1

Valuation of Bonds Valuation of Bonds and Sharesand Shares

2

ObjectivesObjectivesAfter studying this unit, you should be able to:After studying this unit, you should be able to: define value in terms of finance theorydefine value in terms of finance theory recall the procedure for calculating the value of bondsrecall the procedure for calculating the value of bonds recognise the mechanics of valuation of equity sharesrecognise the mechanics of valuation of equity shares

The concept of intrinsic valueThe concept of intrinsic value The intrinsic value of an asset is equal to the present The intrinsic value of an asset is equal to the present

value of the benefits associated with it.value of the benefits associated with it. The expected returns (cash inflows) are discounted The expected returns (cash inflows) are discounted

using the required return commensurate with the risk.using the required return commensurate with the risk. Mathematically, the intrinsic value of an asset is given Mathematically, the intrinsic value of an asset is given

by :by :VV00 = = C C11 + + CC22 + + C C33 +…++…+ C Cnn

(1+i)(1+i)11 (1+i) (1+i)22 (1+i) (1+i)3 3 (1+i) (1+i)n n

3

Where ;V0= value of the asset at time zero (t=0)C1,2…n= expected cash flow at the end of period.i = discount rate or the required rate of return on cash flowsn = expected life of an asset

The concept of intrinsic valueThe concept of intrinsic value

4

Concept of book valueConcept of book value The value at which an asset is carried on a balance The value at which an asset is carried on a balance

sheet. To calculate, take the cost of an asset minus the sheet. To calculate, take the cost of an asset minus the accumulated depreciation.accumulated depreciation.

The net asset value of a company, calculated by total The net asset value of a company, calculated by total assets minus intangible assets (patents, goodwill) and assets minus intangible assets (patents, goodwill) and liabilities.liabilities.

Book value of a share is calculated by dividing the net Book value of a share is calculated by dividing the net worth by the number of outstanding shares.worth by the number of outstanding shares.

Shareholders net worth = Assets – LiabilitiesShareholders net worth = Assets – Liabilities Net worth = Paid-up capital + Reserves + SurplusNet worth = Paid-up capital + Reserves + Surplus

5

Concept of book valueConcept of book value The following factors explain the concept of book value:The following factors explain the concept of book value: Replacement value Replacement value is the amount a company is required to spend is the amount a company is required to spend

if it were to replace its existing assets in the present condition. It is if it were to replace its existing assets in the present condition. It is difficult to find the cost of assets presently used by the company.difficult to find the cost of assets presently used by the company.

Liquidation value Liquidation value is the amount a company can realise if it sold the is the amount a company can realise if it sold the assets after winding up its business. It will not include the value of assets after winding up its business. It will not include the value of intangibles as the operations of the company will cease to exist.intangibles as the operations of the company will cease to exist.

Liquidation value is generally the minimum value a company might Liquidation value is generally the minimum value a company might accept if it sold its business.accept if it sold its business.

Going concern value Going concern value is the amount a company can realise if it is the amount a company can realise if it sells its business as an operating one. This value is higher than sells its business as an operating one. This value is higher than the liquidation value.the liquidation value.

6

Concept of book valueConcept of book value Market valueMarket value is the current price at which the asset or is the current price at which the asset or

security is being sold or bought in the market. Market security is being sold or bought in the market. Market value per share is generally higher than the book value value per share is generally higher than the book value per share for profitable and growing firm’s value.per share for profitable and growing firm’s value.

7

8

Valuation of BondsValuation of Bonds BondsBonds

are long-term debt instruments/fixed income (debt) instruments issued are long-term debt instruments/fixed income (debt) instruments issued by government agencies or big corporate houses to raise large sums of by government agencies or big corporate houses to raise large sums of money.money.

Coupon Rate -Coupon Rate - The coupon rate, which is generally fixed, determines the The coupon rate, which is generally fixed, determines the

periodic coupon or interest payments. It is expressed as a periodic coupon or interest payments. It is expressed as a percentage of the bond's face value. It also represents the percentage of the bond's face value. It also represents the interest cost of the bond to the issuer.interest cost of the bond to the issuer.

Maturity Date/Period -Maturity Date/Period - The maturity date represents the date on which the bond The maturity date represents the date on which the bond

matures, matures, i.e.,i.e., the date on which the face value is repaid. The last the date on which the face value is repaid. The last coupon payment is also paid on the maturity date. coupon payment is also paid on the maturity date.

9

Valuation of BondsValuation of Bonds Par or Face Value -Par or Face Value -

The amount of money that is paid to the bondholders at maturity. The amount of money that is paid to the bondholders at maturity. It also generally represents the amount of money borrowed by It also generally represents the amount of money borrowed by the bond issuer. the bond issuer.

Market valueMarket value is the price at which the bond is traded in the stock exchange. is the price at which the bond is traded in the stock exchange.

Market price is the price at which the bonds can be bought and Market price is the price at which the bonds can be bought and sold, and this price may be different from par value and sold, and this price may be different from par value and redemption value.redemption value.

