Lectures 3 and 4Lectures 3 and 4

Multi-period valuation models: Cash Flow and Accrual Based Valuation

Textbook reading:Ch. 4, 5, 6 & 7 from Penman.

Paper:

• Francis J., Olsson P. and Oswald D. (2000). Comparing the Accuracy and Explainability of Dividend, Free Cash Flow, and Abnormal Earnings Equity Value Estimates. Journal of Accounting Research. Vol. 38 (1), pp. 45-70.

• Ohlson J. (1995). Earnings, Book Values, and Dividends in Equity Valuation. Contemporary Accounting Research. Vol. 11, No. 2 (spring), pp.661-687.

• Demirakos E., Strong N., and Walker M. (2010). Does Valuation Model Choice Affect Target Price Accuracy? European Accounting Review. Vol. 19 (1), pp.35-72.

Cash Flow Based Valuation ModelsCash Flow Based Valuation Models

d1 d2 d3 d4 d5Dividend Flow

1 2 3 4 50

TVT

T

d T

Equity

The terminal value, TVT is the price payoff, PT when the share is sold

Valuation issues :The forecast target: dividends, cash flow, earnings?

The time horizon: T = 5, 10, ?

The terminal value

The discount rate

CF1 CF2 CF3 CF4 CF5

A (going concern) firm1 2 3 4 50

T

TVT

The Dividend Discount Model: Targeting DividendsThe Dividend Discount Model: Targeting Dividends

• DDM:

Problems: How far does one project?

• Does

provide a good estimate of VE0?

(i) Dividend policy can be arbitrary and not linked to value added.(ii) The firm can borrow to pay dividends; this does not create value(iii) Think of a firm that “pays no dividends”

• The dividend irrelevancy concept

• The dividend conundrum: Equity value is based on future dividends, but forecasting dividends over finite horizons does not give an indication of this value

• Conclusion: Focus on creation of wealth rather than distribution of wealth.

...)1()1(1 3

32

210

EEE

E

r

D

r

D

r

DV

TE

T

EEE

E

r

D

r

D

r

D

r

DV

)1(...

)1()1(1 33

221

0

Some Math: The Value of a Perpetuity and a Some Math: The Value of a Perpetuity and a Perpetuity with GrowthPerpetuity with Growth

The Value of a PerpetuityA perpetuity is a constant stream that continues without end (annuity). If the future dividends are expected to be a perpetuity, the capitalised value of the dividend stream is:

Value of a perpetual dividend stream =

The Value of a Perpetuity with GrowthIf dividends are forecasted to grow at a constant rate, the capitalised value of the dividend stream adjusted for the growth rate is: Value of a dividend growing

at a constant rate =

E

E

r

DV 1

0

gr

DV

E

E

1

0

Terminal Values for the DDMTerminal Values for the DDM

A. Capitalize expected terminal dividends (in no growth)

B. Capitalize expected terminal dividends with growth

Will it work?

In practice, analysts tend to estimate the TV by applying a multiple to a projected terminal value of a fundamental (e.g., Eps, Bps, FCFE, Sales).

E

TTT r

DPTV 1

gr

DPTV

E

TTT

1

Dividend Discount Model: Dividend Discount Model: Advantages and DisadvantagesAdvantages and Disadvantages

AdvantagesAdvantages• Easy concept: dividends are

what shareholders get, so forecast them

• Predictability: dividends are usually fairly stable in the short run so dividends are easy to forecast (in the short run)

LimitationsLimitations• Relevance: dividends payout is

not related to value, at least in the short run; dividend forecasts ignore the capital gain component of payoffs.

• Forecast horizons: typically requires forecasts for long periods; terminal values for shorter periods are hard to calculate with any reliability

When It Works BestWhen It Works Best• When payout is permanently tied to the value generation in the firm.

For example, when a firm has a fixed payout ratio (dividends/earnings).

Multistage DDM

The assumption of constant g (i.e. Gordon Growth Model) is not realistic for most firms.

