Simon Benninga. Financial Modelling 3-rd edition

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158 Chapter 4

Classical SML Tax-Adjusted SML

= r

+ b [E(r

) − r

]

where

= risk-free interest rate

b = sensitivity of stock’s

returns to market return

()

Cov( ,

Var

PPG M

)

E(r

) = anticipated

return on the market

= r

(1 − T

) + b [E(r

) − r

(1 − T

)]

where

= risk-free interest rate

b = sensitivity of stock’s returns to

market return

()

Cov ,

Var

PPG M

E(r

) = anticipated return on the market

= ﬁ rm’s tax rate

Using monthly return data for PPG and the S&P 500 (the latter rep-

resenting the stock market) can compute PPG’s b as 0.8473. The follow-

ing chart graphs S&P 500 returns (column C) on the x-axis against PPG

returns (column G):

ABC D EFG H I J KLMN

Beta 0.8672 <-- =SLOPE(G6:G65,C6:C65)

Date

SP500

Return

Date

PPG

Return

Dec-95 615.93 Dec-95 38.98

Jan-96 636.02 3.21% <-- =LN(B6/B5) Jan-96 39.83 2.16% <-- =LN(F6/F5)

Feb-96 640.43 0.69% Feb-96 39.76 -0.18%

Mar-96 645.5 0.79% Mar-96 41.91 5.25%

Apr-96 654.17 1.33% Apr-96 43.41 3.52%

May-96 669.12 2.26% May-96 44.65 2.84%

Jun-96 670.63 0.23% Jun-96 42.07 -5.97%

Jul-96 639.95 -4.68% Jul-96 42.50 1.02%

Aug-96 651.99 1.86% Aug-96 42.87 0.88%

Sep-96 687.33 5.28% Sep-96 47.22 9.65%

Oct-96 705.27 2.58% Oct-96 49.50 4.71%

Nov-96 757.02 7.08% Nov-96 53.48 7.75%

Dec-96 740.74 -2.17% Dec-96 49.01 -8.74%

Jan-97 786.16 5.95% Jan-97 46.71 -4.79%

Feb-97 790.82 0.59% Feb-97 49.20 5.19%

Mar-97 757.12 -4.35% Mar-97 47.44 -3.64%

Apr-97 801.34 5.68% Apr-97 47.77 0.69%

May-97 848.28 5.69% May-97 51.37 7.25%

Jun-97 885.14 4.25% Jun-97 51.37 0.00%

Jul-97 954.31 7.52% Jul-97 56.56 9.63%

Aug-97 899.47 -5.92% Aug-97 55.95 -1.08%

Sep-97 947.28 5.18% Sep-97 55.67 -0.50%

COMPUTING THE BETA FOR PPG

Uses monthly data, Dec. 1995 - Dec. 2000

Computing the Beta for PPG

using monthly price data for PPG and the SP500

y = 0.8672x - 0.0087

= 0.3027

-22%

-17%

-12%

-7%

-2%

13%

18%

23%

-16% -11% -6% -1% 4% 9%

SP500 return

PPG return

We use the method outlined in section 2.7.3 to compute E(r

aEPS g

PEPS

()

() ()

∗+

000

7 66 percent

159 Building a Financial Model: The Case of PPG Corporation

where a is 50 percent (the payout ratio), g is 6 percent (the growth rate

of market equity payouts), and P

/ EPS

is equal to 32 (the market price-

earnings ratio). Using this estimate, we ﬁ nd the following two (very

close) estimates for the CAPM cost of equity:

CBA

Market price/earnings multiple, December 2000 32

Equity cash flow payout ratio 50.00%

Anticipated growth of market equity cash flow 6.00%

Expected market return, E(r

)

7.66% <-- =B3*(1+B4)/B2+B4

Treasury bill rate, December 2000 0.51%

PPG's tax rate, T

36.28% <-- ='Page 138, top and page 139'!B35

Method 3: r

using the SML

Equity beta 0.8672

, cost of equity

6.71% <-- =B6+B10*(B5-B6)

