The Pet Company has recently discovered a type of rock which, when crushed, is extremely absorbent. It is expected that the firm will experience (beginning now) an unusually high growth rate (20%) during the period (3 years) when it has exclusive rights to the property where this rock can be found. However, beginning with the fourth year the firm's competition will have access to the material, and from that time on the firm will assume a normal growth rate of 8% annually. During the rapid growth period, the firm's dividend payout ratio will be relatively low (20%), to conserve funds for reinvestment. However, the decrease in growth will be accompanied by an increase in dividend payout to 50%. Last year's earnings were $2.00 per share (E0) and the firm's cost of equity is 10%. What should be the current price of the common stock?

$70.26

Explanation:

Dividend payout ratio = Dividend per share / Earning per share

r = cost of equity = 10%, or 0.10

Discounting factor = 1 /(1 + r)^n

n = year

a. For during the rapid growth period

Dividend payout ratio = 20%, or 0.20

Growth rate = 20%, or 0.20

Earnings per share in year 1 =  Last year's earnings per share * (1 + Growth rate) = $2 * (1 + 0.20) = $2.40 per share

Dividend per share in year 1 = Dividend payout ratio * Earning per share in year 1 = 0.20 * $2.40 = $0.48 per share

PV of year 1 dividend per share = $0.48 * (1/1.10^1) = $0.436363636363636

Earnings per share in year 2 =  Earnings per share in year 1 * (1 + Growth rate) = $2.40 * (1 + 0.20) = $2.88 per share

Dividend per share in year 2 = Dividend payout ratio * Earning per share in year 2 = 0.20 * $2.88 = $0.5760 per share

PV of year 2 dividend per share = $0.5760 * (1/1.10^2) = $ 0.47603305785124

Earnings per share in year 3 =  Earnings per share in year 2 * (1 + Growth rate) = $2.88 * (1 + 0.20) = $3.4560 per share

Dividend per share in year 3 = Dividend payout ratio * Earning per share in year 3 = 0.20 * $3.4560 = $0.6912 per share

PV of year 3 dividend per share = $0.6912 * (1/1.10^3) = $0.51930879038317

b. For during the slow growth period

Dividend payout ratio = 50%, or 0.50

Growth rate = 8%, or 0.08

Earnings per share in year 4 =  Earnings per share in year 3 * (1 + Growth rate during slow growth) = $3.4560 * (1 + 0.08) = $3.73248

Dividend per share in year 4 = Dividend payout ratio * Earning per share in year 4 = 0.50 * $3.73248 = $1.86624 per share

Dividend per share in year 5 = Dividend per share in year 4 * (1 + Growth rate during slow growth) = $1.86624 * (1 + 0.08) = $2.0155392

Stock price in year 4 = Dividend per share in year 5 / (r - Growth rate during slow growth) = $2.0155392 / (0.10 - 0.08) = $100.77696

PV of stock price in year 4 = $100.77696 * (1/1.10^4) = 68.8320196707875

c. Calculation of the current price of the common stock

Current price of the common stock = PV of year 1 dividend per share + PV of year 2 dividend per share + PV of year 3 dividend per share + PV of stock price in year 4 = $0.436363636363636 + $0.47603305785124 + $0.51930879038317 + $68.8320196707875 = $70.26

Therefore, the current price of the common stock is $70.26.

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