Chapter 4 -- The Valuation of Long-Term Securities

4.1

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Chapter 4Chapter 4

The Valuation ofLong-TermSecuritiesThe Valuation ofLong-TermSecurities

4.2

Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer.

After studying Chapter 4,you should be able to:After studying Chapter 4,you should be able to:

1.Distinguish among the various terms usedto express value.

2.Value bonds, preferred stocks, and commonstocks.

3.Calculate the rates of return (or yields) ofdifferent types of long-term securities.

4.List and explain a number of observationsregarding the behavior of bond prices.

4.3

Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer.

The Valuation ofLong-Term SecuritiesThe Valuation ofLong-Term Securities

•Distinctions Among ValuationConcepts

•Bond Valuation

•Preferred Stock Valuation

•Common Stock Valuation

•Rates of Return (or Yields)

•Distinctions Among ValuationConcepts

•Bond Valuation

•Preferred Stock Valuation

•Common Stock Valuation

•Rates of Return (or Yields)

4.4

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What is Value?What is Value?

•Going-concern value •Going-concern value represents theamount a firm could be sold for as acontinuing operating business.

•Liquidation value •Liquidation value represents theamount of money that could berealized if an asset or group ofassets is sold separately from itsoperating organization.

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Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer.

What is Value?What is Value?

(2) a firm: total assets minusliabilities and preferred stock aslisted on the balance sheet.

•Book value •Book value represents either:

(1) an asset: the accounting valueof an asset – the asset’s costminus its accumulateddepreciation;

•Book value •Book value represents either:

(1) an asset: the accounting valueof an asset – the asset’s costminus its accumulateddepreciation;

4.6

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What is Value?What is Value?

•Intrinsic value •Intrinsic value represents theprice a security “ought to have”based on all factors bearing onvaluation.

•Market value •Market value represents themarket price at which an assettrades.

4.7

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Bond ValuationBond Valuation

•Important Terms

•Types of Bonds

•Valuation of Bonds

•Handling SemiannualCompounding

•Important Terms

•Types of Bonds

•Valuation of Bonds

•Handling SemiannualCompounding

4.8

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Important Bond TermsImportant Bond Terms

maturity value MV•The maturity value (MV) [or facevalue] of a bond is the statedvalue. In the case of a US bond,the face value is usually $1,000.

bond•A bond is a long-term debtinstrument issued by acorporation or government.

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Important Bond TermsImportant Bond Terms

discount rate•The discount rate (capitalization rate)is dependent on the risk of the bondand is composed of the risk-free rateplus a premium for risk.

coupon rate •The bond’s coupon rate is the statedrate of interest; the annual interestpayment divided by the bond’s facevalue.

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Different Types of BondsDifferent Types of Bonds

perpetual bondA perpetual bond is a bond that nevermatures. It has an infinite life.

(1 + kd)1

(1 + kd)2

(1 + kd)

V =

+ ... +

= 



t=1

(1 + kd)t

or I (PVIFA kd,  )

IkdV = I / kd [Reduced Form]

4.11

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Perpetual Bond ExamplePerpetual Bond Example

perpetual bondBond P has a $1,000 face value andprovides an 8% annual coupon. Theappropriate discount rate is 10%. What isthe value of the perpetual bond?

I$80 I = $1,000 ( 8%) = $80.

kd10% kd = 10%.

VIkd V = I / kd [Reduced Form]

$8010% $800 = $80 / 10% = $800.

I$80 I = $1,000 ( 8%) = $80.

kd10% kd = 10%.

VIkd V = I / kd [Reduced Form]

$8010% $800 = $80 / 10% = $800.

4.12

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N:“Trick” by using huge N like 1,000,000!

I/Y:10% interest rate per period (enter as 10 NOT 0.10)

PV:Compute (Resulting answer is cost to purchase)

PMT:$80 annual interest forever (8% x $1,000 face)

FV:$0 (investor never receives the face value)

“Tricking” theCalculator to Solve“Tricking” theCalculator to Solve

I/Y

PMT

Inputs

Compute

1,000,000 10 80 0

–800.0

4.13

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Different Types of BondsDifferent Types of Bonds

non-zero coupon-paying bondA non-zero coupon-paying bond is acoupon paying bond with a finite life.

