Post on 23-Dec-2015
FIN351: lecture 6
The cost of capital
The application of the portfolio theory and CAPM
FIN351: lecture 6
Today’s plan
What have we accomplished in the last lecture?
Cost of capital• Capital structure and WACC
• Calculate WACC without tax
• Calculate WACC with tax
The market efficiency concept
FIN351: lecture 6
What have we learned in the last lecture?
Beta (β): Measuring market risk or systematic risk of a security• Which is defined as the contribution of a
security to the risk on the market portfolio,
• Mathematically,
• How to understand β intuitively?
)~(
)~,~(
m
mii RVar
RrCov
FIN351: lecture 6
What have we learned in the last lecture? (1)
05 10 15
Number of Securities
Po
rtfo
lio
sta
nd
ard
dev
iati
on
Market risk
Uniquerisk
FIN351: lecture 6
What have we learned in the last lecture? (2)
The beta of a portfolio• The beta of a portfolio will be an weighted
average of the betas of the securities in the portfolio.
The expected return of a portfolio• The expected return of a portfolio will be an
weighted average of the expected returns of the securities in the portfolio.
FIN351: lecture 6
What have we learned in the last lecture? (3)
CAPM (Capital Asset Pricing Model) • The risk premium on each security is
proportional to the market risk premium and the beta of the security.
• That is, )( fmifi rRrr
portfoliomarkettheforpremiumriskrR
iurityforpremiumriskrr
fm
fi
sec
FIN351: lecture 6
What have we learned in the last lecture? (4)
0
2
4
6
8
10
12
14
16
0 0.2 0.4 0.6 0.8 1 1.2
Beta
Exp
ecte
d R
etu
rn (
%)
. The graphic representation of CAPM in
the expected return and Beta plane
rf
Security Market Line
Rm
FIN351: lecture 6
What have we learned in the last lecture? (5)
We can use the Beta of the project cash flows to measure the risk of the project and use CAPM to get the discount rate or the expected return required by investors •
)( fmprojectfproject rRrr
FIN351: lecture 6
What have we learned in the last lecture? (6)
Some results• The Beta of the market portfolio is 1.
• The Beta of the risk-free asset is 0.
• The portfolio weights can be negative, but their sum must be 1.
FIN351: lecture 6
Example 1
You have $1 million of your own money to invest in stock A and B. You short-sell $1 million stock A and then invest in stock B. The expected returns for stock A and B are 15% and 20%, respectively. The risk-free rate is 5%. Stock A has a beta of 1.5 and stock B has a beta of 2.0.The expected rate of return for the market portfolio is 13%.
Please use two approaches to calculate the expected rate of return on your portfolio?
FIN351: lecture 6
Solution
%25%8*5.2%5
5.22*25.1*1
p
p
R
%252.0*215.0*1 pR
First, calculate the portfolio weight as follows:
(1)The expected rate of return of a portfolio is the weighted average of the
rates of return of the securities in the portfolio.
2;1 BA xx
(2) The beta of a portfolio is the weighted average of the betas of the securities in the portfolio. Then use CAPM to calculate the expected return
FIN351: lecture 6
The cost of capital
Cost of Capital • The expected return the firm’s investors
require if they invest in securities or projects with comparable degrees of risk.
FIN351: lecture 6
The cost of capital for the bond
The cost of capital for the bond• It is the YTM, the expected return required by
the investors.
• That is
• The expected return on a bond can also be calculated by using CAPM
tddd r
principalcpn
r
cpnr
cpn
111
P2bond
)( fmdfd rRrr
FIN351: lecture 6
Example 2
A bond with a face value of $2000 matures in 5 years. The coupon rate is 8%. If the market price for this bond is $1600.(a) What is the expected return on this bond or
what is the cost of debt or interest rate for this bond?
(b) Suppose that the YTM is 9%, what is the market value of this bond?
