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Kulkarni Dr.P.R.Kulkarni 1 9/13/2011Chapter Objectives: Chapter Objectives Explain the fundamental characteristics of bonds (or debentures), preference shares and ordinary shares, Show the use of the present value concepts in the valuation of shares and bonds. Learn about the linkage between the share values, earnings and dividends and the required rate of return on the share. Focus on the uses and misuses of price-earnings ( P/E ) ratio. 2 9/13/2011 Dr.P.R.KulkarniIntroduction: Introduction The goal of any investor or corporate is to maximize the profit. The finance manager needs to have the basic knowledge and understanding of the framework of security valuation. The concept of time value of money provide a fundamental background for the valuation of bonds and stocks. 3 Dr.P.R.Kulkarni 9/13/2011Valuation of assets: Valuation of assets Valuation is the process that links risk and return to determine the worth of an assets –bonds and stock. There are three key inputs required for the valuating the assets. Cash flows : Value of assets is decided based on the expected cash flow) return. Timing : Timing of return is another input that is require for valuation of asset. It is period over which returns are expected. Required return : It is another and very important input needed for valuation of asset. Expected rate of return depends on the level of risk associated with the given investment. Required rate of return varies from investment to investment . The greater the risk, greater is the rate of return expected and vice-versa. 4 Dr.P.R.Kulkarni 9/13/2011Security: Security Financial assets or securities are assets that represent a claim to future cash flows. Bond: A bond is a debt security, in which the authorized issuer owes the holders a debt and is obliged to repay the principal and interest at a later date. Equity: Capital raised from the owners by issuing securities representing the ownership claim to the economic unit. 5 Dr.P.R.Kulkarni 9/13/2011Bond Terminology : Bond Terminology Par Value : Value stated on the face of the bond that the firm promises to repay at the time of maturity. Coupon Rate : It is the specific interest rate stated on the bond and payable to the bond holder. Maturity Period : The period for which the bond is valid. 6 Dr.P.R.Kulkarni 9/13/2011Cash Flows for Stockholders: Cash Flows for Stockholders If you buy a share of stock, you can receive cash in two ways The company pays dividends You sell your shares, either to another investor in the market or back to the company As with bonds and the price of the stock is the present value of these expected cash flows. 7 Dr.P.R.Kulkarni 9/13/2011Concept of valuation: Concept of valuation Valuation is the process that links risk and return to determine the worth of assets. It can be applied to financial assets/securities to determine their worth at given point of time. A security can be regarded simply as a series of dividends or interest payments received over the period of time. Therefore value of any security can be defined as the present of these future cash streams. 8 Dr.P.R.Kulkarni 9/13/2011Concept of Value: Concept of Value Replacement of Value: is the amount that company would be required to spend if it were to replace the existing assets in the current condition. Liquidation Value: is the amount a company can realized if it sells its assets after having terminated the business. Going concern value is the amount that company can realized if it sells its business as an operating one. Market value: of an assets or security is the current price at which assets or security is being sold. 9 Dr.P.R.Kulkarni 9/13/2011Valuation of Assets in General: Valuation of Assets in General The following applies to any financial asset : V = Current value of the asset C t = Expected future cash flow in period (t) k = Investor’s required rate of return Note : When analyzing various assets (e.g., bonds, stocks), the formula below is simply modified to fit the particular kind of asset being evaluated. 