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78106_07_Web_Ch07A_p01-02

# 78106_07_Web_Ch07A_p01-02 - WEB EXTENSION Derivation of...

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W E B E X T E N S I O N 7A Derivation of Valuation Equations T he derivation of the formulas for the values of a perpetual preferred stock and the values of a constant growth stock are presented in this extension. V ALUES OF A P ERPETUAL P REFERRED S TOCK The value of a perpetual preferred stock is given by V ps ¼ D ps ð 1 þ r ps Þ 1 þ D ps ð 1 þ r ps Þ 2 þ þ D ps ð 1 þ r ps Þ (7A-1) For a partial sum up to N, Equation 7A-1 may be rewritten as follows: V ps ¼ D ps 1 ð 1 þ r ps Þ 1 þ 1 ð 1 þ r ps Þ 2 þ þ 1 ð 1 þ r ps Þ N " # (7A-2) Multiply both sides of Equation 7A-2 by (1 + r ps ), which yields V ps ð 1 þ r ps Þ ¼ D ps 1 þ 1 ð 1 þ r ps Þ 1 þ 1 ð 1 þ r ps Þ 2 þ þ 1 ð 1 þ r ps Þ N 1 " # (7A-3) Subtract Equation 7A-2 from Equation 7A-3 to obtain V ps ð 1 þ r ps 1 Þ ¼ D ps 1 1 ð 1 þ r ps Þ N " # (7A-4) As N , 1/(1 + r ps ) N 0 and Equation 7A-4 approaches V ps ð r ps Þ ¼ D ps Thus we obtain Equation 7-8 from the chapter: V ps ¼ D

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78106_07_Web_Ch07A_p01-02 - WEB EXTENSION Derivation of...

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