Asset Valuation
P.V. Viswanath
Based on Damodaran’s Corporate Finance
Discounted Cashflow Valuation
t = n CF
t
Value = 
t
t =1 (1 + r)
where,



n = life of the asset
CFt = cashflow in period t
r = discount rate reflecting the riskiness of the
estimated cashflows
P.V. Viswanath
2
Two Measures of Discount Rates
 Cost of Equity: This is the rate of return required
by equity investors on an investment. It will
incorporate a premium for equity risk -the greater
the risk, the greater the premium. This is used to
value equity.
 Cost of capital: This is a composite cost of all of
the capital invested in an asset or business. It will
be a weighted average of the cost of equity and the
after-tax cost of borrowing. This is used to value
the entire firm.
P.V. Viswanath
3
Equity Valuation
Figure 5.5: Equity Valuation
Assets
Cash flows considered are
cashflows from assets,
after debt payments and
after making reinvestments
needed for future growth
Liabilities
Assets in Place
Growth Assets
Debt
Equity
Discount rate reflects only the
cost of raising equity financing
Present value is value of just the equity claims on the firm
Free Cash Flow to Equity = Net Income – Net Reinvestment (capex as well as
change in working capital) – Net Debt Paid (or + Net Debt Issued)
P.V. Viswanath
4
Firm Valuation
Figure 5.6: Firm Valuation
Assets
Cash flows considered are
cashflows from assets,
prior to any debt payments
but after firm has
reinvested to create growth
assets
Liabilities
Assets in Place
Growth Assets
Debt
Equity
Discount rate reflects the cost
of raising both debt and equity
financing, in proportion to their
use
Present value is value of the entire firm, and reflects the value of
all claims on the firm.
Free Cash Flow to the Firm = Earnings before Interest and Taxes (1-tax rate) – Net
Reinvestment
Net Reinvestment is defined as actual expenditures on short-term and long-term assets less
depreciation.
The tax benefits of debt are not included in FCFF because they are taken into account in the firm’s
cost of capital.
P.V. Viswanath
5
Valuation with Infinite Life
DISCOUNTED CASHFLOW VALUATION
Expected Growth
Firm: Growth in
Operating Earnings
Equity: Growth in
Net Income/EPS
Cash flows
Firm: Pre-debt cash
flow
Equity: After debt
cash flows
Firm is in stable growth:
Grows at constant rate
forever
Terminal Value
Value
Firm: Value of Firm
CF1
CF2
CF3
CF4
CF5
CFn
.........
Forever
Equity: Value of Equity
Length of Period of High Growth
Discount Rate
Firm:Cost of Capital
Equity: Cost of Equity
P.V. Viswanath
6
Valuing the Home Depot’s Equity
 Assume that we expect the free cash flows to equity at
Home Depot to grow for the next 10 years at rates much
higher than the growth rate for the economy. To estimate the
free cash flows to equity for the next 10 years, we make the
following assumptions:



