copyright 2014 by diane scott docking 1 stock valuation video: how the market really works
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Copyright 2014 by Diane Scott Docking 1
Stock Valuation
Video: How the Market Really works
Copyright 2014 by Diane Scott Docking 2
Learning Objectives Understand how to calculate stock returns Understand how stock prices (values) are
determined when dividends grow at a constant rate dividend growth is nonconstant
Identify factors that affect stock prices
Copyright 2014 by Diane Scott Docking 3
Stock Valuation The price of a share of stock is the total value of
the company divided by the number of shares outstanding
Stock price by itself doesn’t represent firm value Number of shares outstanding
Stock price is determined by the demand and supply for the shares
Investors try to value stocks and purchase those that are perceived to be undervalued by the market
New information creates re-evaluation
4Copyright 2014 by Diane Scott Docking
Stock Returns
The returns on a stock over one period (Rt) can be divided into capital gains and dividend returns:
Pt = stock price at time t
Dt = dividends paid over time t – 1 to t
(Pt – Pt – 1) / Pt – 1 = capital gain over time t – 1 to t
Dt / Pt – 1 = return from dividends paid over time t – 1 to t
The returns on a stock over one period (Rt) can be divided into capital gains and dividend returns:
Pt = stock price at time t
Dt = dividends paid over time t – 1 to t
(Pt – Pt – 1) / Pt – 1 = capital gain over time t – 1 to t
Dt / Pt – 1 = return from dividends paid over time t – 1 to t
111
1
1
t
tt
t
tt
t
tt P
PD
P
PP
P
DR
Dividend Yield
Capital Gains Rate
Copyright 2014 by Diane Scott Docking 5
Example: Determining Rate of Return
Union Corporation currently pays an annual dividend of
$1.00. The current stock price is $50. At the end of 1
year, the stock price is $55.
What is Union Co.’s annual rate of return on its stock?
return totalgains capitaldividend
1
1
11
12%10%2%50
6
50
5
50
1
50
5055
50
1
t
tt
t
t
P
PP
P
DR
Copyright 2014 by Diane Scott Docking 6
Example: Stock Return CalculationJake buys 10 shares of AVU stock at $55.10 and sells it 1
year later for $56.30 after collecting a $0.30 dividend per
share.
1. What is Jake’s pre-tax holding period return?
return totalgains capitaldividend
1
1
1_1
%178.2%544.010.55
50.1
10.55
20.1
10.55
30.
10.55
10.5530.56
10.55
30.
2.722%
t
tt
t
tBT P
PP
P
DR
Copyright 2014 by Diane Scott Docking 7
Example: Stock Return Calculation (cont.)2. If the dividend is taxed at the ordinary rate = 28% and the
capital gains at 15%, what is Jake’s after tax holding period return?
return totalgains capitaldividend
1
1
1_1
%851.1%392.0
10.55
236.1
10.55
02.1
10.55
216.
10.55
85.20.1
10.55
72.30.
15.110.55
10.5530.5628.1
10.55
30.
11
2.243%
ratecg
t
ttrateord
t
tAT t
P
PPt
P
DR
Copyright 2014 by Diane Scott Docking 8
Example: 2 year Stock Return Calculation
Jake buys 10 shares of AVU stock at $55.10 and sells it 2
years later for $56.30 after collecting a $0.30 dividend per
share per year.
1. What is Jake’s pre-tax holding period return?CF0 = - $55.10
CF1 = $.30
CF2 = $.30 + $56.30 = $56.60
Therefore IRR = 1.6246%
OR
PV = -$55.10
n = 2
PMT = .30
FV = $56.30
YTM = 1.6246%
Copyright 2014 by Diane Scott Docking 9
Stock Valuation Methods
The Dividend-Discount Model Estimating Dividends in the Dividend-Discount
Model Total Payout and Free Cash Flow Valuation
Models Valuation Based on Comparable Firms Valuation Using P/E Ratios Economic Value Added (EVA) Approach Information, Competition, and Stock Prices
Copyright 2014 by Diane Scott Docking 10
Dividend-Discount Model
The Dividend-Discount Model Zero or No growth in dividends, but unlimited life Zero growth in dividends, but limited life Constant growth in dividends Nonconstant growth in dividends
Copyright 2014 by Diane Scott Docking 11
Dividend-Discount Model
The price of a stock reflects the present value of the stock's future dividends
D0 = dividend in period 0 expected to remain constant forever
rs = discount rate or required rate of return on the stock
Zero Growth in Dividends
sr
DP 0
0
Perpetuity Dividend Model
Copyright 2014 by Diane Scott Docking 12
Example: Zero Dividend Growth Model
Joan’s Fabric Corp. pays an annual dividend of $5.00 per share on its Preferred stock. This dividend is expected to remain constant into the future. The expected rate of return on the stock is 6.50%. What is the current market price of the stock?
