Some investors expect Mazzeo Industries to have an irregular dividend pattern for several years and then to grow at a constant rate. Dividends are expected to grow by 25% for two years and 20% for the next three years. After that, growth will fall to a constant rate of 7%. Last year’s dividend was $1.00. This amount of risk justifies a 14% required rate of return. If these projections are correct, what should the stock be valued at today?
USE AT LEAST 4 DECIMAL PLACES
P0 = [{D0 * (1 + g1)} / (1 + r)] + [{D0 * (1 + g1)2} / (1 + r)2] + [{D0 * (1 + g1)2 * (1 + g2)} / (1 + r)3] + [{D0 * (1 + g1)2 * (1 + g2)2} / (1 + r)4] + [{D0 * (1 + g1)2 * (1 + g2)3} / (1 + r)5] + [{D0 * (1 + g1)2 * (1 + g2)3 * (1 + gC)} / {(r - gC) * (1 + r)5}]
= [{$1 * (1 + 0.25)} / (1 + 0.14)] + [{$1 * (1 + 0.25)2} / (1 + 0.14)2] + [{$1 * (1 + 0.25)2 * (1 + 0.20)} / (1 + 0.14)3] + [{$1 * (1 + 0.25)2 * (1 + 0.20)2} / (1 + 0.14)4] + [{$1 * (1 + 0.25)2 * (1 + 0.20)3} / (1 + 0.14)5] + [{$1 * (1 + 0.25)2 * (1 + 0.20)3 * (1 + 0.07)} / {(0.14 - 0.07) * (1 + 0.14)5}]
= $1.10 + $1.20 + $1.27 + $1.33 + $1.40 + $21.44 = $27.73
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