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