BU283: Financial Management I
Taught by:
Matthew Civello
Hrishi Lariya
cive1970@mylaurier.c
lari5080@mylaurier.ca
a
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Agenda
1. Chapter 07 - Interest and Bonds
1. Chapter 05 - Risk and Return
1. Chapter 06 - Portfolio Theory
1. Chapter 08 - Stock Valuation and Market Efficiency
Bond Qs - Key Points
●
Bond yields and bond prices are inversely
related
○
●
Yield is the return received by an investor. Cheap bonds
mean better returns (higher yields)
Longer term bonds have higher yields
○
○
Long term → more risk → higher yields
When longer term bonds don’t have higher yields, the yield
curve is “inverted”
Bond Qs - Key Points
●
Real vs Nominal interest rates
○
○
●
Prices of longer term bonds are more sensitive to changes in yield
○
●
Real interest rate: interest rate if inflation was nonexistent
Nominal interest rate: interest rate adjusted for inflation
Longer term bonds → more interest rate risk
Bond returns come from 2 sources (bondholder perspective)
○
○
Capital gains/losses (comes from changes in the bond price)
Interest (coupons + interest on reinvested coupons)
Coupon Bond Question
Springfield Nuclear Energy Inc. bonds are currently trading at $903.55. The
bonds have a face value of $1,000, a coupon rate of 8.5% with coupons paid
annually, and they mature in 15 years. What is the yield to maturity of the
bonds?
Coupon Bond Question
Consider an annual coupon bond with a face value of $100, 14 years to
maturity, and a price of $92. The coupon rate on the bond is 6%. If you can
reinvest coupons at a rate of 2.5% per annum, then how much money do you
have if you hold the bond to maturity?
Coupon Bond Question
Iron Maiden became the first heavy-metal band to sell bonds when it
arranged a $30 million deal in February 1999. The collateral on the bonds
(and source of cash flow for interest and principal payments) consisted of
future royalties from the band's albums like "The Number of the Beast."
Each bond in the issue had a face value of $1,000, a term of 11 years and
paid semiannual coupons at the rate of 8.5%. The yield to maturity on the
bond was 7.5%. At what price did each of the bonds sell?
Chapter 05
Introduction to Risk and Return
The Risk-Return Relationship
Investors study the characteristics of assets to determine the likelihood of its actual cash flows meeting
projections.
The uncertainty regarding the assets cash flows constitutes risk.
Once perceived riskiness is established, the market
will determine a sufficient expected return to induce
investors to purchase the asset.
Risk is determined by:
1. Determined by the uncertainty of future cash flows
2. Uncertainty is the result of factors peculiar to each asset
Return on a Single Asset
Return on an asset comes from two sources:
1. Capital Gain
2. Dividend Yield
Holding Period Return (HPR) - The percentage return on an asset for the period that you have held/are
holding for.
-
The holding period return on an asset is the sum of its capital gain and dividend yield
HPRi = (Ending Price - Beginning Price + Dividends) / (Beginning Price)
HPRi = [(Ending Price - Beginning Price)/Beginning Price] + (Dividend / Beginning Price)
Return on a Single Asset
Return on an asset comes from two sources:
1. Capital Gain
2. Dividend Yield
Holding Period Return (HPR) - The percentage return on an asset for the period that you have held/are
holding for.
-
The holding period return on an asset is the sum of its capital gain and dividend yield
HPRi = (Ending Price - Beginning Price + Dividends) / (Beginning Price)
HPRi = [(Ending Price - Beginning Price)/Beginning Price] + (Dividend / Beginning Price)
Capital Gain
Dividend Yield
Example: Return on a Single Asset
(Pearson Revel: Practice Section 5.2, Question 1)
Suppose that you purchased 2,000 shares of Pan Am Airlines at the beginning of the year for $15.32. By
the end of the year, the stock price had appreciated to $18.57. At the end of the year, Pan Am paid a
dividend of $0.87 per share. Calculate the return on your investment over the year.