More realistic to use 2 or 3 stage models:

• Growth phase – when company enjoys abnormally high growth (dividends may be low or zero)

• Transition phase – earnings etc growth slows – transition to maturity

• Mature phase – company reaches maturity and earns its opportunity cost of capital. g settles at a long-term level

Two-stage DDM

Two versions (both assume constant growth at a mature stage):

1. Abrupt transition between stage 1 and stage 2 growth:

n

t Ln

Ln

st

tS

grr

ggD

r

gDV

1

000 )()1(

)1()1(

)1(

)1(

T

g gS

gL

Two-stage DDM

2. The H-model - assumes that growth declines linearly over time from some initial super-normal rate (gS) to the normal rate (gL)

Where H = half-life in years of the declining-growth period

Some intuition on the H-model: On average, the expected excess growth rate in the supernormal period will be (gS – gL)/2. Through 2H periods, a total excess amount of dividends over the level given by gL of 2HD0(gS – gL)/2 is expected. This term is the H-model upward adjustment to the first dividend term, reflecting the extra expected dividends as growth declines from gS to gL.

For more details on H-model read Fuller and Hsia (1984)

)(

)(

)(

)1( 000

L

LS

L

L

gr

ggHD

gr

gDV

T

gS

gL

Example (H-Model)

During the past 5 years XYZ Plc’s dividends grew at 24% per year, but analysts’ consensus is that the growth rate is to decline linearly over the next 6 years to a final perpetual growth rate of 6%. The current dividend is £1.37 per share and the required rate of return on XYZ’s equity is 10%. Today’s share price is £57.

What is the current fundamental value of XYZ’s share?Is XYZ fairly priced?

Three-stage DDMThree periods: 1. short-term high growth period2. transitional period3. long-term perpetual growth period

)()1(

)()1(

)1(

)1(

1

00

Lk

LSkLkk

tt

tS

grr

ggHDgD

r

gDV

H-model discounted back to present

T

gS

gL

Cash flows for a going concern firmCash flows for a going concern firm

Cash flow from operations (inflows)

Cash investment (outflows)

Free cash flow

Time, t

C1 C2 C3 C4

I1 I2 I3 I4

C1-I1 C2-I2 C3-I3 C4-I4

C5

I5

C5-I5

1 2 43 5

Free cash flow is cash flow from operations that results from investments minus cash used to make investments.

Cash flow from operations (inflows) C1 C2 C3 C4 C5 ---> Cash investment I1 I2 I3 I4 I5 ---> (outflows)

Free cash flow C1 I1 C2 I2 C3 I3 C4 I4 C5 I5 --->

________________________________________________ --->

Time, t 1 2 3 4 5

The Discounted Cash Flow (DCF) ModelThe Discounted Cash Flow (DCF) Model

FOV

D0

F0

E0 VVV

DT

TTTTE V

r

CV

r

IC

r

IC

r

IC

r

ICV 03

3322211

0 )1()1()1()1()1(

The Continuing Value for the DCF ModelThe Continuing Value for the DCF Model

A. Capitalize terminal free cash flow

B. Capitalize terminal free cash flow with growth

Will it work?

r1T1T

T

ICCV

g

ICCV 1T1T

T

r

DCF Valuation: The Coca-Cola CompanyDCF Valuation: The Coca-Cola Company

Cost of capital is 9%; the terminal growth rate of FCF is forecasted at 5% p.a. The value of debt as of the end of 1999 is $4,435. The number of shares outstanding is 2,472.

2000E 2001E 2002E 2003E 2004ECash from operations: 3,657 4,097 4,736 5,457 5,929Cash investments: 947 1,187 1,167 906 618

Free cash flow:

PV of FCF:

Total PV of FCF to 2004:

Continuing value (CV):

Present value of CV:

Enterprise value:

Value of net debt:

Value of equity:

Value per share:

Assuming the current price per share for Coke is $57:

Reverse engineer as follows:

Can Coke maintain this growth rate?

Reverse Engineering: What Forecasts are Implied by the Reverse Engineering: What Forecasts are Implied by the Current Market Price?Current Market Price?

