Dividend Policy resolves two questions:
Question 1: Does dividend policy affect firm value?
Question 2: If so, What is the optimal level of distribution ratio i.e., % Net Income to be distributed as dividend (Payout ratio). These issues are discussed under Irrelevance Theories (Modigliani and Miller’s Model) and
Relevance Theories (Walter’s Model , Gordon’s Model)
09 Chapter modelChapter 9. Stocks and Their Valuation (Models)Thi.docxhoney725342
09 Chapter modelChapter 9. Stocks and Their Valuation (Models)This model is similar to the bond valuation models developed in Chapter 7 in that we employ discounted cash flow analysis to find the value of a firm's stock.THE DISCOUNTED DIVIDEND MODEL (Section 9-4)The value of any financial asset is equal to the present value of future cash flows provided by the asset. Stocks can be evaluated in two ways: (1) by finding the present value of the expected future dividends, or (2) by finding the present value of the firm's expected future free cash flows, subtracting the market value of the debt and preferred stock to find the total value of the common equity, and then dividing that total value by the number of shares outstanding to find the value per share. Both approaches are examined in this spreadsheet.When an investor buys a share of stock, he/she typically expects to receive cash in the form of dividends and then, eventually, to sell the stock and to receive cash from the sale. Moreover, the price any investor receives is dependent upon the dividends the next investor expects to earn, and so on for different generations of investors. The basic dividend valuation equation is:P0 =D1+D2+. . . .Dn( 1 + rs )( 1 + rs ) 2( 1 + rs ) nThe dividend stream theoretically extends on out forever, i.e., n = infinity. It would not be feasible to deal with an infinite stream of dividends, but if dividends are expected to grow at a constant rate, we can use the constant growth equation as developed in the text to find the value.CONSTANT GROWTH STOCKS (Section 9-5)In the constant growth model, we assume that the dividend will grow forever at a constant growth rate. This is a very strong assumption, but for stable, mature firms, it can be reasonable to assume that the firm will experience some ups and downs throughout its life but those ups and downs balance each other out and result in a long-term constant rate. In addition, we assume that the required return for the stock is a constant. With these assumptions, the price equation for a common stock simplifies to the following expression:P 0 =D 1( r s − g )The long-run growth rate (g) is especially difficult to measure, but one approximates this rate by multiplying the firm's return on equity by the fraction of earnings retained, ROE x
(1 – Payout ratio). Generally speaking, the long-run growth rate is likely to fall between 5% and 8%.EXAMPLEAllied Food Products just paid a dividend of $1.15, and the dividend is expected to grow at a constant rate of 8.3%. What stock price is consistent with these numbers, assuming a 13.7% required return?D0$2.15g8.3%rs13.7%P0 =D1=D0 (1+g)=$2.33( rs − g )( rs − g )0.054P0 =$43.12STOCK PRICE SENSITIVITYOne of the keys to understanding stock valuation is knowing how various factors affect the stock price. We construct below a series of data tables and a graph to show how the stock price is affected by changes in the dividend, the growth rate, and rs. R ...
Slide 1
7-1
Cash Flows for Stockholders
• If you own a share of stock, you can receive
cash in two ways
The company pays dividends
You sell your shares, either to another investor in
the market or back to the company
• As with bonds, the price of the stock is the
present value of these expected cash flows
Dividends → cash income
Selling → capital gains
In this module, we turn to the other major source of financing for corporations, common and preferred stock.
The goal of financial management is to maximize stock prices, so an understanding of what determines
share values is obviously a key concern. The dividends currently being paid are one of the primary factors
we look at when we attempt to value common stocks. This module explores dividends, stock values, and
the connection between the two.
A share of common stock is more difficult to value in practice than a bond, for at least three reasons.
First, with common stock, not even the promised cash flows are known in advance.
Second, the life of the investment is essentially forever, since common stock has no maturity.
Third, there is no way to easily observe the rate of return that the market requires.
However, we can come up with the present value of the future cash flows for a share of stock making some
assumptions.
Slide 2
7-2
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
– You believe you can sell the stock for $14 at that
time.
– You require a return of 20% on investments of this
risk
– What is the maximum you would be willing to
pay?
Slide 3
7-3
One Period Example
• D1 = $2 dividend expected in one year
• R = 20%
• P1 = $14
• CF1 = $2 + $14 = $16
• Compute the PV of the expected cash flows
33.13$
20.1
)142(
P
0
Note, the calculation can also be done as:
FV = 14; PMT = 2; I/Y = 20; N = 1; CPT PV = -13.33
Slide 4
7-4
Two Period Example
• 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
$14.70 at the end of year 2.
– Now how much would you be willing to pay?
33.13$
)20.1(
)70.1410.2(
20.1
2
P
20
Calculator: CF0 = 0; C01 = 2; F01 = 1; C02 = 16.80; F02 = 1; NPV; I =
20; CPT NPV = 13.33
We can use uneven cash flow keys.