The net income of $1,614 million will grow 15% a year each year
for the next 10 years.
The firm will reinvest 75% of the net income back into new
investments each year, and its net debt issued each year will be 10%
of the reinvestment.
To estimate the terminal price, we assume that net income will grow
6% a year forever after year 10. Since lower growth will require less
reinvestment, we will assume that the reinvestment rate after year 10
will be 40% of net income; net debt issued will remain 10% of
reinvestment.
P.V. Viswanath
7
Estimating cash flows to equity: The
Home Depot
Year
1
2
3
4
5
6
7
8
9
10
Net Income
$
1,856
$
2,135
$
2,455
$
2,823
$
3,246
$
3,733
$
4,293
$
4,937
$
5,678
$
6,530
Reinvestment Needs Net Debt Paid
$
1,392
$
(139)
$
1,601
$
(160)
$
1,841
$
(184)
$
2,117
$
(212)
$
2,435
$
(243)
$
2,800
$
(280)
$
3,220
$
(322)
$
3,703
$
(370)
$
4,258
$
(426)
$
4,897
$
(490)
Sum of PV of FCFE =
P.V. Viswanath
$
$
$
$
$
$
$
$
$
$
FCFE
603
694
798
917
1,055
1,213
1,395
1,605
1,845
2,122
PV of FCFE
$
549
$
576
$
603
$
632
$
662
$
693
$
726
$
761
$
797
$
835
$6,833
8
Terminal Value and Value of Equity
today
 FCFE11 = Net Income11 – Reinvestment11 – Net Debt Paid
(Issued)11
= $6,530 (1.06) – $6,530 (1.06) (0.40) – (-277) = $ 4,430 million
 Terminal Price10 = FCFE11/(ke – g)
= $ 4,430 / (.0978 - .06) = $117,186 million
 The value per share today can be computed as the sum of the
present values of the free cash flows to equity during the
next 10 years and the present value of the terminal value at
the end of the 10th year.
Value of the Stock today = $ 6,833 million + $
117,186/(1.0978)10
= $52,927 million
P.V. Viswanath
9
Valuing Boeing as a firm
 Assume that you are valuing Boeing as a firm, and
that Boeing has cash flows before debt payments
but after reinvestment needs and taxes of $ 850
million in the current year.
 Assume that these cash flows will grow at 15% a
year for the next 5 years and at 5% thereafter.
 Boeing has a cost of capital of 9.17%.
P.V. Viswanath
10
Expected Cash Flows and Firm Value
 Terminal Value = $ 1710 (1.05)/(.0917-.05) = $ 43,049
million
Year
Cash Flow
Terminal
Value
1
$978
$895
2
3
4
5
$1,124
$1,293
$1,487
$1,710
$943
$994
$1,047
$28,864
$43,049
Value of Boeing as a firm =
P.V. Viswanath
Present
Value
$32,743
11
What discount rate to use?
 Since financial resources are finite, there is a hurdle that
projects have to cross before being deemed acceptable.
 This hurdle will be higher for riskier projects than for safer
projects.
 A simple representation of the hurdle rate is as follows:
Hurdle rate = Return for postponing consumption +
Return for bearing risk
Hurdle rate = Riskless Rate + Risk Premium
 The two basic questions that every risk and return model in
finance tries to answer are:


How do you measure risk?
How do you translate this risk measure into a risk premium?
P.V. Viswanath
12
The Capital Asset Pricing Model
 Uses variance as a measure of risk
 Specifies that a portion of variance can be diversified away,
and that is only the non-diversifiable portion that is
rewarded.
 Measures the non-diversifiable risk with beta, which is
standardized around one.
 Relates beta to hurdle rate or the required rate of return:
Reqd. ROR = Riskfree rate + b (Risk Premium)
 Works as well as the next best alternative in most cases.
P.V. Viswanath
13
Inputs required to use the CAPM
 According to the CAPM, the required rate of return on an
asset will be:
Required ROR = Rf + b (E(Rm) - Rf)
 The inputs required to estimate the required ROR are:
(a) the current risk-free rate
(b) the expected market risk premium (the premium expected
for investing in risky assets over the riskless asset)
(c) the beta of the asset being analyzed.
P.V. Viswanath
14
The Riskfree Rate
 For an investment to be riskfree, i.e., to have an actual return be
equal to the expected return, there must be:


No default risk; this usually means a government-issued security; but, not
all governments are default free.
No uncertainty about reinvestment rates.
 In practice, the riskfree rate is the rate on a zero coupon
government bond matching the time horizon of the cash flow
being analyzed.
 Using a long term government rate (even on a coupon bond) as
the riskfree rate on all of the cash flows in a long term analysis
will yield a close approximation of the true value.
P.V. Viswanath
15
Measurement of the risk premium
 The risk premium is the premium that investors
demand for investing in an average risk investment,
relative to the riskfree rate.
 As a general proposition, this premium should be



greater than zero
increase with the risk aversion of the investors in that
market
increase with the riskiness of the “average” risk
investment
P.V. Viswanath
16
The Historical Premium Approach
 This is the default approach used by most to arrive at the
premium to use in the model
 In most cases, this approach does the following


it defines a time period for the estimation (1926-Present, 1962Present....)
it calculates average returns on a stock index during the period
 it calculates average returns on a riskless security over the period
 it calculates the difference between the two
 and uses it as a premium looking forward
 The limitations of this approach are:


