Question

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1. Using the following information to evaluate a stock price.
   A stock just paid its dividend of $2.00 and its required return is 13%.

1. Assume g is non-constant, the growth rate is 30% for Year 0 to Year 1, 25% for Year 1 to Year 2, 15% for Year 2 to Year 3, and then long-run constant g = 6%, what is the stock price?
2. Assume that the dividends are growing at 10% for the first two years and then grow at 6% forever after. What is the stock price?

Answer 1

a). P0 = [{D0 x (1 + g1)} / (1 + r)] + [{D0 x (1 + g1) x (1 + g2)} / (1 + r)²] +

[{D0 x (1 + g1) x (1 + g2) x (1 + g3)} / (1 + r)³] + [{D0 x (1 + g1) x (1 + g2) x (1 + g3) x (1 + gC)}

/ {(r - gC) x (1 + r)³}]

= [($2 x 1.30) / 1.13] + [($2 x 1.30 x 1.25) / 1.13²] + [($2 x 1.30 x 1.25 x 1.15) / 1.13³] +

  [($2 x 1.30 x 1.25 x 1.15 x 1.06) / {(0.13 - 0.06) x 1.13³}]

= $2.30 + $2.55 + $2.59 + $39.22 = $46.66

b). P0 = [{D0 x (1 + g1)} / (1 + r)] + [{D0 x (1 + g1)²} / (1 + r)²] +

[{D0 x (1 + g1)² x (1 + gC)} / {(r - gC) x (1 + r)²}]

= [($2 x 1.10) / 1.13] + [($2 x 1.10²) / 1.13²] + [($2 x 1.10² x 1.06) / {(0.13 - 0.06) x 1.13²}]

= $1.95 + $1.90 + $28.70 = $32.54