Example: Return on a Single Asset
(Pearson Revel: Practice Section 5.2, Question 1)
Suppose that you purchased 2,000 shares of Pan Am Airlines at the beginning of the year for $15.32. By
the end of the year, the stock price had appreciated to $18.57. At the end of the year, Pan Am paid a
dividend of $0.87 per share. Calculate the return on your investment over the year.
HPRi = [(Ending Price - Beginning Price) / Beginning Price] + (Dividends / Beginning Price)
HPRi = [(18.57 - 15.32) / 15.32] + (0.87 / 15.32)
HPRi = 0.21 + 0.06 = 27%
Simple Average vs. Compound Average
Arithmetic (Simple) Average Return - The return calculated where compounding is ignored
Average Return = 1/n (∑ ki)
Geometric (Compound) Average Return - The return calculated that recognizes interest or earnings
paid on accumulated interest or earnings
Geometric Return = (Ending Value / Beginning Value) (1 / n) - 1
Example: Average vs. Geometric Return
Consider the following price and return information.
Year
Price
1
$10
2
$20
100%
3
$10
- 50%
(i) Calculate the arithmetic return
(ii) Calculate the geometric return
Return
Example: Average vs. Geometric Return
Consider the following price and return information.
(i)
Year
Price
Return
1
$10
2
$20
100%
3
$10
- 50%
Calculate the arithmetic return
k = (100% + (-50%)) / 2
k = 25%
(ii) Calculate the geometric return
k = ($10 / $10) (1/3) - 1
k = 0%
The compound return is the annual return that would have made $10
grow into $10 over two years with compounding.
If you invested $10 and it became $10 in two years, that is a 0% return
This shows why geometric return is a better measure of investment
return.
Expected Return
Expected Return (E(k)) - The return that is expected to be earned each period on a given asset in the
future.
Note: Expected return is the weighted average of all possible future returns on an asset
E(k) = Pr1(ki) + Pr2(k2) + … + Prn(kn)
Where:
ki = ith state of nature
Pri= Probability of the ith occurrence
n = Number of possible outcomes
Example: Expected Return
(Pearson Revel: Practice Section 5.2, Question 4)
What is the expected return for a security if​ there's a 39% probability of returning 8% and a 61%
probability of returning 22%​?
E(k) = Pr1(ki) + Pr2(k2) + … + Prn(kn)
E(k) = (0.39 * 0.08) + (0.61 * 0.22)
E(k) = 0.1654 = 16.54%
Risk of a Single Asset
Standard Deviation of returns on an asset measures the risk of that asset. Greater deviations from the
mean is a greater standard deviation. Therefore, a higher standard deviation indicates higher risk.
Standard Deviation (𝞼) = [∑(ki - E(k))2 x Pri]1/2
Where:
E(k) = Expected return
ki = Return of the ith outcome
Pri = Probability of the ith occurrence
n = Number of outcome evaluated
Note: You should do this in your calculator. Excel does not account for differing probabilities across
states of nature and so will give you an incorrect answer when these probabilities do in fact differ.
Risk of a Single Asset
Standard Deviation of returns on an asset measures the risk of that asset. Greater deviations from the
mean is a greater standard deviation. Therefore, a higher standard deviation indicates higher risk.
Steps:
1.
2.
3.
4.
5.
Compute the expected return
Subtract each return from expected value
Square each deviation to eliminate negative signs
Multiply each squared deviation by states of nature and sum
Compute the square root
Note: You should do this in your calculator. Excel does not account for differing probabilities across
states of nature and so will give you an incorrect answer when these probabilities do in fact differ.
Example: Risk of a Single Asset
(Pearson Revel: Practice Section 5.3, Question 1)
You believe that next year there is a 25% probability of a recession and 75% probability that the
economy will be normal. If your stock will yield -12% in a recession and 20% in a normal year, what is
the standard deviation of the stock?
Example: Risk of a Single Asset
(Pearson Revel: Practice Section 5.3, Question 1)
You believe that next year there is a 25% probability of a recession and 75% probability that the
economy will be normal. If your stock will yield -12% in a recession and 20% in a normal year, what is
the standard deviation of the stock?
