<< ńņš. 12(āńåćī 39)ŃĪÄÅŠĘĄĶČÅ >>

(You will need to compute changes in deferred taxes, which are \$20 ā’ \$16 = \$4 in 2001, as
well as changes in working capital.) Can you compute an estimate of cash ļ¬‚ows produced by
this ļ¬rm?

Q 9.16 What are the cash ļ¬‚ows produced by PepsiCoā™s projects in 1999, 2000, and 2001? What
are the cash ļ¬‚ows available to residual equity shareholders in 1999, 2000, and 2001?
ļ¬le=ļ¬nancials.tex: LP
224 Chapter 9. Understanding Financial Statements.

9Ā·5. Summary

The chapter covered the following major points:

ā¢ There are four required ļ¬nancial statements: the balance sheet, the income statement, the
shareholdersā™ equity statement, and the cash ļ¬‚ow statement. Although every company
reports its numbers a little diļ¬erent, the major elements of these statements are fairly
standard.

ā¢ Financial statements also serve more purposes than just NPV calculations, and are well
worth studying in more detailā”elsewhere.

ā¢ Earnings (net income) are not the cash ļ¬‚ow inputs required in an NPV analysis.

ā¢ Accountants use āaccrualsā in their net income (earnings) computation, which we need to
undo in order to extract actual cash ļ¬‚ows.

ā¢ The primary long-term accrual is ādepreciation,ā an allocation of capital expenditures.
The prime operation to undo this is to add back depreciation and subtract out capital
expenditures.

ā¢ The primary short-term accrual is āchanges in working capital,ā an allocation of soon-
expected but not-yet-executed cash inļ¬‚ows and cash outļ¬‚ows. Examples are accounts
payables, accounts receivables, and tax payables. The prime operation to undo them is
to add back changes in working capital.

ā¢ If a cash ļ¬‚ow statement is available, it conveniently handles most of the diļ¬culties in
undoing accruals for the NPV analysis. However, accountants believe interest expense to
be a cost of operations, while ļ¬nanciers believe it to be a payout to owners. Thus, interest
expense requires special handling.

ā¢ Formula 9.18 shows how to compute cash ļ¬‚ows that accrue to project owners (debt plus
equity). It is cash ļ¬‚ow from operating activity, plus cash ļ¬‚ow from investing equity, plus
interest expense.

ā¢ Formula 9.19 shows how to compute cash ļ¬‚ows that accrue to levered equity owners
(equity only). It is the cash ļ¬‚ow that accrues to project owners, plus net issuance of debt,
minus interest expense.

A ļ¬nal observation: the most diļ¬cult part to analyzing ļ¬nancial statements for me is getting
the signs right.
ļ¬le=ļ¬nancials.tex: RP
225
Section A. Appendix: Supplementary Financials ā” Coca Cola.

Appendix

A. Appendix: Supplementary Financials ā” Coca Cola

The following tables provide further ļ¬nancial statements for Coca Cola and PepsiCo. They are
here to give you a feeling for what real-world ļ¬nancial statements look likeā”maybe a little
more complicated and involved than what we covered, but you should still be able to extract
the components that matter.
Solve Now!
Q 9.17 The 2002 10-K Annual Statement of Coca Cola is available from Edgar. (If need be, you
can use the ļ¬nancials provided on Page 226. However, it would be good for you to look this
up on the Web, instead.) Approximate the cash ļ¬‚ows that you would use in valuing Coca Cola.
Then, use the cash ļ¬‚ow statement. How diļ¬erent are the numbers that Coca Cola reports from
those that you would infer from the income statement combined with capital expenditures and
depreciation (i.e., from our ļ¬rst formula, 9.12 on Page 213)? What if you had used our second
formula 9.17 on Page 217, which also subtracts out changes in working capital?
226
a. Coca Colaā™s Financials From EdgarScan

Table 9.11. Coca Colaā™s Financials from EdgarScan, Restated.

Cash Flow Statement December
2001 2000 1999
Income Statement December

ļ¬le=ļ¬nancials.tex: LP
Net Income 3,969 2,177 2,431
2001 2000 1999
+ Depreciation and Depletion 803 773 792
= Revenues 20,092 19,889 19,284
+ Deferred Taxes 56 3 97
COGS 6,044 6,204 6,009
+ Non-Cash Items ā“256 1,484 1,120
+ SG&A (incl. Depreciation) 8,696 8,551 8,480
+ Changes In Working Capital ā“462 ā“852 ā“557
+ Other Expenses 0 1,443 813
Total Operating Activity
= 4,110 3,585 3,883
ā“ = Total Operating Expenses 14,740 16,198 15,302
Capital Expenditures ā“769 ā“733 ā“1,069
Operating Income
= 5,352 3,691 3,982

Chapter 9. Understanding Financial Statements.
+ Investments ā“1 ā“218 ā“342
+ Other Net Income 607 155 174
+ Other Investing ā“418 ā“214 ā“2,010
EBIT
= 5,959 3,846 4,156
Total Investing Activity
= ā“1,188 ā“1,165 ā“3,421
+ Interest Expense 289 447 337
Income Before Tax
= 5,670 3,399 3,819 Dividends ā“1,791 ā“1,685 ā“1,580
ā“ Income Tax 1,691 1,222 1,388 + Net Issuance of Stock ā“113 ā“198 ā“153
Income After Tax
= 3,979 2,177 2,431 + Net Issuance of Debt ā“926 ā“585 +956
ā“ Extraordinary Items -10,000 0 0 Total Financing Activity
= ā“2,830 ā“2,072 ā“471
Net Income
= 3,969 2,177 2,431 ā“ Foreign Exchange Eļ¬ects ā“45 ā“140 ā“28
Net Change In Cash
= 47 208 ā“37
Section A. Appendix: Supplementary Financials ā” Coca Cola.
b. Coca Colaā™s Financials From Yahoo!Finance

Table 9.12. Coca Cola ļ¬nancial statements from Yahoo!Finance, Not Restated

Cash Flow Statement December
2001 2000 1999
Income Statement December
Net Income 3,969 773 792
2001 2000 1999
+ Depreciation and Depletion 803 773 792
= Revenues 20,092 20,458 19,805
+ Deferred Taxes
COGS 6,044 6,204 6,009
+ Non-Cash Items
+ SG&A 8,696 10,563 9,814
+ Changes In working capital
+ Depreciation and Amortization
Total Operating Activity
= 4,110 3,585 3,883
+ Unusual Expenses
Capital Expenditures ā“769 ā“733 ā“1,069
= Total Operating Expenses
ā“

ļ¬le=ļ¬nancials.tex: RP
+ Investments ā“1 ā“218 ā“518
Operating Income
= 5,352 3,691 3,982
+ Other Investing ā“418 ā“214 ā“1,834
+ Other Net Income 607 155 174
Total Investing Activity
= ā“1,188 ā“1,165 ā“3,421
EBIT
= 5,959 3,846 4,156
ā“ Interest Expense 289 447 337 Financing Cash Flow Items
Income Before Tax
= 5,670 3,399 3,819 + Dividends ā“1,791 ā“1,685 ā“1,580
ā“ Income Tax 1,691 1,222 1,388 + Net Issuance of Stock ā“113 ā“198 ā“153
Income After Tax
= 3,979 2,177 2,431 + Net Issuance of Debt ā“926 ā“585 +956
ā“ Extraordinary Items -10,000 0 0 Total Financing Activity
= ā“2,830 ā“2,072 ā“471
Net Income
= 3,969 2,177 2,431 ā“ Foreign Exchange Eļ¬ects ā“45 ā“140 ā“28
Net Change In Cash
= 47 208 ā“37

227
ļ¬le=ļ¬nancials.tex: LP
228 Chapter 9. Understanding Financial Statements.

Q 9.18 What are the economic project cash ļ¬‚ows you would use for Coca Cola from 1999 to
2001?

B. Appendix: Abbreviated PepsiCo Income Statement and Cash
Flow Statement

Abbreviated and summarized statements may appear in a variety of venues, such as www.marketguide.com,
the SECā™s Edgar, or Price-Waterhouse-Coopersā™ EdgarScan.