(1 + kd)1

(1 + kd)2

n(1 + kd)n

V =

+ ... +

I + MV

= 

t=1

(1 + kd)t

nnV = I (PVIFA kd, n) + MV (PVIF kd, n)

n(1 + kd)n

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Bond C has a $1,000 face value and providesan 8% annual coupon for 30 years. Theappropriate discount rate is 10%. What is thevalue of the coupon bond?

Coupon Bond ExampleCoupon Bond Example

V V= $80 (PVIFA10%, 30) + $1,000 (PVIF10%, 30)= $80 (9.427) + $1,000 (.057)

[Table IV] [Table II] [Table IV] [Table II]

$811.16= $754.16 + $57.00= $811.16.

V V= $80 (PVIFA10%, 30) + $1,000 (PVIF10%, 30)= $80 (9.427) + $1,000 (.057)

[Table IV] [Table II] [Table IV] [Table II]

$811.16= $754.16 + $57.00= $811.16.

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N:30-year annual bond

I/Y:10% interest rate per period (enter as 10 NOT 0.10)

PV:Compute (Resulting answer is cost to purchase)

PMT:$80 annual interest (8% x $1,000 face value)

FV:$1,000 (investor receives face value in 30 years)

I/Y

PMT

Inputs

Compute

30 10 80 +$1,000

-811.46

Solving the CouponBond on the CalculatorSolving the CouponBond on the Calculator

(Actual, rounding

error in tables)

4.16

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Different Types of BondsDifferent Types of Bonds

zero coupon bondA zero coupon bond is a bond thatpays no interest but sells at a deepdiscount from its face value; it providescompensation to investors in the formof price appreciation.

n(1 + kd)n

V =

n= MV (PVIFkd, n)

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V $57.00V= $1,000 (PVIF10%, 30)= $1,000 (0.057)= $57.00

Zero-CouponBond ExampleZero-CouponBond Example

Bond Z has a $1,000 face value anda 30 year life. The appropriatediscount rate is 10%. What is thevalue of the zero-coupon bond?

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N:30-year zero-coupon bond

I/Y:10% interest rate per period (enter as 10 NOT 0.10)

PV:Compute (Resulting answer is cost to purchase)

PMT:$0 coupon interest since it pays no coupon

FV:$1,000 (investor receives only face in 30 years)

I/Y

PMT

Inputs

Compute

30 10 0 +$1,000

–57.31

Solving the Zero-CouponBond on the CalculatorSolving the Zero-CouponBond on the Calculator

(Actual - rounding

error in tables)

4.19

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Semiannual CompoundingSemiannual Compounding

kd2(1) Divide kd by 2

n2(2) Multiply n by 2

I2(3) Divide I by 2

kd2(1) Divide kd by 2

n2(2) Multiply n by 2

I2(3) Divide I by 2

Most bonds in the US pay interesttwice a year (1/2 of the annualcoupon).

Adjustments needed:

Most bonds in the US pay interesttwice a year (1/2 of the annualcoupon).

Adjustments needed:

4.20

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2 2n(1 + kd/2 ) 2*n

2 (1 + kd/2 )1

Semiannual CompoundingSemiannual Compounding

non-zero coupon bondA non-zero coupon bond adjusted forsemi-annual compounding.

V =

+ ... +

2I / 2

2I / 2 + MV

= 

2n2*n

t=1

2 (1 + kd /2 )t

2I / 2

22 2n2 2n= I/2 (PVIFAkd /2 ,2*n) + MV (PVIFkd /2 ,2*n)

2 2n(1 + kd /2 ) 2*n

2I / 2

2 (1 + kd/2 )2

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V V= $40 (PVIFA5%, 30) + $1,000 (PVIF5%, 30)= $40 (15.373) + $1,000 (.231)

[Table IV] [Table II] [Table IV] [Table II]

$845.92= $614.92 + $231.00= $845.92

V V= $40 (PVIFA5%, 30) + $1,000 (PVIF5%, 30)= $40 (15.373) + $1,000 (.231)

[Table IV] [Table II] [Table IV] [Table II]

$845.92= $614.92 + $231.00= $845.92

Semiannual CouponBond ExampleSemiannual CouponBond Example

Bond C has a $1,000 face value and providesan 8% semi-annual coupon for 15 years. Theappropriate discount rate is 10% (annual rate).What is the value of the coupon bond?

