chapter 18 - valuing stocks

8/7/2019 CHAPTER 18 - VALUING STOCKS

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PFE Chapter 18, Stock valuation page 1

CHAPTER 18: VALUING STOCKS*

This version: October 22, 2003

Chapter contents

Overview......................................................................................................................................... 2

18.1. Valuation method 1: The current market price of a stock is the correct price (the efficient

markets approach)........................................................................................................................... 4

18.2. Valuation method 2: The price of a share is the discounted value of the future anticipated

free cash flows ................................................................................................................................ 7

18.3. Valuation method 3: The price of a share is the present value of its future anticipated

equity cash flows discounted at the cost of equity........................................................................ 18

18.4. Valuation method 4, comparative valuation: Using multiples to value shares.................. 21

18.5. Intermediate summary ........................................................................................................ 28

18.6. Computing Targets WACC, the SML approach ............................................................... 28

18.7. Computing Targets cost of equity rEwith the Gordon model........................................... 36

Summing up.................................................................................................................................. 37

Exercises ....................................................................................................................................... 39

*Notice: This is a preliminary draft of a chapter ofPrinciples of Finance by Simon Benninga

([email protected]). Check with the author before distributing this draft (though

you will probably get permission). Make sure the material is updated before distributing it. All

the material is copyright and the rights belong to the author.


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Overview

In chapter 17 we discussed the valuation of bonds. This chapter deals with the valuation

of stocks. Whereas the valuation of bonds is a relatively straightforward matter of computing

yields to maturity, the valuation of stocks is much more difficult. The difficulty lies both in the

greater uncertainty about the cash flows which need to be discounted in order to arrive at a stock

valuation and in the computation of the correct discount rate.

In this chapter we discuss four basic approaches to stock valuation:

Valuation method 1, the efficient markets approach. In its simplest form the

efficient markets approach states that the current stock price is correct. A somewhat

more sophisticated use of the efficient markets approach to stock valuation is that a

stocks value is the sum of the values of its components. We explore the implications

of these statements in section 18.1.

Valuation method 2, discounting the future free cash flows (FCF). Sometimes

called the discounted cash flow (DCF) approach to valuation, this method values the

firms debt and its equity together as the present value of the firms future FCFs. The

discount rate used is the weighted average cost of capital (WACC). This method is

the valuation approach favored by most finance academics. We discuss this approach

in section 18.2 and discuss the computation of the WACC in sections 18.5 and 18.6.

In this chapter we do not discuss the concept or the computation of the free cash

flowthis was done previously in Chapters 7-9.

Valuation method 3, discounting the future equity payouts. A firms shares can

also be valued by discounting the stream of anticipated equity payouts at an


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appropriate cost of equity rE. The concept of equity payout (the sum of a firms total

dividends plus its stock repurchases) was previously discussed in Chapter 6.

Valuation method 4, multiples. Finally we can value a firms shares by a

comparative valuation based on multiples. This very common method involves ratios

such as the price-earnings (P/E) ratio, EBITDA multiples, and more industry specific

multiples such as value per square foot of store space or value per subscriber.

With the exception of the multiple method 4, almost all of the material in this chapter is

also discussed elsewhere in this book. For example, the efficient markets approach to valuation

is also discussed in Chapter 15, and the Gordon dividend model (which values a firms equity by

discounting its anticipated dividend stream) is also discussed in Chapters 6 and 9. WACC

computations are to be found in Chapters 5 and 15. The purpose of this chapter is to bring

together these dispersed materials into a (hopefully coherent) whole.

Finance concepts discussed in this chapter

Discounted cash flows, free cash flows (FCF)

Cost of capital, cost of equity, cost of debt, weighted average cost of capital (WACC)

Equity premium

Beta, equity beta, asset beta

Two-stage growth models

Excel functions used

Sum, NPV, If

Data table


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18.1. Valuation method 1: The current market price of a stock is the correct

price (the efficient markets approach)

The simplest stock valuation is based on the efficient markets approach (Chapter 15).

This approach says that the current market price of a stock is the correct price . In other words:

The market has already done the difficult job stock valuation, and its done this correctly,

incorporating all of the relevant information Theres a lot of evidence for this approach, as you

saw in Chapter 15.

This valuation method is very simple to apply:

Question: IBM looks a bit expensive to meits price has been going up for the last 3

months. What do you think: Is IBMs stock price currently underpriced or overpriced?

Answer: At Podunk U., we learned that markets with a lot of trading are in general

efficient, meaning that the current market price incorporates all the readily-available

information about IBM. SoI dont think IBM is either underpriced or overpriced. Its

actually correctly priced.

Heres another example of the use of this approach:

Question: Ive been thinking of buying IBM, but Ive have been putting it off. The

price has gone up lately, and Im going to wait until it comes down a bit. It seems a bit

high to me right now. What do you think?

