Data: g=5% g2=0.
10
D0 1.5 0 1 2 3 4
g1 (1-3years) 5% D0 D1 D2 D3 D4
g2 (4 -- infinity) 10% 1.500 1.575 1.654 1.736 1.910
D1 =D0*(1+g1)^1 =1.5*(1+0.05)^1 1.575
=D0*(1+g1)^2 =D1*(1+g1)^1 =1.575*(1.05)^1 1.654
D2
=1.50*(1.05)^2 1.654
D3 =D0*(1+g1)^3 =1.50*(1.05)^3 1.736
D4 =D3*(1+0.10)^1 =D0(1+g1)^3*(1+g2)^1 1.910
D5 =D0(1+g1)^3*(1+g2)^2 2.101 =1.5*(1.05^3)*(1.1^2)
data g1=0.05 g2=0.10
D0 1.5 0 1 2 3 4
g1 (1-3 years) 5% 0.05 D0 D1 D2 D3 D4
g2 (4-forever) 10% 0.1 1.500 1.575 1.654 1.736 1.910
D1 =D0*(1+g1)^1 =1.50*(1+.05)^1 1.575 1.910
D2 =D0*(1+g1)^2 =1.50*(1+.05)^2 1.654
D3
D4
D5
g2=0.10
5
D5
2.101
g2=0.10
5
D5
Data
D1 1.5
g 7% 0.07 (Constant)
rs 15% 0.15
P0 ?
P0 =1.5/(0.15-0.07)
P0 $ 18.750
Data
P0 20
D0 1 D1 D0*(1+g)^1 =1*1.1^1 1.1
g 0.1 constant
P1 ?
rs ?
P0=D1/(rs-g) ==>rs-g=D1/P0 ==>rs=(D1/P0)+g =(1.1/20)+0.1 0.155
P1=D2/(rs-g)
D2 1.21
P1 =1.21/(0.155-0.10) 22
?
A company currently pays a dividend of $2 per share (D0 = $2). It is estimated that the company’s dividend will grow at a
for the next 2 years, then at a constant rate of 7% thereafter. The company’s stock has a beta of 1.2, the riskfree rate is 7
risk premium is 4%. What is your estimate of the stock’s current price?
Data
D0 2
g1 (1-2 years) 20% 0.2
g2(3-- forever) 7% 0.07 constant
Beta 1.2 CAPM, ITS USED TO CALCULATE rs or return on investment by stock holders
RfR 7.50% ]
MRP 4% 0.04 D1/1+rs D2/(1+rs)^2 D3/(rs-g)*(1+rs)^2
P0 ? 50.52504 2.4 2.88 3.0816
P0 2.137 2.284 46.104 50.525
CAPM- rs=Rfr+(MRP*Beta) =0.075+(0.04*1.2) 0.123 46.10424
1. Time line with dividends and growth rates
2. DDM and Constant model setup
3. Calculations of dividends
4. Discount all the dividens
5. Add discounted dividends calculated in step 2 to find the P0
ompany’s dividend will grow at a rate of 20% per year
beta of 1.2, the riskfree rate is 7.5%, and the market
ck’s current price?
tock holders
0.053
Data
V 50
D 5
r ?
V=D/rps
rps=D/V =5/50 0.1
Data
Industry information
G (constant) 0.06 P0=D1/(rs-g) rs=(D1/P0)+g rs=0.07+0.06
Dividend yield=D1/P0 0.07
Firm information
g1 0.5
g2 0.25
g3 (constant) 0.06
D0 1
P0 ? Use non-constant growth model
rs 0.13
P0=DDM+Constant growth model g1=0.5 g2=0.25 g3=0.06(constant)
P0 D1 D2 D3
1.5 1.875 1.988
P0=[(D1/(1+rs)^1)+(D2/(1+rs)^2)]+[P2/(1+rs)^2]
P0=[(D0(1+g1)/(1+rs)^1)+(D0(1+g1)(1+g2)/(1+rs)^2)]+[D3/(rs-g3)(1+rs)^2]
P2 (constant growth model)=D3/(rs-g3) P2=D3/rs-g
D1=D0*(1+g1) =1*(1+0.5)^1 1.5
D2=D0*(1+g1)*(1+g2) =1*(1.5)^1*(1.25) 1.875
D3=D0(1+g1)*(1+g2)*(1+g3) =1*1.5*1.25*1.06 1.988
P0=[(1.5/(1.13)^1)+(1.875/(1.13)^2)]+[1.988/(0.13-0.06)*(1.13)^2]
25.037
rs=0.07+0.06 0.13
Ewald Company’s current stock price is $36, and its last dividend was $2.40. In view of Ewald’s strong financial position a
its consequent low risk, its required rate of return is only 12%. If dividends are expected to grow at a constant rate g in the
future, and if rs is expected to remain at 12%, then what is Ewald’s expected stock price 5 years from now?
