3.

STOCK VALUATION
Prof. Prashant Das, PhD
COMMON STOCK (EQUITY)
▪ Common stocks (equity) represents a
share of ownership in a corporation Market Value Asset
▪ Common stockholders have no explicit
contract to get their money back; but
are entitled to the “residual claim” after Equity
other stakeholders have received their
due
Debt
▪ Stock ownership is represented in
terms of number of shares held by an
investor WRT to total number of shares
outstanding
▪ Equity (share) holders can influence Liability Balance Sheet
($)
the management of a corporation
through their exercise of voting rights
Equity value can not be negative
(“Limited Liability”)
WHY ARE STOCKS VALUED?

▪ The book value of stock is often inaccurate

▪ Inaccurate valuation of some intangible assets (trademarks, patents, etc.)
▪ Ignores the value of synergy

▪ Analysts can estimate the share price for IPOs

▪ Managers may strategize on how to maximize the share price

▪ Analysts can assess the under- or over-pricing of stocks

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SOME VALUATION-RELATED METRICS

▪ Book Value - Net worth of the firm according to the balance sheet

▪ Dividend - Periodic cash distribution from the firm to the shareholders

▪ P/E Ratio - Price per share divided by earnings per share

▪ P/B Ratio – Market Capitalization/ Book Value of Equity

▪ Market Value Balance Sheet - Financial statement that uses market value of assets

and liabilities

4
VALUATION BY COMPARABLES

More useful when a company’s dividends Price-to-EBITDA

are not stabilized 𝑀𝑎𝑟𝑘𝑒𝑡 𝐶𝑎𝑝𝑖𝑡𝑎𝑙𝑖𝑧𝑎𝑡𝑖𝑜𝑛+𝐵𝑜𝑜𝑘 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑑𝑒𝑏𝑡
=
Ratio comparisons 𝐸𝐵𝐼𝑇𝐷𝐴

𝑃 𝑃𝑟𝑖𝑐𝑒 𝑝𝑒𝑟 𝑠ℎ𝑎𝑟𝑒 Price-to-Sales

▪
𝐸
= 𝐸𝑎𝑟𝑛𝑖𝑛𝑔 𝑁𝑒𝑡 𝐼𝑛𝑐𝑜𝑚𝑒 𝑝𝑒𝑟 𝑠ℎ𝑎𝑟𝑒 𝑀𝑎𝑟𝑘𝑒𝑡 𝐶𝑎𝑝𝑖𝑡𝑎𝑙𝑖𝑧𝑎𝑡𝑖𝑜𝑛+𝐵𝑜𝑜𝑘 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑑𝑒𝑏𝑡
= 𝑆𝑎𝑙𝑒𝑠
𝑃 𝑃𝑟𝑖𝑐𝑒 𝑝𝑒𝑟 𝑠ℎ𝑎𝑟𝑒
▪ = 𝐵𝑜𝑜𝑘 𝑣𝑎𝑙𝑢𝑒 𝑝𝑒𝑟 𝑠ℎ𝑎𝑟𝑒
𝐵 ▪ Using trailing twelve months (TTM) or
forecast measures
▪ Usefulness of either method depends
on time/ industry
▪ Outliers must be excluded (to avoid
excessive subjectivity)

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 https://economictimes.indiatimes.com/maruti-suzuki-india-
ltd/stocks/companyid-11890.cms

PE reported here uses TTM EPS. If you used EPS forecast, would the PE be higher or lower? 5
TRADING
Market Depth

Trading Types

▪ Market Order
▪ Limit Order
▪ Stop-Loss

Source: Zerodha
EXPECTED RETURN

Cash flow analysis requires a discount rate estimation. The Expected return is the
discount rate.
Expected Return - The percentage yield that an investor forecasts from a specific
investment over a set period of time. Sometimes called the market capitalization
rate.

Div1 + P1 − P0 Div10 P − P0
Expected return = r = = + 1
P0 P0 P0

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EXAMPLE: ONE-YEAR INVESTMENT
3M is expected to pay a dividend of $1.92 per share in the coming year. You expect the
stock price to be $85 per share at the end of the year. Investments with equivalent risk
have an expected return of 11%.