10 Dr.P.R.Kulkarni 9/13/2011Example: Example Calculate the value of the assets if the annual cash flow is Rs 2000 per year for 7 years if discount rate is 18 % . Vo = 2000 × PVIF 18 %, 7 =2000 ×3.812 =7624 11 Dr.P.R.Kulkarni 9/13/2011The value of financial assets: The value of financial assets Dr.P.R.Kulkarni 12 0 1 2 n k CF 1 CF n CF 2 Value ... 9/13/2011Valuation of Bonds: Valuation of Bonds Bonds are negotiable promissory notes that can be used by individuals, business firm, government and government agencies. Bonds issued by the government or public sector in India are secured. Private sector companies can issue secured or unsecured bonds. Interest rate is fixed and known to investors. Expected cash flow consist of annual interest payment and principal at time of redemption. 13 Dr.P.R.Kulkarni 9/13/2011Bond Value with Maturity: Bond Value with Maturity P = C x PVIFA kd n +F x PVIF kd, n 14 Dr.P.R.Kulkarni 9/13/2011Value of Bond: Value of Bond Value of bond or any asset is equal to the present value of the cash flows expected from it. Let, Po = Market Price or Value of Bond C = Annual Coupon Payments in Rupees. n = number of years to maturity. K d = required rate of return or discount rate F= Maturity Value or Par Value t = time period when payment is received. 15 Dr.P.R.Kulkarni 9/13/2011Example: Example A bond whose par value is Rs 1000 bears a coupon rate of 12 %and has maturity period of 3 years. The required rate of return on the bond is 10 %. What is the value of this bond? P o = Interest ( c) x ( PVIFA K d , n ) + F (PVIF K d n ) 16 Dr.P.R.Kulkarni 9/13/2011Slide 17: V o =Rs 120 (PVIFA 10%,3 Yrs ) + Rs 1000 (PVIF 10%,3 yrs ) = Rs 120 x 2.487 + 1000 x0.751 = Rs298.44 +Rs 751 = Rs 1049.44 17 Dr.P.R.Kulkarni 9/13/2011Example 2: Example 2 Consider the case where an investor purchase a bond whose face value is Rs 1000, maturity period is 5years,and nominal coupon rate is 7%. The required rate of return is 8%. What should be he willing to pay now to purchase the bond if it mature at par? 18 Dr.P.R.Kulkarni 9/13/2011Solution: Solution Annual interest payable for 5 years= Rs 70 Principle repayable amount at end of 5 yrs =Rs 1000 The intrinsic value or the present value of bond =Rs 70 (PVIFA 8%,5yrs ) + Rs 1000( PVIF 8%,5yrs ) =Rs 70 x 3.993 +Rs 1000 x 0.681 =279.51 +681 =Rs 960.51 19 Dr.P.R.Kulkarni 9/13/2011Bonds Value with Semi-Annual Interest: Bonds Value with Semi-Annual Interest Some of the Bonds carry interest payments semi-annually. Hence the bond valuation equation can be modified as: Annual interest payment must divided by two to obtain the interest payment semi-annually. Number of years to maturity will have to be multiplied by two to get the number of half yearly period. Discount rate has to be divided by two to get the discounted rate for half-yearly period. With these modification the bond valuation equation becomes: 20 Dr.P.R.Kulkarni 9/13/2011Bond Value (Semi-Annual Payments): Bond Value (Semi-Annual Payments) Po= I/2 (PVIFA K d/2 , 2n )+M (PVIF K d/2.2n ) 21 Dr.P.R.Kulkarni 9/13/2011Example: Example A bond of Rs 1000 value carries a coupon rate of 10% and maturity period of 6 years. Interest is payable semi- annually. If required arte of rate of return is 12%.Calculate the value of bonds. 