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Valuation of Securities

B y ; - ) A j a y r a n a , S o n a m g u p t a ,S h i v a n i , G u r p r e e t , S h i l p a

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Fixed income securities

These securities are the ones on which the issuing company

is bound to pay or has an obligation to provide regularreturns at a fixed rate to investors in the form of interest ordividend payment . These are ;

1. Debentures / bonds

2. Preference shares

Fluctuating income securities

These securities are the ones on which the issuing companyis not bound to pay or has no obligation to provide regular

returns at a fixed rate to investors in the form of interest ordividend payment. These are Equity shares of a company.

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SeveralKinds of ValueThere are several types of value, of which we are concerned

with three:

Book Value - The assets historical cost less its accumulateddepreciation

Market Value - The price of an asset as determined in acompetitive marketplace

Intrinsic Value - The present value of the expected future cashflows discounted at the decision makers required rate of

return

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Bonds-

1. A bond is a tradable instrument that represents a debt owed to

the owner by the issuer. Most commonly, bonds pay interestperiodically (usually semiannually) and then return theprincipal at maturity.

2. Most corporate, and some government, bonds are callable. Thatmeans that at the companys option, it may force the

bondholders to sell them back to the company.

Types of Bonds -1. Government Bonds - These basically long term bonds issued by

RBI on behalf of GOI.

2. Corporate Bonds - Companies borrow money by issuing bondscalled corporate bonds or corporate debentures.

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Types of Corporate Bonds1. Straight Bonds - It is also called as plain vanilla bond. It pays fixed

periodic coupon over its life and returns the principle on the maturity

date.2. Zero Coupon bonds -It does not carry regular interest payments. It is

issued at a step discount on face value and redeemed at face value onmaturity.

3. Floating Rate bonds - These do not pay fixed interest but pay a

benchmark rate such as the treasury bill interest rate.

4. Commodity Linked Bonds -The pay off on commodity linked bondsdepends to a certain extent on the price of the commodity.

5. Bonds with embedded options These options give certain rights to theinvestors or issuers:

1. Convertible Bonds - Gives the bond holder the right to convert them into equity

share on certain terms

2. Callable Bonds - Gives the issuer the right to redeem the bonds issued by themon certain terms

3. Puttable Bonds - Gives the investor the right to prematurely sell the bonds back

to the issuer on certain terms.

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Bond Yields -Bonds are generally traded on the basis of their prices. Howeverthey are not usually compared on the basis of their prices because ofsignificant variations in their cash flow patterns and other features.Instead they are compared in yields.

Commonly employed yield measures -

Current Yield

1. It related the annual coupon interest to the market price.Current yield= Annual Interest/Price

Eg : The current yield of a 10 year and 12% coupon rate bond with par valueof Rs.1000 and selling of Rs.950 is

= .12*1000/950 = 12.63

2. It reflects only coupon interest rates. It does not consider capital gain orloss that an investor will realize if the bond is purchased at discount orpremium. It ignores time value of money

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Yield to Maturity -This method is employed to anticipate the gross rate of returnsoffered by the bond over its life.

C= Annual Interest in Rupees

M=Maturity Value in Rupees

n=No of years left to maturity

P=Price of bond

r=Coupon Rate

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Eg: A Rs.1000 par value bond carrying a coupon rate of9% and maturing after 8 years .The bond is currentlyselling for Rs.800. What if the YTM on this bond?

800= [90/(1+r)8]+ [1000/(1+r)8]

By hit and Trial=90 (PVAF 12%,8 yrs) + 1000 (PVF 12%,8 yrs)= Rs.851.0

=90 (PVAF 14%,8 yrs) + 1000 (PVF 14%,8 yrs) =Rs. 768.1=90 (PVAF 13%,8 yrs) + 1000 (PVF 13%,8 yrs) =Rs. 808

Applying interpolation:

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

OR

YTM = C+(M-P)/n = 90+(1000-800)/8 = 13.1%0.4M+0.6P 0.4*1000 + 0.6*800

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Yield to Call -

Some bonds carry a call feature that entitles the issuer tobuy back the bonds prior to the stated maturity date. Forsuch bonds both YTC and YTM are calculated:

YTC=[C/(1+r)t

]+ [M*/(1+r)n*

]

Where n*= No of years until the call date

M*=Call Price

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Risks in Bond -

1. Inflation Risk - The interest rates are declared in nominal terms. Thus itshould be adjusted with the expected inflation.

2. Default Risk -It is the risk that the borrower may not pay the interest orprinciple on time.

3. Call risk - The issuer may buy back the bond when the interest rates are

declining. This risk is attractive from the issuer point of view but not fromthe investor point of view.

4. Liquidity Risk - Barring for some of the popular govt securities most of thedebt instruments are not traded actively. Thus there is poor liquidity inthe debt market and the investors face difficulties in trading the same.