92.76$065.
00.500
sr
DP
Copyright 2014 by Diane Scott Docking 13
Dividend-Discount Model
The price of a stock reflects the present value of the stock's future dividends
t = period
Dt = dividend in period t
rs = discount rate or required rate of return on the stock
Zero Growth in Dividends
Non-Perpetuity Dividend Model
1
0)1(t
ts
t
r
DP
Copyright 2014 by Diane Scott Docking 14
Example: 1-period Dividend Growth Model
Mary expects Longs Drug Stores to pay an annual dividend of $.56 per share in the coming year and to trade $45.50 per share at the end of the year. Investments with equivalent risk to Longs’ stock have an expected return of 6.80% What is the most Mary would pay today for
Longs’ stock? What dividend yield and capital gain rate would
Mary expect at this price?
Copyright 2014 by Diane Scott Docking 15
Example: 1-period Dividend Growth Model
What is the most Mary would pay today for Longs’ stock?
What dividend yield and capital gain rate would Mary expect at this price?
At this price, Longs’ dividend yield is Div1/P0 = 0.56/43.13 = 1.30%.
The expected capital gain is $45.50 - $43.13 = $2.37 per share, for a capital gain rate of 2.37/43.13 = 5.50%.
Total return is 1.30% + 5.50% = 6.80%
13.43$)068.1(
50.45
)068.1(
56.0
)1()1(
11
11
11
0
ss r
P
r
DP
Copyright 2014 by Diane Scott Docking 16
Example: Multiyear Dividend Growth Model
Suppose Mary plans to hold the stock for two years. She expects the price to be $45.50 at the end of two years. Mary would receive dividends in both year 1 and year 2 before selling the stock, as shown in the following timeline:
What is the most Mary would pay today for Longs’ stock?
Copyright 2014 by Diane Scott Docking 17
Example: Multi-year Dividend Growth Model
What is the most Mary would pay today for Longs’ stock?
91.40$)068.1(
50.45
)068.1(
56.0
)068.1(
56.0
)1()1()1(
221
22
22
11
0
sss r
P
r
D
r
DP
Copyright 2014 by Diane Scott Docking 18
Dividend-Discount Model
The price of a stock reflects the present value of the stock's future dividends
t = period
Dt = dividend in period t
rs = discount rate
g = the nominal growth rate of earnings over time.
Constant Dividend Growth Model
gr
D
gr
gDP
s
t
s
t
t
10 )1(
Copyright 2014 by Diane Scott Docking 19
Example 1: Constant Dividend Growth Model
Consolidated Edison, Inc. (Con Edison), is a regulated utility company that services the New York City area. Suppose Con Edison just paid $2.30 per share in dividends. Its equity cost of capital is 7% and dividends are expected to grow by 2% per year in the future.
What is the current value of Con Edison’s stock?
Copyright 2014 by Diane Scott Docking 20
Example 1: Constant Dividend Growth Model
What is the current value of Con Edison’s stock?
gr
D
gr
gDP
ss
100
1
02.07.
346.2
02.07.
02.130.20
P
92.46$05.
346.20 P
Copyright 2014 by Diane Scott Docking 21
Example 2: Constant Dividend Growth Model
Suppose Johnson & Johnson plans to pay $2.85 per share in dividends in the coming year. Its equity cost of capital is 9% and dividends are expected to grow by 3% per year in the future.
What is the estimated value of Johnson & Johnson’s stock?
Copyright 2014 by Diane Scott Docking 22
Example 1: Constant Dividend Growth Model
What is the current value of Johnson & Johnson’s stock?
gr
DP
s 1
0
50.47$06.
