Preferred Stock Valuation No ownership as with common stock Give higher return than bonds (debt) V PS :Value of Preferred Stock, $100/sh D PS : Preferred Stock Dividend, $10/sh K PS : Return On Investment or Required Return of Preferred Stock investors, eg. 10% (Risk Free Return + Risk)

Stocks Calculation: ROI = K PS = D PS = 10 = 0.1 = 10% V PS 100 V PS = D PS = 10 = 100 k PS 0.1

Stocks If require ROI = 12% = K ps D PS = 10 V PS = D P s = 10 = 83.3 k ps 0.12

Common Stock Valuation P t = Stock price at time t D t = Dividend at time t D 0 = Dividend at time t = 0 (just paid) D 1 = Dividend at time t = 1 (1 year from today) K S = Return on Investment on Common Stock

Common Stock Valuation D 1 = D 0 ( 1 + g ) 1 D 2 = D 0 ( 1 + g ) 2 where g : expected annual growth (or increase) in dividend (%)

Example: Find Dividend (given g = 5%) D 0 = $10 D 1 = 10.5 = 10 ( ) 1 = D 0 (1+g) t D 2 = = 10 ( ) 2 or 10.5 ( ) 1 Common Stock Valuation

Example: FV = ? 10% PV = 100 n=1 FV = PV ( 1 + i ) n PV = FV ; ( 1 + i) n Common Stock Valuation

N 10% INPUTS I/YRFVPMTPV OUTPUT

Common Stock Valuation Example: D 1 =10 P 1 = 100 i=?% PV = yr K S = 10 / 100 = 10%

Common Stock Valuation N -100 INPUTS I/YRFVPMTPV OUTPUT %

Common Stock Valuation Example: D 1 =10 P 1 = 100 K S = 10% 1 yr P 0 =PV = ?

Common Stock Valuation N 100 INPUTS I/YRFVPMTPV OUTPUT % 100

Common Stock Valuation P 2 D 1 D 2 1 yr 2 yr P 0 = ? P 0 = D 1 + D 2 + P 2 (1+k) 1 (1+k) 2 (1+k) 2

Common Stock Valuation P 0 = D 1 + D 2 + D D n + P n (1+k) 1 (1+k) 2 (1+k) 3 (1+k) n (1+k) n If n  Example: P n = 100/sh = FV, n = 99 k = 15% PV = ?

Common Stock Valuation N -100 INPUTS I/YRFVPMTPV OUTPUT 99015%

Common Stock Valuation P 0 = D 1 + D 2 + D D n + P n (1+k) 1 (1+k) 2 (1+k) 3 (1+k) n (1+k) n If n   P n 0 (1+k) n Therefore, P 0 = D 1 + D 2 + D D n (1+k) 1 (1+k) 2 (1+k) 3 (1+k) n

Common Stock Valuation P 0 = D 1 + D 2 + D D n (1+k) 1 (1+k) 2 (1+k) 3 (1+k) n can be written as: P 0 = D 0 (1+g) 1 + D 0 (1+g) 2 + D 0 (1+g) 3 (1+k) 1 (1+k) 2 (1+k) D 0 (1+g) n (1+k) n

Common Stock Valuation P 0 = D 0 [ (1+g) 1 + (1+g) 2 + (1+g) 3 + (1+g) n ] (1+k) 1 (1+k) 2 (1+k) 3 (1+k) n (1+k) P 0 = D 0 [ 1 + ( 1+g ) 1 + ( 1+g ) 2 + ( 1+g ) n-1 ] (1+g) 1+k 1+k 1+k ( 1+k ) P 0 - P 0 = D 0 [ 1- ( 1+g ) n ] 1+g 1+k

Common Stock Valuation If n  and k > g, ( 1+g ) n 0 1+k then, ( 1+k ) P 0 - P 0 = D 0 1+g P 0 [ 1+k - 1 ] = D 0 1+g

Common Stock Valuation P 0 [ 1+k-1-g ] = D 0 1+g P 0 [ k-g ] = D 0 1+g P 0 = D 0 ( 1+g ) = D 1 k-g k-g

Common Stock Valuation Example: g = 5%,D 0 = 10 D 1 = 10.5 (10 x 1.05) k s = 18% What is the value of the stock? P 0 = D 1 = 10.5 = = PV k-g

