Time-Weighted Dividend Question

Dear All: “Assume an investor purchases a share of stock for $50 at time t=0, and another share at $65 at time t=1, and at the end of year 1 and year 2, the stock paid a $2.00 dividend. Also, at the end of year 2, the investor sold both shares for $70 each.” My question is, for the time-weighted rate of return, the HPY for year one is calculated using a dividend of $2, HPY= (65+2)/50-1 But, why is the dividend $2, because there are two shares you own at the end of year one. I mean if you a share at time 0, and a share at time 1, and there is a $2/share dividend at the end of time 1, then shouldn’t the dividend for year 1 be $4? -Richard

I guess the assumption is that he bought the stock after before the dividend was issued