1
Valuation of BondsValuation of Bonds
and Sharesand Shares
2
ObjectivesObjectives
After studying this unit, you should be able to:After studying this unit, you should be able to:
 ...
The concept of intrinsic valueThe concept of intrinsic value
 The intrinsic value of an asset is equal to the presentThe ...
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 balanceThe value at which an asse...
Concept of book valueConcept of book value
 The following factors explain the concept of book value:The following factors...
Concept of book valueConcept of book value
 Market valueMarket value is the current price at which the asset oris the cur...
8
Valuation of BondsValuation of Bonds
 BondsBonds
are long-term debt instruments/fixed income (debt) instruments issueda...
9
Valuation of BondsValuation of Bonds
 Par or Face Value -Par or Face Value -
 The amount of money that is paid to the ...
10
Types of BondsTypes of Bonds
 Irredeemable bonds or perpetual bonds-Irredeemable bonds or perpetual bonds-
 Bonds whi...
11
Types of BondsTypes of Bonds
 Redeemable bonds -Redeemable bonds -
 Bonds with maturity date. They are of two types i...
12
ExampleExample
13
Bond values with semi-annualBond values with semi-annual
interest paymentsinterest payments
 In reality, it is quite c...
ExampleExample
14
15
Zero Coupon BondsZero Coupon Bonds
 Zero Coupon BondsZero Coupon Bonds
 a zero coupon bond will pay its stated face o...
16
ExampleExample
Bond yield measuresBond yield measures
 The bond yield measures are categorised into twoThe bond yield measures are categ...
Bond yield measuresBond yield measures
 Yield To Maturity (YTM):Yield To Maturity (YTM): Yield To MaturityYield To Maturi...
19
ExampleExample
 Josephe purchased a bond for $1,000 with 5-years maturity period. The BondJosephe purchased a bond for...
20
YTM approximationYTM approximation
methodmethod
 The trial and error method to obtain the rate of return (iThe trial a...
21
YTM approximationYTM approximation
method-Examplemethod-Example
 A company issues a bond with a face value of Rs. 5000...
Bond Value TheoremsBond Value Theorems
 The following factors affect the bond value theorems:The following factors affect...
Bond Value TheoremsBond Value Theorems
 When the required rate of return (iWhen the required rate of return (idd) is grea...
Bond Value TheoremsBond Value Theorems
 Solution:Solution:
 When iWhen idd is equal to the coupon rate, the intrinsic va...
Bond Value TheoremsBond Value Theorems
 When iWhen idd is greater than the coupon rate, the intrinsicis greater than the ...
Bond Value TheoremsBond Value Theorems
 When iWhen idd is less than the coupon rate, the intrinsicis less than the coupon...
Bond Value TheoremsBond Value Theorems
 Number of years of maturityNumber of years of maturity
 When iWhen idd is greate...
Bond Value TheoremsBond Value Theorems
 After 1 year, the maturity period is 6 years,After 1 year, the maturity period is...
Bond Value TheoremsBond Value Theorems
 Yield to Maturity:Yield to Maturity: A bond’s price varies inverselyA bond’s pric...
Valuation of SharesValuation of Shares
 There are two types of shares: Preference andThere are two types of shares: Prefe...
Valuation of SharesValuation of Shares
 The dividends are not cumulative for equityThe dividends are not cumulative for e...
Valuation of SharesValuation of Shares
 Redemption –Redemption – Preference shares have a maturityPreference shares have ...
Valuation of preferenceValuation of preference
sharesshares
 Preference shares like bonds carry a fixed rate ofPreference...
Valuation of ordinaryValuation of ordinary
sharesshares
 People hold common stocks:People hold common stocks:
1.1. to obt...
Valuation of ordinaryValuation of ordinary
sharesshares
 People hold common stocks:People hold common stocks:
1.1. to obt...
Dividend capitalisationDividend capitalisation
modelmodel
 When a shareholder buys a share, he is actuallyWhen a sharehol...
Dividend capitalisationDividend capitalisation
modelmodel
 Two assumptions are made to apply this approach.Two assumption...
Single period valuationSingle period valuation
modelmodel
 This model holds well when an investor holds anThis model hold...