it assumes that the risk aversion of investors has not changed in a
systematic way across time. (The risk aversion may change from
year to year, but it reverts back to historical averages)
it assumes that the riskiness of the “risky” portfolio (stock index) has
not changed in a systematic way across time.
P.V. Viswanath
17
Historical Average Premiums for the
United States
Historical period Stocks - T.Bills
Stocks - T.Bonds
Arith
Geom
Arith
Geom
1926-1999
9.41%
8.14%
7.64%
6.60%
1962-1999
7.07%
6.46%
5.96%
5.74%
1981-1999
13.24%
11.62%
16.08%
14.17%
Considering that market rates of return since 1999 have been
lower, it is probably more appropriate to use a market risk
premium, which is somewhat lower, such as 5.5%
P.V. Viswanath
18
Estimating Beta
 The standard procedure for estimating betas is to
regress stock returns (Rj) against market returns
(Rm) Rj = a + b Rm

where a is the intercept and b is the slope of the
regression.
 The slope of the regression corresponds to the beta
of the stock, and measures the riskiness of the
stock.
P.V. Viswanath
19
Setting up for the Estimation
 Decide on an estimation period

Services use periods ranging from 2 to 5 years for the regression



Decide on a return interval - daily, weekly, monthly


Longer estimation period provides more data, but firms change.
Shorter periods can be affected more easily by significant firm-specific
event that occurred during the period
Shorter intervals yield more observations, but suffer from more noise.
Noise is created by stocks not trading and biases all betas towards one.
 Estimate returns (including dividends) on stock


Return = (PriceEnd - PriceBeginning + DividendsPeriod)/ PriceBeginning
Included dividends only in ex-dividend month
 Choose a market index, and estimate returns (inclusive of
dividends) on the index for each interval for the period.
P.V. Viswanath
20
Choosing the Parameters: Boeing




Period used: 5 years
Return Interval = Monthly
Market Index: S&P 500 Index.
For instance, to calculate returns on Boeing in May 1995,




Price for Boeing at end of April= $ 27.50
Price for Boeing at end of May = $ 29.44
Dividends during month = $0.125 (It was an ex-dividend month)
Return =($29.44 - $ 27.50 + $ 0.125)/$27.50= 7.50%
 To estimate returns on the index in the same month




Index level (including dividends) at end of April = 514.7
Index level (including dividends) at end of May = 533.4
Dividends on the Index in May = 1.84
Return =(533.4-514.7+1.84)/ 514.7 = 3.99%
P.V. Viswanath
21
Boeing’s Historical Beta
Boeing versus S&P 500: 10/93-9/98
10.00%
Regression
line
5.00%
Returns on Boeing
-25.00%
-20.00%
-15.00%
-10.00%
-5.00%
0.00%
0.00%
5.00%
10.00%
15.00%
20.00%
-5.00%
Beta is slope of this line
-10.00%
-15.00%
Each point represents a month
of data.
-20.00%
Returns on S&P 500
P.V. Viswanath
22
The Regression Output




ReturnsBoeing = -0.09% + 0.96 ReturnsS & P 500
R squared=29.57%
Intercept = -0.09%
Slope = 0.96
P.V. Viswanath
23
Estimating Expected Returns:
December 31, 1998
 Boeing’s Beta = 0.96
 Riskfree Rate = 5.00% (Long term Government
Bond rate)
 Risk Premium = 5.50% (Approximate historical
premium)
 Expected Return = 5.00% + 0.96 (5.50%) = 10.31%
P.V. Viswanath
24
Fundamental Determinants of Betas
 Type of Business: Firms in more cyclical businesses or that
sell products that are more discretionary to their customers
will have higher betas than firms that are in non-cyclical
businesses or sell products that are necessities or staples.
 Operating Leverage: Firms with greater fixed costs (as a
proportion of total costs) will have higher betas than firms
will lower fixed costs (as a proportion of total costs)
 Financial Leverage: Firms that borrow more (higher debt,
relative to equity) will have higher equity betas than firms
that borrow less.
P.V. Viswanath
25
Determinant 1: Product Type
 Industry Effects: The beta value for a firm
depends upon the sensitivity of the demand for its
products and services and of its costs to
macroeconomic factors that affect the overall
market.


