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Valuation of Securities

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What is Value?

In general, the value of an asset is the price that awilling and able buyer pays to a willing and ableseller

Note that if either the buyer or seller is not bothwilling and able, then an offer does not establish thevalue of the asset

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Several Kinds of Value

There are several types of value, of which we areconcerned with three: Book Value - The assets historical cost less its accumulated

depreciation Market Value - The price of an asset as determined in a

competitive marketplace

Intrinsic Value - The present value of the expected futurecash flows discounted at the decision makers required rateof return

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Determinants of Intrinsic Value

There are two primary determinants of the intrinsicvalue of an asset to an individual: The size and timing of the expected future cash flows

The individuals required rate of return (this is determined bya number of other factors such as risk/return preferences,returns on competing investments, expected inflation, etc.)

Note that the intrinsic value of an asset can be, and

often is, different for each individual (thats whatmakes markets work)

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Types of Securities

Debentures

Equity

Preference Shares

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Bonds

A bond is a tradeable instrument that represents adebt owed to the owner by the issuer. Mostcommonly, bonds pay interest periodically (usuallysemiannually) and then return the principal at

maturity. Most corporate, and some government, bonds are

callable. That means that at the companys option, itmay force the bondholders to sell them back to the

company.

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Types of Bonds

Government Bonds

These basically long term bonds issued by RBI onbehalf of GOI.

Corporate Bonds

Companies borrow money by issuing bonds calledcorporate bonds or corporate debentures.

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Types of Corporate Bonds

Straight Bonds

It is also called as plain vanilla bond. It pays fixedperiodic coupon over its life and returns the principleon the maturity date.

Zero Coupon bonds

It does not carry regular interest payments. It isissued at a step discount on face value and redeemedat face value on maturity.

Floating Rate bonds

These do not pay fixed interest but pay a benchmarkrate such as the treasury bill interest rate.

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Types of Corporate Bonds (Conti.) Bonds with embedded options

These options give certain rights to the investors or issuers:

1. Convertible Bonds

Gives the bond holder the right to convert them into equityshare on certain terms

2. Callable BondsGives the issuer the right to redeem the bonds issued bythem on certain terms

3. Puttable Bonds

Gives the investor the right to prematurely sell the bonds

back to the issuer on certain terms. Commodity Linked Bonds

The pay off on commodity linked bonds depends to a certainextent on the price of the commodity

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Bond Yields

Bonds are generally traded on the basis of theirprices. However they are not usually comparedon the basis of their prices because of significantvariations in their cash flow patterns and otherfeatures. Instead they are compared in yields.

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Commonly employed yield measures

Current Yield

1. It related the annual coupon interest to the marketprice.

Current yield= Annual Interest/Price

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

= .12*1000/950 = 12.63

2. It reflects only coupon interest rates. It does notconsider capital gain or loss that an investor willrealise if the bond is purchased at discount orpremium. It ignores time value of money

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Commonly employed yield measures (Conti.)

Yield to Maturity

This method is employed to anticipate the gross rateof returns offered by the bond over its life.

C= Annual Interest in Rupees

M=Maturity Value in Rupees

n=No of years left to maturityP=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 CallSome bonds carry a call feature that entitles the

issuer to buy back the bonds prior to the statedmaturity date. For such bonds both YTC and YTM

are calculated:

YTC=[C/(1+r)t]+ [M*/(1+r)n*]

Where n*= No of years until the call dateM*=Call Price

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Risks in Bond

Inflation RiskThe interest rates are declared in nominal terms. Thus it shouldbe adjusted with the expected inflation.

Default Risk

It is the risk that the borrower may not pay the interest orprinciple on time.

Call risk

The issuer may buy back the bond when the interest rates aredeclining. This risk is attractive from the issuer point of view

but not from the investor point of view. Liquidity Risk

Barring for some of the popular govt securities most of the debtinstruments are not traded actively. Thus there is poor liquidityin the debt market and the investors face difficulties in trading

the same.

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Risks in Bond (Conti.)

Reinvestment Risk

When the bond pays periodic interest there is a riskthat the interest payments may have to be reinvestedat a lower interest rate. This risk is greater for bonds

with longer maturity and higher interest payment. Foreign Exchange Risk

If a bond has payments that are dominated byforeign currency it rupee cash flow is uncertain as

there is a risk of depreciation of rupee in comparisonto foreign currency.

Interest Rate Risk

Interest rates tend to vary causing fluctuations in

bond prices.

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Bond Terminology

There are several terms with which you must befamiliar to solve bond valuation problems: Coupon Rate - This is the stated rate of interest on the bond.

It is fixed for the life of the bond. Also, this rate time theface value determines the annual interest payment amount.

Face Value - This is the principal amount (nominally, theamount that was borrowed). This is the amount that will berepaid at maturity

Maturity Date - This is the date after which the bond nolonger exists. It is also the date on which the loan is repaidand the last interest payment is made.