What is the most you would pay (P) for 3M stock today?
𝐷𝑖𝑣1 𝑃 $1.92 $85
𝑃0 = 1+𝑟
1
+ 1+𝑟 = 1.1
+ 1.1
= $78.31

What are the dividend yield (y) and capital gains (g)?
𝐷𝑖𝑣1 $1.92
𝑦0 = = $78.31 = 2.45%
𝑃0

𝑃1 −𝑃0 $85−$78.31
𝑔0 = 𝑃0
= $78.31
= 8.55%
VALUATION BY DCF ANALYSIS
The value of any stock is the present value of its future cash flows. This reflects the
DCF formula. Dividends represent the future cash flows of the firm.

PV(stock) = PV(expected future dividends)

Div
∞

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VALUATION BY DCF
Dividend Discount Model - Computation of today’s stock price which states that
share value equals the present value of all expected future dividends
Div1 Div 2 Div H + PH
P0 = + + ... +
(1 + r ) (1 + r )
1 2
(1 + r ) H

H
Div t PH
P0 =  +
t =1 (1 + r ) t
(1 + r ) H

H - Time horizon for your investment.

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EXAMPLE: VALUATION BY DCF
Current forecasts are for XYZ Company to pay dividends of $3, $3.24, and $3.50
over the next three years, respectively. At the end of three years, you anticipate
selling your stock at a market price of $94.48. What is the price of the stock given a
12% expected return?

3.00 3.24 3.50 + 94.48

PV = + +
(1 + .12)1 (1 + .12) 2 (1 + .12) 3
PV = $75.00
This method requires an estimate of the terminal value ($94.48 in this example). The
terminal value estimated as a perpetuity assumes a stabilized growth in dividends
after a few years in the future.
What are the contributions of (1) dividend stream and (2) terminal value in stock
valuation?
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WHEN THE GROWTH IS STABLE…

Given:
𝐷𝑖𝑣1 = $5
𝑃𝑟𝑖𝑐𝑒0 = $100

𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑 𝑔𝑟𝑜𝑤𝑠 𝑎𝑛𝑛𝑢𝑎𝑙𝑙𝑦 𝑏𝑦 10%

∴ 𝑃𝑟𝑖𝑐𝑒 𝑔𝑟𝑜𝑤𝑠 𝑎𝑛𝑛𝑢𝑎𝑙𝑙𝑦 𝑏𝑦 10%

Div1   1+ g  
H
PH
P0 = 1 −   +
r − g   1 + r   (1 + r ) H
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When the growth rate is stable, even if the holding period is finite, over
long enough horizons, the contribution of the terminal value tends to zero.
It is fair to consider a stock as a perpetuity.

PV = stock price today ( P0 ); CF = Div1 Div1

Capitalization rate = r = +g
Div1 P0
As t →  | P0 =
r−g
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STOCK PRICE AND EARNINGS PER SHARE

▪ Present Value of Growth Opportunities (PVGO) - Net present value of a firm’s

future investments.

▪ Sustainable Growth Rate - Steady rate at which a firm can grow:

= plowback ratio x return on equity

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STOCK PRICE AND PVGO
Example: Our company forecasts to pay a $8.33 dividend next year, which represents
100% of its earnings. This will provide investors with a 15% expected return. Instead,
we decide to plowback 40% of the earnings at the firm’s current return on equity of
25%. What is the value of the stock before and after the plowback decision?

No Growth With Growth

8.33 g = .25  .40 = .10
P0 = = $55 .56
.15 5.00
P0 = = $100.00
.15 − .10
If the company did not plowback some earnings, the stock price would remain at $55.56.
With the plowback, the price rose to $100.00. The difference between these two
numbers is called the present value of growth opportunities (PVGO).

PVGO = $100-$55.56 = $44.44

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ESTIMATING THE DISCOUNT RATE
Example
Northwest Natural Gas stock was selling for $49.43 per share at the start of 2015.
Dividend payments for the next year were expected to be $2.00 a share. What is
the dividend yield, assuming no growth?

