Transcript Chapter 4: The valuation of long

Chapter 4: The valuation of longterm securities
• Study objectives
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Distinctions among valuation concepts
Bond valuation
Preferred stock valuation
Common stock valuation
Rates of Return
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What does it mean?
• What is a cynic? A man who knows the
price of everything and the value of
nothing.---Oscar Wilde
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Why shall we know the valuation
of long-term securities?
• Make investment decisions
• Determine the value of the firm
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Distinctions among valuation
concepts
• Liquidation value versus going-concern value
– Liquidation value is the amount of money that could be
realized if an asset or a group of assets (e.g., a firm) is
sold separately from its operating organization.
– Going-concern value is the amount a firm could be sold
for as a continuing operating business
• The computation of liquidation value and goingconcern value is very different
– As in accounting, the security valuation models that we
will discuss in this chapter will generally assume that
we are dealing with going-concern
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Book value versus market value
• The book value of an asset is the accounting value
of the asset---the asset’s cost minus its
accumulated depreciation.
• The book value of a firm is equal the dollar
difference between the firm’s total assets and its
liabilities and preferred stock as listed on its
balance sheet
– Because book value is based on historic values and
estimations, it may not be accurate after a long period
of time
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Book value versus market value
• In general, the market value of an asset is simply
the market price at which the asset (or a similar
asset) trades in an open market place.
• For a firm, market value often viewed as being the
higher of the firm’s liquidation or going concern
value
– Market value often outrival book value as to decision
relevance, because market value takes risk, future
opportunity, current cash flow in account.
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Market value versus intrinsic
value
• For an actively traded security, the market value
would be the last reported price at which the
security was traded.
– For an inactively traded security, an estimated market
price would be needed
• The intrinsic value of a security is what the price
of a security should be if properly priced based on
all factors bearing on valuation---assets, earnings,
future prospects, management, and so on.
– If markets are reasonably efficient and informed, the
current market price of a security should fluctuate
closely around its intrinsic value
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The valuation approach
• The valuation approach taken in this chapter
is one of determining a security’s intrinsic
value. This value is the present value of the
cash flow stream provided to the investor,
discounted at a required rate of return
appropriate for the risk involved
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Bond valuation
• A bond is a security that pays a stated amount of
interest to the investor, period after period, until it
is finally retired by the issuing company
– In China, bond interest may not be paid annually, but
until the retirement of the bond
• Face value is the stated value of an asset. In the
case of a bond, the face value is usually $1000
– The face value is supposed to be paid back to the
bondholders as the principal, no matter what the
purchasing price of the bond
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Bond Valuation
• Coupon rate: the stated rate of interest on a bond;
the annual interest payment divided by bond’s face
value
• The factors that affect the valuation of bond
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Face value
Coupon rate
Required rate of return
Maturity
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The Model of Bond Valuation
Vb 
n
MV
n
(1 r )
  (1 r )t
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It
t 1
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Perpetual Bonds
• A bond that never matures (rarely exists
now)
Vb 
n

