Transcript Document

6-1
Key Concepts and Skills
• Know the important bond features
and bond types
• Understand:
– Bond values and why they fluctuate
– Bond ratings and what they mean
– The impact of inflation on interest rates
– The term structure of interest rates and
the determinants of bond yields
6-2
Bond Definitions
• Bond
– Debt contract
– Interest-only loan
•
•
•
•
•
Par value (face value) ~ $1,000
Coupon rate
Coupon payment
Maturity date
Yield to maturity
6-3
Key Features of a Bond
• Par value:
– Face amount
– Re-paid at maturity
– Assume $1,000 for corporate bonds
• Coupon interest rate:
– Stated interest rate
– Usually = YTM at issue
– Multiply by par value to get coupon
payment
6-4
Key Features of a Bond
• Maturity:
– Years until bond must be repaid
• Yield to maturity (YTM):
– The market required rate of return for bonds of
similar risk and maturity
– The discount rate used to value a bond
– Return if bond held to maturity
– Usually = coupon rate at issue
– Quoted as an APR
6-5
Bond Value
• Bond Value = PV(coupons) + PV(par)
• Bond Value = PV(annuity) + PV(lump sum)
• Remember:
– As interest rates increase present values
decrease ( r → PV  )
– As interest rates increase, bond prices
decrease and vice versa
6-6
Spreadsheet Formulas
=FV(Rate,Nper,Pmt,PV,0/1)
=PV(Rate,Nper,Pmt,FV,0/1)
=RATE(Nper,Pmt,PV,FV,0/1)
=NPER(Rate,Pmt,PV,FV,0/1)
=PMT(Rate,Nper,PV,FV,0/1)
• Inside parens: (RATE,NPER,PMT,PV,FV,0/1)
• “0/1” Ordinary annuity = 0 (default)
Annuity Due = 1 (must be entered)
6-7
Graphical Relationship Between
Price and Yield-to-maturity
1500
1400
Bond Price
1300
1200
1100
1000
900
800
700
600
0%
2%
4%
6%
8%
10%
12%
14%
Yield-to-maturity
6-8
Bond Prices:
Relationship Between Coupon and Yield
• Coupon rate = YTM Price = Par
• Coupon rate < YTM Price < Par
–“Discount bond” … Why?
• Coupon rate > YTM Price > Par
–“Premium bond” … Why?
6-9
Bond Value ($) vs Years
remaining to Maturity
Premium
CR>YTM
YTM = CR
1,000
M
CR<YTM
Discount
30
25
20
15
10
5
0
6-10
Interest Rate Risk
• Price Risk
– Change in price due to changes in
interest rates
– Long-term bonds have more price risk
than short-term bonds
– Low coupon rate bonds have more price
risk than high coupon rate bonds
6-11
Interest Rate Risk
• Reinvestment Rate Risk
– Uncertainty concerning rates at which
cash flows can be reinvested
– Short-term bonds have more reinvestment
rate risk than long-term bonds
– High coupon rate bonds have more
reinvestment rate risk than low coupon
rate bonds
6-12
Figure 6.2
6-13
Computing Yield-to-Maturity YTM
• Yield-to-maturity (YTM) = the market
required rate of return implied by the
current bond price
• With a financial calculator,
– Enter ,, ., /, and 0
– Remember the sign convention
/ and 0 need to have the same sign (+)
. the opposite sign (-)
%6-14
YTM with Annual Coupons
Consider a bond with a 10% annual
coupon rate, 15 years to maturity and a
par value of $1000. The current price is
$928.09.
– Will the yield be more or less than 10%?
15
928.09
1000
100
I
n
pv (- for fin calc)
fv
pmt
11% Result = YTM
Using Excel: =RATE(15, 100, -928.09, 1000, 0)
6-15
Table 6.1
6-16
Debt versus Equity
• Debt
–
–
–
–
Not an ownership interest
No voting rights
Interest is tax-deductible
Creditors have legal
recourse if interest or
principal payments are
missed
– Excess debt can lead to
financial distress and
bankruptcy
• Equity
– Ownership interest
– Common stockholders
vote to elect the board of
directors and on other
issues
– Dividends are not tax
deductible
– Dividends are not a
liability of the firm until
declared. Stockholders
have no legal recourse if
dividends are not
declared
– An all-equity firm cannot
go bankrupt
6-17
The Bond Indenture
“Deed of Trust”
Contract between issuing company and
bondholders includes:
– Basic terms of the bonds
– Total amount of bonds issued
– Secured versus Unsecured
– Sinking fund provisions
– Call provisions
• Deferred call
• Call premium
– Details of protective covenants
Return 6-18
to Quiz
Bond Ratings – Investment
Quality
• High Grade
– Moody’s Aaa and S&P AAA – capacity to pay is
extremely strong
– Moody’s Aa and S&P AA – capacity to pay is very
strong
• Medium Grade
– Moody’s A and S&P A – capacity to pay is strong,
but more susceptible to changes in
circumstances
– Moody’s Baa and S&P BBB – capacity to pay is
adequate, adverse conditions will have more
Return
impact on the firm’s ability to pay
to Quiz
6-19
Bond Ratings - Speculative
• Low Grade
– Moody’s Ba, B, Caa and Ca
– S&P BB, B, CCC, CC
– Considered speculative with respect to capacity
to pay. The “B” ratings are the lowest degree
of speculation.
• Very Low Grade
– Moody’s C and S&P C – income bonds with no
