The Valuation of Long-Term SecuritiesTopic: Preferred Stock & common stock
Preferred Stock is a type of stock that promises a (usually) fixeddividend, 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.Par Value: The par value represents the claim of the preferredstockholder against the value of the firm.Preferred Dividend / Preferred Dividend RateThe preferred dividend rate is expressed as a percentage of thepar value of the preferred stock. The annual preferred dividend isdetermined by multiplying the preferred dividend rate times thepar value of the preferred stock.
DivP DivP DivPV= (1 + kP) 1 + (1 + kP) 2 + ... + (1 + kP)∞ ∞ DivP =Σ or DivP(PVIFA k ) t=1 (1 + kP) t P, ∞ This reduces to a perpetuity! V = DivP / kP
Stock PS has an 8%, $100 par value issueoutstanding. The appropriate discount rateis 10%. What is the value of the preferredstock?stock DivP = $100 ( 8% ) = $8.00. $8.00 kP = 10%. 10% V = DivP / kP = $8.00 / 10% = $80
Common stock represents an ownership interest in aCorporation. It has two features:It entitles its owner to dividends, but only if thecompany has earnings out of which dividends can bepaid, and only if management chooses to paydividends rather than retaining and reinvesting allthe earnings.Stock can be sold at some future date, hopefullyat a price greater than the purchase price. If thestock is actually sold at a price above its purchaseprice, the investor will receive a capital gain.
Basic dividend valuation model accounts forthe PV of all future dividends. Div1 Div2 Div∞ V= (1 + ke)1 + (1 + ke)2 + ... + (1 + ke)∞ ∞ Divt Divt: Cash Dividend =Σ (1 + ke)t at time t t=1 ke: Equity investor’s required return
The basic dividend valuation model adjusted for the future stock sale. Div1 Div2 Divn + PricenV= (1 + ke)1 + (1 + ke)2 + ... + (1 + k )n en: The year in which the firm’s shares are expected to be sold.Pricen: The expected share price in year n.
The dividend valuation model requires theforecast of all future dividends. Thefollowing dividend growth rate assumptionssimplify the valuation process.Constant GrowthNo GrowthGrowth Phases
The constant growth model assumes that dividends will grow forever at the rate g. D0(1+g) D0(1+g)2 D0(1+g)∞V = (1 + k )1 + (1 + k )2 + ... + (1 + k ) ∞ e e e D1: Dividend paid at time 1. D1 = g: The constant growth rate. (ke - g) ke: Investor’s required return.
Stock CG has an expected dividendgrowth rate of 8%. Each share of stockjust received an annual $3.24 dividend.The appropriate discount rate is 15%.What is the value of the common stock? stockD1 = $3.24 ( 1 + .08 ) = $3.50VCG = D1 / ( ke - g ) = $3.50 / ( .15 - .08 ) =$50
A common stock whose future dividends are notexpected to grow at all; that is, g = 0. D1 D2 DVZG = + + ... + ∞ (1 + ke)1 (1 + ke)2 (1 + ke)∞ D1 D1: Dividend paid at time 1. = ke ke: Investor’s required return.
Stock ZG has an expected growth rate of0%. Each share of stock just received anannual $3.24 dividend per share. Theappropriate discount rate is 15%. What isthe value of the common stock? stockD1 = $3.24 ( 1 + 0 ) = $3.24VZG = D1 / ( ke - 0 ) = $3.24 / ( .15 - 0 ) = $21.60
The growth phases model assumes thatdividends for each share will grow at twoor more different growth rates. n D0(1+g1) t ∞ Dn(1+g2)tV =Σ + Σ (1 + ke)t t=1 (1 + ke) t t=n+1
Note that the second phase of the growthphases model assumes that dividends willgrow at a constant rate g2. We can rewritethe formula as: n D0(1+g1)t 1 Dn+1V =Σ + (1 + ke)n (ke - g2) t=1 (1 + ke)t
Stock GP has an expected growth rate of 16% forthe first 3 years and 8% thereafter. Each share ofstock just received an annual $3.24 dividend pershare. The appropriate discount rate is 15%. Whatis the value of the common stock under thisscenario?
0 1 2 3 4 5 6 ∞ D1 D2 D3 D4 D5 D6 Growth of 16% for 3 years Growth of 8% to infinity!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 Growth Phase #1 plus the infinitely long Phase #2 D1 D2 D30 1 2 3 4 5 6 ∞ D4 D5 D6Note that we can value Phase #2 using the Constant Growth Model
V3 = D4 We can use this model because dividends grow at a constant 8% k-g rate beginning at the end of Year 3.0 1 2 3 4 5 6 ∞ D4 D5 D6Note that we can now replace all dividends from year 4 to infinity with the value at time t=3, V3! Simpler!!
0 1 2 3 New Time Line D1 D2 D30 1 2 3 D4 Where V3 = V3 k-gNow we only need to find the first four dividends to calculate the necessary cash flows.