FIN 614: Financial Management
Larry Schrenk, Instructor
1. Some Methods and Issues
2. Stock Valuation
1. Constant Dividend Model
2. (Constantly) Growing Dividend Model
3. Mixed Model
Discounted Dividend Model (DDM)
A Discounted Cash Flow Model (DCF)
P/E Ratio Methodologies
Other Ratio Methodologies
Capital Asset Pricing Model (CAPM)
Relative Valuation
Free Cash Flow
A Discounted Cash Flow Model (DCF)
Stock Cash Flows Uncertain:
Determined by the Board of Directors
Not Required
Proceeds from Sale of Stock Uncertain
Contrast: Bond Cash Flows are Fixed
Difficulties in Stock Valuation:
Dividend Cash Flows not Known in Advance
Life of Stock is Essentially Forever
Hard to Determine Required Rate of Return
for a Stock
Price =
d1  P1
1 r 
d1 
Price =
d2  P2
1 r 
1 r 
d2 
d1 
Price =
Price =
Pi = Price in Year i
di = Dividend in Year i
2
r = Discount Rate
d3  P3
1 r 
2
1

r
 
1 r 
3
d3
d1
d2



2
3
1 r  1 r  1 r 

Motivation
Dividends are the cash flows derived from
common stock.
The price is the present value of cash flows.
Thus, the price of a common share should
be the present value of its dividends
Problems
Dividends (especially far future ones) are
not easily estimated.
Constant Model
Dividends remain constant
Growth Model
Dividends change at a constant rate
Mixed Model
Dividends change at different rates
If dividend is constant, then stock is a
perpetuity.
VCE
d

rCE
VCE = Value/Price of Common Equity
d = Dividend from Common Equity
rCE = Discount Rate for Common Equity
If a stock is always expected to pay an
annual dividend of $4.00 and r = 7%, then
VCE
4.00

 $57.14
0.07
If dividend is changing at a constant
rate, then stock is a growing perpetuity.
VCE
d1

rCE  g
VCE = Value/Price of Common Equity
d1 = Dividend (Next Period) from Common Equity
rCE = Discount Rate for Common Equity
g = Dividend Growth Rate
If a stock has just paid an annual dividend
of $4.00, and the dividend is expected to
increase (infinitely) at 2% (r = 7%), then
VCE
4.00(1.02)

 $81.60
0.07  0.02
The same methodology applies if the
dividend is expected to decline.
If a stock has just paid an annual dividend
of $4.00, and the dividend is expected to
decrease (infinitely) at 2% (r = 7%), then
VCE
4.00(0.98)

 $43.56
0.07   0.02 
Both Patterns Possible
But not likely to apply to very many firms
Generally, dividends change at
different rates over time
A high growth firm might increase is cash
flows at 30% for a few years, but this could
not be sustained for any extended period.
What will be IBM’s dividend 12 years
from now?
No matter what you said…You’re only
guessing!
No Rational Way to Estimate Long Term
Dividends
To alleviate this problem, we divide the
forecast of dividends into two periods:
Short Term Prediction/Horizon
Long Term Prediction/Horizon
0
1
2
3
t
d0
d1
d2
d3
dt
Short Term
Long Term
Period over which we can reasonably
estimate the expected dividends:
As specific dollar amounts, or
E.g., $4.00 $4.15 $4.25 $4.90
As subject to some growth forecast
E.g., $4.00 growing at 10% for 4 years
Dividend ‘Smoothing’
Period over which we cannot predict
dividends.
We cannot ignore the long term,
For many firms the long term provides
much of the value of the firm.
NOTE: The more value is derived from the future, the harder
to use the DDM as a method.
Estimate the long term dividends as
growing at a constant rate or
reasonable growth rate.
Estimate as constant or growing perpetuity.
Infinite growth rate cannot be very large.
One good estimate is the long term growth
for the economy, perhaps 3 or 4%.
1) Value of the short term dividends as PV
of the individual dividends.
2) Value of the long term dividends as a
delayed growing perpetuity.
NOTE: It is a delayed growing perpetuity
because the long term dividends do not
begin until after the short term dividends end.
3) Stock Price = PVshort term + PVlong term
EXAMPLE
A firm has just paid an annual dividend of
$2.00. That dividend is expected to grow at
a rate of 30% for one year, 20% for the next
two years, then level off to a long term
growth rate of 3%. If the discount rate is
12%, what should be the price of the
stock?
Data:
d0 = 2
g1 = 30%
g2-3 = 20%
di = Dividend from Common Equity in Year i
g4+ = 3%
r = 12%
g i = Dividend Growth Rate from Common Equity in Year i
r = Discount Rate for Common Equity
Data
d0 = 2; g1 = 30%; g2-3 = 20%; g4+ = 3%; r = 12%
Dividend Calculation
d1 = 2(1.30) = 2.60
d2 = 2(1.30)(1.20) = 3.12
d3 = 2(1.30)(1.20)2 = 3.74
d4 = 2(1.30)(1.20)2 (1.03) = 3.85
The Timeline
0
1
2
3
4
d0
d1
d2
d3
d4
2.00
2.60
3.12
3.74
3.85
Short Term
Long Term
Data:
d0 = 2; g1 = 30%; g2-3 = 20%; g4+ = 3%; r = 12%
Short Term Dividends:
d1 = 2.60
VST
d2 = 3.12
d3 = 3.74
2.60
3.12
3.74



 7.47
2
3
(1.12) (1.12) (1.12)
If Cash Flow Starts at t = 1,
PV is at t = 0
If Cash Flow Starts at t = m,
PV is at t = m – 1
If Cash Flow Starts at t = 20,
PV is at t = 19
PV of perpetuity is one period prior to the
first cash flow,
So it must be discounted from that
period.
I promise to pay you $100 per year starting in 5
years (r = 10%). What is the PV?
Apply perpetuity formula:
PV = 100/0.10 = $1000
This $1000 is in Year 4 dollars.
Discount it back to the present
N = 4; I% = 10; PV = ?; PMT = 0; FV = -1000
PV = $683.01
Data:
d0 = 2; g1 = 30%; g2-3 = 20%; g4+ = 3%; r = 12%
Long Term
d4 = 3.85
VLT
3.85
1

 30.45
3
0.12  0.03 1.12 
Data:
d0 = 2; g1 = 30%; g2-3 = 20%; g4+ = 3%; r = 12%
VCE  VST  VLT  7.47  30.45  $37.92
or
VCE
2.60
3.12
3.74
3.85
1




 37.92
3
2
3
(1.12) (1.12) (1.12)
0.12  0.03 1.12 
Short Term
Long Term
VCE
d1
d2
dn
d n 1
1


 

2
n
(1  r ) (1  r )
(1  r )
r  g 1  r n
where n = the last period of the short term
FIN 614: Financial Management
Larry Schrenk, Instructor