Slide 5
7-5
Three Period Example
• What if you decide to hold the stock for three
years?
– In addition to the dividends at the end of years 1 and 2,
you expect to receive a dividend of $2.205 at the end of
year 3 and the stock price is expected to be $15.435.
– Now how much would you be willing to pay?
33.13$
)20.1(
)435.15205.2(
)20.1(
10.2
20.1
2
P
320
Calcultator: CF0 = 0; C01 = 2; F01 = 1; C02 = 2.10; F02 = 1; C03 = 17.64;
F03 = 1; NPV; I = 20; CPT NPV = 13.33
Slide 6
7-6
Devel.
1. Nicks Enchiladas Incorporated has preferred stock outstand.docxjackiewalcutt
1. Nick's Enchiladas Incorporated has preferred stock outstanding that pays a dividend of $5 at
the end of each year. The preferred stock sells for $35 a share. What is the stock's required rate of
return? Round the answer to two decimal places.
%
2. A stock is expected to pay a year-end dividend of $2.00, i.e., D1 = $2.00. The dividend is
expected to decline at a rate of 5% a year forever (g = −5%). If the company is in equilibrium and
its expected and required rate of return is 15%, which of the following statements is CORRECT?
a. The company's dividend yield 5 years from now is expected to be 10%.
b. The company's current stock price is $20.
c. The company's expected capital gains yield is 5%.
d. The constant growth model cannot be used because the growth rate is negative.
e. The company's expected stock price at the beginning of next year is $9.50.
3. The expected return on Natter Corporation's stock is 14%. The stock's dividend is expected to
grow at a constant rate of 8%, and it currently sells for $50 a share. Which of the following
statements is CORRECT?
a. The stock's dividend yield is 7%.
b. The current dividend per share is $4.00.
c. The stock's dividend yield is 8%.
d. The stock price is expected to be $54 a share one year from now.
e. The stock price is expected to be $57 a share one year from now.
4. Investors require a 16% rate of return on Brooks Sisters' stock (rs = 16%).
a. What would the value of Brooks's stock be if the previous dividend was D0 = $2.75 and if
investors expect dividends to grow at a constant compound annual rate of (1) - 4%, (2)
0%, (3) 7%, or (4) 10%? Round your answers to the nearest cent.
1. $
2. $
3. $
4. $
b. Using data from part a, what is the Gordon (constant growth) model's value for Brooks
Sisters's stock if the required rate of return is 16% and the expected growth rate is (1)
16% or (2) 24%? Are these reasonable results? Explain.
1. (Yes or No)
2. (Yes or No)
c. Is it reasonable to expect that a constant growth stock would have g > rs? ( Yes or No)
5. Brushy Mountain Mining Company's ore reserves are being depleted, so its sales are falling.
Also, its pit is getting deeper each year, so its costs are rising. As a result, the company's earnings
and dividends are declining at the constant rate of 6% per year. If D0 = $3 and rs = 13%, what is
the value of Brushy Mountain Mining's stock? Round your answer to the nearest cent.
$
6. Boehm Incorporated is expected to pay a $3.70 per share dividend at the end of this year (i.e.,
D1 = $3.70). The dividend is expected to grow at a constant rate of 10% a year. The required rate
of return on the stock, rs, is 18%. What is the value per share of the company's stock? Round your
answer to the nearest cent.
$
7. A company currently pays a dividend of $1.5 per share, D0 = 1.5. It is estimated that the
comp ...
Dividend policy
What is Dividend?
What is dividend policy?
Theories of Dividend Policy
Relevant Theory
Walter’s Model
Gordon’s Model
Irrelevant Theory
M-M’s Approach
Traditional Approach
Referred to:
Prasanna Chandra
how to sell pi coins at high rate quickly.DOT TECH
Where can I sell my pi coins at a high rate.
Pi is not launched yet on any exchange. But one can easily sell his or her pi coins to investors who want to hold pi till mainnet launch.
This means crypto whales want to hold pi. And you can get a good rate for selling pi to them. I will leave the telegram contact of my personal pi vendor below.
A vendor is someone who buys from a miner and resell it to a holder or crypto whale.
Here is the telegram contact of my vendor:
@Pi_vendor_247
More Related Content
Similar to pdfslide.net_1-finc4101-investment-analysis-instructor-dr-leng-ling-topic-equity-valuation.pptx
Dividend Policy resolves two questions:
Question 1: Does dividend policy affect firm value?