Answer: At Podunk U. we would call you a contrarian . You believe that if the price of

a stock has gone up, it will go back down (and the opposite). But this technical approach

(see Chapter 15) to stock valuation doesnt seem to work very well. So if you want to


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buy IBM, go ahead and do so now. Theres nothing in the price runup of the last couple

of months which indicates that there will now be a price rundown.

Some more sophisticated efficient markets methods

Efficient markets valuations dont always have to be as simplistic as the above examples.

In Chapter 15 we looked at additivity, a fundamental tenet of efficient markets. The principle of

additivity says that the value of a basket of goods or financial assets should equal the sum of the

values of the components. Additivity can often be used to value stocks.

Heres a very simple example: ABC Holding Corp., a publicly-traded company, owns

shares in two publicly traded companies. Besides owning these subsidiaries, ABC does little

else.

ABC HOLDING COMPANY

Owns:60% of XYZ Widgets

50% of QRM Smidgets

ABC has 30,000 shares outstanding

XYZ Widgets

Market value of shares: $1,000,000

QRM Smidgets

Market value of shares: $875,000

Figure 18.1. Ownership structure of ABC Holding Company


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What should be the value of a share of ABC Holding? The obvious way to do this is in

the following spreadsheet, which computes the share value of ABC to be $34.58:

123

456789

A B C D E

Number of ABC shares 30,000

ABC owns shares in

Percentage

of shares

owned by

ABC

Market

value

Market value

of ABC

holdings

in company

XYZ Widgets 60% 1,000,000 600,000


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1

23

456789

A B C D E

Number of ABC shares 30,000

ABC owns shares in

Percentage

of shares

owned by

ABC

Market

value

Market value

of ABC

holdings

in company

XYZ Widgets 60% 1,600,000 960,000


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Defining the Free Cash FlowProfit after taxes This is the basic measure of the profitability of the

business, but it is an accounting measure that includesfinancing flows (such as interest), as well as non-cashexpenses such as depreciation. Profit after taxes does not

account for either changes in the firms working capital orpurchases of new fixed assets, both of which can beimportant cash drains on the firm.

+ Depreciation This noncash expense is added back to the profit after tax.

+ after-tax interest payments (net) FCF is an attempt to measure the cash produced by thebusiness activity of the firm. To neutralize the effect ofinterest payments on the firms profits, we:

Add back the after-tax cost of interest on debt(after-tax since interest payments are tax-deductible),

Subtract out the after-tax interest payments on cashand marketable securities.

- Increase in current assets When the firms sales increase, more investment is neededin inventories, accounts receivable, etc. This increase incurrent assets is not an expense for tax purposes (and istherefore ignored in the profit after taxes), but it is a cashdrain on the company.

+ Increase in current liabilities An increase in the sales often causes an increase infinancing related to sales (such as accounts payable or taxespayable). This increase in current liabilitieswhen relatedto salesprovides cash to the firm. Since it is directly

related to sales, we include this cash in the free cash flowcalculations.

- Increase in fixed assets at cost An increase in fixed assets (the long-term productive assetsof the company) is a use of cash, which reduces the firmsfree cash flow.

FCF = sum of the above

Figure 18.2. Defining the free cash flow. We have previously discussed FCFs and their use invaluation in Chapters 7-9.


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CALCULATING THE FIRM'S SHARE VALUE

FROM THE FREE CASH FLOWS AND WACC

Predict firm's future free cash flows (FCF).In Chapters 8 & 9 we did this using a pro

forma model.

Compute the firm's weighted average cost of capital(WACC):

Discount some of the free cash flows and the terminal value to get theenterprise value of the firm:

The terminal value is what the firm will be worth on date N. We've

multiplied by (1+WACC)0.5

because cash flows are assumed to occur inmidyear.

Subtract debt value from firm value to get total equityvalue:

Divide equity value by the number of

shares to derive the share value:

Total equity valueShare value

Number of shares=

( ) ( ) ( )0.5

1

* 11 1

N

tt N

t

Enterprise value

FCF Terminal Value WACCWACC WACC =

= + + + +

Add initial cash balances to enterprise value to get total value of the firm's

assets:

Equity value Total asset value Debt value=

( )1E D CE D

WACC r r T E D E D

= + + +

E D

C

Where r is the cost of equity, r is the

cost of debt, and T is the firm's tax rate

Total asset value Enterprise value Initial cash= +

Discount the all future free cash flows to get the enterprise value of the

firm:

We've multiplied by (1+WACC)0.5 because cash flows are assumed to

occur in midyear.