22 Dr.P.R.Kulkarni 9/13/2011solution: solution Value of bond =Rs50 (PVIFA 6%,12Yeaes ) +1000 PVIF 6%,12 Years. Rs 50 (8.384 ) +1000 (0.497) = Rs 419.2+ 497 = Rs 916.20 23 Dr.P.R.Kulkarni 9/13/2011The Current Yield: The Current Yield Current yield is the annual interest divided by the bonds current value. Current yield considers only the annual interest and does not account for the capital gain or loss. Suppose annual interest is Rs 60 and price of bond is Rs 883.40. The current yield =60÷ 883.40=6.8 It is calculated as CY = 9/13/2011 24 Dr.P.R.KulkarniExample on current Yield: Example on current Yield X purchased Rs 1000 par value bond. The coupon payment on this bond is Rs 80 (8%).The current price of the bond is Rs 800. What is current yield on this bond?. Current yield = coupon interest ÷ current market price Current yield =80 ÷ 800 =0.10= 10% 25 Dr.P.R.Kulkarni 9/13/2011Calculating Yield to Maturity: Calculating Yield to Maturity Trial and Error : Keep guessing until you find the rate whereby the present value of the interest and principal payments is equal to the current price of the bond. (necessary procedure without a financial calculator or computer). Easiest Approach : Use a computer or financial calculator. Note, however, that it is extremely important to understand the mechanics that go into the calculations. 26 Dr.P.R.Kulkarni 9/13/2011Slide 27: Yield to maturity refers to effective rate of return expected by the owner of bond if bond is held to maturity. In technical term , it can be define as “ Discount rate that equates the present value of all bonds expected future cash flows with current market price of the bond “ In other word YTM is nothing but Internal rate of return (IRR) and is measured by computing the present value of interest and principal payment. This can measured by the following formulas. 27 Dr.P.R.Kulkarni 9/13/2011Slide 28: Suppose the market price of bond is Rs 883.40( face value being Rs 1000). The bond will pay interest at 6 percent per annum foe 5 years, after it will be redeemed at par. What is the bond’s YTM? (Answer 10%) 883.40 = 28 Dr.P.R.Kulkarni 9/13/2011Bond Yield to Maturity: Bond Yield to Maturity Bond Yields are the actual returns that an investor can receives by purchasing the bond at the current market price. 29 Dr.P.R.Kulkarni 9/13/2011Slide 30: YTM=Yield to maturity I=Annual interest payment F=maturity value of bonds/Par value of bond P= present value of the bonds N=years of maturity 30 Dr.P.R.Kulkarni 9/13/2011Example: Example Consider a Rs 1000 par value bond carrying a coupon rate of 9%, maturity after 8 years. The bond is currently selling for Rs 800. What is YTM on this bond. (use the second Formula) YTM =90+1000-800/8 ÷ o.4x1000+0.6x800 =13.1 % 31 Dr.P.R.Kulkarni 9/13/2011Solution: Solution YTM =90+1000-800/8 ÷ o.4x1000+0.6x800 =13.1 % 32 Dr.P.R.Kulkarni 9/13/2011Example 2: Example 2 The bond of zeta Industries ltd with par value of Rs 500 is currently traded at Rs 435. The coupon rate is 12% and it has the maturity period of 7 years. What is yield to maturity ? 33 Dr.P.R.Kulkarni 9/13/2011Solution: Solution Use the second formula =60 + ( 500- 435 ) ÷7 ÷ 0.4 × 500 +0.6× 435 =60 + 9.285 ÷200 + 261 = 15.03 % 34 Dr.P.R.Kulkarni 9/13/2011Yield to Call : Yield to Call For calculating the yield to call , the call period would be different from the maturity period and the call (or redemption) value could be different from the maturity value. Example : Suppose the 10% 10-year Rs 1,000 bond is redeemable (callable) in 5 years at a call price of Rs 1,050. The bond is currently selling for Rs 950.The bond’s yield to call is 12.7%. 35 9/13/2011 Dr.P.R.KulkarniPerpetual Bonds – Irredeemable bonds: Perpetual Bonds – Irredeemable bonds Perpetual bonds , also called consol , has an indefinite life and therefore, it has no maturity value. Perpetual bonds or debentures are rarely found in practice. 36 9/13/2011 Dr.P.R.KulkarniPerpetual Bonds: Perpetual Bonds Suppose that a 10 per cent Rs 1,000 bond will pay Rs 100 annual interest into perpetuity. What would be its value of the bond if the market yield or interest rate were 15 per cent? The value of the bond is determined as follows : Po = Po = 100 =Rs 667 0.15 37 Dr.P.R.KulkarniSlide 38: A perpetual bond’s yield-to-maturity : 38 Dr.P.R.Kulkarni 9/13/2011Realized Yield: Realized Yield The realized yield on the bond is the actual yield earned by the investor and is computed by the equation : Po ( 1+r)ⁿ = total cash received by the investors at end of period n. The above equation can written as : Po ( FVIFr ŉ ) =Total return + Purchase Price. The realized yield can also be calculated by the following formula. 