Question 2: If so, What is the optimal level of distribution ratio i.e., % Net Income to be distributed as dividend (Payout ratio). These issues are discussed under Irrelevance Theories (Modigliani and Miller’s Model) and
Relevance Theories (Walter’s Model , Gordon’s Model)
09 Chapter modelChapter 9. Stocks and Their Valuation (Models)Thi.docxhoney725342
09 Chapter modelChapter 9. Stocks and Their Valuation (Models)This model is similar to the bond valuation models developed in Chapter 7 in that we employ discounted cash flow analysis to find the value of a firm's stock.THE DISCOUNTED DIVIDEND MODEL (Section 9-4)The value of any financial asset is equal to the present value of future cash flows provided by the asset. Stocks can be evaluated in two ways: (1) by finding the present value of the expected future dividends, or (2) by finding the present value of the firm's expected future free cash flows, subtracting the market value of the debt and preferred stock to find the total value of the common equity, and then dividing that total value by the number of shares outstanding to find the value per share. Both approaches are examined in this spreadsheet.When an investor buys a share of stock, he/she typically expects to receive cash in the form of dividends and then, eventually, to sell the stock and to receive cash from the sale. Moreover, the price any investor receives is dependent upon the dividends the next investor expects to earn, and so on for different generations of investors. The basic dividend valuation equation is:P0 =D1+D2+. . . .Dn( 1 + rs )( 1 + rs ) 2( 1 + rs ) nThe dividend stream theoretically extends on out forever, i.e., n = infinity. It would not be feasible to deal with an infinite stream of dividends, but if dividends are expected to grow at a constant rate, we can use the constant growth equation as developed in the text to find the value.CONSTANT GROWTH STOCKS (Section 9-5)In the constant growth model, we assume that the dividend will grow forever at a constant growth rate. This is a very strong assumption, but for stable, mature firms, it can be reasonable to assume that the firm will experience some ups and downs throughout its life but those ups and downs balance each other out and result in a long-term constant rate. In addition, we assume that the required return for the stock is a constant. With these assumptions, the price equation for a common stock simplifies to the following expression:P 0 =D 1( r s − g )The long-run growth rate (g) is especially difficult to measure, but one approximates this rate by multiplying the firm's return on equity by the fraction of earnings retained, ROE x
(1 – Payout ratio). Generally speaking, the long-run growth rate is likely to fall between 5% and 8%.EXAMPLEAllied Food Products just paid a dividend of $1.15, and the dividend is expected to grow at a constant rate of 8.3%. What stock price is consistent with these numbers, assuming a 13.7% required return?D0$2.15g8.3%rs13.7%P0 =D1=D0 (1+g)=$2.33( rs − g )( rs − g )0.054P0 =$43.12STOCK PRICE SENSITIVITYOne of the keys to understanding stock valuation is knowing how various factors affect the stock price. We construct below a series of data tables and a graph to show how the stock price is affected by changes in the dividend, the growth rate, and rs. R ...
Slide 1
7-1
Cash Flows for Stockholders
• If you own a share of stock, you can receive
cash in two ways
The company pays dividends
You sell your shares, either to another investor in
the market or back to the company
• As with bonds, the price of the stock is the
present value of these expected cash flows
Dividends → cash income
Selling → capital gains
In this module, we turn to the other major source of financing for corporations, common and preferred stock.
The goal of financial management is to maximize stock prices, so an understanding of what determines
share values is obviously a key concern. The dividends currently being paid are one of the primary factors
we look at when we attempt to value common stocks. This module explores dividends, stock values, and
the connection between the two.
A share of common stock is more difficult to value in practice than a bond, for at least three reasons.
First, with common stock, not even the promised cash flows are known in advance.
Second, the life of the investment is essentially forever, since common stock has no maturity.
Third, there is no way to easily observe the rate of return that the market requires.
However, we can come up with the present value of the future cash flows for a share of stock making some
assumptions.
Slide 2
7-2
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
– You believe you can sell the stock for $14 at that
time.
– You require a return of 20% on investments of this
risk
– What is the maximum you would be willing to
pay?
Slide 3
7-3
One Period Example
• D1 = $2 dividend expected in one year
• R = 20%
• P1 = $14
• CF1 = $2 + $14 = $16
• Compute the PV of the expected cash flows
33.13$
20.1
)142(
P
0
Note, the calculation can also be done as:
FV = 14; PMT = 2; I/Y = 20; N = 1; CPT PV = -13.33
Slide 4
7-4
Two Period Example
• 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
$14.70 at the end of year 2.
– Now how much would you be willing to pay?
33.13$
)20.1(
)70.1410.2(
20.1
2
P
20
Calculator: CF0 = 0; C01 = 2; F01 = 1; C02 = 16.80; F02 = 1; NPV; I =
20; CPT NPV = 13.33
We can use uneven cash flow keys.
Slide 5
7-5
Three Period Example
• What if you decide to hold the stock for three
years?
– In addition to the dividends at the end of years 1 and 2,
you expect to receive a dividend of $2.205 at the end of
year 3 and the stock price is expected to be $15.435.
– Now how much would you be willing to pay?