Table 9.13. PepsiCo Income Statement, Restated for Acquisitions.

Consolidated Income Statement December
2001 2000 1999
(in millions)

Net Sales
=
New PepsiCo \$26,935 \$25,479 \$22,970
Bottling operations ā“ ā“ 2,123
= Total Net Sales 26,935 21,661 25,093

Costs and Expenses
Cost of Goods Sold 10,754 10,226 10,326
Selling, General & Administrative Expenses 11,608 11,104 11,018
Note: sg&a incl. depreciation of 917 946 963

Amortization of Intangible Assets 165 147 193
Merger-related Costs (Unusual Expenses) 356 ā“ ā“
Other Impairment and Restructuring (Unusual Expenses) 31 184 73
= Total Costs and Expenses
ā“ 22,914 21,661 21,610

Operating Income
=
New PepsiCo 4,021 3,818 3,430
Bottling operations and equity investments ā“ ā“ 53
Total Operating Project 4,021 3,818 3,483

a. Bottling equity income and
transaction gains/(losses), net 160 130 1,083
b. Interest Expense (219) (272) (421)
c. Interest Income 67 85 130
= Net Interest Income, a-c (Gains&Losses) =8 =ā“57 =792

Income Before Income Taxes
= 4,029 3,761 4,275

Provision for corporate income tax
ā“ 1,367 1,218 1,770
Income After Income Taxes
= 2,662 2,543 2,505

ā“ Extraordinary Items 0 0 0
Net Income
= \$ 2,662 \$ 2,543 \$ 2,505
ļ¬le=ļ¬nancials.tex: RP
229
Section B. Appendix: Abbreviated PepsiCo Income Statement and Cash Flow Statement.

Table 9.14. PepsiCo Abbreviated Cash Flow Statement, Restated for Acquisitions.

Cash Flow Statement December
2001 2000 1999
(in millions)

Net Income 2,662 2,543 2,505
+ Depreciation, Depletion, Amortization 1,082 1,093 1,156
+ Deferred Taxes (changes in) 162 33 573
+ Non-Cash Items 211 355 ā“708
+ Changes in Working Capital 84 416 79
Total Operating Activity
= 4,201 4,440 3,605
Capital Expenditures ā“1,324 ā“1,352 ā“1,341
+ Other Investing ā“1,313 ā“644 169
Total Investing Activity
= ā“2,637 ā“1,996 ā“1,172

Financing Cash Flow Items ā“5 ā“254 ā“382
+ Dividends ā“994 ā“949 ā“935
+ Net Issuance of Stock ā“579 ā“740 ā“902
+ Net Issuance of Debt ā“341 ā“705 391
Total Financing Activity
= ā“1,919 ā“2,648 ā“1,828
ā“ Foreign Exchange Eļ¬ects 0 ā“4 3
Net Change In Cash
= ā“355 ā“208 608
ļ¬le=ļ¬nancials.tex: LP
230 Chapter 9. Understanding Financial Statements.

Solutions and Exercises

1. Accruals, speciļ¬cally depreciation and delayed payments/receipts.
2. Uncle Sam uses Accounting methods to compute corporate income taxes. Secondary inļ¬‚uences, not dis-
cussed in the text, come from the fact that many contracts are contingent on accounting numbers (e.g., debt
covenants).

3. Do it!
4. A 12% instead of a 10% interest rate would increase the NPV of the tax obligation from \$46.77 to \$50.16.
Therefore, the project value would decrease by \$3.39.
5. The income statementis now

Year 1 2 3 4 5
Sales (Revenues) \$80 \$80 \$80 \$80 \$80
ā“ Cost of Goods Sold \$6 \$6 \$6 \$6 \$6
(COGS)
ā“ Selling, General & Admin- \$8 \$8 \$8 \$8 \$8
istrative Expenses (SG&A)
= EBITDA \$66 \$66 \$66 \$66 \$66
ā“ Depreciation \$30 \$30 \$30 \$30 \$0
= EBIT (Operating Income) \$36 \$36 \$36 \$36 \$66
ā“ Interest Expense - \$8 \$8 \$8 \$8
= EAIBT (or EBT) \$36 \$28 \$28 \$28 \$58
ā“ Corporate Income Tax \$18 \$14 \$14 \$14 \$29
= Net Income \$18 \$14 \$14 \$14 \$29

Cash Flow Statement Excerpt
Year 1 2 3 4 5
Capital Expenditures ā“\$120 - - - -
Net Debt Issue +\$100 - - - ā“\$100

The cash ļ¬‚ow formula is EBIT plus depreciation (or use EBITDA instead) minus capital expenditures, minus
corporate income tax: \$36 + \$30 ā’ \$120 ā’ \$18 = ā’\$72. The ļ¬rst levered equity cash ļ¬‚ows are ā’\$72 + \$100 =
+\$28.
Discount
Cash Flow Rate 1 2 3 4 5 NPV
Machine 8% ā“\$54 \$66 \$66 \$66 \$66 \$152.41
Uncle Sam 8% ā“\$18 ā“\$14 ā“\$14 ā“\$14 ā“\$29 ā“\$69.81
Project 8% ā“\$72 +\$52 +\$52 +\$52 +\$37 \$82.60
Loan 8% +\$100 ā“\$8 ā“\$8 ā“\$8 ā“\$108 \$0
Levered Ownership 8% +\$28 +\$44 +\$44 +\$44 ā“\$71 \$82.60

6. The answer will eventually be posted on my website. (It is not there yet.)

7.

Year 0 1 2 3 4 5 6
Reported Net Income \$0 \$100 \$100 \$300 \$300 \$100 \$0
Reported accounts receivables \$0 \$100 \$120 \$340 \$320 \$120 \$0
Change in accounts receivables \$0 \$100 \$20 \$220 ā“\$20 ā“\$200 ā“\$120
Cash Flow \$0 \$0 \$80 \$80 +\$320 +\$300 +\$120

The ļ¬rmā™s customers did not all pay the next period. Therefore, the cash ļ¬‚ows were delayed.
ļ¬le=ļ¬nancials.tex: RP
231
Section B. Appendix: Abbreviated PepsiCo Income Statement and Cash Flow Statement.

8. The cash ļ¬‚ows are

Quarter 0 1 2 3 4 5 6 7
Reported Net Income \$0 \$100 \$200 \$300 \$200 \$100 \$0 \$0
Immediate Cash Flows \$0 \$50 \$100 \$150+ \$100+ \$50+ \$0 \$0
+ Delayed Cash Flows +\$50 +\$100 +\$150 +\$100 +\$50
ā’ = Cash Flows =\$0 =\$50 =\$100 =\$200 =\$200 =\$200 =\$100 =\$50
ā’ Change in A/R - \$50 \$100 \$100 \$0 ā“\$100 ā“\$100 ā“\$50
ā’ Accounts Receivables \$0 \$50 \$150 \$250 \$250 \$150 \$50 \$0

It is easier to obtain the change in A/R ļ¬rst: we know that Net Income minus the Change in A/R must add up to
cash ļ¬‚ows. So, Change in A/R = Net Income ā’ cash ļ¬‚ows. And, knowing Change in A/R, accounts receivables
itself requires simply adding up.
9. In Year 1, Amazonia has cash inļ¬‚ows of \$100 (\$25 net income plus \$75 change in accounts payables). In
Year 2, Amazonia has another \$100 in sales, but payables stay the same. (It has to pay its old suppliers \$75,
even though it gets to keep \$75 from its new suppliers.) So, Amazonia gets cash inļ¬‚ows of \$25 only. In Year 3,
Amazonia gets net income cash inļ¬‚ows of \$100, plus the \$225 change in payables, for cash inļ¬‚ows of \$325.
Finally, in Year 4, Amazonia has cash outļ¬‚ows of \$300. The pattern is thus

Month Jan Feb Mar Apr May
ā’\$300
Cash Flows \$0 \$100 \$25 \$325

Note that Amazonia has total 5-month cash ļ¬‚ows of \$150, just as it has total 5-month net income of \$150.
The working capital has only inļ¬‚uenced the timing attribution.
10. Short term accruals. To manipulate long-term accruals, managers would have to manipulate the depreciation
schedule, and though this is possible a few times, if it is done often, it will most surely raise eyebrows.
11. For example, a ļ¬rm can take out a reserve against a judgment in a pending lawsuit. Or, it could assume that
customers will pay their bills less than they actually will.
12. For example, a ļ¬rm could pay all its payables immediately, instead of delaying them.