Redemption value -Redemption value - is the amount the bondholder gets on maturity. A bond may be is the amount the bondholder gets on maturity. A bond may be

redeemed at par, at a premium (bondholder gets more than the redeemed at par, at a premium (bondholder gets more than the par value of the bond), or at a discount (bondholder gets less par value of the bond), or at a discount (bondholder gets less than the par value of the bond.) than the par value of the bond.)

10

Types of BondsTypes of Bonds Irredeemable bonds or perpetual bonds-Irredeemable bonds or perpetual bonds-

Bonds which will never mature. The face value is known, and Bonds which will never mature. The face value is known, and the interest received on such bonds is constant and received at the interest received on such bonds is constant and received at regular intervals and hence, the interest receipt resembles regular intervals and hence, the interest receipt resembles perpetuity.perpetuity.

The present value is calculated as: The present value is calculated as: VV00 = I = IAA/i/idd . . Where;Where; VV0 0 - Present Value of the bond, I - Present Value of the bond, IAA – Interest amount payable – Interest amount payable

annually and iannually and idd – is the required rate of interest – is the required rate of interest

Example:Example: If a company offers to pay Rs. 70 as interest on a bond of Rs. If a company offers to pay Rs. 70 as interest on a bond of Rs.

1000 per value and the current yield is 8%, the value of the 1000 per value and the current yield is 8%, the value of the bond is 70/0.08 which is equal to Rs. 875.bond is 70/0.08 which is equal to Rs. 875.

11

Types of BondsTypes of Bonds Redeemable bonds -Redeemable bonds -

Bonds with maturity date. They are of two types in respect of Bonds with maturity date. They are of two types in respect of interest payments; one with annual interest payments and the interest payments; one with annual interest payments and the other one with semi-annual interest paymentsother one with semi-annual interest payments

Bonds with annual interest paymentsBonds with annual interest payments The holder of a bond receives a fixed annual interest for a The holder of a bond receives a fixed annual interest for a

specified number of years and a fixed principal repayment at specified number of years and a fixed principal repayment at the time of maturity.the time of maturity.

The PV or Intrinsic Value of such bonds is given by:The PV or Intrinsic Value of such bonds is given by:

PV = IPV = IAA/( 1+i/( 1+idd))nn + F/(1+i + F/(1+idd))nn . . Where ; PV – Present Value Where ; PV – Present Value of the bond, Iof the bond, IAA – Interest Amount payable annually, F – Par – Interest Amount payable annually, F – Par Value or the Principal payable at the end of maturity period, iValue or the Principal payable at the end of maturity period, i dd – – required rate of interest, n- maturity period of the bond.required rate of interest, n- maturity period of the bond.

12

ExampleExample

13

Bond values with semi-annual Bond values with semi-annual interest paymentsinterest payments

In reality, it is quite common to pay interest on bonds semi-In reality, it is quite common to pay interest on bonds semi-annually. The value of bonds with semi-annual interest is much annually. The value of bonds with semi-annual interest is much more than the ones with annual interest payments.more than the ones with annual interest payments.

The PV of Bonds with semi annual interest payments is given by:The PV of Bonds with semi annual interest payments is given by:PV = IPV = IAA/2/(1+i/2/(1+idd/2)/2)2n2n + F/(1+i + F/(1+idd/2)/2)2n 2n . .

NB: the variables are as defined in the previous example.NB: the variables are as defined in the previous example.

ExampleExample

14

15

Zero Coupon BondsZero Coupon Bonds Zero Coupon BondsZero Coupon Bonds a zero coupon bond will pay its stated face or par value at a zero coupon bond will pay its stated face or par value at

maturity. It pays no other future cash flows during its life. Zeroes maturity. It pays no other future cash flows during its life. Zeroes are also known as pure discount bonds. The return here comes are also known as pure discount bonds. The return here comes entirely as a capital gain.entirely as a capital gain.

It is also known as Deep Discount Bonds (DDBs)It is also known as Deep Discount Bonds (DDBs) The face value is the amount payable to the holder of the The face value is the amount payable to the holder of the

instrument on maturity. Thus, no interest or any other type of instrument on maturity. Thus, no interest or any other type of payment is available to the holder before maturity.payment is available to the holder before maturity.

The value of DDB or Zero Coupon Bonds is calculated as:The value of DDB or Zero Coupon Bonds is calculated as:BB00(DDB) = F/(1+i(DDB) = F/(1+idd))nn

Where BWhere B00- Value of the Bond, F- Face value payable at maturity, I- Value of the Bond, F- Face value payable at maturity, I dd – – required rate of interest, n – bond life or maturity periodrequired rate of interest, n – bond life or maturity period

16

ExampleExample

Bond yield measuresBond yield measures The bond yield measures are categorised into two The bond yield measures are categorised into two

parts – current yield and the yield to maturity.parts – current yield and the yield to maturity. Current yield: Current yield: Current yield measures the rate of Current yield measures the rate of

return earned on a bond if it is purchased at its return earned on a bond if it is purchased at its current market price and the coupon interest that is current market price and the coupon interest that is received.received.

