bonds and stock valuation
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1
The Valuation of The Valuation of Long-Term Long-Term SecuritiesSecurities
The Valuation of The Valuation of Long-Term Long-Term SecuritiesSecurities
Bond & Stock Bond & Stock ValuationValuation
Bond & Stock Bond & Stock ValuationValuation
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The Valuation of The Valuation of Long-Term SecuritiesLong-Term Securities
The Valuation of The Valuation of Long-Term SecuritiesLong-Term Securities
Distinctions Among Valuation Concepts
Bond Valuation
Preferred Stock Valuation
Common Stock Valuation
Rates of Return (or Yields)
Distinctions Among Valuation Concepts
Bond Valuation
Preferred Stock Valuation
Common Stock Valuation
Rates of Return (or Yields)
3
What is Value?What is Value?What is Value?What is Value?
Going-concern valueGoing-concern value represents the amount a firm could be sold for as a continuing operating business.
Going-concern valueGoing-concern value represents the amount a firm could be sold for as a continuing operating business.
Liquidation valueLiquidation value represents the amount of money that could be realized if an asset or group of assets is sold separately from its operating organization.
Liquidation valueLiquidation value represents the amount of money that could be realized if an asset or group of assets is sold separately from its operating organization.
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In general, the value of an asset is the price that a willing and able buyer pays to a willing and able seller
Note that if either the buyer or seller is not both willing and able, then an offer does not establish the value of the asset
What is Value?What is Value?What is Value?What is Value?
5
Several Kinds of “ValueSeveral Kinds of “Value””
There are several types of value, of which we are concerned with three: Book Value - The asset’s historical cost less
its accumulated depreciation Market Value - The price of an asset as
determined in a competitive marketplace Intrinsic Value - The present value of the
expected future cash flows discounted at the decision maker’s required rate of return
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Bond ValuationBond ValuationBond ValuationBond Valuation
Important Terms
Types of Bonds
Valuation of Bonds
Handling Semiannual Compounding
Important Terms
Types of Bonds
Valuation of Bonds
Handling Semiannual Compounding
7
BondsBonds
A bond is a tradeable instrument that represents a debt owed to the owner by the issuer. Most commonly, bonds pay interest periodically (usually semiannually) and then return the principal at maturity.
Most corporate, and some government, bonds are callable. That means that at the company’s option, it may force the bondholders to sell them back to the company.
(Refer to the bonds valuation handout)
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Bond TerminologyBond Terminology
There are several terms with which you must be familiar to solve bond valuation problems: Coupon Rate - This is the stated rate of interest on the bond.
It is fixed for the life of the bond. Also, this rate time the face value determines the annual interest payment amount.
Discount Rate - (capitalization rate or market required rate of return) is dependent on the risk of the bond and is composed of the risk-free rate plus a premium for risk.
Face Value - This is the principal amount (nominally, the amount that was borrowed). This is the amount that will be repaid at maturity
Maturity Date - This is the date after which the bond no longer exists. It is also the date on which the loan is repaid and the last interest payment is made.
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Calculating the Value of a BondCalculating the Value of a Bond
There are two types of cash flows that are provided by a bond investments: Periodic interest payments (usually every six months,
but any frequency is possible) Repayment of the face value (also called the principal
amount, which is usually $1,000) at maturity The following timeline illustrates a typical bond’s cash
flows:
0 1 2 3 4 5
100 100 100 100 1001,000
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We can use the principle of value additivity to find the value of this stream of cash flows
Note that the interest payments are an annuity, and that the face value is a lump sum
Therefore, the value of the bond is simply the present value of the annuity-type cash flow and the lump sum:
Calculating the Value of a Bond Calculating the Value of a Bond (Cont) (Cont)
DiscussedIn the
subsequent slides
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Different Types of BondsDifferent Types of BondsDifferent Types of BondsDifferent Types of Bonds
Perpetual Bond
Non-Zero Coupon Bond
Zero Coupon Bond
Perpetual Bond
Non-Zero Coupon Bond
Zero Coupon Bond
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Different Types of BondsDifferent Types of BondsDifferent Types of BondsDifferent Types of Bonds
A perpetual bondperpetual bond is a bond that never matures. It has an infinite life.
A perpetual bondperpetual bond is a bond that never matures. It has an infinite life.
(1 + kd)1 (1 + kd)2 (1 + kd)V = + + ... +I II
=
t=1(1 + kd)t
Ior I (PVIFA kd, )
V = II / kkdd [Reduced Form]
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Perpetual Bond ExamplePerpetual Bond ExamplePerpetual Bond ExamplePerpetual Bond Example
Bond P has a $1,000 face value and provides an 8% coupon. The appropriate discount rate is
10%. What is the value of the perpetual bondperpetual bond?
Bond P has a $1,000 face value and provides an 8% coupon. The appropriate discount rate is
10%. What is the value of the perpetual bondperpetual bond?
II = $1,000 ( 8%) = $80$80.
kkdd = 10%10%.
VV = II / kkdd [Reduced Form]
= $80$80 / 10%10% = $800 $800.
