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**Unformatted text preview: **Equity Valuation Formulas 1 Consider a company that pays expected dividends D 1 , D 2 , D 3 going out forever. The price of this company would then be: P = D 1 1 + r + D 2 (1 + r ) 2 + D 3 (1 + r ) 3 + ··· . where r is the discount rate for investments of similar risk. Its hard to forecast dividends for every period going forward. So we begin with some simplifying assumptions. Constant Dividends Suppose that the stock pays the same dividend every year forever: P = D 1 + r + D (1 + r ) 2 + ··· What would the price be in this case? P = D r This formula can be related to the price-earnings ratio. To do this, say that the relation- ship between earnings and dividends is approximated by D = (1- b ) E where b denote the plowback ratio – the portion of earnings that is kept in the firm. 1- b is paid out as dividends. Substituting in P = (1- b ) E r Then, the price-earnings ratio equals: P E = 1- b r 1 Notes for Finance 100 (sections 301 and 302) prepared by Jessica A. Wachter. Constant Dividend Growth In reality, some companies grow faster than others. A model of firm value based onIn reality, some companies grow faster than others....

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