It is calculated as : CY =Coupon Interest/ Current It is calculated as : CY =Coupon Interest/ Current Market PriceMarket Price

Example :Example : A bond pays $100 as coupon interest. A bond pays $100 as coupon interest. The current market price of the bond is $850. what is The current market price of the bond is $850. what is the current yield of the bond?. ANS : 100/850 = the current yield of the bond?. ANS : 100/850 = 11.8% 11.8% 17

Bond yield measuresBond yield measures Yield To Maturity (YTM): Yield To Maturity (YTM): Yield To Maturity Yield To Maturity

(YTM) is the rate of return earned by an investor who (YTM) is the rate of return earned by an investor who purchases a bond and holds it till its maturity.purchases a bond and holds it till its maturity.

The YTM is the discount rate equalling the present The YTM is the discount rate equalling the present values of cash flow to the current market values of cash flow to the current market price/purchase price.price/purchase price.

So,a bond’s YTM may be defined as the Internal So,a bond’s YTM may be defined as the Internal Rate of Return (IRR) for a given level of risk.Rate of Return (IRR) for a given level of risk.

18

19

ExampleExample Josephe purchased a bond for $1,000 with 5-years maturity period. The Bond Josephe purchased a bond for $1,000 with 5-years maturity period. The Bond

currently sells at $883.40. The bond paid an annual 6% coupon. What is his currently sells at $883.40. The bond paid an annual 6% coupon. What is his realized rate of return?realized rate of return?

nn

PV = PV = Σ Σ [CF[CF tt / (1+r) / (1+r)tt]] t=0t=0

Solution:Solution: VV00 = I*PVIFA (i = I*PVIFA (idd, n) + F*PVIF (i, n) + F*PVIF (idd, n), n) 883.4 = 60*PVIFA(id, 5yrs) + 1000*PVIF(i883.4 = 60*PVIFA(id, 5yrs) + 1000*PVIF(idd, 5yrs), 5yrs) By tr ial and error method let us take id = 10%By tr ial and error method let us take id = 10% = 60*PVIFA(10%,5yrs) +1000* PVIF (10%,5yrs)= 60*PVIFA(10%,5yrs) +1000* PVIF (10%,5yrs) = 60*3.791 +1000*.621= 60*3.791 +1000*.621 = 227.46 + 621 = = 227.46 + 621 = 848.46 (848.46 ( We need to equate this value withWe need to equate this value with the current market the current market

price of Rs.883.40 by reducing the iprice of Rs.883.40 by reducing the idd rate) rate) Let us try iLet us try i dd = 9% = 9% = 60*3.890 + 1000*.650= 60*3.890 + 1000*.650 = 233.40 + 650 = 883.40 = current market price. Hence = 233.40 + 650 = 883.40 = current market price. Hence YTM is 9%YTM is 9%

20

YTM approximation YTM approximation methodmethod The trial and error method to obtain the rate of return (iThe trial and error method to obtain the rate of return (i dd) is a ) is a

very tedious procedure and requires lots of time. very tedious procedure and requires lots of time. The following formula can be used as a ready reference The following formula can be used as a ready reference

formula:formula:

21

YTM approximation YTM approximation method-Examplemethod-Example A company issues a bond with a face value of Rs. 5000. It is A company issues a bond with a face value of Rs. 5000. It is

currently trading at Rs. 4500. The interest rate offered by currently trading at Rs. 4500. The interest rate offered by the company is 12%,and the bond has a maturity period of 8 the company is 12%,and the bond has a maturity period of 8 years. What is the YTM?years. What is the YTM?

ANS: ANS: F = 5,000 P = 4,500 I=600 (0.12*5,000) n=8F = 5,000 P = 4,500 I=600 (0.12*5,000) n=8 Therefore YTM ={ 600+[(5000-4500)/8]}/[(5000+4500)/2]Therefore YTM ={ 600+[(5000-4500)/8]}/[(5000+4500)/2]

= 13.94%= 13.94%

Bond Value TheoremsBond Value Theorems The following factors affect the bond value theorems:The following factors affect the bond value theorems:1.1. Relationship between the required rate of return (iRelationship between the required rate of return (idd) )

and the coupon rateand the coupon rate2.2. Number of years to maturityNumber of years to maturity3.3. Yield To Maturity (YTM)Yield To Maturity (YTM) Relationship between the required rate of Relationship between the required rate of

return ( ireturn ( i dd ) and the coupon rate) and the coupon rate When the required rate of return is equal to the When the required rate of return is equal to the

coupon rate, the value of the bond is equal to its par coupon rate, the value of the bond is equal to its par value. i.e., If ivalue. i.e., If idd = Coupon rate; then Bond value = Par = Coupon rate; then Bond value = Par valuevalue 22

