COMPARISON TO OTHER CASH FLOW DEFINITIONS

The de¬nition of net cash ¬‚ow available for distribution to stockholders

in equation (1-20b) can be summarized in the following way:

Activity Symbol Description

Operating NI Net income

GAIN Gains ( losses) on the sale of property, plant, and equipment

DEPR Depreciation and other noncash charges

RWC Increases ( decreases) in required working capital*

Investing CAPEXP Capital expenditures

SALESFA Selling price of property, plant, and equipment disposed of or retired

Financing LTD Increases ( decreases) in long-term debt

SALSTK Proceeds received from the sale of stock

TRSTK Payments for treasury stock

AET Additional equity transactions

*After adjusting for required cash.

This is easily compared to other de¬nitions that have been provided

in the authoritative literature. For example, one group of authors (Pratt,

16. C* C CReq

PART 1 Forecasting Cash Flows

18

Reilly, and Schweihs 1996) have proposed the following de¬nition of net

cash ¬‚ow available for distribution to stockholders in their Formula 9-3

(at 156“157):

Description

Net income

Depreciation and other non-cash charges

Increases ( decreases) in required working capital

Capital expenditures

Selling price of property, plant, and equipment disposed of or retired

Increases ( decreases) in long term debt

Implicitly, this de¬nition assumes that gains and losses on the sale

of property, plant, and equipment and the selling price of property, plant,

and equipment disposed of or retired are immaterial. Likewise, this def-

inition assumes that the proceeds from the sale of stock, payments made

for treasury stock, and additional equity transactions are also immaterial.

These assumptions are quite reasonable and can safely be made in a

large number of cases.17 However, it is important for the analyst to realize

that these assumptions are being made.

It is well known that when calculating value by capitalizing a single

initial cash ¬‚ow, the consequences of making adjustments to the initial

cash ¬‚ow are magni¬ed considerably. It is important for the analyst to

understand how these hidden assumptions might in¬‚uence the amount

of initial cash ¬‚ow being capitalized. Perhaps it is even more important

for the analyst to take into account how these assumptions might impact

the future cash ¬‚ows available for distribution to stockholders.

For example, if a company were to routinely to sell its equipment

for signi¬cant sums, the analyst would be remiss if he or she overlooked

the cash ¬‚ows from these sales.

CONCLUSION

Careful consideration of mathematics in this chapter should enhance the

analyst™s understanding of important accounting relationships and the

˜˜whys™™ of the Statement of Cash Flows. It should also make the analyst

aware of the simplifying assumptions embedded in abbreviated de¬ni-

tions of cash ¬‚ow available for distribution to stockholders. Hopefully,

this awareness will result in superior valuations in those instances where

the making of these simplifying assumptions is unwarranted.

BIBLIOGRAPHY

Abrams, Jay B. 1997. ˜˜Cash Flow: A Mathematical Derivation.™™ Valuation (March 1994):

64“71.

Pratt, Shannon P., Robert F. Reilly, and Robert P. Schweihs. 1996. Valuing a Business: The

Analysis and Appraisal of Closely Held Companies, 3rd ed. New York: McGraw-Hill.

17. With respect to the proceeds from the sale of stock, it is unlikely that a ¬rm would sell its

stock in order to obtain cash for distribution to its stockholders. However, sometimes large

sales of stock do occur.

