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cash but having no impact on the income statement. These transactions
are classi¬ed as investing or ¬nancing activities. Investing activities in-
clude the acquisition of long-lived assets as well as their disposition when
no gains or losses are involved.2 Financing activities include obtaining
and repaying funds from debt and equity holders and providing the own-
ers with a return on their investment.
Either the direct or the indirect method may be used as a basis for
reporting cash ¬‚ows from operating activities. Under the direct method
the enterprise lists its major categories of cash receipts from operations
(such as receipts from product sales and receipts from consulting services)
and cash disbursements for operations (such as payments for inventory,
wages, interest, and taxes). The difference between these receipts and dis-
bursements is the net cash ¬‚ow from operations.
Under the indirect method, net cash ¬‚ow from operations is found
by adjusting net income for changes in related asset and liability accounts.
For example, an increase in accounts receivable indicates that cash receipts
from sales are less than reported revenues. Receivables increase as a result


2. This introductory comment presumes the long-lived assets are sold for their net book values. Of
course, when gains or losses on disposition are involved they do appear in the income
statement. The treatment of these gains and losses is addressed later in the chapter.




PART 1 Forecasting Cash Flows
4
of failing to collect all revenues reported. Therefore, the amount of the
increase in accounts receivable would have to be subtracted from net
income to arrive at net cash ¬‚ow from operations. Likewise, a decrease
in wages payable would indicate that cash payments for wages were
greater than the expenses shown in the income statement. Payables de-
crease when payments exceed the amount of expenses reported. There-
fore, the amount of the decrease in wages payable also would have to be
subtracted from net income to arrive at net cash ¬‚ow from operations.
Usually it is easy to follow the logic of the adjustment required to
infer the cash ¬‚ow associated with any single reported revenue or expense.
However, most statements of cash ¬‚ows require a number of such ad-
justments, which often result in confusing entanglements.
Many business and real estate appraisers spend a signi¬cant part of
their careers forecasting cash ¬‚ows. The objective of this chapter is to
improve their understanding of the cash ¬‚ow statement and its interre-
lationship with the balance sheet and the income statement. Appraisers
who read this chapter will, we hope, be able to understand better the
cash ¬‚ow logic and distinguish true cash ¬‚ows from shortcut approxi-
mations thereof.
To achieve this result, this chapter provides a mathematical deriva-
tion of the cash ¬‚ow statement using the indirect method. A realistic
numerical example and an intuitive explanation accompany the mathe-
matical derivation.3


THE MATHEMATICAL MODEL
In what follows, be careful to distinguish between equations and tables,
as they both have the same numbering system to describe them. Equa-
tions always have some algebraic expression at the top, even if there are
numbers below that serve as speci¬c examples of the equations.


A Preliminary Explanation of Cash Flows
The following is a list of the symbols that will be used in this chapter.
Balance Sheet
C cash
OCA other current assets
GPPE gross property, plant, and equipment
AD accumulated depreciation
NPPE net property, plant, and equipment
A total assets
CL current liabilities
LTD long-term debt


3. Surely it would be possible to examine in detail every conceivable type of accounting
transaction and its relation to cash ¬‚ow. Here, certain transactions such as recapitalizations,
the effects of accounting changes, and inventory write-downs have not been considered. The
authors feel the additional complication of their inclusion would more than offset any
bene¬ts.




CHAPTER 1 Cash Flow: A Mathematical Derivation 5
L total liabilities
CAP total stockholder™s equity
Property, plant, and Equipment
CAPEX capital expenditures
DEPR depreciation expense
RETGBV gross book value of retired property, plant and equip-
ment
RETAD accumulated depreciation on retired assets
SALESFA selling price of property, plant and equipment disposed
of or retired
Stockholders™ Equity
NI net income
DIV dividends paid
SALSTK sale of stock
TRSTK purchase of stock
OET other equity transactions
AET additional equity transactions
Required Working Capital
RWC required working capital
CReq required cash
The balance sheets for Feathers R Us for 1999 and 2000 are presented
in Table 1-1. The changes in the balance sheet accounts from one year to
the next are shown in the right column. On the far left the symbols used
later to refer to these accounts in mathematical expressions have been
repeated.
The balance sheet for the current year (t 2000) is in balance. The
total assets equal $3,150,000, total liabilities equal $1,085,000, and the total
liabilities and equity also equal $3,150,000. This can be shown as:
At Lt CAPt
(1-1)
3,150,000 1,085,000 2,065,000
Likewise, the balance sheet for the preceding year (t 1 1999) is in
balance.
At Lt CAPt
1 1 1 (1-2)
2,800,000 1,075,000 1,725,000
Subtracting the beginning balance sheet from the ending balance sheet
shows that the changes from one year to the next are also in balance.
A L CAP (1-3)
350,000 10,000 340,000
Greater detail can be shown for each of the terms in equation (1-3).
The change in total assets ( A) consists of the change in cash ( C), the
change in other current assets ( OCA), and the change in net property,
plant, and equipment. Net property, plant, and equipment (NPPE) is
gross property, plant, and equipment (GPPE) less the accumulated de-
preciation (AD) on these assets. As shown in Table 1-3 below, the change



