Valuation of Bonds and Stocks(3)

VALUATION OF BONDS AND STOCKS

By Prof Sameer Lakhani

OUTLINE Distinction among valuation concepts Bond Valuation Bond Yields Bond Market Preferred Stock Valuation Equity Valuation : Dividend Discount Model Equity Valuation : PE Ratio Approach Earnings-Price Ratio, Expected Return, and Growth Stock Market

OUTLINE Distinction among valuation concepts Bond Valuation Bond Yields Bond Market Preferred Stock Valuation Equity Valuation : Dividend Discount Model Equity Valuation : PE Ratio Approach Earnings-Price Ratio, Expected Return, and Growth Stock Market

CONCEPTS OF VALUE Liquidation Value Going Concern Value Book Value

(Valuation are based on Going Concern Basis)

(BV of Equity = BV of Assets ± BV of Liabilities)

Market Value Intrinsic Value (Present Value of Cash flow stream expected from the security discounted at a rate of return appropriate for the risk associated with the security

TERMINOLOGY Par Value : Value stated on the face of the bond Coupon Rate : Par Value * Coupon Rate Maturity Period : Par Value is payable.

Value of a Bond = PV of the cash flow expected from An estimate of expected cash flows An estimate of the required return

VALUE OF A BOND

P

n =

t=1

C

(1+r)

t

+

M

(1+r) n

P = C x PVIFA r,n + M x PVIF r,n Assumptions: Coupon Interest rate is fixed for the term of the bond

Annual coupon payments & next coupon payment is exactly a year no Bond will be redeemed at par on Maturity.

ILLUSTRATION

To illus trate h ow t o compu te the p r ic e of a b o nd, co 10-year, 12 p er c ent coupo n b o nd wi th a p ar va lu e of 1,0 us a ssum e that the req ui red yi e ld o n th is b o nd is 13 p er c a s h flows fo r th is b o nd are a s follows:

10 ann u a l coupo n p ay m ent s of Rs . 120 Rs . 1000 p r i n cip a l re p ay m ent 10 year s f r om n ow T he va lu e of the b o nd is: P = 12 0 x PVIFA 1 3% , 1 0 yrs + 1, 000 x PVIF

= 120 x 5.426 + 1,000 x 0.295 = 651.1 + 295 = Rs . 946.1

1 3% , 1 0 yr s

VALUE OF A BOND WITH SEMI-ANNUAL INTEREST B o nd s

p ay Intere st Se mi Ann u a lly m ean s o n c e in every six mo nth s. eq u atio n need s to be mo d ifi ed a lo ng the following line s:

B ond

T he ann u a l Intere s t p aym ent , C mus t be d iv ided by two to o bta in s e mi a intere s t p aym ent. N um ber of year s to m atu r ity mus t be mul tiplied by two to get the n um ber year ly p er io d s . D iscou nt rate ha s to be d iv ided by two to get the d iscou nt rate a pplic ab le year ly p er io d s .

P

2n

=

t=1

C/2

(1+r/2) t

+

M

(1+r/2) 2n

P = C/ 2 x (PVIFA r/2,2n ) + M (PVIF r2,2n )

ILLUSTRATION

A s an illus trat io n, co n si der an 8 year, 12 p er c ent cou wi th a p ar va lu e of Rs . 100 o n w h ic h i ntere s t is p aya ann u a ll y. T he req ui red ret u rn o n th is b o nd is 14 p er c en Va lu e of the b o nd is:

P

16 = t=1

6 (1.07)

t

+

100 (1.07)16

= 6(PVIFA 7%,16 ) + 100 (PVIF 7%,16 )

= Rs . 6(9.447) + Rs .100 (0.339) = Rs . 90.

PRICE-YIELD RELATIONSHIP

A ba sic p r op erty of b o nd is that its p r ic e var ie s inver s e ly with A s the req ui red y ie ld de c rea se s the PV of the c a s h flow In c rea hen c e the p ric e In c rea s e s . When the req ui red y ie ld In c rea s e s the PV of c a s h flow de c rea hen c e the p r ic e de c rea s e s .

