Class 4 Stock Valuation Yr Hi Yr Lo Stock Sym 123 1/8 93 1/8 IBM IBM Div Yld % PE Vol 1 4.84 4.2 16 14591 Day Hi Day Lo Close Net Chg 115 113 114 3/4 +1 3/8 slide 1 slide 3 Hi = 123 1/8: 52 Lo = 93 1/8: 52 Stock = IBM: Sym = IBM: Div = 4.84: Yld % = 4.2: ( ) PE = 16: ( 4 ) Vol 1s = 14591*1; Hi = 115: Lo = 113: Close = 114 3/4: Chg = 1 3/8: Stock Valuation (What is a stock)? (Definition) (Stock markets) (Different styles) (Stock pricing) (Understanding return) 1 (1 period case) 2 (2 period case) (Infinite period case) (Stock pricing with growth) slide 4 slide 13
Stock Valuation (Variations and deeper understanding) (Different dividend growth at different times) g (Where does g come from)? (Value with investment opportunities) Price-earning ratio (P/E) What is a stock? (Definition),.(Ownership claim on the company s assets/profits.) (Residual claim) (Voting right) Stock markets (Primary markets) (Secondary markets) Different styles (Preferred stock) (Common stock) slide 14 slide 16 Stock pricing 1 period case (1 ) IBM? P = Div 1 /(1+r) + P 1 /(1+r) 2 period case (2 ) P = Div 1 /(1+r) + Div 2 /(1+r) 2 + P 2 /(1+r) 2 Infinite period case ( ) P = Div 1 /(1+r) + Div 2 /(1+r) 2 + Div 3 /(1+r) 3 DIV DIV DIV DIV P = + + + +... 1 2 3 4 1 2 3 4 ( 1+ r) ( 1+ r) ( 1+ r) ( 1+ r) DIV1 1 DIV 2 DIV3 DIV 4 = + 1 1 + + +... 1 2 3 ( 1+ r) ( 1+ r) ( 1+ r) ( 1+ r) ( 1+ r) DIV1 1 DIV1+ P1 = + = 1+ r ( ) ( ) { P } 1 1 1 1+ r 1+ r DIV1+ P1 P r = P slide 18 slide 22
r. DIV1 + P1 P r = P. DIV1+ P1 P DIV1 P1 P r = = + P P P 1. D1+ P1 P = 1+ r Stock pricing with growth : g Div 2 = Div 1 (1+g), Div 3 = Div 2 (1+g) = Div 1 (1+g) 2, P = Div 1 /(1+r) + Div 2 /(1+r) 2 + Div 3 /(1+r) 3 = Div 1 /(1+r) + Div 1 (1+g)/(1+r) 2 + Div 1 (1+g) 2 /(1+r) 3 = Div 1 /(r-g) Gordon s dividend discount model ( ) slide 23 slide 25 1) 2) r DIV DIV 1 1 p = r = + g r g p DIV r g r 1 1 1 = + & = + p P P g = P1 P P DIV P P Example $1/ 1% 3 Year 1: Div 1 = $1 Year 2: Div 2 = Div 1 (1+.1) = $11 Year 3: Div 3 = Div 2 (1+.1) = Div 1 (1+.1) 2 = $12.1 15%,? P = Div 1 /(r-g) = 11%? P = slide 27 slide 32