$140,904shares 2,472 x $57 MVo

$4,435-1.5386

g - 0.09g)(1 x 311,5

5386.1

311,5

4116.1

551,4

2950.1

569,3

1881.1

910,2

1.09

2,710140,904$

rate)growth % 6.2 a ( 062.0g

Simple ValuationsSimple Valuations

Simple valuations use very short forecasts horizons, and isolate more speculative, long-term forecasts. Accordingly, we anchor on “what we know” or are relatively sure about.

A simple DCF for Coca-Cola, 2000

DebtNet 11

gr

ICV E

O

315,63$$4,435 05.009.0

710,2

Reverse Engineering a Simple Valuation: Coca-ColaReverse Engineering a Simple Valuation: Coca-Cola

435,4$g-0.09

2,710 140,904$0 MV

Applying the simple model to reverse engineer Coke’s stock price:

%) 7.13 is rate(growth 0713.0g

Steps for a basic DCF ValuationSteps for a basic DCF Valuation

1. Forecast free cash flow to a horizon2. Discount the free cash flow to present value3. Calculate a continuing value at the horizon with an estimated

growth rate4. Discount the continuing value to the present5. Add 2 and 46. Subtract net debt

Will DCF Valuation Always Work?Will DCF Valuation Always Work?

A Firm with Negative Free Cash Flows: General Electric Company

In millions of dollars, except per-share amounts.

2000 2001 2002 2003 2004

Cash from operations 30,009 39,398 34,848 36,102 36,484Cash investments 37,699 40,308 61,227 21,843 38,414Free cash flow (7,690) (910) (26,379) 14,259 (1,930)

Earnings 12,735 13,684 14,118 15,002 16,593Earnings per share (eps) 1.29 1.38 1.42 1.50 1.60Dividends per share (dps) 0.57 0.66 0.73 0.77 0.82

Calculating Free Cash Flows from EarningsCalculating Free Cash Flows from Earnings

It is difficult to forecast free cash flows without forecasting earnings. First forecast earnings and then make adjustments to convert earnings to cash flow from operations. Follow the following steps:

i. Forecast earnings available to common/ordinaryii. Forecast accruals (the difference between earnings and cash flow from

operations in the cash flow statement)iii. Calculate cash flow from operations (Step (i) - Step (ii))iv. Forecast cash investments in operationsv. Calculate forecasted free cash flow, C - I (Step (iii) - Step (iv))

Definition of FCFF:

Free Cash Flow to the Firm (FCFF) = CF available to the firm’s suppliers of capital after all operating expenses (incl. taxes) have been paid and necessary investments in working capital (e.g., stock) and fixed capital (e.g., PPE) have been made.

Definition of FCFE:

Free Cash Flow to the Equity (FCFE) = CF available to ordinary shareholders after all operating expenses, interest, and principal payments have been paid and necessary investments in working and fixed capital have been made.

Popular versions of DCF models: FCFE and FCFF:Popular versions of DCF models: FCFE and FCFF:

Computation of FCFE and FCFF:Computation of FCFE and FCFF:

Starting from the Statement of Cash Flow:

FCFE = CFO – FCInv + Net Borrowing

FCFF= CFO + Int(1-Tax rate)* – FCInv

Starting from the Income statement (add-back method):

FCFF = Net Income+ net noncash charges (NNC)+ Interest expense(1-Tax rate)- Net Investment in fixed capital (FCInv)- Net Investment in working capital (WCInv)

=> FCFF = ER + NCC + Int(1-Tax rate) – FCInv – WCInv=> FCFE = ER + NCC – FCInv – WCInv + Net Borrowing=> FCFE = FCFF - Int(1-Tax rate) + Net Borrowing

*If the after-tax interest expense was taken out of CFO, as with US GAAP, then after-tax interest must be added back to get FCFF.

The NCC which are added back to Net Income include:• depreciation, amortisation, impairment of intangibles• restructuring charges (expense)• losses• deferred taxes

The NCC which are subtracted from the bottom line earnings include:• Restructuring charges (income resulting from reversal)• Gains

Working capital = Current assets (excluding cash and cash equivalents) – Current liabilities (excluding notes payable and the current portion of long-term debt)

Net Investment in working capital (WCInv) == working capital (for year t) – working capital (for

year t-1)

Valuation using the FCFF definition of cash flow:Valuation using the FCFF definition of cash flow:

The FCFF approach yields an estimated value for the entire firm.

the appropriate discount rate is WACC.

