Company going public - should ee buy stock at issue price or exercise stock options?

[Guest benefitsmom]

My young daughter's company is going public. Employees may buy stock at the issue price. She also has stock options which would allow her to buy stock at a cost approximately $5 below the issue price. Management sent out an e-mail discouraging employees from exercising their options (they told employees there's a 180 day lock in period during which they could lose money if the stock price goes down, and the purchase might create an alternative minimum tax issue). It seems to me that if she buys the stock at the issue price, she could lose more money (but she'd only be locked in for 25 days if she buys stock at the issue price.)

Her options do not expire for a while, but she might leave the company to return to school (next January, before the expiration of the 180 lock in period, so it's likely she couldn't do a cashless exercise of the options). I don't have the stock option plan document or SPD but I wonder if her options might expire either upon termination or within some time period after termination, and if she'd be better off exercising her options at the lower price than buying the stock at the issue price.

Does anybody have any advice? Thank you!