I had the same case and you can ask for more info like percent in good standing etc.

Am I wrong to think that the 96% is not relevant? I think it should be (1-p)(Avg Profit)-(p)(Avg Loss) = 1M. Solve for p that justifies spending $1M to deny 4% of applications. This is of course assuming that the 96% are profitable in the net.

So, they pay $1M dollars to verify. Assume $1M is only justified if they save >= $1M by verifying. Given: - 40,000 people are denied (4% of the applications) - the number people that need to default to lose $1M in defaults is: 1M/(avg-losses-per-default) Then: (1M/avg-loss-per-default)/40,000 is the percentage of the defaulters needed to cost $1,000,000 in defaults. I'd ask for a definition of 'justify' to verify the assumption above.

I think if we know the % of good and % of bad customers we can calculate the total Profit as P=(% good of 960000 )*(AVg. Rev from good) - (% bad of 960000 )*(AVg. loss from bad) - 1M (from background check) Assuming the average loss per denied customer is same as the average loss from bad customer and lets call it x. The % of denied would be = 100*(P/Avg Loss)/400000

I think if we know the % of good and % of bad customers we can calculate the total Profit as P=(% good of 960000 )*(AVg. Rev from good) - (% bad of 960000 )*(AVg. loss from bad) - 1M (from background check) Assuming the average loss per denied customer is same as the average loss from bad customer and lets call it x. The % of denied would be = 100*(P/x)/400000