Notation: Let Pn = Price at time n Dn = Dividend at time n Yn = Earnings in period n r = retention ratio = (Yn Dn) / Yn = 1 Dn/ Yn = 1 - dividend payout ratio En = Equity at the end of year n k = discount rate g = dividend growth rate = r x ROE ROE = Yn / En-1 for all n>0. We will further assume that k and ROE are constant, and that r and g are constant after the first dividend is paid.

A. Using the Discounted Dividend Model, calculate the price P0 if D1 = 20, k = .15, g = r x ROE = .8 x .15 = .12, and Y1 = 100 per share

B. What, then, will P5 be if: D6 = 20, k = .15, and g = r x ROE = .8 x .15 = .12?

C. If P5 = your result from part B, and assuming no dividends are paid until D6, what would be P0? P1? P2?

D. Again, assuming the facts from part B, what is the relationship between P2 and P1 (i.e., P2/P1)? Explain why this is the result.

E. If k = ROE, we can show that the price P0 doesnt depend on r.

To see this, let g = r x ROE, and ROE = Yn / En-1, and since r = (Yn Dn) / Yn , then D1 = (1 r) x Y1 and P0 = D1 / (k g) P0 = [(1 r) x Y1] / (k g) P0 = [(1 r) x Y1] / (k g), but, since k = ROE = Y1 / E0 P0 = [(1 r) x Y1] / (ROE r x ROE) P0 = [(1 r) x Y1] / (Y1 / E0 r x Y1 / E0) P0 = [(1 r) x Y1] / (1 r) x Y1 / E0), and cancelling (1 r) P0 = Y1 / (Y1/E0) = Y1 x (E0 / Y1) = E0