Overview

• Fundamental analysts use information

Chapter Eighteen concerning the current and prospective
profitability of a company to assess its fair
market value

Equity Valuation • Alternative measures of a company’s value

Models • Dividend discount models
• P/E ratios
• Free cash flow models
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Valuation by Comparables Limitations of Book Value

• Purpose of fundamental analysis is to identify • Shareholders are sometimes called “residual
stocks that are mispriced relative to some claimants”
measure of “true” value that can be derived from
observable financial data • Book values are based on historical cost, while
• Valuation ratios are commonly used to assess the market values measure the current values of
valuation of one firm compared to others in the assets and liabilities
• Based on the original cost of the asset less any
same industry depreciation, amortization or impairment costs
• P/E, P/B, P/S, PEG
• The data source is firm’s 10Q/10K report • Market values generally will not match historical
• Ratios like price/sales are useful for valuing start-ups values
that have yet to generate positive earnings
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Liquidation Value and Tobin’s Q Financial Highlights of Microsoft

• Net amount that could be realized by selling
the assets of a firm after paying the debt is
liquidation value
• Good representation of a “floor” for the stock’s
price
• Replacement cost is the cost to replace a
firm’s assets
• Tobin’s q is the ratio of market value of the firm to
replacement cost
• Trends towards 1

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 Intrinsic Value vs. Market Price Required Return

• The return on a stock is composed of cash • CAPM gives the required return, k:
dividends and capital gains or losses
k  r f    E ( rM )  r f 
E ( D1 )   E ( P1 )  P0 
Expected HPR= E ( r ) 
P0
• If the stock is priced correctly, expected
• The expected HPR may be more or less than return will equal required return
the required rate of return • k is the required rate of return
• Variation based on the stock’s risk – the market capitalization rate
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Intrinsic Value and Market Price Dividend Discount Models (DDM)

• The intrinsic value (V0) is the “true” value,

according to a model D1 D2 D3
V0     ...
• If intrinsic value > market value, the stock is 1  k 1  k  1  k 3
2

considered undervalued and a good investment

• V0 = current value
• Trading signal • Dt = dividend at time t
• IV > MV  Buy • k = required rate of return
• IV < MV  Sell • DDM says V0 = the present value of all
• IV = MV  Hold expected future dividends into perpetuity
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Constant Growth DDM Constant Growth DDM

(1 of 2) (2 of 2)

• A stock just paid an annual dividend of $3/share

D 1  g  D • Dividend is expected to grow at 8% indefinitely
V0  0  1
kg kg • Market capitalization rate is 14%
• V0 = current value
• Dt = dividend at time t D1 $3.24
V0    $54
• k = appropriate risk-adjusted interest rate k  g .14  .08
• g = dividend growth rate

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 Discounted Cash Flow (DCF)
DDM Implications
Formula
• The constant-growth rate DDM implies that a
stock’s value will be greater:
1. The larger its expected dividend per share
2. The lower the market capitalization rate, k
3. The higher the expected growth rate of
dividends
• DCF formula often used in rate hearings for
regulated public utilities
• The stock price is expected to grow at the • Focus on “fair” profit
same rate as dividends
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Dividend Growth for Two Earnings Present Value of Growth

Reinvestment Policies Opportunities
• Present value of growth opportunities (PVGO)
is the net present value of a firm’s future
investments
• The value of the firm is the sum of the
following:
• Value of assets already in place (no-growth value)
• Net present value of the future investments the
firm will make, or PVGO E
P0  1
 PVGO
k
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Life Cycles and Multistage Growth Models Financial Ratios in Two Industries

Firms typically pass through life cycles with different dividend profiles.

Early Years Later Years

• Ample opportunities for profitable • Attractive opportunities for reinvestment

reinvestment in the company may become harder to find

• Payout ratios are low • Production capacity is enough to meet

market demand
• Growth is correspondingly rapid
• Competitors enter the market

• Firms may choose to pay out a higher

fraction of earnings as dividends

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 Price-Earnings Ratio and Growth Price-Earnings Ratio and Growth
Opportunities (1 of 3) Opportunities (2 of 3)
• The ratio of PVGO to E/k is equivalent to the • When PVGO = 0, P0 = E1/k
component of firm value due to growth • The stock is valued like a nongrowing perpetuity
opportunities to the value reflecting assets
already in place • As PVGO becomes an increasingly dominant
contributor to price, the P/E ratio can rise
P0 1  PVGO  dramatically
 1
E1 k  E 
 k 
• P/E ratio reflects the market’s optimism
concerning a firm’s growth prospects
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Price-Earnings Ratio and Growth