Bond Value TheoremsBond Value Theorems When the required rate of return (iWhen the required rate of return (idd) is greater than ) is greater than

the coupon rate, the value of the bond is less than its the coupon rate, the value of the bond is less than its par value.i.e., If ipar value.i.e., If idd > Coupon rate; then, Bond value < > Coupon rate; then, Bond value < Par ValuePar Value

ExampleExample Sugam Industries wishes to issue bonds with Rs. 100 Sugam Industries wishes to issue bonds with Rs. 100

as par value, coupon rate of 12%, and YTM of 5 as par value, coupon rate of 12%, and YTM of 5 years. What is the value of the bond if the required years. What is the value of the bond if the required rate of return of an investor is 12%, 14%, and 10%?rate of return of an investor is 12%, 14%, and 10%?

23

Bond Value TheoremsBond Value Theorems Solution:Solution: When iWhen idd is equal to the coupon rate, the intrinsic value is equal to the coupon rate, the intrinsic value

of the bond isequal to its face value.of the bond isequal to its face value. I f iI f i dd is 12%, is 12%, VV00 = I*PVIFA (i = I*PVIFA (idd, n) + F*PVIF (i, n) + F*PVIF (idd, n), n) = 12*PVIFA (12%, 5) + 100*PVIF (12%, 5)= 12*PVIFA (12%, 5) + 100*PVIF (12%, 5) = 12*3.605 + 100*0.567= 12*3.605 + 100*0.567 = 43.3 + 56.7= 43.3 + 56.7 = Rs. 100 (Intr insic value = Face value)= Rs. 100 (Intr insic value = Face value)

24

Bond Value TheoremsBond Value Theorems When iWhen idd is greater than the coupon rate, the intrinsic is greater than the coupon rate, the intrinsic

value of the bond is less than its face value.value of the bond is less than its face value. I f iI f i dd is 14%, is 14%, VV00 = I*PVIFA (i = I*PVIFA (idd, n) + F*PVIF (i, n) + F*PVIF (idd, n), n) =12*PVIFA (14%, 5) + 100*PVIF (14%, 5)=12*PVIFA (14%, 5) + 100*PVIF (14%, 5) =12*3.433 + 100*0.519=12*3.433 + 100*0.519 = 41.20 + 51.9= 41.20 + 51.9 = Rs. 93.1 (Intrinsic value <Face value)= Rs. 93.1 (Intrinsic value <Face value)

25

Bond Value TheoremsBond Value Theorems When iWhen idd is less than the coupon rate, the intrinsic is less than the coupon rate, the intrinsic

value of the bond is greater than its face value.value of the bond is greater than its face value. I f iI f i dd is 10%, is 10%, V0 = I*PVIFA (iV0 = I*PVIFA (idd, n) + F*PVIF (i, n) + F*PVIF (idd, n), n) =12*PVIFA (10%, 5) + 100*PVIF (10%, 5)=12*PVIFA (10%, 5) + 100*PVIF (10%, 5) =12*3.791 + 100*0.621=12*3.791 + 100*0.621 = 45.49 + 62.1= 45.49 + 62.1 = Rs. 107.59 (Intr insic value > Face value)= Rs. 107.59 (Intr insic value > Face value)

26

Bond Value TheoremsBond Value Theorems Number of years of maturityNumber of years of maturity When iWhen idd is greater than the coupon rate, the discount is greater than the coupon rate, the discount

on the bond declines and hence value increases as on the bond declines and hence value increases as maturity approaches.maturity approaches.

Example: Example: To show the effect of the above, consider To show the effect of the above, consider a case of a bond whose face value is $100 with a a case of a bond whose face value is $100 with a coupon rate of 11% and a maturity of 7 years.coupon rate of 11% and a maturity of 7 years.

I f iI f i dd is 13%, then, is 13%, then, VV00 = I*PVIFA (i = I*PVIFA (idd, n) + F*PVIF (i, n) + F*PVIF (idd, n), n) = 11*PVIFA (13%, 7) + 100*PVIF (13%, 7)= 11*PVIFA (13%, 7) + 100*PVIF (13%, 7) = 11*4.423 + 100*0.425= 48.65 + 42.50= 11*4.423 + 100*0.425= 48.65 + 42.50 = $.91.15= $.91.15

27

Bond Value TheoremsBond Value Theorems After 1 year, the maturity period is 6 years, After 1 year, the maturity period is 6 years,

the value of the bond is:the value of the bond is: V0 = I*PVIFA (iV0 = I*PVIFA (idd, n) + F*PVIF (i, n) + F*PVIF (idd, n), n) = 11*PVIFA (13%, 6) + 100*PVIF (13%, 6)= 11*PVIFA (13%, 6) + 100*PVIF (13%, 6) = 11* 3.998 + 100*0.480= 11* 3.998 + 100*0.480 = 43.98 + 48= 43.98 + 48 = $ 91.98.= $ 91.98. The value of the bond increases with the passage of The value of the bond increases with the passage of

time (one year later) as “itime (one year later) as “idd” is higher than the ” is higher than the coupon rate (13%>11%).coupon rate (13%>11%).

the reverse happens when required rate of return is the reverse happens when required rate of return is lower than the coupon rate. Reverse the rates for the lower than the coupon rate. Reverse the rates for the previous example and work out.previous example and work out.

