Valutation and rates of return ROR, class notes

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© 2021 MCGRAW HILL
Microsoft® PowerPoint® Presentation
Prepared by Kathy Faber, Conestoga College
CHAPTER
10
Valuation and
Rates of Return

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Chapter 10-
Outline
Valuation: Concepts and Relation
with Financing and Investment
Decisions
Valuation (price, yield) of:
 Bonds
 Preferred Stock
 Common Stock
Valuation Using the Price-
Earnings Ratio
Summary and Conclusions
© 2021 MCGRAW HILL

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Learning Objectives
© 2021 MCGRAW HILL
• Describe the valuation of a financial asset as
based on the present value of future cash
flows. (LO1)
Describe
• Propose that the required rate of return in
valuing an asset is based on the risk involved.
(LO2)
Propose
• Assess the current value (price) of bonds,
preferred shares (perpetuals), and common
shares based on the future benefits (cash
flows). (LO3)
Assess

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Learning Objectives
© 2021 MCGRAW HILL
• Evaluate the yields on financial claims based
on the relationship between current price and
future expected cash flows. (LO4)
Evaluate
• Describe the use of a price-earnings ratio to
determine value. (LO5)
Describ
e

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Figure 10-1
The relationship between time value of money,
required return, cost of financing, and investment
decisions
© 2021 MCGRAW HILL

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Valuation
Concepts
A financial asset (security) is a
claim against a firm, government
or individual for future expected
cash flows.
Examples of financial assets are
bonds, preferred stocks and
common stocks.
Valuation of a financial asset is
to determine the present value
of those future anticipated cash
flows using an appropriate
discount rate.
© 2021 MCGRAW HILL

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Valuation
Concepts-
Yield
An investment decision should be
made by:
comparing the price (or market
value) of a financial asset to its
present value.
determining the discount rate that
equates the market value of a
financial asset with the present value
of its future expected cash flows.
This discount rate is the market-
determined required rate of
return (ROR) or yield.
© 2021 MCGRAW HILL

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Valuation:
Concepts
and Relation
with
Financing
and
Investment
Decisions
Financial assets are issued by firms to
attract funds from investors.
Therefore, the required or expected
rate of return or yield on these
financial assets is the cost of financing
for issuing firms.
In turn, the issuing firm must earn at
least this rate of return on its projects
(the capital budgeting decision) in
order to add value to shareholders’
wealth.
© 2021 MCGRAW HILL

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Yield
The Real Rate of Return:
represents the opportunity cost of the
investment
in the early 1990’s, 5-7%, but now
about 2 to 3%
Inflation Premium:
a premium to compensate for the
effects of inflation
Since 2000 slightly less than 2%
Risk Premium:
a premium associated with business
and financial risk
default, liquidity and maturity risk
typically, 2-6%
© 2021 MCGRAW HILL

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The
Required
Rate of
Return
The Required Rate of
Return
= Real Rate of Return
+ Inflation Premium
+ Risk Premium
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Example of
a Required
Rate of
Return
© 2021 MCGRAW HILL
+ Real rate of return 3%
+ Inflation premium 4
= Risk-free rate 7%
+ Risk premium 3
= Required rate of return 10%

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Valuation of
Financial
Assets
Valuation of a financial asset is
based on determining present
value of future cash flows.
Required rate of return (discount rate)
Depends on market’s perceived level
of risk associated with individual
security
Also competitively determined among
companies seeking financial capital
Implies investors willing to accept low
return for low risk and vice versa
Previous efficient use of capital results
in lower required rate of return for
investors
© 2021 MCGRAW HILL

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Valuation of
Bonds
Calculating the Value of a Bond
Cash flows discounted at Y (the
yield to maturity)
Value of Y determined in bond
market
Bond Price is the NPV of Bond Cash
Flows
© 2021 MCGRAW HILL
+ PV interest payments
+ PV principal paid at maturity
= Price of bond

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Valuation of
Bonds –
Formula
Method
We calculate the value of a bond using this
formula:
Pb = +
where,
Pb = price of a bond today
t = time
n = number of periods the funds will be invested
It = interest payments
Y = yield to maturity
Pn = principal payment at maturity
© 2021 MCGRAW HILL

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Valuation of
Bonds –
Formula
Method:
Example
Let’s assume that we have a bond with
a face value of $1,000 paying 10%
annual interest over 20 years and a
yield of 10%.
We would calculate the price of this
bond using the formula:
Pb = +
= +
= ($90.91+$82.64+…+$14.86) + $148.64
= $1,000
Given the large number of interest
payments, this method is time
consuming
© 2021 MCGRAW HILL

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Valuation of
Bonds –
Alternate
Formula
Method
The stream of interest payments are an
annuity, so we could substitute the
formula for an annuity into our bond
formula:
Pb = A+
t = time
n = number of periods
A = interest payments
Y = yield to maturity
Pn = principal payment at maturity
© 2021 MCGRAW HILL

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Valuation of
Bonds –
Alternate
Formula
Method:
Example
Let’s look at that same bond with a face
value of $1,000 paying 10% annual
interest over 20 years yielding 10%.
We would calculate the price of this
bond using the alternate formula:
Pb = A+
= $100+
= $851.36+ $148.64
= $1,000
© 2021 MCGRAW HILL

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Valuation of
Bonds –
Calculator
Method
We can use a financial calculator
to calculate the present value
(price) of a bond:
© 2021 MCGRAW HILL

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Valuation of
Bonds –
Calculator
Method:
Example
Let’s look at that same bond with a face
value of $1,000 paying 10% annual
interest over 20 years yielding 10%.
© 2021 MCGRAW HILL

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Valuation of
Bonds – MS
Excel
Method
We can calculate the price of a bond with MS Excel
using one of these functions:
PV(rate,nper,(pmt),(fv),[type],[guess])
Variables in (round brackets):
rate = the rate of interest
nper = the total number of periods
pmt = the value of any payments made
fv = the future value of the lease
Variables in [square brackets] may be left blank:
type = the type of payments made either type 0
(end of period) or type 1 (beginning of period)
guess = if you wish, you can guess the rate
© 2021 MCGRAW HILL

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Valuation of Bonds – MS Excel Method:
Example
Let’s look at that same bond with a face value of $1,000 paying 10%
annual interest over 20 years yielding 10%.
© 2021 MCGRAW HILL
A B C D E
1 rate I/Y 10% “=PV(C1,C2,C3,C4)
2 nper N 20 “=PV(rate,nper,(pmt),(fv),[type])
3 pmt PMT -$100 $1,000.00
4 fv FV -$1,000

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Changing
the Yield to
Maturity
and the
Impact on
Bond
Valuation
Assume inflation premium goes
up from 4 to 6 percent,
everything else constant:
How would this change the price
of our bond?
© 2021 MCGRAW HILL
+ Real rate of return 3%
+ Inflation premium 6
= Risk-free rate 9%
+ Risk premium 3
= Required rate of return 12%

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Valuation of
Bonds –
Alternate
Formula
Method:
Example 2
Let’s assume our required yield is now
12%. Our bond has a face value of $1,000
paying 10% annual interest over 20 years.
We would calculate the price of this bond
using the alternate formula:
Pb = A+
= $100+
= $746.94+ $103.67
= $850.61
© 2021 MCGRAW HILL

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Valuation of Bonds – Calculator Method:
Example 2
Let’s assume our required yield is now 12%. Our bond has a
face value of $1,000 paying 10% annual interest over 20
years.
© 2021 MCGRAW HILL

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Valuation of Bonds – MS Excel Method:
Example 2
Let’s look at that same bond with a face value of $1,000 paying 10%
annual interest over 20 years yielding 10%.
© 2021 MCGRAW HILL
A B C D E
1 rate I/Y 12% “=PV(C1,C2,C3,C4)
2 nper N 20 “=PV(rate,nper,(pmt),(fv),[type])
3 pmt PMT -$100 $850.61
4 fv FV -$1,000

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Relationship
Between
Bond Prices
and Yields
Bond prices are inversely related to
bond yields
 If Yields decrease, the Price of
Bonds increase
 If Yields increase, the Price of
Bonds decrease
Distinguish between the bond
yield and the coupon rate, which
equals coupon/par value.
As interest rates in the economy
change, the price or value of a
bond changes.
© 2021 MCGRAW HILL

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Table 10-1
Bond price
sensitivity to
yield to
maturity
© 2021 MCGRAW HILL
(10% interest payment, 20 years to maturity)
Yield to
Maturity
PV of
Coupons
PV of
Principal Bond Price
2% $1,635.14 + $672.97 = $2,308.11
4% 1,359.03 + 456.39 = 1,815.42
6% 1,146.99 + 311.80 = 1,458.80
7% 1,059.40 + 258.42 = 1,317.82
8% 981.81 + 214.55 = 1,196.36
9% 912.85 + 178.43 = 1,091.29
10% 851.36 + 148.64 = 1,000.00
11% 796.33 + 124.03 = 920.37
12% 746.94 + 103.67 = 850.61
13% 702.48 + 86.78 = 789.26
14% 662.31 + 72.76 = 735.07
16% 592.88 + 51.39 = 644.27
20% 486.96 + 26.08 = 513.04
25% 395.39 + 11.53 = 406.92

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Time to
Maturity
 Time to maturity influences impact
of change in yield to maturity on
valuation
 Longer maturity means greater
impact of changes in yield
 Amount (premium) above par value
reduced as number of years to
maturity decreases
 Amount (discount) below par value
reduced with progressively fewer
years to maturity
 Effect of time to maturity on bond
price sensitivity
© 2021 MCGRAW HILL

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Table 10-2
Bond price
sensitivity to
time to
maturity
changes
Time period in
years (of 10%
coupon bond)
Bond price
with 8% yield
to maturity
Bond price
with 12%
yield to
maturity
0 $1,000.00 $1,000.00
1 1,018.52 982.14
5 1,079.85 927.90
10 1,134.20 887.00
15 1,171.19 863.78
20 1,196.36 850.61
25 1,213.50 843.14
30 1,225.16 838.90
© 2021 MCGRAW HILL

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Figure 10-2 Relationship between time to
maturity and bond price*
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*The relationship in the graph is not symmetrical in nature

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Finance in Action
The Ups and Downs of Bond Prices
© 2021 MCGRAW HILL

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Determining
Yield to
Maturity
from the
Bond Price
Here, we are trying to find the
yield to maturity (Y) that will
equate interest payments (It) and
principal payments (Pn) to price of
bond (Pb)
Easiest methods to find the yield
on a bond are:
 Financial calculator
 Spreadsheet (e.g., MS Excel)
© 2021 MCGRAW HILL

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Determining Yield – Calculator Method:
Example
Let’s look at a bond with a face value of $1,000 paying 11%
annual interest over 15 years. If the price is $932.89, what
is the yield?
© 2021 MCGRAW HILL

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Determining Yield – MS Excel Method:
Example
Let’s look at a bond with a face value of $1,000 paying 11%
annual interest over 15 years. If the price is $932.89, what
is the yield?
© 2021 MCGRAW HILL
A B C D E
1 pv PV -$932.89 “=RATE(15,110,-932.89,1000)
2 nper N 15 “=Rate(nper,(pmt),(pv),(fv),[type])
3 pmt PMT $110 11.98%
4 fv FV $1,000

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Semi-Annual
Interest and
Bond Prices
Most bonds in Canada and the
United States pay interest semi-
annually.
To make the conversion from an
annual to semi-annual analysis,
we follow three steps:
1. Divide the annual interest
(coupon) rate by 2
2. Multiply the number of years
by 2
3. Divide the annual yield to
maturity by 2
© 2021 MCGRAW HILL

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Valuation of Bonds – Calculator Method:
Example 3
Let’s look at a bond with a face value of $1,000
paying 10% semi-annual interest over 20 years
yielding 12%.
© 2021 MCGRAW HILL

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Valuation of
Preferred
Stock
Preferred stock represents
perpetuity, having no maturity
date
Fixed dividend payment carrying
a higher order of precedence
than common stock dividends
No binding contractual obligation
of interest on debt
Does not have:
Ownership privilege of common
stock
Legal provisions that could be
enforced on debt
© 2021 MCGRAW HILL

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Valuation of Preferred Stock
Cash flows from a preferred stock where:
Pp = Price of preferred stock
Dp = Annual dividend for preferred stock (constant)
Kp = Required rate of return (discount rate)
© 2021 MCGRAW HILL

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Valuation of Preferred Stock
Generally, preferred stock is a perpetuity:
Pp = +…+
The Price (Pp) of preferred stock will then use the
formula for the present value of a perpetuity of
constant dividends (Dp) at the discount rate Kp:
Pp =
© 2021 MCGRAW HILL

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Valuation of
Preferred
Stock –
Example
Assuming $10 annual dividend and stockholder
requires 10% rate of return, price of the
preferred stock is:
Pp = = = $100.00
Increased Required Rate of Return
If the required rate of return of investors
increased to 12%, the price would change to:
Pp = = = $833.33
Decreased Required Rate of Return
If the required rate of return of investors
increased to 8%, the price would change to:
Pp = = = $125.00
© 2021 MCGRAW HILL

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Determining
the Required
Rate of
Return (Yield)
from the
Market Price
(Preferred)
Pp = (reverse the position of Pp and Kp)
Kp =
Assuming the annual preferred dividend
(Dp) is $10, and the price of the preferred
stock (Pp) is $100, the required rate of
return (yield) is:
Kp = = = 10%
A higher market price provides quite a
decline in the yield
Kp = = = 7.69%
© 2021 MCGRAW HILL

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Valuation of
Common
Stock
Investors place value on common
shares based on the firm’s ability
to generate cash flow or earnings
Therefore, a share of common
stock can be valued based on the
present value of:
A. Expected stream of future
dividends (dividend valuation
model)
B. Expected future earnings
(price/earnings model)
© 2021 MCGRAW HILL

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Dividend Model
Generally applied (with modifications) to three different
situations:
1. No growth in dividends (valued like preferred
stock)
2. Constant growth in dividends
3. Variable growth in dividends (Appendix 10B)
Yield (Rate of Return) reflects the dividend yield on the stock
and the expected growth rate in the dividend
© 2021 MCGRAW HILL

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Dividend Model – Cash Flows
Generally preferred stock is a perpetuity:
P0 = +…+
Where,
P0 = price of common stock today
D = Dividend for each year;
Ke = Required rate of return for common stock
© 2021 MCGRAW HILL

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Dividend Model – No Growth in Dividend
Common stock pays constant dividend as in preferred stock
No-growth policy does not hold much appeal for investors
P0 =
P0 = Price of common stock today
D1 = Current annual common stock dividend (constant) at end of year
Ke = Required rate of return for common stock
Assuming a dividend of $1.87 and required return of 12%,
P0 = = $15.58
© 2021 MCGRAW HILL

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Dividend Model –
Constant Growth in Dividend
General valuation process:
P0 = + +…+
Where,
P0 = Price of common stock today
D1 = D0(1 + g)1
= Dividend in year 1,
D2 = D0 (1 + g)2
= Dividend in year 2
g = Constant growth rate in dividends
Ke = Required rate of return for common stock (discount rate)
© 2021 MCGRAW HILL

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Dividend
Model –
Constant
Growth in
Dividend
Formula
The formula shown can be modified to a simple
form if:
1. The firm has a constant dividend growth rate (g)
2. The discount rate (Ke) exceeds the growth rate (g)
P0 =
Where
P0 = Price of the stock today
D1 = Dividend at the end of the first year
Ke = Required rate of return (discount rate)
g = Constant growth rate in dividends
Assuming a dividend of $2.00, a required return of
12% and a growth rate of 7%, price of stock is:
P0 = = $40.00
© 2021 MCGRAW HILL

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Determining
the Inputs
for the
Dividend
Valuation
Model
Dividends
 annual reports or investment web sites
The required rate of return, Ke can be estimated
 Using the Capital Asset Pricing Model (CAPM)
(examined in Appendix 11A)
 Or by using the current yield for long-term
Government of Canada bond and a risk
premium based on the level of risk of the
common shares
The growth rate “g”
 best estimated from the historical growth rate
in dividends projected in the future
 “g” can be estimated from the growth in EPS,
revenues per share, or cash flow per share if
one or the other of these items are not
available.
© 2021 MCGRAW HILL

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Common
Stock
Valuation
Model
Based on
Future
Stock Value
To know present value of
investment:
 Assume stock held for three
years then sold
 Adding present value of three
years of dividends and present
value of stock price after three
years gives present value of
benefits
The appropriate formula:
P3 =
© 2021 MCGRAW HILL

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Determining
the Required
Rate of
Return (Yield)
from the
Market Price
(Common)
P0 = (reverse P0 and Ke)
Ke = + g
Assuming the price of the
preferred stock $40, the annual
preferred dividend is $2.00 and
growing at a constant rate of 7%,
the required rate of return is:
Ke = + 7% = 5% + 7% = 12%
© 2021 MCGRAW HILL

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The Price-
Earnings
Ratio
Concept
and
Valuation
The Price-Earnings (P/E) ratio
represents a multiplier applied to
current earnings to determine the
value of a share of stock in the market.
The P/E ratio is influenced by:
 the earnings and sales growth of the
firm
 the risk (or volatility in performance)
 the debt-equity structure of the firm
 the dividend policy
 the quality of management
 other factors
© 2021 MCGRAW HILL

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High vs. Low
P/Es
A stock with a high P/E ratio:
indicates positive expectations for the future of
the company
means the stock is more expensive relative to
earnings
 typically represents a successful and
fast-growing company
 is called a growth stock
A stock with a low P/E ratio:
 indicates negative expectations for the
future of the company
 may suggest that the stock is a better value
or buy
 is called a value stock
© 2021 MCGRAW HILL

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Variable
Growth in
Dividends
 Most common finance
literature assumes common
share valuation with no growth
or constant growth in
dividends
 When the firm experiences
very rapid growth it is called
supernormal growth
 Appendix 10B discusses the
valuation of a supernormal
growth firm
© 2021 MCGRAW HILL

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Summary
and
Conclusions
Valuation of financial assets –
bonds, preferred stock, and
common stock – is determining
the present value of future cash
flows.
The discount rate used in the
valuation process is called the
rate of return or yield to
maturity.
The yield (ROR) is composed of a
real rate of return, an inflation
premium, and a risk premium.
© 2021 MCGRAW HILL

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Summary
and
Conclusions
– Part 2
The price, or current value, of a
bond is equal to the present value
of interest (or coupon) payments
(It) over the life of the bond plus
the present value of the principal
payment (Pn) at maturity.
The discount rate used is the yield
to maturity (Y).
The value of preferred stock is the
present value of an infinite stream
of level dividend payments.
© 2021 MCGRAW HILL

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Summary
and
Conclusions
– Part 3
In general, the value of common
stock is also the present value of
an expected stream of future
dividends. However, there are 3
possible scenarios.
The price-earnings (P/E) ratio is
an easy rule of thumb used to
determine the value of a
common stock.
© 2021 MCGRAW HILL

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Appendix
10B
Variable
Growth in
Dividends
When the firm experiences very
rapid growth it is called
supernormal growth.
Dividends from supernormal
growth firm is represented
graphically as:
© 2021 MCGRAW HILL

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Appendix 10B
Stock
valuation of a
supernormal
growth firm
Let’s assume that the firm paid a
dividend over the last 12
months of $1.67; this
represents the current dividend
rate
Dividends are expected to grow
by 20% over the supernormal
growth period (n) of 3 years
Dividends will then grow at a
normal constant rage (g) of 5%
The required rate of return (Ke) =
9%
© 2021 MCGRAW HILL

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Appendix 10B
Stock
valuation of a
supernormal
growth firm –
Part 2
Step #1: Present Value of Supernormal
Dividends
D0 = $1.67
D1 = D0 = $1.67= $2.00
D2 = D0 = $2.00= $2.40
D3 = D0 = $2.40= $2.88
We then discount these values back at 9% to
calculate the present value during the
supernormal growth period.
© 2021 MCGRAW HILL
Supernormal
Dividends
Present Value of Dividends during
Supernormal Period (Ke = 9%)
D1 $2.00 $1.83
D2 2.40 2.02
D3 2.88 2.22
$6.07

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Appendix 10B
Stock
valuation of a
supernormal
growth firm –
Part 3
Step #2: Present Value of Future Stock Price
We first find the future stock price at the end
of the supernormal growth period (P3):
P3 =
We can calculate the value for D4:
D4 = D3 = $2.88 = $3.02
Using the dividend model, we calculate the
value of the stock at the end of the 3rd
period:
P3 = = = = $75.50
Present value of future price P3:
PV = = $58.30
© 2021 MCGRAW HILL

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