E(k) = (0.25 * -0.12) + (0.75 * 0.20)
E(k) = 0.12
Standard Deviation (𝞼) = [∑(ki - E(k))2 x Pri]½
Standard Deviation (𝞼) = [(-0.12 - 0.12)2 * 0.25 + (0.20 - 0.12)2 * 0.75)]½
Standard Deviation (𝞼) = 0.1386 = 13.86%
Example: Risk of a Single Asset
It costs $1,000 to play the following game. If it rains tomorrow, you win $1,100, which is a 10% rate of
return. If it does not rain tomorrow, you win $900, which is a -10% rate of return. Assume that there is a
50% chance of rain. What is the variance of the returns?
Example: Risk of a Single Asset
It costs $1,000 to play the following game. If it rains tomorrow, you win $1,100, which is a 10% rate of
return. If it does not rain tomorrow, you win $900, which is a -10% rate of return. Assume that there is a
50% chance of rain. What is the variance of the returns?
Standard deviation is the square root of the variance. So, variance is the standard deviation squared.
E(k) = (0.50 * 0.10) + (0.50 * -0.10)
E(k) = 0%
Variance (𝞼2) = ∑(ki - E(k))2 x Pri
Variance (𝞼2) = [(0.10 - 0)2 * 0.50] + [(-0.10 - 0)2 * 0.50]
Variance (𝞼2) = 0.01
Expected Return of a Portfolio
The expected return for a portfolio is the weighted average of the expected returns of each individual
security within that portfolio, where weights are the weight of the security within the portfolio.
Portfolio Weight (Wi) = Amount invested in i / Total amount invested
Expected Return (E(kp)) = w1E(k1) + … + wnE(kn)
Where:
w1 = Portfolio weight of asset i
E(ki) = Expected return of asset i
Example: Expected Return on a Portfolio
Your portfolio has an expected return of 13.25​%. The portfolio includes two stocks. The first stock has a
weight of 0.65 and the second has a weight of 0.35. If the expected return on the first stock is 15​%, then
what is the expected return on the second stock in percentage​ terms?
Example: Expected Return on a Portfolio
Your portfolio has an expected return of 13.25​%. The portfolio includes two stocks. The first stock has a
weight of 0.65 and the second has a weight of 0.35. If the expected return on the first stock is 15​%, then
what is the expected return on the second stock in percentage​ terms?
E(kp) = w1E(k1) + w2E(k2)
0.1325 = (0.65 * 0.15) + (0.35 * X)
0.1325 - 0.0975 = 0.35X
0.035 = 0.35X
X = 0.10 = 10%
Risk of a Portfolio
The risk of a portfolio of assets cannot be calculated with a weighted average of each asset’s
standard deviation.
Why? If asset A and asset B both have a standard deviation of 1, any combination of these assets two
assets would yield a weighted average standard deviation of 1. But...
Risk of a Portfolio
The risk of a portfolio of assets cannot be calculated with a weighted average of each asset’s
standard deviation.
Why? If asset A and asset B both have a standard deviation of 1, any combination of these assets two
assets would yield a weighted average standard deviation of 1.
The standard deviation of this portfolio is 0, not 1:
Both assets have a standard deviation of 1, the returns exactly offset each other (perfect negative correlation).
Risk of a Portfolio
The risk of a portfolio is driven by the correlation of the assets within it:
Correlation - A predictable relationship between observations in which the movement over time of one
item is related (correlated) to the movement of of another.
The degree of correlation (r) can vary from -1 (perfect negative) to 1 (perfect positive)
Positive Correlation - Correlated movement in the same direction
Negative Correlation - Correlated movement in the opposite direction
Correlation between assets is a tool for investors to limit the risk within their portfolio. By combining
multiple risky assets, we can create a portfolio with less risk than each of the assets within it. This is
called diversification.
Note: Diversification can reduce risk, but never completely eliminate it.
Let’s take a break.
See you in 15 minutes!
