# valuation of money stocks and bond

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```					Valuation of
Money,
Stock; and
Bonds
The Time Value of Money

• Simple and compound interest
• Future Values and Compound Interest
mT
    r 
fvm ,T    1    
    m
• As m approaches infinity, the factor

1  
m        r
r        e
m
where e = 2.71828
The Time Value of Money
• Given continuous compounding, the future
value of a dollar n periods hence is

rT
fvT  e
The Time Value of Money
The Time Value of Money
• Annually Compounded Interest Rates
(Effective Interest Rate)
(EIR)
= (1+ i/m)m -1
Vs
Annual Percentage Rates (i)

= Monthly rate X 12
= Quarterly rate X4
The Time Value of Money
Present Values
Pv = Future Value After “t” Periods
(1+r)t
DF is always <1 and keeps decreasing with increasing “t”
The Time Value of Money
Compounding     m     Interest                   EIR
Period               per        (1+i/m)m       %
period
%
1 year      1        6           (1.06)1      6.00

Semiannually   2        3           (1.03)2     6.0900

Quarterly     4       1.5         (1.015)4     6.134

Monthly      12      0.5        (1.005)12     6.1678

Weekly       53    0.11538    (1.0011538)52   6.1800

Daily       365   0.01644    (1.0001644)365 6.1831

Continuous     ∞     Almost 0     (2.718)0.06   6.1837
Calculating Present Value
Present Value for Single Period:
PV = C X DF
= C / (1+r)
Present Value for Several Periods of Varying
Amounts:
PV (A+B+C+D….) = C1 + C2 + C3 + C4 +…
(1+r) (1+r)2 (1+r)3 (1+r)4
=  E [ Ct]
( 1+ r)t
The Time Value of Money
Annuity
Fv = C[(1+ r/m)nm -1]
r/m
Pv = C[(1+ r/m)nm -1] =            1   -           1
r/m (1+ r/m)nm               r           r (1+r)t
Growing Annuities =     C1   + C1 (1 + g) + C1(1 + g)2 …. + C1 (1 + g) t-1
+
(1+ r)    (1 +r)2      (1 +r)3            (1 + r)t

= C1          1           -       (1 + g)t
(r - g)           (r - g) (1 + r)t
Types of Annuities
 Ordinary Annuity
 Annuity Due
PV Annuity Due = PV Ordinary Annuity for (t-1) Payments
+
Initial Payment

 Annuity Deferred
PV Annuity Deferred = PV Ordinary Annuity
(1 + r)n-1
Where n = No. of years annuity delayed
General Annuity – when compounding
periods and payment periods do not
coincide
There are two ways that we can do it:
1) Convert the interest rate to the effective
rate for the payment period
2) Convert the payments to EACs that
correspond with the compounding periods
Convert the interest rate to the effective rate
for the payment period
R=100 per month for 03 years
i = 14% pa, being compounded daily
Effective daily rate = .14/365 =0.0003836 or
0.03836%
(For 28 days a month and for calendar months?)
Effective monthly rate = (1+ 0.0003836)28 -1
= 0.010796 = 1.0796%
PV of loan = 100      1    -       1
0.010796 0.010796(1+ 0.010796)39
= 3169.28
Convert the payments to EACs that correspond
with the compounding periods
R=100
i = 14% pa, being compounded daily
Effective daily rate = .14/365 =0.0003836 or 0.03836%
EAC =?
100 =EAC       1    -             1
0.0003836      0.0003836(1+ 0.0003836)28
EAC = 3.553 per day
PV of loan =3.353    1      -         1
0.0003836 0.0003836(10.0003836)1092

= 31169.28
Relationship between Present Value, Future
Value and Equivalent Annuity Cash Flows

Multiply EAC by                           Multiply PV by
present value              PV          inverse of present
annuity factor                        value annuity factor

EAC        EAC

FV
Multiply EAC by
Multiply FV by                          Future value
inverse of Future                        annuity factor
value annuity factor
Perpetuities
Pv of Perpetuity = C/r
Pv of Growing Perpetuity = C1      C2 (1 + g)   C3(1 + g)2
+            +               ….
(1 +r)     (1 + r)2     (1+ r)3 +

=      C1
(r - g)
Declining Discount Factor?