II = $1,000 ( 8%) = $80$80.
kkdd = 10%10%.
VV = II / kkdd [Reduced Form]
= $80$80 / 10%10% = $800 $800.
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Different Types of BondsDifferent Types of BondsDifferent Types of BondsDifferent Types of Bonds
A non-zero coupon-paying bondnon-zero coupon-paying bond is a coupon-paying bond with a finite life.A non-zero coupon-paying bondnon-zero coupon-paying bond is a coupon-paying bond with a finite life.
(1 + kd)1 (1 + kd)2 (1 + kd)nn
V = + + ... +I I + MVI
= nn
t=1(1 + kd)t
I
V = I (PVIFA kd, nn) + MV (PVIF kd, nn)
(1 + kd)nn
+ MV
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Bond C has a $1,000 face value and provides an 8% annual coupon for 30 years. The
appropriate discount rate is 10%. What is the value of the coupon bond?
Bond C has a $1,000 face value and provides an 8% annual coupon for 30 years. The
appropriate discount rate is 10%. What is the value of the coupon bond?
Coupon Bond ExampleCoupon Bond ExampleCoupon Bond ExampleCoupon Bond Example
VV = $80 (PVIFA10%, 30) + $1,000 (PVIF10%, 30) = $80 (9.427) + $1,000 (.057)
[[Table IVTable IV] ] [[Table IITable II]]
= $754.16 + $57.00= $811.16 $811.16 (D to R)
VV = $80 (PVIFA10%, 30) + $1,000 (PVIF10%, 30) = $80 (9.427) + $1,000 (.057)
[[Table IVTable IV] ] [[Table IITable II]]
= $754.16 + $57.00= $811.16 $811.16 (D to R)
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Coupon Bond Example Coupon Bond Example ( Ms Excel Approach)( Ms Excel Approach)
Present Value CalculationsFuture Value 1000.00Years 30Rate 10%Present Value $57.31
Present Value of an AnnuityPayment 80Interest Rate 10%Number of Payments 30Present Value $754.15
VALUE $811.46
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Different Types of BondsDifferent Types of BondsDifferent Types of BondsDifferent Types of Bonds
A zero-coupon bondzero-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.
A zero-coupon bondzero-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.
(1 + kd)nn
V =MV
= MV (PVIFkd, nn)
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VV = $1,000 (PVIF10%, 30)= $1,000 (.057)= $57.00 (D to R) $57.00 (D to R)
VV = $1,000 (PVIF10%, 30)= $1,000 (.057)= $57.00 (D to R) $57.00 (D to R)
Zero-Coupon Bond Zero-Coupon Bond ExampleExample
Zero-Coupon Bond Zero-Coupon Bond ExampleExample
Bond Z has a $1,000 face value and a 30-year life. The appropriate
discount rate is 10%. What is the value of the zero-coupon bond?
Bond Z has a $1,000 face value and a 30-year life. The appropriate
discount rate is 10%. What is the value of the zero-coupon bond?
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Non-Zero Coupon Bond Example Non-Zero Coupon Bond Example ( Ms Excel Approach)( Ms Excel Approach)
Present Value CalculationsFuture Value 1000.00Years 30Rate 10%Present Value $57.31
VALUE $57.31
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Semiannual CompoundingSemiannual CompoundingSemiannual CompoundingSemiannual Compounding
(1) Divide kkdd by 22
(2) Multiply nn by 22
(3) Divide II by 22
(1) Divide kkdd by 22
(2) Multiply nn by 22
(3) Divide II by 22
Most bonds in the U.S. pay interest twice a year (1/2 of the annual
coupon).
Adjustments needed:
Most bonds in the U.S. pay interest twice a year (1/2 of the annual
coupon).
Adjustments needed:
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(1 + kd/2 2 ) 22*nn(1 + kd/2 2 )1
Semiannual CompoundingSemiannual CompoundingSemiannual CompoundingSemiannual Compounding
A non-zero coupon bondnon-zero coupon bond adjusted for semiannual compounding.
A non-zero coupon bondnon-zero coupon bond adjusted for semiannual compounding.
V = + + ... +I / 22 I / 22 + MV
= 22*nn
t=1(1 + kd /2 2 )t
I / 22
= I/22 (PVIFAkd /2 2 ,22*nn) + MV (PVIFkd /2 2 , 22*nn)
(1 + kd /2 2 ) 22*nn+
MV
I / 22(1 + kd/2 2 )2
22
VV = $40 (PVIFA5%, 30) + $1,000 (PVIF5%, 30) = $40 (15.373) + $1,000 (.231)
[[Table IVTable IV] ] [[Table IITable II]]
= $614.92 + $231.00= $845.92 ( D to R) $845.92 ( D to R)
VV = $40 (PVIFA5%, 30) + $1,000 (PVIF5%, 30) = $40 (15.373) + $1,000 (.231)
[[Table IVTable IV] ] [[Table IITable II]]
= $614.92 + $231.00= $845.92 ( D to R) $845.92 ( D to R)
Semiannual Coupon Semiannual Coupon Bond ExampleBond Example
Semiannual Coupon Semiannual Coupon Bond ExampleBond Example
Bond C has a $1,000 face value and provides an 8% semiannual coupon for 15 years. The
appropriate discount rate is 10% (annual rate). What is the value of the coupon bond?