33.13$
)20.1(
)435.15205.2(
)20.1(
10.2
20.1
2
P
320
Calcultator: CF0 = 0; C01 = 2; F01 = 1; C02 = 2.10; F02 = 1; C03 = 17.64;
F03 = 1; NPV; I = 20; CPT NPV = 13.33
Slide 6
7-6
Devel.
1. Nicks Enchiladas Incorporated has preferred stock outstand.docxjackiewalcutt
1. Nick's Enchiladas Incorporated has preferred stock outstanding that pays a dividend of $5 at
the end of each year. The preferred stock sells for $35 a share. What is the stock's required rate of
return? Round the answer to two decimal places.
%
2. A stock is expected to pay a year-end dividend of $2.00, i.e., D1 = $2.00. The dividend is
expected to decline at a rate of 5% a year forever (g = −5%). If the company is in equilibrium and
its expected and required rate of return is 15%, which of the following statements is CORRECT?
a. The company's dividend yield 5 years from now is expected to be 10%.
b. The company's current stock price is $20.
c. The company's expected capital gains yield is 5%.
d. The constant growth model cannot be used because the growth rate is negative.
e. The company's expected stock price at the beginning of next year is $9.50.
3. The expected return on Natter Corporation's stock is 14%. The stock's dividend is expected to
grow at a constant rate of 8%, and it currently sells for $50 a share. Which of the following
statements is CORRECT?
a. The stock's dividend yield is 7%.
b. The current dividend per share is $4.00.
c. The stock's dividend yield is 8%.
d. The stock price is expected to be $54 a share one year from now.
e. The stock price is expected to be $57 a share one year from now.
4. Investors require a 16% rate of return on Brooks Sisters' stock (rs = 16%).
a. What would the value of Brooks's stock be if the previous dividend was D0 = $2.75 and if
investors expect dividends to grow at a constant compound annual rate of (1) - 4%, (2)
0%, (3) 7%, or (4) 10%? Round your answers to the nearest cent.
1. $
2. $
3. $
4. $
b. Using data from part a, what is the Gordon (constant growth) model's value for Brooks
Sisters's stock if the required rate of return is 16% and the expected growth rate is (1)
16% or (2) 24%? Are these reasonable results? Explain.
1. (Yes or No)
2. (Yes or No)
c. Is it reasonable to expect that a constant growth stock would have g > rs? ( Yes or No)
5. Brushy Mountain Mining Company's ore reserves are being depleted, so its sales are falling.
Also, its pit is getting deeper each year, so its costs are rising. As a result, the company's earnings
and dividends are declining at the constant rate of 6% per year. If D0 = $3 and rs = 13%, what is
the value of Brushy Mountain Mining's stock? Round your answer to the nearest cent.
$
6. Boehm Incorporated is expected to pay a $3.70 per share dividend at the end of this year (i.e.,
D1 = $3.70). The dividend is expected to grow at a constant rate of 10% a year. The required rate
of return on the stock, rs, is 18%. What is the value per share of the company's stock? Round your
answer to the nearest cent.
$
7. A company currently pays a dividend of $1.5 per share, D0 = 1.5. It is estimated that the
comp ...
Dividend policy
What is Dividend?
What is dividend policy?
Theories of Dividend Policy
Relevant Theory
Walter’s Model
Gordon’s Model
Irrelevant Theory
M-M’s Approach
Traditional Approach
Referred to:
Prasanna Chandra
how to sell pi coins at high rate quickly.DOT TECH
Where can I sell my pi coins at a high rate.
Pi is not launched yet on any exchange. But one can easily sell his or her pi coins to investors who want to hold pi till mainnet launch.
This means crypto whales want to hold pi. And you can get a good rate for selling pi to them. I will leave the telegram contact of my personal pi vendor below.
A vendor is someone who buys from a miner and resell it to a holder or crypto whale.
Here is the telegram contact of my vendor:
@Pi_vendor_247
Seminar: Gender Board Diversity through Ownership NetworksGRAPE
Seminar on gender diversity spillovers through ownership networks at FAME|GRAPE. Presenting novel research. Studies in economics and management using econometrics methods.
The secret way to sell pi coins effortlessly.DOT TECH
Well as we all know pi isn't launched yet. But you can still sell your pi coins effortlessly because some whales in China are interested in holding massive pi coins. And they are willing to pay good money for it. If you are interested in selling I will leave a contact for you. Just telegram this number below. I sold about 3000 pi coins to him and he paid me immediately.
Telegram: @Pi_vendor_247
what is the best method to sell pi coins in 2024DOT TECH
The best way to sell your pi coins safely is trading with an exchange..but since pi is not launched in any exchange, and second option is through a VERIFIED pi merchant.
Who is a pi merchant?
A pi merchant is someone who buys pi coins from miners and pioneers and resell them to Investors looking forward to hold massive amounts before mainnet launch in 2026.
