VALUATION OF COMMON
STOCK
A FEW MORE LESSONS
Dangers in Constant-Growth Formulas
•
•
•
•
NO FIRM IN REALITY HAVE A PERPETUAL GROWTH AT A FIXED RATE.
FIR’M PROFITABILITY ALSO DECREASES OVER TIME.
SO WITH RETURN ON EQUITY
FOR EXAMPLE, SUPPOSE A FIRM AT PRESENT HAVING 25% RoE, FACES A SUDDEN FALL IN ITS BY
10%. SO, NOW IT BECOMES 15%. NATURALLY ITS GROWTH RATE WOULD DRASTICALLY FALL.
• SAY IT WAS RETAINING EARLIER 80% OF ITS EQUITY EARNINGS WHEREAS NOW DUE TO FALL IN
BUSINESS GROWTH IT WOULD BE WISER TO RETAIN LESS FOR OBVIOUS REASONS. THUS IF IT
REATAINS 50% INSTEAD, THE g WOULD BE 0.5*0.15, or, 7.5%. IT’S A DRASTIC FALL( EARLIER g
WAS 0.8*0.25=20%).
• THEREFORE, IN SUCH CASES, IN REALITY, IT WOULD BE WISER TO USE GENERAL DCF FORMULA
FOR VAUATION AS FOLLOWS
Po=D1 /(1+r)+ D2/(1+r)^2+ D3/(1+r)^3+….+ Dn/(1+r)^n
EXAMPLE
Phoenix produces dividends in three consecutive years of
10, 12, and 14.40, respectively. The dividend in year 4 is
estimated to be 16.56 and should grow in perpetuity at
15%. Given a discount rate of 12%, what is the price of the
stock?TWO STAGE GROWTH MODEL.xlsx
The Link between Stock Price and Earnings Per Share
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.
• Ratio of dividends to earnings per share.
Retention Ratio.
• Fraction of earnings retained by the firm.
1
The Link between Stock Price and Earnings Per Share
Example
Our company forecasts to pay an ₹8.33 dividend next year,
which represents 100% of its earnings. This will provide
investors with a 15% expected return. Instead, we decide
to plow back 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
Po= 8.33/0.15= ₹55.53
With Growth
g= 0.4*0.25 or .010
D1= 8.33*0.6=5
Po= (5/(0.15-0.10) = ₹100
2
PRESENT VALUE OF GROWTH OPPORTUNITIES (PVGO)
Example continued
If the company did not plow back 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). And in this case, it would be:
PVGO= 100-55.53= ₹44.47
The Link between Stock Price and Earnings Per Share
Concluded
Net present value of a firm’s future investments
=
PVGO of a FIRM
James Walter’s Model on Dividend
• P= D + (EPS – D)*(r/k)
k
• Where, r= return on investment; k= cost of equity
• First component, D/k= present value of an infinite stream of dividend
• Second component, [(EPS- D)*(r/k)]/k= present value of an infinite
stream of return from retained earnings
6/6/2022
Professor Manipadma Datta
8
Example
Growth firm: r>k
Normal firm: r=k
Declining firm : r<k
r=20%
k=15%
EPS=₹10
r=15%
k=15%
EPS=₹10
r=15%
k=20%
EPS=₹10
Pay 100% of EPS
P= (10/.0.15)+0= ₹66.67
Pay 100% of EPS
P= (10/0.15)+0= ₹66.67
Pay 100% of EPS
P= (10/0.15)=₹66.67
Pay 50% of EPS
P=[ (5/0.15)+{(105)*(20/15)]/0.15)}]=
33.33+44.44=₹77.77
Pay 50% of EPS
P= (5/0.15)+(5/0.15)=₹66.67
Pay 50% of EPS
P= [(5/0.15)+{(10-5)*(15/20)}/0.15}]
33.33+25=₹58.33
6/6/2022
Professor Manipadma Datta
9
So, it is vindicated,
Growth firm tends to pay lesser dividend and its share value consists of
mainly PVGO.
In in case of declining firm, it happens exactly the rese=verse.
6/6/2022
Professor Manipadma Datta
10
Valuation Format
1
Valuing a Business or Project
The value of a business or project is usually
computed as the discounted value of free cash
flows out to a valuation horizon (H).
The valuation horizon is sometimes called the
terminal value and is calculated like PVGO.
FCF1
FCF2
FCFH
PVH
PV 

 ... 

1
2
H
(1  r ) (1  r )
(1  r )
(1  r )H
Valuation Format
2
Valuing a Business or Project
FCF1
FCF2
FCFH
PV 

 ... 

1
2
H
(1  r ) (1  r )
(1  r )
PV  free cash flows
PVH
H
(1  r )
PV horizon value
FREE CASH FLOW TO EQUITY(FCFE)
FCFE=
PAT− PREFERENCE DIVIDEND
−(CAPEX − DEPRECIATION)±(NET CHANGE IN
WORKING CAPITAL)
+ (NEW DEBT ISSUE − DEBT REPAYMENT
+(NEW PREFERENCE ISSUE − REDEMPTION)
Equity Value=
∞
𝑡=1 𝐹𝐶𝐹𝐸𝑡
÷ (1 + 𝑅𝑜𝐸)^𝑡
EXAMPLE
1
Asset value, start of year
2
3
4
5
6
7
8
9
10
10.00
11.20
12.54
14.05
15.31
16.69
18.19
19.29
20.44
21.67
Earnings
1.20
1.34
1.51
1.69
1.84
2.00
2.18
2.31
2.45
2.60
Investment
1.20
1.34
1.51
1.26
1.38
1.50
1.09
1.16
1.23
1.30
Free cash flow (FCF)
0.00
0.00
0.00
0.42
0.46
0.50
1.09
1.16
1.23
1.30
Asset value, end of year
11.20
12.54
14.05
15.31
16.69
18.19
19.29
20.44
21.67
22.97
Return on assets (ROA)
0.12
0.12
0.12
0.12
0.12
0.12
0.12
0.12
0.12
0.12
Asset growth rate
0.12
0.12
0.12
0.09
0.09
0.09
0.06
0.06
0.06
0.06
0.12
0.12
0.09
0.09
0.09
0.06
0.06
0.06
Earnings growth rate, from
previous year
6/6/2022
0.12
Professor Manipadma Datta
14
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%.
PV(FCF) 
0
0
0
0.42 0.46
.50





1.1 1.1 2 1.1 3 1.1 4 1.1 5 1.1 6
 0.90
Horizon Value= 1.09/(0.10-0.06)=₹27.3 million
PV of Horizon Value= 27.3/(0.10-0.06)= ₹15.4 million
Therefore, PV of Business= 0.9+15.4= ₹16.3 million