Bond C has a $1,000 face value and provides an 8% semiannual coupon for 15 years. The
appropriate discount rate is 10% (annual rate). What is the value of the coupon bond?
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Semi Annual Coupon Bond Example Semi Annual Coupon Bond Example
( Ms Excel Approach)( Ms Excel Approach)Present Value CalculationsFuture Value 1000.00Years 30Rate 5%Present Value $231.38
Present Value of an AnnuityPayment 40Interest Rate 5%Number of Payments 30Present Value $614.90
VALUE $846.28
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Different Types of StocksDifferent Types of Stocks
•Preferred Stock
•Common Stock
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Preferred StockPreferred Stock is a type of stock that promises a (usually) fixed dividend, but at
the discretion of the board of directors.
Preferred StockPreferred Stock is a type of stock that promises a (usually) fixed dividend, but at
the discretion of the board of directors.
Preferred Stock ValuationPreferred Stock ValuationPreferred Stock ValuationPreferred Stock Valuation
Preferred Stock has preference over common stock in the payment of dividends and claims on assets.
Preferred Stock has preference over common stock in the payment of dividends and claims on assets.
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Preferred Stock ValuationPreferred Stock ValuationPreferred Stock ValuationPreferred Stock Valuation
This reduces to a perpetuityperpetuity!This reduces to a perpetuityperpetuity!
(1 + kP)1 (1 + kP)2 (1 + kP)VV = + + ... +DivP DivPDivP
=
t=1 (1 + kP)t
DivP or DivP(PVIFA kP, )
VV = DivP / kP
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Preferred Stock ExamplePreferred Stock ExamplePreferred Stock ExamplePreferred Stock Example
DivDivPP = $100 ( 8% ) = $8.00$8.00.
kkPP = 10%10%.
VV = DivDivPP / kkPP = $8.00$8.00 / 10%10% = $80 $80
DivDivPP = $100 ( 8% ) = $8.00$8.00.
kkPP = 10%10%.
VV = DivDivPP / kkPP = $8.00$8.00 / 10%10% = $80 $80
Stock PS has an 8%, $100 par value issue outstanding. The appropriate
discount rate is 10%. What is the value of the preferred stockpreferred stock?
Stock PS has an 8%, $100 par value issue outstanding. The appropriate
discount rate is 10%. What is the value of the preferred stockpreferred stock?
Similar toPerpetual
Bonds
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Common Stock ValuationCommon Stock ValuationCommon Stock ValuationCommon Stock Valuation
Pro rata share of future earnings after all other obligations of the firm (if any remain).
Dividends maymay be paid out of the pro rata share of earnings.
Pro rata share of future earnings after all other obligations of the firm (if any remain).
Dividends maymay be paid out of the pro rata share of earnings.
Common stock Common stock represents a residual ownership position in the corporation.Common stock Common stock represents a residual ownership position in the corporation.
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Common Stock ValuationCommon Stock ValuationCommon Stock ValuationCommon Stock Valuation
(1) Future dividends
(2) Future sale of the common stock shares
(1) Future dividends
(2) Future sale of the common stock shares
What cash flows will a shareholder receive when owning shares of
common stockcommon stock?
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Dividend Valuation ModelDividend Valuation ModelDividend Valuation ModelDividend Valuation Model
Basic dividend valuation model accounts for the PV of all future dividends.
Basic dividend valuation model accounts for the PV of all future dividends.
(1 + ke)1 (1 + ke)2 (1 + ke)V = + + ... +
Div1DivDiv2
=
t=1(1 + ke)t
Divt Divt: Cash dividend at time t
ke: Equity investor’s required return
Divt: Cash dividend at time t
ke: Equity investor’s required return
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Adjusted Dividend Adjusted Dividend Valuation ModelValuation Model
Adjusted Dividend Adjusted Dividend Valuation ModelValuation Model
The basic dividend valuation model adjusted for the future stock sale.
The basic dividend valuation model adjusted for the future stock sale.
(1 + ke)1 (1 + ke)2 (1 + ke)nn
V = + + ... +Div1 Divnn + PricennDiv2
nn: The year in which the firm’s shares are expected to be sold.
Pricenn: The expected share price in year nn.
nn: The year in which the firm’s shares are expected to be sold.
Pricenn: The expected share price in year nn.
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Dividend Growth Dividend Growth Pattern AssumptionsPattern Assumptions
Dividend Growth Dividend Growth Pattern AssumptionsPattern Assumptions
The dividend valuation model requires the forecast of all future dividends. The
following dividend growth rate assumptions simplify the valuation
process.
Constant GrowthConstant Growth
No GrowthNo Growth
The dividend valuation model requires the forecast of all future dividends. The
following dividend growth rate assumptions simplify the valuation
process.