28

Bond Value TheoremsBond Value Theorems Yield to Maturity: Yield to Maturity: A bond’s price varies inversely A bond’s price varies inversely

with yield. This is because as the required yield with yield. This is because as the required yield increases, the present value of the cash flow increases, the present value of the cash flow decrease and hence the price decreasesdecrease and hence the price decreases

29

Valuation of SharesValuation of Shares There are two types of shares: Preference and There are two types of shares: Preference and

ordinary or equity shares.ordinary or equity shares. The following are some important features of The following are some important features of

preference and equity shares:preference and equity shares: Dividends – Dividends – Rate is fixed for preference Rate is fixed for preference

shareholders. They can be given cumulative rights, shareholders. They can be given cumulative rights, that is, the dividend can be paid off after that is, the dividend can be paid off after accumulation.accumulation.

The dividend rate is not fixed for equity The dividend rate is not fixed for equity shareholders. They change with an increase or shareholders. They change with an increase or decrease in profits. decrease in profits.

30

Valuation of SharesValuation of Shares The dividends are not cumulative for equity The dividends are not cumulative for equity

shareholders, that is, they cannot be accumulated shareholders, that is, they cannot be accumulated and distributed in the later years. Dividends are not and distributed in the later years. Dividends are not taxable.taxable.

Claims – Claims – In the event of the business closing down, In the event of the business closing down, the preference shareholders have a prior claim on the the preference shareholders have a prior claim on the assets of the company. Their claims shall be settled assets of the company. Their claims shall be settled first and the balance, if any, will be paid off to equity first and the balance, if any, will be paid off to equity shareholders. Equity shareholders are residual shareholders. Equity shareholders are residual claimants to the company’s income and assets.claimants to the company’s income and assets.

31

Valuation of SharesValuation of Shares Redemption –Redemption – Preference shares have a maturity Preference shares have a maturity

date on which the company pays off the face value of date on which the company pays off the face value of the shares to the holders.the shares to the holders.

Preference shares can be of two types – redeemable Preference shares can be of two types – redeemable and irredeemable.and irredeemable.

Irredeemable preference shares are perpetual. Irredeemable preference shares are perpetual. Equity shareholders have no maturity date.Equity shareholders have no maturity date. Conversion – Conversion – A company can issue convertible A company can issue convertible

preference shares. After a particular period, as preference shares. After a particular period, as mentioned in the share certificate, the preference mentioned in the share certificate, the preference shares can be converted into ordinary shares.shares can be converted into ordinary shares.

32

Valuation of preference Valuation of preference sharesshares

Preference shares like bonds carry a fixed rate of Preference shares like bonds carry a fixed rate of dividend or return.dividend or return.

Symbolically, this can be expressed as:Symbolically, this can be expressed as: PP00= D= Dpp/{1+K/{1+Kpp))nn } + P } + Pnn/{(1+K/{(1+Kpp))nn} or} or PP00 = D = Dpp*PVIFA (K*PVIFA (Kpp, n) + P, n) + Pnn *PVIF (Kp, n) *PVIF (Kp, n) Where PWhere P00= Price of the share, P= Price of the share, Pnn = Face Value of the = Face Value of the

preference sharepreference share DDpp= Dividend on preference share= Dividend on preference share KKpp= Required rate of return on preference share= Required rate of return on preference share n= Number of years to maturityn= Number of years to maturity 33

Valuation of ordinary Valuation of ordinary sharesshares

People hold common stocks:People hold common stocks:1.1. to obtain dividends in a timely mannerto obtain dividends in a timely manner2.2. to get a higher amount when soldto get a higher amount when sold Generally, shares are not held in perpetuity. An Generally, shares are not held in perpetuity. An

investor buys the shares, holds them for some time investor buys the shares, holds them for some time during which he gets dividends, and finally sells it off during which he gets dividends, and finally sells it off to get capital gains. to get capital gains.

Intrinsic value can be referred to as the value of a Intrinsic value can be referred to as the value of a stock which is justified by assets, earnings, stock which is justified by assets, earnings, dividends, definite prospects, and the factor of the dividends, definite prospects, and the factor of the management of the issuing company.management of the issuing company.

34

Valuation of ordinary Valuation of ordinary sharesshares

People hold common stocks:People hold common stocks:1.1. to obtain dividends in a timely mannerto obtain dividends in a timely manner2.2. to get a higher amount when soldto get a higher amount when sold Generally, shares are not held in perpetuity. An Generally, shares are not held in perpetuity. An

investor buys the shares, holds them for some time investor buys the shares, holds them for some time during which he gets dividends, and finally sells it off during which he gets dividends, and finally sells it off to get capital gains. to get capital gains.

