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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.
This analysis shows that gross property, plant, and equipment are
increased by capital expenditures (CAPEXP) and decreased by original
book value of any assets retired (RETGBV). This relationship is restated
as equation (1-9).
GPPE CAPEXP RETGBV (1-9)
70,000 175,000 105,000
Likewise, accumulated depreciation is increased by depreciation ex-
pense and decreased by the accumulated depreciation on any assets re-
tired. This relationship is restated as equation (1-10).


T A B L E 1-3




Feathers R Us
ANALYSIS OF PROPERTY, PLANT,
& EQUIPMENT
For Calendar Year 2000

GPPE AD NPPE

Gross Prop, Accumulated Net Prop,
Symbols Plant & Equip Depreciation Plant & Equp

Balance, 1999 830,000 30,000 800,000
CAPEXP Capital expenditures 175,000 175,000
DEPR Depreciation expense 30,000 30,000
Retirements
RETGBV Gross book value 105,000 105,000
RETAD Accumulated depreciation 20,000 20,000
Balance, 2000 900,000 40,000 860,000
Change in the balance 70,000 10,000 60,000




CHAPTER 1 Cash Flow: A Mathematical Derivation 9
AD DEPR RETAD (1-10)
10,000 30,000 20,000

Substituting equations (1-9) and (1-10) into equation (1-8) and rearranging
the terms results in equation (1-11):7

C NI OCA CL
DEPR
CAPEXP RETGBV RETAD
LTD OET (1-11)
375,000 90,000 (85,000) 35,000
30,000
175,000 105,000 20,000
(25,000) 250,000

The bold symbols in equation (1-11) are the symbols that have been
changed by the substitutions described. For example DEPR, CAPEXP,
RETGBV, and RETAD in equation (1-11) did not appear in equation
(1-8).
To this point, only the book value of any assets retired has been
considered. Most often, the retirement or disposition of assets involves a
gain or a loss (a ˜˜negative™™ gain). This gain is the difference between the
selling price of the property, plant, and equipment (SALESFA) and their
net book values (RETGBV RETAD). The assets in this illustration were
sold for $115,000, producing a gain of $30,000. This is shown in equation
(1-12).

GAIN SALESFA (RETGBV RETAD) (1-12)
30,000 115,000 (105,000 20,000)

Equation (1-13) below is simply a rearrangement of equation (1-12).

RETGBV SALESFA GAIN RETAD (1-13)
105,000 115,000 30,000 20,000

Substituting equation (1-13) into equation (1-11) results in:8

C NI DEPR OCA CL
CAPEXP RETAD
SALESFA GAIN RETAD
LTD OET
375,000 90,000 30,000 (85,000) 35,000
175,000 20,000
115,000 30,000 20,000
(25,000) 250,000
(1-14)



7. Equation (1-8): C NI OCA + CL ( GPPE AD) + LTD + OET
Equation (1-9): GPPE CAPEXP RETGBV
8. Equation (1-11): C NI + DEPR OCA + CL CAPEXP + RETGBV RETAD + LTD +
OET




PART 1 Forecasting Cash Flows
10
After canceling the RETAD and RETAD terms and rearranging,
equation (1-14) simpli¬es to Equation (1-15):9
C NI GAIN DEPR OCA CL
CAPEXP SALESFA
LTD OET (1-15)
375,000 90,000 30,000 30,000 (85,000) 35,000
175,000 115,000
(25,000) 250,000
The ¬rst line of equation (1-15) represents cash ¬‚ows from operating
activities, which is found by making certain adjustments to net income
such as adding back depreciation and other noncash expenses, subtract-
ing changes in other current assets, and adding changes in current lia-
bilities. These adjustments will be explained in more detail later in the
chapter. The second line in the equation represents cash ¬‚ows from in-
vesting activities, and the third line represents a preliminary version of
cash ¬‚ows from ¬nancing activities.

An Explanation of Cash Flows with More Detail for Equity
Transactions
Frequently the details of the other equity transactions (OET), referred to
in equation (1-6), are also important. In this example the statement of
stockholder equity included three common types of equity transactions:
(DIV) issuing cash dividends, (SALSTK) selling stock, and (TRSTK) pur-
chasing treasury stock. These are shown in Table 1-4 below.
During the year the company paid cash dividends of $50,000, sold
some additional shares of stock for $350,000, and bought back some stock
for $50,000. The net effect of these three transactions (OET) is a $250,000
increase in stockholder™s equity. This is summarized in equation (1-16).
The term AET has been added to equation (1-16) to represent additional
equity transactions.10
OET SALSTK TRSTK DIV AET (1-16)
250,000 350,000 50,000 50,000 0
Substituting this last expression into equation (1-15) results in equation
(1-17) below.11