13. See Page 220.
14. Yes. Cash ļ¬‚ows just have diļ¬erent timing. For example, ļ¬rmā™s capital expenditures are not booked immedi-
ately, but the sum of all lifetime depreciation adds up to the sum of all lifetime capital expenditures. (This
abstracts away from some pathological accounting cases that we have not covered.).
15. Use the Formula on Page 220:

2001 2000 1999
Earnings before Interest and Taxes (EBIT) 120 85 75
ā“ Corporate Income Tax ā“ 34 20 16
4ā— 16ā—
+ Changes in deferred taxes + ?
= Net Operating Proļ¬t = 90 81 ?
20ā
+ Depreciation + 25 23
= Gross Cash Flow = 115 104 ?
ā— ā—
ā“ Increase in Working Capital ā“ 10 5 ?
ā“ Capital Expenditures ā“ 0 30 200
= Free Cash Flow from Operations = 105 69 ?

ā—
Note that the balance sheet gave the level of deferred taxes and the level of working capital, not the changes
in these variables. You had to compute the diļ¬erences yourself. ā  Depreciation is only available from the
cash ļ¬‚ow statement, not from the balance sheet.
16. Use Formulas 9.18 and 9.19. PepsiCoā™s project cash ļ¬‚ows, available for satisfaction of both creditors and
shareholders, are

Cash Flow from Operating Activity 4,201 4,440 3,605
+ Cash Flow from Investing Activity ā“2,637 ā“1,996 ā“1,172
+ Interest Expense + (ā“8) 57 (ā“792)
= Cash Flow From Projects 1,556 2,501 1,641

PepsiCoā™s shareholder cash ļ¬‚ows are
ļ¬le=ļ¬nancials.tex: LP
232 Chapter 9. Understanding Financial Statements.

Cash Flow from Operating Activity 4,201 4,440 3,605
+ Cash Flow from Investing Activity ā“2,637 ā“1,996 ā“1,172
+ Net Issuance of Debt ā“341 ā“705 391
= Cash Flow To Equity 1,223 1,739 2,824

17. For reference, in 2001, the cash ļ¬‚ow statement reports depreciation of +\$803, and capital expenditures of
ā’\$769. Our ļ¬rst formula 9.12 was net income plus depreciation minus corporate income tax, or \$3,969+\$803-
\$769=\$4,003. Looking at the actual Coca Cola 2001 cash ļ¬‚ow statement on Page 226, our calculation omits
deferred taxes (+\$56), non-cash items (-\$256), changes in working capital (-\$462), and āinvestmentsā of
ā’\$418 ā’ \$1. In total, our ļ¬rst formula 9.12 therefore would have omitted \$1,081. Our second formula 9.17
would have captured at least changes in working capital, for an error reduction of \$462, and a total error of
\$619.
18. Economic project cash ļ¬‚ows are operating activity cash ļ¬‚ows plus investing activitiy cash ļ¬‚ows plus interest:

1999 2000 2001
Operating Activity 3,883 3,585 4,110
Investing Activity ā“3,421 ā“1,165 ā“1,188
Interest Paid 337 447 289
Economic Project Cash Flows 799 2,867 3,211

(All answers should be treated as suspect. They have only been sketched, and not been checked.)

However bad my answers to exercises in earlier chapters may have been, the solutions
in this chapter are probably worse. I am notoriously bad when it comes to keeping the
correct signs. I have no future as an accountant! Before this chapter is formally ļ¬nished,
this section will be quadruply checked.
CHAPTER 10
Valuation From Comparables

A Practical Approach
last ļ¬le change: Mar 13, 2006 (10:43h)

last major edit: Apr 2004, Dec 2004

You now know how to read ļ¬nancial statements, how to obtain cash ļ¬‚ows from ļ¬nancial state-
ments, and how to value them. You also know that forecasting cash ļ¬‚ows is a very diļ¬cult
task. Are there any shortcuts? Are there any good alternatives to NPV? Is there anything else
you can do with ļ¬nancial statements?
Surprisingly, the answer is yes. There is one alternative approach often resorted to by practition-
ers. It is called āvaluation by comparables,ā or ācompsā for short. Executed correctly, comps
can give answers that are as good as those you can obtain with a thorough NPV analysisā”
though they are not always the same. In practice, sometimes the NPV study gives a better value
estimate, and sometimes the method of comparables does.
The basic idea behind valuation by comparables is simple and best understood by analogy:
assume that you want to determine the value of 5 red marbles. If black marbles cost \$2 a piece,
and if you are willing to make the assumption that red marbles are valued like black marbles,
then you can compute that the value of your 5 red marbles should be \$10. It is not necessary
to forecast what value marbles will have in the future or what discount factor to apply: the
market price of black marbles has already taken this information into account.
Of course, the more similar black marbles are to red marbles, the better this method will work.
(If black marbles are made from coal and red marbles are made from rubies, you will undervalue
your red marbles!) The method of comparables therefore assumes that public markets already
value comparable ļ¬rms appropriatelyā”or at least that they misvalue your ļ¬rm the same way
that they misvalue other ļ¬rmsā”so that the value of your ļ¬rm or your new project can be
assessed in terms of its similarity to comparable ļ¬rms.

233
ļ¬le=comparables.tex: LP
234 Chapter 10. Valuation From Comparables.

10Ā·1. Comparables vs. NPV

Let us begin with a very brief example. In early 2006ā Dell had a market value of \$71.5 billion
Just to show you what
we are talking about... and earnings of \$3 billion, giving it a P/E ratio of 23.5. Say you are wondering how much Gateway
should be worth, given that it had earnings of \$49.6 million. By the method of comparables,
you would postulate that Gateway is just like Dell. Each dollar of earnings should translate into
\$23.5 of value. Therefore, you would claim that Gateway should be worth

Value of Gateway ā Ā· \$49.6 million ā \$1.2 billion.
23.5
(10.1)
Dell P/E Ā· Gateway E

(In reality, Gateway was worth about \$925 million.)
The idea of comparables is the same as that of NPVā”both are attempts to value your project
NPV is also a comparable
in a sense. relative to other projects that are available. In NPV analysis, you compare your own project to
another-project benchmark through the opportunity cost of capital. NPV also tells you exactly
what mattersā”future cash ļ¬‚owsā”and how you should weight diļ¬erent cash ļ¬‚ows relative to
one another. In theory, you cannot do better than NPV. But in practice, it is so very diļ¬cult to
estimate these future cash ļ¬‚ows. There is also no objective standard when you are measuring
the future. If you say the expected cash ļ¬‚ows in 10 years are \$1 million, and I say that they are
\$5 million, which one is right?
Comparables try to measure project similarity not through estimates of future cash ļ¬‚ows, but
Comparables proxy for
future cash ļ¬‚ows with an through something that is available today. If ļ¬rms with similar earnings also have similar future
available measure today.
cash ļ¬‚ows (or at least similar present values of all future cash ļ¬‚ows), then earnings are a good
proxy for what you really wantā”plus we can objectively agree on what these earnings are today.
In using todayā™s earnings instead of a full estimate of future cash ļ¬‚ows, we therefore trade oļ¬
your judgmental uncertainty about the future cash ļ¬‚ow against your judgmental uncertainty
about how good your current earnings approximate the future cash ļ¬‚ow stream.
Both NPV and comparables are based on relative valuation, but comparables lean more heavily
When NPV will work
better and when on immediately similar projects and the assumption that the market has valued these correctly.
comparables will work
NPV is a bit more forgiving, in that the opportunity cost of capital uses a broader swath of al-
better.
ternatives than just a couple of similar-looking ļ¬rms in an industry. Consequently, NPV makes
it easier to compare an investment in PepsiCo to, say, an investment in Treasuries and the
stock market. Here, the method of comparables would fail, because these alternatives seem
so dissimilar to PepsiCo that you would have no faith in a comparables-derived estimates. In
contrast, comparables make it easier to compare an investment in PepsiCo to, say, an invest-
ment in Coca Cola. With similar characteristics, you can reasonably assume that you can rely
on the ļ¬nancial markets having gotten Coca Colaā™s valuation based on future cash ļ¬‚ows and fu-
ture discount factors right, so you are in eļ¬ect free-riding on a wonderfully accurate valuation
already provided for you by the ļ¬nancial markets.
Solve Now!
Q 10.1 When negotiating, would you value your next residence by the method of comparables,
or by the method of NPV? If comparables, what kind of ratio might you use?
ļ¬le=comparables.tex: RP
235
Section 10Ā·2. The Price-Earnings (PE) Ratio.