Chapter 06
Portfolio Theory
Risk of a Portfolio Cont...
The risk of a portfolio of assets is found by computing its standard deviation, which is driven by the
individual variances and correlation between the assets.
Where:
wi = Weight of asset i
𝝈2 = Variance of asset i
𝝈 = Standard deviation of asset i
Many-asset portfolio risk is driven by the average covariance of the assets.
Example: Risk of a Portfolio
Consider the data provided in the table for portfolio of assets A and B. The portfolio weights and
variances are given in the table. The variances are expressed in decimal form. For example, if standard
deviation is 50% then the variance is 0.502 = 0.25. The correlation of returns of the two assets is 0.39.
What is the standard deviation of the portfolio?
Asset A
Asset B
Portfolio Weight
0.53
0.47
Variances
0.1369
0.4096
Standard Deviation
0.37
0.64
Example: Risk of a Portfolio
Consider the data provided in the table for portfolio of assets A and B. The portfolio weights and
variances are given in the table. The variances are expressed in decimal form. For example, if standard
deviation is 50% then the variance is 0.502 = 0.25. The correlation of returns of the two assets is 0.39.
What is the standard deviation of the portfolio?
Asset A
Asset B
𝝈 = [(0.532*0.372 + 0.472*0.642.+ 2*0.53*0.47*0.39*0.37*0.64]2
Portfolio Weight
0.53
0.47
𝝈 = 0.4535
Variances
0.1369
0.4096
Standard Deviation
0.37
0.64
Types of Risk
Risk can be divided into two types:
1. Diversifiable Risk (Unsystematic) - Risk that can be eliminated through diversification
-
Affects one or few assets
For example, loss of a major customer, death of a CEO
1. Non-Diversifiable Risk (Systematic) - Risk that cannot be eliminated through diversification
-
Affects all assets to some extent
For example, war, sudden change in monetary policy
Total Risk = Non-diversifiable risk + Diversifiable risk
Example: Types of Risk
Categorize each of the following as systematic or unsystematic risk:
1. ABC Corporation is being investigated by the SEC for fraudulent behaviour
1. Samsung is forced to recall the Galaxy Note because of a flammable battery
1. The economy faces a major downturn
1. XYZ Corporation’s biggest competitor successfully launches a new product line
1. There is a significant hike in the corporate tax rate
Example: Types of Risk
Categorize each of the following as systematic or unsystematic risk:
1. ABC Corporation is being investigated by the SEC for fraudulent behaviour (Unsystematic)
1. Samsung is forced to recall the Galaxy Note because of a flammable battery (Unsystematic)
1. The economy faces a major downturn (Systematic)
1. XYZ Corporation’s biggest competitor successfully launches a new product line (Unsystematic)
1. There is a significant hike in the corporate tax rate (Systematic)
The Efficient Set
Efficient Set (Markowitz) - The set of all efficient portfolios across all standard deviations. This is a
collection of portfolios with the highest possible return at each level of standard deviation.
New Efficient Set (Sharpe) - The set of all portfolios formed by combining the risk free asset and the
market portfolio.
-
According to Sharpe’s model, all investors optimally hold the same assets in the same proportion
Risk Free Asset - An asset with no variation in its return, and no risk of default.
1. Standard deviation of returns is zero
2. The correlation of returns with any other asset is 0
Market Portfolio - The portfolio that includes every capital asset held in proportion to its market value
relative to market value of all assets in total
The market portfolio is very large and diversified, it thus has no unsystematic risk.
Example: Value-Weighted Portfolio
Value-Weighted Portfolio - A portfolio in which the weights of each asset are equal to the value of
each asset relative to the total value of all assets in the portfolio
kp = w1k1 + … wiki
Asset
# Shares
Price
Value
Weight
Stock A
5 Shares
$100
$500
500/600 = 83.33%
Stock B
5 Shares
$20
$100
100/600 = 16.67%
Note: The weight is not based on shares held, it is based on value.