Variations and deeper understanding 3 (g 1 ) (g 2 ) P = Div 1 /(1+r) + Div 1 (1+g 1 )/(1+r) 2 + Div 1 (1+g 1 ) 2 /(1+r) 3 + Div 1 (1+g 1 ) 2 (1+g 2 )/(1+r) 4 + Div 1 (1+g 1 ) 2 (1+g 2 ) 2 /(1+r) 5 + Div 1 (1+g 1 ) 2 (1+g 2 ) 3 /(1+r) 6 + = Div 1 /(1+r) + Div 1 (1+g 1 )/(1+r) 2 + Div 1 (1+g 1 ) 2 /(1+r) 3 + (1/(1+r) 3 [Div 1 (1+g 1 ) 2 (1+g 2 )/(r-g 2 )] = A + B slide 34 slide 36 Example A = Div 1 /(1+r) + Div 1 (1+g 1 )/(1+r) 2 + Div 1 (1+g 1 ) 2 /(1+r) 3 = Div 1 /(r-g) [Div 1 (1+g 1 ) 3 /(r-g 1 )]/(1+r) 3 = g1 (PV for whole growth (g 1 ) perpetuity) -g1 4 (PV for growth (g 1 ) perpetuity after t=3 to infinity) Example: Yuhoo Inc $1.15 (t=1). Year 2 (t=2) to Year 1 (t=1) 1 % 5%. 15%? A + B = Div 1 /(r-g) [Div 1 (1+g 1 ) 3 /(r-g 1 )]/(1+r) 3 + (1/(1+r) 3 [Div 1 (1+g 1 ) 2 (1+g 2 )/(r-g 2 )] slide 37 slide 39
.. : + - - + =. 1%.. + - = slide 43 slide 44 = - D = E - I. : p = t t t = t= 1 + D E t t t ( 1+ k ) t= 1 ( 1+ k ) t= 1 ( 1 k) I... slide 46 slide 48
. 6% 2%. : 12/.15 = $8 $6 $8. wealth = 1*(.4 + 8 8 8 wealth = 1*(.4 +.6* *(.4 +.6* *(.4 +.6* *(...)))) 6 6 6.8*(.4 +.8*(.4 +.8*(...)))) slide 5 slide 53 1+ a + a = 1*.4* = $2 wealth = 1*(.4 +.8*(.4 +.8*(.4 +.8*(...)))) = 1*.4*(1+.8*(1+.8*(1+.8*(...)))) 2 3 wealth = 1*.4*(1+.8 +.8 +.8 +...) 2 + a 3 1 +... = 1 a 1 1-.8 slide 54 g? g? (Where does g come from?)? = ( ) + slide 57
g? 1 + g = / = 1+ (/ ) g = (/ ) 6 Price = = $2.15.6*.2 g = (Retention ratio, Plowback ratio) (Return of Equity = ROE) (Plowback ratio) = 1 (payout ratio). slide 58 slide 59 Example 6 Price = = $1.15.6*.15 Example Yuhoo Inc. $1M = 4% ROE = 1%? g =.4.1 =.4 = 4% slide 6 slide 65
Value with investment opportunities (Value with investment opportunities) :, ) Growth, Inc. Earnings, Inc. $1,, 1% P? Value with investment opportunities ) Growth Inc. 13% 1% 5% plowback ratio = 5%. P G? P (G) = No growth PV + PVGO = EPS/r + PVGO slide 67 slide 68 Price-earning earning ratio (P/E) Class 4b: P = E 1 /r + NPV P/E (Price-earning ratio) P /E 1 = 1/r + NPV/ E 1. slide 73 slide 75
?.... slide 78 slide 79. = 5, = $2 Cash 2 Debt 2 Other 1 Equity 1 Total 12 Total 12 slide 8 slide 81
: 2 1 Cash 1 Debt 2 Other 1 Equity 9 Total 11 Total 11 : : (1) (1) $2 $1,,. $2. $2 $18.. Were 12 slide 83 slide 84 : : (2) (2) $2 5, 5, 45,. : : $9,,/45, = $2.. slide 85 slide 86
: : (2) 2 1 Cash 1 Debt 2 Other 1 Equity 9 Total 11 Total 11 (3).... Were 12 slide 87 slide 88 Modigliani and Miller. Modigliani and Miller 1) $2M 2) NPV? =>? slide 89 slide 9
Modigliani and Miller 1) $2M 2) NPV? =>? Modigliani and Miller MM. ( ) ( ) slide 91 slide 92 (1).. : (2) (3) ( ) ( ). slide 93 slide 94
(4)... slide 95