Two questions my father always used to ask (as a pair).
What is the upside potential?
What is the downside risk?
Quantify that downside risk. How much would you lose if the new system failed to various degrees? Estimate percentages for the various degrees (and I would estimate utter failure at 5% to 10% at least. If you have any records of failed projects, you might be able to calculate something precise). Multiply the percentages by the losses. Add them up. This is the "expected value" (shown as a negative) of failure.
The next negative number is the "opportunity cost". The staff who are rewriting a working system could be doing something more profitable. Estimate the amount of time it will take to write the new system. Estimate the cost of the staff - and multiply it by four. Explain that a multiplier of between three and five is necessary to cover holidays, training, sickness, management, unproductive time, overheads like rent and computers and, of course, profit. I wish I had some authority to quote you on this, but I assure you it's accurate. If the auditors are around, they will probably know their own chargeout rates. Ask them what the rate is divided by the pay per hour. Explain what you are doing and that you are only looking for an approximation.
To be fair, it is essential that you put in the savings that the new system will make - the upside potential. These are the costs of failure you used earlier, but the percentages will be lower because the chance of total failure of a working system is known to be zero (but put in something like 1% anyway). Don't gild the lily - you don't need to. This is the "expected value" of the new system - a positive number.
Add the three numbers up - two negative and a positive. This is the loss (negative) that can reasonably be expected from taking a decision to rewrite the system. Of course, if the number comes out positive, you should rewrite. But based on what you have said, it won't. Prepare a presentation and show it to a beancounter. Use the terms I have put in quotes - they are standard accounting terminology that will be understood. Then let the beancounter kill the project for you.
Sorry about the absence of bullet points, and good luck!
John Davies B.Acc, CA(SA), ACMA but no programming qualifications whatsoever