7. valuation of securities

8/3/2019 7. Valuation of Securities

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Financial Management I

7. Valuation of Securities

Dr. Suresh

[email protected]

Phone: 40434399, 25783850


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Course Content - Syllabus

*Book reference

Sr Title ICMR Ch. PC Ch. IMP Ch.

1 Introduction to Financial Management 1* 1 12 Overview of Financial Markets 2* 2 -3 Sources of Long-Term Finance 10* 17 20, 214 Raising Long-term Finance - 18* 20, 21, 235 Introduction to Risk and Return 4* 8, 9 4, 56 Time Value of Money 3* 6 27 Valuation of Securities 5* 7 38 Cost of Capital 11* 14 99 Basics of Capital Expenditure

Decisions 18* 11 810 Analysis of Project Cash Flows - 12* 10, 1111 Risk Analysis and Optimal Capital

Expenditure Decision - 13* 12

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Valuation of Securities

Reference Books

1. Financial Management, ICMR Book, Chapter 5

2. Financial Management, Prasanna Chandra, 7th

Edition,

Chapter 7

3. Financial Management, I. M. Pandey, 9th Edition,

Chapter 3


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SyllabusValuation of Securities

1. Concept of Valuation

2. Bond Valuation

3. Equity Valuation: Dividend Capitalization Approach

and Ratio Approach

4. Valuation of Warrants and Convertibles


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Investments in bonds and equity

Valuation is based on time value of money, risk and

returns.

Finance manager needs to have knowledge of valuation

Needs the understanding of the company over a time

span

Estimation of future profitability and growth


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Concept of Valuation

Security can be regarded as a series of dividends or

interest payments receivable over a period of time.

Therefore value of any security can be defined as the

present value of these cash streams. This present value is

also called as intrinsic value of an asset. It is expressed as

below


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Where V0 = Value of the asset at time 0, which is P0,

present value of an asset

Ct = Expected cash flow at the end of period t

k = Discount rate or required rate of return on

the cash flows

n = Expected life of an asset

n

n

2

2100

k)(1C...

k)(1C

k)(1C)P(orV

n

1t

t

t

k)(1

C


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Example

Calculate the value of an asset if the annual cash flow is

Rs. 2000 per year for next 7 years and the discount rate

is 18%.

Solution

Present value of an asset

= 2000 x PVIFA(18%,7year)

= 2000 x 3.812

= Rs. 7624

n

1tt

t0

k)(1

CV

7

1tt

)18.0(12000


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Concepts of Value

Book value

Replacement value

Liquidation value

Going concern value

Market value


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Book Value: This is an accounting concept. Assets are

recorded at historical costs and they are depreciated over

years. Book value may include intangible at acquisition

cost minus amortized value. Book value of debt is stated

at the outstanding amount. The difference between the

book value of assets and liabilities is equal to

shareholders funds or net worth (which is equal to paid-

up equity capital plus reserves and surplus).

Replacement value: is an amount required to replace an

existing assets in the current condition.


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Liquidation value: is an amount that a company can

realize if it sells its assets after terminating its business. It

is generally a minimum value which a company may

accept if it sells its business.

Going concern value: is an amount a company can realize

if it sells its business as an operating one. Its value would

always be higher than the liquidation value.

Market value: of an asset or security is the current price at

which the asset or security is being sold or bought in the

market.


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2. Bond Valuation

Bond are negotiable promissory notes that can be used by

governments, government agencies, business firms or

individuals. Bonds issued by the government or public

sector companies in India are generally secured. Private

sector companies issue secured or unsecured bonds. In

case of bonds, the rate of interest is fixed. A bond is

redeemable after a specific period.

Face value: is the value stated on the face of he bond and is

also known as par value. It is an amount specified to

repay after a time o maturity. Bond is generally issued at

face value usually Rs. 100 and sometimes Rs. 1000.


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2. Bond Valuation

Coupon Rate or Interest: is payable on the face value of

the Bond.

Maturity: Bond is issued for a specific period of time. It is

repaid on maturity. Typically corporate bonds have a

maturity of 7-10 years, whereas government bonds have

maturity period up to 20-25 years.

Redemption value: is a value which a bondholder gets on

maturity is called redemption value.

Market value: Bond may be traded in a stock exchange.

