4-+Valuation+of+Money +Stocks +Bonds

8/8/2019 4-+Valuation+of+Money +Stocks +Bonds

1/38

Valuation of

Money,

Stock; and

Bonds


2/38

The Time Value of Money

Simple and compound interest

Future Values and Compound Interest

As m approaches infinity, the factor

where e = 2.71828

,

1

mT

m T

rfv

m

= +

( )1m

rrm

e+


3/38

The Time Value of Money Given continuous compounding, the future

value of a dollar n periods hence is

r TTfv e=


4/38



5/38


Annually Compounded Interest Rates

(Effective Interest Rate)

(EIR)

= (1+ i/m)m -1

VsAnnual Percentage Rates (i)

= Monthly rate X 12

= Quarterly rate X4


6/38


Present Values

Pv = Future Value After t Periods

(1+r)t

DF is always


7/38

The Time Value of MoneyCompounding

Periodm Interest

per

period%

(1+i/m)mEIR

%

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


8/38

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


9/38

The Time Value of MoneyAnnuity

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)tGrowing Annuities= C

1C

1(1 g) C

1(1 g)2 C

1(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

+

++

+++++ +.+

+

+

+

-- -


10/38

Types of Annuities

Ordinary Annuity

Annuity DuePV AnnuityDue =PV Ordinary Annuity for (t-1) Payments

+

Initial Payment

Annuity Deferred

PV AnnuityDeferred = PV OrdinaryAnnuity

(1 + r)n-1

Where n = No. of years annuity delayed


11/38

General Annuity when compoundingperiods 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 period2) Convert the payments to EACs that

correspond with the compounding periods


12/38

Convert the interest rate to the effective ratefor the payment period

R=100 per month for 03 yearsi = 14% pa, being compounded daily

Effective daily rate = .14/365 =0.0003836 or0.03836%

(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 - 10.010796 0.010796(1+ 0.010796)39

= 3169.28


13/38

Convert the payments to EACs that correspondwith the compounding periods

R=100i = 14% pa, being compounded daily

Effective daily rate = .14/365 =0.0003836 or 0.03836%EAC =?

100 =EAC 1 - 10.0003836 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


14/38

Relationship between Present Value, Future

Value and Equivalent Annuity Cash Flows

PV

EACEAC

FV

Multiply PV byinverse of present

value annuity factor

Multiply EAC byFuture value

annuity factor

Multiply EAC bypresent valueannuity factor

Multiply FV byinverse of Future

value annuity factor


15/38

Perpetuities

Pv of Perpetuity = C/r

Pv of Growing Perpetuity = C1

C2(1 g) C

3(1 g)2

(1 r) (1 r)2 (1 r)3

= C1

(r - g)

+ ++ +

+ + +.

+


16/38

Declining Discount Factor?

Basis of Capital Market A dollar tomorrow has value lower than

a dollar today

There is no money machine (arbitrage)


17/38


Net Present Value of Project

= Pv ofCash flows outRequired Investment

Remember:A risky dollar is worth less than a

safe one

Other Names:

Present Value or just Pv

Discounted ValueMarket Price

Market Value


18/38

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 bonds price to present

value) Rate of Return on Bonds The %age rate of

actual income upon investment by holding a bondfor a specific period


19/38

Effects of interest rates on bonds market

values/Prices

PV of bondpayments

Interest rate, %

Th Ti V l f B d


20/38


Reading the Financial Pages

Treasury Bonds

Maturity AskRate 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

CouponRate p.a

It is in32nds

YTM ofInvestorIt is quoted in 32nds

Prices are100 + 10/32 = 100.315% of Face value

(Spread of 2/32)&

116+ 17/32 = 116.375%of Face value

(Spread of 4/32)

Note

Th Ti V l f B d


21/38

The Time Value of BondsReading the Financial Pages

Other Bonds

Cur. Net

Bonds Yld Vol Close Chg

AT&T 81 /8 22 7.7 84 105 1/4

CouponRate p.a.

of 1 % offace vale

Interest income as percentage of theBonds price

Interest income =81.25 (8 1/8% of 1000)Bonds Price =1052.50

Cur. Yld = 81.25/1052.50 = 0.077 =7.7%

Year ofmaturity

105 of the facevalue

How to show pricebelow par value?


22/38


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 Thediscount rate that makes the present value of a

bonds payments equal to its price (Diff in facevalue 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

Standard

& Poors

Moodys


23/38

YTM %

Abnormal Yield Curve

Normal Yield Curve

Maturity Period

The Term Structure of Interest Rates(Relationship between time to maturity and yield to maturity)


24/38

The Term Structure of Interest Rates

Short term yield is lower than long termyield

Why not the investors go for only long

term bonds?


25/38

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

0

200

400

600

800

Years

Years (1947-1992)

ConsumerPrice

Index

(1947=100)

Series1

Purchasing

Power

adjusted value

of dollar


26/38

Real Future value of investment

= Investment X (1+ nominal interest rate)

(1+ Inflation rate)Real rate of interest

= (1+ nominal interest rate) - 1

(1+ inflation rate)Approximately it is the diff of NIR and IR if Nos. are

smallReal Cash Flow = Nominal Cash Flow

(1+Inflation rate)

Current cash flows to be discounted by the nominal interestrate and the real cash flows by the real interest rate

Rate at which the

purchasing power

of an investment

increases


27/38

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)


28/38

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 differentin different years?


29/38

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


30/38

Valuation of Common Stock

Book Value and Market Value

Liquidation Value

Going Concern Value The diff. betweenBook value and liquidation value- Can be

traced to:Extra Earning Power

Intangible assets; and

Value of Future Investments

V l i C St k


31/38

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 CapitalYield appreciation

Todays Price = P0 = DIV1 + P1

1+ r


32/38

Valuing Common StockP1 is dependent upon all future cash flows

P1 = P2 + DIV21+ 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

..



33/38


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 = DIVr

V l i C St k


34/38


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

If the company pays a constant dividend a

Perpetuity

PD0= DIV

1

r

PD0 = EPS1r



35/38


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

= (Because DIV1 = DIV0 X g)

Provided: a) g is constant b) g < r

c) Dividend is paid d) There is no loss

DIV0 (1+g)

r - g


36/38


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 DIV

1and g So that subject company offers an

Investors set the stock Price adequate expected rate of return r


37/38


Growth Stocks and Income Stocks

o Payout Ratioo Plowback Ratio

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

1-POR(b)

EPS/BVPS


38/38

Some Warnings about Constant-Growth Model

r is only for a single share . A large number of

equal risk securities may be taken intoaccount

Resist applying it to firms with high currentrates 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 itsassessment of shares value. You may bemaking poor dividend forecast

Remember:There are no mechanical rules toforecasting future

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4-+Valuation+of+Money +Stocks +Bonds