( ) ( )

0.5

1 * 11

t

tt

FCF

Enterprise value WACC WACC

=

= +

+

Alternatively

Figure 18.3: Flow diagram for a FCF valuation


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Valuation 2: Example 1a basic example

It is 31 December 2003 and you are trying to value Arnold Corp, which finished 2003

with a free cash flow of $2 million. The company has debt of $10 million and cash balances of

$1 million You estimate the following financial parameters for the company:

The future anticipated growth rate of the FCF is 8%

The WACC of Arnold is 15%

You can now estimate the value of Arnold:

The enterprise value of Arnold is the present value of future anticipated FCFs discounted

at the WACC:

( )( )

0.5

1

This factor "corrects"for the fact that FCFs occur

This is the PV throughout the year.formula, assuming thatFCFs occur at year-end

* 11

t

tt

FCFEnterprise value WACC

WACC

FCF

=

= +

+

=

( )

( )( )

( )( )

0.52003

1

Future FCFs are expectedto grow at rate .

0.52003

This formula wasgiven in Chapter ???

1* 1

1

1* 1

t

tt

g

gWACC

WACC

FCF gWACC

WACC g

=

++

+

+= +

Doing the computations in an Excel spreadsheet shows that the enterprise value of Arnold

Corp. is $33,090,599 and that the estimated per-share value is $24.09:


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1

2345678910111213

A B C

2003 FCF (base year) 2,000,000Future FCF growth rate 8%WACC 15%End-2003 debt 10,000,000End-2003 cash 1,000,000Number of shares outstanding 1,000,000

Enterprise value 33,090,599


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( ) ( )( )

50.5

1 6

This factor "corrects"for the fact that FC

The PV of the "high The PV of the "normalgrowth" FCFs growth" FCFS

* 11 1

t t

t tt t

FCF FCF Enterprise value WACC

WACC WACC

= =

= + + + +

Fs occurthroughout the year.

Theres a valuation formula which can be derived using techniques described in the

appendix to Chapter 1:

( )5

2003 2003

In the spreadsheet this is called1

"term 1" and is called "term1 factor"1

11

1 11

111

1

high

high

high h

high

g

WACC

Enterprise value

g

FCF g FCF gWACC

gWACC

WACC

+

+

=

+ + ++ + ++ +

( )( )

( )

5

0.5

5

In the spreadsheet this is called"term 2"

1* 1

1

igh normal

normal

gWACC

WACC gWACC

+ + +

The spreadsheet below shows that Xanthums enterprise value is $27,040,649 (cell B15)

and that its per-share value is $8.18 (cell B21):


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1

23

4

5

67

8910111213141516171819

2021

A B C

2003 FCF (base year) 1,000,000

High growth rate, ghigh 35%

Normal growth rate, gnormal 10%

Number of high growth years 5Term 1 factor: (1+ghigh)/(1+WACC) 113%


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All income from the Station Building partnership will flow through to the shareholders,

who will pay taxes on the income at their personal tax rates. Aunt Sarahs tax rate is

40%.

Station Building will be depreciated over 40 years, giving an annual depreciation of

$500,000 per year.

The building is fully rented out and brings up annual rents of $7 million. You do not

anticipate that these rents will increase over the next 10 years.

Maintenance, property taxes, and other miscellaneous expenses for Station Building cost

about $1 million per year.

The agent who is putting together the partnership has proposed selling Station Building

after 10 years. He estimates that the market price of the building will not change much

over this periodmeaning that the market price of Station Building in year 10 is

anticipated to be $20 million, like its price today.

In your valuation of the Station Building shares, you see that the annual free cash flow

(FCF) to Aunt Sarah is $152,000 (cell B16 in the spreadsheet below). This FCF will be available

to her in years 1-10, and is based on the buildings profit before taxes of $5,500,000, which will

be spread equally among the partners.

The terminal value of the building is $20,000,000, which on a per-share basis is $800,000

(cell B19). At the time the building is sold in year 10, its accumulated depreciation is

$5,000,000, so that its book value is $15,000,000. To compute Aunt Sarahs cash flow from this

terminal value, we deduct the per-share book value of the building ($600,000, cell B20) from the

sale price to arrive at taxes of $80,000 on the profit from the sale of the building (cell B22). The


15/39


cash flow from the sale is the $800,000 sale price minus the taxes--$720,000 as shown in cell

B23.

1

234

5678

91011121314

151617181920

212223

24

2526272829

30313233

343536

37

A B C D E F G

Building cost 20,000,000Depreciable life (years) 40Annual rents 7,000,000

Annual expenses 1,000,000Annual depreciation 500,000


16/39


years, and you anticipate that these rates will continue for years 1-5. However, after year 5 you

anticipate a big slowdown in Formaniss FCF growth, as its industry matures.

Here are the relevant facts about Formanis:

The companys FCF for the current year is $1,000,000.

You anticipate that the FCF for years 1-5 will grow at a rate of 25% per year.

You anticipate a growth rate of FCFs of 6% per year for years 6, 7, (termed the long-

term growth rate in the spreadsheet below).

The company has 5 million shares outstanding.

The valuation formula is:

( ) ( ) ( ) ( ) ( )

( )

( )( )

3 51 2 4

2 3 4 5

5

5

This is the terminal value:an explanation is given in Chapter ??

