Question

AVZ is a​ start-up company who is using all its cash to growth so it does not plan to pay dividends for the next

5 years.

The company then plans to start paying annual cash dividends starting in year 6 of ​$6.00 for 12

years. ​ Thereafter, the company will assume a constant growth dividend policy and the estimated growth rate in dividends forever after that point is

4​%.

The price of the stock is set to yield a return of

11%.

What is the price of this stock​ today?

Answer 1

P0 = D6 / (1 + r)⁶ + D7 / (1 + r)⁷ + D8 / (1 + r)⁸ + D9 / (1 + r)⁹ + D10 / (1 + r)¹⁰ + D11 / (1 + r)¹¹ +

D12 / (1 + r)¹² + D13 / (1 + r)¹³ + D14 / (1 + r)¹⁴ + D15 / (1 + r)¹⁵ + D16 / (1 + r)¹⁶ +

D17 / (1 + r)¹⁷ + D17(1 + g) / [(r - g)(1 + r)¹⁷]

= [$6/1.11⁶] + [$6/1.11⁷] + [$6/1.11⁸] + [$6/1.11⁹] + [$6/1.11¹⁰] + [$6/1.11¹¹] + [$6/1.11¹²] +

[$6/1.11¹³] + [$6/1.11¹⁴] + [$6/1.11¹⁵] + [$6/1.11¹⁶] + [$6/1.11¹⁷] +

[($6 x 1.04) / {(0.11 - 0.04) x 1.11¹⁷}]

= $3.21 + $2.89 + $2.60 + $2.35 + $2.11 + $1.90 + $1.72 + $1.55 + $1.39 + $1.25 + $1.13

+ $1.02 + $15.12 = $38.24