Single period valuationSingle period valuation
model-Examplemodel-Example
 XYZ India Ltd’s share is expected to touch Rs....
Multi period valuationMulti period valuation
modelmodel
 An equity share can be held at an indefinite period asAn equity ...
Multi period valuationMulti period valuation
modelmodel
 The above equation can also be modified to find theThe above equ...
Types of DividendsTypes of Dividends
 There are 3 types of dividends:There are 3 types of dividends:
1.1. Constant divide...
Types of DividendsTypes of Dividends
 B. Valuation with constant growth inB. Valuation with constant growth in
dividendsd...
Types of DividendsTypes of Dividends
 C.C. Valuation with changing growth inValuation with changing growth in
dividendsdi...
Types of DividendsTypes of Dividends
 C.C. Valuation with changing growth inValuation with changing growth in
dividendsdi...
Types of DividendsTypes of Dividends
 The price of the equity share of such a firm isThe price of the equity share of suc...
Types of DividendsTypes of Dividends
47
ExampleExample
 Aikins Pharma’s current dividend is GH¢5. It expects to have aAikins Pharma’s current dividend is GH¢5. I...
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
,...
ExampleExample
 The discounted value of this price is 235.42/(1.15)5 =The discounted value of this price is 235.42/(1.15)...
Other approaches toOther approaches to
equity valuationequity valuation
 Book value approach:Book value approach:
 The B...
Other approaches toOther approaches to
equity valuationequity valuation
 Example:Example: Dovlo Ltd. has total assets wor...
Other approaches toOther approaches to
equity valuationequity valuation
 Liquidation valueLiquidation value
 The liquida...
Other approaches toOther approaches to
equity valuationequity valuation
 Price earnings ratioPrice earnings ratio
 The p...
Other approaches toOther approaches to
equity valuationequity valuation
 Retention rateRetention rate
 rr = fraction of ...
SummarySummary
 Valuation is the process which links the risk and return toValuation is the process which links the risk ...
SummarySummary
 Cash flows for preference share are also a fixedCash flows for preference share are also a fixed
amount, ...
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Bond valuation presentation unit 4

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Valuation methods for Bonds and shares

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Bond valuation presentation unit 4

  1. 1. 1 Valuation of BondsValuation of Bonds and Sharesand Shares
  2. 2. 2 ObjectivesObjectives After 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
  3. 3. The concept of intrinsic valueThe concept of intrinsic value  The intrinsic value of an asset is equal to the presentThe 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 discountedThe 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 givenMathematically, the intrinsic value of an asset is given by :by : VV00 == CC11 ++ CC22 ++ CC33 +…++…+ CCnn (1+i)(1+i)11 (1+i)(1+i)22 (1+i)(1+i)33 (1+i)(1+i)nn 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 flows n = expected life of an asset
  4. 4. The concept of intrinsic valueThe concept of intrinsic value 4
  5. 5. Concept of book valueConcept of book value  The value at which an asset is carried on a balanceThe value at which an asset is carried on a balance sheet. To calculate, take the cost of an asset minus thesheet. To calculate, take the cost of an asset minus the accumulated depreciation.accumulated depreciation.  The net asset value of a company, calculated by totalThe net asset value of a company, calculated by total assets minus intangible assets (patents, goodwill) andassets minus intangible assets (patents, goodwill) and liabilities.liabilities.  Book value of a share is calculated by dividing the netBook 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
  6. 6. 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 valueReplacement value is the amount a company is required to spendis the amount a company is required to spend if it were to replace its existing assets in the present condition. It isif 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 valueLiquidation value is the amount a company can realise if it sold theis the amount a company can realise if it sold the assets after winding up its business. It will not include the value ofassets 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 mightLiquidation value is generally the minimum value a company might accept if it sold its business.accept if it sold its business.  Going concern valueGoing concern value is the amount a company can realise if itis the amount a company can realise if it sells its business as an operating one. This value is higher thansells its business as an operating one. This value is higher than the liquidation value.the liquidation value. 6