1 1 1 1 1

* 1 -1*

-1

FCF FCF FCF FCF FCF Formanis value

WACC WACC WACC WACC WACC

FCF long term growth rate

WACC long term growth rateWACC

= + + + ++ + + + +

++

+

To value Formanis, we first predict the FCFs for years 1-5 (cells B9:B13 of the

spreadsheet). The present value of these FCFs is $6,465,787 (cell B20). The terminal value

represents the year-5 present value of the Formanis cash flows for years 6, 7, . To compute

the terminal value, we assume that Formaniss cash flows for these years grow at the long-term

growth rate:

( ) ( ) ( )

( )

( )

( )

( )

( )

( )

6 7 7

2 2

2

5 5

2

3

5

2

-5 , 6,7,...

. . .1 1 1

* 1 - . * 1 - .

1 1

* 1 - .. . .

1

Terminal value year PV of Formanis FCFs years

FCF FCF FCF

WACC WACC WACC

FCF long term growth rate FCF long term growth rate

WACC WACC

FCF long term growth rate

WACC

F

=

= + + ++ + +

+ += +

+ +

++ +

+

=( )

( )5 * 1 -

-

CF long term growth rate

WACC long term growth rate

+


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In cell B17 below the terminal valueassuming a long-term FCF growth rate of 6%is

$17,025,596.

1234567

89101112131415

1617181920

212223

A B C

Current FCF 1,000,000Anticipated growth rate, years 1-5 25%WACC 15%Long-term growth rate, after year 5 6%Number of shares outstanding 5,000,000

Year

Anticipated

FCF

1 1,250,000


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From an Excel point of view, the terminal value method allows us to do interesting

sensitivity analyses. For example, here is the per-share value of Formanis for a variety of

long-term growth rates and WACCs; we use the Data Table technique described in

Chapter ???:

26

2728293031

32

A B C D E F

Long-term growth rate $2.99 0% 2% 4% 6%

WACC 15% 2.51 2.64 2.80 2.9920% 2.11 2.22 2.35 2.5025% 1.80 1.89 1.99 2.12

30% 1.55 1.62 1.70 1.81

Sensitivity analysis: Per share value of Formanis

with different WACC and long-term growth. Year 1-5 growth

rate = 25%

=B23

Varying the year 1-5 growth rate gives different values. In the table below, for example,

weve assumed that year 1-5 growth is 20%:

26

272829303132

A B C D E F

Long-term growth rate $3.01 0% 2% 4% 6%

WACC 15% 2.38 2.54 2.75 3.0120% 2.00 2.13 2.30 2.5125% 1.70 1.81 1.95 2.1230% 1.46 1.55 1.66 1.81

Sensitivity analysis: Per share value of Formanis

with different WACC and long-term growth. Year 1-5 growth

rate = 20%

=B23

18.3. Valuation method 3: The price of a share is the present value of its

future anticipated equity cash flows discounted at the cost of equity

In the previous section we backed into the equity valuation of the firm, by first

calculating the value of the firms assets (the enterprise value plus initial cash balances), and then

subtracting from this number the value of the firms debts. In this section we present another


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method for calculating the value of the firms equitywe directly discount the value of the

firms anticipated payouts to its shareholders.

As an example consider Haul-It Corp., which has a steady record of paying dividends and

repurchasing shares. The company has 10 million shares outstanding. Heres a spreadsheet with

the valuation model:

1

2

34

5

6

78

9

1011

1213

14

1516

1718

1920

212223

2425

26

2728

2930

3132

3334

35

3637

A B C D E F G

1998 1999 2000 2001 2002

Repurchases $1,440,000 $2,410,000 $3,500,000 $6,820,000 $4,830,000Dividends $3,950,000 $3,997,000 $4,238,000 $4,875,000 $5,100,000

Total cash paid to equity holders $5,390,000 $6,407,000 $7,738,000 $11,695,000 $9,930,000

Compound annualgrowth, 1998-2002 16.50%


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Between 1998 and 2002, Haul-Its payouts to its equity holders have increased at an

impressive rate of 16.50% per year (cell B7). The companys cost of equity rE is 25% (cell B9).1

Assuming that future equity payout growth equals historical growth, Haul-It is valued at $136

million (cell B15), which gives a per-share value of $13.62.

The equity value of the company is the discounted value of the future anticipated equity

payouts:

( ) ( )

( ) ( )

( )

( )

( )

( )

2003 2004 2004

2 3

2 3

2002 2002 2002

2 3

2002

....1 1 1

1 1 1....

1 1 1

1 9,930,000 1.16

E E E

E E E

E

Equity payout Equity payout Equity payoutEquity value

r r r

Equity payout g Equity payout g Equity payout g

r r r

Equity payout g

r g

= + + ++ + +

+ + += + + +

+ + +

+= =

( )5136,164,862

25.00% 16.50%=

Dividing the equity value by the number of shares outstanding gives the estimated value

per share:

136,164,86213.62

10,000,000

Equity valueValue per share

Shares outstanding= = =

Why do finance professionals shun direct equity valuation?

