# accrual accounting and valuation: pricing earnings chapter 6

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Accrual Accounting and Accrual Accounting and Valuation: Pricing EarningsValuation: Pricing Earnings

Chapter 6Chapter 6

Accrual Accounting at Valuation: Accrual Accounting at Valuation: Pricing EarningsPricing Earnings

Chapter 5 showed how to price book values in the

balance sheet and calculateintrinsic price-to-book

ratios.

Chapter 7 begins the financial statement analysisthat is necessary to carry

out the price-to-book and price-earnings valuations discussed

in Chapters 5 and 6

This chapter shows how to price earnings in the income

statement and calculateintrinsic price-earnings

ratio

The web page has more applications of the techniques

in this chapter

Link to previous chapter

This Chapter

Link to next chapter

Link to web page

How areprice-earnings

ratios determined?

How doesthe analystinfer themarket’s

forecast ofearnings growth?

How do valuationmethods protectthe investor frompaying too much

for earningsgrowth?

How is the firmvalued fromforecasts of

earnings growth?When should an

investor notpay for growth?

What You Will Learn From This What You Will Learn From This ChapterChapter

• 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.

The Concept Behind the P/E RatioThe 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

Beware of Paying Too Much for Beware of Paying Too Much for Earnings GrowthEarnings 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 toomuch for earnings growth

Reminder: Residual Earnings Valuation Reminder: Residual Earnings Valuation Protects You From Paying Too Much Protects You From Paying Too Much For EarningsFor 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.

The Prototype Savings AccountThe Prototype Savings Account

2000 2001 2002 2003 2004 2005 Earnings withdrawn each year (full payout) Earnings 5 5 5 5 5 Dividends 5 5 5 5 5 Book value 100 100 100 100 100 100 Residual earnings 0 0 0 0 0 Earnings growth rate 0 0 0 0 0 Cum-dividend earnings 5 5.25 5.51 5.79 6.08 Cum-dividend earnings growth rate 5% 5% 5% 5% No withdrawals (zero payout) Earnings 5 5.25 5.51 5.79 6.08 Dividends 0 0 0 0 0 Book value 100 105 110.25 115.76 121.55 127.63 Residual earnings 0 0 0 0 0 Earnings growth rate 5% 5% 5% 5% Cum-dividend earnings 5 5.25 5.51 5.79 6.08 Cum-dividend earnings growth rate 5% 5% 5% 5%

2005.0

1

return required

1 P/E Forward

100$05.0

5$

return required

earnings forward account savings of Value

The Trailing P/E and Forward P/EThe Trailing P/E and Forward P/E

1P/E Trailing NormalP/E Forward Normal

return required

return required 1 P/E Trailing Normal

return required

1 P/E Forward Normal

earnings]current not but price,current reduce [Dividends

Earnings

Dividend Price P/E Trailing

Earnings

Price P/E Forward

0

00

1

0

Cum-Dividend EarningsCum-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 5.00 5.00 5.00 5.00

Dividend reinvested @ 5% 0.25 0.51 0.79 1.08

Cum-dividend earnings 5.00 5.25 5.51 5.79 6.08

(2001) Dividend 0.05 (2002) Earnings (2002) earnings dividend-Cum

The two accounts have different (ex-dividend) earnings growth,but the same cum-dividend earnings growth

Normal EarningsNormal Earnings

Normal Earnings is earnings growing at the required rate of return:

5.25 1 (2003) Earnings Normal

(2001) Earnings 1.05 (2002) Earnings Normal

:account savingsthe For

Earnings Earnings Normal 1tEt

05.

= 1.05 x 5.00= 5.25

= 5.5125

Abnormal Earnings Growth (AEG)Abnormal Earnings Growth (AEG)

Abnormal Earnings Growth is growth over normal earnings growth

AEG = Cum-dividend earnings – Normal earnings

For the Savings account:

05125.55125.52003

025.525.52002

AEG

AEG

Lessons from the Savings AccountLessons 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.