I will leave the telegram contact of my personal pi merchant to trade pi coins with.
@Pi_vendor_247
Currently pi network is not tradable on binance or any other exchange because we are still in the enclosed mainnet.
Right now the only way to sell pi coins is by trading with a verified merchant.
What is a pi merchant?
A pi merchant is someone verified by pi network team and allowed to barter pi coins for goods and services.
Since pi network is not doing any pre-sale The only way exchanges like binance/huobi or crypto whales can get pi is by buying from miners. And a merchant stands in between the exchanges and the miners.
I will leave the telegram contact of my personal pi merchant. I and my friends has traded more than 6000pi coins successfully
Tele-gram
@Pi_vendor_247
how to sell pi coins in all Africa Countries.DOT TECH
Yes. You can sell your pi network for other cryptocurrencies like Bitcoin, usdt , Ethereum and other currencies And this is done easily with the help from a pi merchant.
What is a pi merchant ?
Since pi is not launched yet in any exchange. The only way you can sell right now is through merchants.
A verified Pi merchant is someone who buys pi network coins from miners and resell them to investors looking forward to hold massive quantities of pi coins before mainnet launch in 2026.
I will leave the telegram contact of my personal pi merchant to trade with.
@Pi_vendor_247
What price will pi network be listed on exchangesDOT TECH
The rate at which pi will be listed is practically unknown. But due to speculations surrounding it the predicted rate is tends to be from 30$ — 50$.
So if you are interested in selling your pi network coins at a high rate tho. Or you can't wait till the mainnet launch in 2026. You can easily trade your pi coins with a merchant.
A merchant is someone who buys pi coins from miners and resell them to Investors looking forward to hold massive quantities till mainnet launch.
I will leave the telegram contact of my personal pi vendor to trade with.
@Pi_vendor_247
how to sell pi coins on Bitmart crypto exchangeDOT TECH
Yes. Pi network coins can be exchanged but not on bitmart exchange. Because pi network is still in the enclosed mainnet. The only way pioneers are able to trade pi coins is by reselling the pi coins to pi verified merchants.
A verified merchant is someone who buys pi network coins and resell it to exchanges looking forward to hold till mainnet launch.
I will leave the telegram contact of my personal pi merchant to trade with.
@Pi_vendor_247
Lecture slide titled Fraud Risk Mitigation, Webinar Lecture Delivered at the Society for West African Internal Audit Practitioners (SWAIAP) on Wednesday, November 8, 2023.
how can I sell pi coins after successfully completing KYCDOT TECH
Pi coins is not launched yet in any exchange 💱 this means it's not swappable, the current pi displaying on coin market cap is the iou version of pi. And you can learn all about that on my previous post.
RIGHT NOW THE ONLY WAY you can sell pi coins is through verified pi merchants. A pi merchant is someone who buys pi coins and resell them to exchanges and crypto whales. Looking forward to hold massive quantities of pi coins before the mainnet launch.
This is because pi network is not doing any pre-sale or ico offerings, the only way to get my coins is from buying from miners. So a merchant facilitates the transactions between the miners and these exchanges holding pi.
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Message: @Pi_vendor_247 on telegram.
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#kyc #mainnet #picoins #pi #sellpi #piwallet
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where can I find a legit pi merchant onlineDOT TECH
Yes. This is very easy what you need is a recommendation from someone who has successfully traded pi coins before with a merchant.
Who is a pi merchant?
A pi merchant is someone who buys pi network coins and resell them to Investors looking forward to hold thousands of pi coins before the open mainnet.
I will leave the telegram contact of my personal pi merchant to trade with
@Pi_vendor_247
2. 2
Learning objectives
1. Distinguish between the intrinsic value and price
of a share of common stock.
2. Calculate the intrinsic value of a firm using
dividend discount models
Constant dividend growth model
Multistage dividend growth model
3. Use the constant growth model to relate growth
opportunities to stock value.
4. Calculate the P/E ratio for a constant growth firm.
5. Discuss the free cash flow valuation methods.
4. 4
Why equity valuation?
Identify mispriced equity securities.
How?
By calculating “intrinsic” or “true” value of a
stock using valuation models.
These valuation models make use of
information concerning current & future
profitability.
This approach of identifying mispriced
stocks is called fundamental analysis.
5. 5
Intrinsic value vs. market price (1)
Intrinsic value, V0
Present value of all expected future cash
flows to the stock investor. The cash
flows are discounted at the appropriate
required rate of return, k.
Expected future cash flows consist of:
1. cash dividends
2. sale price: proceeds from the ultimate sale
of the stock
6. 6
Intrinsic value vs. market price (2)
Intrinsic value is your (the analyst’s)
estimate of what a stock is really worth.
Intrinsic value (V0) can differ from the
current market price (P0).