Valuation method 3, the direct valuation of equity is so simple that it may surprise you

that it is rarely used. There are several reasons for this, none of which we can fully explain at

this point in the book:

The direct equity valuation method depends on projected equity payouts (that is,

dividends plus share repurchases), whereas Method 3 depends on projected free cash

1 At this point we do not discuss how we arrived at this cost of equity. For a recapitulation of cost of capital

techniques, see sections 18.??? 18.???.


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flows. Whereas a firms equity payouts are a function of management decisions about

dividends and stock repurchases, FCFs are a function of the firms operating

environmentits sales, costs, capital expenditures, and so on. Because many

components of the FCFs are determined by the firms operating environment rather than

management decisions about dividends, analysts are generally more comfortable

predicting FCFs.

The FCF Method 3 discounts future FCFs at the firms weighted average cost of capital

(WACC). The equity payout method 4 discounts future equity payouts at the firms cost

of equity rE. For reasons we will explain in Chapters 19 - 20, the cost of equity rE is very

sensitive to the firms debt-equity ratio, whereas the WACC is not as sensitive to the

debt-equity ratio.2

18.4. Valuation method 4, comparative valuation: Using multiples to value

shares

The last valuation technique we discuss is based on a comparison of financial ratios for

different companies. This valuation technique is often referred to as using multiples. The

technique is based on the logic that financial assets which are similar in nature should be priced

the same way.

2 For reasons explained in Chapter 19, the WACC may in fact be completely invariant to a firms leverage. If this is

so, we can value a firm based on Method 3 without worrying about its leverage.


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A simple example: Using the price/earnings (P/E) ratio for valuation

The price/earnings ratio is the ratio of a firms stock price to its earnings per share:

/stock price

P E

earnings per share

= .

When we use the P/E for valuation, we assume that similar firms should have similar P/E ratios.

Heres an example: Shoes for Less (SFL) and Lesser Shoes (LS) are both shoe stores

located in similar communities. Although SFL is bigger than LS, having double the sales and

double the profits, the companies are in most relevant respects similarmanagement, financial

structure, etc. However, the market valuation of the two companies does not reflect their

similarity: The P/E ratio of SFL is significantly lower than that of LS, as can be seen in the

spreadsheet below:

1

2

345678

9

A B C D

SFL:

Shoes

for Less

LS:

Lesser

Shoes

Sales 30,000 15,000Profits 3,000 1,500Number of shares 1,000 1,000Shareprice 24 18Equity value 24,000 18,000


23/39


Kroger (KR) and Safeway (SWY)

Heres a slightly more involved example. The next page gives the Yahoo profiles for

these companies, both of which are in the supermarket business. Some of the data from these

profiles is in the spreadsheet below, which shows 5 multiples for these two firms.

1

2345678

910111213

14151617

18

192021

222324

2526

A B C D E F

KR SWY

Who's more

highly valued?

Stock price 18.09 26.91


24/39


equity. However, the accounting numbers are heavily influenced by the age of the assets,

the depreciation and other accounting policies, so that this ratio is not so accurate.

Enterprise market to book ratio: The enterprise value is the value of the firms equity

plus its net debt (defined as book value of debt minus cash). Row 18 above measures the

firms net debt by subtracting the cash balances from the book value of the debt. The

enterprise market to book ratio shows that Kroger is valued more highly than Safeway.

Market enterprise value to EBITDA: Earnings before interest, taxes, depreciation, and

amortization (EBITDA) is a popular Wall Street measure of the ability of a firm to

produce cash. In spirit it is similar to the free cash flow concept discussed in this chapter,

though it ignores changes in net working capital and capital expenditures. The market

enterprise value to EBITDA ratio shows that Safeway is actually more highly valued than

Kroger.

Market enterprise value to Sales ratio: This one of the many other ratios we could use

to compare these two firms. As a percentage of its sales, Safeway is more highly valued

than Kroger; this perhaps reflects Safeways ability to extract more cash for its

shareholders from each dollar of sales. Or perhaps it reflects greater shareholder

optimism about the future sales growth rate.

Using multiples to value firmssummary

The multiple method of valuation is a highly effective way of comparing the values of

several companies, as long as the companies being compared are truly comparable .


25/39


Comparability is complicated, however, and you should be careful: Truly comparable firms will

have similar operational characteristics such as sales, costs, etc. and also similar financing.4

4 Were getting ahead of ourselves, as we did in the previous footnote. The point is that it doesnt make sense to

compare the stock price of two operationally similar firms if one is financed with a lot of debt and the other firm is

financed primarily with equity. This point is a result of the discussion in Chapters 19-20. For more details see

Chapter 10 ofCorporate Finance: A Valuation Approach by Simon Benninga and Oded Sarig (McGraw-Hill 1997).