39 Dr.P.R.Kulkarni 9/13/2011Realized Yield to Maturity: Realized Yield to Maturity It is the real rate of return from a bond assuming different future investment rates. F = Future Value of Cash Flows P = Present Value of Bond Example 2 40 Dr.P.R.Kulkarni 9/13/2011Relationship Between Price & YTM: Relationship Between Price & YTM 41 Dr.P.R.Kulkarni S.No . Bond Type Price YTM 1 Par Mkt. Price = Par Value YTM = Coupon Rate 2 Discount Mkt. Price < Par Value YTM > Coupon Rate 3 Premium Mkt. Price > Par Value YTM > Coupon Rate 9/13/2011Bond value theorems: Bond value theorems Based on the bond valuation model, several bond value theorems have been derived which state the effect on the following factors on bond value. Relationship between the requirement rate of return and coupon rate. Number of year of maturity. Yield to maturity 42 Dr.P.R.Kulkarni 9/13/2011Theorem I: Theorem I When required rate of return is equal to coupon rate, the value of the bond is equal to par value. Example: par value of bond is Rs 100, coupon rate is 12%, require rate of return is 12%. Maturity period is 5 years. V=I (Annuity of require rate of return )+Face Value of bond ( pv of required rate of return) V=I (PVIFA r,5 )+F (PVIF r,5 ) V= 12(3.605) +100 (0.567)=43.26+56.7=100 43 Dr.P.R.Kulkarni 9/13/2011Theorem II: Theorem II When required rate of return is greater than the coupon rate, the value of the bond is less than the par value. Example: Par value of bond =Rs 100,reqired rate of return =14%, coupon rate =12%, maturity period 5years. V=I(PVIFA r,5 ) + F( PVIF r,5 ) V=12x3.433 +100x0.516 V=41.433+51.9 =93.1 44 Dr.P.R.Kulkarni 9/13/2011Theorem III : Theorem III When the required rate of return is less than the coupon rate, the value of the bond is greater than bond value. Example : Bond par value =Rs 100, coupon rate =12%, required rate 10%Maturity=5years V=I (PVIFA r,5 ) +F( PVIF r,5 ) V=12x3.791 +100 x0.621 V=45.492 +62.1 =107.59 45 Dr.P.R.Kulkarni 9/13/2011Bond Theorem -IV: Bond Theorem -IV “A similar percentage change in YTM affects the bonds with a higher YTM more than it does bond with lower YTM.” 46 Dr.P.R.Kulkarni 9/13/2011Example: Example A bond whose par value is Rs 1000, bears a coupon rate of 12%and maturity period of 3 years. The required rate of return on the bond is 10%. What is value of this bond. Solution Annual Interest rate : 1000 x 12% =Rs 120 Principle repayment : Rs 1000 P = Rs 120 (PVIFA 10%,3yrs )+ Rs 1000 (PVIF 10%,3yrs) P=120x2.484 +1000x0.751 =1049.44 47 Dr.P.R.Kulkarni 9/13/2011Slide 48: Equity Valuation 9/13/2011 48 Dr.P.R.KulkarniValuation of Shares: Valuation of Shares A company may issue two types of shares: ordinary shares and preference shares Features of Preference and Ordinary Shares Claims Dividend Redemption Conversion 49 9/13/2011 Dr.P.R.KulkarniSlide 50: The preference share may be issued with or without maturity period. Redeemable preference shares are with the maturity. Irredeemable shares are shares without maturity. The holders of preference shares get dividend at fixed rate. 50 Dr.P.R.Kulkarni 9/13/2011Valuation of Preference Shares: Valuation of Preference Shares The value of the preference share would be the sum of the present values of dividends and the redemption value. Po = Dividend x PVIFA kp , n +Maturity Value x PVIF kp , n A formula similar to the valuation of bond can be used to value preference shares with a maturity period: 51 9/13/2011 Dr.P.R.KulkarniExample : Example Suppose an investor is considering the purchase of a 12 years,10% Rs 100 par value preference share. The redemption value of the preference share on maturity is Rs 120. The investor’s required rate of return is 14%. What should investor be willing to pay for the share now? Po = 10 x PVIFA 14,12 + 120 x PVIF 14,12 = 52 Dr.P.R.Kulkarni 9/13/2011Valuation of Irredeemable Preference Shares: Valuation of Irredeemable Preference Shares Preference share with no stated maturity, can be valued as a perpetuity of dividend D. 53 Dr.P.R.Kulkarni 9/13/2011Why equity: Why equity Investor invest in equity because it gives better return than bonds Equity stock can be held as protective measure during the inflation. Intrinsic value is the value of the stock which is justified by the assets, earning, dividends, definite prospects and the factor of the management of the issuing company. 