Exercise 1. Dividend Discount Model. The dividend discount model is a way of valuing a company based on the theory that a stock is worth the discounted sum of all of its future dividend payments. In other words, it is used to value stocks based on the net present value of the future dividends. Assume that each stock of the company pays a dividend D, at the end of every year, t = 1,2,3,..., and denote by r > 0 the constant annual interest rate (use yearly compounding). a What is the price of the stock if the dividends have constant growth rate g > 0 (i.e., D +1 (1+9)D; for each t E N)? Your result should only depend on Di, r and 9 and no longer contain an infinite sum. Hint: Calculate the net present value of the dividend stream. b What is the price of the stock if the dividends increase by a constant amount I every year (i.e., D++1 = Dt +I for each t N)? Your result should only depend on D1, r and I and no longer contain an infinite sum. Hint: Derive first a formula for the expression - tt for -1 0 the constant annual interest rate (use yearly compounding). a What is the price of the stock if the dividends have constant growth rate g > 0 (i.e., D +1 (1+9)D; for each t E N)? Your result should only depend on Di, r and 9 and no longer contain an infinite sum. Hint: Calculate the net present value of the dividend stream. b What is the price of the stock if the dividends increase by a constant amount I every year (i.e., D++1 = Dt +I for each t N)? Your result should only depend on D1, r and I and no longer contain an infinite sum. Hint: Derive first a formula for the expression - tt for -1