Intrinsic value can be referred to as the value of a Intrinsic value can be referred to as the value of a stock which is justified by assets, earnings, stock which is justified by assets, earnings, dividends, definite prospects, and the factor of the dividends, definite prospects, and the factor of the management of the issuing company.management of the issuing company.

35

Dividend capital isation Dividend capital isation modelmodel

When a shareholder buys a share, he is actually When a shareholder buys a share, he is actually buying the stream of future dividends. buying the stream of future dividends.

Therefore, the value of an ordinary share is Therefore, the value of an ordinary share is determined by capitalising the future dividend stream determined by capitalising the future dividend stream at an appropriate rate of interest.at an appropriate rate of interest.

under the dividend capitalisation approach, the value under the dividend capitalisation approach, the value of an equity share is the discounted present value of of an equity share is the discounted present value of dividends received plus the present value of the dividends received plus the present value of the resale price expected when the share is disposed.resale price expected when the share is disposed.

36

Dividend capital isation Dividend capital isation modelmodel

Two assumptions are made to apply this approach. Two assumptions are made to apply this approach. They are:They are:

1.1. Dividends are paid annually.Dividends are paid annually.2.2. First payment of dividend is made after one year from First payment of dividend is made after one year from

the day that the equity share is bought.the day that the equity share is bought.

37

Single period valuation Single period valuation modelmodel This model holds well when an investor holds an This model holds well when an investor holds an

equity share for one year.equity share for one year. The price of such a share will be:The price of such a share will be:

38

Single period valuation Single period valuation model-Examplemodel-Example XYZ India Ltd’s share is expected to touch Rs. 450 XYZ India Ltd’s share is expected to touch Rs. 450

one year from now. The company is expected to one year from now. The company is expected to declare a dividend of Rs. 25 per share.declare a dividend of Rs. 25 per share.

What is the price at which an investor would be What is the price at which an investor would be willing to buy if his or her required rate of return is willing to buy if his or her required rate of return is 15%?15%?

Solution:Solution: PP00 = D = D11/(1+K/(1+Kee) + P) + P11/(1+K/(1+Kee)) = {25/(1+0.15)} + {450/(1+0.15)}= 21.74 + 391.30= {25/(1+0.15)} + {450/(1+0.15)}= 21.74 + 391.30 = Rs. 413.04= Rs. 413.04 An investor would be willing to buy the share at Rs. An investor would be willing to buy the share at Rs.

413.04413.04 39

Multi period valuation Mult i period valuation modelmodel An equity share can be held at an indefinite period as An equity share can be held at an indefinite period as

it has no maturity date. The value of an equity share it has no maturity date. The value of an equity share of infinite duration is equal to the discounted value of of infinite duration is equal to the discounted value of the flow of dividend of infinite period.the flow of dividend of infinite period.

It is given by:It is given by:

40

Multi period valuation Mult i period valuation modelmodel The above equation can also be modified to find the The above equation can also be modified to find the

value of an equity share for a finite period.value of an equity share for a finite period. It is found by:It is found by:

41

Types of DividendsTypes of Dividends There are 3 types of dividends:There are 3 types of dividends:1.1. Constant dividendsConstant dividends2.2. Constant growth of dividendsConstant growth of dividends3.3. Changing growth rates of dividendsChanging growth rates of dividends A. Valuation with constant dividendsA. Valuation with constant dividends If constant dividends are paid year after year, then:If constant dividends are paid year after year, then: PP00 = D = D11/(1+K/(1+Kee))11 + D + D22/(1+K/(1+Kee))22 + D + D33/(1+K/(1+Kee))33 +………..+ D +………..+ D∞∞//

(1+K(1+Kee)) Simplifying this we get: P = D/KSimplifying this we get: P = D/Kee

42

Types of DividendsTypes of Dividends B. Valuation with constant growth in B. Valuation with constant growth in

dividendsdividends Here, we assume that dividends tend to increase with time as Here, we assume that dividends tend to increase with time as

and when businesses grow over time. If the increase in dividend and when businesses grow over time. If the increase in dividend is at a constant compound rate, then is at a constant compound rate, then Po = DPo = D 11 / (K / (K ee – g) – g)

Where, Where, gg stands for constant compound growth rate. stands for constant compound growth rate. Example: Monica Labs are expected to pay Rs. 4 as dividend Example: Monica Labs are expected to pay Rs. 4 as dividend

per share next year. The dividends are expected to grow per share next year. The dividends are expected to grow perpetually at 8%. Calculate the share price today if the market perpetually at 8%. Calculate the share price today if the market capitalisation is 12%.capitalisation is 12%.

Solution:Solution: PP oo = D = D 11 / (K / (K ee – g) – g) PP00 = 4/(0.12-0.08) = Rs. 100 = 4/(0.12-0.08) = Rs. 100 The share price today would be Rs. 100.The share price today would be Rs. 100.

