Strategic Financial Management The Valuation of Long-Term Securities Khuram Raza ACMA, MS Finance Scholar

Bond Valuation bond A bond is a long-term debt instrument issued by a corporation or government.  Face Value  Coupon Rate Different Types of Bonds  Perpetual Bonds  Bonds with a Finite Maturity Nonzero Coupon Bonds. Zero-Coupon Bonds Perpetual Bonds Ik d V = I / k d Nonzero Coupon Bounds Zero Coupon Bounds

Bond Valuation Semiannual Compounding k d 2 (1) Divide k d by 2 n2 (2) Multiply n by 2 I2 (3) Divide I by 2 k d 2 (1) Divide k d by 2 n2 (2) Multiply n by 2 I2 (3) Divide I by 2 Most bonds in the US pay interest twice a year (1/2 of the annual coupon). Adjustments needed: Most bonds in the US pay interest twice a year (1/2 of the annual coupon). Adjustments needed:

Preferred stock :A type of stock that promises a (usually) fixed dividend, but at the discretion of the board of directors. It has preference over common stock in the payment of dividends and claims on assets. Preferred Stock Valuation perpetuity This reduces to a perpetuity! (1 + k P ) 1 (1 + k P ) 2  (1 + k P )  V V = Div P =   t=1 (1 + k P ) t Div P  or Div P (PVIFA k P,  ) V V = Div P / k P

Common Stock Valuation (1) Future dividends (2) Future sale of the common stock shares (1) Future dividends (2) Future sale of the common stock shares common stock What cash flows will a shareholder receive when owning shares of common stock?

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 investor’s required return Div t :Cash Dividend at time t k e : Equity investor’s required return

Adjusted Dividend Valuation Model The basic dividend valuation model adjusted for the future stock sale. (1 + k e ) 1 (1 + k e ) 2 n (1 + k e ) n V = Div 1 nn Div n + Price n Div 2 n n:The year in which the firm’s shares are expected to be sold. n n Price n :The expected share price in year n. n n:The year in which the firm’s shares are expected to be sold. n n Price n :The expected share price in year n.

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 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

Constant Growth Model 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) D1D1 D 1 :Dividend paid at time 1. g : The constant growth rate. k e : Investor’s required return. D 1 :Dividend paid at time 1. g : The constant growth rate. k e : Investor’s required return. D 0 (1+g) 2

Constant Growth Model common stock Stock CG has an expected dividend growth rate of 8%. Each share of stock just received an annual $3.24 dividend. The appropriate discount rate is 15%. What is the value of the common stock? D 1 $3.24$3.50 D 1 = $3.24 ( ) = $3.50 V CG D 1 k e $ $50 V CG = D 1 / ( k e - g ) = $3.50 / ( ) =$50 common stock Stock CG has an expected dividend growth rate of 8%. Each share of stock just received an annual $3.24 dividend. The appropriate discount rate is 15%. What is the value of the common stock? D 1 $3.24$3.50 D 1 = $3.24 ( ) = $3.50 V CG D 1 k e $ $50 V CG = D 1 / ( k e - g ) = $3.50 / ( ) =$50

Zero Growth Model 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 ZG = D1D1 DD = keke D1D1 D 1 :Dividend paid at time 1. k e : Investor’s required return. D 1 :Dividend paid at time 1. k e : Investor’s required return. D2D2

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 V =  t=1 n  t=n+1  + D 0 (1 + g 1 ) t D n (1 + g 2 ) t Growth Phases Model

D 0 (1 + g 1 ) t D n+1 Growth Phases Model 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

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 Example 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.  D 1 D 2 D 3 D 4 D 5 D 6 Growth of 16% for 3 years Growth of 8% to infinity!

Growth Phases Model Example Now we need to find the present value of the cash flows Actual Values –0.08 Where $78 =

Growth Phases Model Example We determine the PV of cash flows. D 1 D 1 $3.76 $3.27 PV(D 1 ) = D 1 (PVIF 15%, 1 ) = $3.76 (0.870) = $3.27 D 2 D 2 $4.36 $3.30 PV(D 2 ) = D 2 (PVIF 15%, 2 ) = $4.36 (0.756) = $3.30 D 3 D 3 $5.06 $3.33 PV(D 3 ) = D 3 (PVIF 15%, 3 ) = $5.06 (0.658) = $3.33 P 3 $5.46 P 3 = $5.46 / ( ) = $78 [CG Model] P 3 P 3 $78 $51.32 PV(P 3 ) = P 3 (PVIF 15%, 3 ) = $78 (0.658) = $51.32 We determine the PV of cash flows. D 1 D 1 $3.76 $3.27 PV(D 1 ) = D 1 (PVIF 15%, 1 ) = $3.76 (0.870) = $3.27 D 2 D 2 $4.36 $3.30 PV(D 2 ) = D 2 (PVIF 15%, 2 ) = $4.36 (0.756) = $3.30 D 3 D 3 $5.06 $3.33 PV(D 3 ) = D 3 (PVIF 15%, 3 ) = $5.06 (0.658) = $3.33 P 3 $5.46 P 3 = $5.46 / ( ) = $78 [CG Model] P 3 P 3 $78 $51.32 PV(P 3 ) = P 3 (PVIF 15%, 3 ) = $78 (0.658) = $51.32

Calculating Rates of Return (or Yields) cash flows 1. Determine the expected cash flows. market price (P 0 ) 2. Replace the intrinsic value (V) with the market price (P 0 ). market required rate of return discounted cash flows market price 3. Solve for the market required rate of return that equates the discounted cash flows to the market price. cash flows 1. Determine the expected cash flows. market price (P 0 ) 2. Replace the intrinsic value (V) with the market price (P 0 ). market required rate of return discounted cash flows market price 3. Solve for the market required rate of return that equates the discounted cash flows to the market price.

Calculating Rates of Return (or Yields) a $1,000-par-value bond with the following characteristics: a current market price of $761, 12 years until maturity, and an 8 percent coupon rate (with interest paid annually). We want to determine the discount rate that sets the present value of the bond’s expected future cash-flow stream equal to the bond’s current market price.

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 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 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 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