The market portfolio is value-weighted → The weights are the relative values of each asset in the
portfolio
Example: Value-Weighted Portfolio
A value-weighted index is made of shares in two companies. On Day 1 you build a portfolio to mimic
the index with 15% invested in Company 1 and 85% invested in Company 2. On Day 2, what trades do
you need to make to adjust your portfolio weights so that your portfolio earns the same return as the
index from Day 2 to Day 3?
Company 1
Company 1
Company 2
Company 2
Day
Price
Shares
Outstanding
Price
Shares
Outstanding
1
6.62
400
10.00
1,500
2
7.53
400
10.54
1,500
3
8.82
400
11.07
1,500
Example: Value-Weighted Portfolio
A value-weighted index is made of shares in two companies. On Day 1 you build a portfolio to mimic
the index with 15% invested in Company 1 and 85% invested in Company 2. On Day 2, what trades do
you need to make to adjust your portfolio weights so that your portfolio earns the same return as the
index from Day 2 to Day 3?
Day
Company 1
Company 1
Company 2
Company 2
Price
Shares
Outstanding
Price
Shares
Outstanding
1
6.62
400
10.00
1,500
2
7.53
400
10.54
1,500
3
8.82
400
11.07
1,500
You do not need to make any trades.
Because your portfolio mimics the
index on day 1, the weights will
change in the same proportion as the
value of the shares change.
Example: Value-Weighted Portfolio
A value-weighted index is made of shares in the two companies. In order for your portfolio to earn the same
return as the index from Day 2 to Day 3, what portfolio weight do you need for Company 1 on Day 2?
Company 1
Company 1
Company 2
Company 2
Day
Price
Shares
Outstanding
Price
Shares
Outstanding
1
6.62
400
10.00
1,500
2
7.53
400
10.54
1,500
3
8.82
400
11.07
1,500
Example: Value-Weighted Portfolio
A value-weighted index is made of shares in the two companies. In order for your portfolio to earn the same
return as the index from Day 2 to Day 3, what portfolio weights do you need on Day 2?
Day
Company 1
Company 1
Company 2
Company 2
Price
Shares
Outstanding
Price
Shares
Outstanding
1
6.62
400
10.00
1,500
2
7.53
400
10.54
1,500
3
8.82
400
11.07
1,500
To mimic the index, your weights must be the
same as the index:
Total Value = 7.53*400 + 10.54*1500
Total Value = $18,822
C1 Weight = (7.53*400) / 18882
C1 Weight = 16%
C2 Weight = (10.54*1500) / 18822
C2 Weight = 84%
Stock Market Indices
Sharpe’s Market Portfolio would be impossible to mimic for most people because it composed of
thousands of assets.
This problem is avoided using a proxy for the market portfolio:
Stock Market Index - A statistical indicator showing the relative value of a basket of stocks compared
to the value in a base year
-
Example: Standard & Poor's 500 (S&P500), NASDAQ
Exchange Traded Fund (ETF) - A basket of securities that mimics the composition of a target index
seeking to achieve the same return as that target index.
Systematic Risk and Beta
Recall: The market portfolio does not contain unsystematic risk. Therefore, investors who hold the
market portfolio are only concerned with systematic risk.
Beta measures:
1. The amount of systematic risk in an individual asset
2. The marginal risk that an individual asset adds to the market portfolio
Where:
COV(ki,kM) = Covariance of returns between asset i and the market portfolio
𝝈2M = Variance of the market portfolio
Intuition Behind Beta
Recall: The market portfolio does not contain unsystematic risk. Therefore, investors who hold the
market portfolio are concerned only with systematic risk.
Beta = Market Risk
Beta is telling us how much the return on a stock changes in response to a change in the return of the
market:
-
Beta = 0.5 → The return on a stock changes 50% as much as the market
Beta = 1.0 → The return on a stock changes the same amount as the market
Beta = 1.5 → The return on a stock changes 150% as much as the market
Therefore, a higher beta signals higher risk because the stock is volatile relative to the market.
Example: Beta
ABC Corporation stock has a correlation with the market of 0.55. ABC's standard deviation of returns is
40% and standard deviation of the market is 15%. What is ABC Corporation's beta?
