Click to edit Master style,Click to edit Master text styles,Second Level,Third Level,Fourth Level,Fifth Level,4-,62,Chapter 4,The Valuation of Long-Term Securities,Chapter 4The Valuation of Long,The Valuation of Long-Term Securities,Distinctions Among Valuation Concepts,Bond Valuation,Preferred Stock Valuation,Common Stock Valuation,Rates of Return (or Yields),The Valuation of Long-Term S,What is Value?,Going-concern value,represents the amount a firm could be sold for as a continuing operating business.,Liquidation value,represents the amount of money that could be realized if an asset or group of assets is sold separately from its operating organization.,What is Value?Going-concern va,What is Value?,(2),a firm,: total assets minus liabilities and preferred stock as listed on the balance sheet.,Book value,represents either,(1),an asset,: the accounting value of an asset - the assets cost minus its accumulated depreciation;,What is Value?(2) a firm: tota,What is Value?,Intrinsic value,represents the price a security ought to have?based on all factors bearing on valuation.,Market value,represents the market price at which an asset trades.,What is Value?Intrinsic value,Bond Valuation,Important Terms,Types of Bonds,Valuation of Bonds,Handling Semiannual Compounding,Bond ValuationImportant Terms,Important Bond Terms,The,maturity value,(,MV,) or face value of a bond is the stated value. In the case of a U.S. bond, the face value is usually $1,000.,A,bond,is a long-term debt instrument issued by a corporation or government.,Important Bond TermsThe maturi,Important Bond Terms,The,discount rate,(capitalization rate) is dependent on the risk of the bond and is composed of the risk-free rate plus a premium for risk.,The bonds,coupon rate,is the stated rate of interest; the annual interest payment divided by the bonds face value.,Important Bond TermsThe discou,Different Types of Bonds,A,perpetual bond,is a bond that,never,matures. It has an infinite life.,(1 +,k,d,),1,(1 +,k,d,),2,(1 +,k,d,),V =,+,+ . +,I,I,I,=,t=1,(1 +,k,d,),t,I,or,I,(PVIFA,k,d,),=,I,/,k,d,Reduced Form,Different Types of BondsA perp,Perpetual Bond Example,Bond P has a $1,000 face value and provides an,8% coupon,. The appropriate,discount rate is 10%,. What is the value of the,perpetual bond,?,I,= $1,000 (,8%,) =,$80,.,k,d,=,10%,.,V,=,I,/,k,d,Reduced Form,=,$80,/,10%,=,$800,.,Perpetual Bond ExampleBond P h,Different Types of Bonds,A,non-zero coupon bond,is a coupon paying bond with a finite life.,(1 +,k,d,),1,(1 +,k,d,),2,(1 +,k,d,),n,V =,+,+ . +,I,I,+,MV,I,=,n,t=1,(1 +,k,d,),t,I,=,I,(PVIFA,k,d,n,) +,MV,(PVIF,k,d,n,),(1 +,k,d,),n,+,MV,Different Types of BondsA non-,Bond C has a $1,000 face value and provides an,8% annual coupon,for,30 years,. The appropriate,discount rate is 10%,. What is the value of the,coupon bond,?,V,=,$80,(PVIFA,10%,30,) +,$1,000,(PVIF,10%,30,),=,$80,(9.427,) +,$1,000,(.057,),Table IV,Table II,= $754.16 + $57.00=,$811.16,.,Coupon Bond Example,Bond C has a $1,000 face value,Different Types of Bonds,A,zero coupon bond,is a bond that pays no interest but sells at a deep discount from its face value; it provides compensation to investors in the form of