5. Reinvestment Risk - When the bond pays periodic interest there is a riskthat the interest payments may have to be reinvested at a lower interestrate. This risk is greater for bonds with longer maturity and higherinterest payment.

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Risks in Bond (Conti.)

6. Foreign Exchange Risk - If a bond has payments that are dominatedby foreign currency it rupee cash flow is uncertain as there is arisk of depreciation of rupee in comparison to foreign currency.

7 .Interest Rate Risk - Interest rates tend to vary causing fluctuations

in bond prices.

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Bond Terminology -

1. There are several terms with which you must be familiarto solve bond valuation problems:

1. Coupon Rate - This is the stated rate of interest on the bond. It isfixed for the life of the bond. Also, this rate time the face valuedetermines the annual interest payment amount.

2. Face Value - This is the principal amount (nominally, the amountthat was borrowed). This is the amount that will be repaid atmaturity

3. Maturity Date - This is the date after which the bond no longerexists. It is also the date on which the loan is repaid and the last

interest payment is made.

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Calculating the Value of a Bond -

1.

There are two types of cash flows that are provided by a bondinvestments:

1. Periodic interest payments (usually every six months, but anyfrequency is possible)

2. Repayment of the face value (also called the principal amount, which

is usually $1,000) at maturity2. The following timeline illustrates a typical bonds cash flows:

0 1 2 3 4 5

100 100 100 100 100

1,000

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Calculating the Value of a Bond (cont.)

Redeemable Bond

Vd=I(ADFI)+F(DFF)

Vd= Value of Bond or Debenture

I=Interest Payable on bond/Coupon Rate

ADFI=Annuity discount factor applicable to interest

DFF= Appropriate discount factor applicable to face value

F= Face Value

Irredeemable Bond

Vd=A/i

A=Interest Amount

i = Expected Rate of Interest

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Bond Valuation: An Example

Assume that you are interested in purchasing a bondwith 5 years to maturity and a 10% coupon rate. Ifyour required return is 12%, what is the highest pricethat you would be willing to pay?

0 1 2 3 4 5

100 100 100 100 100

1,000

= Present value for annuity for 100 @ 12% + present value of1000 for 5 years @ 12%

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Some Notes About Bond Valuation

1. The value of a bond depends on several factors such astime to maturity, coupon rate, and required return

2. We can note several facts about the relationship betweenbond prices and these variables:

1. Higher required returns lead to lower bond prices, and vice-versa

2. Higher coupon rates lead to higher bond prices, and vice versa

3. Longer terms to maturity lead to lower bond prices, and vice-versa

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Valuation of debenture / Bonds

A debenture/bond is a tradable instrument thatrepresents a debt owed to the owner by the issuer. Mostcommonly, bonds pay interest periodically (usuallysemiannually) and then return the principal at maturity.

Debentures can be classified as ;-

1. Redeemable

2. Non redeemable / Perpetual

3. Convertible

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Valuation Mechanism Valuation of Redeemable Debentures

Valuation of Deep Discount Debentures / Bonds Valuation of Non redeemable Debentures

Valuation of Convertible Debentures

Valuation of Redeemable DebenturesValue of these debentures is the present value of inflows to be

received by the investor in future. The inflows are like regular

interest payment every year , till the date of maturity and thepayment of maturity value at the end of maturity period.

CALCULATION :-

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Formula ;-

Vd = IX PVIFAr,n +M X PVIFr,n

Here

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Valuation of Deep Discount Debentures / Bondsa deep discount debenture is the one , which does not carry any rate of

interest and where the company is not bound to pay interest at regular

intervals . Herein , it is issued at a discount to face value and redeemable atpar on the maturity . The discount rate is the investors required rate ofreturn .

CALCULATION :-

FORMULA - Vd= M x PVIFr,n

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Solution -

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Valuation of Non redeemable DebenturesA perpetual debenture is the one in which a company is to pay the

interest at a regular interval throughout the life of the company ,

but the principal amount is not refunded by the company duringits life time . Therefore , the investor will receive only the interestevery as specified by the company , the value of this is nothing butthe value of a perpetuity discounted at investors required rate ofreturn .

FORMULA

Vd= I/r x 100

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Solution -

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Valuation of Convertible Debentures

FORMULA

Vd= I x PVIFAr,n+ M x PVIFr,n

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Solution -

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Valuation of preference share -

Features of preference shares are similar to debentures , with the

only difference that in preference shares , the company pays thedividend and in case of debenture , it the interest . Therefore ,value of preference share can be calculated in the same way as indebentures . Preference shares can be different types redeemable , non redeemable and convertible . The sameformulae and process of debentures valuation can be appliedwith the little change of replacing the interest amount with thedividend amount . Preferred stock represents an ownershipclaim on the firm that is superior to common stock in the event of

liquidation. Typically, preferred stock pays a fixed dividendperiodically and the preferred stockholders are usually notentitled to vote as are the common shareholders.

