PE ratios (a) Consider the following asset pricing equation P_t = D_t+1 + P_t+1/1 + r. P_t is the real price of one share of stock and D_t is the real dividend payment per share at time t. The company pays out all profits in dividends and the real interest rate is constant. Show that if the company lasts forever, and if the real interest rate is constant, then P_t = D_t+1/1 + r + D_t+2/(1 + r)^2 + D_t+3/(1 + r)^3 + .. (b) Suppose dividends grow indefinitely at rate g so that D_t+1 = (1 + g) D_t. Assume that 0 PE* (PE* is the price/dividend ratio you computed in part (b)) then P_t/D_t is expected to grow without bound. (You may answer this question mathematically or with a diagram.) (iii) Show that if P_t/D_t > PE*, then the growth rate in the price/dividend ratio approaches a constant number as t rightarrow infinity. What is this number