Simon Benninga. Financial Modelling 3-rd edition

Подождите немного. Документ загружается.

148 Chapter 4

4.7 Free Cash Flows and Valuation

We haven’t yet determined the cost of capital of this company (we do so

in sections 4.10–4.12). Suppose it’s 10 percent. Then here’s a valuation:

BACDEF

ASSETS

2000 2001 2002 2003 2004 2005

Cash and short-term investments 111

111 111 111 111 111

Receivables 1,563

1,639 1,702 1,769 1,837 1,909

Inventories - total 1,121

1,097 1,140 1,184 1,230 1,278

Other current assets 298

287 299 310 322 335

Total current assets

3,093 3,134 3,252 3,374 3,501 3,633

Property, plant, and equipment, gross 7,089

7,669 8,291 8,958 9,674 10,441

Depreciation, depletion, and amortization

(accumulated) 4,148

4,613 5,116 5,660 6,248 6,882

Property, plant, and equipment, net 2,941

3,055 3,174 3,298 3,426 3,559

Investments and advances 320

320 320 320 320 320

Intangibles 1,700

1,700 1,700 1,700 1,700 1,700

Other assets 1,071

1,156 1,248 1,347 1,454 1,569

TOTAL ASSETS

9,125

9,366 9,694 10,039 10,401 10,781

LIABILITIES

2000 2001 2002 2003 2004 2005

Accounts payable 764 762 791 822 854 887

Accrued expense 606 650 675 701 728 757

Other current liabilities 12 12 12 12 12 12

Debt 2,971 2,997 3,102 3,212 3,328 3,450

Deferred taxes 543 564 586 609 633 657

Minority interest 128 128 128 128 128 128

Other liabilities 1,004 1,130 1,271 1,431 1,610 1,812

EQUITY

Common stock 484 484 484 484 484 484

Capital surplus 102 102 102 102 102 102

Retained earnings 6,019 6,440 6,867 7,297 7,730 8,165

Less: treasury stock 3,508 3,903 4,325 4,760 5,209 5,673

Total stockholders equit

3,097 3,124 3,128 3,124 3,107 3,078

TOTAL LIABILITIES AND EQUITY

9,125 9,366 9,694 10,039 10,401 10,781

149 Building a Financial Model: The Case of PPG Corporation

Following are some comments on our valuation.

4.7.1 Terminal Value

As discussed in Chapter 3, we’ve used a perpetuity model to arrive at

the ﬁ rm’s terminal value:

Terminal value

Long-term growth rate)

Long-ter

∗+

−

FCF

WACC

2005

mm growth rate

The estimate of the long-term growth rate (5% in this example) and the

estimate of the difference between this long-term growth and the WACC

(also 5% in our example) is critical for the valuation. Our 5 percent

estimate for long-term growth is based on the assumption that in mature

markets, such as those in which PPG operates, growth will be approxi-

mated by real growth of the economy (∼2% per year) plus inﬂ ation (∼2–

4% per year). A small change in the long-term growth assumption can

100

101

102

103

104

105

106

107

108

109

110

111

112

113

114

BACDEFGH

FREE CASH FLOW (FCF) 2001 2002 2003 2004 2005

Profit after tax 709 726 742 757 773

Add back depreciation 465 503 544 587 634

Change in net working capital

Increase in operating current assets -41 -118 -122 -127 -132

Add increase in operating current liabilities 41 55 57 59 62

Subtract capital expenditures -580 -622 -667 -716 -767

Subtract increase in other assets -85 -92 -99 -107 -115

Add back after-tax interest 127 130 135 140 145

FCF

636 583 589 594 598

Valuing PPG

WACC 10.00%

Long-term free cash flow growth rate 5%

Year

2001 2002 2003 2004 2005

FCF 636 583 589 594 598

Terminal 12,565 <-- =G100*(1+B97)/(B96-B97)

Total 636 583 589 594 13,163

Discounted value 10,574 <-- =NPV(B96,C102:I102)*(1+B96)^0.5

Add back initial cash 111

Firm value 10,685

Subtract total debt value, Dec.00 4,646 <-- =SUM(B69:B72) -- this is controversial!