Cyclical companies have higher betas than non-cyclical
firms
Firms which sell more discretionary products will have
higher betas than firms that sell less discretionary
products
P.V. Viswanath
26
Determinant 2: Operating Leverage
Effects
 Operating leverage refers to the proportion of the
total costs of the firm that are fixed.
 Other things remaining equal, higher operating
leverage results in greater earnings variability
which in turn results in higher betas.
P.V. Viswanath
27
Determinant 3: Financial Leverage
 As firms borrow, they create fixed costs (interest
payments) that make their earnings to equity
investors more volatile.
 This increased earnings volatility which increases
the equity beta
P.V. Viswanath
28
Equity Betas and Leverage
 The beta of equity alone can be written as a function of the
unlevered beta and the debt-equity ratio
bL = bu (1+ ((1-t)D/E)
where
bL = Levered or Equity Beta
bu = Unlevered Beta
t = Corporate marginal tax rate
D = Market Value of Debt
E = Market Value of Equity
 The unlevered beta measures the riskiness of the business
that a firm is in and is often called an asset beta.
P.V. Viswanath
29
Effects of leverage on betas: Boeing
 The regression beta for Boeing is 0.96. This beta is a levered
beta (because it is based on stock prices, which reflect
leverage) and the leverage implicit in the beta estimate is the
average market debt equity ratio during the period of the
regression (1993 to 1998)
 The average debt equity ratio during this period was
17.88%.
 The unlevered beta for Boeing can then be estimated:(using
a marginal tax rate of 35%)
= Current Beta / (1 + (1 - tax rate) (Average Debt/Equity))
= 0.96 / ( 1 + (1 - 0.35) (0.1788)) = 0.86
P.V. Viswanath
30
Betas are weighted Averages
 The beta of a portfolio is always the market-value
weighted average of the betas of the individual
investments in that portfolio.
 Thus,


the beta of a mutual fund is the weighted average of the
betas of the stocks and other investment in that portfolio
the beta of a firm after a merger is the market-value
weighted average of the betas of the companies involved
in the merger.
P.V. Viswanath
31
The Boeing/McDonnell Douglas
Merger
Company
Beta Debt
Equity
Firm Value
Boeing
0.95 $ 3,980 $ 32,438
$
36,418
McDonnell Douglas 0.90
$ 2,143 $ 12,555 $
14,698
P.V. Viswanath
32
Beta Estimation: Step 1
 Calculate the unlevered betas for both firms
Boeing = 0.95/(1+0.65*(3980/32438)) = 0.88
McDonnell Douglas = 0.90/(1+0.65*(2143/12555))
= 0.81
 Calculate the unlevered beta for the combined firm
Unlevered Beta for combined firm
= 0.88 (36,418/51,116) + 0.81 (14,698/51,116)
= 0.86
P.V. Viswanath
33
Beta Estimation: Step 2
 Boeing’s acquisition of McDonnell Douglas was
accomplished by issuing new stock in Boeing to cover the
value of McDonnell Douglas’s equity of $12,555 million.
Debt = McDonnell Douglas Old Debt + Boeing’s Old Debt
= $3,980 + $2,143 = $6,123 million
Equity = Boeing’s Old Equity + New Equity used for
Acquisition
= $ 32,438 + $ 12,555 = $44,993 million
D/E Ratio = $ 6,123/44,993 = 13.61%
New Beta = 0.86 (1 + 0.65 (.1361)) = 0.94
P.V. Viswanath
34
The Home Depot’s Comparable Firms
Compa ny Na me
Buil ding Materi als
Catal ina Ligh ting
Cont'l Material s Corp
Eagl e Hardware
Emco Li mite d
Fas tena l Co.
HomeBa se Inc.
Hughe s Sup ply
Lowe's Cos .
Waxma n In dustries
Wes tburn e In c.
Wol ohan Lum ber
Sum
Averag e
Market Cap $ (Mil)
Beta
$13 6
1.0 5
$16
1
$32
0.5 5
$61 2
0.9 5
$18 7
0.6 5
$1,157
1.2 5
$22 7
1.1
$61 0
1
$12 ,554
1.2
$18
1.2 5
$60 7
0.6 5
$76
0.5 5
$16 ,232
0.9 3
P.V. Viswanath
Deb t Due 1-Yr Ou t
$1
$7
$2
$6
$39
$16
$1
$11 1
$6
$9
$2
$20 0
Lon g-Term Deb t
$11 3
$19
$7
$14 6
$11 9
$
$11 6
$33 5
$1,046
$12 1
$34
$20
$2,076
35
Estimating The Home Depot’s
Bottom-up Beta
 Average Beta of comparable firms = 0.93
 D/E ratio of comparable firms =
(200+2076)/16,232 = 14.01%
 Unlevered Beta for comparable firms =
0.93/(1+(1-.35)(.1401)) = 0.86
 If the Home Depot’s D/E ratio is 20%, our bottomup estimate of Home Depot’s beta is
0.86[1+(1-.35)(.2)] = 0.9718
P.V. Viswanath
36
From Cost of Equity to Cost of Capital
 The cost of capital is a composite cost to the firm of
raising financing to fund its projects.
 In addition to equity, firms can raise capital from
debt
P.V. Viswanath
37
Estimating the Cost of Debt
 If the firm has bonds outstanding, and the bonds are traded,
the yield to maturity on a long-term, straight (no special
features) bond can be used as the interest rate.
 If the firm is rated, use the rating and a typical default spread
on bonds with that rating to estimate the cost of debt.
 If the firm is not rated,