interest being paid
– Moody’s D and S&P D – in default with
principal and interest in arrears
6-20
Government Bonds
• Treasury Securities = Federal government debt
– Treasury Bills (T-bills)
• Pure discount bonds
• Original maturity of one year or less
– Treasury notes
• Coupon debt
• Original maturity between one and ten years
– Treasury bonds
• Coupon debt
• Original maturity greater than ten years
6-21
Zero Coupon Bonds
• Make no periodic interest payments
(coupon rate = 0%)
• Entire yield-to-maturity comes from the
difference between the purchase price
and the par value (capital gains)
• Cannot sell for more than par value
• Sometimes called zeroes, or deep
discount bonds
• Treasury Bills and U.S. Savings bonds are
good examples of zeroes
6-22
Floating Rate Bonds
• Coupon rate floats depending on some index
value
• Examples – adjustable rate mortgages and
inflation-linked Treasuries
• Less price risk with floating rate bonds
– Coupon floats, so is less likely to differ
substantially from the yield-to-maturity
• Coupons may have a “collar” – the rate
cannot go above a specified “ceiling” or
below a specified “floor”
6-23
Bond Markets
• Primarily over-the-counter transactions
with dealers connected electronically
• Extremely large number of bond issues,
but generally low daily volume in single
issues
• Getting up-to-date prices difficult,
particularly on small company or
municipal issues
• Treasury securities are an exception
6-24
Inflation and Interest Rates
• Real rate of interest
=Change in purchasing power
• Nominal rate of interest
= Quoted rate of interest,
= Change in purchasing power and inflation
• The ex ante nominal rate of interest
includes our desired real rate of return
plus an adjustment for expected inflation
6-25
The Fisher Effect
The Fisher Effect defines the relationship
between real rates, nominal rates and
inflation
(1 + R) = (1 + r)(1 + h)
R = nominal rate (Quoted rate)
r = real rate
h = expected inflation rate
Approximation: R = r + h
Return
to Quiz 6-26
Example 6.6
If we require a 10% real return and we
expect inflation to be 8%, what is the
nominal rate?
– R = (1.1)(1.08) – 1 = .188 = 18.8%
– Approximation: R = 10% + 8% = 18%
– Because the real return and expected
inflation are relatively high, there is
significant difference between the actual
Fisher Effect and the approximation.
6-27
Term Structure of Interest Rates
• Term structure: The relationship between
time to maturity and yields, all else equal
– The effect of default risk, different coupons,
etc. has been removed.
• Yield curve: Graphical representation of
the term structure
– Normal = upward-sloping  L/T > S/T
– Inverted = downward-sloping  L/T < S/T
Return
to Quiz
6-28
Figure 6.5 A – Upward-Sloping
Yield Curve
REPLACE with FIGURE 6.5 A
6-29
Figure 6.5 B – DownwardSloping Yield Curve
6-30
Figure 6.6 – Treasury Yield
Curve
6-31
Factors Affecting Required
Return
• Default risk premium – bond ratings
• Taxability premium – municipal versus taxable
• Liquidity premium – bonds that have more
frequent trading will generally have lower
required returns
• Maturity premium – longer term bonds will tend
to have higher required returns.
Anything else that affects the risk of the cash flows to
the bondholders will affect the required returns
Return
to Quiz 6-32
Key Concepts and Skills
• Understand how stock prices depend on
future dividends and dividend growth
• Be able to compute stock prices using the
dividend growth model
• Understand how corporate directors are
elected
• Understand how stock markets work
• Understand how stock prices are quoted
7-33
Cash Flows for Stockholders
• If you own a share of stock, you can
receive cash in two ways
– The company pays dividends
– You sell your shares, either to another
investor in the market or back to the company
• As with bonds, the price of the stock is the
present value of these expected cash
flows
– Dividends → cash income
– Selling → capital gains
7-34
One Period Example
• Suppose you are thinking of purchasing
the stock of Moore Oil, Inc.
– You expect it to pay a $2 dividend in one year
– You believe you can sell the stock for $14 at
that time.
– You require a return of 20% on investments of
this risk
– What is the maximum you would be willing to
pay?
7-35
One Period Example
•
•
•
•
•
D1 = $2 dividend expected in one year
R = 20%
P1 = $14
CF1 = $2 + $14 = $16
Compute the PV of the expected cash
flows
P0 
( 2  14 )
 $ 13 . 33
1 . 20
7-36
Two Period Example
• What if you decide to hold the stock for two
years?
–
–
–
–
D1 = $2.00
CF1 = $2.00
CF2 = $2.10 + $14.70 = $16.80
D2 = $2.10
P2 = $14.70
Now how much would you be willing to pay?
P0 
2
1 . 20

