Class 5 - Stocks We want to attempt to value a stock. Stocks often provide dividends, and also provide the sale price when the stock is sold. If Ptrepresents the value of the stock [it may be the value of all the shares, or the valueshare, depending on the context] at time t, Div retresents the dividend at time t, and r is the appropriate discount rate, then: P 0 = Div 11+r) + P 11+r) P 1 Div 21+r) + P (2+r) P = Div (1+r) + Div (1+r) + P (1+r) 2 0 1 2 2 2 3 Continuing we get: P = 0iv (1+1) + Div (1+r2 + Div (1+r) 3 In the case of constant dividends, Div = Div = 1and P = 2ivr (using th0 perpetuity formula) In the case of constant growth Div = Div (1+1), Div =0Div (1+g) etc2 1 P 0 Div (r1g) * The above model, *, is called the dividend discount model, or the Gordon model, named after Professor Myron Gordon of the University of Toronto. Exercise: Differential growth growth at rate g for the1first T years and growth at rate g 2 after that. Draw a picture describing the series of dividends (start from Div in 1 year)1and derive the formula for the price, P, of the stock. Where does the g come from in the Gordon model? The theory is: Earnings next year = Earning this year + Retained Earnings this year x Return on Retained earnings Therefore, dividing both sides by earning this year, we get: Earnings next yearEarnings this year = 1 + Retained Earnings this yearEarnings this year x Return on Retained earnings 1 www.notesolution.com

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