but that would have taken 84 cells of space and not been interesting reading, to say the least.)

In practice, we recommend that analysts look at the detailed data—in this case, monthly data— to see whether there are outliers or other unusual patterns in the data. Analysts might find, for example, that the costs of VIP surgeries have increased dramatically over the 12-month period, suggesting that such costs will be higher in the future than predicted by the cost driver estimate.

After the analysts have assigned all costs to the appropriate activities, they should divide the sum of the costs for each activity by the sum of the cost driver volumes for the same activity. In Exhibit 5.11, the hospital administrator divides the costs by the sum of the cost driver volumes, in the second row. The cost driver volumes are the same as appeared in the last row of Exhibit 5.9. The bottom row in Exhibit 5.11 shows the resulting cost driver rates. These rates correspond to the regression coefficients that are described in the text previously and that appear in Exhibit 5.10. The cost driver rates using account analysis are close to those estimated from multiple regression, but not exactly the same.

One item in Exhibit 5.11 that might seem puzzling is the category called ‘‘Fixed (Facility) Costs.’’ You can think of the cost driver in Exhibit 5.11 labeled ‘‘Fixed (Facility) Costs’’ ($93,763 per month) as corresponding to the ‘‘intercept’’ in Panel A of Exhibit 5.10.

Fixed (facility) costs are those that the organization incurs that are not related to a particular cost driver but are required to keep the facility going. Building lease and depreciation, property

EXHIBIT 5.11 CHICAGO HOSPITAL

Account Analysis Total Overhead Operating Room Use Operating Room Setup VIP Patients Number of Operating Rooms Used Special Surgeries Fixed (Facility) Costs Costs ... $5,481,000 $1,030,620 $719,740 $168,388 $169,614 $2,267,482 $1,125,156 Cost driver volumes... 5,790 hours 2,716 hours 43 patients 81 rooms 389 surgeries 12 months Cost driver rates... $178

per hour

$265 per setup hour

$3,916 per patient $2,094 per room $5,829 per surgery $93,763 per month

taxes, and salaries of top administrators are classic examples of facility costs. We call them ‘‘fixed’’ because they do not vary with any of the cost drivers. In practice, they are not fixed in the long run—they can be changed with strategic decisions. For example, if Chicago Hospital gets

In document BENEMÉRITA UNIVERSIDAD AUTÓNOMA DE PUEBLA FACULTAD DE CIENCIAS DE LA COMUNICACIÓN (página 48-52)