4.22

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N:15-year semiannual coupon bond (15 x 2 = 30)

I/Y:5% interest rate per semiannual period (10 / 2 = 5)

PV:Compute (Resulting answer is cost to purchase)

PMT:$40 semiannual coupon ($80 / 2 = $40)

FV:$1,000 (investor receives face value in 15 years)

I/Y

PMT

Inputs

Compute

30 5 40 +$1,000

–846.28

The Semiannual CouponBond on the CalculatorThe Semiannual CouponBond on the Calculator

(Actual, rounding

error in tables)

4.23

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Semiannual CouponBond ExampleSemiannual CouponBond Example

Let us use another worksheet on yourcalculator to solve this problem. Assumethat Bond C was purchased (settlementdate) on 12-31-2004 and will be redeemedon 12-31-2019. This is identical to the 15-year period we discussed for Bond C.

What is its percent of par? What is thevalue of the bond?

4.24

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Solving the Bond ProblemSolving the Bond Problem

Press:

2nd Bond

12.3104 ENTER ↓

8 ENTER ↓

12.3119 ENTER ↓

↓ ↓ ↓

10 ENTER ↓

CPT

Source: Courtesy of Texas Instruments

4.25

Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer.

Semiannual CouponBond ExampleSemiannual CouponBond Example

1.What is itspercent of par?

2.What is thevalue of thebond?

•84.628% of par(as quoted infinancial papers)

•84.628% x$1,000 facevalue = $846.28

4.26

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Preferred StockPreferred Stock is a type of stockthat promises a (usually) fixeddividend, but at the discretion ofthe board of directors.

Preferred Stock ValuationPreferred Stock Valuation

Preferred Stock has preference overcommon stock in the payment ofdividends and claims on assets.

4.27

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Preferred Stock ValuationPreferred Stock Valuation

perpetuityThis reduces to a perpetuity!

(1 + kP)1

(1 + kP)2

(1 + kP)

VV =

+ ... +

DivP

= 



t=1

(1 + kP)t

DivP

or DivP(PVIFA kP,  )

VV = DivP / kP

4.28

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Preferred Stock ExamplePreferred Stock Example

DivP$8.00kP10%VDivPkP$8.0010% $80DivP = $100 ( 8% ) = $8.00.kP = 10%.V = DivP / kP = $8.00 / 10% = $80

preferred stockStock PS has an 8%, $100 par valueissue outstanding. The appropriatediscount rate is 10%. What is the value ofthe preferred stock?

4.29

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Common Stock ValuationCommon Stock Valuation

•Pro rata share of future earningsafter all other obligations of thefirm (if any remain).

may•Dividends may be paid out ofthe pro rata share of earnings.

•Pro rata share of future earningsafter all other obligations of thefirm (if any remain).

may•Dividends may be paid out ofthe pro rata share of earnings.

Common stock Common stock represents aresidual ownership position in thecorporation.

4.30

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Common Stock ValuationCommon Stock Valuation

(1) Future dividends

(2) Future sale of the commonstock shares

(1) Future dividends

(2) Future sale of the commonstock shares

common stockWhat cash flows will a shareholderreceive when owning shares ofcommon stock?

4.31

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Dividend Valuation ModelDividend Valuation Model

Basic dividend valuation model accountsfor the PV of all future dividends.

(1 + ke)1

(1 + ke)2

(1 + ke)

V =

+ ... +

Div1

Div

Div2

= 



t=1

(1 + ke)t

Divt

Divt:Cash Dividendat time t

ke: Equity investor’srequired return

Divt:Cash Dividendat time t

ke: Equity investor’srequired return

4.32

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Adjusted DividendValuation ModelAdjusted DividendValuation Model

The basic dividend valuation modeladjusted for the future stock sale.

(1 + ke)1

(1 + ke)2

n(1 + ke)n

V =

+ ... +

Div1

nnDivn + Pricen

Div2

nn:The year in which the firm’sshares are expected to be sold.

nnPricen:The expected share price in year n.

nn:The year in which the firm’sshares are expected to be sold.

nnPricen:The expected share price in year n.

4.33

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Dividend GrowthPattern AssumptionsDividend GrowthPattern Assumptions

The dividend valuation model requires theforecast of all future dividends. Thefollowing dividend growth rate assumptionssimplify the valuation process.

Constant GrowthConstant Growth

No GrowthNo Growth

Growth PhasesGrowth Phases

The dividend valuation model requires theforecast of all future dividends. Thefollowing dividend growth rate assumptionssimplify the valuation process.