10Ā·2. The Price-Earnings (PE) Ratio

The kind of ratios that you would be most interested in have value in their numeratorsā”for Why not Price Cash Flow
Ratio?
example, the price-earnings ratio. The reason is that if you obtain a good estimate for what a
reasonable price-earnings ratio is, you merely need to multiply the proper ratio by your projectā™s
or ļ¬rmā™s earnings, and out comes an estimate of price,

Price
Ā· Xour project ā’ Price Estimate for your Project .
X (10.2)
from comparables

The most important such ratio is the price-earnings ratio. The reason is that earnings are
often seen as best representatives of future cash ļ¬‚ows. At ļ¬rst glance, this may seem odd to
you. After an entire chapter on how to compute cash ļ¬‚ows in order to avoid net income, why
compute a price-earnings ratio, rather than a price-cash ļ¬‚ow ratio? The reason is that cash
ļ¬‚ows are usually more āspikyā than earnings. When a ļ¬rm makes a large capital expenditure
or acquisition, it may have a large negative cash ļ¬‚ow one year, followed by positive cash ļ¬‚ows
in the following years. This is not a problem in an NPV analysis, because the higher future cash
ļ¬‚ows will also enter in the future terms. But, for computing a representative ratio with just
one yearā™s information, the current accounting earnings are probably more representative than
a current cash ļ¬‚ow would be. After all, earnings try to smooth inļ¬‚ows and outļ¬‚ows of large
expenditures over many periods. It is a number which accountants have created for the very
purpose which we need here: a representative number for a ālong-termā picture.

10Ā·2.A. Deļ¬nition

The price-earnings ratio is commonly abbreviated as P-E ratio, P/E ratio, or PE Ratio. The The price-earnings ratio
is price divided by
P/E ratio divides the overall ļ¬rm market valueā”its market priceā”by the income ļ¬‚ow (earnings)
(expected or current )
the ļ¬rm generates. (Later in our chapter, we shall discuss some other ratiosā”and it will then earnings, either
become clear why the P/E ratio is the most popular comparables measure.) In the real world, per-share or overall.
price-earnings ratios are often but not always quoted as the current market price divided by
the expected earnings for the next year (as determined by a consensus among analysts). The ad-
vantage is that expected earnings focus more on the future than on the most recently reported
earnings. This suits us well, because valuation is forward-looking, not backward looking. In-
cidentally, in much of this chapter, we use the growing perpetuity formula 3.13 (on Page 40),
which already calls for next yearā™s earnings, anyway. In any case, the intuition would remain
the same if you used the most recently reported earnings. Therefore, this chapter keeps the
language a bit looseā”and even forgets to note that future earnings are a random variable, for
which we really mean the expected value.
Let us start by exploring the meaning of the P/E ratio with an example. A ļ¬rm with a market Firm-value and
price-per-share based
value of P = \$200 million and expected earnings of E = \$10 million next year would have a
ratios are the same.
price-earnings ratio of 20. Both inputs could be expressed in per-share terms, rather than in
aggregate value. So, if this ļ¬rm has 40 million shares outstanding, each share would be worth
P = \$5 and produce earnings of E = \$0.25. The price-earnings ratio would still be 20.
We now want to value a project that is quite similar to this ļ¬rm and has earnings of E = \$3 per Our ļ¬rst comparables
valuation.
share. What should your projectā™s per-share value be?

Price Estimate = Comparable Price Earnings Ratio Ā· Our Earnings
(10.3)
= Ā· = \$60 .
20 \$3
ļ¬le=comparables.tex: LP
236 Chapter 10. Valuation From Comparables.

One way to look at the price-earnings ratio is that it attaches an implicit overall value to each
Other interpretations.
dollar of earnings. In this case, each extra dollar of earnings translates into an extra \$20
worth of valuationā”the shares sell for twenty times earnings. Sometimes you should use the
reciprocal of the P/E ratio, the earnings yield,

(Expected) Earnings 1
Earnings Yield = = (10.4)
.
Price P/E Ratio

You can view the earnings-yield as telling you the percentage of price that is due to current
earnings. In our example, the earnings yield would be 10/200 = 5%. If the earnings are zero or
negative, the price-earnings ratio is meaningless, and often indicated as NA or N/A. In contrast,
the earnings-price ratio (earnings yield) can reasonably be negative and meaningful. If the
earnings are positive, then a higher price-earnings ratio implies a lower earnings-price yield
and vice-versa.

10Ā·2.B. Why P/E Ratios diļ¬er

Our ļ¬rst goal in constructing a valuation by comparables is to determine where price-earnings
P/E ratios differ due to
growth differences (and ratios come from, and what they say about the ļ¬rm. The main reason why P/E Ratios diļ¬er
expected rates of
across ļ¬rms and industries is that expectations diļ¬er as to how todayā™s earnings relate to
return).
future cash ļ¬‚owsā”the expected growth rate. If you believe that todayā™s earnings will be the
last, your value estimate per dollar of current earnings should be lower than if you believe that
it is a very low proxy of much better times to come.

Important: The price-earnings ratio is higher when the ļ¬rm has more growth
opportunities.

There is also an inļ¬‚uence of leverage hereā”ļ¬rms that are more levered have lower price-
earnings ratios, a topic that we will cover in Section 10Ā·3.E.

Direct Diļ¬erences in Earnings Growth
We can illustrate this in a ātraditionalā growing perpetuity framework. Assume that a ļ¬rmā”call
Determining a sensible
price-earnings ratio for it Aā”is expected to earn cash of \$100 next year, and its appropriate cost of capital is 15%. This
a hypothetical ļ¬rm,
ļ¬rm is a perpetuity whose income will grow by 5% per annum forever. The growing perpetuity
which is a simple
formula 3.13 on Page 40 states that the value of this ļ¬rm is
growing perpetuity.

\$100
= = \$1, 000
VA
15% ā’ 5%
(10.5)
Exp Cash FlowA ā EA
ValueA ā PA = .
Exp Interest RateA ā’ Exp Growth RateA

With a price of \$1,000 and expected earnings of \$100, Aā™s price divided by its expected earnings
is
PA \$1, 000
= = 10
EA \$100
(10.6)
EA
PA 1
E (ĖA )ā’E (gA )
r Ė
= = .
E (ĖA ) ā’ E (gA )
EA EA r Ė

What if the ļ¬rm grew not by 5% but by 10% per year (forever)? Then the price earnings ratio
Faster growing ļ¬rms
have higher would be
price-earnings ratios. PA 1
= = 20 .
15% ā’ 10%
EA (10.7)
1
= .
E (ĖA ) ā’ E (gA )
r Ė
ļ¬le=comparables.tex: RP
237
Section 10Ā·2. The Price-Earnings (PE) Ratio.