Pr o b le m: C oupo n rate of 14 p er c ent issu ed 3 year s ag o fo r Rs 1000 (Par Va lu e).T he o rig ina l M atu rity of the b o nd w a s 10 year s re sid u a l m atu rity n ow is 7 year s . T he Intere s t rate ha s f a ll en 3 year s & Inve s to r n ow ex p e c t a retu rn of 10 p erc ent from b o nd. What is the p ric e of th is b o nd n ow? An sw er : 1194.5

Pro b le m: T here is a r is e in Intere s t rate, inve s to rs ex p e c t a r 18 p erc ent. b o nd. What is the p ric e of th is b o nd n ow? An sw er : 848.5

PRICE-YIELD RELATIONSHIP

Coupon Rate, Required Yield, & Price

To sum up , the re latio n sh ip bet w een the c

rate, the req uired y ie ld, and the p r ic e is a s follo C oupo n rate > R eq ui red y ie ld Pr ic e > Par (Pre mium b o nd)

C oupo n rate > R eq uired yie ldPr ic e = Par C oupo n rate < R eq uired yie ldPr ic e < Par (D iscou nt b o nd)

PRICE - YIELD RELATIONSHIP

Pr ic e of a b o nd mus t be eq u a l t o to its p ar va lu e at m atu rity a ssuming that there de f ault, b o nd p ric e s change s with t im e. F o r E.g. A b o nd that is redee m ab le fo r Rs year s w hen it m atu re s will have a p ric e of Rs 1000 at m atu rity n o m atter w hat the is .If its p ric e is s ay Rs 1100 it is s a id to be a p re mium b o nd. If the req uired yie ld bet w een n ow and the m atu rity date the p re mium will de cline o ver t im e a s sh ow .On the o ther hand if the b o nd ha s a cu rrent p ric e of s ay Rs 900 it is s a id t o be a d T he d iscou nt too will d is app ear o ver tim e a s s h ow n by C u rve B .On l y w hen the C u rre Par Va lu e there is n o change in p ric e a s t im e p a ss e s a ssumi ng that the req uired y c hange bet w een n ow and the m atu rity date. PRICE CHANGES WITH TIME VALUE OF B OND

PREMIUM BOND: r d = 11% A PAR VALUE BOND: r d = 13% DISCOUNT BOND: r d = 15%

8

7

6

5

4

3

2

B

1

0 YEARS TO MATURITY

BOND PRICE THEOREMS 1. BOND PRICES & YIELDS MOVE IN OPPOSITE DIRECTIONS 2. BOND PRICES ARE MORE SENSITIVE TO YIELD CHANGES THE LONGER THEIR MATURITIES 3. THE PRICE SENSITIVITY OF BONDS TO YIELD CHANGES INCREASES AT A DECREASING RATE WITH MATURITY

4. HIGH COUPON BOND PRICES ARE LESS SENSITIVE TO YIELD CHANGES THAN LOW COUPON BOND PRICES

5. WITH A CHANGE IN YIELD OF A GIVEN NUMBER OF BASIS POINTS, THE ASSOCIATED PERCENT GAIN IS LARGER THAN THE PERCENT LOSS.

BOND YIELDS CURRENT YIELD : It relates annual coupon payment to the market price. ANNUAL INTEREST PRICE

Problem: The current yield of a 10 year, 12 percent coupon bond with a par value of Rs 1000 and selling for Rs 950 is ??? (12.63%)

Interpretation: Current yield calculation reflects only the coupon interest rate. It does not considers the capital gain or loss that an investor will realize if the bond is purchas discount or premium and held till maturity. It also ignores the time value of money. is an incomplete and simplistic measure of yield

BOND YIELDS

YIELD TO MATURITY : YTM of a bond is the Interest rate that makes the present v of the cash flow receivable from owning the bond equal to the price of the bond.

Problem: Consider Rs 1000 par value bond carrying a coupon rate of 9 percent maturing aft years. Thee bond is currently selling for Rs 800.What is the YTM of the bond? C

=

P

800 AT r AT r

= = =

C

(1+ r ) 8

+

C

(1+ r ) 2 90

7

t =1

(1+ r )

+ «.

(1+ r ) n

M

+

(1+ r ) n

1,000

+

(1+ r ) 8

t

13% « RHS = 808 14% « RHS = 768.1

808 - 800 YTM = 13% + (14% - 13% ) * = 13.2% 808 - 768.1 C

YTM

+ (M -

P)

/n

0.4 M + 0.6

Linear Interpolation

Approximation

P

YTM calculation considers the current coupon income as well as the capital gain or the Investor will realize by holding the bond to maturity. It takes into account timing of cash

BOND YIELDS

YIELD TO CALL : Bonds carrying a call feature entitles the issuer to call (buy bac bond prior to the stated maturity days in accordance with a call schedule ( which sp call price for each call date).