  7. 7. Concept of book valueConcept of book value  Market valueMarket value is the current price at which the asset oris the current price at which the asset or security is being sold or bought in the market. Marketsecurity is being sold or bought in the market. Market value per share is generally higher than the book valuevalue 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. 8. 8 Valuation of BondsValuation of Bonds  BondsBonds are long-term debt instruments/fixed income (debt) instruments issuedare long-term debt instruments/fixed income (debt) instruments issued by government agencies or big corporate houses to raise large sums ofby 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 theThe coupon rate, which is generally fixed, determines the periodic coupon or interest payments. It is expressed as aperiodic coupon or interest payments. It is expressed as a percentage of the bond's face value. It also represents thepercentage 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 bondThe 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 lastthe 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. 9. 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 byIt 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 andMarket price is the price at which the bonds can be bought and sold, and this price may be different from par value andsold, 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 beis the amount the bondholder gets on maturity. A bond may be redeemed at par, at a premium (bondholder gets more than theredeemed at par, at a premium (bondholder gets more than the par value of the bond), or at a discount (bondholder gets lesspar 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. 10. 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, andBonds which will never mature. The face value is known, and the interest received on such bonds is constant and received atthe interest received on such bonds is constant and received at regular intervals and hence, the interest receipt resemblesregular 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;  VV00 - 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 the1000 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. 11. 11 Types of BondsTypes of Bonds  Redeemable bonds -Redeemable bonds -  Bonds with maturity date. They are of two types in respect ofBonds with maturity date. They are of two types in respect of interest payments; one with annual interest payments and theinterest 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 aThe holder of a bond receives a fixed annual interest for a specified number of years and a fixed principal repayment atspecified 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 ValueWhere ; 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, idd –– required rate of interest, n- maturity period of the bond.required rate of interest, n- maturity period of the bond.
  12. 12. 12 ExampleExample
  13. 13. 13 Bond values with semi-annualBond 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 muchannually. 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)2n2n .. NB: the variables are as defined in the previous example.NB: the variables are as defined in the previous example.
  14. 14. ExampleExample 14
  15. 15. 15 Zero Coupon BondsZero Coupon Bonds  Zero Coupon BondsZero Coupon Bonds  a zero coupon bond will pay its stated face or par value ata zero coupon bond will pay its stated face or par value at maturity. It pays no other future cash flows during its life. Zeroesmaturity. It pays no other future cash flows during its life. Zeroes are also known as pure discount bonds. The return here comesare 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 theThe face value is the amount payable to the holder of the instrument on maturity. Thus, no interest or any other type ofinstrument 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, Idd –– required rate of interest, n – bond life or maturity periodrequired rate of interest, n – bond life or maturity period
  16. 16. 16 ExampleExample
  17. 17. Bond yield measuresBond yield measures  The bond yield measures are categorised into twoThe 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 ofCurrent yield measures the rate of return earned on a bond if it is purchased at itsreturn earned on a bond if it is purchased at its current market price and the coupon interest that iscurrent market price and the coupon interest that is received.received.  It is calculated as : CY =Coupon Interest/ CurrentIt 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 isThe 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
  18. 18. Bond yield measuresBond yield measures  Yield To Maturity (YTM):Yield To Maturity (YTM): Yield To MaturityYield 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 presentThe YTM is the discount rate equalling the present values of cash flow to the current marketvalues of cash flow to the current market price/purchase price.price/purchase price.  So,a bond’s YTM may be defined as the InternalSo,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. 19. 19 ExampleExample  Josephe purchased a bond for $1,000 with 5-years maturity period. The BondJosephe 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 hiscurrently 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 = ΣΣ [CF[CFtt / (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 trial and error method let us take id = 10%By trial 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 marketthe 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 idd = 9%= 9%  = 60*3.890 + 1000*.650= 60*3.890 + 1000*.650
  20. 20. 20 YTM approximationYTM approximation methodmethod  The trial and error method to obtain the rate of return (iThe trial and error method to obtain the rate of return (idd) 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 referenceThe following formula can be used as a ready reference formula:formula:
  21. 21. 21 YTM approximationYTM approximation method-Examplemethod-Example  A company issues a bond with a face value of Rs. 5000. It isA company issues a bond with a face value of Rs. 5000. It is currently trading at Rs. 4500. The interest rate offered bycurrently trading at Rs. 4500. The interest rate offered by the company is 12%,and the bond has a maturity period of 8the 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%