t 1
I
(1 r ) t
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 I /r
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Bonds with a Finite Maturity
• Typical coupon bonds (limited outstanding
period, annually paid interest)
• V=I(PVIFAr,n)+MV(PVIFr,n)
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Example
• The Brothers determines to issue 10000
$1000-par-value bonds with 10% coupons.
The bonds will be retired in 9 years. The
Brothers decides to issue the bond at $1020.
If Mr. White wants to buy the bond and his
required rate of return is 8%, should Mr.
White buy the bond?
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Example
• V=$100(PVIFA8%,9)+$1000(PVIF8%,9)=$11
24.70
• Because V>P, Mr. White should buy the
bond
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Zero-coupon bond
• A zero-coupon bond is a bond that pays no
interest but sells at a deep discount from its
face value; it provides compensation to
investors in the form of price appreciation
• The interest of a zero-coupon bond is the
remainder of the face value less issuing
price
• V=MV/(1+r)n
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Example
• Suppose that Pace Enterprises issues a zerocoupon bond having a 10-year maturity and
a $1000 face value. If the investor’s
required return is 12%, then
• V=$1000/(1+12%)10=$322
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Seminal compounding of interest
• Although some bonds (typically those issued in
European Markets) make interest payments once a
year, most bonds issued in America pay interest
twice a year. As a result, it is necessary to modify
our bond valuation model
• V=(I/2)(PVIFAr/2,2n)+MV(PVIFr/2,2n), here I is the
nominal interest of the bond and n is the years that
the bond exists
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Example
• To illustrate, if the 10% coupon bonds of the U.S.
Blivet Corporation have 12 years to maturity and
our nominal annual required rate of return is 14%,
the value of one $1000-par-value bond is
• V=($50/2)(PVIFA14/2,24)+MV(PVIF14/2,24)=$770.4
5
• Why V<par value? Because required
return>coupon rate
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Preferred Stock Valuation
• Preferred stock is a type of stock that promises a
(usually) fixed dividend, but at the discretion of
the directors. It has preference over common stock
in the payment of dividends and claims on assets
• Cumulative and noncumulative preferred stock
• A cumulative preferred stock is a stock whose
dividend not paid out is deferred to later years
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Example
• To illustrate the payment of different types
of dividends, the following data from the
Boston Lakers Basketball Team will be used.
Assume that outstanding stock includes:
preferred stock (5%, $10 par value 6000
shares issued and outstanding) $60000,
common stock ($5 par value, 8000 shares
issued and outstanding) $40000
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Example
case
3
Preferred
dividend
feature
noncumula
tive
noncumula
tive
cumulative
4
cumulative 2
1
2
Years
in
arrears
---
Total
Preferred
dividend dividend
Common
dividend
2000
2000
0
---
4000
3000
1000
2
7000
7000
0
11000
9000
2000
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The valuation of preferred stock
• The payment of preferred stock is similar to an annuity, so
the valuation model of a preferred stock is :
• Vp=Dp/R
• If Margana Cipher Corporation had a 9%, $100-par-value
preferred stock issue outstanding and your required return
was 14% on this investment, its value per share to you
would be Vp=Dp/R=$64.29
• In China, no listed company has issued preferred stock
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Common stock valuation
• Common stock is the security that represent
the ultimate ownership (and risk) position in
a corporation
• The difficult issues of valuation: uncertainty
and payment of stock dividend, different
risk levels, etc.
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Are dividends the foundation
• Case 1: hold the stock for a long time
V
D1
(1 r )
n
 (1 r )2  ... (1 r ) n   (1 r )t
Dn
D2
Dt
t 1
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Are dividends the foundation
• Case 2: hold the stock for a short time (e.g.,
2 years)
• Note: D1, D2…Dn and P2 are all estimates
V
D1
(1 r )
 (1 r ) 2  (1 r )2
D2
P2
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A logical question to the models
• The logical question to raise at this time is: why do the
stocks of companies that pay no dividends have positive,
often quite high, values?
• The answer is: investors expect to sell the stock in the
future at a price higher than they paid for it.
• Terminal value depends on the expectations of the
marketplace viewed from the terminal point. The ultimate
expectation is that the firm will eventually pay dividends,
either regular or liquidating, and that future investors will
receive a company-provided cash return on their
investment
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Dividend Discount Models
• Constant Growth
• Assume that dividends grow at a constant rate. But
in real life, few companies do this. We shall learn
this in corporate finance---dividend policy
• Assume that D0 is the present dividend per share
and g is the growth rate of dividend, so D1 is (1+g)
D0 , D2 is D0 (1+g)2,…Dn is D0 (1+g)n
• According to the valuation model, constant growth
stock is valuated as:
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Constant Growth
V 
D0 (1 g )
(1 r )
 ......


D0 (1 g )
(1 r )
D0 (1 g )
(r g )

