How to apply the PV concept
FIN 819: lecture 2' 1

Today’s plan
 Review what we have learned in the last lecture
 Valuing stocks
•
Some terms about stocks
•
Valuing stocks using dividends
•
Valuing stocks using earnings
•
Valuing stocks using free cash flows
FIN 819: lecture 2' 2

Some terms about stocks
Book Value – The value of the stocks according to the balance sheet.
Liquidation Value - Net proceeds that would be realized by selling the firm’s assets and paying off its creditors.
Market Value Balance Sheet - Financial statement that uses market value of assets and liabilities.
FIN 819: lecture 2' 3

Some terms about stocks
Secondary Market - market in which already issued securities are traded by investors.
Dividend - Periodic cash distribution from the firm to the shareholders.
P/E Ratio - Price per share divided by earnings per share.
Dividend yield – Dividends per share over the price of per share
FIN 819: lecture 2' 4

Example
 IBM has a trading price of $70 per share.
Its annual earnings per share is $5. Its annual dividend per share is $3.5. What are the P/E and the dividend yield?
 P/E=70/5=14
 Dividend yield=3.5/70=1/20=0.05
FIN 819: lecture 2' 5

Valuing Common Stocks using dividends (first approach)
Dividend Discount Model - Computation of today’s stock price which states that share value equals the present value of all expected
P
0 future dividends plus the selling price of the stock.

( 1
Div
 r
1
)
1

( 1
Div
 r
2
)
2
Div
H

P
H
( 1
 r )
H
H - Time horizon for your investment.
FIN 819: lecture 2' 6

Example
 George has bought one IBM share in the beginning of this year and decides to hold this share until next year. The expected dividend this year is $10 per share and the stock is expected to sell at
$110 per share in the end of the year. If the cost of the capital is 10%, what is the current stock price?
FIN 819: lecture 2' 7

Solution
 P
0
=(110+10)/(1+0.1)=$109.1
FIN 819: lecture 2' 8

Valuing common stocks using dividends
Example
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?
FIN 819: lecture 2' 9

Solution
0
0

3 .
00
( 1

.
12 )
1

$ 75 .
00

3 .
24
( 1

.
12 )
2

3 .
50

94 .
48
( 1

.
12 )
3
FIN 819: lecture 2' 10

Valuing common stocks using dividends
If we forecast no growth, and plan to hold out stock indefinitely, we will then value the stock as the PV of a PERPETUITY .
(
)

0

1
1
Assumes all earnings are paid to shareholders.
FIN 819: lecture 2' 11

Example
 Suppose that a stock is going to pay a dividend of $3 every year forever. If the discount rate is 10%, what is the stock price for the following cases:
•
(a) you invest and hold it forever?
•
(b) you invest and hold it for two years?
•
(c) you invest and hold it for 20 years?
FIN 819: lecture 2' 12

Solution


(a) P
0
=3/0.1=$30
(b)P
0
=PV (annuity) + PV( the stock price at year 2)
= 3/1.1 + 3/1.1
2 +(3/0.1)/1.1
2
= 3/0.1=$30
(c) P
0
=PV (annuity of 20 years) +
PV (the stock price at the year of 20)
=$30
FIN 819: lecture 2' 13

Valuing Common Stocks
Gordon Growth Model: A version of the dividend growth model in which dividends grow at a constant rate (Gordon Growth
Model) .
Stocks can be valued as a perpetuity with a growth rate, if you want to hold this stock forever, that is
P
0
 r
Div

1 g
FIN 819: lecture 2' 14

Example
 Suppose that a stock is going to pay a dividend of $3 next year. Dividends grow at a growth rate of 3%. If the discount rate is 10%, what is the stock price for the following cases:
•
(a) you buy and hold it forever?
•
(b) you buy and hold it for two years?
•
(c) you buy and hold it for 20 years?
FIN 819: lecture 2' 15

Solution


(a) P
0
=3/(0.1-0.03)=$42.86
(b)P
0
=PV (annuity) + PV( the stock price at year 2)
= 3/1.1 + 3*1.03/1.1
2 +(3*1.03
3 /(0.1-
0.03))/1.1
2
= 3/(0.1-0.03)=$42.86
(c) P
0
=PV (annuity of 20 years) +
PV (the stock price at the year of 20)
=$42.86
FIN 819: lecture 2' 16

Capitalization 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 .
Expected Return
 
Div
 
P
1 1 0
P
0
FIN 819: lecture 2' 17

Example
If Fledgling Electronics is selling for $100 per share today and is expected to sell for $110 one year from now, what is the expected return if the dividend one year from now is forecasted to be $5.00?
FIN 819: lecture 2' 18

Solution
According to the formula,
Expected Return

5

110

100
100

.
15
FIN 819: lecture 2' 19

Capitalization rate
The formula for the capitalization rate can be broken into two parts.
Capital. Rate = Dividend Yield + Capital Appreciation
Expected Return
 
Div
1

P
0
P

P
1 0
P
0
FIN 819: lecture 2' 20

Using dividends models to derive the capitalization rate
Capitalization Rate can be estimated using the perpetuity formula, given minor algebraic manipulation.
P
0
 r
Div
1
 g r