  22. 22. 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 rate 2.2. Number of years to maturityNumber of years to maturity 3.3. Yield To Maturity (YTM)Yield To Maturity (YTM)  Relationship between the required rate ofRelationship between the required rate of return (ireturn (idd ) and the coupon rate) and the coupon rate  When the required rate of return is equal to theWhen the required rate of return is equal to the coupon rate, the value of the bond is equal to its parcoupon 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
  23. 23. 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 itsthe 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. 100Sugam Industries wishes to issue bonds with Rs. 100 as par value, coupon rate of 12%, and YTM of 5as par value, coupon rate of 12%, and YTM of 5 years. What is the value of the bond if the requiredyears. 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
  24. 24. Bond Value TheoremsBond Value Theorems  Solution:Solution:  When iWhen idd is equal to the coupon rate, the intrinsic valueis equal to the coupon rate, the intrinsic value of the bond isequal to its face value.of the bond isequal to its face value.  If iIf idd 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 (Intrinsic value = Face value)= Rs. 100 (Intrinsic value = Face value) 24
  25. 25. Bond Value TheoremsBond Value Theorems  When iWhen idd is greater than the coupon rate, the intrinsicis 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.  If iIf idd 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
  26. 26. Bond Value TheoremsBond Value Theorems  When iWhen idd is less than the coupon rate, the intrinsicis 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.  If iIf idd 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 (Intrinsic value > Face value)= Rs. 107.59 (Intrinsic value > Face value) 26
  27. 27. Bond Value TheoremsBond Value Theorems  Number of years of maturityNumber of years of maturity  When iWhen idd is greater than the coupon rate, the discountis greater than the coupon rate, the discount on the bond declines and hence value increases ason the bond declines and hence value increases as maturity approaches.maturity approaches.  Example:Example: To show the effect of the above, considerTo show the effect of the above, consider a case of a bond whose face value is $100 with aa 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.  If iIf idd 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
  28. 28. 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 ofThe 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 isthe reverse happens when required rate of return is lower than the coupon rate. Reverse the rates for thelower than the coupon rate. Reverse the rates for the 28
  29. 29. Bond Value TheoremsBond Value Theorems  Yield to Maturity:Yield to Maturity: A bond’s price varies inverselyA bond’s price varies inversely with yield. This is because as the required yieldwith yield. This is because as the required yield increases, the present value of the cash flowincreases, the present value of the cash flow decrease and hence the price decreasesdecrease and hence the price decreases 29
  30. 30. Valuation of SharesValuation of Shares  There are two types of shares: Preference andThere are two types of shares: Preference and ordinary or equity shares.ordinary or equity shares.  The following are some important features ofThe following are some important features of preference and equity shares:preference and equity shares:  Dividends –Dividends – Rate is fixed for preferenceRate 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 afterthat is, the dividend can be paid off after accumulation.accumulation.  The dividend rate is not fixed for equityThe dividend rate is not fixed for equity shareholders. They change with an increase orshareholders. They change with an increase or decrease in profits.decrease in profits. 30
  31. 31. Valuation of SharesValuation of Shares  The dividends are not cumulative for equityThe dividends are not cumulative for equity shareholders, that is, they cannot be accumulatedshareholders, that is, they cannot be accumulated and distributed in the later years. Dividends are notand 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 thethe preference shareholders have a prior claim on the assets of the company. Their claims shall be settledassets of the company. Their claims shall be settled first and the balance, if any, will be paid off to equityfirst and the balance, if any, will be paid off to equity shareholders. Equity shareholders are residualshareholders. Equity shareholders are residual claimants to the company’s income and assets.claimants to the company’s income and assets. 31
  32. 32. Valuation of SharesValuation of Shares  Redemption –Redemption – Preference shares have a maturityPreference shares have a maturity date on which the company pays off the face value ofdate 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 – redeemablePreference 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 convertibleA company can issue convertible preference shares. After a particular period, aspreference shares. After a particular period, as mentioned in the share certificate, the preferencementioned in the share certificate, the preference shares can be converted into ordinary shares.shares can be converted into ordinary shares. 32
  33. 33. Valuation of preferenceValuation of preference sharesshares  Preference shares like bonds carry a fixed rate ofPreference 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