Example: Beta
ABC Corporation stock has a correlation with the market of 0.55. ABC's standard deviation of returns is
40% and standard deviation of the market is 15%. What is ABC Corporation's beta?
COV = 0.55 * 0.40 * 0.15
COV = 0.033
ß = COV / 𝞂2M
ß = 0.033 / 0.152
ß = 1.47
Example: Beta
Last year the market's return was 4% and ABC Corporation earned 6%. This year the market yielded
14%. If ABC Corporation's Beta is 1.50, what is its return this year?
Example: Beta
Last year the market's return was 4% and ABC Corporation earned 6%. This year the market yielded
14%. If ABC Corporation's Beta is 1.50, what is its return this year?
Beta is the change in return of the stock in response to the change in return on the market. 1.5 means that
ABC will change 1.5x the change in the market.
The change in the market return was 10% → The change in ABC is 15% (10% * 1.50)
The return on ABC is their return last year plus the change in their return this year:
k = 6% + 15%
k = 21%
Estimating Beta
To estimate beta, we must plot the asset against the returns on the market portfolio. The slope of the line
of best fit is the beta of the asset.
Characteristic Line - Line of best fit when the return of an asset is plotted against the return on the
market portfolio
Recall: Beta is the change in the return on a stock in response to change in return in the market by 1.
The slope tells us the vertical change (return on the stock) in response to a one unit change on the x-axis
(return on the market)
Example: Estimating Beta
Use the following price information to find the beta of XYZ Corporation:
S&P500
XYZ Corporation
January
1844.93
40.36
February
1863.38
41.97
March
1919.28
43.23
Example: Estimating Beta
Use the following price information to find the beta of XYZ Corporation:
S&P500
Return
XYZ
Return
January
1844.93
40.36
February
1863.38
(1863.38 -1844.93) / 1844.93 = 1%
41.97
(41.97-40.36) / 40.36 = 4%
March
1919.28
(1919.28 - 1863.38) / 1863.38 = 3%
43.23
(43.23 - 41.97) / 41.97 = 3%
Beta is the slope (rise over run) of the characteristic line:
ß = (∆XYZ) / (∆S&P500)
ß = (0.03 - 0.04) / (0.03 - 0.01)
ß = -0.01 / 0.02
ß = -0.5
Properties of Beta
Three fundamental properties of beta:
1. Beta of the market portfolio is 1
Beta measures returns against returns of the market portfolio. The return of the market portfolio
changes in direct proportion to itself.
1. Beta of the risk free asset is 0
Return on the risk free asset is constant. It does change in in any proportion to the market
portfolio
(no covariance).
1. Beta of a portfolio is a weighted average of each individual beta within it
Example: Properties of Beta
Consider the following historic information on the market, the risk-free rate (T-Bills) and two mutual
funds, Templeton and Fidelity. If you had invested 56.64% of your wealth in Fidelity and the remainder
in Templeton, what was your portfolio’s beta?
Example: Properties of Beta
Consider the following historic information on the market, the risk-free rate (T-Bills) and two mutual
funds, Templeton and Fidelity. If you had invested 56.64% of your wealth in Fidelity and the remainder
in Templeton, what was your portfolio’s beta?
Bp = w1B1 + w2B2
Bp = (0.4336 * 1.3) + (0.5664 * 0.5)
Bp = 0.85
Example: Properties of Beta
(Pearson Revel: Practice Section 6.3, Question 4)
You are building a portfolio out of a​ risk-free asset and a risky asset. The​ risk-free rate is 3.9% and the
expected return on the risky asset is 12.5%. The beta of the risky asset is 0.709. You want your portfolio
to have an expected return of 20.6% and a beta of 1.221. You have $1,000 of your own money to invest.
What is the dollar value of your investment in the risky asset and what are the portfolio weights on the
risky and​ risk-free assets?