The P/E ratio is higher. So, high price-earnings ratios are a reļ¬‚ection of the marketā™s expectation
about how fast the ļ¬rm will grow relative to its cost of capital.
What if the market expected this ļ¬rm to shrink by 5% each year? Such a ļ¬rm would have a Slower growing ļ¬rms
have lower
price-earnings ratio of only
price-earnings ratios.
PA 1
= =5 (10.8)
.
15% ā’ (ā’5%)
EA
Cigarette producers, for example, may suļ¬er from negative annual growth rates and as a result
have low price-earnings ratios. In May 2002, RJR Nabisco and Philip Morris (now Altria) had
P/E ratios of about 12. Contrast this with high-growth ļ¬rms, such as AMGEN (a high-tech
pharmaceutical), which had a P/E ratio of about 40 and Microsoft, which had a P/E ratio of
about 45.
Despite everything I have just written, you can also ļ¬nd some companies that have performed High growth rates for
shrinking companies?
poorly and even shrunk, but which still have high P/E ratios. For example, in October 2005,
Sun Microsystems had a P/E ratio of 45ā”three times as high as Microsoftā™s then P/E ratio of 16.
Does this mean our theory is wrong? On the contrary! P/E is a value ratio relative to current
earnings. Sun was generally believed to have experienced very tough times after about 2003.
Presumably the market did not expect Sunā™s low earnings in 2004 and 2005 to be representative
of its long-term earnings. Instead, it expected Sunā™s future earnings to be much higher than its
somewhat distressed 2005 earnings. Relative to its 2005 earnings, Sun may indeed be a growth
company!
Do you ļ¬nd it confusing that the earnings can grow by 5%, but investors expect to receive 15% The growth rate of
earnings is not the
rate of return? Shouldnā™t investorsā™ expected rate of return be the growth rate of earnings?
expected rate of return
Noā”not at all. (Indeed, the expected rate of return (E(Ė)) cannot be equal to the growth rate
r to investors.
of earnings (E(g)), or the NPV would be inļ¬nite.) The reason is that the price today already
Ė
capitalizes all future earnings. Although we have already discussed why there is no direct
link between earnings and rates of return (in Section 3Ā·1.B), this is so important it deserves
another example. Say that the appropriate cost of capital for a ļ¬rm is 10%, and it will produce
\$100 next year, \$50 the next year, and \$0 thereafter. There is no uncertainty. Clearly, the
cashļ¬‚ows/earnings of the ļ¬rm are shrinking dramatically. But the value of the ļ¬rm today is
\$100/1.1 + \$50/1.12 ā \$132.23. Next year, the investor will receive \$100 and hold a remaining
project of \$50/1.11 ā \$45.45, for a total wealth of \$145.45. The (expected) rate of E(Ė) isr
\$145.45/\$132.23 ā’ 1 = 10%, even though the growth rate of earnings is negative.

The Present Value of Growth Opportunities (PVGO)
Another way to express the same informationā”to give perspective about the meaning of PVGO (Present Value of
Growth Opportunities).
P/E ratiosā”comes from decomposing a ļ¬rm into two components: the ratio of one hypothet-
ical ļ¬rm that has the projected earnings of the company, but has stopped growing; and the
ratio of another hypothetical ļ¬rm that has zero earnings right now and consists just of the
projected growth opportunities. The latter part is called the Present Value of Growth Op-
portunities (PVGO). You can split the market value of any companyā”regardless of its actual
earningsā”into these two components.
For example, consider three ļ¬rms, all priced at \$150 and all with an appropriate cost of capital An example split of
ļ¬rmsā™ earnings into
of 10%. The ļ¬rst ļ¬rm has expected earnings of \$15, the second ļ¬rm has expected earnings of
āsteadyā and āPVGO.ā
\$12, and the third ļ¬rm has expected earnings of \$20. We will decompose each ļ¬rmā™s value into
the two components.
Stability: The ļ¬rst ļ¬rm is worth
\$15
\$150 = + = \$150+?
?
10%
(10.9)
E
= + PVGO .
P
E (Ė)
r

To be an equality, the question mark must stand for \$0. The market has priced this ļ¬rst ļ¬rm
exactly as if it had no expectation of any future growth. Thus, 100% of this ļ¬rmā™s value comes
from the āsteady component,ā and 0% from the āgrowth component.ā Eventually, in the very
ļ¬le=comparables.tex: LP
238 Chapter 10. Valuation From Comparables.

long-run, you would expect mature and stable companies to settle into this mode.
Growth: In contrast, if the second ļ¬rm, also trading at \$150, earned only a constant \$12 forever,
its constant growth component would only be worth \$120,
\$12
\$150 = + = \$120 + ?
?
10%
(10.10)
E
= + PVGO .
P
E (Ė)
r

Therefore, this ļ¬rmā™s āsteady componentā is worth \$120, and its growth opportunities must be
worth PVGO = \$30. Taking this further, we would say that \$30/\$150 = 20% of the ļ¬rmā™s value
is due to future growth opportunities above and beyond a steady business.
Decline: Finally, if the third ļ¬rm were expected to earn a constant \$15 forever, it should have
been worth \$150 today. To justify its market value of \$150, you must believe that it will have
negative growth in the future,
\$20
\$150 = + = \$200 + ?
?
10%
(10.11)
E
= + PVGO ,
P
E (Ė)
r

speciļ¬cally, a subtractive part worth PVGO = ā’\$50. This ļ¬rm would not maintain a steady
business.

Table 10.1. Various E/P Ratios in Early November 2004

E (Ė) E (Ė)
r r
P/E PVGO/P PEG P/E PVGO/P PEG
Google 50 10% 80% 2.2 Coca Cola 20 6% 20% 2
Pixar 45 8% 72% 2 Exxon 15 7% 5% 2
Cisco 20 12% 60% 1.4 Procter&Gamble 19 5% 0% 1.8
PepsiCo 20 10% 50% 2 Altria (P.Morris) 12 6% ā“40% 1.3
Microsoft 21 8% 40% 2 GM 8 9% ā“40% 1.2
Home Depot 17 9% 35% 1.3 U.S. Steel 6 11% ā“50% 0.5
Boeing 20 7% 30% 2 Ford Motor 7 9% ā“60% 1.2
Wal-Mart 21 7% 30% 1.5 RJR Nabisco 10 6% ā“65% 1.5

All inputs are from Yahoo!Finance. No attempt has been made to adjust for debt ratio. The ratio PVGO/P = 1 ā’
1/[E (Ė)Ā·P/E ratio]. P/E ratios are forward-looking. The cost of capital estimate is rough, and computed as 5%+3%Ā·Ī²
r
(except Google, which I made up). The cost of capital is the subject of the next part of the book and comes with a
good deal of uncertainty. Therefore, PVGO/P is intentionally heavily rounded. PEG ratios are quoted directly from
Yahoo!Finance as based on 5-yr expected earnings. It divides the P/E ratios by analystsā™ expected growth rate of
earnings.

Table 10.1 computes the PVGO as a fraction of ļ¬rm value from the ļ¬rmā™s P/E ratio and an
A sample of ļ¬rms.
estimate of the cost of capital (the subject of Part III). Apparently, the market believes that the
future lies with Google (\$44 billion in market cap) and Pixar (\$5 billion), and not with U.S. Steel
(\$5 billion) or Ford Motor (\$25 billion). The table also gives another popular ratio, the PEG
ratio, which divides the P/E ratios by analystsā™ expected growth rate of earnings. It combines
information about E(g) and P/E ratio, thus trying to say something about E(Ė). The idea is that
r
Ė
stocks with lower P/E ratios and higher growth rates have lower PEG-ratiosā”and are perhaps
better buys. (I do not know how well or how poorly this measure works for this purpose.)
ļ¬le=comparables.tex: RP
239
Section 10Ā·2. The Price-Earnings (PE) Ratio.

You can also rearrange Formula 10.9 to get a relationship between a ļ¬rmā™s P/E ratio and its cost The E/P yield is the
interest rate plus the
of capital
normalized present
value of growth
E P 1 PVGO
= + PVGO = +
P . opportunities
ā”
E (Ė) E (Ė)
r E r E
(10.12)
\$12 \$150 1 \$30
\$150 = + = + = 12.5
\$30 ā”
10% \$12 10% \$12

The formula states that a stable company without any growth opportunities (E(g) = 0 ā’ Ė
PVGO = 0) has an earnings-price yield equal to its cost of capital, E(Ė). A growing ļ¬rm (E(g) >
r Ė
0 ā’ PVGO > 0) has an earnings-price yield lower than its cost of capital. And a dying ļ¬rm
(PVGO < 0) has an earnings-price yield higher than its cost of capital.