85.2
03.09.
85.20
P
Copyright 2014 by Diane Scott Docking 23
Dividend-Discount Model
Firms experience different growth rates: supernormal growth (gs) and normal growth (g) .
A 4-step process to calculate current price1. Find the PV (P0
’) of the dividends during the period of supernormal growth (gs).
2. Find the price of the stock at the end of the supernormal growth period (n), when normal growth (g) begins using the constant dividends growth model.
NonConstant Dividend Growth Model
n
tt
s
ts
r
gDP
1
0'0 )1(
1
gr
ggD
gr
DP
s
ns
s
nn
101 )1()1(
Copyright 2014 by Diane Scott Docking 24
Dividend-Discount Model
Firms experience different growth rates: supernormal growth (gs) and normal growth (g) .
A 4-step process to calculate current price1. Find the PV (P0
’) of the dividends during the period of supernormal growth (gs).
2. Find the price of the stock at the end of the supernormal growth period (n), when normal growth (g) begins using the constant dividends growth model.
NonConstant Dividend Growth Model
n
tt
s
ts
r
gDP
1
0'0 )1(
1
gr
ggD
gr
DP
s
ns
s
nn
101 )1()1(
Copyright 2014 by Diane Scott Docking 25
Dividend-Discount Model
A 4-step process to calculate current price3. Discount this price (Pn) back to time 0 (P0
”).
4. Add the two components of the stock price together.
NonConstant Dividend Growth Model
ns
n
r
PP
)1("
0
"0
'00 PPP
Copyright 2014 by Diane Scott Docking 26
Example: Valuing a Firm with Two Different Growth Rates
Up and Away Corp. is expected to experience supernormal growth of 30% per year for the next 3 years. After that, the growth rate is expected to drop to 5% for the remainder of the firm’s life. Up and Away’s dividend at the end of last year of $1.60 per share. The firm’s cost of capital is 20%.
What is the value of the firm’s stock?
Copyright 2014 by Diane Scott Docking 27
Example: Valuing a Firm with Two Different Growth Rates
Given: D0 = $1.60; rs = 20%; gs = 30%; g = 5%; n = 3 years
1. Find the PV (P0’) of the dividends during the period of supernormal growth (gs).
3
11
0'0 )20.1(
30.160.1$
)1(
1
tt
tn
tt
s
ts
r
gDP
t Dividend ÷ (1.20)t = PV
1 $1.60(1.30)1 = $2.0800 ÷ (1.20)1 = $1.7333
2 $1.60(1.30)2 = $2.7040 ÷ (1.20)2 = $1.8778
3 $1.60(1.30)3 = $3.5152 ÷ (1.20)3 = $2.0341
∑ = $5.6452 = $5.65 = '0P
Copyright 2014 by Diane Scott Docking 28
Example: Valuing a Firm with Two Different Growth Rates
2. Find the price of the stock at the end of the supernormal growth period (n), when normal growth (g) begins using the constant dividends growth model.
gr
ggD
gr
DP
s
ns
s
nn
101 )1()1(
05.20.
)05.1()30.1(60.1)1()1( 131304
3
gr
ggD
gr
DP
s
s
s
6067.24$15.
6910.3
05.20.
)05.1(5152.3 1
3
P
Copyright 2014 by Diane Scott Docking 29
Example: Valuing a Firm with Two Different Growth Rates
3. Discount this price (Pn) back to time 0 (P0”).
4. Add the two components of the stock price together.
24.14$)20.1(
6067.24$
)1()1( 333"
0
s
ns
n
r
P
r
PP
89.19$24.14$65.5$"0
'00 PPP
Copyright 2014 by Diane Scott Docking 30
Example: Comparing Dividend-Growth Models
Jake is considering buying Polo stock which is currently
priced at $62 per share. Polo paid a dividend at the end of
last year of $2.50 per share. Jake’s required rate of return is
5%. Should Jake buy the stock, assuming:
1. The dividend is expected to continue into the foreseeable future?
2. The dividend is expected to grow at a constant rate of 1% into the foreseeable future?
3. The dividend is expected to grow at a rate of 3% for the next 4 years and then at a rate of 1% thereafter?
Copyright 2014 by Diane Scott Docking 31
Example: Comparing Dividend-Growth Models
1. The dividend is expected to continue into the foreseeable future?
Do NOT Buy. Priced too high.