54 Dr.P.R.Kulkarni 9/13/2011Characteristics of Equity: Characteristics of Equity Infinite Life Returns in the form of dividends and price appreciation. Variable and uncertain returns. 55 Dr.P.R.Kulkarni 9/13/2011The Single Period Model: The Single Period Model The value of equity which will be held for a single period ( 1 year) and will be sold at the end of the period is given as 56 Dr.P.R.Kulkarni 9/13/2011Slide 57: Where : Po =current market price of the share D 1 = is the dividend expected P 1 =is the price of the share expected K e =required rate of return. 57 Dr.P.R.Kulkarni 9/13/2011Example: Example Mercury India ltd is expected to declare a dividend of Rs 2.50 and reach the price of Rs 35.00 a year. The required rate of return is 13 %. What is price at which the share would sold ? Solution The current price = 2.50÷1.13 +35 ÷1.13 = 2.21 +31.00 =33.21 What happens if the price of the equity share is expected to grow at a rate of “g “percent annually? If current price P 0, becomes P 0 (1+g) a year hence. 58 Dr.P.R.Kulkarni 9/13/2011Slide 59: We get : After solving this equation : 59 Dr.P.R.Kulkarni 9/13/2011Slide 60: XYZ Solvents Ltd is expected to grow at the rate of 7% per annum and dividend is expected hence is Rs 5.00.If the required rate of return is 12 %, what is price of the share today. The price would be (Po) = 5 0.12 – 0.07 = Rs 100 60 Dr.P.R.Kulkarni 9/13/2011Multi-Period valuation Model: Multi-Period valuation Model Since equity shares have no maturity period, they may be expected to bring a dividend stream of infinite duration. Basic dividend valuation model accounts for the PV of all future dividends. (1 + k e ) 1 (1 + k e ) 2 (1 + k e ) ¥ Po = + + ... + Div 1 Div ¥ Div 2 = S ¥ t=1 (1 + k e ) t Div t Div t : Cash Dividend at time t k e : Equity investor’s required return 9/13/2011 61 Dr.P.R.Kulkarni Multi-period valuation Model : Multi-period valuation Model If the final period is n , we can write the general formula for share value as follows: 62 Dr.P.R.Kulkarni 9/13/2011Zero Growth-Constant dividend: Zero Growth-Constant dividend If dividends are expected at regular intervals forever, then this is like preferred stock and is valued as a perpetuity P 0 = Suppose stock is expected to pay a Rs0.50 dividend every quarter and the required return is 10% with quarterly compounding. What is the price? P 0 = .50 / (.1 / 4) = Rs20 9/13/2011 63 Dr.P.R.KulkarniValuation with constant growth in dividend: Valuation with constant growth in dividend It is assumed that dividends tend to increase over the time because business firm usually grow over time. The growth of dividends is at constant compound rate, than D t =Do Where D t is dividend for year t ,g is constant compound growth rate &Do divided for year 0 The valuation of the share where divided increases at a constant compound rate is : 64 Dr.P.R.Kulkarni 9/13/2011Valuation with constant growth in dividend: Valuation with constant growth in dividend The constant growth model assumes that dividends will grow forever at the rate g . (1 + k e ) 1 (1 + k e ) 2 (1 + k e ) ¥ Po = + + ... + D 0 (1+ g ) D 0 (1+ g ) ¥ = ( k e - g) D 1 D 1 : Dividend paid at time 1. g : The constant growth rate. k e : Investor’s required return. D 0 (1+ g ) 2 9/13/2011 65 Dr.P.R.KulkarniValuation with constant growth in dividend: Valuation with constant growth in dividend Dividends are expected