Constant GrowthConstant Growth

No GrowthNo Growth

Growth PhasesGrowth Phases

4.34

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Constant Growth ModelConstant Growth Model

constant growth model The constant growth model assumes thatdividends 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: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

4.35

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Constant GrowthModel ExampleConstant GrowthModel Example

common stockStock CG has an expected dividendgrowth rate of 8%. Each share of stockjust received an annual $3.24 dividend.The appropriate discount rate is 15%.What is the value of the common stock?

D1$3.24$3.50D1 = $3.24 ( 1 + 0.08 ) = $3.50

VCGD1ke $3.500.15 $50VCG = D1 / ( ke - g ) = $3.50 / (0.15 - 0.08 )= $50

common stockStock CG has an expected dividendgrowth rate of 8%. Each share of stockjust received an annual $3.24 dividend.The appropriate discount rate is 15%.What is the value of the common stock?

D1$3.24$3.50D1 = $3.24 ( 1 + 0.08 ) = $3.50

VCGD1ke $3.500.15 $50VCG = D1 / ( ke - g ) = $3.50 / (0.15 - 0.08 )= $50

4.36

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Zero Growth ModelZero Growth Model

zero growth model The zero growth model assumes thatdividends will grow forever at the rate g = 0.

(1 + ke)1

(1 + ke)2

(1 + ke)

VZG =

+ ... +

D

D1:Dividend paid at time 1.

ke: Investor’s required return.

D1:Dividend paid at time 1.

ke: Investor’s required return.

4.37

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Zero GrowthModel ExampleZero GrowthModel Example

common stockStock ZG has an expected growth rate of0%. Each share of stock just received anannual $3.24 dividend per share. Theappropriate discount rate is 15%. What isthe value of the common stock?

D1$3.24$3.24D1 = $3.24 ( 1 + 0 ) = $3.24

VZGD1ke $3.240.15 $21.60VZG = D1 / ( ke - 0 ) = $3.24 / (0.15 - 0 )= $21.60

D1$3.24$3.24D1 = $3.24 ( 1 + 0 ) = $3.24

VZGD1ke $3.240.15 $21.60VZG = D1 / ( ke - 0 ) = $3.24 / (0.15 - 0 )= $21.60

4.38

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growth phases model The growth phases model assumesthat dividends for each share will growat two or more different growth rates.

(1 + ke)t

V =

t=1



t=n+1



D0(1 + g1)t

Dn(1 + g2)t

Growth Phases ModelGrowth Phases Model

4.39

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D0(1 + g1)t

Dn+1

Growth Phases ModelGrowth Phases Model

growth phases model Note that the second phase of thegrowth phases model assumes thatdividends will grow at a constant rate g2.We can rewrite the formula as:

(1 + ke)t

(ke – g2)

V =

t=1

(1 + ke)n

4.40

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Growth PhasesModel ExampleGrowth PhasesModel Example

Stock GP has an expected growthrate of 16% for the first 3 years and8% thereafter. Each share of stockjust received an annual $3.24dividend per share. The appropriatediscount rate is 15%. What is thevalue of the common stock underthis scenario?

4.41

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Growth PhasesModel ExampleGrowth PhasesModel Example

Stock GP has two phases of growth. The first, 16%,starts at time t=0 for 3 years and is followed by 8%thereafter starting at time t=3. We should view the timeline as two separate time lines in the valuation.



0 1 2 3 4 5 6

D1 D2 D3 D4 D5 D6

Growth of 16% for 3 years

Growth of 8% to infinity!

4.42

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Growth PhasesModel ExampleGrowth PhasesModel Example

Note that we can value Phase #2 using theConstant Growth Model



0 1 2 3

D1 D2 D3

D4 D5 D6

0 1 2 3 4 5 6

Growth Phase

#1 plus the infinitelylong Phase #2

4.43

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Growth PhasesModel ExampleGrowth PhasesModel Example

Note that we can now replace all dividends fromyear 4 to infinity with the value at time t=3, V3!Simpler!!



V3 =

D4 D5 D6

0 1 2 3 4 5 6

k-g

We can use this model because

dividends grow at a constant 8%

rate beginning at the end of Year 3.

4.44

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Growth PhasesModel ExampleGrowth PhasesModel Example

Now we only need to find the first four dividendsto calculate the necessary cash flows.