Where: 

or, assuming constant growth rate for FCFF:

=> Equity Value (V0) = Firm Value0 – Market value of debt 0

10 )1(t tt

WACC

FCFFValueFirm

ed requitymvdebtmv

equitymvTaxRater

equitymvdebtmv

debtmvWACC

)()(

)()1(

)()(

)(

FCFF

FCFF

gWACC

gFCFFValueFirm

)1(0

0

Valuation using FCFE definition of cash flow:Valuation using FCFE definition of cash flow:

The FCFF approach yields an estimated intrinsic value for the firm’s ordinary equity. => the appropriate discount rate is the cost of equity capital.

=>  

or, assuming constant growth rate for FCFF,

Note that growth rate of FCFF and the growth rate of FCFE may not be the same!

10 )1(t tt

r

FCFEValueEquity

FCFE

FCFE

gr

gFCFEValueEquity

)1(0

0

FCFF vs. FCFE in valuation

• FCFE may be more direct and simpler to use (than FCFF) if the company’s capital structure is relatively stable

• FCFF is more preferable in two cases:A levered company with negative FCFEA levered company with a changing capital structure (FCFF

growth might reflect fundamentals more clearly than FCFE growth, which reflects fluctuating amounts of net borrowings). Also, WACC is less sensitive to changes in leverage than r.

DCF Valuation and SpeculationDCF Valuation and Speculation

• Formal valuation aims to reduce our uncertainty about value and to discipline speculation

• The most uncertain (speculative) part of a valuation is the continuing value. So valuation techniques are preferred if they result in a smaller amount of the value attributable to the continuing value

• DCF techniques can result in more than 100% of the valuation in the continuing value

Why Free Cash Flow is not a Value-Added ConceptWhy Free Cash Flow is not a Value-Added Concept

• Cash flow from operations (value added) is reduced by investments (which also add value): investments are treated as value losses

• Value received is not matched against value surrendered to generate value

A firm reduces free cash flow by investing and increases free cash flow by reducing investments:free cash flow is partially a liquidation concept

Note: analysts tend to forecast earnings, not cash flows

Discounted Cash Flow Analysis: AdvantagesDiscounted Cash Flow Analysis: Advantages

AdvantagesAdvantages• Relatively easy concept: cash flows are “real” and easy to think about;

they are not affected by accounting rules• Familiarity: is a straight application of familiar net present value

techniques

When It Works BestWhen It Works Best• When the investment pattern is such as to produce constant free cash

flow or free cash flow growing at a constant rate.• The firm is not dividend paying;• Dividends differ significantly from the firm’s capacity to pay dividends;• Free cash flows align with profitability within a reasonable forecast

period with which the analyst is comfortable; or• The investor takes a control perspective.

Discounted Cash Flow Analysis: DisadvantagesDiscounted Cash Flow Analysis: Disadvantages

Suspect concept: • free cash flow does not measure value added in the short run; value

gained is not matched with value given up.• free cash flow fails to recognize value generated that does not involve

cash flows• investment is treated as a loss of value • free cash flow is partly a liquidation concept; firms increase free cash

flow by cutting back on investments.

Forecast horizons: typically requires forecasts for long periods; terminal values for shorter periods are hard to calculate with any reliability

Validation: it is hard to validate free cash flow forecasts

Not aligned with what people forecast: analysts forecast earnings, not free cash flow; adjusting earnings forecasts to free cash forecasts requires further forecasting of accruals.