to grow at a constant percent per period. P 0 = D 1 /(1+K e ) + D 2 /(1+K e ) 2 + D 3 /(1+K e ) 3 + P 0 = D 0 (1+g) /(1+K e ) + D 0 (1+g) 2 /(1+K e ) 2 + D 0 (1+g) 3 /(1+K e ) 3 + … constant growth. With a little algebra, this reduces to: 9/13/2011 66 Dr.P.R.KulkarniDGM – Example 1 : DGM – Example 1 Suppose Big D, Inc. just paid a dividend of Rs 0.50. It is expected to increase its dividend by 2% per year. If the market requires a return of 15% on assets of this risk, how much should the stock be selling for? P 0 = .50(1+.02) / (.15 - .02) = Rs3.92 9/13/2011 67 Dr.P.R.KulkarniExample 2: Example 2 Shetkani solvents is expected to grow at the rate of 7%per annum and divided expected a year hence is Rs 5.00.If the rate of return is 12%.what is price of the share today. Price would be P 0 = 5.00 ÷ 0.12-0.07 =Rs 100 68 Dr.P.R.Kulkarni 9/13/2011Valuation with Variable growth rate in Dividend: Valuation with Variable growth rate in Dividend Some firms have a super normal growth rate followed by normal growth rate. In this case the price of equity is calculated by the following method. How you will calculate value of equity ? 69 Dr.P.R.Kulkarni 9/13/2011Example: Example Consider the equity share of Venus Lab ltd. D o = current dividend per share = Rs 3.00 n = duration of the period of supernormal growth rate = 5 years g a = growth rate during the period of supernormal growth = 25% g n = normal growth rate after supernormal growth period is over 7%. K e = investor’s required rate of return = 14 % 70 Dr.P.R.Kulkarni 9/13/2011Steps: Steps Calculate dividend stream during supernormal growth period. Step 1 D o =D o current dividend for current period Step II : D 1 =Do (1+g )t Where g is growth in dividend and period is 1 year. D 2 = Do (1 +g )2 for second year. D3 = Do (1+g )3 for third year D4 =Do (1+g )4 for forth year. And so on…… Put the value in the following formula : P 0 = D 0 (1+g)/(1+k) + D 0 (1+g) 2 /(1+k) 2 + D 0 (1+g) 3 /(1+k) 3 + … 71 Dr.P.R.Kulkarni 9/13/2011Pleas note that we have calculated discount value in step 2 Step 3 Now constant growth formula : : Pleas note that we have calculated discount value in step 2 Step 3 Now constant growth formula : 72 Dr.P.R.Kulkarni 9/13/2011Slide 73: Step 4 Discount the value of this price by required rate of return Step 5 Final : Sum of above components Step 1 +Step 5 = your answer. Have you followed ? 73 Dr.P.R.Kulkarni 9/13/2011Example: Example Consider the equity share of Venus Lab ltd. D o = current dividend per share = Rs 3.00 n = duration of the period of supernormal growth rate = 5 years g a = growth rate during the period of supernormal growth = 25% g n = normal growth rate after supernormal growth period is over 7%. K e = investor’s required rate of return = 14 % 74 Dr.P.R.Kulkarni 9/13/2011Steps 1.: Steps 1. Dividend stream during supernormal growth rate-5 yeaars D0 =Rs 3.00 D1= Rs 3 (1+0.25 =1.25) D2= Rs 3 (1.25 )² D3 = Rs 3 (1.25 )³ D4 = Rs 3 (1.25 )4 D5 = Rs 3 (1.25) 5 Calculate the present value of dividend stream : P 0 = D 0 (1+g)/(1+k) + D 0 (1+g) 2 /(1+k) 2 + D 0 (1+g) 3 /(1+k) 3 + … where ke =0.14 =Rs 3.29+3.61 +4.34 +4.76 =Rs 19.96 75 Dr.P.R.Kulkarni 9/13/2011Step 2.: Step 2. After 5 th year the normal growth rate after the supernormal growth s over – 7 percent Now use valuation model with constant Growth in dividend. P5 =3 (1.25 ) 5 (1.07) = 9.8 = Rs140 0.14 -0.07 0.07 Discounted value= 140 ÷ (1.14 ) 5 = RS 72.71 76 Dr.P.R.Kulkarni 9/13/2011Last step: Last step Sum of the above components : Po = Rs 19.96 +Rs 72.71 = Rs 92.67 77 Dr.P.R.Kulkarni 9/13/2011Example: Example Consider the equity share of Venus Lab ltd. D o = current dividend per share = Rs 3.00 n = duration of the period of supernormal growth rate = 5 years g a = growth rate during the period of supernormal growth = 25% g n = normal growth rate after supernormal growth period is over 7%. K e = investor’s required rate of return = 14 % 78 Dr.P.R.Kulkarni 9/13/2011Example 2 : Example 2 Stock GP has an expected growth rate of 16% for the first 3 years and 8% thereafter. Each share of stock just received an annual Rs 3.24 dividend per share. The appropriate discount rate is 15% . What is the value of the common stock under this scenario? 