price appreciation.,(1 +,k,d,),n,V =,MV,=,MV,(PVIF,k,d,n,),Different Types of BondsA zero,V,=,$1,000,(PVIF,10%,30,),=,$1,000,(.057,),=,$57.00,Zero-Coupon Bond Example,Bond Z has a $1,000 face value and a,30 year,life. The appropriate,discount rate is 10%,. What is the value of the,zero-coupon bond,?,V= $1,000 (PVIF10%, 30)=,Semiannual Compounding,(1) Divide,k,d,by,2,(2) Multiply,n,by,2,(3) Divide,I,by,2,Most bonds,in the U.S.,pay interest twice a year (1/2 of the annual coupon).,Adjustments needed,:,Semiannual Compounding(1) D,(1 +,k,d,/,2,),2,*,n,(1 +,k,d,/,2,),1,Semiannual Compounding,A,non-zero coupon bond,adjusted for semiannual compounding.,V =,+,+ . +,I,/,2,I,/,2,+,MV,=,2,*,n,t=1,(1 +,k,d,/,2,),t,I,/,2,=,I,/,2,(PVIFA,k,d,/,2,2,*,n,) +,MV,(PVIF,k,d,/,2,2,*,n,),(1 +,k,d,/,2,),2,*,n,+,MV,I,/,2,(1 +,k,d,/,2,),2,(1 + kd/2 ) 2*n(1 + kd/2 )1Sem,V,=,$40,(PVIFA,5%,30,) +,$1,000,(PVIF,5%,30,),=,$40,(15.373,) +,$1,000,(.231,),Table IV,Table II,= $614.92 + $231.00=,$845.92,Semiannual Coupon Bond Example,Bond C has a $1,000 face value and provides an,8% semiannual coupon,for,15 years,. The appropriate,discount rate is 10% (annual rate),. What is the value of the,coupon bond,?,V= $40 (PVIFA5%, 30) + $1,000,Preferred Stock,is a type of stock that promises a (usually) fixed dividend, but at the discretion of the board of directors.,Preferred Stock has preference over common stock in the payment of dividends and claims on assets.,Preferred Stock Valuation,Preferred Stock is a type of s,Preferred Stock Valuation,This reduces to a,perpetuity,!,(1 +,k,P,),1,(1 +,k,P,),2,(1 +,k,P,),V,=,+,+ . +,Div,P,Div,P,Div,P,=,t=1,(1 +,k,P,),t,Div,P,or,Div,P,(PVIFA,k,P,),V,=,Div,P,/,k,P,Preferred Stock ValuationThis,Preferred Stock Example,Div,P,= $100 (,8%,) =,$8.00,.,k,P,=,10%,.,V,=,Div,P,/,k,P,=,$8.00,/,10%,=,$80,Stock PS has an,8%,$100 par value issue outstanding. The appropriate,discount rate is 10%,. What is the value of the,preferred stock,?,Preferred Stock ExampleDivP,Common Stock Valuation,Prorata share of future earnings after all other obligations of the firm (if any remain).,Dividends,may,be paid out of the prorata share of earnings.,Common stock,represents a residual ownership position in the corporation.,Common Stock ValuationProrata,Common Stock Valuation,(1) Future dividends,(2) Future sale of the common stock shares,What cash flows will a shareholder receive when owning shares of,common stock,?,Common Stock Valuation(1),Dividend Valuation Model,Basic dividend valuation model accounts for the PV of all future dividends.,(1 +,k,e,),1,(1 +,k,e,),2,(1 +,k,e,),V =,+,+ . +,Div,1,Div,Div,2,=,t=1,(1 +,k,e,),t,Div,t,Div,t,:Cash Dividend at time t,k,e,: Equity investors required return,Dividend Valuation ModelBasic,Adjusted Dividend Valuation Model,The basic dividend valuation model adjusted for the future stock sale.,(1 +,k,e,),1,(1 +,k,e,),2,(1 +,k,e,),n,V =,+,+ . +,Div,1,Div,n,+,Price,n,Div,2,n,:The year in which the firms shares are expected to be sold.,Price,n,:The expected share price in year,n,.,Adjusted Dividend Valuation Mo,Dividend Growth Pattern Assumptions,The dividend valuation model requires the forecast of,all,future dividends. The following