Example: Properties of Beta
(Pearson Revel: Practice Section 6.3, Question 4)
You are building a portfolio out of a​ risk-free asset and a risky asset. The​ risk-free rate is 3.9% and the
expected return on the risky asset is 12.5%. The beta of the risky asset is 0.709. You want your portfolio
to have an expected return of 20.6% and a beta of 1.221. You have $1,000 of your own money to invest.
What is the dollar value of your investment in the risky asset and what are the portfolio weights on the
risky and​ risk-free assets?
ßp = w*ß1 + (1-w)*ß2
1.221 = 0.709w + (1-w)*0
1.221 = 0.709w
w1 = 1.722 → $1,722
w2 = - 0.772
Chapter 08
Stock Valuation and Market Efficiency
Stocks
Stocks: A security that represents ownership in an incorporated company (Attend
general meetings, review financial statements and elect members to the board of directors)
Common Shares
Preferred Shares (Hybrid)
Typically give owner one vote per
share
•
Pay a fixed amount of dividends
•
Typically do NOT have voting rights
•
Have a claim on assets and income
after all liabilities (Residual
Claimant)
•
•
Receive anything left after all
liabilities have been covered
If Board of Directors choose to suspend
dividends (hard to do), they must pay
dividends to preferred before common
(Cumulative Dividends)
•
In areas of liquidation receive par value
•
•
Profit can be distributed through
dividends or stock repurchases
Capital Structure
Paid First
Bonds
Paid Last
Preferred
Common
Stock Markets
Primary Market: Market where securities are traded for FIRST time
Initial Public Offering (IPO): Where a firm first offers shares to the public
and the firm becomes a public company
Secondary Market: Market for trading securities after they have been issued
(Exg, NASDAQ and NYSE)
Seasoned Offering: An issue of stock that was offered in the past and has
been traded since
Public Company: Traded publicly on stock exchange
Private Company: Not actively traded and not listed on exchange
Long
Positions
Long Position: An investment where ownership is taken before the security is
sold. (Purchase Precedes Sale) (Buy Low, Sell High)
Exg: Buying a house and hoping price of house will rise and you sell at higher price
Sell
Buy
Calculation:
Bought: $903,800
Sold: $970,000
Capital Gain: $66,200
BUY ONLY IF YOU EXPECT INCREASE IN ASSET PRICE
Short Selling
Short Position: Investor borrows security. It is then sold. Later the
security is bought back to repay the loan.
Profitable only if you buy High and sell low.
Borrow
Buy
Calculation
Borrowed: $9,817
Bought: $8,567
Capital Gain: $1,250
SHORT ONLY IF YOU EXPECT DECREASE IN ASSET PRICE
Valuation of Preferred Stock
Simple preferred stock that is assumed to pay dividends in a perpetuity
(forever)
Practice Problem 2
If a preferred stock sold for $62 a share and $2.11 dividends were paid
annually, what would be the required rate of return?
Practice Problem Answers
If a preferred stock sold for $62 a share and $2.11 dividends were paid
annually, what would be the required rate of return?
Algebraically
Valuation of Common Stock Using
Dividend Discount Model
Calculate current price of stocks using Dividends and returns, allows
you to see if you want to invest or not dependent on assumptions
Practice Problem 3
An investor plans to buy a share of stock today, which will be held for 1 year. The
stock will pay a $1.85 dividend and should sell for $50. If the required return is
11%, how much should investor pay for the stock?
Practice Problem Answers
An investor plans to buy a share of stock today, which will be held for 1 year. The
stock will pay a $1.85 dividend and should sell for $50. If the required return is
11%, how much should investor pay for the stock?
Practice Problem 4
Solution
Constant Growth Model
Assume that dividends grow at a constant periodic rate forever
THE GROWTH RATE IS ASSUMED TO BE LESS THAN REQUIRED RETURN
Constant Growth Model Cont’d
●
●
●
FV = most recently occurring
dividend
PV = earliest occurring dividend
n = # intervals during which
dividends can grow
●
First term = dividend yield
○
●
High yield stocks pay a relatively
high portion of their income in
form of dividends
Second term = capital gain yield
○
Zero / Low yield stocks pay out
a low percentage of income as
dividends, instead investing in
growth
Constant Growth Model Practice (Q5)
Pan American Airlines pays annual dividends on December 31. Today is January 1.