Market value is the price at which the bond is usually

bought or sold.

2 B d V l i


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2. Bond Valuation

Basic Bond Valuation Model

Bondholder receives a fixed annual interest payment for

a certain number of years an a fixed principal payment

(face value or par value) at the time of maturity.

Therefore the present value or the intrinsic value of bond

V0 = I x PVIFA(kd,n) + F x PVIF(kd,n)Where V0 = Present value P0 or intrinsic value of a bond

I = Annual interest payable on the bondF = Face value or the par value or the principle

amount payable on maturity

n = Maturity period of bondk = Re uired rate of return

n

1tn

dt

d

t00

)k(1

F

)k(1

C)P(orV

2 B d V l i


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2. Bond Valuation

Example

A bond with face value Rs. 1000 bears a coupon rate of

12% and has a maturity period of 3 years. The required

rate of return on the bond is 10%. Calculate the value of

this bond?

Solution

Annual interest payable = Rs. 1000 x 12% = Rs. 120

Principal repayable at the end of 3 years = Rs. 1000 Value of the bond

=Rs.120x PVIFA(10%, 3trs)+Rs.1000x PVIF(10%,3yrs)

= 120 x 2.487 + 1000 x 0.751 = Rs. 1049.44

n

1tn

dt

d

t0

)k(1

F

)k(1

CV

2 B d V l i


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2. Bond Valuation

Example

A bond with face value Rs. 1000 bears a coupon rate of 7%

and has a maturity period of 5 years. The required rate

of return on the bond is 8%. What should an investor be

willing to pay now to buy the bond if it matures at par?

Solution

Annual interest payable for 5 yrs = Rs. 1000x7% =Rs. 70

Principal repayable at the end of 5 years = Rs. 1000 Present value of the bond

=Rs.70x PVIFA(8%, 5trs)+Rs.1000x PVIF(8%,5yrs)

= Rs. 70 x 3.993 + Rs. 1000 x 0.681 = Rs. 960.51

n

1tn

dt

d

t0

)k(1

F

)k(1

CV

2 B d V l ti


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2. Bond Valuation

Bond values with Semi-annual Interest

Some of the bonds carry interest payment semi-annually.

Hence bond valuation equation is modified as

= I / 2 x PVIFA(kd/2,2n)+F x PVIF(kd/2,2n)

Where I/2 = Semi-annual interest payment

kd/2= Required rate of return for the half-

year period

2n = Maturity period expressed in half-yearly

periods

2n

1t 2ndtd

0

/2)k(1

F

/2)k(1

I/2V

2 B d V l ti


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2. Bond Valuation

Example

A bond of Rs. 1000 value carries a coupon rate of 10%and

a maturity period of 6 years. Interest is payable semi-

annually. If the required rate of return is 12%, calculate

the value of the bond.

Solution

= Rs. 50 x PVIFA(6%,12yrs)+1000 x PVIF(6%,12yrs)

= 50 x 8.384 + 1000 x 0.497 = Rs. 916.20

2n

1t2n

dt

d

0

/2)k(1

F

/2)k(1

I/2V

12

1t12t

0.12/2)(1

1000

0.12/2)(1

100/2

2 B d V l ti


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2. Bond Valuation

Bond Yield Measures

One Period Rate of Return

If a bond is purchased and then sold one year later, its

rate of return over this single holding period can be

defined as one period rate of return.

The holding period can be calculated on a daily, monthly

or annual basis. If the bond price falls by an amount that

exceeds coupon interest, the rate of return assumes

ne ative values.

period)holdingtheofbeginningat theprice(Purchase

paid)ifinterest(Couponperiod)holdingduringlossorgain(Price

2 B d V l ti


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2. Bond Valuation

Example

Mr. X purchased Rs. 1000 par value bond for Rs. 900. The

coupon payment on this bond is Rs. 80 i.e. 8%. One year

later he sells the bond for Rs. 800. Calculate the rate of

return to Mr. X for this one year period.

Solution

Holding period return

period)holdingtheofbeginningat theprice(Purchase

paid)ifinterest(Couponperiod)holdingduringlossorgain(Price

900

80900)-(800 2.22%or0.0222

900

20

900

80100-

2 B d V l ti


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2. Bond Valuation

Current Yield

Current yield measures the rate of return earned on a

bond if it is purchased at its current market price and if

the coupon interest is received.