9/13/2011 79 Dr.P.R.KulkarniExample 2: Example 2 Stock GP has two phases of growth. The first, 16%, starts at time t=0 for 3 years and is followed by 8% thereafter starting at time t=3 . We should view the time line as two separate time lines in the valuation. 0 1 2 3 4 5 6 D 1 D 2 D 3 D 4 D 5 D 6 Growth of 16% for 3 years Growth of 8% to infinity! 9/13/2011 80 Dr.P.R.KulkarniExample : Example Note that we can value Phase #2 using the Constant Growth Model 0 1 2 3 D 1 D 2 D 3 D 4 D 5 D 6 0 1 2 3 4 5 6 Growth Phase #1 plus the infinitely long Phase #2 9/13/2011 81 Dr.P.R.KulkarniExample 2: Example 2 Note that we can now replace all dividends from year 4 to infinity with the value at time t=3 , V 3 ! Simpler!! V 3 = D4 D5 D 6 0 1 2 3 4 5 6 D 4 k - g We can use this model because dividends grow at a constant 8% rate beginning at the end of Year 3. 9/13/2011 82 Dr.P.R.KulkarniGrowth Phases Model Example: Growth Phases Model Example Now we only need to find the first four dividends to calculate the necessary cash flows. 0 1 2 3 D 1 D 2 D 3 V 3 0 1 2 3 New Time Line D 4 k - g Where V 3 = 9/13/2011 83 Dr.P.R.KulkarniGrowth Phases Model Example: Growth Phases Model Example Now we need to find the present value of the cash flows. 0 1 2 3 3.76 4.36 5.06 7 8 0 1 2 3 Actual Values 5.46 .15 - .08 Where Rs78 = 9/13/2011 84 Dr.P.R.KulkarniSlide 85: Equity Valuation : Ratio approach 9/13/2011 85 Dr.P.R.KulkarniEarning Capitalization Approach: Earning Capitalization Approach Financial analysts have used this P/E model more frequently than any other model. According to this model, the expected earning per share is : Expected PAT –Preference dividend Number of outstanding shares P/ E Ratio is calculated as the price of the share divided by earning per share. The reciprocal of P/E ratio is called earning price ratio or earning yield. Investors in practice seem to attach a lot of importance to P/E ratio. Some people use P/E multiplier to value the share of company. 9/13/2011 86 Dr.P.R.KulkarniThe P/E Ratio Approach: The P/E Ratio Approach The P/E ratio is the ratio of current market price of the share to the earnings per share of the firm. Let P 0 = Value of Equity Share D 1 = Dividend per share E 1 = Earnings per share b = Plough-back ratio ROE = Return on Equity 87 Dr.P.R.Kulkarni 9/13/2011The P/E Ratio Approach: The P/E Ratio Approach The value of equity share is given as 88 Dr.P.R.Kulkarni 9/13/2011Book Value Approach: Book Value Approach Book Value of the share is total net-worth of the equity shareholders divided by the number of shares outstanding. 89 Dr.P.R.Kulkarni 9/13/2011Liquidation Value Approach: Liquidation Value Approach The minimum value of the share in case of liquidating the firm in its current status 90 Dr.P.R.Kulkarni 9/13/2011Valuation of Preference Shares : Valuation of Preference Shares Preference shares provide a fixed rate of returns or dividends and hence can be valued similar to bonds. Redeemable Preference shares are valued as 91 Dr.P.R.Kulkarni 9/13/2011Valuation of Convertible Debentures: Valuation of Convertible Debentures Conversion Ratio (CR) : Number of shares of stock received for each convertible security. Conversion Value (CV) : Conversion Value is obtained by multiplying the conversion ratio by stocks market price. 92 Dr.P.R.Kulkarni 9/13/2011Valuation of Convertible Debentures: Valuation of Convertible Debentures The value of convertible debenture is given as 93 Dr.P.R.Kulkarni 9/13/2011Queries and Suggestion: Queries and Suggestion 94 Dr.P.R.Kulkarni 9/13/2011 You do not have the permission to view this presentation. In order to view it, please contact the author of the presentation.