0 1 2 3

D1 D2 D3

0 1 2 3

New Time

Line

k-g

Where V3 =

4.45

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Growth PhasesModel ExampleGrowth PhasesModel Example

Determine the annual dividends.

D0 = $3.24 (this has been paid already)

D1$3.76 D1 = D0(1 + g1)1 = $3.24(1.16)1 =$3.76

D2$4.36 D2 = D0(1 + g1)2 = $3.24(1.16)2 =$4.36

D3$5.06 D3 = D0(1 + g1)3 = $3.24(1.16)3 =$5.06

D4$5.46 D4 = D3(1 + g2)1 = $5.06(1.08)1 =$5.46

Determine the annual dividends.

D0 = $3.24 (this has been paid already)

D1$3.76 D1 = D0(1 + g1)1 = $3.24(1.16)1 =$3.76

D2$4.36 D2 = D0(1 + g1)2 = $3.24(1.16)2 =$4.36

D3$5.06 D3 = D0(1 + g1)3 = $3.24(1.16)3 =$5.06

D4$5.46 D4 = D3(1 + g2)1 = $5.06(1.08)1 =$5.46

4.46

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Growth PhasesModel ExampleGrowth PhasesModel Example

Now we need to find the present valueof the cash flows.

0 1 2 3

3.76 4.36 5.06

0 1 2 3

Actual

Values

5.46

0.15–0.08

Where $78 =

4.47

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Growth PhasesModel ExampleGrowth PhasesModel Example

We determine the PV of cash flows.

D1D1$3.76 $3.27PV(D1) = D1(PVIF15%, 1) = $3.76 (0.870) = $3.27

D2D2$4.36 $3.30PV(D2) = D2(PVIF15%, 2) = $4.36 (0.756) = $3.30

D3D3$5.06 $3.33PV(D3) = D3(PVIF15%, 3) = $5.06 (0.658) = $3.33

P3$5.46 P3 = $5.46 / (0.15 - 0.08) = $78 [CG Model]

P3P3$78 $51.32PV(P3) = P3(PVIF15%, 3) = $78 (0.658) = $51.32

We determine the PV of cash flows.

D1D1$3.76 $3.27PV(D1) = D1(PVIF15%, 1) = $3.76 (0.870) = $3.27

D2D2$4.36 $3.30PV(D2) = D2(PVIF15%, 2) = $4.36 (0.756) = $3.30

D3D3$5.06 $3.33PV(D3) = D3(PVIF15%, 3) = $5.06 (0.658) = $3.33

P3$5.46 P3 = $5.46 / (0.15 - 0.08) = $78 [CG Model]

P3P3$78 $51.32PV(P3) = P3(PVIF15%, 3) = $78 (0.658) = $51.32

4.48

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D0(1 +0.16)t

Growth PhasesModel ExampleGrowth PhasesModel Example

intrinsic value Finally, we calculate the intrinsic value bysumming all of cash flow present values.

(1 +0.15)t

(0.15–0.08)

V = 

t=1

(1+0.15)n

V = $3.27 + $3.30 + $3.33 + $51.32

V = $61.22V = $61.22

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Solving the Intrinsic ValueProblem using CF RegistrySolving the Intrinsic ValueProblem using CF Registry

Steps in the Process (Page 1)

Step 1:PressCF key

Step 2:Press2ndCLR Workkeys

Step 3: For CF0 Press0Enter ↓ keys

Step 4: For C01 Press3.76Enter ↓ keys

Step 5: For F01 Press1Enter ↓ keys

Step 6: For C02 Press4.36Enter ↓ keys

Step 7: For F02 Press1Enter ↓keys

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Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer.

Solving the Intrinsic ValueProblem using CF RegistrySolving the Intrinsic ValueProblem using CF Registry

Steps in the Process (Page 2)

Step 8: For C03 Press83.06Enter ↓ keys

Step 9: For F03 Press 1Enter ↓ keys

Step 10: Press ↓ ↓ keys

Step 11: PressNPV

Step 12: Press 15Enter ↓keys

Step 13: PressCPT

RESULT: Value = $61.18!

