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Bond and stock valuation Lecture 4
Bond and stock valuation
Lecture 4
Lecture outline Some basic concepts Bond valuation
Perpetual bonds Maturity bonds
Preferred stock valuation Common stock valuation
Constant growth stocks No growth stocks Non-constant growth stocks
Yields on securities
Some basic concepts Liquidation value versus going-concern value
Liquidation value – the amount of money that could be realized if an asset or a group of assets sold separately from its operating organization.
Going-concern value – the amount that a firm could be sold for as a continuing operating business.
Book value versus market value Book value – (1) the book value of an asset is the
accounting value of an asset – the asset’s cost minus its accumulated depreciation, (2) the book value of a firm is the dollar difference between the firm’s total assets and its liabilities and preferred stock listed on its balance sheet.
Market value – the market price at which an asset trades.
Some basic concepts (cont.)
Market value versus intrinsic value Market value – the market price at which an asset
trades Intrinsic value – the price a security ought to have
based on all factors bearing on valuation. In short, intrinsic value of a security is its economic value.
This chapter will consider how to determine a security’s intrinsic value, i.e., what the security ought to be worth based on hard facts.
In general, this value is the present value of the cash-flow stream provided to the investor, discounted at a required rate of return appropriate for the risk involved.
Securities on capital market Securities used in this lecture include:
Bond Government bond
Perpetual bond Maturity bond
Nonzero coupon bond Zero coupon bond
Corporate bond Inconvertible bond Convertible bond Callable bond
Stock Preferred stock Common stock
Distinguish the differences between bond and stock
Government bond
Municipal Bond
Bond valuation Bond – a long-term debt instrument
issued by a corporation or government. Face value – the stated value of a bond,
usually $1000 Coupon rate – the stated rate of interest
on a bond, the annual interest payment divided by the bond’s face value
Perpetual bond (consolidated annuities or consol) – a bond that never matures, issued by Great Britain after Napoleonic Wars
Bond valuation Bond classifications
Government or treasury bond vs. corporate bond
Maturity bond vs. perpetual bond Nonzero coupon bond vs. zero coupon
bond Principle of bond valuation Value of a bond equals the present
value of cash flows generated from the bond.
Bond valuation procedure
Step 1: Estimating the expected cash flows
Step 2: Estimating the discount rate = Risk-free rate + Risk premium
Step 3: Determining present value of the expected cash flows with the discount rate
estimated
Perpetual bond valuation Perpetual bond or consol – A bond that
never matures.
Assume that you buy a perpetual bond which give you the annual interest of 80$ and your required rate of return is 14%. The value of this bond will be:
V = I/kd = 80/0,14 = 571,43$
dtt
dddd k
I
k
I
k
I
k
I
k
IV
121 )1()1(
....)1()1(
Bonds with a finite maturity Nonzero coupon bond valuation
where n is the number of years until final
maturity and MV is the maturity value of the bond.
Ex. A 9-year-maturity bond with the face value of 1000$, and annual coupon rate of 10% and the investor requires a rate of return 12%, the value of the bond will be:
nd
nddd k
MV
k
I
k
I
k
IV
)1()1(....
)1()1( 21
Bonds with a finite maturity Nonzero coupon bond valuation
where n is the number of years until final
maturity and MV is the maturity value of the bond.
Ex. A 9-year-maturity bond with the face value of 1000$, and annual coupon rate of 10% and the investor requires a rate of return 12%, the value of the bond will be:
nd
nddd k
MV
k
I
k
I
k
IV
)1()1(....
)1()1( 21
44.893$)12,01(
1000
)12,01(
100....
)12,01(
100
)12,01(
1009921
V
Bonds with a finite maturity Zero-coupon bond – A bond that pays
no interest but sells at a deep discount from its face value.
Zero coupon bond valuation Assume you want to buy a nonzero coupon
bond with the face value of $1000 and maturity of 10 years. If your required rate of return is 12%, the value of the bond will be:
ndk
MVV
)1(
Semiannual interest compounding bond
Semiannual interest compounding bond valuation
If the 10 percent coupon bonds of Treasury bond have maturity of 5 years, and our nominal required rate of return is 12%, the value of one $1,000-par-value bond is:
nd
n
tt
d k
MV
k
IV
2
2
1 )2/1()2/1(
2/
Semiannual interest compounding bond
Semiannual interest compounding bond valuation
If the 10 percent coupon bonds of Treasury bond have maturity of 5 years, and our nominal required rate of return is 12%, the value of one $1,000-par-value bond is:
nd
n
tt
d k
MV
k
IV
2
2
1 )2/1()2/1(
2/
10
10
1 )2/121(
1000
)2/121(
50
tt
V
01.926$
)2/12.01(
1000
)2/12.01(
50...
)2/12.01(
50
)2/12.01(
50101021
V
Ex: A $100,000 bond has 4 year maturity and annual coupon rate of 8.5%. What is the price of bond if the investor’s required rate of return is (i) 7.5%, (ii) 8.5% and (iii) 9.5%
Ex: A $100,000 bond has 4 year maturity and annual coupon rate of 8.5%. What is the price of bond if the investor’s required rate of return is (i) 7.5%, (ii) 8.5% and (iii) 9.5%
If the required rate of return kd=7.5% => value of the bond V = $103,349
If the required rate of return kd=8.5% => value of the bond V = $100,000
If the required rate of return kd=9.5% => value of the bond V = $96,796
Behavior of bond prices The market required rate of return = the
stated coupon rate => the price of the bond will equal its face value.
