Transcript No Slide Title

Chapter
7
Valuation
Introduction to Finance
Lawrence J. Gitman
Jeff Madura
Learning Goals
Describe the key inputs and basic model
used in the valuation process.
Review the basic bond valuation model.
Discuss bond value behavior, particularly the impact
that required return and time to maturity have
on bond value.
Explain yield to maturity and the procedure
used to value bonds that pay interest annually.
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Learning Goals
Perform basic common stock valuation using each
of three models: zero-growth, constant-growth,
and variable-growth.
Understand the relationships among financial decisions,
return, risk, and stock value.
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Valuation Fundamentals
 The (market) value of any investment asset
is simply the present value of expected cash flows.
 The interest rate that these cash flows are discounted
at is called the asset’s required return.
 The required return is a function of the expected rate
of inflation and the perceived risk of the asset.
 Higher perceived risk results in a higher required
return and lower asset market values.
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Basic Valuation Model
V0 =
CF1
(1 +
k)1
+
CF2
(1 +
k)2
+...+
CFn
(1 + k)n
Where:
V0 = value of the asset at time zero
CFt = cash flow expected at the end of year t
k = appropriate required return
(discount rate)
n = relevant time period
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Basic Valuation Model
 Using present value interest factor notation, PVIFk,n
from Chapter 5, the previous equation can be rewritten as:
V0 = [(CF1 x PVIFk,1)] + [CF2 x (PVIFk,2)] + … + [CFn x (PVIFk,n)]
 Example
 Nina Diaz, a financial analyst for King industries, a diversified
holding company, wishes to estimate the value of three of its
assets—common stock in Unitech, an interest in an oil well,
and an original painting by a well-known artist. Forecasted cash
flows, required returns, and the resulting present values are
shown in Table 7.1 on the following two slides.
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Basic Valuation Model
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Table 7.1 (Panel 1)
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Basic Valuation Model
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Table 7.1 (Panel 2)
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Bond Fundamentals
 A bond is a long-term debt instrument that pays
the bondholder a specified amount of periodic
interest over a specified period of time.
 Note: a bond is equal to debt.
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Bond Fundamentals
 The bond’s principal is the amount borrowed by the
company and the amount owed to the bondholder
on the maturity date.
 The bond’s maturity date is the time at which a bond
becomes due and the principal must be repaid.
 The bond’s coupon rate is the specified interest rate
(or dollar amount) that must be periodically paid.
 The bond’s current yield is the annual interest (income)
divided by the current price of the security.
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Bond Fundamentals
 The bond’s yield to maturity is the yield (expressed
as a compound rate of return) earned on a bond
from the time it is acquired until the maturity date
of the bond.
 A yield curve graphically shows the relationship
between the time to maturity and yields for debt
in a given risk class.
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Bonds with Maturity Dates
 Annual Compounding
B0 =
I1
(1 +
i)1
+
I2
(1 +
i)2
+...+
(In + Pn)
(1 + i)n
 For example, find the price of a 10% coupon bond
with three years to maturity if market interest rates
are currently 10%.
B0 =
100
(1 + .10)1
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+
100
(1 + i)2
+
(100 + 1,000)
(1 + .10)3
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Bonds with Maturity Dates
 Annual Compounding
 Using Microsoft® Excel
• For example, find the price of a 10% coupon bond with three
years to maturity if market interest rates are currently 10%.
Note: the equation
for calculating price is
=PV(rate,nper,pmt,fv)
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Bonds with Maturity Dates
 Annual Compounding
 Using Microsoft® Excel
• For example, find the price of a 10% coupon bond with three
years to maturity if market interest rates are currently 10%.
When the coupon rate
matches the discount rate,
the bond always sells for its
par value.
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Bonds with Maturity Dates
 Annual Compounding
 Using Microsoft® Excel
• What would happen to the bond’s price if interest rates
increased from 10% to 15%?
When the interest rate goes
up, the bond price will
always go down.
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Bonds with Maturity Dates
 Annual Compounding
 Using Microsoft® Excel
• What would happen to the bond’s price it had a 15-year
maturity rather than a 3-year maturity?
And the longer the maturity,
the greater the price decline.
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Bonds with Maturity Dates
 Annual Compounding
 Using Microsoft® Excel
• What would happen to the original 3-year bond’s price
if interest rates dropped from 10% to 5%?
When interest rates go down,
bond prices will always go up.
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Bonds with Maturity Dates
 Annual Compounding
 Using Microsoft® Excel
• What if we considered a similar bond, but with a 15-year
maturity rather than a 3-year maturity?
And the longer the maturity,
the greater the price increase
will be.
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Graphically
Bond prices go down
As interest rates go up
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Bonds with Maturity Dates
 Semi-Annual Compounding
 Using Microsoft® Excel
• If we had the same bond, but with semi-annual coupon
payments, we would have to divide the 10% coupon rate
by two, divided the discount rate by two, and multiply n by
two.
For the original example, divide
the 10% coupon by 2, divide
the 15% discount rate by 2,
and multiply 3 years by 2.
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Bonds with Maturity Dates
 Semi-Annual Compounding
 Using Microsoft® Excel
• If we had the same bond, but with semi-annual coupon
payments, we would have to divide the 10% coupon rate
by two, divided the discount rate by two, and multiply n by
two.
Thus, the value is slightly larger
than the price of the annual
coupon bond (1,136.16)
because the investor receives
payments sooner.
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Coupon Effects
on Price Volatility
 The amount of bond price volatility depends on three basic factors:
 Length of time to maturity
 Risk
 Amount of coupon interest paid by the bond
 First, we already have seen that the longer the term to maturity,
the greater is a bond’s volatility.