P

=

where n

n*

C

7

t =1

(1+ r ) t

+

M

*

(1+ r ) n

M

* = C a ll p rice

*

= n umb er o f y ears u n t i l t he ass um ed ca ll da t e

BOND YIELDS

Problem: Consider a 20 year, 10% semiannual pay bond with a full price of 112 th be called in 5 years at 102 and called at par in 7 years. Calculate the YTM, YTC & y first par call? Answer: C = 5 N = 40 Price 112 Maturity 100 YTM = 5 (PVIFA

r%,40 )

+ 112 (PVIF

r%,40 )

Approximate YTM = 4.384 * 2 = 8.768% Exact YTM = 4.3608 * 2 = 8.7216%

C = 5 N = 10 Price 112 Maturity 102 Yield to First Call = 5 (PVIFA

r%,10 )

+ 102 (PVIF

r%,10 )

Approximate Yield to First Call = 3.7 * 2 = 7.41% Exact Yield to First Call = 3.710 * 2 = 7.421%

BOND YIELDS

Problem: Consider a 20 year, 10% semiannual pay bond with a full price of 112 tha called in 5 years at 102 and called at par in 7 years. Calculate the YTM, YTC & yiel first par call? Answer: C = 5 N = 14 Price 112 Maturity 100 Yield to First par Call = 5 (PVIFA

r%,14 )

+ 102 (PVIF

r%,14 )

Approximate Yield to First par Call = 3.8646 * 2 = 7.7293% Exact Yield to First par Call = 3.873 * 2 = 7.7469%

BOND YIELDS

Realized Yield to Maturity: The YTM calculation assumes that the cash flow receive through the life of a bond are reinvested at a rate equal to the YTM.This assumpti not be valid as reinvestment rate applicable to future cash flow may be different. It necessary to define the future reinvestment rates & figure out the Realized YTM.

Problem: Consider a 1000 par value of bond carrying an Interest rate of 15 percent (payable annually) and maturing after 5 years. The present market price of this bo 850.The reinvestment rate applicable to the future cash flow of this bond is 16 perc

REALISED YIELD TO MATURITY FUTURE VALUE OF BENEFITS 0

1

2

3

4

5

ANNUAL INTEREST

150

150

150

150

150

RE-INVESTMENT PERIOD (IN YEARS)

4

2

1

0

INVESTMENT

850

COMPOUND FACTOR (AT 16 PERCENT) FUTURE VALUE OF INTERMEDIATE CASH FLOWS

3

1.81

1.56

1.35

1.16

271.5

234.0

202.5

174.0

MATURITY VALUE TOTAL FUTURE VALUE

1.00 150.0 1000

= 271.5 + 234.0 + 202.5 + 174.0 + 150.0 + 1000

= 2032

(1+ r* ) 5 = 2032 / 850 = 2.391 r* = 0.19 OR 19 PERCENT

P R O B LE M

T he M ar k et p ric e of a Rs 1000 p ar va lu e b o nd c arry ing coupo n rate of 14 p er c ent and m atu ring a fter 5 year s is Rs 1050.What is the Y TM o n th is b o nd ? What is the a pp r o x im ate Y TM ? What will be the rea liz ed Y TM if the re inve s tm ent rate is 12 p erc ent?

An sw er: Y TM: 12.60% A pp r o x im ate Y TM : 12.62% R ea liz ed Y TM : 12.89%

VALUATION OF PREFERENCE STOCK

P

n =

t=1

D

(1+r p ) t

+

M

(1+r p ) n

S in c e the s trea m of d iv idend s is an o rd inary ann ui ty, w e c an fo rmul a fo r the p re s ent va lu e of an o rd inary ann uity. Hen c e th the p re feren c e s tock is: P o = D x PVIFAr p,n + M x PVIFr p,n

VALUATION OF PREFERENCE STOCK To illus trate h ow t o compu te the va lu e of a p re feren c co n si der an 8 year, 10 p er c ent p re f eren c e s t ock wi th

va lu e of Rs . 1000. T he req ui red retu rn o n th is p re f ere s tock is 9 p er c ent.

