Review
Chapter 13 and Chapter 14
Chapter 13 Outline
• Expected Returns and Variances of a portfolio
• Announcements, Surprises, and Expected
Returns
• Risk: Systematic and Unsystematic
• Diversification and Portfolio Risk
• Systematic Risk and Beta
• The Security Market Line (SML)
Portfolios
Portfolio = a group of assets held by an
investor
• The risk-return trade-off for a portfolio is measured
by the portfolio expected return and standard
deviation, just as with individual assets
Portfolio weights = Percentage of a
portfolio’s total value in a particular asset
3
Portfolio Expected Returns (1)
• The expected return of a portfolio is the weighted
average of the expected returns for each asset in the
portfolio
m
E ( RP )   w j E ( R j )
j 1
• You can also find the expected return by finding the
portfolio return in each possible state and computing
the expected value
4
Calculate Portfolio Variance
• Portfolio variance can be calculated using
the following formula:
  x   x   2 xL xU CORRL,U L U
2
P
2
L
2
L
2
U
2
U
• Correlation is a statistical measure of how 2 assets
move in relation to each other
• If the correlation between stocks A and B = -1,
what is the standard deviation of the portfolio?
Portfolio Diversification
6
Measuring Systematic Risk
• Beta (β) is a measure of systematic risk
• Interpreting beta:
– β = 1 implies the asset has the same systematic
risk as the overall market
– β < 1 implies the asset has less systematic risk
than the overall market
– β > 1 implies the asset has more systematic risk
than the overall market
7
Portfolio Expected Returns and Betas
Rf
Reward-to-Risk Ratio:
• The reward-to-risk ratio is the slope of the line
illustrated in the previous slide
– Slope = (E(RA) – Rf) / A
– Reward-to-risk ratio =
• If an asset has a reward-to-risk ratio = 8?
• If an asset has a reward-to-risk ratio = 7?
9
The Fundamental Result
• The reward-to-risk ratio must be the same for
all assets in the market
E ( RA )  R f
A

E ( RM  R f )
M
• If one asset has twice as much systematic risk
as another asset, its risk premium is twice as
large
10
Security Market Line (2)
11
Chapter 14
COST OF CAPITAL AND LONGTERM FINANCIAL POLICY
The Dividend Growth Model Approach
• Can be rearranged to solve for RE
D1
P0 
RE  g
D1
RE 
g
P0
13
Example
14
Example
15
Example: Estimating the Dividend
Growth Rate
 One method for estimating the growth rate is
to use the historical average
◦
◦
◦
◦
◦
◦

Year
2005
2006
2007
2008
2009
Dividend
1.03
1.13
1.26
1.33
1.40
Percent Change
9.7%
11.5%
5.55%
5.26%
Geom. Av = 7.97%
arithmetic av.=8%
Analysts’ forecast can be used
16
Alternative Approach to Estimating
Growth
 If the company has a stable ROE, a stable dividend
policy and is not planning on raising new external
capital, then the following relationship can be used:
g = Retention ratio x ROE
 A company has a ROE of 17% and payout ratio is 15%.
If management is not planning on raising additional
external capital, what is its growth rate?
Solution: g=17*(1-.15)=14.45%
17
The SML Approach (CAPM)
• Use the following information to compute our
cost of equity
– Risk-free rate, Rf
– Market risk premium, E(RM) – Rf
– Systematic risk of asset, 
E(RA) = Rf + A(E(RM) – Rf)
18
SML example
• Suppose the company has an equity beta of
1.28 and the current risk-free rate is 3.2%. If
the expected market risk premium is 9.8%,
what is the cost of equity capital?
Solution: 15.744%
19
Cost of Equity
• Suppose the company has a beta of 1.45. The market
return is expected to be 15.2% and the current riskfree rate is 4%. Dividends will grow at 5% per year
and last dividend was $1.2. The stock is currently
selling for $7.35. What is our cost of equity?
– Using SML: 20.24%
– Using DGM: 22.14%
20
Cost of Debt example
• Suppose you have a bond issue currently
outstanding that has 17 years left to maturity.
The coupon rate is 8% and coupons are paid
annually. The bond is currently selling for
$955.874 per $1000 bond. What is the cost of
debt?
Solution: 8.5%
21
Cost of Preferred Stock

Preferred stock generally pays a constant
dividend every period

Dividends are expected to be paid every
period forever
• Preferred stock is perpetuity
RP = D / P0
22
Cost of Preferred Stock example
• A company has preferred stock that has an
annual dividend of $2. If the current price is
$15, what is the cost of preferred stock?
Solution: 13.33%
23
Flotation Costs
• The required return depends on the risk, not
how the money is raised
• However, the cost of issuing new securities
should not just be ignored either
• Basic Approach
– Compute the weighted average flotation cost
f A  (E / V )  f E  (D / V )  f D
24
NPV and Flotation Costs example
• A company is considering a project that will
cost $1.2 million. The project will generate
after-tax cash flows of $250,000 per year for 9
years. The WACC is 12% and the firm’s target
D/E ratio is .5 (1/2). The flotation cost for
equity is 4% and the flotation cost for debt is
2%. What is the average flotation cost? What
is the NPV for the project after adjusting for
flotation costs?
25
Solution
•
•
•
•
•
•
D=400,000 fd = 400,000*.02 = 8,000
E=800,000
fE = 800,000*.04 = 32,000
Fac = .0267 + .0067 =.0334=3.34%
PV=(1,240,000)
PVFCF= 1,332,062.448
NPV = 92,062.448
positive