dividend growth rate assumptions simplify the valuation process.,Constant Growth,No Growth,Growth Phases,Dividend Growth Pattern Assump,Constant Growth Model,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,),V =,+,+ . +,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,: Investors required return.,D,0,(1+,g,),2,Constant Growth ModelThe const,Constant Growth Model Example,Stock CG has an expected,growth rate of 8%,. Each share of stock just received an annual,$3.24 dividend,per share. The appropriate,discount rate is 15%,. What is the value of the,common stock,?,D,1,=,$3.24,( 1 +,.08,) =,$3.50,V,CG,=,D,1,/ (,k,e,-,g,) =,$3.50,/ (,.15,-,.08,) =,$50,Constant Growth Model ExampleS,Zero Growth Model,The,zero growth model,assumes that dividends will grow forever at the rate,g,= 0.,(1 +,k,e,),1,(1 +,k,e,),2,(1 +,k,e,),V =,+,+ . +,D,1,D,=,k,e,D,1,D,1,:Dividend paid at time 1.,k,e,: Investors required return.,D,2,Zero Growth ModelThe zero grow,Zero Growth Model Example,Stock ZG has an expected,growth rate,of,0%,. Each share of stock just received an annual,$3.24 dividend,per share. The appropriate,discount rate is 15%,. What is the value of the,common stock,?,D,1,=,$3.24,( 1 +,0,) =,$3.24,V,ZG,=,D,1,/ (,k,e,-,0,) =,$3.24,/ (,.15,-,0,) =,$21.60,Zero Growth Model ExampleSt,D,0,(1+,g,1,),t,D,n,(1+,g,2,),t,Growth Phases Model,The,growth phases model,assumes that dividends for each share will grow at two or more,different,growth rates.,(1 +,k,e,),t,(1 +,k,e,),t,V =,t=1,n,t=n+1,+,D0(1+g1)tDn(1+g2)tGrowth Phase,D,0,(1+,g,1,),t,D,n+1,Growth Phases Model,Note that the second phase of the,growth phases model,assumes that dividends will grow at a constant rate,g,2,. We can rewrite the formula as:,(1 +,k,e,),t,(,k,e,-,g,2,),V =,t=1,n,+,1,(1 +,k,e,),n,D0(1+g1)tDn+1Growth Phases Mod,Growth Phases Model Example,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,$3.24 dividend,per share. The appropriate,discount rate is 15%,. What is the value of the common stock under this scenario?,Growth Phases Model ExampleSto,Growth Phases Model Example,First, determine the annual dividend.,D,0,= $3.24,D,1,=,D,0,(1+,g,1,),1,=,$3.24,(1,.16,),1,=,$3.76,D,2,=,D,0,(1+,g,1,),2,=,$3.24,(1,.16,),2,=,$4.36,D,3,=,D,0,(1+,g,1,),3,=,$3.24,(1,.16,),3,=,$5.06,D,4,=,D,3,(1+,g,2,),1,=,$5.06,(1,.08,),1,=,$5.46,Growth Phases Model ExampleFir,Growth Phases Model Example,Second, determine the PV of cash flows.,PV(,D,1,) =,D,1,(PVIF,15%,1,) =,$3.76,(.870) =,$,3.27,PV(,D,2,) =,D,2,(PVIF,15%,2,) =,$4.36,(.756) =,$,3.30,PV(,D,3,) =,D,3,(PVIF,15%,3,) =,$5.06,(.658) =,$,3.33,P,3,=,$5.46,/ (,.15,-,.08,) = $78 CG Model,PV(,P,3,) =,P,3,(PVIF,15%,3,) =,$78,(.658) =,$,51.32,Growth Phases Model ExampleSec,D,0,(1+,.16,),t,D,4,Growth Phases Model Example,Third, calculate the,intrinsic value,by summing all of cash flow present values.,(1 +,.15,),t,(,.15,-,.08,),V =,t=1,3,+,1,(1+,.15,),n,V = $3.27 + $3.30 + $3.33 + $51.32,V = $61.22,D0(1+.16)tD4Growth Phases Mo,Calculating Rates of Return (or Yields),1. Determine the expected,cash flows,.,2. Replace the intrinsic value (V) with the,market price (P,0,),.,3. Solve for the,market required rate of return,that equates the,discounted cash