For cyclical stocks, the payout rate doesn't mean much. What is important is the amount of the dividend per share, which companies do their best not to cut. This is what causes very erratic payout rates: very low when the economic situation is good, very high at the bottom of a cycle. At best, they'll aim at an average payout rate over the whole cycle, which doesn't mean much as the cycle could be very long.

The worst thing a company can do is to try and keep up paying an unrealistic dividend, given the cyclical nature of the economy. Investors won't believe that it can be maintained over the long term, and will judge the managers to be lacking in responsibility.

Finally, it would appear to be very difficult for a company to aim to achieve a given dividend yield, as this is set by the investor on the basis of a valuation of the share, and not the company. There is no payout rate that can maximise the value of the share. There is the rule of paying out all surplus cash to shareholders whenever the company cannot identify investment projects that would bring in at least the cost of capital.
For more information, see chapter 37 of the Vernimmen.