Method 4: r

using the tax-adjusted SML

Equity beta 0.8672

, cost of equity

6.68% <-- =B6*(1-B7)+B14*(B5-B6*(1-B7))

USING THE CAPM TO COMPUTE PPG'S COST OF EQUITY

4.10.4 What Is PPG’s Cost of Debt r

The simplest way to calculate PPG’s cost of debt r

is to assume that r

is the average current percentage cost of borrowing. This can be calcu-

lated from PPG’s income statement and balance sheets:

CBA

Year 2000 interest expense

from PPG's income statement

193

Year 2000 debt,

from PPG's balance sheet

2,971 <-- ='Balance sheets 1991-2000'!B23

Year 1999 debt,

from PPG's balance sheet

2,790 <-- ='Balance sheets 1991-2000'!C23

Average debt

2,881 <-- =AVERAGE(B3:B4)

Cost of debt, r

6.70% <-- =B2/B5

COMPUTING PPG's COST OF DEBT, r

160 Chapter 4

Note that we use only the ﬁ nancial debt of PPG to compute its cost of

debt r

There are, of course, other ways to calculate r

for PPG: In principle

we should ask what is the ﬁ rm’s marginal cost of borrowing—its cost for

borrowing an extra dollar of debt. Implicitly our method assumes that

PPG’s current cost of borrowing is also its marginal cost.

4.11 What Is PPG’s Weighted Average Cost of Capital?

A little review: In Chapter 2 we deﬁ ned the weighted average cost of

capital (WACC) as the average return that the company has to pay to its

equity and debt investors. Another way of expressing this deﬁ nition is

that the WACC is the average return that stakeholders (equity and bond-

holders) expect to make from the company. If we let r

denote the cost

of equity (the return expected by equity holders) and r

denote the cost

of debt (the return expected by debt holders), then

WACC r

EDC

=∗

+−

()1

where E is the market value of the ﬁ rm’s equity, D is the market value

of the ﬁ rm’s debt, r

is the cost of equity (rate of return demanded or

required by shareholders), r

is the cost of debt, and T

is the ﬁ rm’s tax

rate.

We use 6.70 percent as r

, the cost of debt. As we showed in our analy-

sis of PPG’s income statement in section 4.5, this is PPG’s current cost

of debt.

161 Building a Financial Model: The Case of PPG Corporation

As you can see in cell B34, we’ve taken the easy way out of the WACC

conundrum by choosing the average WACC of the four methods.

4.12 Back to the Valuation—Sensitivity Analyses

As you’ve seen in this chapter, a valuation involves a tremendous amount

of analysis and a bewildering array of assumptions about the ﬁ rm’s

future. Hopefully you’ve done a good job of analysis and you’ve guessed

BA C

Shares outstanding (million) 168 <-- ='Page 137, 140, 141'!B36

Share price, end 2000 46.315

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

Net debt, D 4,535 <-- =SUM('Page 137, 140, 141'!B23:B26)-'Page 137, 140, 141'!B3

Cost of debt, r

6.70% <-- ='Page 159, bottom'!B7

PPG's tax rate, T

36.28% <-- ='Page 138, top and page 139'!B35

Market risk free rate, r

0.51% <-- ='Page 159, top'!B6

Expected market return, E(r

)

7.66% <-- ='Page 159, top'!B5

WACC based on Gordon per-share dividends and interest from financial statements

Stock price, 31dec00 46.31

Dividend, 2000 1.60

Anticipated dividend growth 6.88%

Cost of equity, r

10.57% <-- =B13*(1+B14)/B12+B14

WACC 8.25% <-- =$B$4/($B$4+$B$5)*B15+$B$5/($B$4+$B$5)*$B$6*(1-$B$7)

WACC based on Gordon equity payouts and interest from financial statements

Total equity payout, 2000 518 <-- ='Page 152'!$F$11

Anticipated growth of this payout 11.91% <-- ='Page 152'!$F$13

Cost of equity, r

13.34% <-- ='Page 156'!B20

WACC 10.00% <-- =$B$4/($B$4+$B$5)*B21+$B$5/($B$4+$B$5)*$B$6*(1-$B$7)