Accrual Accounting Based Valuation ModelsAccrual Accounting Based Valuation Models

Project 1:Project 1:

Initial investment (opening book value) $400Required return 10%Forecasted earnings $40

This is a Zero-RE project and Zero NPV project:

DCF Valuation:

400 1.10

0 400 Value

$0 400) x (0.10 - 40

)investment Initialreturn x required(earningsforecast

year for the earnings Residual

40010.1

440V

Project 2:Project 2:

Investment $400Required return 10%Earnings forecast $ 48

Residual earnings = 48 – (0.1 x 400) = 8

Project Value = 400 + [8/1.1] = 407.27

=> Value = Book Value + Present Value of Residual Earnings

Price-to-Book (P/B ratio) = (BV)/(BV) + (PV of RE)/(BV) =

= 1 + (PV of RE)/(BV)

The project adds value:

27.407

1.10

448 valueDCF

Lessons from Projects 1 and 2Lessons from Projects 1 and 2

1. An asset is worth a premium or discount to its book value only if the book value is expected to earn non-zero residual earnings.

• A firm with P/B=1 earns an expected rate of return on its book value equal to the required return, i.e. expected residual earnings are zero.

2. Residual earnings techniques recognize that earnings growth does not add value if that growth comes from investment earning at the required return.

3. Even though an asset does not pay dividends, it can be valued from its book value and earnings forecasts.

4. The valuation is unrelated to free cash flows

5. If one forecasts that an asset will earn a return on its book value equal to the required return, it must be worth its book value

A Model for Anchoring Value on Book ValueA Model for Anchoring Value on Book Value

Value of common equity:

Where RE is residual earnings for equity.

Residual Earnings = comprehensive earnings – [required return for equity X beginning-of-period book value]

...)1()1(1 3

32

2100

r

RE

r

RE

r

REBVV E

1* ttt BVrERRE

Derivation of the Equity Valuation Model: One PeriodDerivation of the Equity Valuation Model: One Period

Valuing a one-period payoff equation:

Substitute for the expected dividend

to get

or

)BV(BVERD 0111

r)(1

BVP

r)(1

BV*ERBP 1101

00

r

)r(1

DPP 11

0

)r(1

BVBVP 1011

0

PER

Derivation of the Equity Valuation ModelDerivation of the Equity Valuation Model

Mult-iperiod:Mult-iperiod:Substituting comprehensive earnings and book value for dividends in each period,

OR:

Or extended for the infinite horizon:

TTT

221

00 r)(1

BVP....

)r(1

RE

r)(1

REBVP

TTT

T1-TT

21201

00 r)(1

BVP

r)(1

BV*ER...

r)(1

BV*ER

r)(1

BV*ERBVP

rrr

1t

t00 )r(1

REBVP

t

Relation Between P/B Ratios and Subsequent RERelation Between P/B Ratios and Subsequent RE_____________________________________________________________________________________

Residual Earnings for P/B Years After P/B Groups Are Formed (Year 0) Group P/B _____________________________________________________________

0 1 2 3 4 5 6_____________________________________________________________________________________

1 (High) 6.20 .173 .230 .218 .213 .211 .200 .204 2 3.66 .121 .144 .142 .140 .148 .149 .139 3 2.82 .101 .112 .108 .108 .101 .103 .116 4 2.33 .089 .100 .099 .096 .097 .108 .123 5 2.00 .076 .082 .080 .088 .085 .086 .094 6 1.76 .064 .066 .064 .058 .066 .071 .076 7 1.58 .057 .058 .058 .056 .061 .059 .073 8 1.43 .047 .052 .047 .049 .053 .060 .068 9 1.31 .040 .040 .041 .044 .046 .055 .056 10 1.22 .035 .036 .035 .040 .047 .054 .054 11 1.13 .032 .034 .035 .040 .045 .051 .055 12 1.05 .028 .027 .028 .032 .040 .043 .046 13 .98 .023 .023 .025 .031 .035 .037 .045 14 .94 .018 .019 .025 .029 .035 .037 .039 15 .85 .009 .008 .013 .020 .028 .033 .041 16 .79 -.001 -.001 .006 .015 .023 .024 .024 17 .72 -.011 -.015 -.005 .008 .011 .021 .022 18 .64 -.024 -.024 -.012 -.003 .008 .010 .017 19 .54 -.042 -.044 -.028 -.015 -.007 -.007 -.006 20 (Low) .39 -.068 -.070 -.041 -.028 -.020 -.017 -.014_____________________________________________________________________________________

Residual income is deflated by book value at the beginning of year 0, the year the P/B groups are formed.

