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Lecture

Class 5

4 Pages
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Department
Rotman Commerce
Course Code
RSM332H1
Professor
Booth

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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 Pt represents the value of the stock [it may be the value of all the shares, or the value/share,
depending on the context] at time t, Divt represents the dividend at time t, and r is the appropriate
discount rate, then:
P0 = Div1/(1+r) + P1/(1+r)
P1 = Div2/(1+r) + P2/(1+r)
P0 = Div1/(1+r) + Div2/(1+r)2 + P2/(1+r)2
Continuing we get: P0 = Div1/(1+r) + Div2/(1+r)2 + Div3/(1+r)3 +
In the case of constant dividends, Div1 = Div2 = … and P0 = Div/r (using the
perpetuity formula)
In the case of constant growth Div1 = Div0(1+g), Div2 = Div1(1+g) etc.
P0 = Div1/(r-g) *
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 g1 for the first T years and growth at rate g2
after that. Draw a picture describing the series of dividends (start from Div1 in 1 year) and
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 year/Earnings this year = 1 + Retained Earnings this year/Earnings this year x Return on
Retained earnings
1
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Description
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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