Estimating Dividend Growth Rates
Opportunities (3 of 3)
𝑔 = 𝑅𝑂𝐸 × 𝑏 • P/E increases:
• As ROE increases
• g = growth rate in dividends • As plowback, b, increases, if ROE > k
• As plowback decreases, if ROE < k
• ROE = Return on Equity
• As k decreases
• b = plowback or retention rate = (1 -
dividend payout rate) P0 1 b

E1 k  ROE x b

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Effect of ROE and Plowback on

P/E and Growth Rate
Growth and the P/E Ratio
• Wall Street rule of thumb suggests the growth
rate ought to be roughly equal to the P/E ratio

• “If the P/E ratio of Coca Cola is 15, you’d

expect the company to be growing at about
15% per year, etc. But if the P/E ratio is less
than the growth rate, you may have found
yourself a bargain.”
Peter Lynch in One Up on Wall Street
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 P/E Ratios and Stock Risk Pitfalls in P/E Analysis

• Holding all else equal, riskier stocks will have • Denominator in the P/E ratio is accounting earnings,
which are influenced somewhat by arbitrary
lower P/E multiples accounting rules
• Earnings management
• Choices on GAAP
• Riskier firms will have higher required rates of • GAAP allows firms some discretion to manage earnings

return, that is, higher values of k, which • Inflation

means the P/E multiple will be lower • in the time of high inflation, historical cost depreciation
and inventory costs will tend to undervalue true economic
P 1 b values. P/E inversely related to inflation

E kg • Reported earnings fluctuate around the business cycle
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P/E Ratios of the

Earnings Growth for Two Companies
S&P 500 Index and Inflation

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Price-Earnings Ratios P/E Ratios for Different Industries

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 CAPE models Other Comparative Valuation Ratios

• Cyclically adjusted P/E ratio • Price-to-book ratio

• Shiller suggests a “cyclically adjusted” P/E ratio • Ratio of price per share divided by book value per
(CAPE) to avoid the problems associated with share
using P/E ratios over different phases of the • Price-to-cash-flow ratio
business cycle • Cash flow is less affected by accounting decisions
• Idea is to divide the stock price by an estimate of than are earnings
sustainable long-term earnings rather than • Ratio of price to cash flow per share
current earnings • Price-to-sales ratio
• Proposed using average inflation-adjusted earnings • Useful for start-up firms that do not have earnings
over an extended period, such as 10 years
• Ratio of stock price to the annual sales per share
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Market Valuation Statistics Free Cash Flow for the Firm (FCFF)
(1 of 2)

1. Discount the FCFF at the weighted-average

cost of capital to find the value of entire firm
• Free cash flow to the firm, FCFF, is the after-tax
cash flow generated by the firm’s operations, net
of investments in fixed as well as working capital
2. Subtracting the value of debt results in the
value of equity

FCFF  EBIT  (1  t )  Depreciation  Cap. Exp.  NWC

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Free Cash Flow for the Firm (FCFF) Free Cash Flow to Equityholders
(2 of 2) (FCFE) (1 of 2)
• Value of the Firm • Alternative approach is to focus on FCFE,
discounting those directly at the cost of equity
T
FCFFt Vt
FirmValue    to obtain the market value of equity
t 1 (1  WACC )t (1  WACC )T
• Free cash flow to equityholders, FCFE
• Differs from FCFF by after-tax interest
• Where expenditures, as well as by cash flow associated
FCFFT 1
Vt  with net issuance or repurchase of debt
WACC  g
FCFE  FCFF  Interest  (1  t )  Debt

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 Free Cash Flow to Equityholders
Comparing the Valuation Models
(FCFE) (2 of 2)
• Intrinsic value of equity • In practice
• Values from the FCF and DDM models may differ
FCFEt T
ET • Analysts are always forced to make simplifying
IntrinsicValue of Equity    assumptions
t 1 (1  k E ) t
(1  k E )T
• Problems with DCF (Discounted Cash Flow)
• Where Models
FCFET 1 • Calculations are sensitive to small changes in
ET  inputs
kE  g
• Growth opportunities and growth rates are hard
to pin down
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Comparing the Valuation Models,

The Aggregate Stock Market
Rio Tinto
• Most popular approach to valuing the overall
stock market is the earnings multiplier
approach applied at the aggregate level

• Some analysts use aggregate version of DDM

rather than an earnings multiplier approach

• S&P 500 taken as leading economic indicator

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Earnings Yield, S&P 500 Index Forecasts Under

S&P 500 vs. 10-Year Treasury Bond Various Scenarios

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