Empirical Evidence: P/E Ratios and Growth Rates
The P/E ratio theory works nicely on paper, but does it hold water in the real world? The Do high growth ļ¬rms in
the real-world have
implication of the theory is that if you plot long-term expected earnings growth (E(gE )) against
Ė
higher P/E ratios?
E/P, you should get a negative relation.

E E
P= āā’ = E (Ė) ā’ E (gE ) . (10.13)
r
E (Ė) ā’ E (gE )
r P
Ė

Unfortunately, to make the theory operationally useful, you have to make two more assump-
tions. First, you do not know the eternal growth rate: you only know the most recent earnings
(E0 ) and the earnings predicted by analysts for next year (call them Ė+1 ), so you can only com-
E
pute the expected growth rate for one year: E( gE ) = (Ė+1 ā’ E0 )/E0 . You have to make the leap
E
that ļ¬rms with higher short-term growth rates also have higher long-term growth rates, so you
can use the former as a stand-in for the latter. Second, each ļ¬rm may have its own costs of
capital (unequal E(Ė)). If ļ¬rms with high growth rates E(gE )ā™s also have suļ¬ciently high costs
r Ė
of capital E(Ė)ā™s, then you might not even be able to see any relationship between earnings
r
yield and earnings growth. Both of these problems could conceivably scramble any negative
expected relationship between the earnings yield and the growth rate of earnings. Thus, you
need to look at the empirical evidence to determine how practically useful the theory is.
Figure 10.1 plots the predicted next-year earnings-growth rate against the earnings yield (the Some detail information
about the ļ¬gure.
ratio of predicted earnings over todayā™s stock price), for ļ¬rms with market capitalization of
\$50 million or more, as of December 2000. Each dot is one ļ¬rm.
The ļ¬gure shows how ļ¬rms with higher earnings growth rates had lower earnings-yields (higher The evidence supports
the theory: high-growth
price-earnings ratios), just as the theory had predicted. Eyeballing the ļ¬gure, you can see that
ļ¬rms have lower E/P
ļ¬rms that are neither growing nor contracting tend to have an earnings price ratio of, say, about (and thus higher P/E)
8% (P/E ā 12), ļ¬rms growing by 20% tend to have a lower earnings price ratio of, say, about 5% ratios.
(P/E ā 20), and ļ¬rms growing by about 40% tend to have an even lower earnings price ratio of,
say, about 2.5% (P/E ā 40).
If you had been hired in December 2000 to assess the value of a privately held ļ¬rm for which Using the ļ¬gure to
estimate a
you only knew the earnings, Figure 10.1 would have been very useful. For example, if this
comparables-based ļ¬rm
ļ¬rm had earnings of \$10 million, and was expected to grow them to \$12 million by December value, as of December
2001, the ļ¬gure would have indicated that this 20% earnings growth rate on average would 2000.
have translated into likely E/P yields between about 2% and 10%, with 5% being perhaps the
best number. Therefore, reasonable value estimates for this company might have been some-
where between 50 Ā· \$12 million ā \$600 million and 10 Ā· \$12 million ā \$120 million, with
20 Ā· \$12 million ā \$240 million being a decent average estimate.
Unfortunately, you cannot use the December 2000 ļ¬gure to assess appropriate P/E ratios today. The ļ¬gure will change,
so you must use a
The reason is that during economic booms, earnings growth is high, and, although P/E ratios
current equivalent for
are high, too, they do not seem high enough; after all, such earnings growth is unsustainable. valuation.
During recessions, earnings growth can be negative. But P/E ratios remain relatively too high,
because investors expect that earnings-growth will eventually improve again. For example, in
December 2000, corporate earnings growth was running at an average rate of +40%, and there-
fore unsustainable. Naturally, if such an earnings growth rate could be sustained forever, the
ļ¬le=comparables.tex: LP
240 Chapter 10. Valuation From Comparables.

Figure 10.1. Relation between 1-Year Predicted Earnings-Growth Rates and 1-Year Predicted
Earnings-Price Yields, as of December 2000.

1ā’Yearā’Predicted Earnings Price Ratio (E/P)

0.4
0.2
0.0
ā’0.2

0.0 0.1 0.2 0.3 0.4 0.5 0.6

1ā’Yearā’Predicted Earnings Growth (gĖ™E)

Analystsā™ consensus earnings forecasts were obtained from I/B/E/S.

Digging Deeper: To reduce the inļ¬‚uence of some extremely unusual ļ¬rms, a few ļ¬rms with E/P yields in excess
of 100% were truncated (āwinsorizedā) at 100%. More importantly, earnings growth (E (gE ), the independent
Ė
variable on the x-axis) was truncated at ā’30% and +50%, again to reduce the inļ¬‚uence of extreme observations.
Firms with such negative growth rates and such high positive growth rates are suļ¬ciently unusual that pretending
that they had just ā’30% or +50% growth is reasonable. Indeed, it is particularly unreasonable to pretend that
negative earnings growth can last forever, so you would not expect a good relationship between price-earnings
ratios and earnings growth for contracting ļ¬rms. Finally, ļ¬rms with lagged negative earnings (not earnings
growth rates!) had to be ignored, too, because it is impossible to compute a meaningful earnings growth rate
when the denominator is negative.

price over todayā™s earnings ratio would have to be truly astronomical! By December 2001, i.e.,
post 9/11, the opposite had happened: the typical current earnings growth rate had dropped
to ā’40%, and yet ļ¬rms were still worth something! So, it is an important point that the rela-
tion between earnings growth and earnings-price yields, using only one-year-ahead earnings
forecasts, does not hold over time. Do not use Figure 10.1 to estimate P/E ratios from earnings
growth today! Instead, if you need to value a ļ¬rm based on its current growth rates today,
recreate the graph and implied E/P yield with data as of today.

P/E Ratios for the S&P500
Let us now apply our insights about P/E ratios to the overall stock market, as exempliļ¬ed
Use the theory on the
S&P500. by a portfolio consisting of all stocks in the S&P 500. What is the relationship between the
expected rate of return in the stock market, ļ¬rmsā™ earnings growths, and the market P/E ratio?
The same intuition should applyā”when the market expects corporate earnings growth to be
higher, it should cause a higher P/E ratio.
ļ¬le=comparables.tex: RP
241
Section 10Ā·2. The Price-Earnings (PE) Ratio.

Figure 10.2. The P/E Ratio of the S&P 500

40
30
P/E Ratio

20
10
0

1880 1900 1920 1940 1960 1980 2000
This is the history of the price-earnings ratio for the S&P500. (The S&P500 index contains the 500 largest publicly
traded ļ¬rms in the United States.) It peaked in March 2002 at a value of 46. (The data are from Shillerā™s website.)
Year

Figure 10.2 graphs the marketā™s P/E ratio. The theory tells us that the growth rate of earnings The popular claim in the
late 1990s: expect 30%
is positively related to the P/E ratio,
from stock market
investments.
E 1
P= ā’ E (g) = E (ĖM ) ā’ (10.14)
r .
Ė
E (ĖM ) ā’ E (g)
r Ė P/E ratio