In earlier example

Coupon interest is Rs. 80

Current market price is Rs. 800

Current yield = 80 / 800 = 0.10 or 10%

Coupon rate and current yield are two different measures.

PriceMarketCurrent

InterestCouponYieldCurrent

2 B d V l ti


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2. Bond Valuation

Yield to Maturity (YTM)It is the rate of return earned by an investor who

purchases a bond and holds it till maturity. YTM is the

discount rate which equals the present value of promised

cash flows to the current market price / purchase price.

Where kd = YTM

n

1tn

dt

d

t00

)k(1F

)k(1C)P(orV

2 B d V l ti


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2. Bond Valuation

Example

Consider a Rs. 1000 par value bond whose current

market price is Rs. 850. The bond carries a coupon rate

of 8% and has a maturity period of 9 years. Calculate

the rate of return an investor earns if he purchases the

bond and holds till maturity.

Solution

=Rs.80x PVIFA(kd%,9yrs)+ Rs.1000x PVIF(kd%,9yrs)

n

1tn

dt

d

t00

)k(1F

)k(1C)P(orV

9

1t9

dt

d )k(1

1000

)k(1

80850Rs.

2 B d V l ti


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2. Bond Valuation

To find out the value of kd in the above equation, several

values of kd will have to be tried out in order to reach the

input value. Therefore to start, consider a discount rate

of 12% for kd. The expression becomes

Rs.80 x PVIFA(12%,9yrs)+ Rs.1000 x PVIF(12%,9yrs)

= Rs. 80 x 5.328 + Rs. 1000 x 0.361

= Rs. 426.24 + 361 = Rs. 787.24

Since the above value is less than Rs. 850 market price, we

have to try with a less discounting rate kd. So let kd =

10% then

2 Bond Val ation


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2. Bond Valuation

Rs.80 x PVIFA(10%,9yrs)+ Rs.1000 x PVIF(10%,9yrs)

= Rs. 80 x 5.759 + Rs. 1000 x 0.424

= Rs. 460.24 + 424 = Rs. 884.72

From above, it is clear that kd lies between 10% and 12%.

We have to use linear interpolation between 10% and

12%.

= 10% + 0.71 = 10.71%

Yield to maturit is 10.71%

787.24-884.72

850-884.72x10%)(12%10%kd

2 Bond Valuation


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2. Bond Valuation

Bond Value TheoremsBased on the bond valuation models, several bond value

theorems have been derived, based on the effects of

following factors on bond values.

Relationship between required rate of return and the

coupon rate

Number of years to maturity

Yield to maturity

n

1tn

dt

d

t00

)k(1

F

)k(1

C)P(orV

2 Bond Valuation


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2. Bond Valuation

Theorem 1

When the required rate of return is equal to the coupon

rate, the value of the bond is equal to its par value.

i.e. id kd = coupon rate,

then value of a bond = par value

Example

Consider a bond with par value Rs. 100, coupon rate

12% and years to maturity 5 years. Calculate the value

of a bond if required rate of return is 12%.

Solution

2 Bond Valuation


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2. Bond Valuation

Vo = I x PVIFA(kd,n) + F x PVIF(kd,n)= 12 x PVIFA(12%,5) + 100 x PVIF(12%,5)

= 12 x 3.605 + 100 x 0.567

= 43.26 + 56.7

= Rs. 100

n

1tn

dt

d

t00

)k(1F

)k(1C)P(orV

2 Bond Valuation


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2. Bond Valuation

Theorem 2

When the required rate of return kd is greater than the

coupon rate, the value of the bond is less than its par

value.

Theorem 3

When the required rate of return kd less than the coupon

rate, the value of the bond is greater than its par value.

3 Equity Valuation: Dividend Capitalization


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3. Equity Valuation: Dividend CapitalizationApproach and Ratio Approach

Equity valuation models are used to determine the

intrinsic value (also called as real value or the fair value)

of the stock. This value is compared with market price of

stock to determine whether the stock is under valued or

over valued. Accordingly investment decisions, buy or

sell of the stocks are decided.

According to dividend discount model, value of an equityshare is discounted present value of dividends received

plus the present value of the sale value expected when

the equity stock is sold.