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Redeemable Preference Share

FORMULA - Vp=D(ADFD)+F(DFF)

here , Vp= Value of Preference ShareD= Dividend Payable on Preference Share

ADFD=Annuity discount factor applicable to dividend

DFF= Appropriate discount factor applicable to face value

F= Face Value

Irredeemable Preference Share

FORMULA - Vp=D/Kphere ,

D= Dividend Amount

Kp =Current Yield

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Valuation of equity -

A share of common stock represents an ownership position

in the firm. Typically, the owners are entitled to vote onimportant matters regarding the firm, to vote on themembership of the board of directors, and (often) to receivedividends.

There are three method of valuation of equity -1. Balance sheet valuation

2. Dividend discount model

3. Free cash flow model

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Common Stock Valuation

1. Just like with bonds, the first step in valuing common stocks

is to determine the cash flows

2. For a stock, there are two:

1. Dividend payments

2. The future selling price

3. Again, finding the present values of these cash flows andadding them together will give us the value

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Balance sheet valuation-Three measures derived from the balance sheet are;

1. Book value,

2. liquidation value, and

3. Replacement cost.

Book value : The book value per share is simply the net worth of thecompany divided by the number of shares.

Liquidation value : The liquidation value per share is equal to:

Value realised - Amt. paid to creditors &pref. sh. Holders.

number of outstanding shares

Replacement cost : The use of this method is based on the premise thatthe market value of a firm cannot deviate too much from itsreplacement cost.

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Dividend discount model

1. The value of an equity share is equal to the present value of

dividends expected from its ownership plus the present value ofthe sale price expected when the equity share is sold

2. Assumptions

3. Dividend paid annually

4. 1st dividend is received 1 year after purchaseTypes of dividend discount model -

1. Single-period valuation model

2. Multi-period valuation model

3. Zero growth model

4. Constant growth model

5. Two stage growth model

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Single period valuation model

1. Where the investor expect to hold the equity share forone year.

1. Expected rate of return

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Multi period valuation model

This is more realistic and complex

P0 = D1+ D

2+ Dn

(1+r) (1+r)2 (1+r)n

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Common Stock Valuation: An Example

Q. Assume that you are considering the purchase of astock which will pay dividends of $2 next year, and$2.16 the following year. After receiving the second

dividend, you plan on selling the stock for $33.33.What is the intrinsic value of this stock if your requiredreturn is 15%?

VCS

2 00

1 15

2 16 33 33

1 152857

1 2

.

.

. .

..

2.00 2.1633.33

?

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Zero growth model:

This model is applicable when the dividend per share

remains constant year after year at a value of D.Po = D/r

Constant Growth model:

It assumes that the dividend received by the shareholder willgrows at a constant rate.

OR,

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Calculating Value of Equity :

Valuation of equity when there is a constant growth ratein dividend for a finite period

D0= Current Dividend

D1= Expected Dividend

g = Growth Rate of Dividend

Kcs = Expected Return on common stock

Vcs = Value of Common Stock

VD g

k gD

k gCS

CS CS

0 1

1

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An Example

Recall our previous example in which the dividendswere growing at 8% per year, and your required returnwas 15%

The value of the stock must be:

V

CS

185 1 08

15 08

2 00

015 08

2857. .

. .

.

. .

.

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Calculating Value of Equity :

When there is constant growth of dividend for infinite period(Earning Capitalisation Approach)

V = Amount of Dividend / Ke

For Example:

ABC Ltd is currently paying dividend @ Rs.60 .The currentyield is 15%. Calculate the value of share.

Answer : 60/.15 = 400

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Two stage growth model :This is the extension of the constant growth model assumes

that the extraordinary growth will continue for a finitenumber of years and there after the normal growth rate

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H model ;

1. Assumptions:

2. Current dividend growth rate is higher(ga)

3. After 2H year the growth rate become gn.

4. At H year the growth rate is exactly halfway between gaand gn.

Po = D0[(1+gn)+H(ga-gn)]/ r-gn

or

P0 = D0(1+gn)/r-gn +D0h(ga-gn)/r-gn

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Free cash flow models This model broadly involves determining the value of the firm as a whole

by discounting the free cash flow to investors and then subtracting the valeof pref. and debt to obtain the value of equity.

Total return = Dividend yield + capital gain yield

Divide the future value in two parts, the explicit forecast period and thebalance period.

Forecast the free cash flow, year by year, during the explicit forecast periodFCF= NOPAT- net investment

Calculate the weighted average cost of capital

WACC= WeRe + WpRp.WdRd(1-t)

Establish the horizon value

Vh=FCFH+1/WACC-g

Estimate the enterprise value

Drive the equity value

Ent. Value Pref. Value Debt value

Compute the value per share

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