1. finance
2. investing
3. stocks

BM410: Investments
Equity Valuation
Objectives
A. Understand the relationship between
intrinsic value and market value
B. Understand the various types of valuation
models, including balance sheet, dividend
discount models, and PE ratios
C. Understand other key metrics used in
valuing securities
A. The Relationship between
Intrinsic Value and Market Value
• What is intrinsic value?
• The present value of a firm’s cash flows discounted
by the firm’s required rate of return
• What is the firm’s market value (or price)?
• The total value of a firm’s outstanding shares times
its market price
• In an efficient market, what should this relationship be?
• In a truly efficient market, the intrinsic value should
equal its market value
• What happens if it doesn’t?
Intrinsic Value (continued)

How do you identify mis-priced securities?
• Determine the intrinsic or fair value of the security.
This can be done by many methods:
• Models, i.e. CAPM, APT (E(rs) = rf + bs [E(rM) - rf ])
• Fundamental analysis
• Balance sheet methods
• Dividend Discount Models (DDMs)
• Then you compare the fair value to the current price
Intrinsic Value (continued)


Do all analysts look at companies the same way?
• No. If you have 30 analysts, you will generally
have more than 60 sets of intrinsic values.
How much is intrinsic value used in the real world?
• It is used much in terms of equity valuation and
financial analysis. These have a more solid
foundation and are not as affected by key
assumptions
• It is not used as much with DDM’s and PV models,
as slight changes in assumptions can have large
changes in a company’s intrinsic value. Also these
models assume a longer time frame generally.
Intrinsic Value (continued)

If DD and PV models is not used as much in
the real world, why are we learning them?
• The concepts are critical to understanding finance
• It can add value in specific cases and companies
• It can be used to support your recommendations
from other models if assumptions are stated clearly
Intrinsic Value (continued)

How do you determine Intrinsic Value?
• It is a value assigned by the analyst
• It is based on specific theories and assumptions
• Analysts use specific models for estimation
• Lots of models exist
• Remember, these models/assumptions are
proxies for reality – not reality
Intrinsic Value (continued)

What happens if the intrinsic value is greater than the
market price?
• Intrinsic Value > Market Price
• Buy
• Intrinsic Value < Market Price
• Sell or Short Sell
• Intrinsic Value = Market Price
• Hold or Fairly Priced or valued
• These models are not as accurate as investors (or
students) would like.
• They are more indicators than directors
• It is more an art than a science!
Questions

Do you understand the relationship between
intrinsic value and market value or price?
B. Understand Various Types
of Equity Valuation Models

Fundamental Stock Analysis: Models of Equity
Valuation
• Basic Types of Models
• 1. Balance Sheet Models
• Book Value
• Liquidation Value
• Replacement Value
• 2. Discounting Models
• Free Cash Flow to the Firm (FCFF)
• Free Cash Flow to Equity (FCFE)
• 3. Dividend Discount Models
• 4. Price/Earning Ratios
1.
•
Balance Sheet Models
Balance sheet models assume that the intrinsic
value of the firm is the value of its assets.
• What is the value of the firms assets?
• Is it the value on the books?
• Is it the value we could really get for the assets
(liquidation value)?
• Is it the value we could get to replace the
assets?
Balance Sheet Models (continued)

1.A. Book Value (per share)
Look at the book value: Equity / shares outstanding
Example: Ford
Assets
243,283 million
Liabilities
219,736 “
Owners Equity
23,547 “
Shares Outstanding
1,169 “
What is the Book Value per share?
$23,547/1,169 = Book value of $20.14 per share
Logic: the value of the assets should be equal to their
value on the books.
Be careful as book value does not tell you
depreciation methods or the true value of the assets
Balance Sheet Models (continued)

1.B. Liquidation value (per share)
The amount of money realized by breaking up the
firm, selling assets and repaying its debt
• Company A has a market value of $250 million
(mn) with $50 mn in debt, cash of $150 mn and
other assets likely worth $200 mn if sold today.
• What is the liquidation value?
• Liquidation value is the cash on hand and what
they could liquidate the other assets for, I.e.
150+200-50 = $300 mn
• Logic: if market price falls below liquidation value,
the firm becomes a takeover target as investors buy
the company and sell it in pieces
Balance Sheet Models (continued)