Basis of Capital Market
• A dollar tomorrow has value lower than
a dollar today
• There is no money machine (arbitrage)
The Time Value of Money

Net Present Value of Project
= Pv of Cash flows out – Required Investment

Remember: A risky dollar is worth less than a
safe one
Other Names:
Present Value or just Pv
Discounted Value
Market Price
Market Value
The Time Value of Bonds
Bonds and Notes
• Bond (10% bonds of 22 etc.)
• Coupon
• Face Value/Par Value/ Maturity Value
(US\$1000)
• Coupon Rate (%age of par value)
• Current Yield
• Yield to Maturity (equates bond’s price to
present value)
• Rate of Return on Bonds – The %age rate of
actual income upon investment by holding a
bond for a specific period
Effects of interest rates on bond’s market
values/Prices

PV of bond
payments

Interest rate, %
The Time Value of Bonds
Reading the Financial Pages
Treasury Bonds
Rate    Mo/Yr               Bids      Ask          Chg        Yld
7   June 93n             100:10     100:12        -1        2.08
111/2 Nov 95              116:17     116:21       - 3        4.27
Note
It is in    YTM of
Coupon             It is quoted in 32nds                     Investor
32nds
Rate p.a                  Prices are
100 + 10/32 = 100.315% of Face value
&
116+ 17/32 = 116.375%
of Face value
The Time Value of Bonds
Reading the Financial Pages
Other Bonds
Cur.                                     Net
Bonds               Yld          Vol          Close         Chg
AT&T 81/8 22        7.7          84           105 ¼         1/4
Year of
maturity
Coupon                         105 ¼ of the face      ¼ of 1 % of
Rate p.a.                           value
face vale
Interest income as percentage of the
Bond’s price
Interest income =81.25 (8 1/8% of 1000)        How to show price
Bond’s Price =1052.50                  below par value?
Cur. Yld = 81.25/1052.50 = 0.077 =7.7%
The Time Value of Bonds
• Bond Price as %age of its face value e.g.
115.87% [ A 5- year 9% Bond with prevailing
interest rate @ 5.3%- 15.87% above the face value]
• Yield to Maturity – Internal rate of return – The
discount rate that makes the present value of a
bond’s payments equal to its price (Diff in face
value and present value of bonds)
• Bonds Rating
• Investment Bonds and Junk Bonds (Bbb/BBB &
above and Ba/BA& below)
• Coupon rate and rate of return
Moody’s       Standard
& Poor’s
The Term Structure of Interest Rates
(Relationship between time to maturity and yield to maturity)

YTM %
Abnormal Yield Curve

Normal Yield Curve

Maturity Period
The Term Structure of Interest Rates

 Short term yield is lower than long term
yield
 Why not the investors go for only long
term bonds?
Nominal and Real Interest Rate
(Inflation and The Time Value of Money)
Consumer Price Index
 %age increase in CPI is the measurement of
Inflation
 Current or nominal dollar and constant or Real
dollar

US CPI 1947-1993
800
Power
Index (1947=100)
Consumer Price

600
400
of dollar
200
Series1
0
Years
Years (1947-1992)
Real Future value of investment
= Investment X (1+ nominal interest rate)
(1+ Inflation rate)
Real rate of interest             Rate at which the
= (1+ nominal interest rate) - 1 of an investment
(1+ inflation rate)            increases
Approximately it is the diff of NIR and IR if
Nos. are small
Real Cash Flow = Nominal Cash Flow
(1+Inflation rate)
Current cash flows to be discounted by the nominal
interest rate and the real cash flows by the real interest
rate
• Price of the bond and its valuation
Price/PV (Bond)= PV (Coupon Payments)+ PV
(Principal)
= (coupon X n-years annuity factor)
+ (final payment X n- year discount factor)
Example: A 07 years 7.5% annual Coupon
rate treasury bond with face value of \$1000
{Suppose the prevailing rate on a similar risk security
(TB) is 5.41%}
Price/ Market value /PV= 75    1     -          1
0.0541     0.0541 (1.0541)7