50$05.
50.200
r
DP
Copyright 2014 by Diane Scott Docking 32
Example: Comparing Dividend-Growth Models
2. The dividend is expected to grow at a constant rate of 1% into the foreseeable future?
Yes buy. Priced too low
125.63$
04.
525.2
01.05.
01.150.20
P
Copyright 2014 by Diane Scott Docking 33
Example: Comparing Dividend-Growth Models
3. The dividend is expected to grow at a rate of 3% for the next 4 years and then at a rate of 1% thereafter?
Given: D0 = $2.50; rs = 5%; gs = 3%; g = 1%; n = 4years
Step 1: Find the PV (P0’) of the dividends during the period of supernormal growth (gs).
4
11
0'0 )05.1(
03.150.2$
)1(
1
tt
tn
tt
s
ts
r
gDP
t Dividend ÷ (1.05)t = PV
1 $2.50(1.03)1 = $2.575 ÷ (1.05)1 = $2.4524
2 $2.50(1.03)2 = $2.6523 ÷ (1.05)2 = $2.4057
3 $2.50(1.03)3 = $2.7318 ÷ (1.05)3 = $2.3598
4 $2.50(1.03)4 = $2.8138 ÷ (1.05)4 = $2.3149
∑ = $9.5328 = $9.53 = '0P
Copyright 2014 by Diane Scott Docking 34
Example: Comparing Dividend-Growth Models
2. Find the price of the stock at the end of the supernormal growth period (n), when normal growth (g) begins using the constant dividends growth model.
gr
ggD
gr
DP
s
ns
s
nn
101 )1()1(
01.05.
)01.1()03.1(50.2)1()1( 141405
4
gr
ggD
gr
DP
s
s
s
0485.71$04.
8419.2
01.05.
)01.1(8138.2 1
4
P
Copyright 2014 by Diane Scott Docking 35
Example: Comparing Dividend-Growth Models
3. Discount this price (Pn) back to time 0 (P0”).
4. Add the two components of the stock price together.
Yes buy. Priced too low
45.58$)05.1(
0485.71$
)1()1( 444"
0
s
ns
n
r
P
r
PP
98.67$45.58$53.9$"0
'00 PPP
Copyright 2014 by Diane Scott Docking 36
Dividends Versus Return and Growth
For another interpretation, note that we can rearrange the constant dividend growth model equation as follows:
Solving for rs:
Solving for g:
gr
DP
s
tt 1
gP
Dr
t
ts 1
t
ts P
Drg 1
0
0
DP
DPrg
t
ts
or
Copyright 2014 by Diane Scott Docking 37
Example: Solving for Investment Return
Carson Co. recently paid a $1.20 dividend. The dividend is expected to grow at a 2% rate. At a current stock price of $36.35, what return are shareholders expecting?
Solve for rs:
02.35.36$
)02.1(20.1$1 gP
Dr
t
ts
%367.505367.02.03367.02.35.36$
224.1$sr
Copyright 2014 by Diane Scott Docking 38
Example: Solving for Growth Rate
Flintstone Co. recently paid a $1.10 dividend. The current stock price of the company is $46.27 and investors expect a 6% return. What is the expected future growth rate in dividends.
Solving for g:
10.127.46
10.17762.2
10.127.46
10.127.4606.
0
0
DP
DPrg
t
ts
%54.35385.3035385.037.47
6762.1g
Copyright 2014 by Diane Scott Docking 39
Limitations of Dividend-Discount Model
We cannot use the constant dividend growth model to value the stock of the following types of firms: Firms that pay no dividends Firms whose growth rate continues to change over
time until they mature
There is great uncertainty associated with any forecast of a firm’s future dividends in relationship to the Dividend-Discount Model
Copyright 2014 by Diane Scott Docking 40
Limitations of Dividend-Discount Model
We cannot use the constant dividend growth model to value the stock of such a firm for two reasons: These firms often pay no dividends when they are
young Their growth rate continues to change over time until
they mature
There is great uncertainty associated with any forecast of a firm’s future dividends in relationship to the Dividend-Discount Model