It's the truth and it's something any half way decent manager can understand. It's not personal it's just a typical business decision for both parties. Expect that they may not match immediately. They will try to get you to wait a year or till the next cycle. The response is that you don't want to wait or leave money on the table due to the time value of money and the risk you are shouldering. Either they concede, sweeten the pot, or pass.
If you do end up with future promises get it in writing signed by your manager. Read it and make sure there are no games.
I wouldn't bother with estimates or middle grounds. Where the rubber meets the road is what kind offer you can get somewhere else. You are asking for a pittance from them and for the most part unless it's a failing business they shouldn't care.