A Bad P/E ModelA Bad P/E Model

Does not work for a savings account!

g-

Earn Value 1

05.1g

A Model of the Forward P/EA 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

34

2321

0 1

1

1 EEEEE

E AEGAEGAEGEarnV

34

232

11

1

EEEE

AEGAEGAEGEarn

The intrinsic P/E

1

E0

Earn

V is given by dividing through by Earn1

Measuring Abnormal Earnings Measuring Abnormal Earnings Growth for EquitiesGrowth for Equities

Abnormal earnings growtht (AEGt) = Cum-dividend earnt - Normal earnt

= [Earnt +(ρE – 1) dt-1] – ρEEarnt-1

Dell: Required return = 11% Eps 2004 = $1.03Nike: 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

$0.00

1.18

1.143

$0.037

$0.74

$4.45

0.074

4.524

3.949

$0.575

Cum-dividend Earnings Growth Cum-dividend Earnings Growth RateRate

Cum-dividend earnings growth rate (plus one):

Note: This is not

1

t

tt Earnings

earningsdividendCumG

1

t

t

earningsdividendCum

earningsdividedCum

Alternative Calculation of AEGAlternative 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 = 1.2602% (a 26.02% growth rate)

AEG2005 = [1.2602 – 1.10] x 3.59

= $0.575

Applying the ModelApplying the Model

1. Forecast one-year-ahead earnings.

2. Add the present of value (at the end of the year 1) of expected abnormal earnings growth for year two ahead and onwards

3. Capitalized the total of forward earnings and the value of abnormal earnings growth.

Applying the ModelApplying the Model

Cum dividend

earnings2

Normal earnings2

Cum dividend

earnings3

Normal earnings3

Cum dividend earnings4

Normal earnings4

Year 4 aheadYear 3 aheadYear 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

+

+

+

+--+

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

Earnings Growth Rate on Forward P/E Ratio

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0 4 8 12 16 20 24 28 32 36 40

Forward P /E Ratio (2000)

Applying the Model: Applying the Model: A Simple ExampleA Simple ExampleForecast for a firm with expected earnings growth of 3 percent per year (in dollars). Required return is 10% per year.

Residual earnings valuation:

71.13303.110.1

36.2100VE

2000

AEG valuation:

71.13303.110.1

071.036.12

10.0

12000

EV

2000 2001 2002 2003 2004 2005

Earnings 12.00 12.36 12.73 13.11 13.51 13.91

Dividends 9.09 9.36 9.64 9.93 10.23 10.53

Book value 100.00 103.00 106.09 109.27 112.55 115.93

RE (0.10) 2.36 2.43 2.50 2.58 2.66

RE growth rate 3% 3% 3% 3% Earnings on reinvested dividends

0.936

0.964

0.993

1.023

Cum-dividend earnings 13.667 14.077 14.499 14.934

Normal earnings

13.596 14.004 14.424 14.857

Abnormal earnings growth 0.071 0.073 0.075 0.077

Earnings growth rate 3% 3% 3% 3%

Cum-dividend earnings growth rate

10.6% 10.6% 10.6% 10.6%

Abnormal earnings growth rate 3% 3% 3%

A Case 1 Valuation: General A Case 1 Valuation: General ElectricElectric

Forecast Year

1999 2000 2001 2002 2003 2004 Dps 0.57 0.66 0.73 0.77 0.82 Eps 1.29 1.38 1.42 1.50 1.60 Dps reinvested at 10% 0.057 0.066 0.073 0.077 Cum-dividend earnings (eps + dps reinvested) 1.437 1.486 1.573 1.677 Normal earnings (1.10 x epst-1) 1.419 1.518 1.562 1.650 Abnormal earnings growth (AEG) 0.018 -0.032 0.011 0.027 Discount rate (1.10t) 1.100 1.210 1.331 1.464 PV of AEG 0.016 -0.026 0.008 0.028 Total PV of AEG 0.017 Total earnings to be capitalized 1.307 Capitalization rate 0.10

Value per share

10.0

307.1

13.07

Required return is 10%In this case, abnormal earnings growth is expected to be zero after 2004

13.07 0.017 1.29 0.10

1 V1999 E

Same as residual earnings valuation

A Case 2 Valuation: Dell ComputerA 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

