... tom. Assume dividends are paid yearly, with the most recent dividend do having just been received an instant ago. The dividend amount grows at a constant, annualized rate of g, i.e. d = (1+g)do will be the amount of the dividend to be paid one year from now. Assume also that the annualized interest rate is r, i.e. one dollar today is worth (1+r) dollars a year from now. (a) Assuming that the stock stops paying dividends just after T years from now, what is the present value of the dividend stream? (b) If the stock is assumed to pay dividends in perpetuity, i.e. T + Qo, what is the present value of the stock? (c) Apply the ratio test to the series you have summed in (b). What conditions on the parameters g, r, and/or do must hold for the series to converge? (d) Now apply the root test to the series in (b). Do you obtain the same conditions on the parameters? (e) Is the convergence you have established in parts (c) and (d) uniform convergence? Why or why not? ... tom. Assume dividends are paid yearly, with the most recent dividend do having just been received an instant ago. The dividend amount grows at a constant, annualized rate of g, i.e. d = (1+g)do will be the amount of the dividend to be paid one year from now. Assume also that the annualized interest rate is r, i.e. one dollar today is worth (1+r) dollars a year from now. (a) Assuming that the stock stops paying dividends just after T years from now, what is the present value of the dividend stream? (b) If the stock is assumed to pay dividends in perpetuity, i.e. T + Qo, what is the present value of the stock? (c) Apply the ratio test to the series you have summed in (b). What conditions on the parameters g, r, and/or do must hold for the series to converge? (d) Now apply the root test to the series in (b). Do you obtain the same conditions on the parameters? (e) Is the convergence you have established in parts (c) and (d) uniform convergence? Why or why not