= 427.60 + 691.56
= \$1119.56

What if the required rate of return is different
in different years?
Valuation of Common Stock
•   Common Stock and Preferred Stock
•   Primary and Secondary markets
•   Stock Exchange Working
•   Reading The Stock Market Listing
•   Dividend
•   Price Earning Ratio
Valuation of Common Stock
• Book Value and Market Value
• Liquidation Value
• Going Concern Value – The diff. between
Book value and liquidation value- Can be
traced to:
 Extra Earning Power
 Intangible assets; and
 Value of Future Investments
Valuing Common Stock
•   Valuing Common Stock
Pay offs to owners comes in two ways
a) Cash Dividend
b) Capital Gains or Losses
Hence:
Expected Return =
r = DIV1 + ( P1 – P0)
P0
= Expected Dividend + Expected Capital
Yield               appreciation

Today’s Price = P0 = DIV1 + P1
1+ r
Valuing Common Stock
P1 is dependent upon all future cash flows
P1 = P2 + DIV2
1+ r
P2 = P3 + DIV3
(1+r)2
…..

P0 =    DIV1 + DIV2 + DIV3 +…..+ DIVH + PH
(1+r) (1+r)2 (1+r)3        (1+r)H

The Dividend Discount Model
Valuing Common Stock
•   Dividend dependent upon:
a) EPS
b) Dividend Policy
The present value of all dividends = PD0
= DIV1 + DIV2 + DIV3 +….. + DIVt
1+ r (1+ r)2 (1+ r)3     (1+ r)t
If constant dividend:
PD0 = DIV 1 + 1         + 1 + ………+ 1
1+ r (1+ r)2 (1+ r)3    (1+ r)t
If t     ∞
PD0 = DIV
r
Valuing Common Stock

The Dividend Discount Model with No Growth
(100% Dividend Pay out Ratio )

If the company pays a constant dividend – a
Perpetuity…
PD0 =   DIV1
r
PD0 = EPS1
r
Valuing Common Stock
The Dividend Discount Model with Constant Growth
(Gordon Growth Model)
DIV1 = 3
DIV2 = 3(1+ g) = 3 (1+.08) = 3.24 (Suppose g = 8%)
DIV3 = 3(1+g)2 = 3 (1+.08)2= 3.50
PD0 = D1 + D1(1+g)2 + D1(1+g)3 +……. = DIV1
1+r     (1+r)2      (1+r)3           r–g
= DIV0 + DIV1 (If the immediate dividend is included)
r–g
= DIV0 (1+g) (Because DIV1 = DIV0 X g)
r-g
Provided:       a) g is constant       b) g < r
c) Dividend is paid    d) There is no loss
Valuing Common Stock
The expected rate of return
PD0 = DIV1 =
r–g
r = DIV1 + g = The Market Capitalization rate
PD0
= Dividend Yield + Growth Rate
DIV1 + g = r = Expected rate of return offered by other, equally risky stocks
PD0

Given DIV1 and g                     So that subject company offers an
Investors set the stock Price         adequate expected rate of return r
Valuing Common Stock
Growth Stocks and Income Stocks
o   Payout Ratio            EPS/BVPS          1-POR
o   Plowback Ratio                               (b)
o   g = Return on Equity X Plowback ratio
o   Present Value of Growth opportunities (PVGO)
o   Sustainable Growth Rates (g)
o   Methods to alter Profits
 Depreciation Methods
 Inventory Evaluation Methods
 Treating R&D Expense as current rather than
Investment
 Methods of Reporting Tax Liabilities
Some Warnings about Constant-Growth Model
• r is only for a single share . A large number of
equal risk securities may be taken into
account
• Resist applying it to firms with high current
rates of growth – Difficult to sustain these
rates
• Avoid using it in inflationary period
• Do not use simple constant-growth formula to
test whether the market is correct in its
assessment of share’s value. You may be
making poor dividend forecast
Remember: There are no mechanical rules to
forecasting future

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 views: 39 posted: 7/7/2010 language: English pages: 38
Description: valuation of bonds and other inventories