CHAPTER 1 Cash Flow: A Mathematical Derivation 19

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CHAPTER 2

Using Regression Analysis

INTRODUCTION

FORECASTING COSTS AND EXPENSES

Adjustments to Expenses

Table 2-1A: Calculating Adjusted Costs and Expenses

PERFORMING REGRESSION ANALYSIS

USE OF REGRESSION STATISTICS TO TEST THE ROBUSTNESS OF

THE RELATIONSHIP

Standard Error of the y Estimate

The Mean of a and b

The Variance of a and b

Precise Con¬dence Intervals

Selecting the Data Set and Regression Equation

PROBLEMS WITH USING REGRESSION ANALYSIS FOR

FORECASTING COSTS

Insuf¬cient Data

Substantial Changes in Competition or Product/Service

USING REGRESSION ANALYSIS TO FORECAST SALES

Spreadsheet Procedures to Perform Regression

Examining the Regression Statistics

Adding Industry-Speci¬c Independent Variables

Try All Combinations of Potential Independent Variables

APPLICATION OF REGRESSION ANALYSIS TO THE GUIDELINE

COMPANY METHOD

Table 2-6: Regression Analysis of Guideline Companies

95% Con¬dence Intervals

SUMMARY

APPENDIX: The ANOVA table

21

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INTRODUCTION

Regression analysis is a statistical technique that estimates the mathe-

matical relationship between causal variables, known as independent var-

iables, and a dependent variable. The most common uses of regression

analysis in business valuation are:

1. Forecasting sales in a discounted cash ¬‚ow analysis

2. Forecasting costs and expenses in a discounted cash ¬‚ow

analysis

3. Measuring the relationship between market capitalization (fair

market value) as the dependent variable and several possible

independent variables for a publicly traded guideline company

valuation approach. Typical independent variables that are

candidates to affect the fair market value are net income

(including nonlinear transformations such as its square, square

root, and logarithm), book value, the debt-to-equity ratio, and so

on.

This chapter is written to provide the appraiser with some statistical

theory, but it is primarily focused on how to apply regression analysis to

real-life appraisal assignments using standard spreadsheet regression

tools. We have not attempted to provide a rigorous, exhaustive treatment

on statistics and have put as much of the technical background discussion

as possible in the appendix to keep the body of the chapter as simple as

possible. Those who want a comprehensive refresher should consult a

statistics text, such as Bhattacharyya and Johnson (1977) and Wonnacott

and Wonnacott (1981). We present only bits and pieces of statistics that

are necessary to facilitate our discussion of the important practical issues.

Even though you may not be familiar with using regression analysis

at all, let alone with nonlinear transformations of the data, the material

in this chapter is not that dif¬cult and can be very useful in your day-to-

day valuation practice. We will explain all the basics you need to use this

very important tool on a daily basis and will lead you step-by-step

through an example, so you can use this chapter as a guide to get ˜˜hands-

on™™ experience.

For those who are unfamiliar with the mechanical procedures to per-

form regression analysis using spreadsheets, we explain that step-by-step

in the section on using regression to forecast sales.

FORECASTING COSTS AND EXPENSES

In performing a discounted cash ¬‚ow analysis, an analyst should forecast

sales, expenses, and changes in balance sheet accounts that affect cash

¬‚ows. Frequently analysts base their forecasts of future costs on historical

averages of, or trends in, the ratio of costs as a percentage of sales.

One signi¬cant weakness of this methodology is that it ignores ¬xed

costs, leading to undervaluation in good times and possible overvaluation

in bad times. If the analyst treats all costs as variable, in good times when

he or she forecasts rapid sales growth, the ¬xed costs should stay constant

(or possibly increase with in¬‚ation, depending on the nature of the costs),

but the analyst will forecast those ¬xed costs to rise in proportion to sales.

PART 1 Forecasting Cash Flows

22

That leads to forecasting expenses too high and income too low in good

times, which ultimately causes an undervaluation of the ¬rm. In bad

times, if sales are forecasted ¬‚at, then costs will be accidentally forecasted

correctly. If sales are expected to decline, then treating all costs as variable

will lead to forecasting expenses too low and net income too high, leading

to overvaluation.

Ordinary least squares (OLS) regression analysis is an excellent tool

to forecast adjusted costs and expenses (which for simplicity we will call

˜˜adjusted costs™™ or ˜˜costs™™) based on their historical relationship to sales.

OLS produces a statistical estimate of both ¬xed and variable costs, which

is useful in planning as well as in forecasting. Furthermore, the regression

statistics produce feedback used to judge the robustness of the relation-

ship between sales and costs.