(I admit to being casual in omitting time subscripts and the expectation on earnings.) Most
ļ¬nance professors believe that the expected rate of return on the stock market, E(ĖM ), has not
r
changed dramatically in the last decades. However, in 1999, bullish analysts proclaimed in the
popular press that the expected rate of return in the stock market would be at least 10% per
year in real terms (inļ¬‚ation-adjusted) foreverā”after all, the recent experience from the last few
years in the nineties had investors earn rates of return closer to 30% than to 10%. It was the
era of the āNew Economy,ā where old formulas (and ļ¬nance professors) no longer applied.
However, the theory should have told you immediately that something was odd. The stock The popular claim in the
late 1990s: bizarre.
marketā™s P/E ratio had reached 30 in 2000. Therefore, such optimists must have believed in
earnings growth E(gE ) = E(Ė) ā’ E/P = 10% ā’ 1/30 ā 6.7% per year, in real terms and forever.
r
Ė
This is a large number, and should have been tough to swallow, because forecasts of GDP growth
(based on its historical long-run average) put its expected real growth rate at only about 2.0ā“
2.5% per year. Either the expected earnings growth was wildly too high, or the expected rate of
return on the market was wildly too high. (Put diļ¬erently, at the historical 4.5% real growth rate,
the P/E ratio of 30 should have only implied an expected real rate of return in the stock market
of only E(ĖM ) ā 2.5%+1/44 ā 5.8% per year.) This argumentā”that either the stock marketā™s P/E
r
multiple or popular stock return expectations were out of line with reasonable earnings growth
estimates (and thus that the stock market was overvalued)ā”was most forcefully advanced in
Robert Shillerā™s bestseller Irrational Exuberance. It was published just before the stock market
peaked in 2000.
We can use our theory to sharpen our insights. Most importantly, let us now be more reasonable A more sensible
approach.
about the expected rate of return on the stock market. In fact, long-run history suggests that
the stock market outperformed the long-term bond by a number of āonlyā 3% to 5% per annum.
Let us presume this number is a constant 4%, where the long-term Treasury-bond is called r20 .
A similar number is often called the equity premium and will be discussed in great detail in
ļ¬le=comparables.tex: LP
242 Chapter 10. Valuation From Comparables.

the next part of our book. Here, we call it the expected rate of return on the market above the
risk-free long-term Treasury bond. Then,

1 1
E (g) = E (ĖM ) ā’ ā’ E (g) ā’ [E (ĖM ) ā’ r20 ] = r20 ā’
r r ,
Ė Ė (10.15)
P/E ratio P/E ratio
around 4%

This gives you the expected growth rate of earnings (net of something like the āequity premiumā)
that is required to justify the marketā™s price-earnings ratio. It is the diļ¬erence between the
expected rate of return and the earnings-yield. More intuitively, when the expected rate of
return on the stock market is high relative to the earnings yield, then the market believes
the expected future earnings will be much higher than they currently are. When the current
earnings yield is high relative to the expected rate of return, then the market believes the
expected future earnings will not have to be much higher than todayā™s earnings. The upper
graph in Figure 10.3 plots these two inputs, and inļ¬‚ation. The lower graph in Figure 10.3 plots
the diļ¬erence, which is the implied growth rate above the equity premium. When this number is
exceedingly high, the theory says that we should scratch our heads and wonder if the market is
overvalued. When this number is exceedingly low, the theory says we should scratch our heads
and wonder if the market is undervalued. One ļ¬nal wrinkle is that because the growth rate
of earnings is a nominal quantity, we can also plot an inļ¬‚ation-adjusted version. Figure 10.3
shows that, with a constant expected rate of return, it no longer appears as if 2000 (or 2002) was
so extreme, after all. In fact, neither the real nor the nominal growth rate of earnings necessary
to sustain the stock market valuation (P/E ratio) has changed much from 1982 to 2005ā”and
although it seems slightly high, by historical standards, the implied future real growth rate of
earnings necessary to sustain the stock market at the current P/E level seems outright ordinary.
ļ¬le=comparables.tex: RP
243
Section 10Ā·2. The Price-Earnings (PE) Ratio.

Figure 10.3. The S&P500 Earnings-Yield, Long-Term Treasury Rate, and Inļ¬‚ation

20
15

Earnings Yield
10

=1/(P/E)
Percent

5

LT Rate
0
ā’5

Inflation
ā’10

1880 1900 1920 1940 1960 1980 2000

Year
5
Percent

ā’5

Nominal E(g)
ā’20

1880 1900 1920 1940 1960 1980 2000

Year
Percent

0
ā’30

Real E(g)

1880 1900 1920 1940 1960 1980 2000

Year

The upper ļ¬gure plots the inverted price-earnings ratio (the earnings yield), as well as the long-term interest rate and
inļ¬‚ation. The lower ļ¬gures plots the nominal and real diļ¬erences between r20 and the earnings yield. According
to the theory, this represents the expected growth rate of earnings, above the equity premium. The bottom ļ¬gure
shows that since the mid 1980s the stock market P/E ratio (level) has been sustainable at a modestly high, but not at
all unusual or extreme required expected inļ¬‚ation-adjusted earnings growth rate. This contrasts with 1918, 1945,
1951, 1975, and 1979, in which the market was very pessimistic; and 1921 and 1932 when the market was very
optimistic.
The data are from Robert Shillerā™s website.
ļ¬le=comparables.tex: LP
244 Chapter 10. Valuation From Comparables.

10Ā·2.C. P/E Ratio Application Example: Valuing Beverage Companies

Table 10.2. Financial Newspaper Printed Financials, from May 31, 2002

YTD 52-Week YLD VOL NET
P/E
%CHG HI LO STOCK (SYM) DIV % 100s CLOSE CHG
13.5 31.91 23.55 Cadbury Schweppes (CSG) .70g 2.4 21 475 29.20 -0.20
15.4 57.91 42.59 Coca Cola (KO) .80 1.5 35 47,565 54.39 0.24
4.6 53.50 43.08 PepsiCo (PEP) .60f 1.2 34 26,539 50.93 0.00

The description of the table states that the P/E ratio is based on the closing price and on diluted per-share earnings ignoring
extraordinary items, as available, for the most recent four quarters. Fully diluted earnings means that all common stock equivalents
(convertible bonds, preferred stock, warrants, and rights) have been included.

Let us now apply our newly found comparables valuation technique. Table 10.2 reproduces
You now apply the
P/E ratio valuation the stock price report from May 31, 2002, in the same format as that of a prominent ļ¬nancial
method to PepsiCo. You
newspaper. (Actually, the most convenient source of ļ¬nancial information on individual stocks
can use common
may no longer be the newspaper. The World-Wide-Web, such as Yahoo!Finance makes it even
newspaper information.
easier to ļ¬nd more comprehensive ļ¬nancial information.) From Table 10.2, you can see that the
price-earnings ratio for Coca Cola was 35, for PepsiCo 34, and for Cadbury Schweppes 21. The
(dayā™s closing) price-per-share for Coca Cola was \$54.39, for PepsiCo \$50.93, and for Cadbury
Schweppes \$29.20. Using this information, you can back out Coca Colaā™s earnings-per-share as

\$54.39 \$54.39
= 35 ā’ EKO = ā \$1.55 . (10.16)
EKO 35

We now proceed with the valuation-by-comparables method, once again using PepsiCo as our
Task: Value PepsiCo now.
guinea pig. Pretend that you do not know PepsiCoā™s value, but you do know PepsiCoā™s internal
ļ¬nancials (earnings). Your task is to value the shares of PepsiCo in light of the value of shares
of Coca Cola. If the P/E comparables valuation method works, you can then check whether your
estimated value roughly ļ¬ts the true value of PepsiCo.

So, can you really use Coca Cola as a comparable company for PepsiCo? To do so requires
Applying Coca Colaā™s
P/E ratio to value
making the heroic assumption that Coca Cola is a company quite similar to PepsiCo in terms of
PepsiCo, given PepsiCoā™s
earnings. ratios and earnings. (The choice of comparable is discussed in general below.) We are indeed
heroes (and heroines), so we assume that Coca Colaā™s P/E ratio of 35 can be applied to PepsiCo
earnings of \$50.93/34 ā \$1.50 per share,
PPEP
= ā’ PPEP = 35 Ā· \$1.50 = \$52.50
35
\$1.50
(10.17)
PPEP PKO
= .
EPEP EKO

The valuation-by-comparables method suggests that PepsiCo should be worth \$52.50. This is
In PepsiCoā™s case,
valuation-by- higher than the \$50.93 that PepsiCo shares are currently trading for, but a diļ¬erence of \$2
comparables against
(about 5%) is well within the range of typical valuation uncertainty. So, here the method of
Coca Cola seems to work
comparables works quite well in predicting a correct market value for PepsiCo.
well.