FIN351: lecture 6
Solution
(a)
(b)
%8.13
)1(
2000
)1(
111601600
55
YTM
YTMYTMYTMYTM
922,1$09.1
2000
09.1*09.0
1
09.0
1160
55
bondP
FIN351: lecture 6
The cost of capital for a stock
The cost of capital for a stock is calculated by using • CAPM
• Dividend growth model
)r-(R+r=r fmfe i
gP
DIVr
gr
DIVP e
e
0
110
FIN351: lecture 6
Example 3
Sock A now pays a dividend of $1.5 per share annually, It is expected that dividend is going to grow at a constant rate of 2%. The current price for stock A is $25 per share. What is the expected return or the cost of capital by investing in this stock?
FIN351: lecture 6
Solution
%12.802.0
02.1*5.125
r
r
Using the dividend discount model, we have
FIN351: lecture 6
Capital structure
Capital Structure• The firm’s mix of debt financing and equity
financing.
• If we use D , E and V to denote the values of debt, equity and firm (asset), respectively.
• Then V=D+E
• The ratio of D/V or D/E can be used to measure the capital structure of the firm.
FIN351: lecture 6
Weighted Average Cost of Capital (WACC)
If you invest in a stock, you require a an expected rate of return, or the cost of capital for the stock
If you invest in a bond, you require a an expected rate of return, or the cost of capital for the bond
Then, if you invest in a a portfolio of all the firm’s securities (debt and stock), what is the expected rate of return you require?
The expected rate of return on a portfolio of all the firm’s securities is called the weighted average cost of capital(WACC). It is also called the expected return on the asset of the firm.
FIN351: lecture 6
WACC (continues)
According to portfolio theory, we know the expected return on a portfolio is the weighted average of the expected returns on the securities of the portfolio.
Thus, WACC for a firm with debt and equity is
de rVD
rVE
WACC
EDVwhere
FIN351: lecture 6
WACC (continue)
In calculating WACC, we have to use market values of debt and equity.
Even if you are given the book value of debt, you may convert this book value to market debt value to calculate WACC
Why do we use market values of debt and equity, but not book values of debt and equity, in calculating WACC?
FIN351: lecture 6
Example 4
Geothermal Inc. has two securities: debt and stocks. The market debt value is $194 million, but the firm’s market value is $647 million. Given that geothermal pays 8% for debt and 14% for equity, what is the Company Cost of Capital?
FIN351: lecture 6
Solution
%2.1214.0*647
45308.0*
647
194WACC
FIN351: lecture 6
Example 5
Executive Fruit has issued debt, preferred stock and common stock. The market value of these securities are $4mil, $2mil, and $6mil, respectively. The required returns are 6%, 12%, and 18%, respectively.• What is the WACC for Executive Fruit, Inc.?
FIN351: lecture 6
Solution
%13
18.0*12
612.0*
12
206.0*
12
4
12624
WACC
V
FIN351: lecture 6
Summary of WACC calculation
Three steps in calculating WACC• First step: Calculate the portfolio weight using
the market value.
• Second step: Determine the required rate of return on each security in the portfolio.
• Third step: Calculate a weighted average of these returns, or the expected return on the protfolio.
FIN351: lecture 6
The impact of tax on WACC
Taxes are an important consideration in the company cost of capital because interest payments are deducted from income before tax is calculated.
Tc)-(1r=
rate)tax -(1 timesdebt) ofcost (pretax =debt ofcost tax -After
d
FIN351: lecture 6
WACC with tax
Weighted -average cost of capital=
eVE
dVD r +Tc)r-(1 =WACC
FIN351: lecture 6
A summary example John Cox, a recent MBA student of SFSU, was asked by his
boss in Geothermal to decide whether the firm should take an expansion project: the cost of the project is $30 million, and the project is expected to generate a perpetual incremental cash flow of $4.5 million. Currently, Geothermal has 20 million shares of common stocks outstanding, with a market price of $22.65 per share. The Beta of the firm’s equity is 1.1. The risk free rate is 4% and the market risk premium is 5.6%. The firm also has long-term debt, with the YTM of 9%. John also got the following information from the firm’s balance sheet:• Debt (12 years maturity, 8% coupon): $200 million
• Common stocks:$110 million If the tax rate is 35%, should John suggest to his boss to take
the project or not?