The market required rate of return < the stated coupon rate => the price of the bond will be more than its face value.
The market required rate of return > the stated coupon rate => the price of the bond will be less than its face value.
The market required rate of return increases => the bond price will fall.
The market required rate of return decreases => the bond price will increase.
Bond price behavior
Bond value
Years
MV
0 5 10 15
kd = kc
kd > kc
kd < kc
Yield on bond Yield to maturity (YTM)
given V, I, MV, and n, you can solve the
equation for YTM Yield to call (YTC)
given V, I, PC, and n, you can solve the
equation for YTC YTM and YTC may be solved by using Goal
seek in Excel
nn YTM
MV
YTM
I
YTM
I
YTM
IV
)1()1(....
)1()1( 21
nn YTC
PC
YTC
I
YTC
I
YTC
IV
)1()1(....
)1()1( 21
A $1000-par-value bond with 5 years until maturity, and an 10 percent coupon rate is selling at $891. What is the YTM of this bond?
To find YTM you solve the equation:
Goal seek can help you find out the YTM =13.11%
5521 )1(
1000
)1(
100....
)1(
100
)1(
100891
YTMYTMYTMYTM
Preferred stock valuation Preferred stock – A type of stock that
Promises a fixed dividend Has no stated maturity
=> preferred stock is similar to perpetual bond Valuation formula
Illustration: Suppose REE issue a preferred stock with $100 par value and 9-percent dividend, and the investor’s required return was 14%,its value per share would be:
V = $9/0.14 = 64.29$
p
p
k
DV Dp: the stated annual dividend per share of
preferred stockkp: the appropriate discount rate
Common stock valuation Dividend discount models
Constant growth V = D1/ (ke – g) No growth, g = 0 V = D1/ke Growth phases
12
21
1
)1()1(...
)1()1( tt
e
t
eee k
D
k
D
k
D
k
DV
1
2
1
10
1
1
11
)1(
)1(
)1(
)1(
ttt
e
ttt
t
tt
e
t
k
gD
k
gDV
Exï: Stock A’s dividend per share at t=1 is expected to be $2. The dividend grows in five years at 10%, then at 6% forever. Is the investor’s required return was 14%, what is the price of this stock? The present value of dividend received in the first five
years
The present value of dividend received from the year 6
Exï: Stock A’s dividend per share at t=1 is expected to be $2. The dividend grows in five years at 10%, then at 6% forever. Is the investor’s required return was 14%, what is the price of this stock? The present value of dividend received in the first five
years
The present value of dividend received from the year 6
Price of stock V = V1+ PV(V2) = 8.99 + 42.63(1+0.14)-5
= 8.99 + 42.63(0.519) = 31.12$
$99.8)14,01(
)10,01(2
)1(
)1( 5
11
101
1
t
t
tt
tt
e
t
k
gDV
)()1(
)1(
)1(
)1(
2
6
6
525
1
22
1
1
1
gk
D
k
gD
k
gDV
ett
e
t
ttt
e
ttt
63.4206.014.0
)06.1()1.1(2
)(
)1()1(
)(
)1(
)(
5
2
25
10
2
25
2
62
gk
ggD
gk
gD
gk
DV
eee
Limitations of the dividend discount model
The model can not apply when the valuing firm retains most its earnings rather than distributes them as dividend.
The model may result in an inaccurate valuation of a firm because of potential errors in determining: the dividend to be paid over the next year The growth rate The required rate of return by the investors
Price-Earnings (PE) method This method is based on the mean PE ratio of
all publicly traded competitors in the respective industry
V = (the expected earnings of firm per share)x(Mean industry PE ratio)
How to determine the PE ratio? Let b denote the retained earning ratio => 1 – b = The
dividend-payout ratio = D1/E1, where D1, E1 are respectively the expected dividend and earnings per share in period 1. Because 1 – b = D1/E1 => (1 – b) E1 = D1
We have: V = D1/(ke – g) = (1 – b)E1/ (ke – g) =>V/E1= (1 – b)/(ke – g)
PE = V/E1 = (1 – b)/(ke – g)
Example illustrated PE method VINATRANS stock with
Par value = 100,000 dong, ke = 20%, g = 10% Number of share outstanding = 80.000, Expected EPS
= 75,000 dong Dividend-payout ratio = 100% PE = (1 – b)/(ke – g) = (1 – 0)/(0.2 – 0.1) = 10 Stock price = 75,000 x 10 = 750,000 dong
BIBICA stock Par value = 10,000 dong, ke = 15%, g = 10% Number of share outstanding = 5,600,000, expected
EPS = 2,400 dong Dividend-payout ratio = 40% PE = (1 – b)/(ke – g) = (1 – 0.4)/(0.15 – 0.1) = 12 Stock price = 2,400 x 12 = 2,800 dong
Limitations of the PE method The PE method may result in an
inaccurate valuation for a firm because of potential errors in: The forecast of the firm’s future earnings The choice of the industry used to derive the PE
ration Some investors could not trust the PE ratio
regardless of how it is derived
Yield on stock Yield on preferred stock
Yield on common stock
These formulas may be used to determine the component cost of capital later on.
00 P
Dk
k
DP p
pp
p
gP
Dk
gk
DP e
e
0
110
Assignments Ross, (2005): 5.3, 5.6, 5.7, 5.9,
5.10, 5.13, 5.17, 5.18, 5.22 Brigham (2002): Mini case Ch9 and
Ch10 Next lecture presentation (group
3): Problem 7.12 by Ross (2005).