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D0 (1 g ) 2
(1 r ) 2
n
n
D1
(r g )
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Constant Growth
• Tip: a common mistake made in using the above
equation is to use, incorrectly, the firm’s most
recent annual dividend for the variable D1 instead
of the annual dividend expected by the end of the
coming year
• g can never be larger than r, why?
• Suppose that LKN, Inc.’s dividend per share at
t=1 is expected to be $4, that it is expected to
grow at a 6% rate forever, and that the appropriate
discount rate is 14%. The value of one share of
LKN stock would be V=$4/(0.14-0.06)=$50
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Conversion to an earnings
multiplier approach
• Assume that a company retains a constant
proportion of its earnings each year; call it b,
then (1-b)=D1/E1, D1=E1(1-b), V=(1-b)E1/(rg), V/E1=(1-b)/(r-g), (1-b)/(r-g) is called
earnings multiplier (EM). V=E1(EM)
• Why we should know earnings multiplier?
Because it bring together value and earnings
of a stock
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No Growth
• Assume that dividends will be maintained at
their current level forever ( a kind of
dividend policy)
• V=D1/r==D0/r. like a preferred stock
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Growth phases
• Firms may exhibit above-normal growth for a
number of years (g may even be larger than r
during this phase), but eventually the growth rate
will taper off.
• Assume that dividends per share are expected to
grow at f compound rate for m years and
thereafter at g, the valuation model is:
m
V 
t 1
D0 (1 f )
(1 r )
t
t

n

t  m 1
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Dm1 (1 g ) t m
(1 r ) t
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Example
• If dividends per share are expected to grow
at 10% compound rate for 5 years and
thereafter at 6%, the required rate is 14%,
how to value the stock?
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Example
5

t 1
$2 (1.10 ) t
(1.14 )
t
 $8.99
[$2 (1.10 ) (1.06 ) /(0.14 0.06 )]
5
(1.14 )
5
 $22.13
$22.13  $8.99  $31.12
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Rates of Return
• If we replace intrinsic value in our valuation
equations with the market price (p0) of the
security, we can then solve for the market
required rate of return.
• This rate, which sets the discounted value of
the expected cash inflows equal to the
security’s current market price, is also
referred to as the security’s market yield
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Rate of return
• It is important to recognize that only when the
intrinsic value of a security to an investor equals
the security’s market value (price) would the
investor’s required rate of return equal the
security’s (market) yield
• Market yields serve an essential function by
allowing us to compare, on a uniform basis,
securities that differ in cash flow provided,
maturities, and current prices
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Yield to maturity (YTM) on
bonds
• Yield to maturity (YTM) is the expected rate of
return on a bond if bought at its current market
price and held to maturity; it is also known as the
bond’s internal rate of return (IRR)
• Mathematically, it is the discount rate that equates
the present value of all expected interest payments
and the payment of principal (face value) at
maturity with the bond’s current market price
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Yield to maturity
n
MV
I
P0   (1YTM

)t
(1YMT ) n
t 1
• The difficult issue is: it is not a linear
function, more complex
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Interpolation---Example
• Consider a $1000-par-value bond with the
following characteristics: a current market price of
$761; 12 years until maturity, and 8% coupon rate
(with interest paid annually)
• Suppose we start with a 10% discount rate and
calculate the present value of the bond’s expected
future cash flows.
V=$80(PVIFA10%.12)+$1000(PVIF10%.12)=$684.12
>761, so YTM>10%
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Interpolation---Example
• Try a 15% discount rate
• V=$80(PVIFA15%.12)+$1000(PVIF15%.12)=$620.68<761, so
YTM<15%
• X/0.05=(864.12-761)/(864.12-620.68)
• X=0.0212
• YTM=X+10%=12.12%
• It is important to keep in mind that interpolation gives only
an approximation of the exact percentage; the relationship
between the two discount rate is not linear with respect to
present value
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Behavior of bond price
• When the market required rate of return is more
than the stated coupon rate, the price of the bond
will be less than its face value---bond discount
• When the market required rate of return is less
than the stated coupon rate, the price of the bond
will be more than its face value---bond premium
• When the market required rate of return equals the
stated coupon rate, the price of the bond will equal
its face value---selling at par
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Behavior of bond price
• If interest rates rise so that the market required
rate of return increases, the bond’s price will fall.
If interest rates fall, the bond’s price will increase
• For a given change in market required return, the
price of a bond will change by a greater amount,
the longer its maturity
• Bond price volatility is inversely related to coupon
rate
• Figure 4-1 relation between bond price and market
required rate of return
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YTM and Semiannual
Compounding
2n
P0  
t 1
I /2
(1 r / 2 ) t
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
MV
(1 r / 2 ) 2 n
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Yield on preferred stock and
common stock
• P0=Dp/r
• P0=D1/(r-g)
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