43

Types of DividendsTypes of Dividends C. C. Valuation with changing growth in Valuation with changing growth in

dividendsdividends Some firms may not have a constant growth rate of Some firms may not have a constant growth rate of

dividends indefinitely.dividends indefinitely. There are periods during which the dividends may There are periods during which the dividends may

grow super normally, that is, the growth rate is very grow super normally, that is, the growth rate is very high when the demand for the company’s products is high when the demand for the company’s products is very high. very high.

After a certain period of time, the growth rate may fall After a certain period of time, the growth rate may fall to normal levels when the returns fall due to fall in to normal levels when the returns fall due to fall in demand for products (with competition setting in or demand for products (with competition setting in or due to availability of substitutes).due to availability of substitutes). 44

Types of DividendsTypes of Dividends C. C. Valuation with changing growth in Valuation with changing growth in

dividendsdividends Some firms may not have a constant growth rate of Some firms may not have a constant growth rate of

dividends indefinitely.dividends indefinitely. There are periods during which the dividends may There are periods during which the dividends may

grow super normally, that is, the growth rate is very grow super normally, that is, the growth rate is very high when the demand for the company’s products is high when the demand for the company’s products is very high. very high.

After a certain period of time, the growth rate may fall After a certain period of time, the growth rate may fall to normal levels when the returns fall due to fall in to normal levels when the returns fall due to fall in demand for products (with competition setting in or demand for products (with competition setting in or due to availability of substitutes).due to availability of substitutes). 45

Types of DividendsTypes of Dividends The price of the equity share of such a firm is The price of the equity share of such a firm is

determined in the followingdetermined in the following manner:manner: 1. Expected dividend flows during periods of 1. Expected dividend flows during periods of

supernormal growth is to be considered and present supernormal growth is to be considered and present value of this is to be computed with the following value of this is to be computed with the following equation:equation:

46

2. Value of the share at the end of the initial growth period is calculated as:

Types of DividendsTypes of Dividends

47

ExampleExample Aikins Pharma’s current dividend is GH¢5. It expects to have a Aikins Pharma’s current dividend is GH¢5. It expects to have a

supernormal growth period running to 5 years during which the supernormal growth period running to 5 years during which the growth rate would be 25%. The company expects normal growth rate would be 25%. The company expects normal growth rate of 8% after the period of supernormal growth period. growth rate of 8% after the period of supernormal growth period. The investor’s required rate of return is 15%. Calculate what the The investor’s required rate of return is 15%. Calculate what the value of one share of this company is worth.value of one share of this company is worth.

Solution:Solution: DD00 = 5, n = 5years, g = 5, n = 5years, gaa (supernormal growth) = 25%, g (supernormal growth) = 25%, gnn (normal (normal

growth) = 8%, Kgrowth) = 8%, Kee = 15%. = 15%. Step 1: Step 1:

48

ExampleExample DD11=5(1.25)=5(1.25)11, D, D22=5(1.25)=5(1.25)22, D, D33=5(1.25)=5(1.25)33, D, D44=5(1.25)=5(1.25)44, D, D55

=5(1.25)=5(1.25)55

The present value of this f low of dividends wil l The present value of this f low of dividends wil l be:be:

= 5(1.25)/(1.15) + 5(1.25)= 5(1.25)/(1.15) + 5(1.25)22/(1.15)/(1.15)22 + 5(1.25) + 5(1.25)33/(1.15)/(1.15)33 + + 5(1.25)5(1.25)44/(1.15)/(1.15)4 4 + 5(1.25)+ 5(1.25)55/(1.15)/(1.15)55

= 5.43+ 5.92 + 6.42 + 6.98 + 7.63 = = 5.43+ 5.92 + 6.42 + 6.98 + 7.63 = 32.3832.38 Step II :Step II : PPnn= (D= (Dnn+1)/(K+1)/(Kee-g)-g) PP55 = D= D66(1+g(1+gnn)/K)/Kee-g-gn n but D but D66= 5(1+ga)= 5(1+ga)55(1+gn)(1+gn)11

= {5(1.25)= {5(1.25)55(1+0.08)} / (0.15-0.08)= 15.26(1.08) / 0.07(1+0.08)} / (0.15-0.08)= 15.26(1.08) / 0.07 = 16.48 / 0.07= = 16.48 / 0.07= 235.42235.42

49

ExampleExample The discounted value of this price is 235.42/(1.15)5 = The discounted value of this price is 235.42/(1.15)5 =

GH¢. 117.12GH¢. 117.12 Step III :Step III :

50

The value of the share is GH¢32.38 + GH¢117.12 = GH¢149.50

Other approaches to Other approaches to equity valuationequity valuation

Book value approach:Book value approach: The Book Value Per Share (BVPS) is the net worth of The Book Value Per Share (BVPS) is the net worth of

the company divided by the number of outstanding the company divided by the number of outstanding equity shares.equity shares.