If V0 > P0: stock is underpriced => buy
If V0 < P0: stock is overpriced => sell or don’t
buy.
7. 7
Market equilibrium
In market equilibrium,
Everyone has the same intrinsic value. So,
intrinsic value equals market price, i.e.,
V0 = P0.
Everyone also demands the same required rate
of return from the stock. So everyone has the
same k. In addition, expected HPR = k.
This common required rate of return is called the
market capitalization rate.
Market capitalization rate: required rate of return
which the market (i.e., everyone) uses to discount
future cash flows.
8. 8
Equity valuation models
Dividend discount models
Constant dividend growth model
Multistage (non-constant) dividend growth
model
Price-earnings ratio (P/E)
Free cash flow models
9. 9
Dividend discount models (DDMs)
Dividend discount models say that the
intrinsic value of a stock is equal to the
present value of all expected future
dividends.
What about cash flow from the ultimate sale of
the stock? Is that included?
Yes, because stock price at time of sale is
again determined by expected dividends at
the time of sale.
10. 10
Dividend discount model:
General formula
1 2 3
0 2 3
....
1 (1 ) (1 )
D D D
V
k k k
= + + +
+ + +
This formula cannot be implemented because it
requires dividend forecasts every year into the
indefinite future.
To implement the DDM, we make assumptions about
how dividends evolve over time.
11. 11
Two versions of DDM
We look at 2 assumptions:
Dividends grow at constant rate
Constant dividend growth model
Dividends grow at different rates over
different periods. At some future date,
dividend growth settles down to a
constant rate.
Multistage (non-constant) dividend
growth model
12. 12
Constant dividend growth model (1)
1. Assume that dividends grow at a
constant rate, g, per period forever.
2. Given this assumption, the intrinsic value
equals
0 1
0
(1 )
D g D
V
k g k g
+
= =
- -
D0 = Dividend
that the firm
just paid
Required rate
of return or
discount rate
Dividend
growth rate
Don’t panic.
D1 = D0(1 + g)
13. 13
Constant dividend growth model (2)
Warning: The model works only if k > g.
Useful properties.
All other things unchanged,
• If D1 increases (decreases), V0 increases
(decreases).
• If g increases (decreases), V0 increases
(decreases).
• If k increases (decreases), V0 decreases
(increases).
14. 14
Constant dividend growth model (3)
Suppose the market is in equilibrium. This
means that stock price is equal to intrinsic
value, i.e., P0 = V0.
Then, stock price is expected to grow at
the same rate as dividends.
That is, the expected rate of price
appreciation in any year will equal the
constant growth rate, g.
P1 = P0 ( 1 + g ) = V1 = V0 ( 1 + g )
15. 15
Expected HPR and k (1)
Continue to assume that P0 = V0 .
Then, expected HPR, E(r) is,
1 1 0
0 0
1
0
( )
D P P
E r
P P
D
g
P
-
= +
= +
Dividend yield Capital gains yield
16. 16
Expected HPR and k (2)
If stock is selling at intrinsic value, P0 = V0
Then required rate of return, k, must equal the
expected HPR. Therefore,
When everyone agrees on the same k (in equilibrium),
we can use the above formula to compute market
capitalization rate.
1
0
D
k g
P
= +
17. 17
Constant dividend stream
If g = 0, then dividends do not grow and
stay the same forever. We have a
constant dividend stream – a perpetuity.
The constant dividend stream assumption
is a special case of the constant growth
model with g = 0.
Implication: with constant dividend stream,
we continue to use the preceding
equations but set g to 0.
18. 18
Applying the constant growth DDM (1)
A common stock pays an annual dividend
per share of $2.10. The risk-free rate is
7% and the risk premium for this stock is
4%. If the annual dividend is expected to
remain at $2.10 forever, what is the value
of the stock? (to two decimal places)
Verify that V0 = $19.09
19. 19
Applying the constant growth DDM (2)
The risk-free rate of return is 10%, the
required rate of return on the market is
15%, and High-Flyer stock has a beta
coefficient of 1.5. If the dividend per share
expected during the coming year, D1, is
$2.50 and g = 5%, at what price should a
share sell?
Hint: use the CAPM to get the market
capitalization rate.
20. 20
Applying the constant growth DDM (3)
Big Oil Inc. just paid a dividend of $10 (i.e.,
D0 = 10.00). Its dividends are expected to
grow at a 4% annual rate forever. The
market capitalization rate is 15%. What is
the price of Big Oil’s common stock? (to 2
decimal places)
Verify that price = $94.55
21. 21
Applying the constant growth DDM (4)
The price of a stock in the market is $62.
You know that the firm has just paid a
dividend of $5 per share (i.e., D0 = 5). The
dividend growth rate is expected to be 6
percent forever. What is the market
capitalization rate for this stock (to 2
decimal places)?
