My understanding was that as you increase the time to expiry of an option, the value of the option increases. However, I have run a bunch of scenarios and have realized that if you assume a dividend yield > 0%, the value of the option starts decreasing after x number of years. In other words, in the first z years, the value of the option increases, and after x years, it starts to decrease. This is even the case if the risk free rate > dividend yield. Can someone please explain to me intuitively why the dividend yield causes the value of the option to decrease after a certain number of years and why the time value of the option doesn't outweigh the effects of the dividend?
Thanks very much.