2.00
 = Dividend yield = .041
49.43

What is the capitalization rate, assuming a growth rate of 7.7%?

r = Dividend Yield + Growth Rate

2.00
= +g = + .077
49.43
= .118
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ESTIMATING THE “G”

Subjective estimate:
▪ one could rely on expert opinions.
▪ Also, in the long run, it should be close to g[GDP]

Alternatively, Dividend Growth Rate can also be derived from applying the return
on equity to the percentage of earnings plowed back into operations.
g = return on equity × plowback ratio
If a firm elects to pay a lower dividend, and reinvest the funds, the stock price may
increase because future dividends may be higher
Payout Ratio - Fraction of earnings paid out as dividends
Plowback Ratio - Fraction of earnings retained by the firm

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 INTUITION BEHIND “G = PLOWBACK RATIO X ROE”
Company generates Earnings
E

Plowed back % = b Distributed %= 1-b

At t=0 At t=0
Invest b.E Dividend 𝐷0 =(1-b).E
Return generated = RoE ∴ 𝑔𝑟𝑜𝑤𝑡ℎ 𝑖𝑛 𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑, 𝑔

𝐷1 −𝐷0
= 𝐷0
At t=1 At t=1
Earning from Plowedback Investment Earning from Original Investment
b.E.RoE E =
1−𝑏 .𝐸+ 1−𝑏 .𝑏.𝐸.𝑅𝑜𝐸 − 1−𝑏 .𝐸
1−𝑏 .𝐸

Total Earning Total Distribution = b.RoE

E +b.E.RoE 𝐷1 =(1-b)*[E +b.E.RoE]
VALUING NON-CONSTANT GROWTH

▪ In most cases, the first few years of cash flows are assumed to be uncertain. The
Terminal value is estimated at a future time when the dividend growth will have
stabilized.
Div1 Div 2 Div H PH Div H +1
PV = + + ... + + | PH =
(1 + r )1 (1 + r ) 2 (1 + r ) H (1 + r ) H r−g

Example: Phoenix produces dividends in three consecutive years of 0, .31, and .65,
respectively. The dividend in year four is estimated to be .67 and should grow in
perpetuity at 4%. Given a discount rate of 10%, what is the price of the stock?

0 .31 .65  1 .67 

PV = + + + 
(1 + .1) (1 + .1) (1 + .1)  (1 + .1) (.10 − .04) 
1 2 3 3

= 9.13
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VALUATION WITH MULTIPLES
In the previous example, consider that the book value of Equity (B) per-share at the
end of year-3 is $4.1 ; and the projected EPS at the end of Year 4 is $1.34. The
earnings have stabilized.
Prevailing P/B in the industry = 2.8
→𝑃𝑉𝐻 = 2.8*4.1 =$11.48
0 .31 .65  11.48 
PV = + + + = 9.37
(1 + .1)1 (1 + .1) 2 (1 + .1)3  (1 + .1)3 

Prevailing P/E in the industry = 8.5

→𝑃𝑉𝐻 = 8.1*1.34 =$11.39
0 .31 .65  11.39 
PV = + + + = 9.30
(1 + .1)1 (1 + .1) 2 (1 + .1)3  (1 + .1)3 
VALUING A BUSINESS

Valuing a Business or Project follows the same logic as stock valuation. However,
unlike a stocks cash flows (i.e. dividends), we discount the company’s free cash
flows and the company’s estimated terminal value.

FCF1 FCF2 FCFH PVH

PV = + + ... + +
(1 + r ) (1 + r )
1 2
(1 + r ) H
(1 + r ) H

PV (free cash flows) PV (horizon value)

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▪ Enterprise Value = Market Value of ▪ WACC = 𝑤𝑒 . 𝐾𝑒 + 𝑤𝑑 . 𝐾𝑑 ; where 𝑤
Equity + Debt – Cash denotes the percent of capital financed.
▪ Market Value of Equity = Enterprise
Value - Debt + Cash
EXAMPLE:
REMEMBER:
To finance an asset, 60% of capital was
raised from debt that costs 10% in
▪ The discount rate for enterprise interest; and the remaining from equity
valuation is different from the discount with an expected return of 20%.
rate for equity valuation
▪ 𝑅𝑒𝑞𝑢𝑖𝑡𝑦 = 𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝐼𝑅𝑅𝑒𝑞𝑢𝑖𝑡𝑦 = 𝐾𝑒
WACC =0.6*10% + 0.4*20% =14%
▪ 𝑅𝑑𝑒𝑏𝑡 = 𝐾𝑑 = 𝐸𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒 𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑟𝑎𝑡𝑒
▪ 𝑅𝑒𝑛𝑡𝑒𝑟𝑝𝑟𝑖𝑠𝑒 = 𝑤𝑒𝑖𝑔ℎ𝑡𝑒𝑑 𝑎𝑣𝑒𝑟𝑎𝑔𝑒 (𝐾𝑒 , 𝐾𝑑 ), The FCF of the enterprise will be
also known as weighted average cost of capital discounted at 14%
(WACC)
RECAP: WHAT IS FREE CASH FLOW (FCF)?
FCF is the cash flow available for payments to capital providers (stockholders and
debtholders) after the company has made investments in fixed assets, new products and
working capital.
▪ Operating cash flow = EBIT(1-Tax Rate) +Depr. & Amort.
= NOPAT +Depr. & Amort.

