I don't know where to start here, but YourCo. will not be better off by £4k. If you are the source of YourCo.'s revenue, then ultimately you are worse off? You cannot possibly be better of by spending "your" revenue on a depreciating asset and paying BIK on it. Depreciation is a non-cash deduction, in any event.
Get a personal loan if you don't want to pay the Tax on the dividend and claim the 45p per mile. BIK on Company Cars does not make sense.
Speak to your Accountant?