 Second, the riskier a bond, the more variable the required return
will be, resulting in greater price volatility.
 Finally, the amount of coupon interest also impacts a bond’s
price volatility.
 Specifically, the lower the coupon rate, the greater will be the bond’s
volatility, because it will be longer before the investor receives
a significant portion (the par value) of the cash flow from his
or her investment.
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Coupon Effects
on Price Volatility
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Price Converges
on Par at Maturity
 It is also important to note that a bond’s price will
approach par value as it approaches the maturity date,
regardless of the interest rate and regardless of the
coupon rate.
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Price Converges
on Par at Maturity
 It is also important to note that a bond’s price will approach par
value as it approaches the maturity date, regardless of the interest
rate and regardless of the coupon rate.
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Yields
 The current yield measures the annual return
to an investor based on the current price.
Current yield =
Annual coupon interest
Current market price
 For example, a 10% coupon bond which is currently
selling at $1,150 would have a current yield of:
Current yield =
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$100
$1,150
= 8.7%
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Yields
 The yield to maturity measures the compound annual
return to an investor and considers all bond cash flows.
It is essentially the bond’s IRR based on the current price.
PV =
I1
(1 +
i)1
+
I2
(1 +
i)2
+...+
(In + Pn)
(1 + i)n
 Notice that this is the same equation we saw earlier when
we solved for price. The only difference then was that we
were solving for a different unknown. In this case, we
know the market price but are solving for return.
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Yields
 The yield to maturity measures the compound annual return to an
investor and considers all bond cash flows. It is essentially the bond’s
IRR based on the current price.
 Using Microsoft® Excel
 For example, suppose we wished to determine the YTM on the following bond.
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Yields
 The yield to maturity measures the compound annual return to an
investor and considers all bond cash flows. It is essentially the bond’s
IRR based on the current price.
 Using Microsoft® Excel
 For example, suppose we wished to determine the YTM on the following bond.
To compute the yield
on this bond we simply
listed all of the bond
cash flows in a column
and computed the IRR.
=IRR(d10:d20)
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Yields
 The yield to maturity measures the compound annual
return to an investor and considers all bond cash flows.
It is essentially the bond’s IRR based on the current price.
 Note that the yield to maturity will only be equal to the current
yield if the bond is selling for its face value ($1,000).
 And that rate will also be the same as the bond’s coupon rate.
 For premium bonds, the current yield > YTM.
 For discount bonds, the current yield < YTM.
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Common Stock Valuation
 Stock returns are derived from both dividends
and capital gains, where the capital gain results
from the appreciation of the stock’s market price due
to the growth in the firm’s earnings. Mathematically,
the expected return may be expressed as follows:
E(r) = D/P + g
 For example, if the firm’s $1 dividend on a $25 stock
is expected to grow at 7%, the expected return is:
E(r) = 1/25 + .07 = 11%
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Stock Valuation Models
 The Basic Stock Valuation Equation
P0 =
D1
(1 + k)1
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+
D2
(1 + k)2
+...+
Dn
(1 + k)n
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Stock Valuation Models
 The Zero Growth Model
 The zero dividend growth model assumes
that the stock will pay the same dividend each year,
year after year.
 For assistance and illustration purposes,
I have developed a spreadsheet tutorial
using Microsoft® Excel.
 A non-functional excerpt from the spreadsheet
appears on the following slide.
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Stock Valuation Models
 The Zero Growth Model
 Using Microsoft® Excel
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Stock Valuation Models
 The Zero Growth Model
 Using Microsoft® Excel
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Stock Valuation Models
 The Constant Growth Model
 The constant dividend growth model assumes that
the stock will pay dividends that grow at a constant
rate each year, year after year.
 For assistance and illustration purposes,
I have developed a spreadsheet tutorial using
Microsoft® Excel.
 A non-functional excerpt from the spreadsheet
appears on the following slide.
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Stock Valuation Models
 The Constant Growth Model
 Using Microsoft® Excel
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Stock Valuation Models
 The Constant Growth Model
 Using Microsoft® Excel
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Stock Valuation Models
 Variable Growth Model
 The non-constant (variable) dividend growth model
assumes that the stock will pay dividends that grow at
one rate during one period, and at another rate in
another year or thereafter.
 A non-functional excerpt from the spreadsheet
appears on the following slide.
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Stock Valuation Models
 The Variable Growth Model
 Using Microsoft® Excel
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Stock Valuation Models
 The Variable Growth Model
 Using Microsoft® Excel
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Stock Valuation Models
 The Variable Growth Model
 Using Microsoft® Excel
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Stock Valuation Models
 The Variable Growth Model
 Using Microsoft® Excel
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Decision Making
and Common Stock Value
 Changes in Dividends or Dividend Growth
 Valuation equations measure the stock value at a point in time
based on expected return and risk.
 Changes in expected dividends or dividend growth can have a
profound impact on the value of a stock.
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Decision Making
and Common Stock Value
 Changes in Dividends or Dividend Growth
 Changes in risk and required return can also have significant
effects on price.
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Decision Making
and Common Stock Value
 Changes in Dividends or Dividend Growth
 Changes in expected dividends or dividend growth
can have a profound impact on the value of a stock.
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Using Microsoft® Excel
 The Microsoft® Excel Spreadsheets used
in the this presentation can be downloaded
from the Introduction to Finance companion
web site: http://www.awl.com/gitman_madura
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Chapter
Introduction to Finance
7
End of Chapter
Lawrence J. Gitman
Jeff Madura