1. Accrual Accounting and Valuation: Pricing Earnings
Chapter 6
Accrual Accounting and Valuation: Pricing Earnings

2. Accrual Accounting at Valuation: Pricing Earnings
Chapter 5 showed how to
price book values in the
balance sheet and calculate
intrinsic price-to-book
ratios.
Link to previous chapter
This Chapter
This chapter shows how to
price earnings in the income
statement and calculate
intrinsic price-earnings
ratio
How are
price-earnings
ratios
determined?
How is the firm
valued from
forecasts of
earnings growth?
When should an
investor not
pay for growth?
How do valuation
methods protect
the investor from
paying too much
for earnings
growth?
How does
the analyst
infer the
market’s
forecast of
earnings
growth?
Link to next chapter
Chapter 7 begins the
financial statement analysis
that is necessary to carry
out the price-to-book and price-
earnings valuations discussed
in Chapters 5 and 6
Link to web page
The web page has more
applications of the techniques
in this chapter

3. What You Will Learn From This Chapter
What “abnormal earnings growth” is.
How forecasting abnormal earnings growth yields the intrinsic P/E ratio.
What is meant by a normal P/E ratio.
The difference between ex-dividend earnings growth and cum-dividend earnings growth.
The difference between a Case 1 and Case 2 abnormal earnings growth valuation.
The advantages and disadvantages of using an abnormal earnings growth valuation and how the valuation compares with residual earnings valuation.
How dividends, share issues, and share repurchases affect abnormal earnings growth.
That abnormal earnings growth is equal to the change in residual earnings
How abnormal earnings growth valuation protects the investor from paying too much for earnings growth.
How abnormal earnings growth valuation protects the investor from paying for earnings that are created by accounting methods.
How to use the abnormal earnings growth model in reverse engineering.
What a PEG ratio is.

4. The Concept Behind the P/E Ratio
Price in numerator of P/E is based on expected future earnings
Earnings in denominator is current (or forward) earnings
P/E is thus based on expected growth in earnings:
for trailing P/E, growth from current earnings onwards
for forward P/E, growth from one-year-ahead earnings onwards
Compare with price-to-book:
P/B is based on expected earnings relative to current book value (ROCE)
ROCE is growth in book value
P/B is based on expected growth in book value

5. Beware of Paying Too Much for Earnings Growth
Investment creates growth but does not necessarily
add value
Earnings growth can be created by the accounting
We need a valuation method that protects us from paying too
much for earnings growth

6. Reminder: Residual Earnings Valuation Protects You From Paying Too Much For Earnings
Earnings from new investment is charged with the required return on investment
Residual earnings before new investment: 10% hurdle rate
RE = 12 – (0.10 x 100) = 2 (ROCE = 12%)
Residual earnings after new investment of $20 million earning at 10%
RE = 14 – (0.10 x 120) = 2
No value added from new investment
Creating earnings by accounting methods increases residual earnings but reduces book value. The net effect is zero. See Chapter 5.
A P/E model must also protect you from paying too much for earnings growth.

7. The Prototype Savings Account

8. The Trailing P/E and Forward P/E

9. Cum-Dividend Earnings
For the zero-payout account:
2001
2002
2003
2004
2005
Cum-dividend earnings
5.00
5.25
5.51
5.79
6.08
For the full-payout account:
Earnings in the account
5.00
Dividend 5%
0.25
0.51
0.79
1.08
Cum-dividend earnings
5.25
5.51
5.79
6.08
The two accounts have different (ex-dividend) earnings growth,
but the same cum-dividend earnings growth

10. Normal Earnings
Normal Earnings is earnings growing at the required rate of return:
= 1.05 x 5.00
= 5.25 =

11. Abnormal Earnings Growth (AEG)
Abnormal Earnings Growth is growth over normal earnings growth
AEG = Cum-dividend earnings – Normal earnings
For the Savings account:

12. Lessons from the Savings Account
1. An asset is worth capitalized forward earnings if abnormal earnings growth is expected to be zero.
2. An asset has a normal P/E ratio if abnormal earnings growth is expected to be zero.
3. Earnings comes from two sources:
earnings from the asset
earnings from reinvesting dividends
4. Dividends do not affect cum-dividend earnings
5. Dividend payout does not affect value.

13. A Bad P/E Model
Does not work for a savings account!

14. A Model of the Forward P/E
Value of savings account = Capitalized forward earnings + Extra value
Extra value = 0
Extra value is added if abnormal earnings growth is forecasted
The model:
Value of equity = Capitalized forward earnings + Extra value for abnormal
earnings growth
The intrinsic P/E
is given by dividing through by Earn1

15. Measuring Abnormal Earnings Growth for Equities
Abnormal earnings growtht (AEGt) = Cum-dividend earnt - Normal earnt
= [Earnt +(ρE – 1) dt-1] – ρEEarnt-1
Dell: Required return = 11% Eps 2004 = $1.03
Nike: Required return = 10% Eps 2004 = $3.59
Dell Computer
Nike Inc.
Eps 2005
Dps 2004
Earnings on reinvested dividends
Cum-dividend earnings 2005
Normal earnings: 2004 earnings growing at required return
Dell: 1.03 x 1.11; Nike: 3.59 x 1.10
Abnormal earnings growth (AEG) 2005
$0.00
$1.18
1.18
1.143
$0.037
$0.74
$4.45
0.074
4.524
3.949
$0.575

16. Cum-dividend Earnings Growth Rate
Cum-dividend earnings growth rate (plus one):
Note: This is not

17. Alternative Calculation of AEG
Abnormal earnings growtht = [Gt – ρE] x earningst-1
where
Gt = Cum-dividend earnings growth rate (plus one)
For Nike:
G2005 = 4.524/3.59 = % (a 26.02% growth rate)
AEG2005 = [ – 1.10] x 3.59
= $0.575

18. Applying the Model Forecast one-year-ahead earnings.
Add the present of value (at the end of the year 1) of expected abnormal earnings growth for year two ahead and onwards
Capitalized the total of forward earnings and the value of abnormal earnings growth.