1.C. Replacement Cost (per share)
The amount of money it would take to replace the
tangible and intangible assets of a company
• Company B is a trucking company valued at $25 mn.
Since Company C takes 60% of the company’s
business and is planning to expand, you know that its
CEO could replicate the trucking company for $20
million and build her own trucking division.
• What is the replacement cost for the trucking
company? $20 million
• Logic: If the market value gets too high above the
replacement cost, competitors would try to replicate
the firm and entering competition would drive down
Balance Sheet Models (continued)

1.D. Tobin’s q
It is the ratio of a firm’s market price to its replacement
cost
In the long run, the market price to replacement cost
will tend toward 1 as investors correctly value the
replacement cost of the assets
- But differences will remain over periods of time
- Logic: Investors will be willing to purchase the
company as long as the company’s market price is
below the replacement cost. As soon as its price is
greater than the replacement cost, competition will
come in, dropping the price to close to its
replacement cost.
2.

Discounting Models
Discounting models assume the intrinsic value
of the company is the present value of the
firms’ expected future cash flows. It is useful
when:
• The company does not pay dividends
• Dividends paid differs from what the firm could pay
• Free cash flows align with profitability within a
specific forecast period
• The investor takes a control perspective
Discounting Models (continued)
 2.A. Free Cash Flow to the Firm (FCFF)
• FCFF is the cash flow available to the company’s
suppliers of capital after all operating expenses
(including taxes) are paid and working and fixed
capital investments are made.
• FCFF = cash prior to the payment of interest to the
debt holders
FCFF = EBIT - taxes + depreciation (non-cash
costs) – capital spending – increase in net
working capital – change in other assets +
terminal value
Discount this at the firm’s WACC
Firm Value = Operating free cash flow
WACC – growth OFCF
Discounting Models (continued)

2.B. Free Cash Flows to Equity (FCFE)
- FCFE is the cash flow available to the company’s
equity shareholders after all operating expenses,
interest, and principle repayments have been made
and necessary investments in working capital and
fixed capital have been made
- FCFE = Adjusts cash flows for debt repayments
- FCFE = EBIT – interest - taxes + depreciation
(non-cash costs) – capital expenditures – increase
in net working capital – principal debt
repayments + new debt issues + terminal value.
Discount at k = required return on equity
Firm Value = Free Cash Flows to Equity/(k – growth FCFE)
Discounting Models (continued)

Calculation Note for Discounting Models:
•
•
•
•
Determine the appropriate discount rate
Set up each of the individual cash flows
Discount each of the individual cash flows
Discount the final cash flow assuming a constant
growth rate = cash flow / (k – g)
• The question remains whether the final cash
flow representative of all future cash flows
• Sum all the discounted cash flows
• Make adjustments as required
3. Dividend Discount Models

Models which take into account discounting
expected future cash flows to gain a reference
for the value of a company
• Dividend Discount Models
General Model
Constant Growth Model
Dividend Discount Models (continued)

Dt
Vo  
t
t  1 (1  k )
3.a. General Model

Vo= Sum [Dt/(1+k)t ]
V0 = Value of Stock
Dt = Dividend
k = Required return
Dividend Discount Models (continued)

3.b. Constant Growth Rate Model
Vo = Do (1+g)/(k-g)
This is for stocks that are growing at a constant
growth rate (assumed for perpetuity)
g = constant perpetual growth rate
b = plowback or retention ratio (rr)
Note: take out the g and the formula becomes the no
growth model
E1 = $5.00 b = 40%
k = 15%
(1-b) = 60%
D1 = $3.00 g = 8%
V0 = 3.00 / (.15 - .08) = $42.86
Dividend Discount Models (continued)

Estimating Dividend Growth Rates
g = ROE x b
• g = growth rate in dividends
• ROE = Return on Equity for the firm
• b = plowback or retention percentage rate
• (1- dividend payout percentage rate)
• Internal Growth Rate (ROE x (1-payout)
• This is the rate that the company can continue to
grow without any additional external financing
• Note: if the firm distributes all its earnings, there is
nothing to allow the firm to continue to grow
Dividend Discount Models (continued)

More Changes to the DDM
• What about growth opportunities?
• Do those impact the value of the company?
• Does the DDM only look at dividends?
• What about earnings on specific projects?
• Can we fix the DDM to look at the value of new
projects?
• There are a number of different DDM models that
can handle each of these situations
Dividend Discount Models (continued)