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For applying the dividend discount model, we will make

following assumptions.

Dividends are paid annually.

First dividend is received one year after the equity

stock is bought.



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Single-period Valuation Model

This model is for an equity stock where an investor holds

it for one year. The price of such equity stock will be

Where, P0 = Present value of the share or current

market price of the share

D1 = Expected dividend a year hence

P1 = expected price of the share a year hence

ke = required rate of return on the equity share

)k(1

P

)k(1

DP

e

1

e

10



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Example: A company is expected to declare a dividend of

Rs. 2.50 and reach a price of Rs. 35 a year hence. What is

the price at which the share would be sold to the

investors now if required rate of return is 13%?

Solution

The present value of the share

)k(1

P

)k(1

DP

e

1

e

10

)13.0(1

35

)13.0(1

2.50

312.21

33.21Rs.



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If the price of the equity share is expected to grow at a rate

of g percent annually, the present price P0 becomes

P0(1+g) a year hence, we get

Simplifying above, we get

)k(1

g)(1P

)k(1

DP

e

0

e

10

g)-(k

DPe

10



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Example: The expected dividend per share on the equity

share of a company is Rs. 2. The dividend per share of a

company has grown at a rate of 5% per year and this

growth is expected to continue in future. Market price of

equity share is also expected to grow at the same rate.

Calculate the present value of the stock if the required

rate of return is 15%.

Solution:g)-(k

DP

e

10

20Rs.0.05)-(0.15

2



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Multi-period Valuation Model

This is more realistic model for an equity valuation.

Since equity shares have no maturity period, they may

be expressed to bring a dividend stream of infiniteduration.

(1)

Where, P0 = present value of the share or currentmarket price of the share

D1 = expected dividend a year henceD2 = expected dividend two years hence

D = expected dividend at the end of infinityk = re uired rate of return on the e uit share

1tt

e

t

e2

e

2

e

10

)k(1

D

)k(1

D...

)k(1

D

)k(1

DP



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Above equation is for valuation of equity share of infinite

duration. For finite duration, same equation can be

applicable, if the investor holds the stock for n years and

then sells it at a price Pn. The value of equity share forfinite duration would be

(2)

Applying dividend discounting principle, value of Pn would

be the present value of the dividend stream beyond the

nth ear evaluated at end of nth ear. This means

n

1tn

e

n

te

t

)k(1

P

)k(1

D

ne

n

ne

n

2e

2

e

10

)k(1

P

)k(1

D...

)k(1

D

)k(1

DP



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Substituting this value of Pn in equation (2) we get

(3)

This is same as equation (1) which may be regarded as a

eneralized multi- eriod valuation formula.

)k(1

D...

)k(1

D

)k(1

DP

e2

e

2n

e

1nn

)k(1

D...

)k(1

D

)k(1

D

)k(1

1

)k(1

D...

)k(1

D

)k(1

DP

e2

e

2n

e

1n

ne

ne

n

2e

2

e

10

)k(1

D...

)k(1

D

)k(1

D...

)k(1

D

)k(1

D

e

1n

e

1n

n

e

n

2

e

2

e

1

1tt

e

t

)k(1

D



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Equation (1) is general enough to permit any dividend

patterns: constant, rising, declining or randomly

fluctuating. Such cases are as below

1. Constant dividends

2. Constant growth of dividends

3. Changing growth rates of dividends



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1. Valuation with constant dividends

We assume that dividend per share is constant year

after year, at a value of D. Then equation (1) becomes

On simplification, this equation becomes

(4)

This is a present value of perpetuity formula, used in

earlier cha ter.

)k(1

D...

)k(1

D

)k(1

DP

e2

ee

0

e

0

k

DP



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2. Valuation with constant growth in dividends

It is assumed that dividends tend to increase at a

constant growth rate (g), because business firms

usually grow over time. Equity share valuation under

this assumption is

Applying the formula for the sum of geometric

progression, this equation simplifies to

...

)k(1

ng)(1D...

)k(1

g)(1D

)k(1

DP

1n

e

1

2

e

1

e

10

g-k

D

P e

1

0

3. Equity Valuation: Dividend Capitalization


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Example: A company is expected to grow at a rate of 7%

per annum and dividend expected a year hence is Rs. 5.

