What he said. Maybe make a little extra noise (a tap on the table, a slightly raised voice) but only if you’re natural about it, like you think you aren’t projecting properly or you’re emphasizing an important point. Don’t look in the CEO’s direction while you’re doing it; preferably look at the screen. Address the VPs and completely ignore the fact that the CEO is napping. He’ll ask the VPs for their opinions later and work off that.
Keep going as though things were completely normal.
This actually works in your favor. The CEO is unlikely to be willing to admit to his subordinates that he wasn’t paying attention. In order to save face, he will be more likely to defer to their judgment.
Far worse would be pitching to a CEO who hung on your every word and questioned every detail of the plan. That sends a message to his subordinates that the boss is wary and will cause them to pull back even if previously they were in favor of hiring you.
Fortune favors the bold. As soon as you realize he’s sleeping, pretend to slip and fall, bouncing heavily off the table on your way down. Yell “oh dear God!” as you’re falling, but then lay on the floor for maybe 3-4 seconds doing nothing but quietly moaning. After which you should spring back to your feet and go on with your presentation like nothing happened.
Take your lead from the VPs. Either this happens often and they habitually proceed without him (in which case someone will gesture you on,) or it’s never happened before and they’ll be at a loss. Most liekly one of them will immeidately be shown as the leader, as the others will look toward him/her. Either way the key is that it’s not your problem, it’s theirs, and you are looking to them for guidance, with a gracious lack of judgment. None of this is spoken, and it takes about 7 nanoseconds.
If they are all indecisive, ask if the group would like to take a five minute break. They will gratefully agree. Then leave the room and go to the bathroom. Come back after 3-4 minutes and when everyone is settled, thank them and continue as if nothing has happened.
which is wonderful, because it tells me who is the person I need to convince. Other than switching my focus to be a bit more intensely on that person than on the rest, I just go on as normal. I’m not hearing any snores, are you?
There have been other situations where I’ve told people to “cut it out with the ‘happy smile while you’re mentally elsewhere’ trick”, but they weren’t clients and it wasn’t the final pitch in a sales sequence: they were employees from my own company, it was the first of many meetings to come, and we needed them to be awake in order to answer our questions. And I knew that it was culturally acceptable (I asked for my American coworker’s permission to switch to Spanish before delivering the “guys, your tricks don’t work on ME, we went to the same schools” message; delivering it in English would have been both less effective and more shaming, while switching to Spanish without asking for permission would have been terribly impolite).