Implied equity value 6,039

Number of shares outstanding, Dec.00

168.22

Implied value per share 35.90

Market price per share, Dec. 00 46.31

PPG over or under-valued? overvalued <-- =IF(B111>B113*1.1,"undervalued",IF(B111<B113/1.1,"overvalued","ok"))

150 Chapter 4

lead to signiﬁ cant differences in the valuation; for example, if we assume

that long-term growth is equal to 6 percent, our valuation of PPG’s stock

increases to $48.64, which leads us to conclude that the current market

valuation is “ok.” (In the spreadsheet cell B114 we’ve deﬁ ned an “ok”

valuation as one that is within 10% of the current market price. Other-

wise the stock is either over- or undervalued.)

100

101

102

103

104

105

106

107

108

109

110

111

112

113

114

BACDEFGH

Valuing PPG

WACC 10.00%

Long-term free cash flow growth rate 6%

Year

2001 2002 2003 2004 2005

FCF 636 583 589 594 598

Terminal 15,856 <-- =G100*(1+B97)/(B96-B97)

Total 636 583 589 594 16,454

Discounted value 12,717 <-- =NPV(B96,C102:I102)*(1+B96)^0.5

Add back initial cash 111

Firm value 12,828

Subtract total debt value, Dec.00 4,646 <-- =SUM(B69:B72) -- this is controversial!

Implied equity value 8,182

Number of shares outstanding, Dec.00

168.22

Implied value per share 48.64

Market price per share, Dec. 00 46.31

PPG over- or undervalued? ok <-- =IF(B111>B113*1.1,"undervalued",IF(B111<B113/1.1,"overvalued","ok"))

4.7.2 Midyear Discounting

As discussed in Chapter 3, we assume that the FCFs and the terminal

value occur throughout the year and not at year-end. As an approxima-

tion, we assume that they occur in midyear. This assumption requires that

the Excel NPV formula in cell B104 be adjusted by a factor of (1 +

WACC)

0.5

4.7.3 Dealing with Initial Cash and Debt

In principle, the valuation format is as follows:

Valuation Schematic

Item Why?

Enterprise value = PV

of future FCFs and

terminal value.

The enterprise value is the discounted value of the ﬁ rm’s

future anticipated business cash ﬂ ows, represented here by

the free cash ﬂ ow (FCF).

Add in initial cash. The cash on the ﬁ rm’s balance sheet at end-year 2000 is

assumed not to be needed for its business activities.

151 Building a Financial Model: The Case of PPG Corporation

Subtract the current

value of the ﬁ rm’s ﬁ nancial

obligations.

Enterprise value + Initial cash = Firm’s current market

value. This value is split between its shareholders and its

debt holders. In our model we approximate the market

value of the ﬁ rm’s debt by the book value of the debt.

Note that the ﬁ rm’s operating current liabilities are not

included in the debt for valuation purposes—they’ve

already been netted out of the FCF.

= Equity valuation

of the ﬁ rm.

This value has to be divided by the number of shares

outstanding to arrive at a per-share valuation.

The implementation of this schematic is problematic, especially as it

regards the ﬁ rm’s debt. The question is, Which of the liability items on

the balance sheet are regarded by the market as ﬁ nancial obligations of

the ﬁ rm? In the preceding valuation we’ve chosen to include all of the

following items as “ﬁ nancial debts” of PPG:

Debt 2,971

Deferred taxes 543

Minority interest 128

Other liabilities 1,004

Many Wall Street analysts would consider this approach too conserva-

tive. They often argue that deferred taxes are not a ﬁ nancial obligation

of the ﬁ rm, and they might even take issue with our listing of other liabili-

ties among the debts of PPG. Obviously, the fewer debts we list, the

higher our valuation of PPG’s equity.

4.7.4 Is PPG Overvalued? Undervalued?

In cell B114, we’ve used a “10 percent” rule: If PPG’s computed stock

price falls within a ±10% range of the current stock price of $46.31, we

call our valuation “ok.” The formula we use is =IF(B111>B113*1.1,

“undervalued”,IF(B111<B113/1.1,“overvalued”,“ok”)).

4.8 What Is PPG’s Dividend Policy?

PPG’s dividend has increased consecutively for the past 31 years. In the

following spreadsheet we show you two different aspects of this dividend

history over the period 1992–2000.

