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 = Y_n / E_n-1, and since r = (Y_n D_n) / Y_n , 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

So, you see that r is not in the final expression for P₀, indicating that r (i.e., retention ration or, equivalently, dividend policy) doesnt matter if k = ROE. Check that changing r from .8 to .6 does not change your answer in part A of this question by re-calculating your result using r = .6.

PART A ANSWERED

D₁ = 20, k = .15, g = r x ROE = .8 x .15 = .12, and Y₁ = 100 per share

P_o = D1 / (k-g)

P_o = 20 / (0.15 0.12)

P_o = 20 / 0.03

P_o = $666.67