Why minimal bonus is not zero
At IBM the bonus is in a range between some minimum and some maximum that depend on where you are in the food chain. The actual annual figure is calculated according to a formula that is a combination of your personal success, your division's success, and IBM's success. If on all three levels the year was very successful you will get the maximal bonus (or close). If the year was lousy for your division and for IBM in general AND you are deemed a slacker by your boss(es) you will get the minimal bonus (or close).
Why minimum != 0? Basically, it reduces your "base salary" that is used to calculate various benefits that IBM may or may not pay you in various jurisdictions. Any payment that is a percentage of your salary is computed from the base pay only (typical example: severance pay in case of termination).
If there are additional tax or other considerations for IBM I don't know. I assume that in most places base+bonus is the employee's income and is therefore taxed in the same way.
The above is for many (all? dunno...) regular IBM employees. I suppose the top executives like to pretend that they are just like the common folk, and their bonus structure is similar (it may be a larger proportion of the overall pay - I don't know). Thus, forgoing any bonus and taking home just the base salary and the associated payments/benefits is understood by poor Joe Q. Ibmer without detailed explanation, regardless of what he might think of the significance of the step.