flows,to the,market price,.,Steps to calculate the rate of return (or Yield).,Calculating Rates of Return (o,Determining Bond YTM,Determine the Yield-to-Maturity (YTM) for the coupon paying bond with a finite life.,P,0,=,n,t=1,(1 +,k,d,),t,I,=,I,(PVIFA,k,d,n,) +,MV,(PVIF,k,d,n,),(1 +,k,d,),n,+,MV,k,d,= YTM,Determining Bond YTMDetermine,Determining the YTM,Julie Miller want to determine the YTM for an issue of outstanding bonds at,Basket Wonders (BW),.,BW,has an issue of,10% annual coupon,bonds with,15 years,left to maturity. The bonds have a current market value of,$1,250,.,What is the YTM?,Determining the YTMJulie Mille,YTM Solution (Try 9%),$1,250,= $100(PVIFA,9%,15,) + $1,000(PVIF,9%,15,),$1,250,= $100(8.061) + $1,000(.275),$1,250,= $806.10 + $275.00,=,$1,081.10,Rate is too high!,YTM Solution (Try 9%)$1,250 =,YTM Solution (Try 7%),$1,250,= $100(PVIFA,7%,15,) + $1,000(PVIF,7%,15,),$1,250,= $100(9.108) + $1,000(.362),$1,250,= $910.80 + $362.00,=,$1,272.80,Rate is too low!,YTM Solution (Try 7%)$1,250 =,.07,$1,273,.02,IRR,$1,250,$192,.09,$1,081,X,$23,.02,$192,YTM Solution (Interpolate),$23,X,=,.07$1,273YTM Solution (In,.07,$1,273,.02,IRR,$1,250,$192,.09,$1,081,X,$23,.02,$192,YTM Solution (Interpolate),$23,X,=,.07$1,273YTM Solution (In,.07$1273,.02,YTM$1250,$192,.09$1081,($23)(0.02) $192,YTM Solution (Interpolate),$23,X,X,=,X,=,.0024,YTM,= .07 +,.0024,=,.0724,or,7.24%,.07$1273YTM Solution (Int,Determining Semiannual Coupon Bond YTM,P,0,=,2,n,t=1,(1 +,k,d,/2 ),t,I,/ 2,= (,I,/2),(PVIFA,k,d,/2, 2,n,) +,MV,(PVIF,k,d,/2, 2,n,),+,MV, 1 + (,k,d,/ 2),2, -1 = YTM,Determine the Yield-to-Maturity (YTM) for the semiannual coupon paying bond with a finite life.,(1 +,k,d,/2 ),2,n,Determining Semiannual Coupon,Bond Price - Yield Relationship,Discount Bond,- The market required rate of return exceeds the coupon rate (Par P,0,).,Premium Bond,-,The coupon rate exceeds the market required rate of return (P,0, Par).,Par Bond,-,The coupon rate equals the market required rate of return (P,0,= Par).,Bond Price - Yield Relationshi,Bond Price - Yield Relationship,Coupon Rate,MARKET REQUIRED RATE OF RETURN (%),BOND PRICE ($),1000,Par,1600,1400,1200,600,0,0 2 4 6 8,10,12 14 16 18,5 Year,15 Year,Bond Price - Yield Relationshi,Bond Price-Yield Relationship,Assume that the required rate of return on a 15 year, 10% coupon paying bond,rises,from 10% to 12%. What happens to the bond price?,When interest rates,rise, then the market required rates of return,rise,and bond prices will,fall,.,Bond Price-Yield RelationshipA,Bond Price - Yield Relationship,Coupon Rate,MARKET REQUIRED RATE OF RETURN (%),BOND PRICE ($),1000,Par,1600,1400,1200,600,0,0 2 4 6 8,10,12 14 16 18,15 Year,5 Year,Bond Price - Yield Relationshi,Bond Price-Yield Relationship (Rising Rates),Therefore, the bond price has,fallen,from $1,000 to $864.10.,The required rate of return on a 15 year, 10% coupon paying bond has,risen,from 10% to 12%.,Bond Price-Yield Relationship,Bond Price-Yield Relationship,Assume that the required rate of return on a 15 year, 10% coupon paying bond,falls,from 10% to 8%. What happens to the bond price?,When interest rates,fall, then the market required rates of return,fall,and