Rabbi Monk in קול התורה says that the use of the term בעצם היום הזה actually means that it took place on Yom Kippur. This connects the blood of the bris with the korbonos of Yom Kippur and allows for some interesting drashos. However, this means that the Malachim had to have come on the 12th of Tishrei (the third day). We have learned that Sarah conceived on Rosh Hashannah following the bris and Yitzchak was born on Pesach after a seven month pregnancy (this includes an Adar Sheni that year).
This means that it took about a year and a half from the bris until Yitzchak was born. This means that Avraham turned 100 after the following Pesach and before the following Yom Kippur, since he was 99 at the time of the Bris. This means that the interpretation of כעת חיה as "this time next year", means that they said that when the sun reaches a particular point in its orbit "next year" (after the following Rosh Hashanah, Yitzchak will be born. Alternatively, it could mean "in the normal course of events" without being a specific time.
On the other hand, those who say that the malachim came on Pesach (like Rashi) follow the interpretation of Rav Shamson Rafael Hirsch, that בעצם היום הזה means in broad daylight and as soon as he was commanded. In this interpretation, Avraham could have just turned 99 or could have been 99 for a while. There is no way that we can logically determine what month he was born in from this part of the Torah. In this case, Yitzchak was born precisely a year later.