If the required rate of return for this stock is 12%,

calculate the valuation of this stock.

Solution

g-k

DP

e

10

0.07-0.12

5

100Rs.0.05

5



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3. Valuation with variable growth in dividends

Some forms have a super normal growth rate followed

by a normal growth rate. Valuation of share will be

During super normal growth period the stock valuation

At the end of super normal growth period, followed by

constant growth period. The valuation in this period

ne

n

ne

1na1

3e

2a1

2e

a1

e

10

)k(1

P

)k(1

)g(1D...

)k(1

)g(1D

)k(1

)g(1D

)k(1

DP

n

1tt

e

t

)k(1

D



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This is discounted to get the present value. Therefore

discounted valuation is

Addition of valuations of both periods, we get

nene

1nn

1tt

e

t0

)k(1

1x

)g(k

D

)k(1

DP

ne

1nn

gk

DP

nene

1n

)k(1

1x

)g(k

D



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Example: A company having current dividend per shareRs. 3. Super normal growth period of 5 years with a

growth rate of 25%. After this, normal growth is 7%.

Investors required rate of return is 14%. Calculate thevaluation of this equity stock.

Solution: 1. Dividends stream during super normal

growth period: D1 = Rs. 3 (1.25)D2 = Rs. 3 (1.25

2)

D3 = Rs. 3 (1.253)

D4 = Rs. 3 (1.254)

D = Rs. 3 (1.255)



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Present value of above stream of dividends is

2. At the end of 5 years, applying a constant growth model

5

5

4

4

3

3

2

2

(1.14)

3(1.25)

(1.14)

3(1.25)

(1.14)

3(1.25)

(1.14)

3(1.25)

(1.14)

3(1.25)

ne

n5

ne

65

gk

)g(1D

g-k

DP

4.764.343.963.613.29Rs.

19.96Rs.

0.07-0.14

)07.1(3(1.25) 5 140Rs.

0.07

9.8



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Discounted value of this price is

Sum of values of both the periods is

Valuation of the share P0 = Rs. 92.67

72.71Rs.(1.14)

1405

72.71Rs.19.96Rs.P0

92.67Rs.

3. Equity Valuation: Ratio Approach


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This is also known as multiplier approach or the relative

valuation approach. This approach is useful in

comparing the stocks in a particular industry sector.

Widely used ratios are

1. Price / Earning ratio (P/E ratio)

2. Price / Book Value ratio (P/BV ratio)

3. Price / Liquidation value ratio (P/L ratio)

3. Equity Valuation: Approach


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3. Equity Valuation: Approach

Price / Earnings Ratio

P/E model is used more frequently than P/B or P/L

models.

Expected earnings per share is

P/E ratios may have wide variations over a time period

depending on the variability of earnings.

sharesequitygoutstandinofNumber

dividendPreferred-PATExpected



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Book Value

Book value per share is the net worth of the company

(paid-up equity capital plus reserves and surplus)

divided by the number of outstanding equity shares.

Liquidation Value

Liquidation value per share is the value realized from

liquidating all assets of the firm minus amount to be paid

to all the creditors and preference shareholders divided

by number of outstanding equity shares.



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. Va uat o o Wa a ts a d Co ve t b es

Warrants and convertible debentures are commonly used

instruments of financing.

Warrant is a call option to buy a stated number of shares.

They entitle the holder to buy a fixed number of sharesat a predetermined price during some specified period of

time. It gives the holder the right to subscribe to the

equity shares of a company. Warrants expire at certain

date. They may also be a perpetual warrants, which

never expire. Warrants are issued to sweeten the

offering. For example, a debenture or a bond is issued by

a company along with warrant.



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Warrant Price

Exercise price of warrants is always greater than the

current market price. Price may be fixed for the entire

life of the warrant or increased periodically. Terms are

specified for number of shares that can be purchased for

each warrant. Usually the ratio is 1:1 i.e. one share for

each warrant.

Convertible Debentures

Convertible debentures are convertible partly or fully

into equity shares.



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Conversion Ratio and Conversion Value

Conversion ratio gives the number of shares to be

received for each convertible security. Conversion value

represents the market value of the convertible if it were

converted into stock.

*****

7. valuation of securities

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