Stock Valuation

Economics 71a: Spring 2007

Mayo 11

Malkiel, 5, 6 (136-144), 8

Lecture notes 4.2

Goals

Dividend valuation model “dividend discount model”

Forecasting earnings, dividends, and prices

Ratio valuationsMalkiel’s “Firm foundations”

Dividend Discount ModelConstant Dividends

Evaluate stream of dividendsStock pays the same constant dividend

foreverAssume some “required return” = k

k = RF + RP k = RF + beta(E(Rm)-RF)

Same as perpetuity formula

Dividend Discount ModelConstant Dividends

€ €

P = PV =d

(1+ k)tt=1

∞

∑ =dk

Dividend Discount ModelGrowing Dividends

Evaluate stream of growing dividends

g = growth rate€

dt = (1+ g)td0

More Growing Dividends

€

PV =(1+ g) t d0

(1+ k) tt=1

∞

∑ = d0 a t

t=1

∞

∑

a =1+ g1+ k

PV =a

(1− a)d0 =

(1+ g)(1+ k)

1−(1+ g)(1+ k)

d0 =

(1+ g)(1+ k)(k − g)(1+ k)

d0

PV =(1+ g)(k − g)

d0 =1

(k − g)d1

Dividend Discount

Must have k>g for this to make senseOtherwise, dividends growing too fastBasic feature: Very sensitive to g

Examples

Let initial d = 1, k=0.05, g=0.02 PV = 1.02/(0.05-0.02) = 34

k = 0.05, g = 0.03 PV = 1.03/(0.05-0.03) = 51.5

Why is this important?Stock pricesSmall changes in beliefs lead to big

changes in prices

What if dividends not growing forever?

Solve this by calculator or computer for d(t)

€

P =dt

(1+ k)tt=1

∞

∑

Goals

Dividend valuation model “dividend discount model”

Forecasting earnings, dividends, and prices

Ratio valuationsMalkiel’s “Firm foundations”

Future Price EstimatesVariable Growth Model

Forecast dividends in early years In last year

Estimate dividend growth Use this to estimate future price

Present Value Calculation(End of year dividends.)

€

P2007 =d2007(1 + k)

+d2008

(1 + k)2+d2009

(1 + k)3+P2009

(1 + k)3

P2009 =(1 + g)

(k − g)d2009

Forecasting Dividends

Forecast sales revenueGuess revenue growth ratesSales tomorrow = (1+g) (Sales today)

Sales -> Earnings

€

Net Profit Margin =Earnings

SalesEarnings = (Net profit margin) x Sales

Earnings/share = Earnings

Total shares

Earnings->Dividends

€

Dividend/share = (payout ratio) x (earnings/share)

Future Price(Guess long term growth, g.)

€

P2009 =(1 + g)

(k − g)d2009

Required Return (CAPM)

Assume the CAPM is working Required return for asset j

RP = risk premium Think of k as the return that a certain asset should

get given its risk level€

k j = RF + RPjk j = RF +β j (RM − RF )

Back to Problem

RF = 3%RM = 8% (difficult)

What Do You Need?

Revenue (sales) forecastsGross profitability estimatesDividend payout estimatesSharesCAPM inputsFuture growth estimates

Microsoft 3 year forecasts

AssumptionsBeta 0.88 Market return 0.08Revenue Growth 0.1 Risk free 0.03P/E 22 Future growth 0.05Div Payout 0.32Profit Margin 0.26Shares (billions) 9.7

2004 2005 2006 2007 2008 2009 Price(2009)Revenue 36.00 40.00 44.00 48.40 53.24 58.56Earnings 8.10 12.25 13.00 12.58 13.84 15.23EPS 0.84 1.26 1.34 1.30 1.43 1.57Dividend/Share 0.27 0.40 0.43 0.42 0.46 0.50 21.98

Required Return 0.0741 2 3 3

Discounted values 0.3865 0.3959 0.4055 17.7398

Present Value 18.93

Connecting to P/E Ratios

Define the following two terms Retention rate

rr = fraction of earnings that go back to firm Dividend payout ratio (dividends/earnings)

Fraction of earnings going to shareholders (1-rr)

Dividends = (1-rr)(earnings)

P/E

€

E t = (1+ g) t E0 , d t = (1− rr)E t

PV =d t

(1+ k) tt=1

∞

∑

PV =(1− rr)E t

(1+ k) tt=1

∞

∑ = (1− rr)E t

(1+ k) tt=1

∞

∑

PV = (1− rr)(1+ g)(k − g)

E0 =(1− rr)(k − g)

E1

P/E Ratios

€

PV = (1− rr)(1+ g)(k − g)

E0 =(1− rr)(k − g)

E1

(1− rr) = div payout ratio

PV/E0 = (1− rr)(1+ g)(k − g)

= P/E Ratio (curent earnings)

PV/E1 =div payout ratio

(k − g)= P/E ratio (future earnings)