(Actual - rounding error in tables)

4.51

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Calculating Rates ofReturn (or Yields)Calculating Rates ofReturn (or Yields)

cash flows1. Determine the expected cash flows.

market price (P0)2. Replace the intrinsic value (V) withthe market price (P0).

market required rate ofreturn discountedcash flows market price3. Solve for the market required rate ofreturn that equates the discountedcash flows to the market price.

cash flows1. Determine the expected cash flows.

market price (P0)2. Replace the intrinsic value (V) withthe market price (P0).

market required rate ofreturn discountedcash flows market price3. Solve for the market required rate ofreturn that equates the discountedcash flows to the market price.

Steps to calculate the rate ofreturn (or Yield).

4.52

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Determining Bond YTMDetermining Bond YTM

Determine the Yield-to-Maturity(YTM) for the annual coupon payingbond with a finite life.

P0 =



t=1

(1 + kd )t

nn= I (PVIFA kd , n) + MV (PVIF kd , n)

n(1 + kd )n

kd = YTM

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Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer.

Determining the YTMDetermining the YTM

$1,250Julie Miller want to determine the YTMfor an issue of outstanding bonds atBasket Wonders (BW). BW has anissue of 10% annual coupon bondswith 15 years left to maturity. Thebonds have a current market value of$1,250.

What is the YTM?What is the YTM?

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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(0.275)

$1,250$1,250 = $806.10 + $275.00

$1,081.10[Rate is too high!]=$1,081.10[Rate is too high!]

4.55

Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer.

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(0.362)

$1,250$1,250 = $910.80 + $362.00

$1,272.80[Rate is too low!]=$1,272.80[Rate is too low!]

4.56

Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer.

0.07$1,273

0.02IRR$1,250 $192

0.09$1,081

X $230.02$192

YTM Solution (Interpolate)YTM Solution (Interpolate)

$23

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Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer.

0.07$1,273

0.02IRR$1,250 $192

0.09$1,081

X $230.02$192

YTM Solution (Interpolate)YTM Solution (Interpolate)

$23

4.58

Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer.

0.07$1273

YTM$12500.02YTM$1250 $192

0.09$1081

($23)(0.02) $192

YTM Solution (Interpolate)YTM Solution (Interpolate)

$23

X =

X = 0.0024

YTM7.24%YTM =0.07 + 0.0024 = 0.0724 or 7.24%

4.59

Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer.

N:15-year annual bond

I/Y:Compute -- Solving for the annual YTM

PV:Cost to purchase is $1,250

PMT:$100 annual interest (10% x $1,000 face value)

FV:$1,000 (investor receives face value in 15 years)

I/Y

PMT

Inputs

Compute

15 -1,250 100 +$1,000

7.22% (actual YTM)

YTM Solutionon the CalculatorYTM Solutionon the Calculator

4.60

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Determining SemiannualCoupon Bond YTMDetermining SemiannualCoupon Bond YTM

P0 =



n2n

t=1

(1 + kd /2 )t

I / 2

nn= (I/2)(PVIFAkd /2, 2n) + MV(PVIFkd /2 , 2n)

[ 1 + (kd / 2)2 ] –1 = YTM

Determine the Yield-to-Maturity(YTM) for the semiannual couponpaying bond with a finite life.

n(1 + kd /2 )2n

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Determining the SemiannualCoupon Bond YTMDetermining the SemiannualCoupon Bond YTM

$950Julie Miller want to determine the YTMfor another issue of outstandingbonds. The firm has an issue of 8%semiannual coupon bonds with 20years left to maturity. The bonds havea current market value of $950.

What is the YTM?What is the YTM?

4.62

Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer.

N:20-year semiannual bond (20 x 2 = 40)

I/Y:Compute -- Solving for the semiannual yield now

PV:Cost to purchase is $950 today

PMT:$40 annual interest (8% x $1,000 face value / 2)

FV:$1,000 (investor receives face value in 15 years)

I/Y

PMT

Inputs

Compute

40 -950 40 +$1,000

4.2626% = (kd / 2)

YTM Solutionon the CalculatorYTM Solutionon the Calculator

4.63

Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer.

Determining SemiannualCoupon Bond YTMDetermining SemiannualCoupon Bond YTM

[ (1 + kd / 2)2 ] –1 = YTM

Determine the Yield-to-Maturity(YTM) for the semiannual couponpaying bond with a finite life.

[ (1 + 0.042626)2 ] –1 = 0.0871

or 8.71%

Note: make sure you utilize the calculatoranswer in its DECIMAL form.

4.64

Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer.