26/39


Figure 18.4: Yahoo profiles for Kroger and Safeway. These profiles form the basis for themultiple valuation illustrated in section 18.4


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The Economist November24th 2001

Economics focus Taking the measureApart from animal spirits, what figures excite stockmarket bulls?

AFTER shares worldwide hit their post-attack lows on September 21st, the DowJones Industrial Average has risen by closeto 20%in what some enthusiasts alreadycall a new bull market. Given dismalforecasts of American growth, plungingconsumer confidence and slashed estimatesfor corporate profits, can any of the toolsthat are used to measure the marketsvalidate the bulls? P/e ratios. One common indicator thebulls seem to have forgotten, at least inAmerica, is the price/earnings (p/e) ratio:the share price divided by earnings pershare. Even when the S&P 500 index hit athree-year low just after the terrorist attacks,the average p/e ratio, at 28, was already

high by historical standards; now it stands at31. In Japan, the average p/e is around 62which, hard to believe, is modest comparedwith the mid-1990s, when analystsattempted to justify p/es of over 100. InEurope, p/e ratios are now blushinglymodest; they average around 16, morecomfortably within historic ranges (see left-hand chart).

Adding to questions about highvaluations in America is uncertainty overthe e in the p/e ratio, the earnings that un-derpin share valuations. Earlier this month,Standard & Poors, a ratings agency,complained that too many companies

artificially boost their profits. A recent studyby the Levy Institute estimates thatoperating profits for the S&P 500 have beeninflated by at least 10% a year over the pasttwo decades, thanks to a mix of one-timewrite-offs and other accounting tricks. Suchsleights of hand mean that American sharesmay be even dearer than they look. Yield ratios. As soaring p/e ratios havebecome harder to justify in recent years, andquestions about earnings have mounted,other indicators have come into fashion.One is the earnings yield ratio, whichcompares returns on government bonds withan implicit earnings yield (in fact, the

inverse of the p/e ratio) to shareholders. Thetheory behind this ratio, popularised byAlan Greenspan, the Fed chairman, someyears ago, is that the earnings yield onshares has moved fairly closely in line with

yields on government bonds, at leastrecently. In late September, plenty ofanalysts pointed to this rule of thumb as anargument that American shares were cheap.

As a relative measure, the earnings yieldratio has the virtue of comparing shares witha riskless alternative, but it is a long wayfrom being an iron law. As Chris Johns ofABN Amro, an investment bank, points out,the relationship between bond yields andequity earnings yields is far less stable thanit at first appears. In America, for most ofthe years since 1873, and even as recently asthe 1970s, shares traded at far higherearnings yieldsthat is, lower p/e ratiosrelative to government bonds than they dotoday (see the right-hand chart).

Earnings yield ratios have a problem.Traditionally, investors have looked to cashdividends as the ultimate source of sharevalue: these are pocketable returns, after all.But as dividends have fallen out of fashion,investors have had to rely on earnings,flawed as they are, as a proxy. Shareholdersface two big risks; first, that without adividend stream they may never recouptheir investment, and second, that the flawsin earnings make profits difficult to gauge.Given these, it seems a stretch to put toomuch faith in a fixed relationship with bondyields, much less the view that shares arefairly valued when these yields are equal. Better ratios. Some point to Tobins Q

the ratio of a firms market value to thereplacement cost of its assetsas the bestway to understand market values. Thiscertainly has appeal, since it reflects thecosts a competitor would face in re-creating

a business. But replacement cost is hard tomeasure, and is of little help in explainingdaily price movements. The next best thing,comparing market prices with the book

value of assets, vastly underestimates thevalue of companies with intangibles such aspatents and brands.

An alphabet soup of ratios is available toescape the flaws of measuring earnings:price-to-EBITDA (earnings before interest,tax, depreciation and amortisation) andprice-to-cashflow, for example. These do asomewhat better job, since they measureprofit in a way that, ideally, is more closelytied to a companys underlyingperformance. But on these measures,according to Peter Oppenheimer of HSBC,stockmarkets in America, Britain andFrance are still highly valued, thoughGerman shares are less so.

Of course, no single metric can unlockthe secrets of share values. But the goodmeasures are those that are useful in bearand bull markets alike. Discounted cash-flow valuation, for instance, is anothermetric that looks at the value of an entirefirm according to the profits it expects infuture. But it relies on a risk premiumthe additional return investors require tocompensate for the risks of holdingshareswhich is both the most important,and the most debated, figure in finance.Differing views about the risk premium can

support almost any equity values. Recentweeks have shown that this slippery idea iscentral in the struggle between the bulls andthe bears. .

Figure 18.4: Article from the Economiston multiple valuation


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PFE Chapter 18, Stock valuation Page 28

18.5. Intermediate summary

In sections 18.1 18.4 weve examined 4 stock valuation methods:

Valuation method 1, the efficient markets approach, is based on the assumption that

market prices are correct.