Data
P0 36$ P0=D1/rs-g P0=D0(1+g)/rs-g 36=2.40(1+g)/(0.12-g)
0.12-g=2.40(1+g)/36
0.12-g=0.067(1+g)
0.12-g=0.067+0.067g
0.12-0.067=0.067g+g
0.053=1.067g
(0.053/1.067)=g
g=0.05
D0 2.40$
rs 0.12
g (constant) ?
P5 =D6/rs-g =D0(1+g)^6/rs-g
=2.40*(1.05)^6/0.12-0.05
45.946
d’s strong financial position and
ow at a constant rate g in the
ars from now?
Snyder Computer Chips Inc. is experiencing a period of rapid growth. Earnings and dividends are expected to
grow at a rate of 15% during the next 2 years, at 13% in the third year, and at a constant rate of 6% thereafter.
Snyder’s last dividend was $1.15, and the required rate of return on the stock is 12%.
a. Calculate the value of the stock today. P0
b. Calculate ^ P1 and ^ P2. P1, P2
c. Calculate the dividend yield and capital gains yield for Years 1, 2, and 3.
Dividend Yield(Year1)=D1/P0
Dividend Yield(Year2)=D2/P1
DY(n years)=Dn/P(n-1)
Dividend Yield(Year2)=D3/P2
Capital Gain Yield (Y1)=(P1-P0)/P0
Capital Gain Yield (Y2)=(P2-P1)/P1
Capital Gain Yield (Y3)=(P3-P2)/P2
Data:
g1 (1-2 years) 0.15
g2 (year 3) 0.13
g3 (year 4 - forever) 0.06
D0 1.15 =1.15*(1+0.15) 1.3225
rs 0.12
n highest value-year 3
P0 =[((1.15*1.15)/(1.12))]+[((1.15*1.15^2)/(1.12^2))]+[((1.15*1.15^2*1.13)/(1.12^3))]+[P3/(0.12-0.06)*(1.1
25.227
P1 =((1.15*1.15^2)/(1.12))+((1.15*1.15^2*1.13)/(1.12^2))+P2/(0.12-0.06)*(1.12^2)
P1 26.932
P0 P1 P2 D3 D4
Dividends 1.521 1.719 1.822
Discounted divide 1.358 1.370 1.452251
P1 sum of all values 24.20419 26.932
P2 =((1.15*1.15^2)/(1.12))+((1.15*1.15^2*1.13)/(1.12^2))+P3/(0.12-0.06)*(1.12^2)
P2 =[D3/(1+rs)^1]+[D4/(rs-g)(1+rs)^1)]
DY1=D1/P0 CGY1=(P1-P0)/P0
DY2=D2/P1 CGY2=(P2-P1)/P1
DY3=D3/P2 CGY3=(P3-P2)/P2
P3=D4/rs-g3
P3=D4/0.12-0.06
nd dividends are expected to
nstant rate of 6% thereafter.
2%.
1.12^3))]+[P3/(0.12-0.06)*(1.12^3)]
.12^2)
.12^2)
Simpkins Corporation is expanding rapidly, and it does not pay any dividends because it currently
needs to retain all of its earnings. However, investors expect Simpkins to begin paying dividends,
with the first dividend of $1.00 coming 3 years from today. The dividend should grow rapidly—at a
rate of 50% per year—during Years 4 and 5. After Year 5, the company should grow at a constant
rate of 8% per year. If the required return on the stock is 15%, what is the value of the stock today?
D3,D4,P4 (constant)
Several years ago, Rolen Riders issued preferred stock with a stated annual dividend of 10% of its $100 par
value. Preferred stock of this type currently yields 8%. Assume dividends are paid annually.
a. What is the value of Rolen’s preferred stock?
b. Suppose interest rate levels have risen to the point where the preferred stock now yields 12%. What would be the new va
Data
Par value 100
Dividend rate 0.1
Dividend Par Value*Dividend rate 10
Yield ( rps ) 0.08 0.12
V=D/r =10/0.08 125
V=D/r =10/0.12 83.33
10% of its $100 par
ally.
What would be the new value of Rolen’s preferred stock?
Annual coupon payment
Current yield (CY)
Current price
Change in price
Capital gains yield (CGY)
Beginning price
Expected Expected
Expected total return YTM
CY CGY
ment
ce
ice
Expected Annual YTM-Expected CY (annual)=Expect. CGY
CGY