Now, let us assume that you instead owned Cadbury Schweppes (CSG), that it was not yet
In Cadbury Schweppesā™s
case, valuation-by-
publicly traded, and that it had just earned \$1.39 per share. (This can be inferred from CSGā™s
comparables against
either PepsiCo or Coca
Cola does not work well.
ļ¬le=comparables.tex: RP
245
Section 10Ā·3. Problems With P/E Ratios.

P/E ratio of 21 and closing price of \$29.20.) Applying the Coca Cola P/E ratio of 35 to Cadbury
Schweppesā™ earnings, you would expect CSG to trade for
PCSG
= ā’ PCSG = 35 Ā· \$1.39 = \$48.67 .
35
\$1.39
(10.18)
PCSG PKO
= ,
ECSG EKO

You would be far oļ¬! The value of Cadbury Schweppes shares in the public markets is \$29.20
per share, not \$48.67 per share. In eļ¬ect, if you believe that the ļ¬nancial market oļ¬ers you the
correct price, then the method of comparables has not worked well in predicting the correct
market value for shares in Cadbury Schweppes. Our next section will be all about why and
when P/E Ratios can break down.
Solve Now!
Q 10.2 Which is likely to have a higher price-earnings ratio: Microsoft or ConAgra?

Q 10.3 A ļ¬rm has earnings of \$230 this year, grows by about 6% each year, and has a price-
earnings ratio of 40. What would its price-earnings ratio be if it could grow by 7% each year
instead? How much would its value increase?

Q 10.4 A ļ¬rm has earnings of \$200, and a price-earnings ratio of 20. What is its implied growth
rate, if its cost of capital is about 10%?

10Ā·3. Problems With P/E Ratios

So, what went wrong in the Cadbury Schweppes valuation? There are basically two possible If comparables are
dissimilar, either the
explanations. The ļ¬rst explanation is that the stock market valuationsā”either of CSG or KO,
market is wrong or the
or bothā”are just plain wrong. In this case, it makes little sense to use the methods of compa- comparable is wrong.
rables. But this scenario is unlikely. If the market values were systematically wrong, you could
presumably easily get rich if you purchased undervalued ļ¬rms. If it is not obvious, Chapter 19
will explain why getting rich is not easyā”and which is why only about half of all investors beat
the marketā”so we will assume that misvaluation is not the principal reason. The second expla-
nation is that your assumption that the two ļ¬rms were basically alike is incorrect. This is the
more likely cause. There is a long litany of reasons why comparables are not really comparable,
and why the technique failed you in valuing Cadbury Schweppes. Here is an outline of possible
problems, on which the remainder of this chapter focuses:

Problems in Selecting Comparable Firms Comparing businesses is almost always problem-
atic. Every ļ¬rm is a unique combination of many diļ¬erent projects. Cadbury Schweppes
owns Dr. Pepper, 7-Up, A&W Root Beer, Canada Dry, Hawaiian Punch, Snapple, Mottā™s
Apple products, Clamato juice, plus some confectionary brands. This may not be compa-
rable to Coca Cola, which owns Coca Cola Bottling, Minute Maid, Odwalla, and some other
drink companies. Each of these businesses has its own proļ¬tability and each may deserve
its own P/E ratio.
Even for the main business, as any soda connoisseur knows, Pepsi Cola and Coca Cola
are not perfect substitutes. Diļ¬erent consumer tastes may cause diļ¬erent growth rates,
especially in diļ¬erent countries.
Selection of comparable ļ¬rms will be discussed in Subsection 10Ā·3.A. P/E ratio aggregation
issues with multi-division ļ¬rms will be covered in Subsection 10Ā·3.B. The worst kind of
averaging P/E ratios will be examined in Subsection 10Ā·3.C.
Problems in Comparing Accounting Numbers Not all accounting statements are prepared the
same way. Here are a few possible discrepancies in regard to the Cadbury Schweppes
valuation:
ļ¬le=comparables.tex: LP
246 Chapter 10. Valuation From Comparables.

ā¢ Maybe as a British ļ¬rm, Cadbury Schweppes uses altogether diļ¬erent accounting
methods.
ā¢ Maybe Cadbury Schweppes has just had an unusual year, or a year in which it plowed
most of its cash into advertising, thereby causing unusually lower earnings for now
and much higher earnings in the future.
ā¢ If you did not use earnings from the most recent four quarters, but instead forecast
earnings over the next four quarters, maybe the numbers would then be more compa-
rable. How to adjust better for diļ¬erences in the timing of reports will be the subject
of Subsection 10Ā·3.D.
ā¢ Maybe Cadbury Schweppes and Coca Cola have diļ¬erent debt ratios. The inļ¬‚uence
of debt on P/E ratios will be explained in Subsection 10Ā·3.E.
ā¢ Maybe extraordinary items (excluded from this measure of earnings) should be in-
cluded to make these ļ¬rms more comparable. The use of other ļ¬nancial ratios will
be discussed in Section 10Ā·4.

10Ā·3.A. Selection of Comparison Firms

The single biggest problem with comparables may be the selection of appropriately comparable
Finding comparables:
general criteria for ļ¬rms. Say, you own a little soda producer, the Your Beverage Corporation (YBC), with earnings
evaluating similarity.
of \$10 million. You want to select public ļ¬rms to use as your comparables from the universe
of ļ¬rms. Usually, this means publicly traded companies. So, which of the 10,000 or so publicly
traded companies are most comparable to your ļ¬rm (or project)? Are ļ¬rms more similar if
they are similar in assets, similar in their business products and services, similar in their geo-
graphical coverage, similar in their age, similar in their size and scale, etc.? Do they have to be
similar in all respects? If so, chances are that not a single of the 10,000 ļ¬rms will qualify!
Let us assume that after extensive research and much agonizing, you have identiļ¬ed the (same)
Which ļ¬rm is the single
best comparable? three companies: KO, PEP, and CSG. Which one is most similar? You know that depending on
which ļ¬rm you select, your valuation could be \$250 million (if Cadbury Schweppes, unlevered,
was most similar), \$410 million (if PepsiCo was most similar), or \$500 million (if Coca Cola was
most similar). Which shall it be?
Selecting comparables depends both on the judgment and on the motives of the analyst. In
Different conclusions
about the value of the the YBC case, one analyst may consider all three ļ¬rms (KO, PEP, and CSG) to be similar, but
same ļ¬rm: Analyst
CSG to be most similar because it is the smallest comparison ļ¬rm. She may determine a good
errors and biases can
P/E ratio would be 30. Another analyst might consider Coca Cola and Pepsi-Co to be better
create wide variations in
valuations.
comparables, because they tend to serve the same market as YBC. He may determine a good
P/E ratio would be 40. The owner of YBC may want to sell out and try to ļ¬nd a buyer willing to
pay as much as possible, so she might claim Coca Cola to be the only true comparable, leading
to a P/E ratio of 50. The potential buyer of YBC may instead claim Cadbury Schweppes to be the
only comparable, and in fact attribute an extra discount to CSG: after all, YBC is a lot smaller
than CSG, and the buyer may feel that YBC deserves only a P/E ratio of 10. There is no deļ¬nitive
right or wrong choice.
Another choice may be not to select either the P/E ratio of 10 or the P/E ratio of 45, but to āsplit
Incorrect, but practical
averaging. Letā™s pray! the diļ¬erence.ā A reasonable P/E ratio that is better than either 10 or 45 may be 30. This might
mean valuations of around \$300 to \$400 million. Unfortunately, though this may be the best
solution, it is not a good solution. The next two section shows you why averaging P/E ratios is
really not a good procedure.
ļ¬le=comparables.tex: RP
247
Section 10Ā·3. Problems With P/E Ratios.

10Ā·3.B. (Non-) Aggregation of Comparables

Companies are collections of many projects. Is the P/E ratio of the company the same as the Can you aggregate (take
averages of) P/E ratios?
weighted average P/E ratio of its subsidiaries, so that you can seamlessly work with either
No!
individual subsidiary P/E ratios or with overall company P/E ratios? Unfortunately, the answer
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