Constant GrowthConstant Growth
No GrowthNo Growth
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Constant Growth ModelConstant Growth ModelConstant Growth ModelConstant Growth Model
The constant growth model constant growth model assumes that dividends will grow forever at the rate g.
The constant growth model constant growth model assumes that dividends will grow forever at the rate g.
(1 + ke)1 (1 + ke)2 (1 + ke)V = + + ... +
D0(1+g) D0(1+g)
=(ke - g)
D1
D1: Dividend paid at time 1.
g : The constant growth rate.
ke: Investor’s required return.
D1: Dividend paid at time 1.
g : The constant growth rate.
ke: Investor’s required return.
D0(1+g)2
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Constant Growth Constant Growth Model ExampleModel Example
Constant Growth Constant Growth Model ExampleModel Example
Stock CG has an expected growth rate of 8%. Each share of stock just received an
annual $3.24 dividend per share. The appropriate discount rate is 15%. What
is the value of the common stockcommon stock?
DD11 = $3.24$3.24 ( 1 + .08 ) = $3.50$3.50
VVCGCG = DD11 / ( kkee - g ) = $3.50$3.50 / ( .15.15 - .08 ) = $50 $50
Stock CG has an expected growth rate of 8%. Each share of stock just received an
annual $3.24 dividend per share. The appropriate discount rate is 15%. What
is the value of the common stockcommon stock?
DD11 = $3.24$3.24 ( 1 + .08 ) = $3.50$3.50
VVCGCG = DD11 / ( kkee - g ) = $3.50$3.50 / ( .15.15 - .08 ) = $50 $50
ke e = D1/V + g
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Zero Growth ModelZero Growth ModelZero Growth ModelZero Growth Model
The zero growth model zero growth model assumes that dividends will grow forever at the rate g = 0.
The zero growth model zero growth model assumes that dividends will grow forever at the rate g = 0.
(1 + ke)1 (1 + ke)2 (1 + ke)
VZG = + + ... +D1 D
=ke
D1 D1: Dividend paid at time 1.
ke: Investor’s required return.
D1: Dividend paid at time 1.
ke: Investor’s required return.
D2
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Zero Growth Zero Growth Model ExampleModel ExampleZero Growth Zero Growth
Model ExampleModel Example
Stock ZG has an expected growth rate of 0%. Each share of stock just received an
annual $3.24 dividend per share. The appropriate discount rate is 15%. What
is the value of the common stockcommon stock?
Stock ZG has an expected growth rate of 0%. Each share of stock just received an
annual $3.24 dividend per share. The appropriate discount rate is 15%. What
is the value of the common stockcommon stock?
DD11 = $3.24$3.24 ( 1 + 0 ) = $3.24$3.24
VVZGZG = DD11 / ( kkee - 0 ) = $3.24$3.24 / ( .15.15 - 0 ) = $21.60 $21.60
DD11 = $3.24$3.24 ( 1 + 0 ) = $3.24$3.24
VVZGZG = DD11 / ( kkee - 0 ) = $3.24$3.24 / ( .15.15 - 0 ) = $21.60 $21.60
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Practice QuestionsPractice Questions
1. Beta Budget Brooms will pay a big $2 dividend next year on its common stock, which is currently selling at $50 per share. What is the market's required return on this investment if the dividend is expected to grow at 5% forever?
2. What is the intrinsic value of a $1,000 face value, zero-coupon bond that matures in 20 years if an investor's required rate of return for the bond is 8%? (Assume annual discounting.)
3. What is the intrinsic value of a $1,000 face value, 8% coupon paying perpetual bond if an investor's required rate of return is 6%? (Assume annual interest payments and discounting.)
4. A $250 face value share of preferred stock, pays a $20 annual dividend and investors require a 7% return on this investment. If the security is currently selling for $276, what is the difference (overvaluation) between its intrinsic and market value (rounded to the nearest whole dollar)?
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Practice QuestionsPractice Questions5. You have just purchased a 15-year, $1,000 par value bond. The
coupon rate on this bond is nine percent (9%) annually, with interest being paid each six months. If you expect to earn a 12 percent nominal rate of return on this bond, how much did you pay for it?
6. WeeWiggly Woodcarvers (WWW) common stock is currently expected to maintain its current earnings level indefinitely (earnings will stay at the current $4.00 per share). Investors in WWW expect to earn 10% on this investment since the firm anticipates retaining only 10% of earnings. What is the intrinsic value of a share of WWW?
7. You have been asked to determine the intrinsic value of a share of Quick Quilters, Inc. (QQ) common stock. The stock most recently paid a $2.00 annual dividend (D0). You expect dividends to grow at a supernormal rate of 15% for the next three years. You then expect that dividends will grow at a normal 5% rate thereafter (indefinitely). As a potential investor, you would expect to earn 10% on this investment. What is the intrinsic value of a share of QQ?