The constant growth dividend discount model can be
used for both for the valuation of companies and for
the estimation of long-term total return of a stock.
Assume:
$20.00 = the price of a stock today, 8% = expected
growth rate of dividends, and $0.60 = Annual
dividend one year forward
A. Using only the data above, compute the expected
long-term total return on the stock using the constant
growth dividend discount model. Show calculations.
B. Briefly discuss two disadvantages of the constant
growth dividend discount model in its application to
investment analysis.
C. Identify two alternative methods to the dividend
Answer
A. Expected Return = k = D1/Po + g = .60/20 +.08 =
11%
B. The model assumes that the dividend growth rate is
forever constant. Therefore, the model cannot be
applied to firms that currently do not pay dividends.
Second, the model is inappropriate when g > k
(which presumably cannot persist indefinitely).
Third, the model cannot handle firms with variable
dividend growth paths.
C. One can use either P/E multiples or market-to-book
multiples exhibited by other firms in the same
industry.
4. Valuing Companies
using PE Ratios

M & A Departments often use PE’s as one way
of valuing companies. They find similar public
companies to the ones they want to make
public, they estimate their fair trading PE
range, and then they apply the PE range to the
new company.
• The fair trading PE range times the EPS gives the
price per share.
PE Ratio Example

In 1996 Montgomery Asset Management of
San Francisco California, a non-public
company, was looking to be sold as its owner,
Montgomery Securities, needed cash to build
up its other operations. Assume it had $10
billion in assets and earns $20 million in
revenues per year. Assuming similar asset
management companies were being sold at 810 times earnings, what is MAM worth?
Answer

Assuming an 8-10 range for PE, MAM would
be worth between $160-200 million.
Price Earnings Ratios (continued)

P/E Ratios are a function of two factors
• Required Rates of Return (k)
• Expected growth in Dividends

Uses
• Valuation of new companies
• Relative valuation versus market and industry
• Note: this is used extensively in the industry.
Research has found that low PE stocks have
given a higher return to Investors than high PE
stocks over the last 70 years
Price Earnings Ratios (continued)
 Price
Earnings Key Terms
• Price Earnings = Price per share/Average Common
diluted Earnings Per Share
• Forward or Prospective PE = Current Price /
Forward EPS
• Historic PE = Year-end Price/Year-end EPS
• Normalized PE = Current Price/normalized earnings
(earnings adjusted to take into account the cycles in
the economy)
• Earnings Yield (E/P) = 1 / Price Earnings
Price Earnings Ratios (continued)


Benefits and Pitfalls of P/Es
Benefits
• Used extensively in the industry
• Generally low PE firms outperform high PE firms
 Pitfalls
• Earnings are accounting earnings, which can be
manipulated through depreciation, inventory, etc.
• Earnings can fluctuate widely around a trend
• You cannot know if the PE is high or low unless you
compare it to a trend, to long-run growth prospects, to
an industry, or to the market
Price Earnings Ratios (continued)

P/E Ratio with no expected growth
P0 = E1 / k
P0 / E1 = 1 / k
where:
• E1 - expected earnings for next year
• E1 is equal to D1 under no growth (100%
payout)
• k - required rate of return
Price Earnings Ratios (continued)

P/E Ratio with Constant Growth
P0 = D1 / (k –g) = E1 (1-b) / [ k – (b x ROE)
P0 / E1 = (1 – b ) / [ k – (b x ROE)]
where:
• b = earnings retention ratio
• ROE = Return on Equity
• Note: since we do not know what P1 will be, the
EMH states that the best estimate of tomorrow’s
price is today’s price, hence we use P0 or today’s
price
PE Example: No Growth



