Question

1. PE ratios a.) Consider the following asset pricing equation D+P. 1+r Pi is the real price of one share of stock and Di 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 t r b.) Suppose dividends grow indefinitely at rate g so D+1-D (1+8). Assume that 0 < g < r . Find an expression for the price/dividend ratio (P. / D ) in terms of r and g only. Call this solution PE . Hint: recall that the infinite sum 1+ z+z3+... - as long as 0 < z < 1 . c.) Suppose-06 and g 03 what is the corresponding price / dividend ratio?

Answer 1

a) Expected return (r) = D_t + 1 + P_t + 1 -P_t/P_t After rearranging P_t = D_t + 1 + P_t + 1 /1 + N = D_t + 2 /1 + r = P_t + 1/1 + r = D_t + 1/1 + r + D_t + 2 + P_t + 2 /(1 + r)^2 After expanding further P_t = D_t + 1 /1 + r + D_t + 2 /(1 + r)^2 + D_t + 3 /(1 + r)^3 + ----+ P_t + n/(1 + r)^n when, n is very large to infinity, the present value at time t of P_t + n is very small to goes to zero Expression for stock price at time t becomes P_t = D_t + 1 /1 + r + D_t + 2 /(1 + r)^2 + D_t + 3 /(1 + r)^3 + ---- + infinity (infinity) b) Dividend growth rate g D_t + 1 = D_t (1 + g) Expression