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ANSWERSANSWERS
1. 9%
2. $214.55
3. $1333.33
4. $9.71; Hence $10 ( due to rounding)
5. $793.53
6. $36.00
7. $54.55
40
Bonds &
Stocks
Yields (Rates of Return )Yields (Rates of Return )
41
Yield to MaturityYield to Maturity
The yield to maturity is an important number in bond valuation.
It is the rate which equates the market price of the bond with the value of the discounted cash flows.
That is, YTM is the kd such that the bond equation holds.
42
Determining Bond YTMDetermining Bond YTMDetermining Bond YTMDetermining Bond YTM
Determine the Yield-to-Maturity (YTM) for the coupon-paying bond
with a finite life.
Determine the Yield-to-Maturity (YTM) for the coupon-paying bond
with a finite life.
P0 = nn
t=1(1 + kd )t
I
= I (PVIFA kd , nn) + MV (PVIF kd , nn
)
(1 + kd )nn
+ MV
kd = YTM
43
44
Determining the YTMDetermining the YTMDetermining the YTMDetermining the YTM
Julie Miller want to determine the YTM for an issue of outstanding bonds at Basket Wonders (BW). BW has an issue of 10% annual coupon bonds with 15 years left to maturity. The
bonds have a current market value of $1,250$1,250.
What is the YTM?What is the YTM?
Julie Miller want to determine the YTM for an issue of outstanding bonds at Basket Wonders (BW). BW has an issue of 10% annual coupon bonds with 15 years left to maturity. The
bonds have a current market value of $1,250$1,250.
What is the YTM?What is the YTM?
45
YTM Solution (Try 9%)YTM Solution (Try 9%)YTM Solution (Try 9%)YTM Solution (Try 9%)
$1,250$1,250 = $100(PVIFA9%,15) + $1,000(PVIF9%, 15)
$1,250$1,250 = $100(8.061) + $1,000(.275)
$1,250$1,250 = $806.10 + $275.00
= $1,081.10$1,081.10[[Rate is too high!Rate is too high!]]
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YTM Solution (Try 7%)YTM Solution (Try 7%)YTM Solution (Try 7%)YTM Solution (Try 7%)
$1,250$1,250 = $100(PVIFA7%,15) + $1,000(PVIF7%, 15)
$1,250$1,250 = $100(9.108) + $1,000(.362)
$1,250$1,250 = $910.80 + $362.00
= $1,272.80$1,272.80[[Rate is too low!Rate is too low!]]
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.07 $1273
.02 YTMYTM $1250$1250 $192
.09 $1081
($23)(0.02) $192
YTM Solution (Interpolate)YTM Solution (Interpolate)YTM Solution (Interpolate)YTM Solution (Interpolate)
$23X
X = X = .0024
YTMYTM = .07 + .0024 = .0724 or 7.24%7.24%
48
YTM Solution ( Ms Excel Approach)YTM Solution ( Ms Excel Approach)YTM (kd) of a NON-ZERO COUPOIN BOND
Present Value Calculations (PVIF) for "M.V."Future Value $1,000.00Years 15
YTM (kd) 7.22%
Present Value $351.45
Present Value of an Annuity for "INTEREST"Future Value $1,000.00Coupon Rate 10%Payment $100.00
YTM (kd) 7.22%
Number of Payments 15Present Value $898.27
VALUE $1,249.72
49
YTM = INT + {(FV – C.P)/n}
(FV + C.P)/2
= 100 + {(1000 – 1250)/15}
(1000+1250)/2
= 0.074 = 7.4%(Approximate)
Yield Approximation FormulaYield Approximation FormulaYield Approximation FormulaYield Approximation Formula
50
Determining Semiannual Determining Semiannual Coupon Bond YTMCoupon Bond YTM
Determining Semiannual Determining Semiannual Coupon Bond YTMCoupon Bond YTM
P0 = 2nn
t=1 (1 + kd /2 )t
I / 2
= (I/2)(PVIFAkd /2, 2nn) + MV(PVIFkd /2 , 2nn)
+ MV
[ 1 + (kd / 2) ]2 -1 = YTM
Determine the Yield-to-Maturity (YTM) for the semiannual coupon-
paying bond with a finite life.
Determine the Yield-to-Maturity (YTM) for the semiannual coupon-
paying bond with a finite life.
(1 + kd /2 )2nn
51
Determining the Semiannual Determining the Semiannual Coupon Bond YTMCoupon Bond YTM
Determining the Semiannual Determining the Semiannual Coupon Bond YTMCoupon Bond YTM
Julie Miller want to determine the YTM for another issue of outstanding
bonds. The firm has an issue of 8% semiannual coupon bonds with 20 years left to maturity. The bonds
have a current market value of $950$950.
What is the YTM?What is the YTM?
Julie Miller want to determine the YTM for another issue of outstanding
bonds. The firm has an issue of 8% semiannual coupon bonds with 20 years left to maturity. The bonds
have a current market value of $950$950.
What is the YTM?What is the YTM?
52
Determining Semiannual Determining Semiannual Coupon Bond YTMCoupon Bond YTM
Determining Semiannual Determining Semiannual Coupon Bond YTMCoupon Bond YTM
[ 1 + (kd / 2) ]2 -1 = YTM
Determine the Yield-to-Maturity (YTM) for the semiannual coupon-
paying bond with a finite life.
