q1 - theoretical price of the stock and i is called the...

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Math 618 Quiz 1 Name: Summer 2011 Algebra/Calculus Reminder From algebra we have 1 + r + r 2 + ··· + r n - 1 = 1 - r n 1 - r . If | r | < 1, then lim n →∞ r n = 0, and the above sum gives the (infinite) sum of the geometric series 1 + r + r 2 + r 3 + ··· = X k =0 r k = lim n →∞ 1 - r n 1 - r = 1 1 - r ( | r | < 1) . (1) Theoretical Price of a Stock A stock pays an annual dividend each year one year after the purchase. As long as the stock holder owns the stock, he receives the dividend payment year after year. Suppose the amount of the dividend is D 1 at the end of the first year, D 2 at the end of the second year, D 3 at the end of the third year, . .. and so on. Under an annual effective interest rate i to consider the present values of all the dividend payments ( v = 1 1+ i ): . . . . . . . . . 0 1 2 3 k D 1 D 2 D 3 . . . D k . . . D 1 v D 2 v 2 D 3 v 3 . . . D k v k . . . ± ± ± ± ± ± The sum of all these present values is called the
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Unformatted text preview: theoretical price of the stock, and i is called the annual yield of the stock. Theoretical Price = D 1 v + D 2 v 2 + D 3 v 3 + ··· + D k v k + ··· Questions (You may need formula ( ?? ) to add the present values.) 1. Find the theoretical price of a stock with an annual effective yield of 6% that pays dividend $1 every year . Answer 2. Find the theoretical price of a stock with an annual effective yield of 6% that pays dividend $1 the first year, and each subsequent dividend is 2% more than the previous year’s dividend. (That is D 1 = 1, D 2 = 1 . 02, D 3 = 1 . 0404, . .., and the k th payment is D k = 1(1 + 0 . 02) k-1 = 1 . 02 k-1 , ...) Answer...
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