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8-1
July 21 Outline
• Bond and Stock Differences• Common Stock Valuation
8-2
Bonds and Stocks: Similarities• Both provide long-term
funding for the organization
• Both are future funds that an investor must consider
• Both have future periodic payments
• Both can be purchased in a marketplace at a price “today”
8-3
Bonds and Stocks: Differences• From the firm’s perspective: a
bond is a long-term debt and stock is equity
• From the firm’s perspective: a bond gets paid off at the maturity date; stock continues indefinitely.
• We will discuss the mix of bonds (debt) and stock (equity) in a future chapter entitled capital structure
8-4
Bonds and Stocks: Differences
• A bond has coupon payments and a lump-sum payment; stock has dividend payments forever
• Coupon payments are fixed; stock dividends change or “grow” over time
8-5
A visual representation of a bond with a coupon payment (C) and a maturity value (M)
1 2 3 4 5
$C1 $C2 $C3 $C4 $C5
$M
8-6
A visual representation of a share of common stock with dividends (D) forever1 2 3 4 5
$D1 $D2 $D3 $D4 $D5 $D∞
∞
8-7
Comparison Valuations
1 2 3Bond
C CCM
P0
0
1 2 3Common Stock
D1 D2 D3 D∞P0
0
8-8
Notice these differences:• The “C’s” are constant and equal• The bond ends (year 5 here)• There is a lump sum at the end
1 2 3 4 5
$C1 $C2 $C3 $C4 $C5
$M
8-9
Notice these differences:• The dividends are typically
different• The stock never ends• There is no lump sum
1 2 3 4 5
$D1 $D2 $D3 $D4 $D5 $D∞
∞
8-10
Cash Flows for Stockholders
If you buy a share of stock, you can receive cash in two ways:
1. The company pays dividends
2. You sell your shares, either to another investor in the market or back to the company
8-11
One-Period Example
Suppose you are thinking of purchasing the stock of Moore Oil, Inc. You expect it to pay a $2 dividend in one year, and you believe that you can sell the stock for $14 at that time.
If you require a return of 20% on investments of this risk, what is the maximum you would be willing to pay?
8-12
Visually this would look like:
1
D1 = $2
P1 = $14
R = 20%
8-13
Compute the Present Value
1
D1 = $2
P1 = $14
R = 20%
$1.67
$11.67
PV =$13.34
1 year = N
20% = Discount rate
$2 = Payment (PMT)
$14 = FV
PV = ?
-13.34
1st
2nd
TI BA II Plus
8-148-14
8-15
Two Period Example
Now, what if you decide to hold the stock for two years? In addition to the dividend in one year, you expect a dividend of $2.10 in two years and a stock price of $14.70 at the end of year. Now how much would you be willing to pay?
8-16
Visually this would look like:
2
D1 = $2
P2 = $14.70
R = 20% 1
D2 = $ 2.10
8-17
Compute the Present Value
2
D1 = $2
P2 = $14.70
R = 20% 1
D2 = $ 2.10$1.67$1.46
$ 10.21
$ 13.34 = P0
8-18
What is the Observed Pattern?
We value a share of stock by bring back all expected future dividends into present value terms; since the corporation does not have a finite life, we must consider all such dividends, even those in the distant future.
8-19
So how do you compute the future
dividends?Three scenarios:
1. A constant dividend (zero growth)
2. The dividends change by a constant growth rate
3. We have some unusual growth periods and then level off to a constant growth rate
So how do you compute the future dividends?We start with the general pricing formula for an annuity with constant growth:
where D1 is next period’s dividend, R is the discount rate, g is the (constant) growth rate, and R > g. Note that as n grows arbitrarily large (goes toward ), then
8-20
0 1
1 (1 ) (1 ),
n ng RP D
R g
10 .
DP
R g
8-21
1. Constant Dividend – Zero Growth• The firm will pay a
constant dividend forever
• This is like preferred stock
• Since g = 0, this implies that
1 10 .
D DP
g RR
8-22
2. Constant Growth Rate of Dividends
Dividends are expected to grow at a constant percent per period; i.e., D2 = D1(1+g), D3 = D1(1+g)2, …, Dn+1 = D1(1+g)n, and so forth. Then we end up with the constant growth formula, AKA the “Gordon” model:
10 .
DP
R g
8-23
Dividend Growth Model (DGM) Assumptions
In order to use the Gordon constant growth model, the following three requirements must be met:
1.The growth of all future dividends must be constant,
2.The growth rate must be smaller than the discount rate ( g < R), and
3.The growth rate must not be equal to the discount rate (g ≠ R)
8-24
DGM – Example 1
Suppose Big D, Inc., just paid a dividend (D0) of $0.50 per share. It is expected to increase its dividend by 2% per year.
