Price of dividend paying stock

Question

Consider a dividend paying stock $S$ and suppose that its value just before a dividend payment of $D >0$ at time $t$ is denoted by $S(t−)$. The price after the payment should be $S(t)=S(t-)-D$?

How can I justify that. Is there an arbitrage argument?

Answer 1

If a stock price is the discounted value of future income, then immediately before the dividend, the future income is the amount $S(t-)$, and immediately after the dividend, the future income is the amount $S(t) = S(t-)-D$. It's lessened by $D$ because that's no longer part of the stream of future income. There's nothing more to it than that.

Answer 2

Not necessarily, because of tax considerations. Depending on the jurisdiction, capital gains may be taxed at a different rate than dividends. Depending on these rates, selling a stock before the dividend at $S(t-)$ may be a better or a worse deal than getting the dividend $D$ and selling at $S(t-)-D$. If enough investors prefer one to the other, it will affect the stock prices.