Ingredients of the ModelIngredients of the Model

For finite horizon forecasts we need three ingredients, besides the cost of capital:

1. The current book value

2. Forecasts of residual earnings (earnings and book values) to horizon

3. Forecasted premium at the horizon

Component 3 is called the continuing value

As efficient prices equal intrinsic values, then

TT

ET

TT

221

0E0 )r(1

BVV

r)(1

RE.....

)r(1

RE

r)(1

REBV

Alternative Measure of Residual EarningsAlternative Measure of Residual Earnings

Residual earnings can also be expressed as:

Where:

11 ** ttttt BVrROCEBVrERRE

tt

t-1

Comprehensive earnings to commonROCE

Book value

Drivers of Residual EarningsDrivers of Residual Earnings

Two Drivers:

1. ROCE

• If forecasted ROCE equals the required return, then RE will be zero, and V = B

• If forecasted ROCE is greater than the required return, then V > B

• If forecasted ROCE is less than the required return, then V < B

2. Growth in book value (net assets) put in place to earn the ROCE

RE will change with change with ROCE and growth in book value

ROCE and P/B Ratios: S&P 500 FirmsROCE and P/B Ratios: S&P 500 Firms

ROCE on P/B Ratio

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

0 2 4 6 8 10 12 14

P rice to Book Ratio (2001)

Steps in Applying the RIV modelSteps in Applying the RIV model

1. Identify the book value in the most recent balance sheet.2. Forecast earnings and dividends up to a forecast horizon.3. Forecast future book values from current book values and your

forecasts of earnings and dividends.4. Calculate future residual earnings from the forecasts of earnings

and book values.5. Discount the residual earnings to present value. 6. Calculate a continuing value at the forecast horizon.7. Discount the continuing value to the present value.8. Add 1, 5, and 7.

A Simple Demonstration and a Simple ModelA Simple Demonstration and a Simple Model

In millions of dollars. Required return is 10% per year. Fixed dividend payout ratio of 75.7%. RE growth rate is forecast at 3%.

Forecast Year0 1E 2E 3E

4E 5EEarnings 12.00 12.36 12.73

13.11 13.51 13.91Dividends 9.09 9.36 9.64

9.93 10.23 10.53Book value 100.00

What is the value of intrinsic price-to-book ratio (P/B) ?

gr

REBVV E

1

00 ?0 EV

Reverse EngineeringReverse Engineering

Determining the implied growth rate:Suppose the actual market cap. of equity (P0) is $133m:

=> g = 3% i.e. the market is forecasting a growth rate for residual earnings of 3% per year

Determining the implied expected return:

Suppose the actual market cap. of equity (P0) is $147m:

=> RE1 = $12.36 – [r × 100.0] => r = 0.0936 => you expect a 9.36% return from buying the stock at the current market price.

gP

10.0

36.2$100$71.133$0

03.0100$2.147$ 1

0

r

REP

Case1: Residual Earning Valuation with Case1: Residual Earning Valuation with ZeroZero RE after T RE after T

V B PV of RE fE0 0 or T periods

53.495.058.3VE0

Required rate of return is 9% Forecast Year

1999 2000E 2001E 2002E 2003EEps 0.73 0.80 0.71 0.47Dps 0.11 0.24 0.25 0.27Bps 3.58 4.20 4.76 5.22 5.41ROCE 20.4% 19.0% 14.9% 9.0%RE 0.408 0.422 0.282 0.000Discount rate 1.09 1.188 1.295 1.412Present value of RE 0.374 0.355 0.217 0.000Total PV of RE to 2003 0.95 Value per share 4.53

Assuming zero RE after period T (zero premium at T):

Case 2: Residual Earning Valuation with Case 2: Residual Earning Valuation with ConstantConstant RE after T RE after T

