Chapter 13

COMMON STOCK VALUATION

Fundamental Analysis

• analysts (or investors) try to determine the intrinsic value of a stock

• If:• intrinsic value < current market value

• overpriced sell stock

• intrinsic value < current market value• underpriced buy stock

Determining Intrinsic Value

• various methods• we will look at several

• all are based on estimates of what will happen in the future

• no method is perfect as based on estimates of certain (unknown) parameters

• cannot predict the future exactly, can only make best guess• therefore, can never true intrinsic value, only your best estimate

• two analysts may come up with different estimates of intrinsic value if:

– They use different valuation models

or– They use the same model but have

different parameter estimates

• If fundamental analysis of intrinsic values is based on estimates, is it useful?

• Yes!• Investors need to make buy/sell decisions based on what the stock is priced at and what they feel it should be worth• Need way to determine what it “should” be worth

• Different investors can have different estimates this is what creates trading

Two Common Valuation Methods

1) Present Value Approach(a) dividend discount model (DDM)(b)Free Cash Flow Valuation

• Value stock based on value of cashflows it generates for the investor

2) Relative Valuation Approach(a) Price-earnings ratio(b) other ratios (price to book, price to sales

etc.)• Value stock by looking at how similar stocks are

valued by the market

Present Value Approach- Dividend Discount Model

• the value of any stock (or other security) is the present value of future cashflows coming from the stock

• for a stock, cashflows received by investors are the dividends

intrinsic value of share = PV of all future dividends

1tt

cs

tcs )k1(

DP

• to implement, need estimates of two things:

1) required return on the stock

2) all future dividends

• required return on stock depends on:• general level of interest rates in economy• risk level of stock

• estimating future dividends:• impossible to predict exactly what all future dividends will be• typically, simplifying assumptions are used • Three cases:

1) Zero Growth2) Constant Growth3) Multiple Growth

Zero Growth Model• Assume that firm does not reinvest anything in itself, pays out all earnings as dividends• it should experience no growth over time:

D0 = EPS0

and D0 = D1 = D2 = ...

• DDM becomes a perpetuity:

cs

00 k

DP

This simple model would generally never apply to common stocks(applies to straight convertible shares)

Constant Growth Model

• dividends are expected to grow at a constant rate, g, forever

• DDM becomes a growing perpetuity

gk

DP

cs

10

where D1 = D0(1+g)

• The constant growth model shows the basic factors which affect stock prices:

gk

DP

cs

10

Future profitability

(via dividends)

Firm Profitability(via dividends)

-Level of interest rates-Risk level of stock

• in constant growth model, g is growth rate in dividends and is also expected appreciation in stock price

• the expected (required) return to the investor can be broken down in to a dividend yield and a capital gain yield (=g)

• in practice, this simple model would only apply to a stock with very stable (in terms of growth) dividends – typically in a fully mature and non-cyclical industry

Multiple Growth Model

• dividends are expected to grow at different rates over different periods

• eventually, dividends enter a period of stable, long term growth which goes on forever

• common to use 2 or 3 different growth rates in practice, or to estimate first few dividends directly and then assume growth rate(s)

ncs

nn

cs

n3

cs

32

cs

2

cs

10 )k1(

P

)k1(

D

)k1(

D

)k1(

D

)k1(

DP

Where:

gk

DP

cs

1nn

• the dividends (D1 to Dn+1) have to be estimated directly using the estimated growth rates

Problems with Present Value Approach

• in theory, DDM is correct but implementation can be hard

• parameters (next dividends, growth rate(s), required return) must be estimated and this is the hard part• we will look at methods to estimate required return, earnings, dividends and growth rates a little later in course

• the intrinsic value calculated can be very sensitive to assumptions made

• DDM best suited to firms which maintain stable payout ratios

• DDM best suited for firms which have reasonably stable growth rates

• does not work well for cyclical firms or firms with erratic earnings

• DDM may work reasonably well for firms in mature industries with stable profits (or growing at stable rate) and an established dividend policy

Another Present Value Approach- Free Cash Flow Valuation

• Many firms do not currently pay dividends• Theoretically, DDM will work, but

extremely difficult to estimate when dividends will begin and what growth rate will be

• Alternative to DDM is calculating present value of Free Cash Flow

Two approaches:1. Free Cash Flow to Equity (FCFE)2. Free Cash Flow to the Firm (FCFF)

Free Cash Flow to Equity:– Estimate how much cash the firm could pay out as

dividends if it wanted to = FCFE– Think of this as “potential” dividends– Calculate present value of future FCFE to get

value of equity

Free Cash Flow to Equity

FCFE = Net Income

+ Depreciation

– Capital Expenditures

– Change in non-cash Working Capital

+ Net New Debt Issued

Free Cash Flow to Equity

• Similar to DDM, estimate a growth rate and then discount at the required return on equity:

Total value of Equity =

• Divide this number by number of shares outstanding to get estimate of intrinsic value of one share

gk

FCFE

CS

1

Free Cash Flow to Firm

• FCFF represents the cashflow available each that could be distributed to all security holders (i.e. shareholders and debt holders)

FCFF = FCFE – Net New debt + Interest(1-tax)

Free Cash Flow to Firm

FCFF = Net Income

+ Depreciation

- Capital Expenditures

- Change in non-cash Working Capital

+ Interest (1 – tax rate)

