Corporate finance chapter 09 valuation of commen stocks

Chapter 9: Valuation of Common Stocks Objective Explain equity evaluation using discounting Dividend policy and wealth Chapter Contents 9.1 Reading stock listings 9.2 The discounted dividend model 9.3 Earning and investment opportunity 9.4 A reconsideration of the price multiple approach 9.5 Does dividend policy affect shareholder wealth? Reading Stock Listings Yr Hi Yr Lo 123 1/8 93 1/8 Stock IBM Sym IBM Div 4.84 Yld % 4.2 PE 16 Vol 100 14591 Day Hi Day Lo Close 115 113 Net Chg 114 3/4 +1 3/8 Present Value of Dividends D1 D2 D3 D4 P0 = + + + + (1 + k ) (1 + k ) ( + k ) (1 + k )  D3 D1  D2 D4 = + + + +  1  (1 + k ) (1 + k )  ( + k ) ( + k ) ( + k )  D1 D1 + P1 { P1} = = + 1 1+ k (1 + k ) (1 + k ) D1 + P1 − P0 k= P0 Expected Rate of Return • The price and dividend next year are expected prices, so – The expected rate of return in any period equals the market capitalization rate, k D1 + P1 − P0 k= P0 Rate Relationship D1 + P1 − P0 D1 P1 − P0 k= = + P0 P0 P0 • This relationship tells you that next year’s expected dividend yield + the expected capital gain yield is equal to the required rate of return Price0 Is Discounted Expected (Dividend1 + Price1) • Price is the present value of the expected dividend plus the end-of-year price discounted at the required rate of return D1 + P1 P0 = 1+ k Ease of Use • Recall from chapter that, for a perpetuity, the present value is the real value of the first cash flow divided by the real rate Dreal p0 = = R Dnominal @ (1 + g ) R Putting This Together D1 p0 = = (1 + g ) R D1  1+ k  (1 + g ) − 1 1+ g  D1 D1 = = (1 + k ) − (1 + g ) k − g Solving for K D1 p0 = ⇔ k−g D1 k= +g p0 10 G = Capital Gains Yield • Comparing prior results: D1 k= +g p0 D1 P1 − P0 & k= + P0 P0 P1 − P0 ⇒ g= P0 11 Earning and Investment Opportunity • To simplify the analysis, suppose that no new shares are issues, and no taxes Dividends = earnings - net new investment “D = E - I” The formula for valuing stock is ∞ ∞ ∞ Dt Et It p0 = ∑ =∑ −∑ t t t t =1 (1 + k ) t =1 (1 + k ) t =1 (1 + k ) 12 Growth Stock 80 80 80 wealth = 100 * (0.4 + 0.6 * * (0.4 + 0.6 * * (0.4 + 0.6 * * ( )))) 60 60 60 wealth = 100 * (0.4 + Kept Original wealth 0.8 * (0.4 + 0.8 * (0.4 + 0.8 * ( )))) Wealth Multiplier Reinvested 13 Growth Stock wealth = 100 * (0.4 + 0.8 * (0.4 + 0.8 * (0.4 + 0.8 * ( )))) = 100 * 0.4 * (1 + 0.8 * (1 + 0.8 * (1 + 0.8 * ( )))) wealth = 100 * 0.4 * (1 + 0.8 + 0.82 + 0.83 + )   = 100 * 0.4 *    - 0.8  = $200 1 + a + a + a + = 1− a 14 Generalize • Let the – V = value of the shares without reinvestment – G = the growth from new investment – R = retention ratio – M = wealth multiplier = g/i – Wealthg = wealth0*(1-r)/(1-w*r) 15 Reinvestment Under Normal Growth Price = = $100 0.15 − 0.6 * 0.15 Cost of Capital Retention Ratio 16 Growth Rate Illustration: Dividends Assets Cash Liab\Equ Debt Other 10 Equity 10 Total 12 Total 12 17 Illustration: Dividend Payment Was Assets Cash Was 10 Liab\Equ Debt Other 10 Equity Total 11 Total 18 11 Were 12 Illustration: Share Repurchase Assets Cash Liab\Equ Debt Other 10 Equity 10 Total 12 Total 12 19 Illustration: Share Repurchase Was Assets Cash Was 10 Liab\Equ Debt Other 10 Equity Total 11 Total 20 11 Were 12 [...]... 1 - 0.8  = $200 1 1 + a + a + a + = 1− a 2 3 14 Generalize • Let the – V = value of the shares without reinvestment – G = the growth from new investment – R = retention ratio – M = wealth multiplier = g/i – Wealthg = wealth0*(1-r)/(1-w*r) 15 Reinvestment Under Normal Growth 6 Price = = $100 0.15 − 0.6 * 0.15 Cost of Capital Retention Ratio 16 Growth Rate Illustration: Dividends Assets Cash Liab\Equ