P/E Ratios

Firms with greater earnings growth will have greater P/E ratios

Firms with higher dividend payouts will have higher P/E ratios

Example: Microsoft ( Price = 27)

P/E = 23 Beta = 0.88, Rm = 0.08, Rf = 0.03

k = 0.03 + 0.88(0.08-0.03) k = 0.074

Growth g = 0.05, 0.06

Div payout ratio 0.32 P/E = 0.32(1.05)/(0.074-0.05) = 14 P/E = 0.32(1.06)/(0.074-0.06) = 24

g, ROE, and rr

€

g =Reinvested earnings

Shareholders equity

g =Reinvested earnings

Total earnings*

Total earnings

Shareholders equity

g = rr * (return on equity)

MSFT = (1- 0.32) * (0.29) = 0.20

Goals

Dividend valuation model “dividend discount model”

Forecasting earnings, dividends, and prices

Ratio valuationsMalkiel’s “Firm foundations”

Ratio Valuations

Find various price ratiosSee if stock looks “cheap” relative to

reference groupAlso, forecast future prices using

forecasts of ratiosNecessary for nondividend paying

stocks

P/E Ratio Comparisons

Find current P/E ratioCompare with industryLow:

BuyHigh

Sell

P/E Price Forecast

Forecast future P/E ratioForecast future earningsFuture price = (P/E)*EDiscount this back to today, and

compare with current priceCan also be used along with dividend

forecasts too

Example: Irobot

Recent IPO Little data to work with

Pays zero dividendsHigh risk

Irobot long range forecasts

AssumptionsBeta 2.2 Market return 0.08Earnings Growth 0.2 Risk free 0.03P/E 94 Long run growth 0.13Div Payout 0.25

Shares (millions) 14

(Millions)2004 2005 2006 2010 2015 (P/E) 2015(Div discount)

Earnings 0.22 2.61 3.56 7.38 18.37 18.37EPS 0.00 0.19 0.25 0.53 1.31 1.31Dividends 0.00 0.00 0.00 0.00 0.00 0.33Price 13.00 49.56 123.33 37.01

Required Return 0.14PV 29.35 37.93 11.38

g, ROE, and rr

€

g =Reinvested earnings

Shareholders equity

g =Reinvested earnings

Total earnings*

Total earnings

Shareholders equity

g = rr * (return on equity)

IRBT = (1- 0.00) * (0.039) = 0.039

P/E Ratios w/o dividends

Remember comment about dividends don’t matter

Value entire earnings stream, since you own this

Max bound on P/E ratioRelated to PEG ratios (P/E)/growth

P/E (without divs)(Upper bound)

€

Et = (1 + g)t E0

PV =Et

(1 + k)tt=1

∞

∑ =Et

(1 + k)tt=1

∞

∑

PV =(1 + g)

(k − g)E0 =

1

(k − g)E1

P /E =(1 + g)

(k − g)

IRobot Again

k = 0.14, g = 0.10 P/E = (1+0.10)/(0.14-0.10) P/E = 27.5

k=0.14, g = 0.13 P/E = (1+0.13)/(0.14-0.13) P/E = 113

Market P/E = 90

Key Problems

Estimating growth with little dataWhat should P/E be?

“Earnings multiple” Compare with other firms Crude dividend discount checks

Lots of guesswork Negative earnings?

S&P 500 P/E Ratio

Other Ratios

Price/CashflowPrice/BookvaluePrice/SalesKey problem:

Find appropriate comparison firms

Data Tools

Stock screening software See Yahoo finance

Goals

Dividend valuation model “dividend discount model”

Forecasting earnings, dividends, and prices

Ratio valuationsMalkiel’s “Firm foundations”

Long-Run stock valuation

Price = PV(dividends/earnings)Stresses uncertainty Malkiel’s “determinants”

Determinant 1: Expected Growth Rate

Remember formulasHigher expected growth -> Higher price

(can be very strong)Big question: How long and by how

much will unusual growth last?

Determinant 2:Dividend Payout

Financial Ratio Div. Payout Ratio = Divs/Earnings

Determinant 3: Risk

Growth rates and interest rates are uncertain

Price should be higher (all things equal) the less risky the earnings stream

Risk is difficult to quantify

Determinant 4:Interest rates

Back to our PV formulasHigher interest rates (lower stock

prices)Two ways to think about it

PV formula Stock market alternatives look better

Malkiel’s Caveats

Financial data is Messy Hard to predict

Evidence1998(Malkiel)

0

10

20

30

40

50

Ford IBM Microsoft

Growth Rate P/E Ratio

What does this say?

Growth rates matterFirst hint of rationality in the stock

marketHow can you tell when a P/E ratio is out

of line?Look at stocks with comparable growth

rates

Valuation Wrap Up

Many toolsNo one right answerSome common sense, and rules of

thumbTry to stay close to sensible

growth/valuation ideas