Required rate of return is 10% Forecast Year1999 2000E 2001E 2002E 2003E 2004E

Eps 1.29 1.38 1.42 1.50 1.60Dps 0.57 0.66 0.73 0.77 0.82Bps 4.32 5.04 5.76 6.45 7.18 7.96ROCE 29.9% 27.4% 24.7% 23.3% 22.3%RE (10% charge) 0.858 0.876 0.844 0.855

0.882Discount rate (1.10) 1.100 1.210 1.331 1.464

1.611Present value of RE 0.780 0.724 0.634 0.584

0.548Total PV of RE to 2004 3.27Continuing value (CV) 8.82 = [0.882/0.1]Present value of CV 5.48 = [0.882/1.611]Value per share 13.07

Assuming constant RE after period T: 07.1348.527.332.4VE0

Case3: Residual Earning Valuation with Case3: Residual Earning Valuation with GrowingGrowing RE after T RE after T

Required rate of return is 11%Forecast Year2000 2001 2002 2003 2004

2005Eps 0.84 0.48 0.82 1.03 1.18Dps 0.0 0.0 0.0 0.0 0.0Bps 2.06 2.90 3.38 4.20 5.23 6.41ROCE 40.8% 16.6% 2 4.3% 24.5% 22.6%RE 0.613 0.161 0.448 0.568 0.605 Discount rate (1.11)t 1.110 1.232 1.368 1.518 1.685Present value of RE 0.553 0.131 0.328 0.374

0.359Total PV of RE to 2005: 1.75 Continuing value (CV) 14.32Present value of CV 8.50Value per share 12.31

The continuing value (CV) with growth at 6.5%:

Present value of CV =

Value per share: 31.1250.875.106.20

EV

32.14065.011.0

065.1605.0

50.8685.1

32.14

Forecasting Target Prices at the horizonForecasting Target Prices at the horizon

ofRECVB TTT PriceTarget

41.520032003 BV E

73.20 32.14 41.6 200520052005 CVBV E

Case 1 (zero RE after forecast horizon => CV=0):

Case 2 (constant RE after forecast horizon):

Case 3 (growing RE after forecast horizon):

16.78 82.8 96.7 200420042004 CVBV E

Converting an Analyst’s Forecast to a Valuation: Nike Inc.Converting an Analyst’s Forecast to a Valuation: Nike Inc.

Forecasts:2009 $3.902010 $4.45Dividend payout ratio forecast: 23%Five-year Eps growth rate forecast: 13%Long-term RE growth rate: 4% (at GDP growth rate)Required Return = 10%

2008A 2009E 2010E 2011E 2012E 2013E

Eps 3.80 3.90 4.45 5.03 5.68 6.42Dps 0.88 0.90 1.02 1.16 1.31 1.48Bps 15.93 18.93 22.36 26.23 30.60 35.54ROCE 24.5% 23.5% 22.5%

21.7% 21.0%RE (10% charge) 2.307 2.557 2.794 3.057

3.360 Discount rate (1.10)t 1.110 1.210 1.331 1.464 1.611Present value of RE 2.097 2.113 2.099 2.088

2.086Total PV to 2009 10.48Continuing value (CV) 58.24Present value of CV 36.15Value per share 62.56

58.24 04.010.0

04.1360.3

CV

Residual Earnings Model: Pros and ConsResidual Earnings Model: Pros and Cons

AdvantagesAdvantages• Focus on value drivers and profitability of investment and growth in investment

that drive value• Incorporates the financial statements and the value already recognized in the

balance sheet. Forecasts the income statement and balance sheet rather than the cash flow statement

• Uses accrual accounting matches value added to value given up and treats investment as an asset rather than a loss of value

• Versatility: can be used with a wide variety of accounting principles• Aligned with what analysts forecast: analysts forecast earnings• Validation: forecasts of RE can be validated in subsequent audited fin. statements• Predictability: dividends are usually fairly stable in the short run so dividends are

easy to forecast

DisadvantagesDisadvantages• Accounting complexity: requires an understanding of how accrual accounting

works• Suspect accounting: relies on accounting numbers that can be suspect• Forecast horizon: forecast horizons can be shorter than for DCF, but the forecast

horizon does depend on the quality of the accrual accounting