Question

Google has paid $2 in dividends one year ago and this year has just paid $4 yesterday. In the next three years the dividends are expected to be $1, $5, and $4 at the end of year three. From there on, the dividend will grow with a yearly growth rate g. What is this implied growth rate that shareholders expect if the stock price today is $40? (The required rate of return for this stock is 10%.)

Answer 1

stock price today = expected dividend year 1/(1+required rate of return) + expected dividend year 2/(1+required rate of return)2 + expected dividend year 3/(1+required rate of return)3 + terminal value/(1+required rate of return)3

terminal value = expected dividend year 3*(1+growth rate)/(required rate of return - growth rate)

$40 = $1/(1+0.10) + $5/(1+0.10)2 + $4/(1+0.10)3 + [$4*(1+g)/(0.10 - g)]/(1+0.10)3

$40 = $1/1.10 + $5/1.102 + $4/1.103 + [$4*(1+g)/(0.10 - g)]/1.103

$40 = $1/1.10 + $5/1.21‬ + $4/1.331‬ + [$4*(1+g)/(0.10 - g)]/1.331

$40 = $0.9091 + $4.1322 + $3.0053 + [$4*(1+g)/(0.10 - g)]/1.331

$40 = $7.1375 + [$4*(1+g)/(0.10 - g)]/1.331

$40 - $7.1375 = [$4*(1+g)/(0.10 - g)]/1.331

[$4*(1+g)/(0.10 - g)] = $32.8625‬*1.331

$4*(1+g)/(0.10 - g) = $43.7399875‬

$4*(1+g) = $43.7399875‬*(0.10 - g)

$4*(1+g) = $4.37399875‬ - 4.37399875‬g

(1+g) = $4.37399875/4 - 4.37399875‬g/4

(1+g) = $1.0934996875‬ - 1.0934996875‬g

g + 1.0934996875‬g = $1.0934996875 - 1

2.0934996875‬g = $0.0934996875‬

g = 0.0934996875‬/2.0934996875 = 0.0447 or 4.47% or rounded off to one decimal place to 4.5%

this implied growth rate is 4.5% that shareholders expect if the stock price today is $40.