Replicating changes in movement speed, over time

When it comes to replicating changes in movement speed over time (such as with a Lerp function), how much of a bandwidth hog will it be?

I figure that if I am replicating a value change per frame, it can start to add up pretty fast.

Also, is there an alternative? Such as replicating a instant value change for all the other clients to see, while your client uses the Lerp to scale the speed over time?

I am still trying to wrap my head around some of the tricks between client and server calls.

Thanks.