Net worth is represented by the total sum of paid-up Net worth is represented by the total sum of paid-up equity shares, reserves, and surplus. equity shares, reserves, and surplus.

Alternatively, this can also be calculated as the Alternatively, this can also be calculated as the amount per share on the sale of the assets of the amount per share on the sale of the assets of the company at their exact book value minus all liabilities company at their exact book value minus all liabilities including preference shares.including preference shares.

51

Other approaches to Other approaches to equity valuationequity valuation

Example:Example: Dovlo Ltd. has total assets worth GH Dovlo Ltd. has total assets worth GH¢500, liabilities worth GH¢300 and preference shares ¢500, liabilities worth GH¢300 and preference shares worth GH¢50 and equity share numbering 10. worth GH¢50 and equity share numbering 10. Calculate BVPS.Calculate BVPS.

Solution:Solution: The BVPS = (500 -300-50)/10= GH¢15The BVPS = (500 -300-50)/10= GH¢15 BVPS does not give a true investment picture. This BVPS does not give a true investment picture. This

relies on historical book values than the company’s relies on historical book values than the company’s earning potential.earning potential.

52

Other approaches to Other approaches to equity valuationequity valuation

Liquidation valueLiquidation value The liquidation value per share is calculated as: The liquidation value per share is calculated as:

{(Value realised by liquidating all assets) – (Amount {(Value realised by liquidating all assets) – (Amount to be paid to all the credit and preference shares)} to be paid to all the credit and preference shares)} divided by number of outstanding shares.divided by number of outstanding shares.

In the above example, if the assets can be liquidated In the above example, if the assets can be liquidated at GH¢450, the liquidation value per share is (GHat GH¢450, the liquidation value per share is (GH¢450 -GH¢350)/10 shares which is equal to GH¢ 10 ¢450 -GH¢350)/10 shares which is equal to GH¢ 10 per share.per share.

53

Other approaches to Other approaches to equity valuationequity valuation

Price earnings rat ioPrice earnings rat io The price earnings ratio reflects the amount investors The price earnings ratio reflects the amount investors

are willing to pay for each cedi of earnings.are willing to pay for each cedi of earnings. Expected earnings per share = [(Expected PAT) – Expected earnings per share = [(Expected PAT) –

(Preference dividend)]/Number of outstanding (Preference dividend)]/Number of outstanding shares.shares.

Expected PAT is dependent on a number of factors Expected PAT is dependent on a number of factors like sales, gross profit margin, depreciation, and like sales, gross profit margin, depreciation, and interest and tax rate.interest and tax rate.

The price earnings ratio has to consider factors like The price earnings ratio has to consider factors like growth rate, stability of earnings, company size, growth rate, stability of earnings, company size, company management team, and dividend payout company management team, and dividend payout ratio.ratio.

54

Other approaches to Other approaches to equity valuationequity valuation

Retention rateRetention rate rr = fraction of earnings that go back to firmrr = fraction of earnings that go back to firm

Dividend payout ratio (dividends/earnings)Dividend payout ratio (dividends/earnings) Fraction of earnings going to shareholders (1-Fraction of earnings going to shareholders (1-

rr)=brr)=b Dividends = b(earnings)Dividends = b(earnings) Firms with greater earnings growth will have greater Firms with greater earnings growth will have greater

P/E ratiosP/E ratios Firms with higher dividend payouts will have higher Firms with higher dividend payouts will have higher

P/E ratios P/E ratios 55

SummarySummary

Valuation is the process which links the risk and return to Valuation is the process which links the risk and return to

establish the asset worth. The value of a bond or a share is the establish the asset worth. The value of a bond or a share is the

discounted value of all their future cash inflows discounted value of all their future cash inflows

(interest/dividend) over a period of time. (interest/dividend) over a period of time.

The discount rate is the rate of return which the investors expect The discount rate is the rate of return which the investors expect

from the securities.from the securities.

In case of bonds, the stream of cash flows consists of annual In case of bonds, the stream of cash flows consists of annual

interest payment and repayment of principal (which may take interest payment and repayment of principal (which may take

place at par, at a premium, or at a discount). The cash flows place at par, at a premium, or at a discount). The cash flows

which occur in each year are a fixed amount. which occur in each year are a fixed amount. 56

SummarySummary Cash flows for preference share are also a fixed Cash flows for preference share are also a fixed

amount, and these shares may be redeemed at par, amount, and these shares may be redeemed at par, at a premium, or at a discount.at a premium, or at a discount.

The equity shareholders do not have a fixed rate of The equity shareholders do not have a fixed rate of return. Their dividend fluctuates with profits. return. Their dividend fluctuates with profits. Therefore, the risk of holding an equity share is Therefore, the risk of holding an equity share is higher than holding a preference share or a bond. higher than holding a preference share or a bond. Equity shareEquity share

valuation is usually done using the dividend valuation is usually done using the dividend capitalisation method. The valuation is based on the capitalisation method. The valuation is based on the flow of dividends.flow of dividends.

57