WACC based on classic CAPM and interest from financial statements

PPG beta 0.8672 <-- ='Page 158'!B2

Cost of equity, r

6.71% <-- =B8+B25*(B9-B8)

WACC 5.81% <-- =$B$4/($B$4+$B$5)*B26+$B$5/($B$4+$B$5)*$B$6*(1-$B$7)

WACC based on tax-adjusted CAPM and interest from financial statements

PPG beta 0.8672 <-- ='Page 158'!B2

Cost of equity, r

6.68% <-- =B8*(1-B7)+B30*(B9-B8*(1-B7))

WACC 5.79% <-- =$B$4/($B$4+$B$5)*B31+$B$5/($B$4+$B$5)*$B$6*(1-$B$7)

Estimated WACC?

7.47% <-- =AVERAGE(B16,B22,B27,B32)

COMPUTING THE WEIGHTED AVERAGE COST

OF CAPITAL (WACC) FOR PPG

7. Our excuse: Between the two Gordon models, we deﬁ nitely favor method 2, which uses

the total equity payout (which gives a higher cost of equity). But we also “really like”

the SML approach to the cost of capital, which gives a cost of equity more approaching

that of method 1. So . . . we’ll take the average and do some sensitivity analysis. Not

heroic, but safe.

162 Chapter 4

right, but prudence requires that you check whether alternative assump-

tions would make a difference in your valuation.

In this section we examine only two factors among the many that affect

the valuation: the WACC and the long-run sales growth of the ﬁ rm.

Building a two-dimensional data table in Excel (see Chapter 31 for

details) gives the following result:

100

101

102

103

104

105

106

107

108

109

110

111

112

113

114

115

116

117

118

119

120

121

122

123

124

125

126

127

BACDEFGHI

Valuing PPG

WACC 7.47%

Long-term free cash flow growth rate 4%

Year 2001 2002 2003 2004 2005

FCF 636 583 589 594 598

Terminal 17,954 <-- =G100*(1+B97)/(B96-B97)

Total 636 583 589 594 18,553

Discounted value 15,509 <-- =NPV(B96,C102:I102)*(1+B96)^0.5

Add back initial cash 111

Firm value 15,620

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

Implied equity value 10,974

Number of shares outstanding, Dec.00

168.22

Implied value per share 65.24

Market price per share, Dec. 00 46.31

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

Long-term FCF growth ?

65.24 1% 3% 4% 5% 6% 7%

6% 43.81 82.49 130.83 275.86 nmf nmf

7% 32.35 55.75 79.14 125.92 266.26 nmf

WACC --> 8% 24.17 39.70 53.28 75.92 121.20 257.05

9% 18.03 28.99 37.76 50.91 72.84 116.68

10% 13.25 21.34 27.41 35.90 48.64 69.87

11% 9.43 15.60 20.01 25.89 34.11 46.46

12% 6.30 11.13 14.46 18.73 24.42 32.40

13% 3.69 7.56 10.13 13.35 17.50 23.02

14% 1.48 4.63 6.67 9.17 12.29 16.31

DATA TABLE: SENSITIVITY OF PPG'S STOCK VALUATION

TO WACC AND LONG-TERM GROWTH RATE

=IF(B96>B97,B111,"nmf")

The highlighted cells in the data table indicate those combinations of

growth and WACC for which PPG is undervalued with respect to its

current market value. Not surprisingly, this outcome occurs for combina-

tions of high growth and low WACC.

An Excel note: The formula calculated by the data table (cell B118)

is a slight variation of cell B111: If the long-term growth rate is less than

the WACC, then the data table gives B111; otherwise it indicates that

there is no meaningful ﬁ gure (“nmf”) for the valuation. This result relates

to our terminal value calculation.

163 Building a Financial Model: The Case of PPG Corporation

Terminal value

Long-term growth rate)

Long-ter

∗+

−

FCF

WACC

2005

mm growth rate

This formula is only meaningful when WACC − Long-term growth

rate > 0.

Exercises

1. Assume that in 2001 PPG sales will grow by 11 percent, in 2002, by 8 percent, in

2003 by −2 percent, and thereafter by 4 percent, which is also the long-term growth.