152 Chapter 4

ABCDEFG

Year

Dividends

per share

Total cash

dividends

Minus

increase

in common

stock and

sur

lus

Plus increase

in treasury

stock

Payout to

equity

1992 0.94 200 -3 14 211 <-- =SUM(C3:E3)

1993 1.04 221 -65 24 181 <-- =SUM(C4:E4)

1994 1.12 238 -12 264 490

1995 1.18 239 -14 571 796

1996 1.26 237 -15 608 829

1997 1.33 239 -2 323 560

1998 1.42 252 -6 208 454

1999 1.52 264 1 70 335

2000 1.60 276 2 240 518

Growth 6.88% 4.13% 11.91% <-- =(F11/F3)^(1/8)-1

CALCULATING THE DIVIDENDS AND EQUITY PAYOUT FOR PPG

PPG: Dividends and Total Equity Payout

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

1.80

1992 1993 1994 1995 1996 1997 1998 1999 2000

Dividends per share

100

200

300

400

500

600

700

800

900

Total equity payout

Dividends per share

Payout to equity

In column B you can see PPG’s dividends per share from 1992 to 2000.

As you can see in the graph, this dividend has indeed increased continu-

ously over this period. The compound growth rate of the dividends is

6.88 percent annually.

Columns C–F examine the total payments of PPG to its shareholders

during this period—the sum of its cash dividends and its share repur-

chases. These columns tell a different (though no less compelling

story):

Column C gives the total dividend payout by PPG.

Column D shows the increases in common stock and surplus—the addi-

tional cash directly paid into PPG by shareholders. This most often rep-

resents money paid in by those exercising employee stock options, but

it can also represent additional funds directly raised from shareholders.

153 Building a Financial Model: The Case of PPG Corporation

For PPG, this number is negative in most years (albeit only slightly),

showing that shareholders paid in small amounts of capital to the ﬁ rm.

Column E shows the increase in treasury stock at cost: This is the amount

spent in each year by PPG to repurchase stock from its shareholders.

Financial economists regard this as another form of dividend. When the

ﬁ rm pays out dividends, it pays out money to all of its shareholders. When

it repurchases stock it directly pays out money to some of its share-

holders (those that tender their stock); the remaining shareholders also

beneﬁ t, since the future proﬁ ts of the ﬁ rm are now split among fewer

shareholders, so that the proportional share of each individual non-

bought-out shareholder is increased. An additional beneﬁ t of repur-

chases is their advantageous tax treatment: Shareholders have to pay an

ordinary income tax rate on their cash dividends, but a “dividend” paid

out as a repurchase is a capital gain and is thus taxed at a lower rate.

Column F sums Columns C–E and computes the total equity payout. This

is the total cash paid by PPG to shareholders. This total equity payout

is larger than the dividend in all years except 1993. Note also the

following:

•

This payout is considerably more variable than the cash dividend alone

(look at the graph of dividends versus total equity payout).

•

The growth rate of the total equity payout—11.91 percent—is much

larger than the growth rate of the dividends.

PPG is very proud of its dividend history—a document on its Web site

brags that “dividends paid increased 31 consecutive years.” PPG is also

proud of its healthy growth in earnings per share; the same document

includes the following graph:

6. One of the enduring mysteries of ﬁ nance is why—given the tax superiority of repur-

chases over regular dividends—ﬁ rms still pay dividends. The answer lies (we think) in

two factors: (1) Many shareholders and analysts regard dividends as a strong signal

about corporate health. (2) A ﬁ rm paying out all its “dividends” as repurchases runs

the risk of having the repurchases reclassiﬁ ed by the Internal Revenue Service as

ordinary income. We should also stress that in many senses this is a peculiarly American

story—the tax system in many European countries (and in Canada) essentially doesn’t

tax dividends as ordinary income.

154 Chapter 4

Source: PPG Web site

Earnings per Share Growth

10.00

10.5% Trend

Adjusted for stock splits.

Excludes non-recurring charges and gains.

1.00

0.10

1968 - 2000

$.81

$2.28

$4.13

$.36

$.19

Earnings per share (EPS) have grown much faster than earnings. Why?

Think about the EPS formula:

EPS =

←

Earnings

Number of shares

Repurchases cause

this denominat

oor

to decrease

Repurchases

cause the EPS

to increase

←

155 Building a Financial Model: The Case of PPG Corporation

4.9 Modeling PPG’s Dividend Policy

We think that PPG’s dividend policy can be modeled most effectively by

assuming the following:

•

Total cash dividends exhibit a steady rate of growth. In the pro forma

valuation model in this chapter we have chosen a dividend growth rate

ABC D E

Year

Earnings

per share

Profits

after taxes

1990 0.95 276

1991 1.90 276

1992 3.01 319

1993 2.78 22

1994 2.43 515

1995 3.80 768

1996 3.96 744

1997 3.97 714

1998 4.52 801

1999 3.27 568

2000 3.60 620

Compound growth 14.25% 8.43% <-- =(C13/C3)^(1/10)-1

Source: Profit-loss 91-00 in this

workbook

PPG: EARNINGS PER SHARE VERSUS EARNINGS

PPG: EPS versus Profits

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

5.00

Year 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999

EPS

100

200

300

400

500

600

700

800

900

Profits

Earnings

per share

Profits

after taxes

156 Chapter 4

of 4.13 percent, equal to the historic compound growth rate of PPG’s

dividends.