P = 100 x PVIFA 9%, 8yr s + 1000 x PVIF 9%, 8 y = 100 x 5.535 x 1000 x 0.502 = Rs . 1110.5

EQUITY VALUATION: DIVIDEND DISCOUNT MODEL

According to DDM the value of an equity share is equal to the

present value of dividends expected from it plus the present va the sale price expected when the equity shares is sold.

Assumptions:

Dividends are paid annually First dividend is received one year after the share is bought.

DIVIDEND DISCOUNT MODEL SINGLE PERIOD VALUATION MODEL P1 D1 P0 = + (1+ r ) (1+ r ) Where

P0=

Current price of equity share

D1 = Dividend expected a year hence P1=

Price of the share expected a year hence

r = Rate of return required on equity share.

Problem: RIL is expected to provide a dividend of Rs 2 & fetch a pr Rs 18 a year hence. What price would it sell for now if investors req rate of return is 12 percent? (Answer 17.86)

DIVIDEND DISCOUNT MODEL

MULTI - PERIOD VALUATION MODEL: Equity shares have no maturity period they may be expected to bring a dividend stream of infinite duration

P0 =

g 7

Dt

t =1 (1+ r ) t

P0 = Price of the equity share today D1 = Dividend expected a year hence. D

g

= Dividend expected at the infinity.

r = Expected return

DIVIDEND DISCOUNT MODEL

ZERO GROWTH MODEL: Assumes dividend per share remain constant year after year. D P0 = r

DIVIDEND DISCOUNT MODEL

DIVIDEND DISCOUNT MODEL

DIVIDEND DISCOUNT MODEL

CONSTANT GROWTH MODEL: Assumes that dividend per sha grows at a constant rate. D1 P0 = r±g (g = grow t h ra t e in dividend is cons t

Problem: ABC ltd is expected to grow at the rate of 6 percent per annum.D expected on ABC equity share a year hence is Rs 2 . What price will you pu your required rate of return for this share is 14 percent? (Answer Rs 25)

Constant growth model includes four variables so if we know any three of can solve for the fourth.

EXPECTED RATE OF RETURN What rate of return can the investor expect, given the current market pric the forecast value of dividend & share price?

r =

D1 P0

+ g

Problem: Expected dividend per share of ABC ltd is Rs 5. The dividend is ex to grow at the rate of 6 percent per year. If the price per share now is Rs 50 the expected rate of return? (Answer 16%)

EXPECTED GROWTH

g = r-

D1 P0

Problem: Equity stock of ABC is currently selling for Rs 30 per share. The dividend expected next year is Rs 2.The investors required rate of return is percent. If the constant growth rate model applies to ABC what is the expe growth rate? (Answer 8.3%)

STRENGTHS & LIMITATIONS OF CONSTANT GROWTH MODEL

DIVIDEND DISCOUNT MODEL SINGLE PERIOD VALUATION MODEL P1 D1 P0 = + (1+ r ) (1+ r ) MULTI - PERIOD VALUATION MODEL g Dt P0 = 7 (1+ r ) t t =1 ZERO GROWTH MODEL D P0 = r CONSTANT GROWTH MODEL D1 P0 = r-g

WHAT DRIVES GROWTH Most stock valuation models are based on the assumption that dividends grow over time. What drives this growth? Two Major drivers of the growth are:

1. Retention Ratio (Ploughback Ratio) 2. Return on Equity (ROE)

Problem: Omega ltd has an Equity (net worth) base of 100 beginning of year 1. I ROE of 20% . It pays out 40% of its equity earnings and plough back 60% of its e earnings. The financial of Omega Limited for 3 year is given. Year 1 Beginning Equity 100 Return on Equity 0.2 Equity Earnings 20 Dividend payout ratio 0.4 Dividends 8 Plougback ratio 0.6 Retained Earnings 12

Year 2 Year 3 112 125.44 0.2 0.20 22.4 25.09 0.4 0.40 8.96 10.04 0.6 0.60 13.44 15.05

Dividends grow @ 12% per annum from 8 to 8.96 & from 8.96 to 10.04. g = ROE * RR i.e. 0.2 * 0.6 = 0.12

