The most effective way to sell the execution of an idea is to describe the use case first. And before you can do that, you need to have both the trust of your client and enough information to figure out what would delight them.
Then, describe what a great solution would do. “If we could use 10,000 square feet of space to profitably service 100 customers an hour…” or “If we built a website that could convert x percent of …” or “If we could blend a wine that would appeal to this type of diner…”
After the use case is agreed on, then feel free to share your sketches, brainstorms and mockups. At that point, the only question is, “does this execution support the use case we agreed on?”