•

Debt equals 32 percent of total assets.

•

Treasury stock (that is, the repurchases of stock from shareholders) is

a plug.

Notice that the total equity payout by PPG to its stockholders depends

on both its free cash ﬂ ow and its ﬁ nancial policies—including the amount

of debt the ﬁ rm chooses.

4.10 Computing PPG’s Cost of Equity r

and Its Cost of Debt r

In this section we follow the format set out in sections 2.9–2.12 to compute

the WACC for PPG. We compute the WACC based on four alternative

models for the cost of equity r

: Two of these methods use the Gordon

dividend model, one on the dividends per share and the second on the

total dividend payouts for PPG. Two additional methods use the CAPM,

one the traditional CAPM and the other a tax-adjusted CAPM.

4.10.1 Using the Gordon Dividend Model to Determine the Cost of Equity r

We can apply this model, which was discussed in Chapter 2, using either

the per-share dividends or the total equity payout. Each version of the

model gives a different cost of equity for PPG:

CBA

Number of shares outstanding, Dec. 2000 (million) 168.22

Share price, 31Dec00 46.31

Equity value, Dec00 7,791 <-- =B2*B3

Method 1: r

Gordon using only dividends

Stock price, 31dec00 46.31

Dividend, 2000 1.60

Anticipated dividend growth 6.88% <-- =Dividends!$B$13

, cost of equity using only dividends

10.57% <-- =B8*(1+B9)/B7+B9

Method 2: r

Gordon using equity payout

Total equity payout, 2000 518 <-- =Dividends!$F$11

Anticipated growth of this payout 11.91% <-- =Dividends!$F$13

, cost of equity using total equity payout

19.35% <-- =B13*(1+B14)/B4+B14

Using the two-stage Gordon model

Number of high-growth years 3

Normal growth after high-growth years 5.00%

, cost of equity using two-stage Gordon model

13.34% <-- =twostagegordon(B4,B13,B14,B18,B19)

CALCULATING THE GORDON MODEL r

FOR PPG

157 Building a Financial Model: The Case of PPG Corporation

As noted in Chapter 2, method 1 uses per-share data, whereas method

2 uses totals—total equity value, total equity payout, and the growth rate

of this payout. Given our estimate of 4 percent sales growth for PPG, we

think it unlikely that the high total equity payout growth of 11.91 percent

will continue ad inﬁ nitum. We therefore also use the two-stage Gordon

model (section 2.4) to derive a third cost of equity (cell B20).

4.10.2 Which Method of Calculating r

Is Better?

This is a trick question! The real question is, What do investors in PPG’s

stock expect when they’re buying the stock. Savvy investors who under-

stand the mechanics of ﬁ nance (like the readers of this book!) will

understand that method 2 represents the economic dividend of PPG.

These investors will calculate PPG’s cost of equity as r

= 19.35

percent.

PPG’s dividend policy—its pride in paying a continuously increasing

dividend per share over such a long period—indicates that it thinks most

investors do not understand the economics of ﬁ rm payouts to sharehold-

ers. If PPG is right, then its cost of equity is considerably lower, r

= 10.57

percent.

This possible contradiction between dividends per share and total

equity payouts completely disappears in a closely held ﬁ rm or in

a sole-ownership situation.

Suppose you owned all the shares in PPG. You could then decide

to pay yourself a “cash dividend per share” (to be taxed at your

ordinary income tax rate) or to pay yourself a “share repurchase”

(taxed at your capital gains rate). You’d immediately recognize

that both payments are economic dividends (meaning: payouts to

shareholders [you, in this case]). You’d also recognize that the only

thing that’s important is the after-tax total payout.

4.10.3 Applying the Security Market Line to Calculate PPG’s Cost of Equity r

In Chapter 2 we presented two approaches to computing the cost of

equity using the CAPM: