Ryerson University Chapter 7 Fundamentals of Corporate Finance Test Answers Toronto Time July.22 12p.mAround 50 questions Fundamentals of Corporate Finance

Ryerson University Chapter 7 Fundamentals of Corporate Finance Test Answers Toronto Time July.22 12p.mAround 50 questions Fundamentals of Corporate Finance test for FrankRose23 Fundamentals of Corporate Finance
Third Canadian Edition
Chapter 7
Valuing Stocks
Part 1
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7-1
Equities
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7-3
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7-4
Chapter Outline
7.1 Stock Basics
7.2 The Dividend-Discount Model
7.3 Estimating Dividends in the DividendDiscount Model
7.4 Limitations of the Dividend-Discount Model
7.5 Share Repurchases and the Total Payout
Model
(Continued)
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7-5
Chapter Outline
7.6 The Discounted Free Cash Flow Model
7.7 Valuation Based on Comparable Firms
7.8 Information, Competition, and Stock Prices
7.9 Individual Biases and Trading
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7-6
Learning Objectives
• Describe the basics of common stock, preferred
stock, and stock quotes
• Value a stock as the present value of its
expected future dividends
• Understand the tradeoff between dividends and growth
in stock valuation
• Appreciate the limitations of valuing a stock based on
expected dividends
• Value a stock as the present value of the company’s
total payout or its free cash flows
(Continued)
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7-7
Learning Objectives
• Value a stock by applying common multiples
based on the values of comparable firms
• Understand how information is incorporated
into stock prices through competition in
efficient markets
• Describe some of the behavioural biases that influence
the way individual investors trade
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7-8
7.1 Stock Basics
• Stock Market Reporting: Stock Quotes
?
Common Stock: A share of ownership in the
corporation, which confers rights to any common
dividends as well as rights to vote on election of
directors, mergers, or other major events.
?
Ticker Symbol: A unique abbreviation assigned to
each publicly traded company.
(Continued)
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7-9
• Rogers Communications Inc. Class B
• TSE: RCI.B or RCI.B.TO
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7 – 10
How do we value Equities?
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How do we value Equities?
• Let’s go back to last chapter
• Bonds and Debentures
• Bonds represent debt obligations – and
therefore are a form of borrowing.
• How did we value Bonds?
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How do we value Equities?
• How did we value Bonds?
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How do we value Equities?
• How did we value Bonds?
• Cash flows!
• Coupons and par value received at maturity
• Or Coupons and price received on sale.
• How did we value Bonds – CASH FLOWS
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How do we value Equities?
• How do we value Equities?
• Cash flows!
• Dividends.
• Cash when we sell the stock
• How do we value Equities – CASH FLOWS
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7.1 Stock Basics
• Common Stock
?
Shareholder Voting
• Straight Voting
• Cumulative Voting
• Classes of Stock
?
Shareholder Rights
• Annual Meeting
• Proxy
?
Proxy Contest
(Continued)
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Key terms and definitions
• Straight voting: Voting for directors during
which shareholders must vote for each director
separately, with each shareholder having as
many votes as shares held.
• Cumulative voting: Voting for directors during
which each shareholder is allocated votes equal
to the number of open spots multiplied by his or
her number of shares.
(Continued)
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Key terms and definitions
• Annual meeting: Meeting held once per year at
which shareholders vote on directors and other
proposals, as well as ask managers questions.
• Proxy: A written authorization for someone else
to vote your shares.
• Proxy contest: A contest between two or more
groups competing to collect proxies to prevail in
the matter up for shareholder vote (such as
election of directors).
(Continued)
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Key terms and definitions
• Preferred stock: Stock with preference over
common shares in payment of dividends and in
liquidation.
• Cumulative preferred stock: Preferred stock for
which all missed preferred dividends must be paid
before any common dividends may be paid.
• Non-cumulative preferred stock: Preferred stock
for which missed preferred dividends do not
accumulate. Only the current dividend is owed
before common dividends may be paid.
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7.1 Stock Basics
• Preferred Stock
?
Cumulative versus Non-Cumulative Preferred Stock
?
Preferred Stock: Equity or Debt
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7.2 The Dividend-Discount Model
• A One-Year Investor
?
Two potential sources of cash flows from owning a
stock:
• Dividends
• Selling Shares
(Continued)
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7.2 The Dividend-Discount Model
•
Equity cost of capital is what the market demands for a
return given the risk involved.
(similar to the discount rate for bonds)
(Continued)
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7.2 The Dividend-Discount Model
• Dividend Yields, Capital Gains, and Total
Returns
?
Dividend Yield: The expected annual dividend of a
stock divided by its current price; the percentage
return an investor expects to earn from the dividend
paid by the stock.
?
Capital Gain: The amount by which the selling
price of an asset exceeds its initial purchase price.
• Capital Gains Rate :An expression of capital gain as a
percentage of the initial price of the asset.
(Continued)
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7.2 The Dividend-Discount Model
• Dividend Yields, Capital Gains, and Total
Returns
?
Total Return : The sum of a stock’s dividend yield
and its capital gain rate.
(Continued)
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7.2 The Dividend-Discount Model
• Dividend Yields, Capital Gains, and Total
Returns
?
The expected total return of the stock should equal
the expected return of other investments available in
the market with equivalent risk.
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Example 7.1 Stock Prices and Returns
Suppose you expect Loblaw Companies Ltd to
pay an annual dividend of $0.56 per share in the
coming year and to trade $45.50 per share at the
end of the year.
If investments with equivalent risk to Loblaw’s
stock have an expected return of 6.80%, what is
the most you would pay today for Loblaw’s stock?
What dividend yield and capital gain rate would
you expect at this price?
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Example 7.1 Stock Prices and
Returns: Plan
• To solve for the beginning price we would pay
now (P0) given our expectations about dividends
(Div1=$0.56) and future price (P1=$45.50) and
the return we need to expect to earn to be
willing to invest (rE=6.8%).
• We can then calculate the dividend yield and
capital gain rate
Div1 + P1
P0 =
1 + rE
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Example 7.1 Stock Prices and
Returns: Execute
Div1 + P1 $0.56 + $45.50
P0 =
=
= $43.13
1 + rE
1.0680
• We see that at this price, Loblaw’s 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%.
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Example 7.1 Stock Prices and
Returns: Evaluate
At a price of $43.13, Loblaw’s expected total
return is 1.30% + 5.50% = 6.80%, which is equal
to its equity cost of capital (the return being paid
by investments with equivalent risk to Loblaw’s).
This amount is the most we would be willing to
pay for Loblaw’s stock.
If we paid more, our expected return would be less
than 6.8% and we would rather invest elsewhere.
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Example 7.1 Stock Prices and Returns
Suppose you expect Richie Brothers Auctions
(RBA.TO) of $1.06 per share in the coming year
and to trade $56.00 per share at the end of the
year.
If investments with equivalent risk to RBA stock
have an expected return of 7.50%, what is the
most you would pay today for RBA’s stock?
What dividend yield and capital gain rate would
you expect at this price?
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7 – 30
Example 7.1 Stock Prices and
Returns: Plan
• To solve for the beginning price we would pay
now (P0) given our expectations about dividends
(Div1=$1.06) and future price (P1=$56.00) and
the return we need to expect to earn to be
willing to invest (rE=7.5%).
• We can then calculate the dividend yield and
capital gain rate
Div1 + P1
P0 =
1 + rE
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Example 7.1 Stock Prices and
Returns: Execute
Po = Div1 +P1 = 1.06+56.00 = 57.06 = 53.08
1+ re
1.075
1.075
• We see that at this price, RBA’s dividend yield
is Div1/P0 = 1.06/53.08 = 2.00%.
• The expected capital gain is
• $56.00 – $53.08 = $2.92 per share, for a capital
gain rate of 2.92/53.08 = 5.50%.
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Example 7.1 Stock Prices and
Returns: Evaluate
At a price of $53.08, RBA’s expected total return
is 2.00% + 5.50% = 7.50%, which is equal to its
equity cost of capital (the return being paid by
investments with equivalent risk to RBA’s).
This amount is the most we would be willing to
pay for RBA’s stock.
If we paid less, our expected return would be more
than 7.5% and we would invest.
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7.2 The Dividend-Discount Model
• A Multi-Year Investor
?
Suppose we planned to hold the stock for two years
• Then we would receive dividends in both year 1 and year
2 before selling the stock, as shown in the following
timeline:
(Continued)
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7.2 The Dividend-Discount Model
• A Multi-Year Investor
?
As a two-year investor, we care about the dividend
and stock price in year 2.
Div1 Div2 + P2
P0 =
+
2
1 + rE
(1 + rE )
(Continued)
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7.2 The Dividend-Discount Model
• Dividend-Discount Model Equation
Div1
Div2
P0 =
+
+
2
1 + rE (1 + rE )
?
+
Divn
(1 + rE )
n
+
Pn
(1 + rE )
n
The price of the stock is equal to the present value
of all of the expected future dividends (cash flows) it
will pay, along with the cash flow from the sale in
year N.
(Continued)
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7.2 The Dividend-Discount Model
• Dividend-Discount Model Equation
?
The price of a stock is equal to the present value of
all of the expected future dividends it will pay.
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7.3 Estimating Dividends in the
Dividend-Discount Model
• Constant Dividend Growth Model: A model
for valuing a stock by viewing its dividends as a
constant growth perpetuity.
?
Assumes that dividends will grow at a constant rate,
g, forever
?
The value of the firm depends on the dividend level
of next year, divided by the equity cost of capital
adjusted by the growth rate
Div1
P0 =
rE ? g
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Example 7.2 Valuing a Firm with
Constant Dividend Growth: Problem
Hydro One is a regulated utility company that
services Ontario.
Suppose Hydro plans to pay $2.30 per share in
dividends in the coming year.
If its equity cost of capital is 7% and dividends are
expected to grow by 2% per year in the future,
estimate the value of Hydro’s stock.
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7 – 39
Example 7.2 Valuing a Firm with
Constant Dividend Growth: Plan
The dividends are expected to grow perpetually at
a constant rate.
The next dividend (Div1) is expected to be $2.30,
the growth rate (g) is 2% and the equity cost of
capital (rE) is 7%.
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Example 7.2 Valuing a Firm with
Constant Dividend Growth: Execute
The price would be:
Div1
$2.30
P0 =
=
= $46.00
rE ? g 0.07 ? 0.02
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Example 7.2 Valuing a Firm with
Constant Dividend Growth: Evaluate
You would be willing to pay 20 times this year’s
dividend of $2.30 to own Hydro One stock
because you are buying claim to this year’s
dividend and to an infinite growing series of
future dividends.
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7 – 42
7.3 Estimating Dividends in the
Dividend-Discount Model
• Changing Growth Rates
?
If the firm is expected to grow at a long-term rate g
after year n + 1, then from the constant dividend
growth model:
Divn +1
Pn =
rE ? g
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Practice Questions 13 and 14 (3rd)
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7.3 Estimating Dividends in the
Dividend-Discount Model
• Changing Growth Rates
• Weakness?
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Example 7.5 Valuing a Firm with Two
Different Growth Rates
Small Fry, Inc. has just invented a potato chip that
looks and tastes like a french fry.
Given the phenomenal market response to this
product, Small Fry is reinvesting all of its earnings
to expand its operations.
Earnings were $2 per share this past year and are
expected to grow at a rate of 20% per year until
the end of year four. At that point, other
companies are likely to bring out competing
products.
(Continued)
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7 – 48
Example 7.5 Valuing a Firm with Two
Different Growth Rates
Analysts project that at the end of year four, Small
Fry will cut its investment and begin paying 60%
of its earnings as dividends.
Its growth will also slow to a long-run rate of 4%.
If Small Fry’s equity cost of capital is 8%, what is
the value of a share today?
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7 – 49
Example 7.5 Valuing a Firm with Two
Different Growth Rates: Plan
We can use Small Fry’s projected earnings growth
rate and payout rate to forecast its future earnings
and dividends.
After year four, Small Fry’s dividends will grow
at a constant 4%, so we can use the constant
dividend growth model (Equation 7.13) to value
all dividends after that point.
Finally, we can pull everything together with the
dividend-discount model.
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Example 7.5 Valuing a Firm with Two
Different Growth Rates: Execute
The following spreadsheet projects Small Fry’s
earnings and dividends:
1
Year
2
Earnings
3
EPS Growth Rate
(versus prior year)
4
EPS
5
Dividends
6
7
0
1
2
3
4
5
6
20%
20%
20%
20%
4%
4%
$2.40
$2.88
$3.46
$4.15
$4.31
$4.49
Dividend Payout Rate
0%
0%
0%
60%
60%
60%
Div
$—
$—
$—
$2.49
$2.59
$2.69
$2.00
(Continued)
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Example 7.5 Valuing a Firm with Two
Different Growth Rates: Execute
• Starting from $2.00 in year zero, EPS grows by
20% per year until year four, after which growth
slows to 4%.
• Small Fry’s dividend payout rate is zero
until year four, when competition reduces its
investment opportunities and its payout rate rises
to 60%.
• Multiplying EPS by the dividend payout ratio, we
project Small Fry’s future dividends in line 4.
(Continued)
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Example 7.5 Valuing a Firm with Two
Different Growth Rates: Execute
• After year four, Small Fry’s dividends will grow
at the expected long-run rate of 4% per year.
• Thus, we can use the year four dividend as the
first dividend in a constant dividend growth
model (g = 4%) to project Small Fry’s share
price at the end of year three. Given its equity
cost of capital of 8%,
Div4
$2.49
P3 =
=
= $62.25
rE ? g 0.08 ? 0.04
(Continued)
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Example 7.5 Valuing a Firm with Two
Different Growth Rates: Execute
We then apply the dividend-discount model with
this terminal value:
Div3
P3
Div1
Div2
$62.25
P0 =
+
+
+
=
= $49.42
2
3
3
3
1 + rE (1 + rE )
(1 + rE ) (1 + rE ) (1.08)
N=3, I/Y = 8, FV = 62.25, PMT = 0, CPT PV = $49.42
(Continued)
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7 – 54
Example 7.5 Valuing a Firm with Two
Different Growth Rates: Evaluate
• The dividend-discount model is flexible enough
to handle any forecasted pattern of dividends.
• Here the dividends were zero for three years and
then settled into a constant growth rate, allowing
us to use the constant growth rate model as a
shortcut.
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7 – 55
7.3 Estimating Dividends in the
Dividend-Discount Model
• Value Drivers and the Dividend-Discount
Model
?
The dividend-discount model includes an implicit
forecast of the firm’s profitability which is
discounted back at the firm’s equity cost of capital.
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7.4 Limitations of the
Dividend-Discount Model
• Uncertain Dividend Forecasts
?
The dividend-discount model values a stock based
on a forecast of the future dividends, but a firm’s
future dividends carry a tremendous amount of
uncertainty.
(Continued)
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7.4 Limitations of the
Dividend-Discount Model
• Non-Dividend-Paying Stocks
?
Many companies do not pay dividends; thus, the
dividend-discount model must be modified.
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7.3 Estimating Dividends in the
Dividend-Discount Model
• Dividends Versus Investment and Growth
?
A Simple Model of Growth
• The dividend each year is equal to the firm’s
earnings per share (EPS) multiplied by its
dividend payout rate (fraction of a firm’s
earnings that the firm pays out as dividends
each year).
(Continued)
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7 – 59
7.3 Estimating Dividends in the
Dividend-Discount Model
•
(Continued)
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7.3 Estimating Dividends in the
Dividend-Discount Model
• Out of $10.00 in EPS $6.00 is paid out as
dividends.
• The balance, $4.00 added to Retained Earnings
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7.3 Estimating Dividends in the
Dividend-Discount Model
• Dividends Versus Investment and Growth
?
A Simple Model of Growth
• The firm can increase its dividend in three ways:
?
It can increase its earnings
?
It can increase its dividend payout rate
?
It can decrease its number of shares
outstanding
(Continued)
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7 – 62
7.3 Estimating Dividends in the
Dividend-Discount Model
• Dividends Versus Investment and Growth
?
A Simple Model of Growth
• If all increases in future earnings result
exclusively from new investment made with
retained earnings, then:
Change in Earnings = New Investment ? Return on New Investment
(Continued)
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7.3 Estimating Dividends in the
Dividend-Discount Model
• Dividends Versus Investment and Growth
?
A Simple Model of Growth
• New investment equals the firm’s earnings multiplied by
its retention rate (fraction of current earnings that the
firm retains):
New Investment = Earnings ? Retention Rate
(Continued)
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7 – 64
7.3 Estimating Dividends in the
Dividend-Discount Model
• Dividends Versus Investment and Growth
?
A Simple Model of Growth
• The growth rate of earnings:
Change in Earnings
Earnings
= Retention Rate ? Return on New Investment
Earnings Growth Rate =
In our example, if the retained earnings generate a
10% return;
.40 X .10 = .04 or 4%
(Continued)
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7 – 65
7.3 Estimating Dividends in the
Dividend-Discount Model
• Dividends Versus Investment and Growth
?
A Simple Model of Growth
• If the firm chooses to keep its dividend payout
rate constant, then the growth in its dividends will
equal the growth in its earnings:
g = Retention Rate ? Return on New Investment
In our ex…
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