Solving the Bond ProblemSolving the Bond Problem

Press:

2nd Bond

12.3104 ENTER ↓

8 ENTER ↓

12.3124 ENTER ↓

↓ ↓ ↓ ↓

95 ENTER 

CPT = kd

Source: Courtesy of Texas Instruments

4.65

Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer.

Determining SemiannualCoupon Bond YTMDetermining SemiannualCoupon Bond YTM

[ (1 + kd / 2)2 ] –1 = YTM

This technique will calculate kd.You must then substitute it into thefollowing formula.

[ (1 + 0.0852514/2)2 ] –1 = 0.0871

or 8.71% (same result!)

4.66

Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer.

Bond Price - YieldRelationshipBond Price - YieldRelationship

Discount BondDiscount Bond – The market requiredrate of return exceeds the coupon rate(Par > P0 ).

Premium Bond –Premium Bond – The coupon rateexceeds the market required rate ofreturn (P0 > Par).

Par Bond –Par Bond – The coupon rate equals themarket required rate of return (P0 = Par).

Discount BondDiscount Bond – The market requiredrate of return exceeds the coupon rate(Par > P0 ).

Premium Bond –Premium Bond – The coupon rateexceeds the market required rate ofreturn (P0 > Par).

Par Bond –Par Bond – The coupon rate equals themarket required rate of return (P0 = Par).

4.67

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Bond Price - YieldRelationshipBond Price - YieldRelationship

Coupon Rate Coupon Rate

MARKET REQUIRED RATE OF RETURN (%)

Coupon Rate Coupon Rate

MARKET REQUIRED RATE OF RETURN (%)

BOND PRICE ($)

1000

Par

1600

1400

1200

600

100 2 4 6 8 10 12 14 16 18

5 Year5 Year

15 Year15 Year

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Bond Price-YieldRelationshipBond Price-YieldRelationship

risesAssume that the required rate of return ona 15 year, 10% annual coupon paying bondrises from 10% to 12%. What happens tothe bond price?

riserisefallWhen interest rates rise, then themarket required rates of return riseand bond prices will fall.

riserisefallWhen interest rates rise, then themarket required rates of return riseand bond prices will fall.

4.69

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Bond Price - YieldRelationshipBond Price - YieldRelationship

Coupon Rate Coupon Rate

MARKET REQUIRED RATE OF RETURN (%)

Coupon Rate Coupon Rate

MARKET REQUIRED RATE OF RETURN (%)

BOND PRICE ($)

1000

Par

1600

1400

1200

600

100 2 4 6 8 10 12 14 16 18

15 Year15 Year

5 Year5 Year

4.70

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Bond Price-YieldRelationship (Rising Rates)Bond Price-YieldRelationship (Rising Rates)

fallen Therefore, the bond price hasfallen from $1,000 to $864.

($863.78 on calculator)

fallen Therefore, the bond price hasfallen from $1,000 to $864.

($863.78 on calculator)

risenThe required rate of return on a 15year, 10% annual coupon payingbond has risen from 10% to 12%.

4.71

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Bond Price-YieldRelationshipBond Price-YieldRelationship

fallsAssume that the required rate ofreturn on a 15 year, 10% annualcoupon paying bond falls from 10% to8%. What happens to the bond price?

fallfallriseWhen interest rates fall, then themarket required rates of return falland bond prices will rise.

fallfallriseWhen interest rates fall, then themarket required rates of return falland bond prices will rise.

4.72

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Bond Price - YieldRelationshipBond Price - YieldRelationship

Coupon Rate Coupon Rate

MARKET REQUIRED RATE OF RETURN (%)

Coupon Rate Coupon Rate

MARKET REQUIRED RATE OF RETURN (%)

BOND PRICE ($)

1000

Par

1600

1400

1200

600

100 2 4 6 8 10 12 14 16 18

15 Year15 Year

5 Year5 Year

4.73

Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer.

Bond Price-Yield Relationship(Declining Rates)Bond Price-Yield Relationship(Declining Rates)

risen Therefore, the bond price hasrisen from $1000 to $1171.

($1,171.19 on calculator)

risen Therefore, the bond price hasrisen from $1000 to $1171.

($1,171.19 on calculator)

fallenThe required rate of return on a 15year, 10% coupon paying bondhas fallen from 10% to 8%.

4.74

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The Role of Bond MaturityThe Role of Bond Maturity

fallAssume that the required rate of returnon both the 5 and 15 year, 10% annualcoupon paying bonds fall from 10% to8%. What happens to the changes inbond prices?