( 2 . 10  14 . 70 )
(1 . 20 )
2
 $ 13 . 33
7-37
Three Period Example
• What if you decide to hold the stock for three
years?
–
–
–
–
–
D1 = $2.00
CF1 = $2.00
D2 = $2.10
CF2 = $2.10
D3 = $2.205
CF3 = $2.205 + $15.435 = $17.640
P3 = $15.435
Now how much would you be willing to pay?
P0 
2
1 . 20

2 . 10
(1 . 20 )
2

( 2 . 205  15 . 435 )
(1 . 20 )
3
 $ 13 . 33
7-38
Developing The Model
• You could continue to push back
when you would sell the stock
• You would find that the price of
the stock is really just the present
value of all expected future
dividends
7-39
Stock Value = PV of Dividends
^
P0 =
D1
(1+R)1
+
D2
+
(1+R)2
Pˆ 0 

D3
+…+
D∞
(1+R)∞
(1+R)3
Dt
 (1  R )
t
t 1
How can we estimate all future dividend payments?
7-40
Estimating Dividends
Special Cases
• Constant dividend/Zero Growth
– Firm will pay a constant dividend forever
– Like preferred stock
– Price is computed using the perpetuity formula
• Constant dividend growth
– Firm will increase the dividend by a constant
percent every period
• Supernormal growth
– Dividend growth is not consistent initially, but settles
down to constant growth eventually
7-41
Zero Growth
• Dividends expected at regular intervals
forever = perpetuity
P0 = D / R
• Suppose stock is expected to pay a
$0.50 dividend every quarter and the
required return is 10% with quarterly
compounding. What is the price?
P0 
0 . 50
. 10
 $ 20
4
7-42
Constant Growth Stock
One whose dividends are expected to
grow forever at a constant rate, g.
D1 = D0(1+g)1
D2 = D0(1+g)2
Dt = Dt(1+g)t
D0 = Dividend JUST PAID
D1 – Dt = Expected dividends
7-43
Projected Dividends
• D0 = $2.00 and constant g = 6%
• D1 = D0(1+g) = 2(1.06)
= $2.12
• D2 = D1(1+g) = 2.12(1.06) = $2.2472
• D3 = D2(1+g) = 2.2472(1.06)
=
$2.3820
7-44
Dividend Growth Model

