7.1 In the late 1980s corporations began to repurchase shares on a large scale. In this problem you are asked to analyze the effect of repurchases on the relation between stock prices and dividends. Consider a firm with fixed cash flow per period, X. The total market value of the firm (including the current cash flow X) is V. This is the present value of current and future cash flow, discounted at a constant rate R: V = (1 + R)X/R. Each period, the firm uses a fraction of its cash llow to repurchase shares at cum-lividend prices, and then uses a fraction (1-1) of its cash flow to pay dividends on the remaining shares. The firm has N, shares outstanding at the beginning of period 1 (before it repurchases shares) 7.1.1 What are the cum-dividend price per share and dividend per share at time ? 7.1.2 Derive a relation between the dividend-price ratio, the growth rate of dividends per share G, and the discount rate R. 7.1 In the late 1980s corporations began to repurchase shares on a large scale. In this problem you are asked to analyze the effect of repurchases on the relation between stock prices and dividends. Consider a firm with fixed cash flow per period, X. The total market value of the firm (including the current cash flow X) is V. This is the present value of current and future cash flow, discounted at a constant rate R: V = (1 + R)X/R. Each period, the firm uses a fraction of its cash llow to repurchase shares at cum-lividend prices, and then uses a fraction (1-1) of its cash flow to pay dividends on the remaining shares. The firm has N, shares outstanding at the beginning of period 1 (before it repurchases shares) 7.1.1 What are the cum-dividend price per share and dividend per share at time ? 7.1.2 Derive a relation between the dividend-price ratio, the growth rate of dividends per share G, and the discount rate R