Determine the Yield-to-Maturity (YTM) for the semiannual coupon-
paying bond with a finite life.
[ 1 + (.042626) ]2 -1 = .0871 or 8.71%
53
Determining Semiannual Determining Semiannual Coupon Bond YTMCoupon Bond YTM
Determining Semiannual Determining Semiannual Coupon Bond YTMCoupon Bond YTM
[ 1 + (kd / 2) ]2 -1 = YTM
This technique will calculate kd. You must then substitute it into the
following formula.
This technique will calculate kd. You must then substitute it into the
following formula.
[ 1 + (.0852514/2) ]2 -1 = .0871 or 8.71% (same result!)
54
YTM Solution ( Ms Excel Approach)YTM Solution ( Ms Excel Approach)YTM (kd) - Semi Annual Compounding
Present Value Calculations (PVIF) for "M.V."Future Value $1,000.00Years 40
YTM (kd/2) 4.263%
Present Value $188.31
Present Value of an Annuity for "INTEREST"Future Value $1,000.00Coupon Rate 4%Payment $40.00
YTM (kd/2) 4.263%
Number of Payments 40Present Value $761.70
VALUE $950.00
55
Note: The investor uses the bond's computed YTM by comparing it to his/her required rate of return on the bond after considering all risk factors. 1) If the investor's required return is
greater than the YTM, the investor should not buy the bond
2) If the investor's required return is less than the YTM, the investor should buy the bond
Guideline to YTMGuideline to YTM
56
57
Bond Price-Yield Bond Price-Yield RelationshipRelationship
Bond Price-Yield Bond Price-Yield RelationshipRelationship
Discount BondDiscount Bond -- The market required rate of return exceeds the coupon rate (Par > P0 ).
Premium BondPremium Bond ---- The coupon rate exceeds the market required rate of return (P0 > Par).
Par BondPar Bond ---- The coupon rate equals the market required rate of return (P0 = Par).
Discount BondDiscount Bond -- The market required rate of return exceeds the coupon rate (Par > P0 ).
Premium BondPremium Bond ---- The coupon rate exceeds the market required rate of return (P0 > Par).
Par BondPar Bond ---- The coupon rate equals the market required rate of return (P0 = Par).
58
Bond Price Par Bond Price Par ( Ms Excel Approach)( Ms Excel Approach)Bond Price (Par)
Coupon Rate = 10%
Present Value Calculations (PVIF) for "M.V."Future Value 1,000.00$ Years 15
YTM (kd) 10.00%
Present Value $239.39
Present Value of an Annuity for "INTEREST"Future Value $1,000.00Coupon Rate 10%Payment $100.00
YTM (kd) 10.00%
Number of Payments 15Present Value $760.61
VALUE $1,000.00
59
Bond Price Discount Bond Price Discount ( Ms Excel Approach)( Ms Excel Approach)Bond Price (Discount)
Coupon Rate = 10%
Present Value Calculations (PVIF) for "M.V."Future Value 1,000.00$ Years 15
YTM (kd) 12.00%
Present Value $182.70
Present Value of an Annuity for "INTEREST"Future Value $1,000.00Coupon Rate 10%Payment $100.00
YTM (kd) 12.00%
Number of Payments 15Present Value $681.09
VALUE $863.78
60
Bond Price Premium Bond Price Premium ( Ms Excel Approach)( Ms Excel Approach)Bond Price (Premium)
Coupon Rate = 10%
Present Value Calculations (PVIF) for "M.V."Future Value 1,000.00$ Years 15
YTM (kd) 8.00%
Present Value $315.24
Present Value of an Annuity for "INTEREST"Future Value $1,000.00Coupon Rate 10%Payment $100.00
YTM (kd) 8.00%
Number of Payments 15Present Value $855.95
VALUE $1,171.19
61
Bond Price-Yield Bond Price-Yield RelationshipRelationship
Bond Price-Yield Bond Price-Yield RelationshipRelationship
Coupon RateCoupon Rate
MARKET REQUIRED RATE OF RETURN (%)
Coupon RateCoupon Rate
MARKET REQUIRED RATE OF RETURN (%)
BO
ND
PR
ICE
($)
1000 Par
1600
1400
1200
600
00 2 4 6 8 1010 12 14 16 18
5 Year5 Year
15 Year15 Year
62
Bond Price-Yield Bond Price-Yield RelationshipRelationship
Bond Price-Yield Bond Price-Yield RelationshipRelationship
Assume that the required rate of return on a 15-year, 10% coupon-
paying bond risesrises from 10% to 12%. What happens to the bond price?
Assume that the required rate of return on a 15-year, 10% coupon-
paying bond risesrises from 10% to 12%. What happens to the bond price?
When interest rates riserise, then the market required rates of return riserise
and bond prices will fallfall.
When interest rates riserise, then the market required rates of return riserise
and bond prices will fallfall.
