Question

Synovec Corp. is experiencing rapid growth. Dividends are expected to grow at 28 percent per year during the next three years, 18 percent over the following year, and then 5 percent per year, indefinitely. The required return on this stock is 11 percent and the stock currently sells for $82 per share. What is the projected dividend for the coming year?

Answer 1

Let Current Dividend be D0

So, Terminal Value, i.e.,

P4 = D5 / (r - g)

= [D0 * (1 + g1)³ * (1 + g2) * (1 + gC)] / [r - gC]

= [D0 * (1 + 0.28)³ * (1 + 0.18) * (1 + 0.05)] / [0.11 - 0.05]

= [D0 * 2.5984] / 0.06

= 43.31[D0]

P0 = [{D0 * (1 + g1)} / (1 + r)] + [{D0 * (1 + g1)²} / (1 + r)²] + [{D0 * (1 + g1)³} / (1 + r)³] + [{D0 * (1 + g1)³ * (1 + g2)} / (1 + r)⁴] + [{D0 * (1 + g1)³ * (1 + g2) * (1 + gC)} / {(r - gC) * (1 + r)⁴}]

P0 = D0 * [{(1 + g1) / (1 + r)} + {(1 + g1)² / (1 + r)²} + {(1 + g1)³ / (1 + r)³} + {{(1 + g1)³ * (1 + g2)} / (1 + r)⁴} + {{(1 + g1)³ * (1 + g2) * (1 + gC)} / {(r - gC) * (1 + r)⁴}}]

$82 = D0 * [{(1 + 0.28) / (1 + 0.11)} + {(1 + 0.28)² / (1 + 0.11)²} + {(1 + 0.28)³ / (1 + 0.11)³} + {{(1 + 0.28)³ * (1 + 0.18)} / (1 + 0.11)⁴} + {{(1 + 0.28)³ * (1 + 0.18) * (1 + 0.05)} / {(0.11 - 0.05) * (1 + 0.11)⁴}}]

$82 = D0 * [1.15 + 1.33 + 1.53 + 1.63 + 28.53]

$82 = D0 * [34.17]

D0 = $82 / 34.17 = $2.40

Dividend next year = D0 * (1 + g1) = $2.40 * (1 + 0.28) = $3.07