Question

A company’s dividend is expected to grow at 20% for the next six years. After that, the growth is expected to be 3% forever. If the required return is 10%, what is the value of the stock at time 6? The dividend just paid was $1.

Answer 1

Price of share at end of year 6 = $43.94

Step-by-step explanation:

Provided information we have,

Current dividend = $1

Growth rate for 6 years = 20%

Dividend at end of year 6 = $1
`*` Future value factor of $1 @ 20% for 6 years = $1
`*` 2.985984 = $2.986 rounded off

After this dividend is supposed to grow at 3% thus Dividend at end of year 7 = $2.986 + 3% = $3.076

Therefore, using dividend growth model we have,

`P_6 = (D_7)/(Ke - g)`

Where P6 = price at end of period 6 = to be calculated

D7 = Dividend paid at end of year 7 = $3.076

Ke = Required rate of return = 10%

g = constant growth rate = 3%

Thus,
`P_6 = (3.076)/(0.10-0.03)`

P6 = $43.94

Thus, price of share at end of year 6 = $43.94