Company XYZ has earnings per share this year of E0 =
$2.50, growth of 0%, and a discount rate from the
CAPM of k = 12.5%. What should its PE be?
Answer:
• With no growth (and 100% payout), the price of
XYZ would be P0 = D/k = $2.50/.125 = $20.00.
• Its PE would be PE = 1/k = 1/.125 = 8.0x or PE
= P0 /EPS1 = 20/2.50 = 8.0x
Note: PE is independent of currency, so there is no
dollar sign in front of it. It is a ratio.
PE Example: Growth
Company XYZ now is under new management, and they
no longer distribute all their earnings as dividends, with
b (or rr) = 60% ROE = 15% (1-b) = 40%. With EPS0
this year of $2.50, k = 12.5%, calculate E1, D1, g, and
their new PE ratio be?
Answer:
E1 = $2.50 (1 + (.6)(.15)) = $2.73
D1 = $2.73 (1-.6) = $1.09
g = 9% or .6 * 15%
P0 = 1.09/(.125-.09) = $31.14
PE = 31.14/2.73 = 11.4x or
PE = (1 - .60) / (.125 - .09) = 11.4x (generally format PE
to one decimal point and place an “x” behind it)
Problem

Explain why the following statements are true /
false / uncertain.
• a. Holding all else constant, a firm will have a
higher P/E if its beta is higher.
• b. P/E will tend to be higher when ROE is
higher (assuming plowback is positive).
• c. P/E will tend to be higher when the plowback
rate is higher.
Answer
a. False. Higher beta means that the risk of the firm is
higher and the discount rate applied to value the cash
flows is higher. For any expected path of earnings
and cash flows the present value of the cash flows,
and therefore, the price of the firm will be lower
when risk is higher. Thus the ratio of price to
earnings will be lower.
b. True. Higher ROE means more valuable growth
opportunities.
c. Uncertain. The answer will depend on a comparison of
the expected rate of return on reinvested earnings
versus the market capitalization rate. If the expected
rate of return on the firm’s projects is higher than the
market capitalization rate, the P/E ratio will increase
as the plowback ratio increases.
Problem




Even Better Products has come out with a new and
improved product. As a result, the firm projects an
ROE of 20%, and it will maintain a plowback ratio
of 0.30 or 30%. Its earnings this year will be $2 per
share. Investors expect a 12% rate of return on the
stock.
At what price and P/E ratio would you expect the
firm to sell?
What is the present value of growth opportunities?
(Remember V0 = E1/k + PVGO so PVGO =
D0(1+g)/(k-g) – E1/k)
What would be the P/E ratio and the present value of
growth opportunities if the firm planned to reinvest
only 20% of its earnings?
Answer
a.
b.
c.
Price and P/E ratio?
g = ROE x b = 20% x .30 = 6%
D1 = $2(1-b) = $2(1 - .30) = $1.40
P0 = D1/(k – g) = $1.40/(.12 - .06) = $23.33 so P/E =
23.33/2 =11.7x
Present value of growth opportunities?
PVGO = P0 – EPS0/k = 23.33 – 2.00/.12 = $6.67
B = 20%
G = ROE x b = 20% x .20 = 4%
D1 = $2(1 – b) = $2(1 - .20) = $1.60
Po = D1/(k-g) = $1.60/(.12 - .04) = $20 P/E = 20/2 =
10
PVGO = P0 – EPS0/K = 20 – 2.00/ .12 = $3.33
Questions

Any questions on methods of equity valuation?
C. Understand the Key Valuation
Metrics in Valuing Securities
 What are the key valuation metrics?
 PE, PBV, PS, DY, POCF, PEBIT, PEVITDA,
P/IGR, and P/EGR
 Why are they important?
 They relate the current market price to key
profitability variables
 They relate the company’s PE ratio to certain types
of growth
1. Price/Earnings (PE=P/EPS)
 PE Ratio
• The most common measures of a firm’s stock price
relative to its earnings--what you are paying for $1
of earnings.
 How is it analyzed?
• Versus its historical average
• If lower that than its history, it may indicate it is
moving into more attractive territory, i.e., growth
is increasing
• Versus the market.
• Gives a historical view. If it is trading at a lower
relative PE, it may be becoming more attractive.
• Versus the industry
• If the relative PE versus the Industry is
declining, it may indicate the stock is becoming
more attractive.
2. Price/Book (PB=P/BVS)


P/BV or PB or Market to Book
 Gives the relationship between the stock price and
the book value of the firm (i.e. owners equity).
How it is analyzed?
 If the PB ratio is high when compared to peer firms,
the stock may be overvalued, all else being equal.
 If the PB is negative, the firm is in serious trouble.
 Remember that owners’ equity is based on
accounting depreciation and may not have
relevance to the actual value of the assets of the
company.
 Generally, the higher the P/BV (or the lower its
inverse, Book to Price) the more expensive the
company.
3. Price/Sales (PS=P/SPS)



