How do business coaches handle the "I can't afford it" objection?

Mostly by making it unnecessary, because by the time it is spoken the framing has usually already failed.

Two things prevent it:

• Publish the investment level. An owner who sees the number before contacting you has already decided it is plausible. The objection largely disappears as a live conversation and becomes a self-selection step instead.
• Frame the engagement against a problem with a cost. An owner who cannot connect your fee to something already costing them money will always find it expensive. One who can see that the bottleneck is costing them a hire, or a margin point, or their weekends, is comparing your fee to that instead of to zero.

When it does come up, the useful response is diagnostic rather than persuasive. Ask what the problem is currently costing. Often the owner has never calculated it, and the calculation is the conversation.

Do not discount to close. An engagement discounted at the start is one where the owner has less committed and typically executes less, which produces the outcome that justifies their doubt.

Sometimes the honest answer is that the timing is wrong.