Question

ABC Company's last dividend was $0.7. The dividend growth rate is expected to be constant at 7% for 4 years, after which dividends are expected to grow at a rate of 4% forever. The firm's required return (rs) is 15%. What is its current stock price (i.e. solve for Po)?

Answer #1

Let the dividend for period i be D_{i}, the cost of
equity be r_{s} and the growth rate beyond year 4
(perpetual growth rate) be g.

Current share price (P_{0}) = D_{1} / (1 +
r_{s}) ^ 1 + D_{2} / (1 + r_{s}) ^ 2 +
D3 / (1 + r_{s})
^ 3 + D_{4} / (1 + r_{s}) ^ 4 + D4 / (1 +
r_{s}) ^ 4 + [D_{4} * (1 + g) / (r_{s} - g)
] / (1 + r_{s}) ^ 4

= 0.7 * (1 + 0.07) / (1 + 0.15) + 0.7 * (1 + 0.07) * (1 + 0.07) / (1 + 0.15) ^ 2 + 0.7 * (1 + 0.07) * (1 + 0.07) * (1 + 0.07) / (1 + 0.15) ^ 3 + 0.7 * (1 + 0.07) * (1 + 0.07) * (1 + 0.07) * (1 + 0.07) / (1 + 0.15) ^ 4 + [0.7 * (1 + 0.07) * (1 + 0.07) * (1 + 0.07) * (1 + 0.07) * (1 + 0.04) / (0.15 - 0.04)] / (1 + 0.15) ^ 4

= 0.75 / (1.07) + 0.80 / (1.07) ^ 2 + 0.86 / (1.07) ^3 + 0.92 / (1.07) ^ 4 + [0.92 * (1.04) / (0.11)] / (1.07) ^ 4

= 0.65 + 0.61 + 0.56 + 0.52 + 6.62

= $8.96

Hence, the current share price is $8.96.

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