  34. 34. Valuation of ordinaryValuation 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 manner 2.2. to get a higher amount when soldto get a higher amount when sold  Generally, shares are not held in perpetuity. AnGenerally, shares are not held in perpetuity. An investor buys the shares, holds them for some timeinvestor buys the shares, holds them for some time during which he gets dividends, and finally sells it offduring 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 aIntrinsic 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 thedividends, definite prospects, and the factor of the management of the issuing company.management of the issuing company. 34
  35. 35. Valuation of ordinaryValuation 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 manner 2.2. to get a higher amount when soldto get a higher amount when sold  Generally, shares are not held in perpetuity. AnGenerally, shares are not held in perpetuity. An investor buys the shares, holds them for some timeinvestor buys the shares, holds them for some time during which he gets dividends, and finally sells it offduring 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 aIntrinsic 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 thedividends, definite prospects, and the factor of the management of the issuing company.management of the issuing company. 35
  36. 36. Dividend capitalisationDividend capitalisation modelmodel  When a shareholder buys a share, he is actuallyWhen 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 isTherefore, the value of an ordinary share is determined by capitalising the future dividend streamdetermined by capitalising the future dividend stream at an appropriate rate of interest.at an appropriate rate of interest.  under the dividend capitalisation approach, the valueunder the dividend capitalisation approach, the value of an equity share is the discounted present value ofof an equity share is the discounted present value of dividends received plus the present value of thedividends received plus the present value of the resale price expected when the share is disposed.resale price expected when the share is disposed. 36
  37. 37. Dividend capitalisationDividend capitalisation 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 fromFirst 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
  38. 38. Single period valuationSingle period valuation modelmodel  This model holds well when an investor holds anThis 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
  39. 39. Single period valuationSingle period valuation model-Examplemodel-Example  XYZ India Ltd’s share is expected to touch Rs. 450XYZ India Ltd’s share is expected to touch Rs. 450 one year from now. The company is expected toone 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 beWhat is the price at which an investor would be willing to buy if his or her required rate of return iswilling 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
  40. 40. Multi period valuationMulti period valuation modelmodel  An equity share can be held at an indefinite period asAn equity share can be held at an indefinite period as it has no maturity date. The value of an equity shareit has no maturity date. The value of an equity share of infinite duration is equal to the discounted value ofof 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
  41. 41. Multi period valuationMulti period valuation modelmodel  The above equation can also be modified to find theThe 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
  42. 42. Types of DividendsTypes of Dividends  There are 3 types of dividends:There are 3 types of dividends: 1.1. Constant dividendsConstant dividends 2.2. Constant growth of dividendsConstant growth of dividends 3.3. 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
  43. 43. Types of DividendsTypes of Dividends  B. Valuation with constant growth inB. Valuation with constant growth in dividendsdividends  Here, we assume that dividends tend to increase with time asHere, we assume that dividends tend to increase with time as and when businesses grow over time. If the increase in dividendand when businesses grow over time. If the increase in dividend is at a constant compound rate, thenis at a constant compound rate, then Po = DPo = D11 / (K/ (Kee – 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 dividendExample: Monica Labs are expected to pay Rs. 4 as dividend per share next year. The dividends are expected to growper share next year. The dividends are expected to grow perpetually at 8%. Calculate the share price today if the marketperpetually at 8%. Calculate the share price today if the market capitalisation is 12%.capitalisation is 12%.  Solution:Solution:  PPoo = D= D11 / (K/ (Kee – 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
  44. 44. Types of DividendsTypes of Dividends  C.C. Valuation with changing growth inValuation with changing growth in dividendsdividends  Some firms may not have a constant growth rate ofSome firms may not have a constant growth rate of dividends indefinitely.dividends indefinitely.  There are periods during which the dividends mayThere are periods during which the dividends may grow super normally, that is, the growth rate is verygrow super normally, that is, the growth rate is very high when the demand for the company’s products ishigh when the demand for the company’s products is very high.very high.  After a certain period of time, the growth rate may fallAfter a certain period of time, the growth rate may fall to normal levels when the returns fall due to fall into normal levels when the returns fall due to fall in demand for products (with competition setting in ordemand for products (with competition setting in or due to availability of substitutes).due to availability of substitutes). 44
  45. 45. Types of DividendsTypes of Dividends  C.C. Valuation with changing growth inValuation with changing growth in dividendsdividends  Some firms may not have a constant growth rate ofSome firms may not have a constant growth rate of dividends indefinitely.dividends indefinitely.  There are periods during which the dividends mayThere are periods during which the dividends may grow super normally, that is, the growth rate is verygrow super normally, that is, the growth rate is very high when the demand for the company’s products ishigh when the demand for the company’s products is very high.very high.  After a certain period of time, the growth rate may fallAfter a certain period of time, the growth rate may fall to normal levels when the returns fall due to fall into normal levels when the returns fall due to fall in demand for products (with competition setting in ordemand for products (with competition setting in or due to availability of substitutes).due to availability of substitutes). 45
  46. 46. Types of DividendsTypes of Dividends  The price of the equity share of such a firm isThe 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 of1. Expected dividend flows during periods of supernormal growth is to be considered and presentsupernormal growth is to be considered and present value of this is to be computed with the followingvalue 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:
  47. 47. Types of DividendsTypes of Dividends 47
  48. 48. ExampleExample  Aikins Pharma’s current dividend is GH¢5. It expects to have aAikins Pharma’s current dividend is GH¢5. It expects to have a supernormal growth period running to 5 years during which thesupernormal growth period running to 5 years during which the growth rate would be 25%. The company expects normalgrowth 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 theThe 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
  49. 49. 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 flow of dividends willThe present value of this flow of dividends will 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)44 + 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-gnn but Dbut 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 49
  50. 50. 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
  51. 51. Other approaches toOther approaches to equity valuationequity valuation  Book value approach:Book value approach:  The Book Value Per Share (BVPS) is the net worth ofThe Book Value Per Share (BVPS) is the net worth of the company divided by the number of outstandingthe company divided by the number of outstanding equity shares.equity shares.  Net worth is represented by the total sum of paid-upNet 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 theAlternatively, this can also be calculated as the amount per share on the sale of the assets of theamount per share on the sale of the assets of the company at their exact book value minus all liabilitiescompany at their exact book value minus all liabilities including preference shares.including preference shares. 51
  52. 52. Other approaches toOther approaches to equity valuationequity valuation  Example:Example: Dovlo Ltd. has total assets worth GHDovlo 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. ThisBVPS does not give a true investment picture. This relies on historical book values than the company’srelies on historical book values than the company’s earning potential.earning potential. 52
  53. 53. Other approaches toOther 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 liquidatedIn 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
  54. 54. Other approaches toOther approaches to equity valuationequity valuation  Price earnings ratioPrice earnings ratio  The price earnings ratio reflects the amount investorsThe 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 factorsExpected PAT is dependent on a number of factors like sales, gross profit margin, depreciation, andlike sales, gross profit margin, depreciation, and interest and tax rate.interest and tax rate.  The price earnings ratio has to consider factors likeThe 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 payoutcompany management team, and dividend payout ratio.ratio. 54
  55. 55. Other approaches toOther 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 greaterFirms with greater earnings growth will have greater P/E ratiosP/E ratios  Firms with higher dividend payouts will have higherFirms with higher dividend payouts will have higher P/E ratiosP/E ratios 55
  56. 56. SummarySummary  Valuation is the process which links the risk and return toValuation is the process which links the risk and return to establish the asset worth. The value of a bond or a share is theestablish the asset worth. The value of a bond or a share is the discounted value of all their future cash inflowsdiscounted 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 expectThe 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 annualIn case of bonds, the stream of cash flows consists of annual interest payment and repayment of principal (which may takeinterest payment and repayment of principal (which may take place at par, at a premium, or at a discount). The cash flowsplace 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
  57. 57. SummarySummary  Cash flows for preference share are also a fixedCash 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 ofThe 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 isTherefore, 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 dividendvaluation is usually done using the dividend capitalisation method. The valuation is based on thecapitalisation method. The valuation is based on the flow of dividends.flow of dividends. 57

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