The longer the bond maturity, thegreater the change in bond price for agiven change in the market requiredrate of return.

The longer the bond maturity, thegreater the change in bond price for agiven change in the market requiredrate of return.

4.75

Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer.

Bond Price - YieldRelationshipBond Price - YieldRelationship

Coupon Rate Coupon Rate

MARKET REQUIRED RATE OF RETURN (%)

Coupon Rate Coupon Rate

MARKET REQUIRED RATE OF RETURN (%)

BOND PRICE ($)

1000

Par

1600

1400

1200

600

100 2 4 6 8 10 12 14 16 18

15 Year15 Year

5 Year5 Year

4.76

Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer.

The Role of Bond MaturityThe Role of Bond Maturity

risenThe 5 year bond price has risen from $1,000 to$1,080 for the 5 year bond (+8.0%).

risen Twice as fast!The 15 year bond price has risen from $1,000 to$1,171 (+17.1%). Twice as fast!

risenThe 5 year bond price has risen from $1,000 to$1,080 for the 5 year bond (+8.0%).

risen Twice as fast!The 15 year bond price has risen from $1,000 to$1,171 (+17.1%). Twice as fast!

fallenThe required rate of return on both the5 and 15 year, 10% annual couponpaying bonds has fallen from 10% to8%.

4.77

Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer.

The Role of theCoupon RateThe Role of theCoupon Rate

lowerFor a given change in themarket required rate of return,the price of a bond will changeby proportionally more, thelower the coupon rate.

lowerFor a given change in themarket required rate of return,the price of a bond will changeby proportionally more, thelower the coupon rate.

4.78

Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer.

Example of the Role ofthe Coupon RateExample of the Role ofthe Coupon Rate

Assume that the market required rate ofreturn on two equally risky 15 year bondsis 10%. The annual coupon rate for BondH is 10% and Bond L is 8%.

What is the rate of change in each of thebond prices if market required rates fallto 8%?

Assume that the market required rate ofreturn on two equally risky 15 year bondsis 10%. The annual coupon rate for BondH is 10% and Bond L is 8%.

What is the rate of change in each of thebond prices if market required rates fallto 8%?

4.79

Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer.

Example of the Role of theCoupon RateExample of the Role of theCoupon Rate

The price for Bond H will rise from $1,000to $1,171 (+17.1%).

Faster Increase!The price for Bond L will rise from $848 to$1,000 (+17.9%). Faster Increase!

The price for Bond H will rise from $1,000to $1,171 (+17.1%).

Faster Increase!The price for Bond L will rise from $848 to$1,000 (+17.9%). Faster Increase!

The price on Bond H and L prior to thechange in the market required rate ofreturn is $1,000 and $848 respectively.

4.80

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Determining the Yield onPreferred StockDetermining the Yield onPreferred Stock

Determine the yield for preferredstock with an infinite life.

P0 = DivP / kP

Solving for kP such that

kP = DivP / P0

Determine the yield for preferredstock with an infinite life.

P0 = DivP / kP

Solving for kP such that

kP = DivP / P0

4.81

Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer.

Preferred Stock YieldExamplePreferred Stock YieldExample

kP = $10 / $100.

kP10%kP = 10%.

kP = $10 / $100.

kP10%kP = 10%.

Assume that the annual dividend oneach share of preferred stock is $10.Each share of preferred stock iscurrently trading at $100. What is theyield on preferred stock?

4.82

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Determining the Yield onCommon StockDetermining the Yield onCommon Stock

Assume the constant growth modelis appropriate. Determine the yieldon the common stock.

P0 = D1 / ( ke – g )

Solving for ke such that

ke = ( D1 / P0 ) + g

Assume the constant growth modelis appropriate. Determine the yieldon the common stock.

P0 = D1 / ( ke – g )

Solving for ke such that

ke = ( D1 / P0 ) + g

4.83

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Common StockYield ExampleCommon StockYield Example

ke = ( $3 / $30 ) + 5%

ke15%ke = 10% + 5% = 15%

ke = ( $3 / $30 ) + 5%

ke15%ke = 10% + 5% = 15%

Assume that the expected dividend(D1) on each share of common stockis $3. Each share of common stockis currently trading at $30 and has anexpected growth rate of 5%. What isthe yield on common stock?