Question

9.3     assume that k = ROE, we can show that the price P₀ does not depend on r. To see this, let g = r x ROE, and ROE = Y_n / E_n-1.

Since r = 1 – (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 ratio or, equivalently, dividend policy) doesn’t matter if k = ROE.

Note that in part a, D₁ = 20 and r = .8. You also know from Chapter 3 that D₁=Y₁ x (1–r), so you can use this to calculate Y₁.

Answer the following question based on the information given above.

Check that changing r from 0.8 to 0.6 does not change your answer in Question 9.2a by re-calculating your result using r = 0.6.                                                                                  (4 marks)

Answer 1