Question

The current price of a stock is $65.88. If dividends are expected to be $1 per share for the next five
years, and the required return is 10%, what should the price of the stock be in five years when you
plan to sell it? If the dividend and required return remain the same, and the stock price is expected to
increase by $1 five years from now, does the current stock price also increase by $1? Why or why
not?

Answer 1

Suppose that the current price (P₀) of a stock is $65.88, dividends are expected to be $1 per share for the next five years (D₁ = D₂ = D₃ = D₄ = D₅), and that we require a rate of return (k_e) of 10%. We can calculate the price of this stock in 5 years using the generalized dividend model, given as: , where D_n is the dividend paid at the end of year n, k_e is the required rate of return, P_n is the price of the stock today in year n, and P₀ is the price of the stock today.

Substituting the information given in the question, we can find the price of the described stock in 5 years (P₅) as follows with the equation above:

The price of this stock in 5 years in $100.

No, the current stock price increases by less than $1 because of the time value of money. A $1 increase in 5 years is worth less than $1 today after we discount this change back in terms of today's money, even if the dividend and required return remain the same.