▪ Operating Capital = Capital Exp. +∆ Net Oper. Working Capital

▪ Free Cash Flow (FCF) = Operating cash flow – Investment in Operating Capital

Capital Exp.
EBIT(1-Tax Rate) +
FCF = + ∆ Net Oper.
Depr. & Amort. Working
37
Capital
VALUING A BUSINESS
Example

Given the cash flows for Concatenator Manufacturing Division, calculate the PV of
near term cash flows, PV (horizon value), and the total value of the firm when r =
10% and g = 6%.

Year 0 1 2 3 4 5 6 7 8 9 10
FCF 0.00 0.00 0.00 0.42 0.46 0.50 1.09 1.16 1.23 1.30
g 9.5% 8.7% 118% 6.4% 6.03% 5.69%
Stabilized cash flows

▪ The growth rate is usually close to growth in revenue

40
VALUING A BUSINESS
Example - continued
Cash flows stabilize from year-7

∴ Year-7 cash flow can be capitalized as the terminal value of Year-6

 1.09  PV(FCF) =
0
+
0
+
0
+
0.42 0.46
+ +
.50
Horizon value =   = 27.3
 .10 − .06  1.1 (1.1)2 (1.1)3 (1.1)4 (1.1)5 (1.1)6
27.30 = 0.90
PV(horizon value) = = 15.4
(1.10) 6

PV(business) = PV(FCF) + PV(horizon value)

= 0.90 + 15.40
= $16.3 million

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BONUS SLIDES: WHEN DO COMPANIES PLOW BACK
Suppose, r = the expected return; RoE = r + x
P = stock price | B = Book value of equity | b = plowback ratio | Earning E = B.RoE

𝐷𝑖𝑣 1−𝑏 .𝐵.𝑅𝑜𝐸

𝑊𝑒 𝑘𝑛𝑜𝑤, 𝑃 = =
𝑟−𝑔 𝑟−𝑏.𝑅𝑂𝐸

𝑃 1−𝑏 .𝑟+ 1−𝑏 .𝑥

→ =
𝐵 1−𝑏 .𝑟−𝑏.𝑥

Three Possibilities:

𝑃
𝑥=0→ =1
𝐵

𝑃
x>0→ >1 → RoE > r: company has growth opportunities, plowback is good
𝐵

𝑃
x<0→ <1 → RoE < r: plowback is bad. Investors are better off collecting Earnings 29
𝐵
MATHEMATICAL DERIVATION OF PVGO
𝐷𝑖𝑣 𝐸𝑃𝑆(1−𝑏) 𝐸𝑃𝑆(1−𝑏)
𝑃0 = = =
𝑟−𝑔 𝑟−𝑔 𝑟−𝑅𝑜𝐸.𝑏
𝐸𝑃𝑆(1−𝑏)
= 𝑅𝑜𝐸.𝑏
𝑟(1− 𝑟 )
𝐸𝑃𝑆 1−𝑏
=
𝑟 1−𝑅𝑜𝐸.𝑏
𝑟
𝑅𝑜𝐸
𝐸𝑃𝑆 1−𝑏 𝐸𝑃𝑆 𝑏( 𝑟 −1)
= 1+ 𝑅𝑜𝐸.𝑏 −1 = 1+ 𝑅𝑜𝐸.𝑏
𝑟 1− 𝑟 𝑟 1− 𝑟
𝑅𝑜𝐸
𝐸𝑃𝑆 𝑏.𝐸𝑃𝑆 −1
= + 𝑟
𝑅𝑜𝐸.𝑏
𝑟 𝑟 1−
𝑟

PVGO