1 FIN 2808, Spring 10 - Tang Chapter 18: Equity Valuation Fin2808: Investments Spring, 2010 Dragon Tang Lectures 13 & 14 Equity Valuation Models March

1FIN 2808, Spring 10 - TangChapter 18: Equity Valuation

Fin2808: Investments

Spring, 2010Dragon Tang

Fin2808: Investments

Spring, 2010Dragon TangLectures 13 & 14

Equity Valuation ModelsMarch 9&11 ， 2010

Readings: Chapter 18Practice Problem Sets: 1,5,7,14, 16,17


How to make money in stocks?How to make money in stocks?


How to make money in stocks?How to make money in stocks?

• Capital gains: buy low/sell high

– Growth companies

• Dividend yields: income stream

– Matured (value) companies


Equity ValuationEquity Valuation

Objectives:

• Calculate the intrinsic value of a firm using either a constant growth or multistage dividend discount model.

• Calculate the intrinsic value of a stock using a dividend discount model in conjunction with a price/earnings ratio.

• Assess the growth prospects of a firm from it P/E ratio.


Balance Sheet Valuation MethodsBalance Sheet Valuation Methods

• Book Value

• Liquidation Value

• Replacement Cost

costt replacemen

pricemarket Q sTobin'


Expected Holding Period ReturnExpected Holding Period Return

yield

gain/losscapital

expected

yield

dividend

expected

P

PPE

P

DE

P

PPEDEE(HPR)

0

01

0

1

0

011

• If E(HPR) > Required Rate of Return(RRR), the stock is a good deal.• RRR is from a pricing model, e.g. CAPM:

•In market equilibrium, E(HPR) = RRR.

))(()( fmXYZfXYZ rrErrE


Intrinsic Value versus Market PriceIntrinsic Value versus Market Price

•V0 (intrinsic value) > P0 (market price) buy

•V0 (intrinsic value) < P0 (market price) sell or sell short

•In market equilibrium, V0 = P0

•k is the market capitalization rate which equates V0 and P0

•If V0 P0, then EMH implies the estimate of k is wrong

Intrinsic value --The present value of a firm’s expected future net cash flows discounted by the required rate of return.

k

PEDEV

1

)()( 110


Dividend Discount ModelsDividend Discount Models

One Period Case:

k

PEDEV

1

)()( 110

Multi-period Case:

HHH

k

PD

k

D

k

DV

1

...11 2

210

Where D1,…, DH and PH are expected values


Dividend Discount ModelsDividend Discount ModelsExample: Whitewater Rapids Company is expected to have dividends grow at a rate of 12% for the next three years. In three years, the price of the stock is expected to be $ 74.46. If Whitewater just paid a dividend of $2.00 and its level of risk requires a discount rate of 10%, what is the intrinsic value of Whitewater stock?


Dividend Discount ModelsDividend Discount Models

...

111 33

221

0

k

D

k

D

k

DV

Dividend discount model (infinite horizon):


Constant Growth DDM (Gordon’s Model)

Constant Growth DDM (Gordon’s Model)

kg

gk

D

gk

gDV

, 1 10

0

...1

1

1

1

1

13

30

2

200

0

k

gD

k

gD

k

gDV


Constant Growth DDMConstant Growth DDMExample: Whitewater Rapids Company is expected to have dividends grow at a constant rate of 6% for the foreseeable future. If Whitewater just paid a dividend of $2.81 and its level of risk requires a discount rate of 10%, what is the intrinsic value of Whitewater stock?


Market Capitalization RateMarket Capitalization Rate

If V0 = P0 :

VD

k g01

kD

Pg 1

0Dividend

YieldCapital

Gains Yield

Gordon’s Model:

If g = 0: k

D

k

D

gk

gDV 100

0 0

011

Perpetuity


Implications of this ModelImplications of this Model

• If D1 increases, then V0 increases.

• If k decreases, then V0 increases.

• If g increases, then V0 increases.

• If D1 increases X%, then V0 will

increase X%.• g = the capital gains yield

VD

k g01


Dividend Payout Ratioand

Plowback Ratio

Dividend Payout Ratioand

Plowback Ratio

• Dividend Payout Ratio: Percentage of earnings paid out as dividends

• Plowback (or Earning Retention) Ratio:

Fraction of earnings retained and reinvested in the firm


Stock Prices and Investment Opportunities


• If a firm retains earnings and reinvest them in a profitable investment opportunity, dividend may grow “faster”.

• If a firm pays out all dividends nothing gets re-invested, nothing growths.