63
Bond Price-Yield Bond Price-Yield RelationshipRelationship
Bond Price-Yield Bond Price-Yield RelationshipRelationship
Coupon RateCoupon Rate
MARKET REQUIRED RATE OF RETURN (%)
Coupon RateCoupon Rate
MARKET REQUIRED RATE OF RETURN (%)
BO
ND
PR
ICE
($)
1000 Par
1600
1400
1200
600
00 2 4 6 8 1010 12 14 16 18
15 Year15 Year
5 Year5 Year
64
Bond Price-Yield Bond Price-Yield Relationship (Rising Rates)Relationship (Rising Rates)
Bond Price-Yield Bond Price-Yield Relationship (Rising Rates)Relationship (Rising Rates)
Therefore, the bond price has fallen fallen from $1,000 to $864.
Therefore, the bond price has fallen fallen from $1,000 to $864.
The required rate of return on a 15-year, 10% coupon-paying bond
has risenrisen from 10% to 12%.Refer
Slide # 55
65
Bond Price-Yield Bond Price-Yield RelationshipRelationship
Bond Price-Yield Bond Price-Yield RelationshipRelationship
Assume that the required rate of return on a 15-year, 10% coupon-
paying bond fallsfalls from 10% to 8%. What happens to the bond price?
Assume that the required rate of return on a 15-year, 10% coupon-
paying bond fallsfalls from 10% to 8%. What happens to the bond price?
When interest rates fallfall, then the market required rates of return fallfall
and bond prices will riserise.
When interest rates fallfall, then the market required rates of return fallfall
and bond prices will riserise.
66
Bond Price-Yield Bond Price-Yield RelationshipRelationship
Bond Price-Yield Bond Price-Yield RelationshipRelationship
Coupon RateCoupon Rate
MARKET REQUIRED RATE OF RETURN (%)
Coupon RateCoupon Rate
MARKET REQUIRED RATE OF RETURN (%)
BO
ND
PR
ICE
($)
1000 Par
1600
1400
1200
600
00 2 4 6 8 1010 12 14 16 18
15 Year15 Year
5 Year5 Year
67
Bond Price-Yield Relationship Bond Price-Yield Relationship (Declining Rates)(Declining Rates)
Bond Price-Yield Relationship Bond Price-Yield Relationship (Declining Rates)(Declining Rates)
Therefore, the bond price has risenrisen from $1,000 to $1,171.
Therefore, the bond price has risenrisen from $1,000 to $1,171.
The required rate of return on a 15-year, 10% coupon-paying bond
has fallenfallen from 10% to 8%.Refer
Slide # 56
68
The Role of Bond MaturityThe Role of Bond MaturityThe Role of Bond MaturityThe Role of Bond Maturity
Assume that the required rate of return on both the 5- and 15-year, 10% coupon-paying bonds fallfall from 10% to 8%. What happens to the changes in bond prices?
Assume that the required rate of return on both the 5- and 15-year, 10% coupon-paying bonds fallfall from 10% to 8%. What happens to the changes in bond prices?
The longer the bond maturity, the greater the change in bond price for a
given change in the market required rate of return.
The longer the bond maturity, the greater the change in bond price for a
given change in the market required rate of return.
69
Bond Price-Yield Bond Price-Yield RelationshipRelationship
Bond Price-Yield Bond Price-Yield RelationshipRelationship
Coupon RateCoupon Rate
MARKET REQUIRED RATE OF RETURN (%)
Coupon RateCoupon Rate
MARKET REQUIRED RATE OF RETURN (%)
BO
ND
PR
ICE
($)
1000 Par
1600
1400
1200
600
00 2 4 6 8 1010 12 14 16 18
15 Year15 Year
5 Year5 Year
70
Bond Maturity Bond Maturity ( Ms Excel Approach)( Ms Excel Approach)
Coupon Rate = 10%Present Value Calculations (PVIF) for "M.V."Future Value 1000.00Years 5
YTM (kd) 8.00%
Present Value $680.58
Present Value of an Annuity for "INTEREST"Future Value $1,000.00Coupon Rate 10%Payment $100.00
YTM (kd) 8.00%
Number of Payments 5Present Value $399.27
VALUE $1,079.85
5-YEAR MATURITY
71
Bond Maturity Bond Maturity ( Ms Excel Approach)( Ms Excel Approach)
Coupon Rate = 10%Present Value Calculations (PVIF) for "M.V."Future Value 1000.00Years 15
YTM (kd) 8.00%
Present Value $315.24
Present Value of an Annuity for "INTEREST"Future Value $1,000.00Coupon Rate 10%Payment $100.00
YTM (kd) 8.00%
Number of Payments 15Present Value $855.95
VALUE $1,171.19
15-YEAR MATURITY
72
The Role of Bond MaturityThe Role of Bond MaturityThe Role of Bond MaturityThe Role of Bond Maturity
The 5-year bond price has risenrisen from $1,000 to $1,080 for the 5-year bond
(+8.0%).
The 15-year bond price has risenrisen from $1,000 to $1,171 (+17.1%). Twice as fastTwice as fast!!