Valuation method 2, the free cash flow (FCF) approach, values the firm by discounting

the future anticipated FCFs at the weighted average cost of capital (WACC). Sections

18.6 18.7 below show several methods of determining the WACC.

Valuation method 3, the equity payout approach, values all of the firms shares by

discounting the future anticipated payouts to equity. The discount rate is the firms cost

of equity rE.

Valuation method 4, the multiples approach, gives a comparative valuation of firms based

on ratios such as the price-earnings ratio.

In the next sections we discuss some issues related to valuation methods 2 and 3: We

discuss the computation of the weighted average cost of capital (WACC) and the cost of equity

rE (sections 18.6 and 18.7).

18.6. Computing Targets WACC, the SML approach

Valuation method 2 depends on the weighted average cost of capital (WACC), which was

previously discussed in Chapters 6 and 14. In this section we briefly repeat some of the things

said in Chapter 14 and show how to compute the firms WACC using the security market line

(SML).

The basic WACC formula is:


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( )1E D CE D

WACC r r T E D D E

= + + +

To estimate the WACC we need to estimate the following parameters:

the cost of equitythe cost of the firm's debt

market value of the firm's equity

*

market value of the firm's debt

this is usually approximated by th

E

D

rr

E

= number of shares current market value per share

D

==

=

=

e of the firm's debt

the firm's marginal tax rateC

book value

T =

To illustrate the computation of the WACC, we use data for Target Corporation, a large

discount retailer. Figure 18.5 gives the relevant financial information for Target. Using the

Target data, we devote a short subsection to each of the WACC parameters, leaving the cost of

equity rE until last, since it is the most complicated.


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1

2

3

45

6

78

9

10

1112

13

14

15

16

17

18

19

20

2122

2324

25

26

27

2829

30

31

32

33

34

3536

37

38

394041

42

43

44

45

4647

48

49

50

51

52

535455

56

57

58

59

A B C D E

Income statement2002 2001

Revenues 43,917 39,826Cost of sales 29,260 27,143

Sell ing, general and administrat ive expenses 9,416 8,461

Credit card expense 765 463Depreciation 1,212 1,079

Interest expense 588 473

Earnings before taxes 2,676 2,207

Income taxes 1,022 839Net earnings 1,654 1,368

Balance sheetAssets 2002 2001

Cash and cash equivalents 758 499

Accounts receivable 5,565 3,831

Inventory 4,760 4,449

Other current assets 852 869

Total current assets 11,935 9,648

Land, plant, property, and equipment

At cost 20,936 18,442Accumulated depreciation 5,629 4,909

Net land, plant, property and equipment 15,307 13,533

Other assets 1,361 973

Total assets 28,603 24,154

Liabilities and shareholder equity

Accounts payable 4,684 4,160

Accrued liabilities 1,545 1,566

income taxes payable 319 423

Current portion of long-term debt and notes payable 975 905

Total current liabilities 7,523 7,054

Long-term debt 10,186 8,088

Deferred income taxes 1,451 1,152

Shareholders equityCommon stock 1,332 1,173Accumulated retained earnings 8,111 6,687

Total equity 9,443 7,860

Total liabilities and shareholder equity 28,603 24,154

Other relevant information

Shares outstanding 908,164,702

Stock beta 1.16

Stock price, 1 February 2003 28.21

Year Dividends Repurchases

Total

equity

payout

1998 165 0 1651999 178 0 1782000 190 585 775

2001 203 20 223

2002 218 14 232

Growth rate 7.21% 8.89%


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Computing the market value of Targets equity, E

Target has 908,164,702 shares outstanding (cell B47, Figure 18.5). On 1 February 2003,

the day of the companys annual report for its 2002 financial year, the stock price of Target was

$28.21 per share. Thus the market value of the companys equity is 908,164,702*$28.21=

$25,619,326,243. Note that in the spreadsheets all numbers appear in millions, so that Targets

equity value appears as E= $25,619.

Computing the market value of Targets debt, D

The Target balance sheets differentiate between short term debt (Current portion of

long-term debt and notes payablerow 34 of Figure 18.5) and long-term debt (row 37). For

purposes of computing the debt for a WACC computation, both of these numbers should be

added together. This gives debt for Target as:

6789

A B C D2002 2001

Current portion of long-term debt and notes payable 975 905Long-term debt in 2002 and 2001 (columns B and C) 7,523 7,054Total debt, D 8,498 7,959


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Targets income tax rate TC

In 2002 Target paid taxes of $1,022 on earnings of $2,676 (cells B11 and B10

respectively of Figure 18.5). Its income tax rate was therefore 38.19%:

1718

19

A B CEarnings before taxes, 2002 2,676Income taxes 1,022

Corporate tax rate, TC 38.19%


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Here it is in a spreadsheet:

