Answer:
$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.
