val. of bond

8/9/2019 val. of bond

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Valuation of Bonds and Shares

Prepared by

Priyanka Gohil


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Valuation

Valuation is the process of linking riskwith returns to determine the worth ofan asset.

The value of an asset depends on thecash flow it is expected to provide over

the holding period. A security can be evaluated by the

series of dividends or interest paymentsreceivable over a period of time.


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BASIC VALUATION MODEL

Basic valuation model is defined as the value of anasset in terms of the present value of its expected

future cash flows discounted at an appropriate rateof return.

The investors expected minimum rate of return istaken as the appropriate discount rate at the

investments level of risk.


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Valuation Procedure

Asset Characteristics Investor Characteristics

Value of the assets at

the present time

n)1/( iCnVo !


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BASIC VALUATION MODEL

Where,

Vo= Value of the asset at the present timeCn= Expected cash flow at the end of period n

i= Discount rate or required rate of return on thecash flow

n = Expected life of the asset


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Example

Calculate the value of an asset if the annual

cash inflow is Rs. 5000 per year for the next6 years and the discount rate is 16%.

Vo = Cn/ (1+i)n

= 5000/(1+0.16)6

=5000 PVIFA (16%.6y)=5000*3.685= Rs. 18425


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Important Terms of Valuation

Book Value It represents the cost of acquisition less depreciation to

date. It is historical cost less accumulated depreciation, as

shown in the balance sheet. Replacement Value

Amount a company is required to spend if it were to replaceits existing assets in the present condition.

Liquidation Value

Amount a company can realize if it sold the assets after thewinding up of its business.


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Going concern Value

Amount a company can realize if it sells itsbusiness as an operating one

Market Value

Current price at which the asset or

security is being sold or bought in themarket.


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Valuation of Bond

Bond are long term debt instruments

issued by govt. agencies or bigcorporate houses to raise large sums ofmoney.


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Important Terms regarding bondvaluation

Face Value

Coupon rateMaturity period

Redemption value


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Types of Bonds

1. Redeemable Bonds (i.e., Bonds withmaturity period)

2.Irredeemable Bonds (Perpetual bonds)

3. Zero Coupon Bonds


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1. Redeemable Bonds (i.e., Bonds with maturityperiod)

a. Bonds with annual interest payments.

b. Bond with semi annual interest.


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a. Bonds with annual interestpayments.

Vo or Po = nt=1 I/(1+kd)t + F/(1+kd)n

OR

Vo = I *PVIFA (Kd, n) + F* PVIF (Kd, n)Where,Vo= Intrinsic value of the bondPo= Present value of the bondI= Annual interest payable on the bondF= Principal amount (Par value repayable at the maturity time.)n= Maturity period of the bondKd= Required rate of returnt = time period when the payment is received


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Ex. A bond whose face value is Rs. 1,000

has a coupon rate of 10% and a maturityof 10 years. The required rate ofinterest is 10%. What is the value ofthe bond?


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Ex. How to compute the value of bond, considera 10 year ,12% coupon bond with a par value of

1,000. The required yield on this bond is 13percent.

The cash flow for this bond are as follows:o 10 annual coupon payment of Rs. 120.

o Rs. 1,000 principal repayment 10 years fromnow.


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EX.A bond whose face value is Rs. 100

has a coupon rate of 12%and a maturityof 5 years. The required rate ofinterest is 10%. What is the value ofthe bond?


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b. Bond with semi annual interest.

Vo or Po = nt=1 I/2/ (1+Kd/2)t+F/(1+Kd/2)2n

OR

Vo = I/2 *PVIFA (Kd/2, 2n) + F* PVIF (Kd/2, 2n)Where,Vo= Intrinsic value of the bondPo= Present value of the bondF= Principal amount (par value) repayable at the maturity time.

2n= Maturity period of the bond expressed in half- yearly.Kd/2= Required rate of return semi- annually.t = time period when the payment is received


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Ex. A bond of Rs. 1,000 value carries a

coupon rate of 10%, maturity period of6 years. Interest is payable semi-annually. If the required rate of returnis 12%, calculate the value of the bond.


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A 10 year bond of Rs. 1000 has an annual

rate of interest of 12 percent. Theinterest is paid half yearly. What is thevalue of the bond if the required rateof return is,

(i) 12 percent and(ii) 16 percent


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2.Irredeemable Bonds (Perpetual bonds)

Vo= I/id

I = Interest on bondid= Current yield


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Ex. If a company offers to pay Rs. 75 as

interest on a bond of Rs. 1000 par value,and the current yield is 8%,what is thevalue of the bond?


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Ex. Suppose that a 10 percent Rs. 1000

bond will pay Rs. 100 annual interest intoperpetuity? What could be its value ofthe bond if the market yield or interestrate were 15 percent?


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3. Zero Coupon Bonds

A=Po (1+r)n

A=Face Value

Po= Principal invested today

n = No. of years


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Ex. River valley Authority issued Deep

discount Bond of the face value of Rs.1,00,000 payable 25 years later, at anissue price of Rs. 14,600. What is theeffective interest rate earned by an

investor from this bond?