(1  g )
ˆ
P0  D 0 
t
t  1 (1  R )
^
D0(1+g)
P0 =
R-g
t
D1
=
R-g
“Gordon Growth Model”
7-45
DGM – Example 1
• Suppose Big D, Inc. just paid a dividend of $.50.
It is expected to increase its dividend by 2% per
year. If the market requires a return of 15% on
assets of this risk, how much should the stock be
selling for?
• D0= $0.50
P0 
D 0 (1  g )
Rg
• g = 2%
• R = 15%
P0 
0 . 50 (1  . 02 )
. 15  . 02
 $ 3 . 92
7-46
Constant Growth Model Conditions
1.
2.
3.
4.
Dividend expected to grow at g forever
Stock price expected to grow at g forever
Expected dividend yield is constant
Expected capital gains yield is constant
and equal to g
5. Expected total return, R, must be > g
6. Expected total return (R):
= expected dividend yield (DY)
+ expected growth rate (g)
= dividend yield + g
7-47
Nonconstant Growth
• Suppose a firm is expected to increase
dividends by 20% in one year and by 15%
in two years. After that dividends will
increase at a rate of 5% per year
indefinitely. If the last dividend was $1 and
the required return is 20%, what is the
price of the stock?
• Remember that we have to find the PV of
all expected future dividends.
7-48
Nonconstant Growth – Solution
• Compute the dividends until growth levels off
– D1 = 1(1.2) = $1.20
– D2 = 1.20(1.15) = $1.38
– D3 = 1.38(1.05) = $1.449
• Find the expected future price at the beginning
of the constant growth period:
– P2 = D3 / (R – g) = 1.449 / (.2 - .05) = 9.66
• Find the present value of the expected future
cash flows
– P0 = 1.20 / (1.2) + (1.38 + 9.66) / (1.2)2 = 8.67
7-49
Nonconstant + Constant
growth
Basic PV of all Future Dividends Formula
ˆ 
P
0
D1
1  R

1
D2

1  R

2

D3
1  R 
3
D
 ... 

1  R
Dividend Growth Model
ˆ 
P
t
D t 1
R g
7-50
Nonconstant + Constant growth
ˆ 
P
0
D1
D2
P2


1
2
2
1  R 1  R (1  R)

Because
Dt
P2  
t
(
1

R
)
t 3
If g constant after t  2, then
D3
P2 
Rg
7-51
Using the DGM to Find R
Start with the DGM:
P0 
D 0 (1  g)
R - g
D1

R -g
Rearrange and solve for R:
R 
D 0 (1  g)
P0
 g 
D1
 g
P0
7-52
Finding the Required Return
Example
• A firm’s stock is selling for $10.50.
They just paid a $1 dividend and
dividends are expected to grow at
5% per year.
• What is the required return?
7-53
Finding the Required Return
Example
•
•
•
•
P0 = $10.50.
D0 = $1
g = 5% per year.
What is the required return?
R 
D 0 (1  g)
P0
R 
1.00(1.05)
10.50
g
D1
g
P0
 . 05  15 %
7-54
Finding the Required Return
Example
•
•
•
•
P0 = $10.50
D0 = $1
g = 5% per year
What is the dividend
yield?
1(1.05) / 10.50 = 10%
• What is the capital
gains yield?
g =5%
R 
D 0 (1  g)
 g
P0
R 
D1
 g
P0
R 
1.00(1.05)
 . 05  15 %
10.50
Dividend
Yield
Capital Gains
Yield
7-55
Table 7.1
7-56
Features of Common Stock
• Voting Rights
– Stockholders elect directors
– Cumulative voting vs. Straight voting
– Proxy voting
• Classes of stock
– Founders’ shares
– Class A and Class B shares
Return to
Quick Quiz
7-57
Features of Common Stock
• Other Rights
– Share proportionally in declared
dividends
– Share proportionally in remaining assets
during liquidation
– Preemptive right
• Right of first refusal to buy new stock issue
to maintain proportional ownership if
desired
Return to
Quick Quiz
7-58
Dividend Characteristics
• Dividends are not a liability of the firm until
declared by the Board of Directors
– A firm cannot go bankrupt for not declaring
dividends
• Dividends and Taxes
– Dividends are not tax deductible for firm
– Taxed as ordinary income for individuals
– Dividends received by corporations have a
minimum 70% exclusion from taxable income
7-59