Adjustments to Expenses

Prior to performing regression analysis, we should analyze historical in-

come statements to ascertain if various expenses have maintained a con-

sistent pattern or if there has been a shift in the structure of a particular

expense. When past data is not likely to be representative of future ex-

pectations, we make pro forma adjustments to historical results to model

how the Company would have looked if its operations in the past had

conformed to the way we expect them to behave in the future. The pur-

pose of these adjustments is to examine longstanding ¬nancial trends

without the interference of obsolete information from the past. For ex-

ample, if the cost of advertising was 10% of sales for the ¬rst two years

of our historical analysis, decreased to 5% for the next ¬ve years, and is

expected to remain at 5% in the future, we may add back the excess 5%

to net income in the ¬rst two years to re¬‚ect our future expectations. We

may make similar adjustments to other expenses that have changed dur-

ing the historical period or that we expect to change in the future to arrive

at adjusted net income.

Table 2-1A: Calculating Adjusted Costs and Expenses

Table 2-1A shows summary income statements for the years 1988 to 1997.

Adjustments to pretax net income appear in Rows 15“20. The ¬rst ad-

justment, which appears in Rows 15“18, converts actual salary paid”

along with bonuses and pension payments”to an arm™s length salary.

This type of adjustment is standard in all valuations of privately held

companies.

The second type of adjustment is for a one-time event that is unlikely

to repeat in the future. In our example, the Company wrote off a discon-

tinued operation in 1994. As such, we add back the write-off to income

(H19) because it is not expected to recur in the future.

The third type of adjustment is for a periodic expense. We use a

company move as an example, since we expect a move to occur about

every 10 years.1 In our example, the company moved in 1993, 4 years

1. Losses from litigation are another type of expense that often has a periodic pattern.

CHAPTER 2 Using Regression Analysis 23

24

T A B L E 2-1A

Adjustments to Historical Costs and Expenses

A B C D E F G H I J K

4 Summary Income Statements

6 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997

7 Sales $250,000 $500,000 $750,000 $1,000,000 $1,060,000 $1,123,600 $1,191,016 $1,262,477 $1,338,226 $1,415,000

8 Cost of sales 100,000 250,000 375,000 500,000 490,000 505,000 520,000 535,000 550,000 600,000

9 S, G & A expenses 100,000 150,000 250,000 335,000 335,000 360,000 370,000 405,000 435,000 450,000

10 Operating expenses 58,000 68,000 78,000 88,000 83,000 110,000 112,000 117,000 122,000 132,000

11 Other expense 5,000 15,000 20,000 25,000 20,000 43,000 100,000 50,000 50,000 50,000

12 Pretax income $13,000 $17,000 $27,000 $52,000 $132,000 $105,600 $89,016 $155,477 $181,226 $183,000

13 Pre-tax pro¬t margin 5.20% 3.40% 3.60% 5.20% 12.45% 9.40% 7.47% 12.32% 13.54% 12.93%

14 Adjustments:

15 Actual salary 75,000 80,000 85,000 130,000 100,000 100,000 105,000 107,000 109,000 111,000

16 Bonus 3,000 4,000 4,000 20,000 5,000 5,000 5,000 7,000 9,000 10,000

17 Pension 1,000 1,000 1,500 2,000 2,000 2,000 2,000 2,000 2,000 2,000

18 Arms length salary [1] (58,015) (60,916) (63,961) (67,159) (70,517) (74,043) (77,745) (81,633) (85,714) (90,000)

19 Discontinued operations [2] 55,000

20 Moving expense [3] 20,000

21 Adjusted pretax income $7,985 $41,084 $53,539 $136,841 $168,483 $158,557 $178,271 $189,844 $215,511 $216,000

22 Adjusted pretax pro¬t margin 3.19% 8.22% 7.14% 13.68% 15.89% 14.11% 14.97% 15.04% 16.10% 15.27%