What is the current price of stock? Finance

Question

Consider a stock that will pay out a dividends over the next 3 years of $1.15, $1.8, and 2.35 respectively. The price of the stock will be $48.42 at time 3. The interest rate is 9%. What is the current price of the stock?

Answer 1

$D_1=1.15,\, D_2=1.8,\,D_3=2.35, \,P_3=48.42,\,r=9\%$. $$ P_0=\frac{D_1+P_1}{1+r}=\frac{D_1}{1+r}+\frac{D_2+P_2}{(1+r)^2}=\frac{D_1}{1+r}+\frac{D_2}{(1+r)^2}+\frac{D_3+P_3}{(1+r)^3} $$

Answer 2

We have $D_1 = 1.15, D_2 = 1.8, D_3 = 2.35, P_3 = 48.42$ and $r = .09$. We know from the time value of money that $$P_0 = \frac{D_1 + P_1}{1+r} = \frac{D_1}{1+r} + \frac{D_2 + P_2}{(1+r)^2} = \frac{D_1}{1+r} + \frac{D_2}{(1+r)^2} + \frac{D_3 + P_3}{(1+r)^3}$$ Now just plug in what we have and you are done :)