Question

The Ramirez Company's last dividend was $1.5. Its dividend growth rate is expected to be constant at 15% for 2 years, after which dividends are expected to grow at a rate of 5% forever. Its required return (rs) is 12%. What is the best estimate of the current stock price?

Answer 1

current stock price,
`P_(0)` = $26.84

Step-by-step explanation:

Given,

Most recent dividend,
`D_(0)` = $1.50

Growth rate,
`g_(1)` = 15% = 0.15 (Next 2 years)

`g_(2)` = 5% = 0.05 (remain constant after 2 years)

required rate of return ,
`r_(s)` = 12% = 0.12

We know,

Current stock price,
`P_(0)` = [
`D_(1)` ÷ (1 +
`r_(s)`)] +
`(D_(2) + P_(2))/((1 + r_(s))^(2))`

or,
`P_(0)` = [{
`D_(0)` × (1 +
`g_(1)`)} ÷ (1 +
`r_(s)`)] +
`(D_(0) (1 + g_(1))^(2) + (D_(3))/(r_(s) - g_(2)))/((1 + r_(s))^(2))`

or,
`P_(0)` = [{$1.50 × (1 + 0.15)} ÷ (1 + 0.12)] +
`(1.50*(1+0.15)^(2) + (D_(2) (1 + g_(2)))/((0.12 - 0.05)))/((1+0.12)^(2))`

or,
`P_(0)` = ($1.725 ÷ 1.12) +
`(1.98375 + (1.98375*(1 + 0.05))/(0.07))/(1.2544)`

or,
`P_(0)` = $1.5402 + [(1.98375 + 29.75625) ÷ 1.2544]

or,
`P_(0)` = $1.5402 + (31.74 ÷ 1.2544)

or,
`P_(0)` = $1.5402 + 25.3029

Therefore, current stock price,
`P_(0)` = $26.84