Div
1  g
P
0
FIN 819: lecture 2' 21

Valuing Common Stocks
Example-
If a stock is selling for $100 in the stock market, the cost of capital is 12% and the next year dividend is $3, what might the market be assuming about the growth in dividends?
$100

.
$3.
00
12
 g g

.
09
FIN 819: lecture 2' 22

Some terms about dividend growth rates
 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.
FIN 819: lecture 2' 23

Deriving the dividend growth rate g
Growth can be derived from applying the return on equity to the percentage of earnings plowed back into operations.
ROE

Return on Equity
ROE

EPS
Book Equity Per Share g = return on equity X plowback ratio
FIN 819: lecture 2' 24

Example
Our company forecasts to pay a
$5.00 dividend next year, which represents 100% of its earnings.
This will provide investors with a
12% expected return. Instead, we decide to plow back 40% of the earnings at the firm’s current return on equity of 20%. What is the value of the stock before and after the plowback decision?
FIN 819: lecture 2' 25

Solution
 Without growth
P
0

5
0 .
12

$ 41 .
67
 With growth g

0 .
4 * 0 .
2

0 .
08
P
0

5 * 0 .
6
0 .
12

0 .
08

$ 75
FIN 819: lecture 2' 26

Example (continued)
If the company did not plowback some earnings, the stock price would remain at
$41.67. With the plowback, the price rose to
$75.00.
The difference between these two numbers
(75.00-41.67=33.33) is called the Present
Value of Growth Opportunities (PVGO).
FIN 819: lecture 2' 27

Valuing common stocks using earnings
 We often use earnings to value stocks as
P
0

EPS r
1 
PVGO
 What is the relationship between this formula and the dividend growth formula?
FIN 819: lecture 2' 28

Example
 Firm A has a market capitalization rate of 15%. The earnings are expected to be $8.33 per share next year.
The plowback ratio is 0.4 and ROE is 25%. Every investment in year i is to yield a simple perpetuity starting in year (i+1) with each cash flow equal to total investment times ROE. All the investments have the same capitalization rate.
•
(a) Using the formula P=ESP
1
/r + PVGO to calculate the stock price
•
(b) If ROE is increased, what will happen to the stock price?
Why?
•
(c) Use the dividend model to calculate the stock price?
•
(d) What have you found?
•
(e) Think about why you have this kind of result?
FIN 819: lecture 2' 29

Simple Solution
(a) g=10%, EPS1/r=8.33/0.15=$55.56
PVGO=NPV1/(r-g)=2.22/(0.15-
0.1)=$44.44, P=$100
(b) The price will be increased
(c) P=Div1/(r-g)=5/(0.15-0.1)=$100
FIN 819: lecture 2' 30

Valuing common stocks using
FCF (free cash flows)
The value of a business or stock is usually computed as the discounted value of FCF out to a valuation horizon (H).
 The horizon value is sometimes called the terminal value .
PV

(
FCF
1
1
 r )
1

(
FCF
2
1
 r )
2

...

(
FCF
H
1
 r )
H

( 1
PV
H
 r )
H
FIN 819: lecture 2' 31

FCF and PV
PV

(
FCF
1
1
 r )
1

(
FCF
2
1
 r )
2

...

(
FCF
H
1
 r )
H

( 1
PV
H
 r )
H
PV (free cash flows) PV (horizon value)
FIN 819: lecture 2' 32

FCF and PV
 Free Cash Flows (FCF) should be the theoretical basis for all PV calculations.
 FCF is a more accurate measurement of
PV than either Div or EPS.
 The market price does not always reflect the PV of FCF.
 When valuing a business for purchase, always use FCF.
FIN 819: lecture 2' 33

FCF and PV
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. r=10% and g= 6%
Year
Asset Value
1
10 .
00
2
12 .
00
3
14 .
40
4
17 .
28
5
20 .
74
6
23 .
43
7
26 .
47
8
28 .
05
9
29 .
73
10
31 .
51
Earnings
Investment
Free Cash Flow
.EPS
growth (%)
1.20
2.00
.80
20
1.44
2.40
.96
20
1.73
2.88
1.15
20
2.07
3.46
1.39
20
2.49
2.69
.20
20
2.81
3.04
.23
13
3.18
1.59
1.59
13
3.36
1.68
1.68
6
3.57
1.78
1.79
6
3.78
1.89
1.89
6
FIN 819: lecture 2' 34

FCF and PV
Solution
PV(horizon value)

1
 
6
1 .
59
.
10

.
06

22 .
4
PV(FCF)

-
.80
1.1

.
96
1 .
1
1 .
15
1 .
1
1 .
39
1 .
1
.
20
1 .
1 1
.
23
         
6
 
3 .
6
FIN 819: lecture 2' 35

FCF and PV





FIN 819: lecture 2' 36

How to estimate the horizon value?
 It is very difficult to forecast or estimate the horizon value. There are several ideas that may be used to estimate the horizon value.
•
Competition
•
Constant growth rate
•
P/E ratio
•
Dividend yield
•
Book-to-market ratio
FIN 819: lecture 2' 37