1

2

3456789

1011121314

15

161718

19

20

21

22

23

24

2526

A B C D

Number of shares (million) 908

Market value per share, 1 February 2002 28.21Market value of equity 1 February 2002, E 25,619


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P/E Multiple Model for Estimating E(rM)

We start with the payout form of the Gordon dividend model:

( ) ( )

( )

0

0 0

0 0

Gordon dividend is the dividend payoutmodel ratio, EPS is the current

firm earnings per share

0 0

1 * 1

* 1

/

E

b

D g b EPS gr g g

P P

b gg

P EPS

+ += + = +

+= +

This model is now used to measure the E(rM), using current market data:

( )( )

0 0

0 0

* 1

/

where

b= (in U.S. around 50%)

g= (educated guess)

/ -

M

b gE r g

P EPS

market payout ratio

growth rate of market earnings

P EPS market price earnings ratio

+= +

=

Heres an Excel example:

1

2345

6

7

8

A B C

ESTIMATING E(rM) USING THE P/E RATIO

Market P/E ratio 20.00Market dividend payout ratio, b 50%Estimated growth of market earnings, g 7%

E(rM) 9.68%


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1

2

3456789101112131415161718

1920212223242526

A B C D E F G H I J K

ANNUALIZED REAL RETURNS ON EQUITIES, BONDS, AND BILLS, 1900-2000

Equities Bonds Bills

Equity

premiumAustralia 7.50% 1.10% 0.40% 7.10%


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18.7. Computing Targets cost of equity rE with the Gordon model

An alternative to the CAPM for computing the cost of equity rE is the Gordon model,

which weve previously discussed in Chapter 6. The Gordon model says that the equity value is

the discounted value of future anticipated dividends. The standard version of the Gordon model

is:

( )00

0

0

1

where

current equity payout of firm (total dividends + stock repurchases)

current market value of equity

anticipated equity payout growth rate

E

Div gr g

P

Div

P

g

+= +

=

=

=

For reasons explained in Chapter 6, we think the Gordon model should be used with the

total equity payout, defined as total dividends plus stock repurchases. Below is the calculation

for Target Corp.s WACC using the Gordon model. The spreadsheet is the same as that of the

previous section, except:

Rows 32-36 show Targets equity payoutsthe sum of its dividends and share

repurchasesin each of the last five years. The compound annual growth rate of the

equity payouts is 8.89% per year (cell D38).

Rows 22-25 show the Gordon model calculation of the cost of equity rE. This is

computed as:

( ) ( )00

0

0

1 232* 1 8.89%8.89% 9.88%

25,619

where

current equity payout

current market value of equity

anticipated equity payout growth rate

E

Div gr g

P

Div

P

g

+ += + = + =

=

=

=


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1

23456

789

1011121314

15

16171819

20

2122

2324

25

26272829

30

3132333435363738

A B C D E

Number of shares (million) 908Market value per share, 1 February 2002 28.21Market value of equity 1 February 2002, E 25,619


38/39


and support in the academic community: If market participants have done their work, then the

current price of a share reflects all publicly-available information, and theres nothing else to do.

Valuation method 2, discounted cash flow (DCF) valuation, is the method preferred by

most finance academics and many finance practitioners. This method is based on discounting

the firms projected future free cash flows (FCF) at an appropriate weighted average cost of

capital. The discounted value arrived at in this way is called the firms enterprise value. To

arrive at the valuation of the firms equity, we add cash and marketable securities to the

enterprise value and subtract the value of the firms debt. Dividing by the number of shares

gives the per-share valuation.

Valuation method 3, the direct equity valuation, discounts the projected payouts to equity

holders (defined as the sum of dividends plus share repurchases) by the firms cost of equity rE.

The resulting present value is the value of the firms equity. Although it appears simpler and

more direct than the FCF valuation, direct equity valuation is usually shunned by finance

professionals. This is primarily because the cost of equity is heavily dependent on a firms debt-

equity financing mix, whereas the WACC is not nearly as dependent (and perhaps independent)

of the debt-equity mix.

Valuation method 4, multiple valuation is widely used. This method of valuation arrives

at a relative valuation of the firm by comparing a set of relevant multiples for comparable firms.

When used correctly, multiple valuations can be a powerful tool, but it is often difficult to arrive

at a correct peer group for a particular firm.


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Exercises

1. Do a closed-end exercise based on ABC Holding Corp. Assume that ABC has some costs.

Illustrate the closed-end fund discount.

Thought question: Are you better off buying ABC or the proportions of its subsidiaries?

2. Go back to ABC Holdings:

60%* * 50%* *XYZ share number of QRM share number of

ABC share price XYZ shares price QRM shares

numberofprice

ABC shares

+

=

Suppose you know the share price of ABC and the share price of QRM. What should be the

market price of XYZ?

chapter 18 - valuing stocks

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