Common Stock Valuation If the stock is purchased at $90, K=? 90 = 10.5 P 0 = D 1 k-g = D 1 k k-g P 0 k = D 1 + g P 0 k = 17% Dividend/Stock Price = Dividend Yield

Stock Markets and Stock Reporting I. Stock Markets A. New York Stock Exchange (NYSE) B. American Stock Exchange (AMEX) C. Over-the-counter (OTC) markets D. Smaller regional markets II. Stock Market Reporting 52 Weeks Yld. P-E Sales Net High Low Stock Div. % Ratio 100s High Low Close Chg /8 102 IBM / / /4 +1 3/4 Dividend yield = D/P = $4.40 / $ = 3.8%

Common Stock Valuation FV = 110 i=10% PV = 100 n=1yr FV = PV ( 1 + i ) n

Common Stock Valuation PV(1+i) n = FV 100 (1+0.1) = (1+0.1) 2 = (1+0.1) 3 = 133 FV PV = (1+i) n Value of Stock

Common Stock Valuation Discounted Valuation Approach Know FV Calculate PV (price you have to pay now) or (value of stock or bond) Bond debt - interest Stock - dividend

Common Stock Valuation Own stock one year: d 1 P 1 1 year k% P o d 1 P 1 P o = (1+k) 1 + (1+k) 1 Appraisal Value of Stock

Common Stock Valuation 2 years: P 2 D 1 D 2 1 k%2 P 0 P 0 = D 1 + D 2 + P 2 (1+k) 1 (1+k) 2 (1+k) 2

Common Stock Valuation P 0 = D 1 + D 2 + D D n + P n (1+k) 1 (1+k) 2 (1+k) 3 (1+k) n (1+k) n Make Assumptions: 1)If n  P n (1+i) n 0 2)If D 1 = D o (1+g) 1 Assume dividend D 2 = D o (1+g) 2 rate increases at D n = D o (1+g) n g rate.

Common Stock Valuation Example: D o = $10 g = 5% D 1 =10 (1+0.05) D 1 = $10.5

Common Stock Valuation Equation : (1+k) P 0 = D 0 [ 1 + ( 1+g ) 1 + ( 1+g ) 2 + ( 1+g ) n-1 ] (1+g) 1+k 1+k 1+k P 0 = D 0 (1+g) 1 + D 0 (1+g) 2 + D 0 (1+g) 3 (1+k) 1 (1+k) 2 (1+k) D 0 (1+g) n (1+k) n

Common Stock Valuation Equation : P 0 = D 0 [ (1+g) 1 + (1+g) 2 + (1+g) 3 + (1+g) n ] (1+k) 1 (1+k) 2 (1+k) 3 (1+k) n Equation : ( 1+k ) P 0 - P 0 = D 0 [ 1- ( 1+g ) n ] 1+g 1+k

Don’t Forget... k = ROI (%) = Required Return on Investment g = Dividend Growth

Common Stock Valuation If n  and k > g, then ( 1+g ) n 0 1+k and, ( 1+k ) P 0 - P 0 = D 0 1+g P 0 [ 1+k - 1 ] = D 0 1+g

Common Stock Valuation P 0 [ 1+k-(1+g) ] = D 0 1+g P 0 [ k-g ] = D 0 1+g P 0 = D 0 ( 1+g ) = D 1 k-g k-g

Common Stock Valuation P 0 = D 1 k-g Only when n --  AND k>g Gordon Model or Constant Dividend Growth Model k-g = D 1 / P o k = D 1 / P o + g

Just a Reminder... K R = risk free + risk premium = R f +  (R m - R f ) market return *use S&P 500 risk-free index *use T-Bill Volatility R m - R f = Market Risk Premium

Common Stock Valuation Example: D o =Paid Dividend=$5/share g=Dividend Growth=5% K R =Required Return=10% pay for stock now D o (1+g) $5(1+0.05) P o = K R - g = = $105

Common Stock Valuation Value of Stock = $105 (appraisal value) Stock Price = $110 *Don’t buy the stock because the stock is over valued. (too expensive)

Common Stock Valuation K E = D 1 / P o + g = Expected Return ( Po = Stock Price = $110) D o (1+g) $5(1+0.05) K E = + g = P o $110 K E = 9.7% (Expected Return) K R = 10% (Required Return) Therefore, do not purchase