You’ll find many different reasons for different variations on the above but here’s mine.
I charge an “x” hours minimum (half day rate).
You have to consider the time it takes to get to and from a shoot as well as any equipment checks before hand. While I’m not charging the client for short travel time it is time you’re investing into the project. Some clients will insist the shoot is only 30-45 minutes or whatever but you still have to check gear and travel to and from the location. There’s also the possibility that the client (or you) misjudged the amount of time needed so you have to allow for things to run long. It limits what, if anything, you can book after it that day.
What’s a “half day?”
There’s no correct answer. It depends on your business model. Some have a full day of 8, 10 or even 12 hours. Some allow for a near endless day (a HORRIBLE idea – set a time limit!). A half day might be 4 or 5 hours.
What’s a half day charge?
Some will charge exactly what an hourly rate might be, some more. In other words some might charge 4 hours for the 4 hour half day. Others might charge for 5 hours on a 4 hour half day. The reason being is that you often can’t book a job behind the half day so you charge 5 hours for 4 to both encourage full day bookings and to compensate yourself for the fact that you can’t book behind a half day job. In other words bill 5 hours for 4 hour half day so that 8 hour bill for 8 hour day looks more attractive.
I usually include hourly rates. If a half day (4 hour) shoot goes beyond 4 hours I’ll state the half day as $X and each additional hour as $X per hour.
BTW the above holds true for both corporate and “event” clients. If I book a wedding I state explicitly that it’s for 6 or 8 hours of shooting and that additional shooting costs $X an hour. Some “even” shooters simply charge a flat amount for an open ended day. Unless your rates are very high I think that’s bad business practice. Especially for event work, the more hours you shoot, the longer your editing is going to take too.