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Ex. A ltd. Issued discount bond or Rs.

1000 face value for Rs. 520 today for aperiod of five years. What is theeffective interest rate earned by aninvestor from this bond?


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Bond-Yield Measures:-

1.Current Yield

= Stated (Coupon) Interest per yearCurrent Market price


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Ex. 15% Rs. 200 bond is currently selling

for Rs. 220, what would be the annualcurrent yield?


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Ex. 8% Rs. 1000 bond is currently selling

for Rs. 920, what would be the annualcurrent yield?


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Ex. If annual interest on bond is 60 and

the market price of a bond is Rs. 883.40what would be the annual current yield?


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Ex. What would be the current yield of

a 10 year, 12 percent coupon bond with apar value of Rs. 1000, when selling priceis Rs. 950.


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An Approximation

2. Yield to Maturity (YTM)YTM = {I + (F- P)/n}/0.4F+0.6PYTM = Yield to Maturity

I = Annual interest payment

F= Face value of the bond

P= Current Market price of the bond

n= Number of years to maturity


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Ex. A bond has a face value of Rs. 1000

with a 9 year maturity period . Itscurrent market price is Rs. 850. Itcarries an interest rate of 8%. What isthe YTM on this bond?


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Ex. Rs. 1,000 par value bond, carrying a

coupon rate of 9 percent, maturingafter 8 years. The bond is currentlyselling for Rs. 800. What is the YTM onthis bond?


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Ex. A company issues a bond with a face

value of 5000. It is currently trading atRs. 4,500. The interest rate offered bythe company is 12% and the bond has amaturity period of 8 years. What is

YTM?


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Ex.The bond of the Premier Company Ltd(PCL) are currently selling for Rs. 10,800.

(i) coupon rate of interest, 10 percentannually

(ii) Par value, Rs.10,000

(iii) Years to maturity, 10 years

Compute YTM.


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Bond value Theorems

The following factors affect the bond

value:1. Relationship between the requiredrate of interest (Kd) and the discountrate.

2. Number of years to maturity.

3. YTM


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1. Relationship between the required rate ofinterest (Kd) and the discount rate.

If Kd= coupon rate, then value of

bond = Face valueIf Kd > coupon rate, then value of

bondFace value


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Ex. Sugam Industries wishes to issue

bonds with Rs. 100 as par value, couponrate 12% an YTM 5 years. What is thevalue of bond if the required rate ofreturn of an investor is 12%, 14% and

10%.


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Ex. ABC ltd. Wishes to issue bonds with

Rs. 200 as par value, coupon rate 14% anYTM 5 years. What is the value of thebond if the required rate of return ofan investor is 14%, 16% and 12%.


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2. Number of years to maturity.

If Kd > coupon rate, the value on thebond increases as maturity approaches.

If Kd < coupon rate, the value on thebond decreases as maturity approaches.


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Bond whose face value is Rs. 100 with acoupon rate of 11% and a maturity of 7years. What will be the effect on thebond value if required rate is 13%, and8%. Show calculation for two years.


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Ex. A bond whose face value is Rs. 200with a coupon rate of 10% and amaturity of 8 years. What will be theeffect on the bond value if requiredrate is 12%, and 8%. Show calculation

for two years.


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3. YTM

YTM determining the market value ofthe bond, the bond price will fluctuateto the changes in market interest rates.


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Valuation of Shares

Companys share may be categorized as

1. Equity Shares2. Preference Shares


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Important features of shares

o Dividends

o Claimso Redemption

o Conversion


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1. Valuation of Preference Shares

a. Valuation of irredeemable preferenceshares

b. Valuation of redeemable preferenceshares


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a. Valuation of irredeemable preference shares

Po = Dp

Kp

Po= Current value/ price of Pref. Share

Dp= Annaul dividendKp= Required rate of return/discount rate


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Ex. You own 8% Rs. 100 par valueirredeemable Pref. Shares in AB ltd. Ifthe required rate of return on similarshares is currently 10%. What iscurrent value of your holding?


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Ex. How can we value an irredeemablePref. shares? Consider that a co. hasissued Rs. 100 irredeemable Pref. shareon which it pays a div. of Rs. 9. If therequired rate of return on similar

shares is 11%.


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b. Valuation of redeemable preference shares

Po = Dp/ {1+Kp)t} + Pn /{(1+Kp)n}OrPo = Dp * PVIFA (Kp,n) + Pn * PVIF (Kp,n)Dp= Annual Div.Kp= Req. rate of returnn= Maturity period of pref. sharePn= Red. Value of the Pref.share on

maturity


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EX. Compute the value of a preferencestock, consider an 8 year, 10 percentpreference stock with a par value of Rs.1000. The required return on thispreference stock is 9 percent.


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2. Valuation of Equity Shares

People hold common stocks for two reasons

To obtain dividends in a timely manner

To get a higher amount when sold.


