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7-1
Copyright (C) 2000 by Harcourt, Inc. All rights reserved.
Chapter 7Valuation Concepts
Bond ValuesStock ValuesRates of ReturnMarket Equilibrium
Copyright © 2000 by Harcourt, Inc.
All rights reserved. Requests for permission to make copies of any part of the work should be mailed to the following address: Permissions Department, Harcourt, Inc., 6277 Sea Harbor Drive, Orlando, Florida 32887-6777.
7-2
Copyright (C) 2000 by Harcourt, Inc. All rights reserved.
Basic Valuation
From “The Time Value of Money” we realize that the value of anything is based on the present value of the cash flows the asset is expected to produce in the future.
7-3
Copyright (C) 2000 by Harcourt, Inc. All rights reserved.
V CF1
1 k 1 CF2
1 k 2 CFN
1 k N
CFt
1 k tt1
N
^ ^ ^Asset value
^
Basic Valuation
k = the return investors consider appropriate for holding such an asset - usually referred to as the required return, based on riskiness and economic conditions
CFt = the cash flow expected to be generated by the asset in period t
^
7-4
Copyright (C) 2000 by Harcourt, Inc. All rights reserved.
Valuation of Financial Assets: Bonds - long term debt instruments
Principal Amount, Face Value, Maturity Principal Amount, Face Value, Maturity Value, Par Value:Value, Par Value: The amount of money the firm borrows and promises to repay at some future date, often at maturity.
Coupon Payment:Coupon Payment: The specified number of dollars of interest paid each period, generally each six months, on a bond.
Key Terms
7-5
Copyright (C) 2000 by Harcourt, Inc. All rights reserved.
Coupon Interest Rate:Coupon Interest Rate: The stated annual rate of interest paid on a bond.
Maturity Date:Maturity Date: A specified date on which the par value of a bond must be repaid.
Original Maturity:Original Maturity: The number of years to maturity at the time the bond is issued.
Call Provision:Call Provision: Gives the issuer right to pay off bonds prior to maturity.
Key Terms
7-6
Copyright (C) 2000 by Harcourt, Inc. All rights reserved.
The Basic Bond Valuation Model
kd = required rate of return on a debt instrument
N = number of years before the bond matures
INT = dollars of interest paid each year (Coupon rate x Par value)
M = par or face, value of the bond to be paid off at maturity
7-7
Copyright (C) 2000 by Harcourt, Inc. All rights reserved.
Bond Value
d
k1
MN
1tt
dk1
INT
Nd
k1
MN
dk1
INT...
2d
k1
INT1
dk1
INTd
V
INT(PVIFAkd,N) M(PVIFkd, N)
7-8
Copyright (C) 2000 by Harcourt, Inc. All rights reserved.
Genesco 15%, 15year, $1,000 bonds valued at 15% required rate of return
Vd = $150 (5.8474) + $1,000 (0.1229)
= $877.11 + $122.89 = $1,000
15
15
1.15
1000,1$
15.015.1
11
150$Bond value
Numerical solution:
7-9
Copyright (C) 2000 by Harcourt, Inc. All rights reserved.
Look up the PVIF and PVIFA values in Tables A-1 and A-2 and insert them in the equation
Vd = $150 (5.8474) + $1,000 (0.1229)
= $877.11 + $122.89 = $1,000
Genesco 15%, 15year, $1,000 bonds valued at 15% required rate of return
Tabular solution:
7-10
Copyright (C) 2000 by Harcourt, Inc. All rights reserved.
Genesco 15%, 15year, $1,000 bonds valued at 15% required rate of return
Financial calculator solution:
15 15 150 1000N I/YR PV PMT FV
- 1000
INPUTS
OUTPUT
7-11
Copyright (C) 2000 by Harcourt, Inc. All rights reserved.
Changes in Bond Values Over Time
If the market rate associated with a bond, kd, equals the coupon rate of interest, the bond will sell at its par value.
If interest rates in the economy fall after the bonds are issued, kd is below the coupon rate.
The interest payments and maturity payoff stay the same, but the PVIF and PVIFA values are based on the new kd increasing the bond value
7-12
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Begind,
Begind,Endd,
d
V
VV
valuebond
Beginning
valuebond
Ending
valuebond
Beginning
V
INT
Current yield
Capital gains yield
Current yieldCurrent yield is the annual interest payment on a bond divided by its current market value
Changes in Bond Values Over Time
7-13
Copyright (C) 2000 by Harcourt, Inc. All rights reserved.