2000 2001 2002 2003 2004 2005 2006

Dps 0.0 0.0 0.0 0.0 0.0 0.0

Eps 0.84 0.48 0.82 1.03 1.18 1.35

Dps reinvested (0.11 × dpst-1) 0.00 0.00 0.00 0.00 0.00

Cum-dividend earnings 0.48 0.82 1.03 1.18 1.349

Normal earnings (1.11 × epst-1) 0.932 0.533 0.910 1.143 1.310

Abnormal earnings growth -0.452 0.287 0.120 0.037 0.039

Discount rate (1.11t) 1.110 1.232 1.368 1.518

Present value of AEG -0.408 0.233 0.088 0.025

Total PV of AEG -0.062

Continuing value (CV) 0.873

PV of CV 0.576

Total earnings to be capitalized 1.354

Capitalization rate 0.11

Value per share 12.31

The continuing value calculation:

CV = = 0.873

Present value of CV = = 0.576

11.0

354.1

065.111.1

0393.0

5181.1

873.0

31.12576.0062.084.011.0

12000 EV

Same as residual earnings valuation

Converting Analysts’ Forecasts to a Converting Analysts’ Forecasts to a Valuation: Rebook InternationalValuation: Rebook International

Price = $41 Required return = 10%Consensus eps forecasts:

2005 $3.432006 $3.815-year growth rate = 14%

2004 2005E 2006E 2007E 2008E 2009E

Dps 0.30 0.33 0.38 0.43 0.49Eps 3.43 3.81 4.43 4.95 5.65Dps reinvested (0.10 x dpst-1) 0.030 0.033 0.038 0.043Cum-dividend earnings 3.840 4.373 4.988 5.693Normal earnings (1.10 x epst-1) 3.773 4.191 4.774 5.445Abnormal earnings growth 0.067 0.182 0.214 0.248Cum-div eps growth rate 11.95% 14.78% 14.93% 15.00%Discount rate (1.10t) 1.100 1.210 1.331 1.464Present value of AEG 0.061 0.150 0.161 0.169Total PV of AEG 0.54Continuing value (CV) 4.299PV of CV 2.94Total earnings to be capitalized 6.91

Capitalization rate 0.10

Value per share $69.10

The continuing value calculation:

Present value of CV =

10.0

91.6

4.299 04.110.1

1.04 x 248.0 CV

2.94 4641.1

299.4

Abnormal Earnings Growth is Equal Abnormal Earnings Growth is Equal to the Change in Residual Earningsto the Change in Residual Earnings

....

RE

RE

RE Earn

1 V

EEE

2

E

E3

42

310 1

So, the AEG model can be written as:

AEG t = [earn t + (ρE – 1)d t-1] - ρEearn t-1

By the stocks and flows equation for accounting for the book value of equity (Chapter 2),

Bt-1 = B t-2 + earn t-1 – dt-1, so earn t-1 – dt-1 = B t-1 – Bt-2. Thus,

AEG t = earn t – earn t-1 - (ρE – 1)[Bt-1 – Bt-2]

= [earn t - (ρE – 1)B t-1] - [earn t-1 - (ρE – 1)B t-2]

= RE t – RE t-1

]d1)[earn(ρearnearn 1t1tE1tt

Protection From Earnings Created by Protection From Earnings Created by Accounting: A Restructuring ChargeAccounting: A Restructuring Charge

2000 2001 2002 2003 2004 2005 Earnings 4.00 20.36 12.73 13.11 13.51 13.91

Dividends 9.09 9.36 9.64 9.93 10.23 10.54

Book value 92.00 103.00 106.09 109.27 112.55 115.93 Earnings on reinvested dividends

0.936

0.964

0.993

1.023

Cum-dividend earnings 13.667 14.077 14.499 14.934

Normal earnings

22.396 14.004 14.424 14.857

Abnormal earnings growth (8.729) 0.073 0.075 0.077

Abnormal earnings growth rate 3%

3% 3%

71.13310.103.110.1

073.0

10.1

729.836.20

10.0

12000

EV

Advantages Easy to understand: Investors think in terms of future earnings; investors buy earnings. Focuses directly on the most common multiple used, the P/E ratio.

Uses accrual accounting: Embeds the properties of accrual accounting by which revenues are matched with expenses to measure value added from selling products.