Price to Sales
 Sales multiples are sometimes an indicator of
growth in sales and hence future profits.
How it is analyzed?
 Can be positive or negative
 Note that growth in sales translates into growth
in profits only if the other drivers of profits are
sustained, i.e. profit margins, turnover, etc.
 New companies
 New companies like PS ratios when they don’t
have any earnings. But if earnings fail to
materialize, then PS ratios are irrelevant.
Generally, the lower the PS ratio, the more attractive
the company, all else being equal
4. Dividend Yield (DY=DPS/P)


Dividend Yield
 Certain companies are known for their high
dividend payouts
 Historically we have seen an overall decline in the
market’s dividend yield as firms decided that they
could use dividend payouts more effectively in
their own firms
How is it analyzed?
 DY assesses the amount of dividend an investor will
receive for his dollar if invested at the current share
price.
 A high dividend yield can be perceived as both
positive and negative. Positively, as you have a
return of capital; negatively, as the company has no
5. Price/Operating Cash Flow (POCF=P/OCFS)

Price to Operating Cash Flow
 P/OCF is an important measure of a firm’s health
 It gives an assessment of the firm’s power to
generate operating cash flow on a price per share
basis
 How is it analyzed?
 Firms that are generating a high amount of cash are
perceived to be more attractive than firms which are
not generating cash
 Generally, the lower the P/OCF the more attractive
the firm
6. Price/EBIT (PEBIT=P/EBITS)


Price to Earnings before Interest and Taxes
 In evaluating firms which are potential takeover
targets or which are not making earnings, analysts
often use Price/EBIT, which they would use instead
of Price Earnings (as there are not earnings).
 This gives the relevant ratio assuming the firm had
no other expenses, i.e. debts, taxes, etc.
 This was used in valuing the high-flying tech
firms
How is it analyzed?
 Generally the lower the ratio, the more attractive the
company
 Be careful as this ratio says nothing about overall
profits, but only operating earnings.
7. Price/EBITDA (PEBITDA=P/EBITDAS)


Price to Earnings Before Interest and Taxes and
Depreciation and Amortization
 Used to put a price on firms which have no
earnings but are generating cash and which may be
attractive as acquisition candidates
 P/EBITDA is similar to the Price/EBIT, except that
it includes depreciation and amortization, which are
non-cash charges
How is it analyzed?
 Takeover firms are concerned with the amount of
cash firms are generating assuming no other
charges and taxes. Generally the lower the ratio, the
more attractive the company
8. PE to IGR (PE/Internal Growth Rate or g)


PE to Internal Growth Rate (which is a proxy for a
firm’s sustainable growth rate)
 Used to relate a company’s PE to its sustainable
growth rate
How is it analyzed?
 A low PE stock with a high internal growth rate will
have a low ratio, while a high PE stock with a low
IGR will have a high ratio.
 Generally the lower the ratio, the more attractive the
company.
9. PE to Earnings Growth (PE/EPS Growth)

Price Earnings to Earnings Growth
 Another takeoff on the PE to growth ratio
 Sometimes used this as a screening device, only
looking at companies whose PE divided by
Earnings growth rates are 1 or less
 How is it analyzed?
 Generally, companies are more attractive when this
ratio is lower, as they have not only higher earnings,
but those earnings are expected to growth in the
near future.
 Can be very volatile due to the volatility of earnings
per share growth
 Due to volatility, some investors prefer the PE to
IGR above
Questions

Do you have any questions on the various types
of metrics used in valuing companies?
Problem

Portfolio managers and analysts often compare a
company’s Price Earnings ratio to measures of growth
as indicators of value. Which of the two measures, PE
to IGR or PE to EPS growth, will be more stable and
why?
Answer

The PE to IGR will be more stable as ROE is generally
in the 5-35% range, and earnings per share growth can
be anywhere from –100% to +200% depending on the
company.
Review of Objectives
A. Do
you understand the relationship between
intrinsic value and market value?
B. Are you familiar with the various types of
valuation models, including balance sheet,
dividend discount models, and PE ratios?
C. Do you understand other key metrics used in
valuing securities?