bond prices will,rise,.,Bond Price-Yield RelationshipA,Bond Price - Yield Relationship,Coupon Rate,MARKET REQUIRED RATE OF RETURN (%),BOND PRICE ($),1000,Par,1600,1400,1200,600,0,0 2 4 6 8,10,12 14 16 18,15 Year,5 Year,Bond Price - Yield Relationshi,Bond Price-Yield Relationship (Declining Rates),Therefore, the bond price has,risen,from $1000 to $1171.,The required rate of return on a 15 year, 10% coupon paying bond has,fallen,from 10% to 8%.,Bond Price-Yield Relationship,The Role of Bond Maturity,Assume that the required rate of return on both the 5 and 15 year, 10% coupon paying bonds,fall,from 10% to 8%. What happens to the changes in bond prices?,The longer the bond maturity, the greater the change in bond price for a given change in the market required rate of return.,The Role of Bond MaturityAssum,Bond Price - Yield Relationship,Coupon Rate,MARKET REQUIRED RATE OF RETURN (%),BOND PRICE ($),1000,Par,1600,1400,1200,600,0,0 2 4 6 8,10,12 14 16 18,15 Year,5 Year,Bond Price - Yield Relationshi,The Role of Bond Maturity,The 5 year bond price has,risen,from $1,000 to $1,080.30 for the 5 year bond (,+8.0%,).,The 15 year bond price has,risen,from $1,000 to $1,171 (,+17.1%,).,Twice as fast,!,The required rate of return on both the 5 and 15 year, 10% coupon paying bonds has,fallen,from 10% to 8%.,The Role of Bond MaturityThe 5,The Role of the Coupon Rate,For a given change in the market required rate of return, the price of a bond will change by proportionally more,the,lower,the coupon rate,.,The Role of the Coupon RateFor,Example of the Role of the Coupon Rate,Assume that the,market required rate of return,on two equally risky 15 year bonds is,10%,. The coupon rate for,Bond H,is,10%,and,Bond,L,is,8%,.,What is the rate of change in each of the bond prices if,market required rates,fall to 8%?,Example of the Role of the Cou,Example of the Role of the Coupon Rate,The price for,Bond H,will rise from $1,000 to $1,171 (,+17.1%,).,The price for,Bond L,will rise from $847.88 to $1,000 (,+17.9%,).,Faster Rise,!,The price on,Bond H,and,L,prior to the change in the market required rate of return is,$1,000,and,$847.88,respectively.,Example of the Role of the Cou,Determining the Yield on Preferred Stock,Determine the yield for preferred stock with an infinite life.,P,0,=,Div,P,/,k,P,Solving for,k,P,such that,k,P,=,Div,P,/,P,0,Determining the Yield on Prefe,Preferred Stock Yield Example,k,P,=,$10,/,$100,.,k,P,=,10%,.,Assume that the,annual dividend,on each share of preferred stock is,$10,. Each share of preferred stock is currently trading at,$100,.,What is the,yield,on preferred stock,?,Preferred Stock Yield Examplek,Determining the Yield on Common Stock,Assume the constant growth model is appropriate. Determine the yield on the common stock.,P,0,=,D,1,/ (,k,e,-,g,),Solving for,k,e,such that,k,e,= (,D,1,/,P,0,) +,g,Determining the Yield on Commo,Common Stock Yield Example,k,e,= (,$3,/,$30,) +,5%,k,e,=,15%,Assume that the,expected dividend (D,1,),on each share of common stock is,$3,. Each share of common stock is currently trading at,$30,and has an expected,growth rate,of,5%,.,What is the,yield,on common stock,?,Common Stock Yield Exampleke =,