22. 22
Applying the constant growth DDM (5)
A firm is expected to pay a dividend of
$5.00 on its stock next year. The current
price of this stock is $40 and investors
require a return of 20%. The firm’s
dividends grow at a constant rate. What is
the constant dividend growth rate (g)?
use k = (D1/P0) + g
Verify that g = 7.5%
23. 23
Applying the constant growth DDM (6)
In order to use the constant dividend growth
model to value a stock it must be true that:
a. The required rate of return is less than the expected
dividend growth rate.
b. The expected dividend growth rate is greater than zero.
c. The next dividend (D1) is expected to be greater than
$1.00.
d. The expected dividend growth rate is less than the
required rate of return.
Which statement is correct?
24. 24
Stock prices &
investment/growth opportunities
How do we figure out dividend growth rate, g ?
Growth rate depends on:
1. Investment opportunities embodied in return
on equity, ROE
2. Reinvestment of earnings, represented by
earnings retention ratio, b.
Earnings retention ratio is also called the plowback
ratio.
Growth rate, g = ROE x b
25. 25
Earnings retention ratio and
dividend payout ratio
Earnings retention rate
= reinvested earnings/ total earnings.
A related measure is the dividend payout
ratio.
Dividend payout ratio
= dividends paid/ total earnings
= 1 – retention rate
26. 26
Problem
Geoscience Corp. has a beta of 1.2 and its most
recent EPS is $10 per share. The company just paid
40% of its earnings in dividends. Geoscience Corp will
earn an ROE of 20% per year on all reinvested
earnings forever. The risk-free rate is 8% and the
expected return on the market portfolio is 15%.
a) What is the intrinsic value (V0) of a share of
Geoscience’s stock (to two decimal places)?
b) If the market price of a share is currently $100, and
you expect the market price to be equal to the intrinsic
value one year from now, what is your expected one-
year HPR on Geoscience Corp.’s stock?
27. 27
Earnings retention ratio
affects growth
Suppose ROE > 0 Growth
policy
No-growth
policy
Earnings retention ratio, b b > 0 b = 0
Growth rate, g g > 0 g = 0
Bottomline: If a company reinvests some portion of
earnings back into the business (b > 0), future earnings and
dividends will grow (i.e., g > 0). Otherwise, earnings and
dividends will not grow.
28. 28
Is growth always beneficial?
Does having positive growth always
increase stock price?
No. It depends on the attractiveness of the
firm’s investment opportunities, ROE.
Compared to a no-growth policy,
If ROE > k, then retaining earnings (i.e., b > 0)
will increase stock price.
If ROE < k, then retaining earnings will
decrease stock price.
29. 29
Consider two companies
Growth
Prospects,
Inc (GP)
Dead Beat,
Inc (DB)
No-growth earnings per share $5 $5
Market capitalization rate, k 12.5% 12.5%
No-growth price per share 5/0.125 = 40 5/0.125 = 40
ROE 15% 10%
30. 30
Suppose both companies reinvest
60% of next year’s earnings…
Growth Prospects,
Inc (GP)
Dead Beat, Inc
(DB)
Earnings retention ratio, b 0.6 0.6
Next year’s dividend per
share,
D1 = (1 – b) x 5
$2 $2
Dividend growth rate, g
= ROE x b
9% 6%
Constant dividend growth
model share price
2/(0.125 – 0.09)
= 57.14
2/(0.125 – 0.06)
= 30.77
31. 31
Compare GP and DB
Growth
Prospects, Inc
(GP)
Dead Beat,
Inc (DB)
ROE 15% 10%
Market capitalization rate, k 12.5% 12.5%
No-growth price per share (1) 40 40
Constant div. growth Price (2) 57.14 30.77
Present value of growth
opportunities, PVGO = (2) – (1)
17.14 -9.23
PVGO = Price per share – no-growth price per share
32. 32
Problems involving growth (1)
MF Corp. has an ROE of 16% and a
plowback ratio of 50%. If the coming
year’s earnings are expected to be $2
per share. The market capitalization rate
is 12%.
A. At what price will the stock sell today?
B. At what price do you expect MF shares
to sell for in 3 years?
33. 33
Problems involving growth (2)
Even Better Products has come out with a new
and improved product. As a result, the firm
projects an ROE of 20%, and it will maintain a
retention ratio of 0.30. Its earnings in one year
will be $2 per share. Investors expect a 12%
rate of return on the stock.
a) Calculate the stock price.
b) What is the present value of growth
opportunities (PVGO)?
c) What would be the stock price and PVGO if the
firm reinvests only 20% of its earnings?
34. 34
Multi-stage dividend growth 1
With this assumption, dividends grow at
different rates for different periods of time.
Eventually, dividends will grow at a
constant rate forever.
Time line is very useful for valuing this
type of stocks.
To value such stocks, also need the
constant growth formula.
Best way to learn is through an example.