and it has recently borrowed long term from a bank, use the interest
rate on the borrowing or
estimate a synthetic rating for the company, and use the synthetic
rating to arrive at a default spread and a cost of debt
 The cost of debt has to be estimated in the same currency as
the cost of equity and the cash flows in the valuation.
P.V. Viswanath
38
Estimating Synthetic Ratings
 The rating for a firm can be estimated using the financial
characteristics of the firm. In its simplest form, the rating
can be estimated from the interest coverage ratio
Interest Coverage Ratio = EBIT / Interest Expenses
 Consider InfoSoft, a firm with EBIT of $2000 million and
interest expenses of $ 315 million
Interest Coverage Ratio = 2,000/315= 6.15

Based upon the relationship between interest coverage ratios and
ratings, we would estimate a rating of A for the firm.
P.V. Viswanath
39
Interest Coverage Ratios, Ratings and
Default Spreads
Interest Coverage Ratio
Rating
Default Spread
> 12.5
9.50 - 12.50
7.50 – 9.50
6.00 – 7.50
4.50 – 6.00
3.50 – 4.50
3.00 – 3.50
2.50 – 3.00
2.00 - 2.50
1.50 – 2.00
1.25 – 1.50
0.80 – 1.25
0.50 – 0.80
AAA
AA
A+
A
ABBB
BB
B+
B
BCCC
CC
C
0.20%
0.50%
0.80%
1.00%
1.25%
1.50%
2.00%
2.50%
3.25%
4.25%
5.00%
6.00%
7.50%
< 0.65
D
10.00%
P.V. Viswanath
40
Estimating Market Value Weights
 Market Value of Equity should include the following



Market Value of Shares outstanding
Market Value of Warrants outstanding
Market Value of Conversion Option in Convertible Bonds
 Market Value of Debt is more difficult to estimate because few
firms have only publicly traded debt. There are two solutions:


Assume book value of debt is equal to market value
Estimate the market value of debt from the book value; for Boeing, the
book value of debt is $6,972 million, the interest expense on the debt is $
453 million, the average maturity of the debt is 13.76 years and the pre-tax
cost of debt is 5.50%.
Estimated MV of Boeing Debt =
1


(1

13.76 

6, 972
(1.055 )
453 

13.76  $7, 631
.055

 (1.055)




P.V. Viswanath
41
Estimating Cost of Capital: Boeing
 Equity



Cost of Equity = 5% + 1.01 (5.5%) = 10.58%
Market Value of Equity =
$32.60 Billion
Equity/(Debt+Equity ) =
82%
 Debt