TWO - STAGE GROWTH MODEL

TWO - STAGE GROWTH MODEL

TWO - STAGE GROWTH MODEL

P0

=

D1

1 - 1 +g 1 1+r r - g1

n

+

Pn

(1+ r ) n

WHERE Pn

=

(1+ r ) n

D 1 (1+g1 ) n-1 (1+ g 2 )

r - g2

1 (1+ r ) n

TWO - STAGE GROWTH MODEL

Problem: The current dividend on an equity share of pi Technology is Rs 3.00.Pioneer is expected to enjoy an above growth rate of 40% for 5 years. Thereafter the growth rate w & stabilize at 12%.Equity Investors require a return of 15 pe from pioneer stock. What is the intrinsic value of the equity sh pioneer? (Answer = 28.12 + 299.37 = 327.49)

TWO - STAGE GROWTH MODEL H - MODEL

H MODEL ga gn

H

PO

=

D0

r - gn

2H

(1+ g n ) + H ( g a - g n )

P o = Intr in sic Va lu e of s hare D o = C u rrent d iv idend p er D 0 (1+ g n ) share = + r = R eq uired rate of retu rn r - gn g n = N o r m a l lo ng r u n gr ow th rate ga = H igh gr ow t h ra t e VALUE BASED H = One ha lf of the p erio d ON NORMAL d u r ing w h ic h ga will leve l GROWTH RATE off to g n

INCORRECT FORMULA

D 0 H (g a - g n)

r - gn

CORRECT FORMULA

PREMIUM DUE TO ABNORMAL GROWH RATE

ILLUSTRATION :H MODEL

Problem: The current dividend on equity share of International computers ltd is Rs

present growth rate is 50% .However this will decline linearly over a period of 10 y

then stabilize at 12% .What is the Intrinsic value per share of International compute the Investors require a return of 16% ?

Po =

3 ( 1.12)

+

0.16 ± 0.12 =

84

+

=

226.5

3 * (10 / 2) * (0.50 ± 0.12) 0.16 ± 0.12

142.5

Problem: The current dividend on equity share of ABC ltd is Rs 5.The present grow

is 50% .However this will decline linearly over a period of 8 years and then stabilize

10% .What is the Intrinsic value per share of ABC ltd if the Investors require a retur 18% from this stock? (Answer: 168.75)

THREE STAGE DDM MODEL

THREE STAGE DDM MODEL

Problem: Vardhman Ltd earnings & dividends have been growing at a rate of 18

This growth rate is expected to continue for 4 years. After that the growth rate w 12% for the next 4 years. Thereafter the growth rate is expected to be 6% forever.

dividend per share was Rs 2 and the Investors required rate of return is 15%. Wh Intrinsic value per share? (Answer Rs 16.83 + Rs 23.49 = Rs 40.32)

TERMINAL VALUE

TERMINAL VALUE

IMPACT OF GROWTH ON PRICE, RETURNS, AND P/E RATIO

The expected growth rates of companies differ widely. Some companies ar expected to remain virtually stagnant or grow slowly, other companies are expected to show normal growth, still others are expected to achieve super growth rate. Assuming a constant total required return, differing expected rate means differing stock prices, dividends yields, capital gain yields & Pr Earning ratio. Illustration: Consider three cases: Growth Rate (%) Low growth firm

5

Normal growth firm

10

Supernormal growth firm 15

The expected Earnings per share & dividend per share of each of the three are Rs 3 & Rs 2 respectively. Investors required total return from equity investments is 20%.

IMPACT OF GROWTH ON PRICE, RETURNS, AND P/E RATIO PRICE PO=

LOW GROWTH FIRM

NORMALGROWTH FIRM

SUPERNORMAL GROWTH FIRM

PO

D1

YIELD

r-g

(D 1 / P O )

RS. 2.00 = = RS.13.33 0.20 - 0.05 RS. 2.00

PO

=

= RS.20.00 0.20 - 0.10 RS. 2.00

PO

=

DIVIDEND

= RS.40.00 0.20 - 0.15

CAPITAL

PRICE

GAINS EARNINGS YIELD RATIO (P 1 - P O ) / P O (P / E )

15.0%

5.0%

4.44

10.0%

10.0%

6.67

5.0%

15.0%

13.33

IMPACT OF GROWTH ON PRICE, RETURNS, AND P/E RATIO Results in the above mentioned table suggest the following points: I.

As the expected growth in dividend increases, others things being equ expected return depends more on the capital gains yield and less on th dividend yield.

II.

As the expected growth in dividend increases, others things being equ Price ± Earnings ratio Increases.