The 5-year bond price has risenrisen from $1,000 to $1,080 for the 5-year bond
(+8.0%).
The 15-year bond price has risenrisen from $1,000 to $1,171 (+17.1%). Twice as fastTwice as fast!!
The required rate of return on both the 5- and 15-year, 10% coupon-paying bonds has fallenfallen from 10% to 8%.
73
The Role of the The Role of the Coupon RateCoupon Rate
The Role of the The Role of the Coupon RateCoupon Rate
For a given change in the market required rate of return, the price of a bond will change
by proportionally more, the lowerlower the coupon rate.
For a given change in the market required rate of return, the price of a bond will change
by proportionally more, the lowerlower the coupon rate.
74
Example of the Role of Example of the Role of the Coupon Ratethe Coupon Rate
Example of the Role of Example of the Role of the Coupon Ratethe Coupon Rate
Assume that the market required rate of return on two equally risky 15-year
bonds is 10%. The coupon rate for Bond H is 10% and Bond L is 8%.
What is the rate of change in each of the bond prices if market required
rates fall to 8%?
Assume that the market required rate of return on two equally risky 15-year
bonds is 10%. The coupon rate for Bond H is 10% and Bond L is 8%.
What is the rate of change in each of the bond prices if market required
rates fall to 8%?
75
Example of the Role of the Example of the Role of the Coupon RateCoupon Rate
Example of the Role of the Example of the Role of the Coupon RateCoupon Rate
The price for Bond H will rise from $1,000 to $1,171 (+17.1%).
The price for Bond L will rise from $848 to $1,000 (+17.9%). It rises fasterIt rises faster!!
The price for Bond H will rise from $1,000 to $1,171 (+17.1%).
The price for Bond L will rise from $848 to $1,000 (+17.9%). It rises fasterIt rises faster!!
The price on Bonds H and L prior to the change in the market required rate of
return is $1,000 and $848, respectively.
76
Lower Coupon Rate Lower Coupon Rate ( Ms Excel Approach)( Ms Excel Approach)
Present Value Calculations (PVIF) for "M.V."Future Value 1000.00Years 15
YTM (kd) 10.00%
Present Value $239.39
Present Value of an Annuity for "INTEREST"Future Value $1,000.00Coupon Rate 10%Payment $100.00
YTM (kd) 10.00%
Number of Payments 15Present Value $760.61
VALUE $1,000.00
BOND H (COUPON RATE = 10%)
77
Lower Coupon Rate Lower Coupon Rate ( Ms Excel Approach)( Ms Excel Approach)
Present Value Calculations (PVIF) for "M.V."Future Value 1000.00Years 15
YTM (kd) 10.00%
Present Value $239.39
Present Value of an Annuity for "INTEREST"Future Value $1,000.00Coupon Rate 8%Payment $80.00
YTM (kd) 10.00%
Number of Payments 15Present Value $608.49
VALUE $847.88
BOND L (COUPON RATE = 8%)
78
Determining the Yield on Determining the Yield on Preferred StockPreferred Stock
Determining the Yield on Determining the Yield on Preferred StockPreferred Stock
Determine the yield for preferred stock with an infinite life.
P0 = DivP / kP
Solving for kP such that
kP = DivP / P0
Determine the yield for preferred stock with an infinite life.
P0 = DivP / kP
Solving for kP such that
kP = DivP / P0
Recallfrom
slide #26
79
Preferred Stock Yield Preferred Stock Yield ExampleExample
Preferred Stock Yield Preferred Stock Yield ExampleExample
kP = $10 / $100.
kkPP = 10%10%.
kP = $10 / $100.
kkPP = 10%10%.
Assume that the annual dividend on each share of preferred stock is $10.
Each share of preferred stock is currently trading at $100. What is
the yield on preferred stock?
Assume that the annual dividend on each share of preferred stock is $10.
Each share of preferred stock is currently trading at $100. What is
the yield on preferred stock?
80
Determining the Yield on Determining the Yield on Common StockCommon Stock
Determining the Yield on Determining the Yield on Common StockCommon Stock
Assume the constant growth model is appropriate. Determine the yield
on the common stock.
P0 = D1 / ( ke - g )
Solving for ke such that
ke = ( D1 / P0 ) + g
Assume the constant growth model is appropriate. Determine the yield
on the common stock.
P0 = D1 / ( ke - g )
Solving for ke such that
ke = ( D1 / P0 ) + g
Recallfrom
slide #34
81
Common Stock Common Stock Yield ExampleYield Example
Common Stock Common Stock Yield ExampleYield Example
ke = ( $3 / $30 ) + 5%
kkee = 15%15%
ke = ( $3 / $30 ) + 5%
kkee = 15%15%
Assume that the expected dividend (D1) on each share of common stock is $3. Each share of common stock
is currently trading at $30 and has an expected growth rate of 5%. What is
the yield on common stock?
Assume that the expected dividend (D1) on each share of common stock is $3. Each share of common stock
is currently trading at $30 and has an expected growth rate of 5%. What is
the yield on common stock?
82
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