Value the shares.

2. Using the data from the previous question, do a sensitivity analysis on the Net

PPE/Sales ratio and the value of PPG shares. If PPG succeeds in improving its efﬁ -

ciency in this ratio by 1%, how will this impact the valuation of the shares?

3. At the end of 2000, PPG’s stock was selling for a P/E multiple of 13. Re-examine

the terminal value in the model of sections 4.5–4.6, and assume that it is

erminal value EPS

projec

2005

the 2001

P/E multiple

=∗+13

2005



tted

Book value

PPG debt

How is your valuation of PPG shares affected?

Appendix: Some Accounting Issues

Overview

This appendix covers a number of accounting issues that arise in the

analysis of PPG’s ﬁ nancial statements in this chapter. In each case we

ﬁ rst try to explain the accounting issue and then show how we model the

particular item in our ﬁ rm ﬁ nancial model. Our explanations are infor-

mal and not “accounting based” (meaning that there are no T-accounts

and everything is written directly onto the balance sheet and income

statement).

Deferred Taxes and Accelerated Depreciation

The deferred tax account is often seen on the liabilities side of the

balance sheet. Deferred taxes arise when companies report different

depreciation ﬁ gures to their shareholders and to the IRS.

Here’s a very simple example. We assume that the ﬁ rm has one ﬁ xed

asset that is worth $500. This asset has a depreciable life of two years.

164 Chapter 4

Why?

Students and readers of accounting statements often ask why this double

reporting should occur or even be allowed. The usual justiﬁ cation is as

follows:

•

The reporting of depreciation to shareholders should report the eco-

nomic essence of the situation. In this example the managers of the ﬁ rm

may have thought that the asset had an economic life of two years and

that its use was equally distributed between these two years.

•

The reporting to the tax authorities should utilize the tax system to

maximize shareholder cash ﬂ ows. By reporting more depreciation earlier

(which is what the accelerated depreciation schedule allows), the ﬁ rm

can pay less tax.

How Much Cash Is Generated?

In cells B11:B13 we calculate the cash generated by the ﬁ rm in 2006. This

cash ﬂ ow of the ﬁ rm is determined by its reporting to the tax authorities

(since this reporting determines the actual taxes paid).

ABCD

Sales 1000 Sales 1000

Costs 500 Costs 500

Depreciation 300 Depreciation 250

PBT 200 PBT 250

Taxes (40%) 80 Taxes (40%) 100

PAT 120 PAT 150

DEFERRED TAXES AND ACCELERATED DEPRECIATION

An Example

2006 P&L for tax purposes 2006 P&L for reporting purposes

For reporting this asset’s depreciation to the shareholders, the ﬁ rm uses

straight-line depreciation. For reporting the asset’s depreciation to the

tax authorities, the ﬁ rm uses accelerated depreciation; it reports $300 of

depreciation in year 1 and $200 depreciation in year 2.

Here’s what the

year-1 proﬁ t and loss (P&L) statements look like:

8. In order to simplify subsequent calculations in this section, we assume that (1) all costs

of goods sold are in cash, (2) all sales are in cash, (3) the ﬁ rm purchases no new ﬁ xed

assets, (4) the ﬁ rm has no debt, and (5) the ﬁ rm pays no dividends and issues no new

shares.

165 Building a Financial Model: The Case of PPG Corporation

Cash flow

PAT 120 <-- =B8

Add back depreciation 300 <-- =B5

Cash flow 420 <-- =B12+B11

Changes in the Balance Sheet

We suppose that the ﬁ rm’s balance sheet at the end of 2005 (the year

previous to these calculations) looks like the following:

Now think about the balance sheet at the end of 2006. This is where

things get a bit more complicated:

•

On the one hand, cash balances grow by the cash ﬂ ow, which is deter-

mined by the tax P&L.

Balance Sheet

Assets

Cash 0

Other current assets 0

FA at cost 500

Accumulated depreciation 0

Net fixed assets 500

Total assets 500

Liabilities and equity

Current liabilities 0

Deferred taxes 0

Debt 0

Equity

Stock 200

Accumulated retained 300

Total liabilities and equity 500

2005

166 Chapter 4

Why Call Them Deferred Taxes?