9. Equation (1-14): C NI DEPR OCA CL CAPEXP SALESFA GAIN
RETAD RETAD LTD OET
10. The term additional equity transactions was used to describe equity transactions other than the
sale or purchase of the company™s stock and the payment of dividends. One example of an
additional equity transaction would be the contribution of property to the company in
exchange for an equity interest. For analytical purposes, the increase in equity could be
treated as a source of cash from ¬nancing activities. The corresponding increase in assets
could be treated as a use of cash from investing activities. The net result would be overall
zero effect on cash. Normally, noncash transactions of this nature are not incorporated in
formal statements of cash ¬‚ows but are appended in a separate schedule.
11. Equation (1-15): C NI GAIN + DEPR OCA + CL CAPEXP + SALESFA + LTD +
OET
Equation (1-16): OET SALESTK TRSTK DIV + AET




CHAPTER 1 Cash Flow: A Mathematical Derivation 11
T A B L E 1-4




Feathers R Us
STATEMENT OF STOCKHOLDERS™ EQUITY
For Calendar Year 2000

Additional Total
Capital Paid in Retained Treasury Shareholder
Symbols Stock Capital Earnings Stock Equity

Balance, 1999 100,000 200,000 1,425,000 0 1,725,000
NI Net income 90,000 90,000
Other equity
transactions
DIV Dividends 50,000 50,000
SALSTK Sales of stock 50,000 300,000 350,000
TRSTK Purchase of stock 50,000 50,000
Subtotal OET 50,000 300,000 50,000 50,000 250,000
Balance, 2000 150,000 500,000 1,465,000 50,000 2,065,000




C NI GAIN DEPR OCA CL
CAPEXP SALESFA
LTD SALSTK TRSTK DIV AET (1-17)
375,000 90,000 30,000 30,000 (85,000) 35,000
175,000 115,000
(25,000) 350,000 50,000 50,000 0
Equation (1-17) can be simpli¬ed to the more familiar form:
C Cash flows from operating activities
Cash flows from investing activities
Cash flows from financing activities (1-18)
375,000 210,000
(60,000)
225,000
Equations (1-17) and (1-18) describe the conventional Statement of
Cash Flows shown in Table 1-5.
For the moment we will de¬ne the required change in working capital
as the change in current assets other than cash, less the change in current
liabilities, as shown in equation (1-19).12
RWC OCA CL (1-19)
(120,000) (85,000) 35,000
This illustration is somewhat unusual. Here working capital is being
reduced. This reduction is a source of the cash from operating activities.


12. The de¬nition in equation (1-19) will be modi¬ed later in the chapter.




PART 1 Forecasting Cash Flows
12
T A B L E 1-5




Feathers R Us
ABBREVIATED
STATEMENT OF
CASH FLOWS
For Calendar
Symbols Year 2000

Cash ¬‚ows from operating activities
NI Net income 90,000
Adjustments to reconcile net income to net
cash provided by operating activities:
GAIN Gain on sale of property, plant, & equipment (30,000)
DEPR Depreciation expense 30,000
OCA Decrease in current assets 85,000
CL Increase in current liabilities 35,000 120,000
Net cash provided by operating activities 210,000
Cash ¬‚ows from investing activities
CAPEXP Purchase of property, plant, & equipment (175,000)
SALESFA Sale of property, plant, & equipment 115,000
Net cash used by investing activities (60,000)
Cash ¬‚ows from ¬nancing activities
LTD Increase in long term debt (25,000)
SALSTK Sale of stock 350,000
TRSTK Purchase of treasury stock (50,000)
DIV Payment of dividends (50,000)
Net cash provided by ¬nancing activities 225,000
Net increase in cash 375,000
Cash, January 1, 2000 1,125,000
Cash, December 31, 2000 1,500,000




(In the typical case working capital is being increased. This is usually true
when sales are growing. In these cases, the increase in working capital
represents a use of cash.)
Substituting equation (1-19) into equation (1-17) shows that 13

C NI GAIN DEPR RWC
CAPEXP SALESFA
LTD SALSTK TRSTK DIV AET (1-20)
375,000 90,000 30,000 30,000 (120,000)
175,000 115,000
(25,000) 350,000 50,000 50,000 0

The ¬rst line of equation (1-20) can be rephrased in the following
way:


13. Equation (1-17): C NI GAIN + DEPR OCA + CL CAPEXP + SALESFA + LTD +
SALSTK TRSTK DIV + AET
Equation (1-19): RWC OCA CL




CHAPTER 1 Cash Flow: A Mathematical Derivation 13
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




When deriving the cash ¬‚ows from operating activities, we subtract
the gain (or add the loss) on the sale of property, plant, and equipment
for several reasons. First, these gains and losses simply are not the result
of ˜˜operating™™ activities. They are the result of ˜˜investing™™ activities.
These gains and losses arise when property, plant, and equipment are
sold for more or less than their net book value. Furthermore, the full
amount received for such sales (SALESFA) is included as part of the cash
¬‚ows from investing activities. To show these gains or losses again as part
of cash ¬‚ows from operating activities would erroneously double count

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