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Class Notes
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United States
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Boston College
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Finance
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MFIN 1127
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Jerome Taillard
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Lecture

Description

Corporate Finance
MF 127
Lecture 14
Jérôme Taillard
Spring 2013 Outline of the lecture
1. Recap: What we have learned up to now
2. Quantifying the risk-return trade-off
– CAPM model: Cost of equity What do we know up to now?
1. Role of financial managers
– Maximize shareholder value
• Corporate governance
2. Financial statement analysis
– ROE decomposition
• Working Capital management
3. Big picture concepts:
A. Arbitrage and the Law of one price
B. Discounting cash flows methods
Price any assets by computing PV(all future cash flows)
Perform any capital budgeting decision
» Compute NPV of project and apply NPV rule 1. Financial modeling of cash flows
a. Bonds:
• ≈ Annuity (coupons) + final payoff (Principal)
b. Equity
• Dividends (sometimes earnings)
• Basic ≈ Growing Perpetuity (Dividend growth model)
• Two-stage ≈ Growing Annuity (initial fast growth) +
Growing perpetuity (slower growth after several years)
c. Firm
• Free cash flows ≈ FCFs (forecasted five years out) +
Growing perpetuity (slower growth after several years)
• Still to go:
d. Projects
• Free cash flows generated by project
– Forecasting using pro forma financial statements
• Finite life
• No single pattern in future cash flows
– Important exception: Annuity formula to compute Equivalent Annual costs 2. Financial modeling of discount rates
a. Bonds
• Cost of debt
• Yield-to-Maturity (YTM) concept
• Still to go:
a. Equities
• Cost of equity
• CAPM and equity beta concept
c. Firms
• Financed by using debt (a) and equity (b)
Weighted average cost of capital (WACC) concept
d. Projects
• If similar risk and financing as entire firm, use WACC
• Else need to make adjustments
– Industry beta concept Cost of equity
• GOAL:
– Determine what should be the cost of equity
• APPROACH:
– In two step:
1. Quantifying the risk-return trade-off in Finance
• Chapter 10
2. CAPM model
• Chapter 11 Motivation for studying CAPM
• Capital Asset Pricing Model (CAPM): Nobel prize winning
idea developed by Sharpe (1964), Lintner (1965), and
Black (1972), extending the work of Markowitz (1952) Risk and Return: The big picture
• Humans are generally risk averse
Seek to avoid risk
Need compensation for taking risk
Risk premium
• Most important concept in finance:
– The risk/return tradeoff
• There is “no free lunch”
You cannot get higher returns without taking on more risks
• This lecture is about quantifying this tradeoff
Goal of this lecture: Getting to CAPM formula Fundamental questions in Finance
1. How do we define risk?
2. Can we eliminate some of the risks involved in
an investment?
3. What is the required rate of return for a given
investment?
Cost of equity
Key ingredient for appropriate discount rate of a firm
(WACC) Returns and Risk
• People make decisions based on expected returns
and risksevery day
– Should you skip the corporate finance class this week?
• Return: Extra hours to prepare for exams
• Risk: May miss important tips for exams
• Different people have different perceptions of
expected returns and risk
– Which activity would you prefer?
1. Shopping
2. Golf
3. Sky-Diving Returns and Risk in Finance
• Toassess returns and risks in financial markets we
need to use an objectivemeasure
Need to describe the distribution of stock returns
– What do we mean by distribution? Distribution: Summarizing the future!
• Risky = Uncertain outcome
• To gauge this uncertainty:
1. Listall possible outcomes
2. Probability of occurrence for each outcome Expected return
• Measure of central tendency of distribution
• Definition: Weighted average of each outcome
weights = probabilities of each outcome
Expected Return ER[ ] = P R×
∑ R R
• In our example of BFI:
E[ BFI = −2+%( 020) =0%(0.10) 25%(0.40) 10% Expected profit of a coin toss game
• Suppose:
– Heads: $1 gain
– Tails: $1 loss
• Probability of each event: 50% (fair coin!)
• Hence expected profit = 0.5*(-1)+0.5*(1)=0
If we played this game a million times, our
profit/loss would be close to zero! Variance and Standard deviation
• Measures of dispersion around mean
• Mathematically:
– Variance: Expected squared deviation from the mean
2 2
rR ( E R =[ ])−P ∑R RER ( [ ])
• Standard deviation = Square rootof variance
SD(R (= Var R
• Finance language:
Volatility = Standard deviation Example
• If we take again our example of BFI:
Var [ ] = 25%×− ( −0.20 +0.10× )2 250% (0.10 0.10)
BFI
+×2−% = (0.40 0.10)2 0.045
SD(R) = ( V )0rR421.2% = Higher volatility = Higher risk
Example with the normal (bell-
shaped) distribution
1. In red
Normal distribution with
mean = 0 and std dev = 10
2. In green
Normal distribution with
mean = 0 and std dev = 20
The distribution with greater
standard deviation(volatility)
has greater risk (more
uncertainty): Its distribution is
more spread out around the
mean! How do we come up with a
distribution for stock returns?
• The future is unknown
Distribution summarizes our best guess
• But how do we form our best guess?
– Typically: Use the past as a predictor of the future!
• When is the past a good predictor?
– When the distribution is relativelystable Risk-return trade-off in the past
STOCKS: RISKIER (MORE VOLATILE) BUT ALSO HIGHER RETURN IN THE LONG-RUN Plotting the corresponding returns Statistics vs. Probabilities
1. Statistics = Distribution of historical outcomes
2. Probabilities = Distribution of future outcomes Estimate of expected returns
using historical data
• The averageor mean is computed using
historical stock return data
1 1 T
R = RR++ + ( 1 2 R R T t ∑
T T t=1
• Where, for each time period:
Pt+D t−Pt−1
Rt= P ,
t−1
wherePt−1 Priceat beginningof period
whereP = Priceat endof period
t Estimate of standard deviation
using historical data
• Estimate of variance:
T 2
Var R) = 1 ∑ (Rt− R )
T − 1 t=1
• Why (T-1)?
• Estimate of the standard deviation (volatility)
is just the square root of that number Simple Example
• Compute the standard deviation of the numbers 1, 2, 3, 4 and 5.
• Step 1: Compute the average (here equal to 3)
• Step 2: Compute the deviation and squared deviation from the
average:
Value Deviation Squared Deviation
1 (1 – 3) 4
2 (2 – 3) 1
3 (3 – 3) 0
4 (4 – 3) 1
5 (5 – 3) 4
• The sum of the squared deviations is 10
• This sum divided by 4 (= 5 – 1) equals 2.50
Sample variance = 2.50

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