PART 1 Forecasting Cash Flows
6
T A B L E 1-1




Feathers R Us
ABBREVIATED BALANCE SHEETS
For Calendar Years

Increase
Symbols ASSETS: 1999 2000 (Decrease)

C Cash 1,125,000 1,500,000 375,000
OCA Other current assets 875,000 790,000 (85,000)
Total current assets 2,000,000 2,290,000 290,000
GPPE Gross property, plant, & equipment 830,000 900,000 70,000
AD Accumulated depreciation 30,000 40,000 10,000
NPPE Net property, plant, & equipment 800,000 860,000 60,000
A Total assets 2,800,000 3,150,000 350,000

LIABILITIES

Current liabilities 325,000 360,000 35,000
LTD Long-term debt 750,000 725,000 (25,000)
L Total liabilities 1,075,000 1,085,000 10,000

STOCKHOLDERS™ EQUITY

Capital stock 100,000 150,000 50,000
Additional paid in capital 200,000 500,000 300,000
Retained earnings 1,425,000 1,465,000 40,000
Treasury stock 0 50,000 50,000
CAP Total stockholders™ equity 1,725,000 2,065,000 340,000
Total liabilities & equity 2,800,000 3,150,000 350,000




in net property, plant, and equipment ( NPPE) can be found by subtract-
ing the change in accumulated depreciation from the change in gross
AD).4
property, plant, and equipment ( GPPE
A C OCA ( GPPE AD) (1-4)
350,000 375,000 (85,000) (70,000 10,000)
The change in total liabilities ( L) consists of the change in current lia-
bilities ( CL) and the change in long-term debt ( LTD).
L CL LTD (1-5)
10,000 35,000 (25,000)
To explain the change in stockholder™s equity, the analyst would have
to know the company™s net income, provided in Table 1-2.
This income statement shows that Feathers R Us had net income after
tax (NI) of $90,000. This explains only a portion of the change in the


4. Other long-lived assets, such as intangibles and certain investments, are treated the same as
property, plant, and equipment.




CHAPTER 1 Cash Flow: A Mathematical Derivation 7
T A B L E 1-2




Feathers R Us
INCOME STATEMENT
For Calendar Year
2000

Sales 1,000,000
Cost of sales 600,000
Gross pro¬t 400,000
Sales expense 100,000
General & administrative expense 150,000
Depreciation 30,000
Total expense 280,000
Operating income 120,000
Gain on sale of assets 30,000
Net income before taxes 150,000
60,000
Net Income 90,000




stockholder™s equity. The total change in stockholder™s equity ( CAP) is
equal to net income (NI) and other equity transactions (OET) (de¬nition
is given below equation [1-6]).
CAP NI OET (1-6)
340,000 90,000 250,000
The other equity transactions consist of the purchase and sale of the
company™s stock and the payment of cash dividends.5 A detailed descrip-
tion of these transactions will be provided later in the chapter (refer to
Table 1-4).
Substituting equations (1-4), (1-5), and (1-6) into equation (1-3) results
6
in:
C OCA ( GPPE AD)
CL LTD NI OET (1-7)
375,000 (85,000) (70,000 10,000)
35,000 (25,000) 90,000 250,000
Equation (1-7) can be rearranged to satisfy the objective of the statement
of cash ¬‚ows”providing an explanation of the change in the cash bal-
ance.


5. Here it is assumed that all dividends declared are paid.
6. For the reader™s convenience certain equations are repeated in the footnotes.
Equation (1-3): A L + CAP
Equation (1-4): A C + OCA + ( GPPE AD)
Equation (1-5): L CL + LTD
Equation (1-6): CAP NI + OET




PART 1 Forecasting Cash Flows
8
C NI OCA CL
( GPPE AD)
LTD OET (1-8)
375,000 90,000 (85,000) 35,000
(70,000 10,000)
(25,000) 250,000
Equation (1-8) does provide an explanation of the $375,000 increase
in the cash balance from 1999 to 2000, but it is still somewhat preliminary.
Discussion of this explanation is best deferred until more details have
been incorporated into the model.
Analyzing Property, Plant, and Equipment Transactions
The balance sheets in Table 1-1 show that the net property, plant, and
equipment increased by $60,000. The analyst will want to obtain a more
detailed understanding of this change. This can be accomplished by re-
viewing an analysis of property, plant, and equipment such as the one
shown in Table 1-3.

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