III. High dividend yield and low price earning ratio imply limited growth prospects. IV.

Low dividend yield and high price earning ratio imply considerable gro prospects.

EARNINGS MULTIPLIER APPROACH ± P/E Ratio. P0

=

m E1

DETERMINANTS OF P0

P0

=

=

=

(P /

E

)

D1

r-g E1

(1 -

b)

r - ROE x

(1 - b ) P0/ E1

m

r - ROE x

b

Eq u atio n Ind ic ate s that the f a c to r s th deter mine the P/E ratio are : T he d ividend p ayou t ratio , (1-b) b T he req uired rate of retu rn, r T he ex p e c ted grow th rate , R OE * b

EARNINGS MULTIPLIER APPROACH ± P/E Ratio. P/E ratio & R etentio n ratio: What is the e ff e c t of a c hange in b o n the P/E ratio? It dep end s o n h ow R OE comp ares wi th r. If R OE > r an in c rea s e in b lead s to an in c rea s e in P/E. If R OE = r an in c rea se in b ha s n o eff ec t on P/E. If R OE < r an in c rea s e in b lead s to an de c rea s e in P/E.

P/E ratio & Intere s t rate : T he req uired rate of retu rn o n eq uity s tocks re fle c ts intere s t ra When Interes t rate in c rea s e, req uired rates of retu rn o n a ll s e cu r iti e s in clu d ing s tocks i pus h ing s ecu rity p ric es d ow n w ard s . When Intere s t rate f a lls s ecu rity p ric e ris e. Hen c e inver se relat ion sh ip betw een P/E ratio & interes t rate. P/E ratio & Risk: Other th ing s be ing eq u a l r iski er s tocks have low er P/E multiple s . Risk have h igher req uired rates of retu rn (r) and hen c e low er P/E multiple s . T h is is tru e in a j us t the co n s tant gr ow th mo de l. F o r nay ex p e c ted earn ing s & d i v idend s s trea m , the p re will be low er w hen the s trea m is co n sidered to be r iskier. Hen c e the P/E multipl e will be

P/E ratio & L iq uid ity : Other s th ing s be ing Eq u a l s tocks w h ic h are h igh ly li q uid comm and P/E multiple s &s tocks w h ic h are h igh ly Illiq ui d comm and low er P/E multipl e. Inve s t o r liq uid ity j us t the w ay they va lu e s a f ety & hen c e are willing to give h igher P/E multiple to li s tock .

E / P, EXPECTED RETURN, AND GROWTH 1

2 ««...

E1

= D1 = 15

E2

= D2 = 15

r = 15%

15 P0

=

0.15

= 100

INVESTMENT .. RS. 15 PER SHARE IN YEAR 1 « EARNS 15% 2.25 NPV PER SHARE = - 15 + = 0 0.15 RATE O

RETURN

INCREMENTA CASH FLOW

PRO ECT'S

IMPACT ON

NPV IN

SHARE PRICE

YEAR 1

IN YEAR 0

SHARE PRICE I N Y E A R 0,

P

E

1

/P 0

r

0

0.05

0.75

-1 0

-8 .70

91.30

0.164

0.15

0.10

1.50

-5

-4 .35

95.65

0.157

0.15

0.15

2.25

0

0

0 .15

0.15

0.20

3.00

5

4.35

104.35

0.144

0.15

0.25

3.75

10

8.70

108.70

0.138

0.15

0

IN GENERAL, WE CAN THINK OF THE STOCK PRICE AS TH C A P I TA L I S E D VA LU E O F T H E E A R N I N G S U N D E R T H E A SS U M P T I O N O N O G R O W T H P LU S T H E P R E S E N T VA LU E O F G R O W T H O P P O RT U N I T I E (PVGO).

E P0

=

1

r

+ P VGO

M A N I PU L AT I N G T H I S A B I T, W E G E T E P0

1

=

r

1

-

PVG O P0

FRO M TH I S EQ UATI ON, I T I S CLE AR TH AT : y y y

EARNINGS -PRICE RATIO IS EQUAL TO R WHEN PVGO IS ZERO. EARNINGS -PRICE RATIO IS LESS THAN R WHEN PVGO IS POSITIVE. EARNINGS -PRICE RATIO IS MORE THAN N E GAT I VE .