If the market requires a return of 15% on assets of this risk, how much should the stock be selling for?
8-25
DGM – Example 1 Solution
P0 = .50 ( 1 + .02) .15 - .02
g-R
D
g-R
g)1(DP 10
0
P0 = .51 .13
= $3.92
8-26
DGM – Example 2
Suppose Moore Oil Inc., is expected to pay a $2 dividend in one year. If the dividend is expected to grow at 5% per year and the required return is 20%, what is the price?
8-27
DGM – Example 2 Solution
P0 = 2.00 .20 - .05
g-R
D
g-R
g)1(DP 10
0
P0 = 2.00 .15
= $13.34
8-28
3. Unusual Growth;Then Constant
Growth
Just draw the time line with the unusual growth rates identified and determine if/when you can use the Dividend Growth Model.
Deal with the unusual growth dividends separately.
8-29
Non-constant Growth Problem Statement
Suppose a firm is expected to increase dividends by 20% in one year and by 15% for two years. After that, dividends will increase at a rate of 5% per year indefinitely.
If the last dividend was $1 and the required return is 20%, what is the price of the stock?
8-30
Non-constant Growth Problem Statement
Draw the time line and compute each dividend using the corresponding growth rate:
g = 20% g = 15% g = 15% g = 5% D 0 =
$1.00
1 2 3 4
∞D1 D2 D3
8-31
Non-constant Growth Problem Statement
Draw the time line and compute each dividend using the corresponding growth rate:
g = 20% g = 15% g = 15% g = 5% D 0 =
$1.00
1 2 3 4
∞D1 D2 D3
D1 = ($1.00) (1 + 20%) = $1.00 x 1.20 = $1.20
=1.20
8-32
Non-constant Growth Problem Statement
Draw the time line and compute each dividend using the corresponding growth rate:
g = 20% g = 15% g = 15% g = 5% D 0 =
$1.00
1 2 3 4
∞D1 D2 D3
D2 = ($1.20) (1 + 15%) = $1.20 x 1.15 = $1.38
=1.38
8-33
Non-constant Growth Problem StatementDraw the time line and compute each dividend using the corresponding growth rate:
g = 20% g = 15% g = 15% g = 5% D 0 =
$1.00
1 2 3 4
∞D1 D2 D3
D3 = ($1.38) (1 + 15%) = $1.38 x 1.15 = $1.59
=1.59
8-34
Non-constant Growth Problem StatementNow we can use the DGM starting with the period of the constant growth rate at our time frame of year 3:
g = 20% g = 15% g = 15% g = 5% D 0 =
$1.00
1 2 3 4
∞D1 D2 D3
P3 = D3 (1 + g) / (R – g)P3 = 1.59 (1.05)/ (.20 - .05) = $11.13
R = 20%
8-35
Non-constant Growth Problem Statement
We now have all of the dividends accounted for and we can compute the present value for a share of common stock:
g = 20% g = 15% g = 15% g = 5% D 0 =
$1.00
1 2 3 4
∞D1 D2 D3
R = 20%
1.20 1.38 1.59P3 = 11.13
8-36
Non-constant Growth Problem Statement
g = 20% g = 15% g = 15% g = 5% D 0 =
$1.00
1 2 3 4
∞D1 D2 D3
R = 20%
1.20 1.38 1.59
P3 = 11.13$9.32
8-37
Stock Price Sensitivity to
Dividend Growth, gD1 = $2; R = 20%
0
50
100
150
200
250
0 0.05 0.1 0.15 0.2
Growth Rate
Stoc
k P
rice
Stock Price Sensitivity to
Required Return, RD1 = $2; g = 5%
0
50
100
150
200
250
0 0.05 0.1 0.15 0.2 0.25 0.3
Growth Rate
Sto
ck P
rice
8-38
8-39
Using the DGM to Find R
gP
D g
P
g)1(D R
g-R
D
g - R
g)1(DP
0
1
0
0
100
Start with the DGM and then algebraically rearrange the equation to solve for R:
8-40
Finding the Required Return - Example
Suppose a firm’s stock is selling for $10.50. It just paid a $1 dividend, and dividends are expected to grow at 5% per year. What is the required return? R = [1(1.05)/10.50] + .05 = 15%What is the dividend yield?
1(1.05) / 10.50 = 10%What is the capital gains
yield?
g =5%
8-41
Valuation Using Multiples
We can use the PE ratio and/or the price-sales ratio:
Pt = Benchmark PE ratio X EPSt
Pt = Benchmark price-sales ratio X Sales per sharet
8-42
Stock Valuation Summary