Is it a big birthday (40, 50, 60)? Do you celebrate teachers' birthdays? $100 seems like a lot for a regular birthday, and it's not a great idea to have the teachers be upset. Do you have 10-20 key volunteers who might chip in $5 to $10? Then make it known that the PTO is collecting money for this special birthday. Our PTO has a "sunshine fund" for illnesses and major events (weddings, births), but we have to stay under a $50 limit imposed by the state ethics commission -- and we don't do birthdays.
Is your school a 5013c charity with a defined purpose for fundraising that was approved by the IRS to become tax exempt? If yes, and the statement does not include raising money to pay for teacher or principals birthday gifts then the answer is NO you can't spend money donated for the purpose of charity to buy presents. Parents would need to collect money for that specific purpose outside the guidelines of the PTO.