Discount BondDiscount Bond
A bond that sells below its par value, which occurs whenever the going rate of interest rises above the coupon rate
Premium BondPremium Bond
A bond that sells above its par value, which occurs whenever the going rate of interest falls below the coupon rate
Changes in Bond Values Over Time
7-14
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An increase in interest rates will cause the price of an outstanding bond to fall
A decrease in interest rates will cause the price to rise
The market value of a bond will always approach its par value as its maturity date approaches, provided the firm does not go bankrupt
Changes in Bond Values Over Time
7-15
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Time path of value of a 15% Coupon, $1000 par value bond when interest rates are 10%, 15%, and 20%
Year kd = 10% kd = 15% kd = 20%
0 $1,380.30 $1,000.00 $766.231 $1,368.33 $1,000.00 $769.472 $1,355.17 $1,000.00 $773.373 $1,340.68 $1,000.00 $778.044 $1,324.75 $1,000.00 $783.655 $1,307.23 $1,000.00 $790.386 $1,287.95 $1,000.00 $798.457 $1,266.75 $1,000.00 $808.148 $1,243.42 $1,000.00 $819.779 $1,217.76 $1,000.00 $833.7210 $1,189.54 $1,000.00 $850.4711 $1,158.49 $1,000.00 $870.5612 $1,124.34 $1,000.00 $894.6813 $1,086.78 $1,000.00 $923.6114 $1,045.45 $1,000.00 $958.3315 $1,000.00 $1,000.00 $1,000.00
7-16
Copyright (C) 2000 by Harcourt, Inc. All rights reserved.
Time path of value of a 15% Coupon, $1000 par value bond when interest rates are 10%, 15%, and 20%
$0
$250
$500
$750
$1,000
$1,250
$1,500
1 3 5 7 9 11 13 15
Kd = Coupon Rate
Kd < Coupon Rate
Kd > Coupon Rate
Years
Bond Value
Changes in Bond Values Over Time
7-17
Copyright (C) 2000 by Harcourt, Inc. All rights reserved.
Finding the Interest Rate on a Bond: Yield to Maturity
YTMYTM is the average rate of return earned on a bond if it is held to maturity
Approximate yield to maturity
(does not consider time value of money)
3
M V 2N
V-M INT
bond of valueAverage
gains capital interest
Accrued
Annual
d
d
7-18
Copyright (C) 2000 by Harcourt, Inc. All rights reserved.
Bond Values with Semiannual Compounding
,2N2
k
,2N2
k
2N
d
2N
1tt
d
d
dd
PVIFMPVIFA2
INT
2k
1
M
2k
1
2INT
V
7-19
Copyright (C) 2000 by Harcourt, Inc. All rights reserved.
Interest Rate Risk on a Bond
Interest Rate Price RiskInterest Rate Price Risk - the risk of changes in bond prices to which investors are exposed due to changing interest rates
Interest Rate Reinvestment Rate RiskInterest Rate Reinvestment Rate Risk - the risk that income from a bond portfolio will vary because cash flows have to be reinvested at current market rates
7-20
Copyright (C) 2000 by Harcourt, Inc. All rights reserved.
Current Market Interest Rate, kd
1-Year Bond 14-Year Bond
5% 1,095.24$ 1,989.86$ 10% 1,045.45$ 1,368.33$ 15% 1,000.00$ 1,000.00$ 20% 958.33$ 769.47$ 25% 920.00$ 617.59$
Value of
Value of Long and Short-Term15% Annual Coupon Rate Bonds
7-21
Copyright (C) 2000 by Harcourt, Inc. All rights reserved.
Interest Rate, kd (%)
BondValue
($) 2,000
1,500
1,000
500
0 5 10 15 20 25
14-Year Bond
1-Year Bond
Value of Long and Short-Term15% Annual Coupon Rate Bonds
7-22
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Bond Prices in Recent Years
7-23
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Valuation of Financial Assets - Equity (Stock)
Common StockCommon Stock Preferred StockPreferred Stock
– hybrid• similar to bonds with fixed
dividend amounts• similar to common stock as
dividends are not required and have no fixed maturity date
7-24
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Stock Valuation Models
Terms: Expected DividendsExpected Dividends
investors amongdiffer may estimates
theso values,expected are dividends future All
years twoof end at the expected dividend theis D̂
year thisof end at the paid be it will and
paid, be toexpected dividendnext theis D̂
paidalready dividendrecent most theis D
Year t of end at the recieve
toexpectsr stockholde thedividendD̂
2
1
0
t
Stock Valuation Models
7-25
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aymarket tod in the sells
stock aat which price theP0
Stock Valuation Models
Terms: Market PriceMarket Price
Stock Valuation Models
7-26
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bothor ,book value its price,
market current sasset' thefrom
different bemay and facts by the
justified is investor,an of mind
in the ,asset thatan of value theP̂0
Stock Valuation Models
Terms: Intrinsic ValueIntrinsic Value
Stock Valuation Models
7-27
Copyright (C) 2000 by Harcourt, Inc. All rights reserved.