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Calculating the Value of a Bond

There are two types of cash flows that are providedby a bond investments: Periodic interest payments (usually every six months, but

any frequency is possible) Repayment of the face value (also called the principal

amount, which is usually $1,000) at maturity

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 DebentureI=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 price

that 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 of 1000 for 5 years @ 12%

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Some Notes About Bond Valuation

The value of a bond depends on several factors suchas time to maturity, coupon rate, and required return

We can note several facts about the relationshipbetween bond prices and these variables: Higher required returns lead to lower bond prices, and vice-

versa

Higher coupon rates lead to higher bond prices, and vice

versa Longer terms to maturity lead to lower bond prices, and

vice-versa

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Common Stocks /Equity

A share of common stock represents an ownershipposition in the firm. Typically, the owners areentitled to vote on important matters regarding the

firm, to vote on the membership of the board ofdirectors, and (often) to receive dividends

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There are three method of valuation of equity

Balance sheet valuation

Dividend discount model Free cash flow model

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Common Stock Valuation

Just like with bonds, the first step in valuing commonstocks is to determine the cash flows

For a stock, there are two: Dividend payments

The future selling price

Again, finding the present values of these cash flowsand adding them together will give us the value

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Balance sheet valuation-

three measures derived from the balance sheet are;book value, liquidation value, and replacement cost.

Book value: The book value per share is simply thenet worth of the company divided by the number ofshares.

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Liquidation Value

The liquidation value per share is equal to:

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

number of outstanding shares

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Replacement cost

The use of this method is based on the premise that themarket value of a firm cannot deviate too much fromits replacement cost

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Dividend discount model

The value of an equity share is equal to the presentvalue of dividends expected from its ownership plusthe present value of the sale price expected when the

equity share is soldAssumptions

Dividend paid annually

1st dividend is received 1 year after purchase

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Types of dividend discount model

Single-period valuation model

Multi-period valuation model Zero growth model

Constant growth model

Two stage growth model

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Single period valuation model

Where the investor expect to hold the equity sharefor one year.

For example:

Prestige equity share is expected to provide a dividendof Rs 2 and fetch a price of18 a year hence.what pricewould it sell for now if investors required rate of returnis 12%?

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Current price will be

p0= 2 + 18 =Rs.17.86

( 1.12) (1.12)

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Multi period valuation model

This is more realistic and complex

P0 = D1+ D2+ Dn(1+r) (1+r)2 (1+r)n

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Common Stock Valuation: An Example

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 yourrequired return 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 shareremains constant year after year at a value of D.

P0 = D/r

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Constant growth model:

it assumes that the dividend received by theshareholder will grows at a constant rate.

OR,

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Calculating Value of Equity

Valuation of equity when there is a constant growthrate in dividend for a finite period

D0= Current Dividend

D1= Expected Dividendg = Growth Rate of Dividend

Kcs = Expected Return on common stock

Vcs = Value of Common Stock

VD g

k gD

k gCS

CS CS

0 11

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An Example

Recall our previous example in which the dividendswere growing at 8% per year, and your requiredreturn was 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 forinfinite period (Earning Capitalisation Approach)

V = Amount of Dividend / Ke

For Example:

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

Ans: 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 willcontinue for a finite number of years and thereafter the normal growth rate

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H model

Assumptions:

Current dividend growth rate is higher(ga)

After 2H year the growth rate become gn.

At H year the growth rate is exactly halfway betweenga and gn.

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

orP0 = D0(1+gn)/r-gn +D0h(ga-gn)/r-gn

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Free cash flow models

This model broadly involves determining the valueof the firm as a whole by discounting the free cashflow to investors and then subtracting the vale of

pref. and debt to obtain the value of equity. Total return = Dividend yield + capital gain yield

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Divide the future value in two parts, the explicitforecast period and the balance period.

Forecast the free cash flow, year by year, during the

explicit forecast period

FCF= NOPAT- net invistment

Calculate the weighted average cost of capital

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

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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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Preferred Stock

Preferred stock represents an ownership claim on thefirm that is superior to common stock in the event ofliquidation. Typically, preferred stock pays a fixed

dividend periodically and the preferred stockholdersare usually not entitled to vote as are the commonshareholders.

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Preferred Stock Valuation

Redeemable Preference ShareBasically, the value of a redeemable preference share is the present

value of all the future expected dividend payments and thematurity value, discounted at the required return on preferenceshares.

Value of redeemable preference share=

Dividend1 + Dividend2 +.+ (Dividend n +maturity value)

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

value of an irredeemable preference share =

dividend

required return on preference share

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Example:Let us assume the face value of the preference share is Rs 500 and thestated dividend rate is 12%. The shares are redeemable after 5 yearsperiod. Calculate the value of preference shares if the required rate ofreturn is 13%.

Annual dividend = 500 x 12% =Rs 60

Redeemable Preference share value =

60 + 60 (60+500)

( 1+.13)1 ( 1+.13)2 ( 1+.13)5

Solving for the above equation, we get the value of the preference sharesas Rs 482 (rounded).

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Thank You