Free Cash Flow to Firm• Estimate growth rate for FCFF• Discount future FCFF at the weighted average cost of

capital (WACC)

Value of Firm =

• This is value of overall firm, to get share value subtract value of debt and divide by number of shares

gWACC

FCFF1

Estimating Intrinsic Value- Relative Valuation Approach

• value a stock by comparing it to other stocks

• usually done by comparing the level of some accounting variable such as earnings, sales or book value

• in some industries non-accounting numbers might be used (e.g. # of subscribers in the cable industry, amount of oil reserves in oil industry)

• whatever the basis of comparison, the process is essentially the same

• determine what the relationship between the variable and the stock price “should” be

• use this and the level of the variable for the firm to value the stock

• by far the most common relative valuation approach is based on the price-earnings ratio (P\E ratio)

EPS

P

shareperearnings

pricestockratioE\P

P/E Ratios

• Price of a stock alone does not tell you if it is “expensive” or “cheap”

• price must be measured relative so something

• most common is earnings• how much does the stock cost per dollar of earnings the firm generates?

Using P\E ratios in valuation:

determine what P\E “should” be

“justified P/E ratio”

EPS times justified P\E ratio

estimated intrinsic value

• newspapers often report current P\E ratios for stocks

• usually based on “trailing” earnings (EPS for previous year = EPS0)

• stock valuation generally done using “forward” earnings

• estimate of EPS for next year (EPS1 = the future)

10 EPSE\PjustifiedP

Estimating Justified P\E Ratio

Four basic methods:

1) based on fundamentals of firm (using DDM model)

2) industry average

3) historic average for the firm (or the industry)

4) relative to market overall

Justified P\E from Fundamentals

• if assume the constant growth DDM holds, can be shown that:

gk

ratiopayout

EPS

P

CS1

0

• gives justified P\E based on payout ratio and estimates of kcs and g to calculate justified P\E

• multiply by estimate of EPS1 to get intrinsic value

• the P\E ratio justified by fundamentals also shows the factors that determine the P\E ratio:

1) a higher payout ratio means a higher P\E ratio, all else being equal

2) a higher required return (risk) means a lower P\E ratio, all else being equal

3) a higher growth rate means a higher P\E ratio, all else being equal

• “all else being equal” never really holds since all three variables are related to each other

• The formula for P/E from fundamentals (and the formulae for other ratios that follow) is derived from a simple DDM with a single, stable growth rate (D/(k-g))

• As such, it is only applicable in cases where that formula would apply (mature, stable companies)

• Generally, these formulae are not actually used to generate estimates of P/E (or the other ratios), but rather to understand the factors that make a ratio higher or lower.

• e.g. if a stock has a lower P/E than industry average but is considered lower risk, then the lower P/E may be appropriate. Similarly, a stock with higher growth will have a higher P/E.

• These ideas are sometimes utilized in a regression framework: e.g. for many firms you have growth rates and P/E ratios. Regress P/E on growth to determine the relationship. Based on another firm’s growth rate you can then use the regression parameters to estimate what an appropriate P/E should be.

Comparison to Industry Average:

• average P\E ratio of comparable firms

• may have to make adjustments for differences• e.g. differences in growth potential, risk level etc.

Comparison to Historic P\E Ratio for Firm:

• average P\E ratio for the firm in the past

• or, average P\E ratio for industry in the past

• have to adjust for changes in the firm/industry

Average Industry P\E RatiosAverages over 1999-2004 in Canada:

Autos and Auto Parts 16.93Banks 13.19Biotechnology 34.11Metals and Mining 24.58Steel 14.48Food and Staples Retailing 17.52Utilities 17.58Retailing 12.61

Source: FPinfomart.ca

Comparison to Market Overall

– company or industry’s P\E ratio relative to ratio for market

• e.g. if firm has P\E ratio that is historically 1.5 times as big as average market ratio, use that fact and current market P\E to estimate firm’s P\E

– Average P/E on TSX approximately 16 to 18 on average

Problems with Using P\E Ratio for Valuation

• if other firms are over- or under-valued in the market than estimating P\E ratio by looking at industry or market can simply repeat the error

• if earnings are negative, P\E ratio meaningless

• earnings can be very volatile, makes P\E ratios very volatile

P/E Ratios over time

• average P/E since 1999 for Steel sector:

Source: FPinfomart.ca

1999 7.75 2000 8.53 2001 25.20 2002 20.93 2003 20.03 2004 4.45

Market-to-Book Ratio

• price divided by book value of equity per share• determine justified market-to-book and multiply by book value to estimate intrinsic value

• Advantages: - Book value of equity (BV) less volatile than EPS- BV rarely negative

• Disadvantages:- BV based on accounting numbers, may have little meaning for some types of firms - comparison of firms difficult if accounting standards different

• justified market to book ratio estimated in same ways as P\E

• from fundamentals, assuming constant growth DDM:

gk

)g1(ratiopayoutROE

BV

P

CS

0

0

0

Price-Sales Ratio

• price divided by sales per share• determine justified price-sales ratio and multiply by sales per share to estimate intrinsic value

Advantages:- sales not as volatile as earnings- sales do not depend on accounting standards very much- sales never negative

Disadvantages:- sales do not reflect cost structure of the firm

• justified sales-price ratio can be estimated in same four ways as the other ratios

• from fundamentals, assuming constant growth DDM:

gk

)g1(ratiopayoutinargmincomenet

Sales

P

CS0

0