35. 35
Multi-stage dividend growth 2
ABC Co. is expected to pay dividends at the end of the
next three years of $2, $3, $3.50, respectively. After
three years, the dividend is expected to grow at 5%
constant annual rate forever. If the market capitalization
rate for this stock is 15%, what is the current stock price?
T = 0
$2.00 $3.00 $3.50
Dividends grow
at 5% forever
T =1 T = 2 T = 3 T = 4
36. 36
What to do?
1. Place yourself at t = 3 and use the
constant growth formula to find PV of
dividend stream after year 3. Call this P3.
2. Find the PV of P3.
3. Find PV of dividends at t=1, t=2 and t=3.
4. Current stock price = sum of 2, 3 and 4.
38. 38
Another type of
multi-stage growth problem
Malcolm Manufacturing, Inc. just paid a $2.00
annual dividend (that is, D0 = 2.00). Investors
believe that the firm will grow at 10% annually for
the next 2 years and 6% annually forever
thereafter. Assuming a required return of 15%,
what is the current price of the stock (to 2 decimal
places)?
Use timeline to ‘see’ the problem better.
Verify that stock price = $25.29
39. 39
Price-earnings (P/E) ratios
P/E ratio is the ratio of current price per
share (P0) to next year’s expected
earnings per share (EPS).
How do we use P/E ratio to value a stock?
1. Forecast next year’s EPS, E1.
2. Forecast P/E ratio, P0/E1.
3. Multiple P/E by EPS to get current
estimate of price.
(P0/E1) x E1 = P0
40. 40
P/E ratio and
constant growth model
If a company has a constant dividend
growth rate and the market is in
equilibrium (i.e., V0=P0), then we have an
explicit formula for the P/E ratio!
Recall that b = retention ratio, k = market capitalization rate.
)
(
1
1
0
b
ROE
k
b
E
P
41. 41
P/E questions (1)
ABC Co. has an ROE of 25%, a CAPM
beta of 1.2 and a retention ratio of 40%.
The risk-free rate is 6% and the market
risk premium is 5%. What is ABC’s P/E
ratio?
42. 42
P/E questions (2)
Analog Electronic Corporation has an ROE =
9% and a beta of 1.25. It plans to maintain
indefinitely its traditional plowback ratio of 2/3.
The most recent earnings per share is $3 per
share. The expected market return is 14% and
the risk-free rate is 6%.
a) What is Analog’s stock price?
b) Calculate the P/E (P0/E1) ratio.
c) Calculate the PVGO.
43. 43
Free Cash Flow Valuation Approach
Dividend discount models don’t work for
companies which do not pay dividends.
For non-dividend paying companies, we
can use free cash flow valuation approach.
There are two versions:
Free cash flow to the firm (FCFF)
Free cash flow to equity holders (FCFE)
44. 44
Free Cash Flow to the Firm (FCFF) (1)
FCFF: cash flow that accrues from the firm’s
operations, net of investments in capital and net
working capital.
FCFF represent cash flows available to both
debt and equity holders.
FCFF = EBIT(1 – tc) + Depreciation – capital
expenditures – increase in NWC
EBIT = earnings before interest and taxes
tc = corporate tax rate
NWC (net working capital) = current asset – current
liability
45. Free Cash Flow to the Firm (FCFF) (2)
Capital expenditure includes:
1. acquiring fixed, and in some cases, intangible assets
2. repairing an existing asset so as to improve its useful
life
3. upgrading an existing asset if its results in a superior
fixture
4. preparing an asset to be used in business
5. restoring property or adapting it to a new or different
use
6. starting or acquiring a new business
45
46. 46
Free Cash Flow to the Firm (FCFF) (3)
Find the PV of the firm by discounting the year-
by-year FCFF plus some estimate of terminal
value, PT.
Firm Value=
where
Market value of equity = Firm value – market value of debt.
)
1
(
)
1
(
1 WACC
P
WACC
FCFF T
T
t
t
t
g
WACC
FCFF
P T
T
1
47. 47
Free Cash Flow to Equity Holders (FCFE)
FCFE: Free cash flow available to equity holders.
FCFE = FCFF – interest expense(1 – tc) + increases in
net debt
Find the market value of equity by discounting the year-
by-year FCFE plus some estimate of terminal value, PT.
is the cost of equity.
E
K
g
k
FCFE
P
where
k
P
k
FCFE
equity
of
value
market
E
T
T
T
E
T
T
t
t
E
1
1 )
1
(
)
1
(
48. 48
Summary
1. Distinguish between the intrinsic value and price.
2. Calculate intrinsic value using dividend discount
models
Constant dividend growth model
Multistage dividend growth model
3. Discuss the use of the P/E ratio to value common
stock.
4. Calculate the P/E ratio for a constant growth firm.
5. Discuss the free cash flow valuation methods.