FIN351: lecture 6
Solution
%9.8)1(
7.18509.1
200)
09.1*09.0
1
09.0
1(*16
45365.22*20
%16.10%6.5*1.1%4
%9
1212
ed
e
d
rED
Ert
ED
DWACC
D
E
r
r
FIN351: lecture 6
Investment vs. Financing
Investment decisions or capital budgeting is about how to take projects to maximize V.
Financing decisions are about how to raise capital (E or D) to finance the projects to be taken
Asset Liabilities and equity
VDebt: D
Equity: E
FIN351: lecture 6
Market Efficiency
Market efficiency is concerned about whether capital markets have all information about the cash flows and risk of projects.
Financing and market Efficiency
FIN351: lecture 6
Efficient capital markets
Efficient Capital Markets – If capital markets are efficient, then security prices reflect all relevant information about asset values ( cash flows and risk)
FIN351: lecture 6
Market efficiency and random walk
Market efficiency concepts are very abstract.
How can we use a simple way to check whether the stock market (one of the capital markets) is efficient or not?• If the stock price follows a random walk, then
the stock market is efficient.
FIN351: lecture 6
What is a random walk of stock prices?
The movement of stock prices from day to day DO NOT reflect any pattern.
Statistically speaking, the movement of stock prices is random.
FIN351: lecture 6
A Random Walk example
$103.00
$100.00
$106.09
$100.43
$97.50
$100.43
$95.06
Coin Toss Game
Heads
HeadsHeads
Tails
Tails
Tails
FIN351: lecture 6
Three forms of market efficiency
The random walk concept is still abstract Financial economists have used three
more specific forms to characterize or judge market efficiency.• Weak-form
• Semi-strong form
• Strong form
FIN351: lecture 6
Weak-form of market efficiency
Weak Form Efficiency - Market prices reflect all information contained in the history of past prices, or you cannot use past stock prices to predict future prices
Technical Analysts - Investors who attempt to identify over- or undervalued stocks by searching for patterns in past prices.
FIN351: lecture 6
Efficient Market Theory
Last Month
This Month
Next Month
$90
70
50
EI’s Stock Price
Cycles disappear
once identified
FIN351: lecture 6
Semi-strong form of market efficiency
Semi-Strong Form Efficiency - Market prices reflect all publicly available information such as earnings, price-to-earnings ratios,etc.
Fundamental Analysts - Analysts who attempt to fund under- or overvalued securities by analyzing fundamental information, such as earnings, asset values, and business prospects.
FIN351: lecture 6
Efficient Market Theory
-16
-11
-6
-14
9
14
19
24
2934
39
Days Relative to annoncement date
Cu
mu
lati
ve A
bn
orm
al R
etu
rn
(%)
Announcement Date
FIN351: lecture 6
Market Efficiency
0
5
10
15
20
25
Av
era
ge
re
turn
, pe
rce
nt
Highest
Book-Market Ratio
Fama & FrenchReturn vs. Book-Market
FIN351: lecture 6
Strong form of market efficiency
Strong Form Efficiency - Market prices reflect all information that could in principle be used to determine true value.
Inside trading• Investors use private information to predict
future price movements
FIN351: lecture 6
Efficient Market Theory
-16
-11
-6
-14
9
14
19
24
2934
39
Days Relative to annoncement date
Cu
mu
lati
ve A
bn
orm
al R
etu
rn
(%)
Announcement Date
FIN351: lecture 6
Some exercises
1. If stock markets are efficient, what should the correlation between stock returns for two non-overlapping periods?
2. Which is the most likely to contradict the weak-form of efficiency
a. Over 25% of mutual funds outperform the market on average
b. Insiders can make abnormal profits
c. Every January, the stock market earns abnormal return
FIN351: lecture 6
Several types of securities
Three types of securities• Common Stock
• Preferred stock
• Corporate debt
FIN351: lecture 6
Common Stock
Common stocks have the following forms:• Treasury stock
• Issued shares
• Outstanding shares
• Authorized share capital
• Par value
Ownership of the corporation
FIN351: lecture 6
Corporate debt
Corporate bonds• Primary rate
• Funded debt
• Sink fund
• Callable bond
• Subordinate debt
• Secure debt
FIN351: lecture 6
Preferred stock
Preferred stock and common stock• Priority and voting rights
Preferred stock and bond• Obligation and bankruptcy