The justiﬁ cation for the name is that “deferred taxes” are taxes that the

ﬁ rm will have to pay at some point in the future. Suppose, for example,

that the 2007 P&Ls for the ﬁ rm are exactly the same as those for 2006,

with the exception of the depreciation. This time, as you can see in the

next spreadsheet, the situation is reversed: The ﬁ rm pays more taxes to

the IRS than it reports to its shareholders. This fact causes the deferred

tax account to decrease.

ABCDE F

Balance Sheet

2006

Assets

Cash 0 420 <-- =B18+B13

Other current assets 0 0 <-- =B19

FA at cost 500 500

Accumulated depreciation 0 250 <-- =B22+E5

Net fixed assets 500 250

Total assets 500 670

Liabilities and equity

Current liabilities 0 0

Deferred taxes 0 20 <-- =E7-B7+B28

Debt 0 0

Equity

Stock 200 200

Accumulated retained 300 450 <-- =B32+E8

Total liabilities and equity 500 670

Assumptions:

1. All COGS in cash

2. All Sales in cash

3. No new assets purchased

4. No debt repaid or taken out

5. No dividends paid or stock sold or repurchased

2005

Depreciation is

reported

from the shareholder

P&L

Cash balances

grow by the cash

flow (determined

by the tax P&L)

Accumulated

retained earnings

grow by the PAT

from the shareholder

P&L

The PLUG! Without this, the asset side of

the balance sheet grows by 420 - 200= 220,

whereas the liabilities/equity side grows by

180.

•

On the other hand, depreciation and the change in accumulated

retained earnings are determined by the shareholder P&L.

The result is that the asset side of the balance sheet grows by $170: An

increase of $420 in cash balances from which is netted out an increase

of $250 in depreciation. However, the liabilities side of the balance sheet

grows by only $150 (the PAT reported to shareholders).

Since it’s an immutable rule of accounting that the change in the right-

hand side of the balance sheet must equal the change in the left-hand

side, there must be a balancing item. This item—$20 in our example—is

“Deferred taxes”:

167 Building a Financial Model: The Case of PPG Corporation

Modeling Deferred Taxes

There are two possible ways to model deferred taxes. One way would be

to model accelerated depreciation, as illustrated in appendix 2 to Chapter

3. Having modeled accelerated depreciation, we can then take the dif-

ference between an accelerated depreciation allowance and a straight-

line depreciation allowance and derive the increment to deferred taxes.

We prefer a second method, which is illustrated in this chapter: Instead

of modeling accelerated depreciation, we assume that depreciation is

ABCDEF

Sales 1000 Sales 1000

Costs 500 Costs 500

Depreciation 200 Depreciation 250

PBT 300 PBT 250

Taxes (40%) 120 Taxes (40%) 100

PAT 180 PAT 150

Cash flow

PAT 180 <-- =B8

Add back depreciation 200 <-- =B5

Cash flow 380 <-- =B12+B11

Balance Sheet

2004

Assets

Cash 420 800 <-- =B18+B13

Other current assets 0 0 <-- =B19

FA at cost 500 500

Accumulated depreciation 250 500 <-- =B22+E5

Net fixed assets 250 0

Total assets 670 800

Liabilities and equity

Current liabilities 0 0

Deferred taxes 20 0 <-- =E7-B7+B28

Debt 0 0

Equity

Stock 200 200

Accumulated retained 450 600 <-- =B32+E8

Total liabilities and equit

y 670 800

DEFERRED TAXES AND ACCELERATED DEPRECIATION

The next year--asset is fully depreciated

2007 P&L for tax purposes 2007 P&L for reporting purposes

2003

Depreciation

is reported

from the

shareholder

P&L

Cash balances

grow by the cash

flow (determined

by the tax P&L)

Accumulated

retained earnings

grow by the PAT

from the

shareholder P&L

Accumulated depreciation is zero in

2007--the firm's actual taxes paid are

higher by $20 than taxes reported to

shareholders.