CHAPTER 18 - VALUING STOCKS
Transcript of CHAPTER 18 - VALUING STOCKS
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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
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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
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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
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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
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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 .
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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).
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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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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
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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?