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Dividend Capitalization Model

o The value of share is the presentvalue of its future stream of dividends

o AS per dividend capitalization approach,the value of an equity share is, The present value of dividends expected from

ownership+

value of the sale price expected when the share issold.


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a. Single period valuation model

This model holds well when an investor expectsto hold the equity share for one year.

Po = D1 + P1(1+Ke) (1+Ke)

Where,

Po = Current market price of the shareD1 = Expected dividend after one yearP1 =Expected price of the share after one yearKe= Required rate of return on the equity share


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Ex. Prestiges equity share is expectedto provide a dividend of Rs. 2.00 andfetch a price of Rs. 18.00 a year hence.What is the price at which an investorwould be willing to buy if his required

rate o return ins 12%?


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EX. Gammon India Ltd.s share isexpected to touch Rs. 450 one yearfrom now. The company is expected todeclare a dividend of Rs. 25 per share.What is the price at which an investor

would be willing to buy if his requiredrate of return is 15%?


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EX. ABC Ltd.s share is expected totouch Rs. 200 one year from now. Thecompany is expected to declare adividend of Rs. 20 per share. What isthe price at which an investor would be

willing to buy if his required rate oreturn ins 13%?


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b. Multi-period valuation model

1. Constant dividends

2. Constant growth of dividends3. Changing growth rates of dividends.


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1. Constant dividends

P = D/Ke

Where,P =Value of share

D = Constant dividend per share

Ke = Required return of investors


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Ex. The per share dividend of PremierInstruments Ltd. (PIL) remains constantindefinitely at Rs. 10. Assuming arequired rate of return of 16 percent,compute the value of PILs shares.


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Ex. The per share dividend of ShyamLtd. remains constant indefinitely at Rs.15. Assuming a required rate of returnof 14 percent, compute the value ofShyam Ltd.s shares.


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2. Constant growth of dividends

Po = D1/ Ke-g

Where,P =Value of share

D = Constant dividend per share

Ke = Required return of investorsg = growth rate in dividend


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Ex. The Premier Instrument ltd. Isexpected to grow at 7 % per annum andthe dividend expected to be paid off isRs. 3. If the rate of return is expectedto be 16%, what is the price of the

share one would be expec`ted to paytoday?


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EX. Sagar automobiles ltd.s share istraded at Rs. 180. The company isexpected to grow at 8% per annum andthe dividend expected to be paid off isRs. 8. If the rate of return is expected

to be 12%, What is the price of theshare one would be expected to paytoday?


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3. Valuation with variable growth in dividends:

Step 1

Expected dividend flows during periods of supernormal growth is to beconsidered and present value of this its to be computed with following equation:

Po = D1 { 1- (1+g1)n }1+keke-g1

D1= Expected dividend D1 = Do (1+g1)g1 = Extraordinary growth rate applicable for n yearsDo = Current dividendKe = Require rate of return on equity shares


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Step 2Expected dividend flows during periods of normal growth is to

be considered and present value of this its to be computed withfollowing equation:

{D1 (1+g1)n-1 (1+g2) } { 1 }

ke-g2 (1+ke)n

D1 = Dividend expected a year henceg1 = Extraordinary growth rate applicable for n yearsg2 = Normal growth rate applicable for n yearsKe = required rate of return


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Step 3

Add both the present value compositeto find the value composites to find thevalue Po of the share,

Po = D1 { 1- (1+g1)n } + {D1 (1+g1)n-1 (1+g2) } { 1 }

1+r r-g2 (1+r)nr-g1


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Ex. The current dividend on an equity share ofVertigo Limited is Rs. 2.00. Vertigo is

expected to enjoy an above-normal growthrate of 20 percent for a period of 6 years.

Thereafter the growth rate will fall andstabilise at 10 percent. Equity investorsrequire a return of 15 percent. What is theintrinsic value of the equity share of vertigo?


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Ex. Souparnika Pharmas current dividend isRs. 5. It expects to have a supernormal

growth period running to 5 years during whichthe growth rate would be 25%. The companyexpects normal growth rate of 8% after theperiod of supernormal growth period. Theinvestors required rate of return is 15%.Calculate what the value of one share of thiscompany is worth.

Other approaches to equity valuation


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Other approaches to equity valuation

Book value approach

Liquidation valuePrice Earning Ratio


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Book value approach

The book value per share is the networth of the company divided by thenumber of outstanding equity shares.

= Net worth

Outstanding equity shares.


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EX. A one Ltd. Has total assets worthRs. 500 Cr., liabilities worth Rs. 300 Cr.,and preference shares worth Rs. 50 Cr.And equity shares numbering 10 Cr.


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Liquidation Value

(Value realized by liquidating all assets)(Amount to be paid to all creditors andpreference share)/ Divided by numberof outstanding shares

P i E i R ti


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Price Earning Ratio

P/E ratio = (1-b)/ r- (ROE*b)

Where,1-b is dividend pay out ratio

R is required rate of return

ROE *b is expected growth rate

val. of bond

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