19. Total earnings plus growth
Applying the Model
Cum dividend earnings2
Normal earnings2
Cum dividend earnings3
Normal earnings3
Cum dividend earnings4
Normal earnings4
Year 4 ahead
Year 3 ahead
Year 2 ahead
Abnormal Earnings2
Abnormal Earnings3
Abnormal Earnings4
Forward Earnings1
Year 1 ahead
PV of AEG2
Total earnings plus growth
Current Value
Capitalize
Discount by 
Discount by 2
Discount by 3
Forecasts
PV of AEG3
PV of AEG4 + -

20. Forward P/E Ratios and Subsequent Earnings Growth Rates: S&P 500 Firms

21. Applying the Model: A Simple Example
Forecast for a firm with expected earnings growth of 3 percent per year
(in dollars). Required return is 10% per year.
Residual earnings valuation:
AEG valuation:

22. A Case 1 Valuation: General Electric
Required return is 10%
In this case, abnormal earnings growth is expected to be zero after 2004
Same as residual earnings valuation

23. A Case 2 Valuation: Dell Computer
Required return is 11%
In this case, abnormal earnings growth is expected to grow at a 6.5
percent rate after 2006
Forecast Year
Dps
Eps
Dps reinvested (0.11 × dpst-1)
Cum-dividend earnings
Normal earnings (1.11 × epst-1)
Abnormal earnings growth
Discount rate (1.11t)
Present value of AEG
Total PV of AEG
Continuing value (CV)
PV of CV
Total earnings to be capitalized
Capitalization rate
Value per share
The continuing value calculation:
CV = = 0.873
Present value of CV = = 0.576
Same as residual earnings valuation

24. Converting Analysts’ Forecasts to a Valuation: Rebook International
Price = $ Required return = 10%
Consensus eps forecasts:
2005 $3.43
2006 $3.81
5-year growth rate = 14%
E 2006E 2007E 2008E 2009E
Dps
Eps
Dps reinvested (0.10 x dpst-1)
Cum-dividend earnings
Normal earnings (1.10 x epst-1)
Abnormal earnings growth
Cum-div eps growth rate % % % %
Discount rate (1.10t)
Present value of AEG
Total PV of AEG 0.54
Continuing value (CV)
PV of CV
Total earnings to be capitalized 6.91
Capitalization rate 0.10
Value per share $69.10
The continuing value calculation:
Present value of CV =

25. Abnormal Earnings Growth is Equal to the Change in Residual Earnings
AEG t = [
earn
+ (ρ E –
1)d - 1 ] ρ
By the stocks and flows equation for accounting for the book value of equity (Chapter 2), B
= B 2
+ earn d
, so earn
. Thus,
= earn (ρ )[
1)B
= RE RE
So, the AEG model can be written as:

26. Protection From Earnings Created by Accounting: A Restructuring Charge

27. Abnormal Earnings Growth Analysis

28. Reverse Engineering: S&P 500
S&P 500, January 2004: 1000
Earnings forecasts:
S&P 500 payout ratio = 31%
Required return = 4% + 5% = 9%
Earnings $53.00 $58.20
Dividends (31% payout)
Reinvested dividends at 9%
Cum-dividend earnings $59.679
Normal earnings ($53 x 1.09)
AEG $1.909
With these ingredients, we are ready to reverse engineer:
g = (a 3.9% growth rate)
Compare with GDP growth rate
Forward P/E = 18.87

29. Reverse Engineering Growth Forecasts: Reebok
Price = $41
E 2006E
Dps
Eps
Dps reinvested (0.10 x dpst-1)
Cum-dividend earnings
Normal earnings (1.10 x epst-1)
Abnormal earnings growth
g = 1.0 (no growth expected)
Analysts were forecasting growth!

30. Reverse Engineering Expected Returns: The Simple Example
Market Price = million
The formula is:
A bit ugly, but is works!

31. Implied Earnings Forecasts
Earnings Forecast = Normal earnings forecast + AEG forecast Forecast of earnings from prior year’s dividends
Reebok:
Normal earnings2007 = $4.191
AEG2007= $0.067 (no growth from 2006)
Reinvested dividends2007 = $0.033
The market’s implied eps forecast for 2007:
= $ – 0.033
= $4.225
Implied eps growth rate for 2007 = $4.225/$3.81 = 10.89%

32. The Market’s Eps Growth Path: Reebok
BUY
SELL

33. Building Blocks of an AEG Valuation: Reebok
(1) Value from capitalized forward earnings, about which one is reasonably certain
(2) Value from capitalizing two-year-ahead abnormal earnings growth
(3) Value from forecasts of long-term growth, the most speculative part of the valuation.

34. The “Greenspan” Model
If Earnings Yield is less than 10-year treasury note yield,
stocks are overpriced
In 1998: “irrational exuberance” speech
Treasury yield = 5.60% (P/E = 17.86)
Earnings yield = 4.75% (P/E = 21.05)
A good model?
Different risk for bonds and stocks
 P/E should be higher for bonds (and earnings yields lower)
Stocks deliver AEG, bonds do not
 P/E can be higher for stocks (and earnings yields lower)

35. P/E Ratios and Interest Rates: 1963 – 2003
Median P/E ratios and interest rates (in percentages) on
one-year Treasury bills

36. The PEG Ratio PEG RATIO = P/E 1-year ahead percentage earnings growth
Does it work as a screen?