Versatility: Can be used under a variety of accounting principles (Chapter 16). Aligned with what people forecast: Analysts forecast earnings and earnings growth. Disadvantages Accounting complexity: Requires an understanding of how accrual accounting works. Concept complexity: Requires an appreciation of the concept of cum-dividend earnings; that is, value is based on earnings to be earned within the firm and from earnings from the reinvestment of dividends. Sensitive to the required return estimate: As the value derives completely from forecasts that are capitalized at the required return, the valuation is sensitive to the estimate used for the required return. Residual earnings valuations derive partly from book value that does not involve a required return. Application to strategy: Does not give an insight into the drivers of earnings growth, particularly balance sheet items, so is not suited to strategy analysis. Suspect accounting: Relies on earnings numbers that can be suspect (Chapter 17). Forecast horizon: Forecast horizons can be shorter than those for DCF analysis and more value is typically recognized in the immediate future. But the forecast horizon does depend on the quality of the accrual accounting (Chapter 16).

Abnormal Earnings Growth Analysis Abnormal Earnings Growth Analysis

Reverse Engineering: S&P 500Reverse Engineering: S&P 500

S&P 500, January 2004: 1000

Earnings forecasts:

2004 53.00

2005 58.20

S&P 500 payout ratio = 31%

Required return = 4% + 5% = 9%

2004 2005

Earnings $53.00 $58.20

Dividends (31% payout) 16.43

Reinvested dividends at 9% 1.479

Cum-dividend earnings $59.679

Normal earnings ($53 x 1.09) 57.770

AEG $1.909

With these ingredients, we are ready to reverse engineer:

g = 1.039 (a 3.9% growth rate)

Compare with GDP growth rate

g - V E

09.1

909.100.53

09.0

110002003

Forward P/E = 18.87

Reverse Engineering Growth Reverse Engineering Growth Forecasts: ReebokForecasts: Reebok

Price = $41

2004 2005E 2006E

Dps 0.30 0.33

Eps 3.43 3.81

Dps reinvested (0.10 x dpst-1) 0.030

Cum-dividend earnings 3.840

Normal earnings (1.10 x epst-1) 3.773

Abnormal earnings growth 0.067

g = 1.0 (no growth expected)

Analysts were forecasting growth!

gV E

- 10.1

067.0 43.3

10.0

1 $41 2004

Reverse Engineering Expected Reverse Engineering Expected Returns: The Simple ExampleReturns: The Simple Example

Market Price = 147.2 million

The formula is:

A bit ugly, but is works!

03.1

36.121

1 22004

AEG million $147.2 V E

9.36 12.73 AEG Set 36.1212

return) expected 9.35% (a 0935.1p

1 x 11

12

0

12

g

Earn

EarnEarn

P

EarnAAp

0

112

1 where

P

dpsgA

Implied Earnings ForecastsImplied 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:

= $4.191 + 0.067 – 0.033= $4.225

Implied eps growth rate for 2007 = $4.225/$3.81 = 10.89%

The Market’s Eps Growth The Market’s Eps Growth Path: ReebokPath: Reebok

11.08%

10.89%

10.72%

10.56%

10.42%10.30%

10.19%

9.75%

10.00%

10.25%

10.50%

10.75%

11.00%

11.25%

11.50%

2006 2007 2008 2009 2010 2011 2012

BUY

SELL

Building Blocks of an AEG Building Blocks of an AEG Valuation: ReebokValuation: Reebok

Current Market Value

forwardearnings

Val

ue P

er S

hare

$41.00$6.70

$34.30

Captalized Forward

Value from Value from Value from

(1) (2) (3)

Earnings

short-term long-term forecasts forecasts

(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.

The “Greenspan” ModelThe “Greenspan” Model

• If Earnings Yield is less than 10-year treasury note yield, stocks are overpriced

• In 1998: “irrational exuberance” speechTreasury 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)

P/E Forward

1

Price

earnings Forward yield Earnings

P/E Ratios and Interest P/E Ratios and Interest Rates: 1963 – 2003Rates: 1963 – 2003

0

2

4

6

8

10

12

14

16

18

20 interest rate P/E ratio

Median P/E ratios and interest rates (in percentages) on one-year Treasury bills

The PEG RatioThe PEG Ratio

PEG RATIO = P/E

1-year ahead percentage earnings growth

Does it work as a screen?