After-tax Cost of debt =
Market Value of Debt =
Debt/(Debt +Equity) =
5.50% (1-.35) = 3.58%
$ 8.2 Billion
18%
 Cost of Capital = 10.58%(.80)+3.58%(.20) = 9.17%
P.V. Viswanath
42
Estimating the Expected Growth Rate
Expected Growth
Net Income
Retention Ratio=
1 - Dividends/Net
Income
X
Operating Income
Return on Equity
Net Income/Book Value of
Equity
Reinvestment
Rate = (Net Cap
Ex + Chg in
WC/EBIT(1-t)
P.V. Viswanath
X
Return on Capital =
EBIT(1-t)/Book Value of
Capital
43
Expected Growth in EPS
gEPS = (Retained Earningst-1/ NIt-1) * ROE
= Retention Ratio * ROE
= b * ROE
• ROE = (Net Income)/ (BV: Common Equity)
• This is the right growth rate for FCFE
• Proposition: The expected growth rate in earnings
for a company cannot exceed its return on equity in
the long term.
P.V. Viswanath
44
Expected Growth in EBIT And
Fundamentals
 Reinvestment Rate and Return on Capital
gEBIT = (Net Capex + Change in WC)/EBIT(1-t) * ROC
= Reinvestment Rate * ROC
 Return on Capital =
(EBIT(1-tax rate)) / (BV: Debt + BV: Equity)
 This is the right growth rate for FCFF
 Proposition: No firm can expect its operating income to
grow over time without reinvesting some of the operating
income in net capital expenditures and/or working capital.
P.V. Viswanath
45
Getting Closure in Valuation
 A publicly traded firm potentially has an infinite
life. The value is therefore the present value of cash
t =  CF
t
Value = 
flows forever.
t
t = 1 (1+ r)
 Since we cannot estimate cash flows forever, we
estimate cash flows for a “growth period” and then
estimate a terminal value, to capture the value at the
end of the period: Value = t =N CFt t  Terminal Value
t = 1 (1 + r)
P.V. Viswanath
N
(1 + r)
46
Stable Growth and Terminal Value
 When a firm’s cash flows grow at a “constant” rate forever,
the present value of those cash flows can be written as:
Value = (Expected Cash Flow Next Period) / (r - g) where,
r = Discount rate (Cost of Equity or Cost of Capital)
g = Expected growth rate
 This “constant” growth rate is called a stable growth rate
and cannot be higher than the growth rate of the economy in
which the firm operates.
 While companies can maintain high growth rates for
extended periods, they will all approach “stable growth” at
some point in time.
 When they do approach stable growth, the valuation formula
above can be used to estimate the “terminal value” of all
cash flows beyond.
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Estimating Stable Growth Inputs
 Start with the fundamentals:

Profitability measures such as return on equity and capital, in stable
growth, can be estimated by looking at



industry averages for these measure, in which case we assume that this
firm in stable growth will look like the average firm in the industry
cost of equity and capital, in which case we assume that the firm will
stop earning excess returns on its projects as a result of competition.
Leverage is a tougher call. While industry averages can be used here
as well, it depends upon how entrenched current management is and
whether they are stubborn about their policy on leverage (If they are,
use current leverage; if they are not; use industry averages)
 Use the relationship between growth and fundamentals to
estimate payout and net capital expenditures.
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Estimating Stable Period Net Cap Ex
gEBIT
= (Net Capex + Change in WC)/EBIT(1-t) * ROC
= Reinvestment Rate * ROC
Therefore, Reinvestment Rate = gEBIT / Return on Capital
 For instance, assume that Disney in stable growth will grow
5% and that its return on capital in stable growth will be
16%. The reinvestment rate will then be:
Reinvestment Rate for Disney in Stable Growth = 5/16 =
31.25%
 In other words,

the net capital expenditures and working capital investment each
year during the stable growth period will be 31.25% of after-tax
operating income.
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Relative Valuation
 In relative valuation, the value of an asset is derived from
the pricing of 'comparable' assets, standardized using a
common variable such as earnings, cashflows, book value or
revenues. Examples include -• Price/Earnings (P/E) ratios

and variants (EBIT multiples, EBITDA multiples, Cash Flow multiples)
• Price/Book (P/BV) ratios

and variants (Tobin's Q)
• Price/Sales ratios
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Multiples and DCF Valuation
 Gordon Growth Model: P  rDPS
g
 Dividing both sides by the earnings,
1
0
n
P0
Payout Ratio * (1  g n )
 PE =
EPS0
r-gn
 Dividing both sides by the book value of equity,
P0
ROE * Payout Ratio * (1  g n )
 PBV =
BV 0
r-g
n
 If the return on equity is written in terms of the retention
ratio and the expected growth rate
P0
ROE - gn
 PBV =
BV 0
r-gn
 Dividing by the Sales per share,
P0
Profit Margin * Payout Ratio * (1  g n )
 PS =
Sales 0
r-gn
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