12.7V is a more than adequate starting voltage, damage is likely to occur if it is regularly allowed to discharge to around 12.2V or less, and it is also likely to present starting problems at such a low voltage, and discharge the battery further, into the damagingly low realms where sulphating of the plates is rapid. If your brand new battery is discharging from 12.7v to 11.7v in a week, you definitely have a leak and this could be down to one or more of the diodes in the voltage regulator failing. The alternator will tend to give out a high voltage long after it should have reduced, as it is pushing power into both the battery, and the leak, rather like pumping water into a tank with a hole in. When you switch off the supply, your briefly full battery continues to leak back through the diodes. When you leave your car after you have been for a drive, try disconnecting the wires from the alternator. If the battery remains fully charged, you have isolated the problem. If it continues to discharge, then it isn't the alternator!
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