Yesterday, PAN AM paid a dividend of $1.86. Dividends are expected to increase
by 27% this coming year and then drop a long-run (perpetual) growth rate of 2.5%.
Investors expect a return of 8.1% on PAN AM shares. What is the fair price for
PAN AM?
a.
b.
c.
d.
$29.53
$25.31
$33.74
$42.18
Constant Growth Model Answers
Practice Problem 6
Solution
Practice Problem 7 with non-constant
growth
Solution
Problem 8 with non-constant growth
The last dividend paid was $2 per share. They are expected to grow at a 20% rate
for the next 3 years, then at a constant 10% thereafter. The required return of
shareholders is 15%. What is the most you would be willing to pay for this stock?
Solution
McNally’s Solution
Stock Repurchases and Total Payout
Model
Stock Repurchase: The repurchase of stock by a firm from its existing
stockholders. It is a method to distribute cash without paying dividends
Open Market Share Repurchase: A company instructs its broker to buy shares on the open market prevailing
market prices. The shares are then cancelled and no longer outstanding. (Most Common)
Fixed-Price Tender Offer: A one-time offer by a company looking to acquire another company that includes
desire to purchase a certain number of shares at a fixed price. (Premium Price)
Dutch Auction Share Repurchase: A company announces a target repurchase quantity and invites
shareholders to offer their sales for sale.
Total Payout Model: Provides an estimate of stock price by discounting dividends
and share repurchases
Total Payout Model
TPM values a company’s total equity
Total Payout Model Practice Problem (Q9)
Analysts expect Sturk Industries to make payouts of $2.00 billion at the end of this year. Assume
that all payouts occur annually at the end of the year and that we are at the beginning of the year.
Analysts forecast that Sturk’s payouts will grow at 2.5% in perpetuity. Sturk stockholders required a
return of 12%. Sturk has 1.44 billion shares outstanding. What is the fair price for Sturk’s shares
today?
Total Payout Model Answers
Analysts expect Sturk Industries to make payouts of $2.00 billion at the
end of this year. Assume that all payouts occur annually at the end of the
year and that we are at the beginning of the year. Analysts forecast that
Sturk’s payouts will grow at 2.5% in perpetuity. Sturk stockholders
required a return of 12%. Sturk has 1.44 billion shares outstanding. What
is the fair price for Sturk’s shares today?
Practice Problem Q10
Solution
Price Earnings Valuation Method
The Price/Earnings (P/E): measure of how much the market is willing to pay for
$1 of earnings from a firm
It can be used to estimate the value of a firm’s stock
Alternative valuation model when dividend and repurchase data is not available
Typically going to use an industry P/E constant in calculations
P/E Theory Question (Q11)
Answer
P/E Question (Q12)
Company Z is currently priced at $29. They just reported
earnings per share of $0.75. What is the P/E ratio that
investors are willing to pay for a share of Company Z’s stock?
P/E Question Answers
Company Z is currently priced at $29. They just reported earnings per share of
$0.75. What is the P/E ratio that investors are willing to pay for a share of
Company Z’s stock?
PE Question (Q13)
Powell Motors has a P/E constant of 15 and 121 million shares
outstanding. Analysts forecast net income to be $257.7 million in the
next year. What is the fair price for a share of Powell Motors?
PE Question (14)
Powell Motors has a P/E constant of 15 and 121 million shares outstanding.
Analysts forecast net income to be $257.7 million in the next year. What is the fair
price for a share of Powell Motors?
Thank you!
Good luck on your midterm :)
Extra Practice
Extra Practice: Bonds
Extra Practice: Bonds
Extra Practice: Bonds
Extra Practice: Beta
Extra Practice: Beta
Extra Practice: Beta
Extra Practice: Beta
Extra Practice: Beta
Extra Practice: Beta
Extra Practice: Valuation
Extra Practice: Valuation
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