R

WHEN PVGO IS

NE T P R ESEN T VALUE

NE T P R ESEN T VALUE

Firm p aying n o d iv idend s : It som et im e s ha pp en s that a comp any a lth ou gh earn s p rofit b u t

d o e s n o t de clare d iv i dend s . H ow would d iv i dend c a pita liz at io n mo de l ex pla in the s hare va u nder suc h circums tan c es?.In f a c t

STOCK MARKET Principal Exchanges The National Stock Exchange The Bombay Stock Exchange

Veritable Transformation Screen-based Trading Electronic Delivery Rolling Settlement

STOCK MARKET INDICES Bombay Stock Exchange Sensitive Index (Sensex) Base year 1978-79

p

100

30 shares Value-weighted index of the free float S & P CNX Nifty Base period ; November 3, 1995 50 shares Value-weighted index

p

1,000

SUMMING UP

T he ter m va lu e is us ed i n d iff erent sen s e s . Liquidation value , going concern value , book value , market value , a intrinsic value are the mos t commo n l y us ed co n c e p t s of va lu e. T he intrinsic value of any a ss et, rea l o r finan ci a l, is eq u a l to the p re sent va lu e of the c a sh flows ex p e c ted from i t. Hen c e, deter min i ng the va lu e of an a ss et req uire s an e stim ate of ex p e c ted c a sh flows and an e s tim ate of the req uired ret u rn. T he va lu e of a b o nd is:

P =

n

t= 1

C

(1+r) t

+

M

(1+r) n

SUMMING UP A ba sic p r op erty of a b o nd is that i t s p r ic e var i e s i nver s e l y wi th y i e l d. T he re lat io n s h ip bet w een coupon rate , required yield , and b o nd p r ic e is a s follows: C oupo n rate < R eq uired y ie ld Pr ic e < Par (D iscou nt b o C oupo n rate = R eq uired y ie ld Pric e = Par C oupo n rate > R eq ui red y iePr ldic e > Par (Pre mium b o nd)

T he current yield o n a b o nd is de fined a s: Ann u a l intere s t Pr ic e.

SUMMING UP T he yield to maturity (Y TM ) o n a b o nd is the rate of ret u rn the i nve s t o r earn s w hen he b u y s the b o nd and h ol d s i t t ill m It is the va lu e of r in the b o nd va lu at io n mo de l. F o r e s t Y TM read ily, the following a pp ro x im at io n m ay be used Y TM =

C + ( M - P )/n 0.4 M + 0.6 P

A cco rd i ng t o the dividend discount model , the va lu e of an eq uity share is eq u a l to the p re s ent va lu e of d iv idend s e ed from i ts ow ner s h ip .

If the d iv idend p er s hare re m a in s co n stant rate, the va lu s hare is: PO = D / r

SUMMING UP

If the d i v i dend p er s hare gr ows at a co n s tant rate, the va lu e of the s hare is: P O = D 1 / (r ± g ) T he t wo k ey dr iver s of d i v i dend gr ow th are (a) plou ghba and (b) ret u rn o n eq uity. T he va lu e p er s hare, a cco rd i ng t o the H model is: P =

D o (1+g n )

r ± gn

+

D O H ( g a -g n )

r - gn

An a pp ro a c h to va lu atio n, p ra c tis ed wide ly by inve s tm ent ana lys ts , i the P/E ratio a pp ro a c h. T he va lu e of an eq uity s hare, u nder a pp r o a c h, is e s tim ated a s follows: PO = E1 x PO / E1

SUMMING UP

T he s tock p ric e m ay be co n si dered a s the c a pita lis ed va

of the earn i ng s u nder the a ssump t io n of n o gr ow th plu p re s ent va lu e of gr ow th oppo rtu n i t i e s .

T he s tock m ar k et co n sis ts of a primary segment and a

secondary segment . T he p r i n cip a l b ou r s e s are the Nationa Stock Exchange and the Bombay Stock Exchange ,

a ccou nting fo r the b ulk of the trad ing o n the Ind ian s m ar k et.

G

ENE R AL T HEO RY ON VALUAT ION

G

ENE R AL T HEO RY ON VALUAT ION

G

ENE R AL T HEO RY ON VALUAT ION

G

ENE R AL T HEO RY ON VALUAT ION

G

ENE R AL T HEO RY ON VALUAT ION

G

ENE R AL T HEO RY ON VALUAT ION

G

ENE R AL T HEO RY ON VALUAT ION