"A project pays a dividend of $0.75 next year and then grows at 12% for 3 more years, and then grows at 8% indefinitely thereafter, find PV"
Okay so first step is to find the initial value of perpetuity at t(4) = 15.05 Then discount each dividend payment back so three payments. Then final step is to discount to value of the perpetuity back to t(0).
My question is when plugging into the Present value formula how come we are supposed to use t = 3 instead of t = 4?
I just never understood the logic of it.
edit = interest rate is 15%
First, project don't pay dividends, but rather stocks pay dividends. Second, always draw timeline. The first cash flow at $t=0$ is assumed to be zero so $c_0=0.$ The second one at $t=1$ is $c_1=0.75,$ so $c_2=0.75(1.12), c_3=0.75(1.12)^2$ and $c_4=0.75(1.12)^3. $ The next one is $c_5=0.75(1.12)^3(1.08)$ and all other cash flows are equal to $c_5$ because they form a perpetuity, then $c_i=c_5$ for all $i \geq 5.$ The discount factor for $i=15 \%$ is $v=\frac{1}{1+i}=\frac{1}{1.15}$ then you should proceed by discounting everything to time zero
$$PV=c_1v+c_2v^2+c_3v^3+c_4v^4+(\frac{c_5}{0.08})v^4.$$
Remember that when you're computing the PV of a perpetuity with constant cash flows the PV is one step behind i.e. in this case, in our timeline $\frac{c_5}{0.08}$ is located at $t=4$ because it's the PV of the perpetuity starting at $t=5,$ so we should discount it back $4$ times to get $(\frac{c_5}{0.08})v^4.$