Figure 12.1 Dividend Growth for Two Earnings Reinvestment

Policies

Figure 12.1 Dividend Growth for Two Earnings Reinvestment

Policies


Plowback Ratio and GrowthPlowback Ratio and Growth

g b ROE

Where:

ROE = Return on Equityb = Plowback Ratio (or Earning Retention Ratio)




Present valueno-growth

(b=0 or ROE=k)

Present value of growth OpportunitiesPVGO > 0 if ROE>kPVGO <0 if ROE<k

b)k-(ROE

-b)(E

gk

DP

111

0

PVGO 10

k

EP


Estimating GrowthEstimating GrowthExample: Takeover Target has a plowback ratio of 60% and an ROE of 10%. If it expects earnings to be $ 5 per share, what is the present value of Takeover’s growth opportunities if the appropriate capitalization rate is 15%? What is the PVGO?


Life Cycles and the Constant Growth Model

Life Cycles and the Constant Growth Model

Changing growth rates:

temporary high(or low) growth

permanentconstant growth

V

D

k

D

k

D

k

D

k

H

H

H

H01 2

2

1

11 1 1 1

. . . . . .


Changing Growth RateChanging Growth RateExample: Whitewater Rapids Company is expected to have dividends grow at a rate of 12% for the next three years. In three years, the dividends will settle down to a more sustainable growth rate of 6% which is expected to last “forever.” If Whitewater just paid a dividend of $2.00 and its level of risk requires a discount rate of 10%, what is the intrinsic value of Whitewater stock?


Price-Earning (P/E) RatiosPrice-Earning (P/E) Ratios

• Ratio of Stock price to its earnings per share• Useful for firm valuation:

• Problems:– Forecasts of E– Forecasts of P/E

E

PEP


P/E Ratios and GrowthP/E Ratios and Growth

PVGOk

EP 1 0

kEkE

P

11

0 PVGO1

1

If PVGO = 0: PEk0

1


Numerical Example: No GrowthNumerical Example: No Growth

E0 = $2.50 g = 0 k = 12.5%

P0 = D/k = $2.50/.125 = $20.00

P/E = 1/k = 1/.125 = 8


P/E Ratios and ROEP/E Ratios and ROE

bk

b

E

P

ROE

1

1

0

P/E ratio rises with ROE but not necessarily with b

1/k

ROE<k

ROE>k

b

P/E


Numerical Example with GrowthNumerical Example with Growth

b = 60% ROE = 15% (1-b) = 40%

E1 = $2.50 (1 + (.6)(.15)) = $2.73

D1 = $2.73 (1-.6) = $1.09

k = 12.5% g = 9%

P0 = 1.09/(.125-.09) = $31.14

P/E = 31.14/2.73 = 11.4

P/E = (1 - .60) / (.125 - .09) = 11.4


Figure 12-3 P/E Ratio of the S&P 500 Index and

Inflation

Figure 12-3 P/E Ratio of the S&P 500 Index and

Inflation


Caveat with P/E RatiosCaveat with P/E Ratios

• High plowback ratio (b) High Growth Rate (g) (g = ROE*b)

BUT

• High g (if due to high b) High P/E ratio

• Practitioners: high P/E as proxy of high dividend growth (g)


P/E ratio and RiskP/E ratio and Risk

Holding everything equal:

High risk (k), Low P/E.

Why do small-risky firm have high P/E?

gk

b

E

P

1


Pitfalls in P/E AnalysisPitfalls in P/E Analysis

• Earnings are based on accounting data

Current price and current earnings

Future expected earnings is more appropriate

• In P/E formula, E is an expected trend

• In financial pages, E is the actual past period's earnings


Figure 12-6 P/E RatiosFigure 12-6 P/E Ratios


Combining P/E and DDMCombining P/E and DDM

VD

k

D

k

D

k

D P E EPS

k0

1 22

33

441 1 1 1


The Aggregate Stock Market:Earning Multiplier Approach

The Aggregate Stock Market:Earning Multiplier Approach

VPE

E

where

P EE P

and E P is the earnings yield

M

/1


Other Valuation Ratios & Approaches

Other Valuation Ratios & Approaches

• Price-to-book

• Price-to-cash flow

• Price-to-sales

• Present Value of Free Cash Flow


SummarySummary• Valuation approaches:

-Balance sheet values-Present value of expected future dividends

• DDM states that the price of a share of stock is equal to the present value of all future dividends discounted at the appropriate required rate of return

• Constant growth model DDM:

• P/E ratio is an indication of the firm's future growth opportunities

• Models used for the firm can be used to forecast the behavior of the aggregate stock market

gk

DV

1

0

Documents

1 FIN 2808, Spring 10 - Tang Chapter 18: Equity Valuation Fin2808: Investments Spring, 2010 Dragon Tang Lectures 13 & 14 Equity Valuation Models March