Year teach of end at the
stock theof price expected theP̂t
Stock Valuation Models
Terms: Expected PriceExpected Price
Stock Valuation Models
7-28
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shareper dividendsin
change of rate expected theg
Stock Valuation Models
Terms: Growth RateGrowth Rate
Stock Valuation Models
7-29
Copyright (C) 2000 by Harcourt, Inc. All rights reserved.
sinvestmentother
on available returns and riskiness
itsgiven acceptableconsider
rsstockholde stock thatcommon
aon return of rate minimum theks
Stock Valuation Models
Terms: Required Rate of ReturnRequired Rate of Return
Stock Valuation Models
7-30
Copyright (C) 2000 by Harcourt, Inc. All rights reserved.
stock of
share a of pricecurrent by the
divided dividend expected theP
D̂
0
1
Stock Valuation Models
Terms: Dividend YieldDividend Yield
Stock Valuation Models
7-31
Copyright (C) 2000 by Harcourt, Inc. All rights reserved.
year theof beginning at the price
itsby dividedyear given a during
gain) (capital pricein change theP
PP
0
01
Stock Valuation Models
Terms: Capital Gain YieldCapital Gain Yield
Stock Valuation Models
7-32
Copyright (C) 2000 by Harcourt, Inc. All rights reserved.
ˆ k s the rate of return on a common
stock that an individual investor
expects to receive; equal to the
expected dividend yield plus the
expected capital gains yield
Stock Valuation Models
Terms: Expected Rate of ReturnExpected Rate of Return
Stock Valuation Models
7-33
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yield gains capital the
plus yield dividend the toequal
fact; after the receives,actually
investor individualan stock that
common aon return of rate theks
Stock Valuation Models
Terms: Actual Rate of ReturnActual Rate of Return
Stock Valuation Models
7-34
Copyright (C) 2000 by Harcourt, Inc. All rights reserved.
Expected Dividends as the Basis for Stock Values
If you hold a stock forever, all you receive is the dividend payments
The value of the stock today is the present value of the future dividend payments
7-35
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Value of Stock Vs ˆ P 0 PV of expected future dividends
ˆ D 1
1 k s 1
ˆ D 21 k s 2
ˆ D 1 ks
ˆ D t
1 k s tt1
Expected Dividends as the Basis for Stock Values
7-36
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Stock Values with Zero Growth
A Zero Growth StockZero Growth Stock is a common stock whose future dividends are not expected to grow at all
02 DD̂ ...D̂D̂ and 0, g1
s2
s1
s
0k1
D...
k1
D
k1
D P̂
7-37
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Normal, or Constant, Growth
Growth that is expected to continue into the foreseeable future at about the same rate as that of the economy as a whole
g = a constant
7-38
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Normal, or Constant, Growth(Gordon ModelGordon Model)
ˆ P 0 D0 1 g 1
1 k s 1
D0 1 g 2
1 ks 2 D0 1 g
1 ks
gk
D̂
gk
g1D
s
1
s
0
7-39
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Expected Rate of Return on a Constant Growth Stock
Dividend yield Expected growth rate, or capital gains yield
g D̂
k̂0
1s
P
7-40
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Valuing Stocks with Nonconstant Growth
Nonconstant Growth:Nonconstant Growth: The part of the life cycle of a firm in which its growth is either much faster or much slower than that of the economy as a whole
7-41
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1. Compute the value of the dividends that experience nonconstant growth, and then find the PV of these dividends
2. Find the price of the stock at the end of the nonconstant growth period, at which it has become a constant growth stock, and discount this price back to the present
3. Add these two components to find the intrinsic value of the stock, .
Valuing Stocks with Nonconstant Growth
ˆ P 0
7-42
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Stock Market Equilibrium
1. The expected rate of return as seen by the marginal investor must equal the required rate of return,
2. The actual market price of the stock must equal its intrinsic value as estimated by the marginal investor,
k̂x = kx,
P0 = P0^
7-43
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Changes in Stock Prices
Investors change the rates of return required to invest in stocks
Expectations about the cash flows associated with stocks change
7-44
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The Efficient Markets Hypothesis
The weak formThe weak form of the EMH states that all information contained in the past price movements is fully reflected in current market prices.
The semistrong formThe semistrong form states that current market prices reflect all publicly available information
The strong formThe strong form states that current market prices reflect all pertinent information, whether publicly available or privately held.
7-45
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Valuation of Real (Tangible) Assets
A company proposes to buy a machine so it can manufacture a new product. After five years the machine will be worthless, but during the five years it is used, the company will be able to increase its net cash flows by the following amounts:
7-46
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Year Expected Cash Flow, CF 1 $120,000
2 $100,000 3 $150,000 4 $80,000 5 $50,000
To earn a 14% return on investments like this, what is the value of this machine?
Valuation of Real (Tangible) Assets
7-47
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Cash Flow Time Lines
0 1 2 3 4 514%
$120,000 $100,000 $150,000 $80,000 $50,000
PV of $120,000
PV of $100,000
PV of $150,000
PV of $80,000
PF of $50,000
Asset Value =V0
54321 14.1
000,50$
14.1
000,80$
14.1
000,150$
14.1
000,100$
14.1
000,120$
7-48
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End of Chapter 7 Valuation Concepts