Here is the way I think you have to approach this problem.
[Correcting this a 2nd time.]
1) VW was a ~$90B company until just before this scandal according to this chart - I'm assuming that the chart was in $USD. IMO, no settlement can come in at above 1/2 of that or the company is dead.
https://ycharts.com/companies/VLKPY/market_cap
2) Here's a rough back of the envelope calculation of the cost of a buyout of all the existing cars.
a) Find the rough value of all those cars according to Kelley BlueBook. A 2009 TDI sportwagen has a Kelley BB value of ~$9.5k, and a 2014 TDI sportwagen (like mine - e.g. with sunroof and stick) has a Kelley BB value of $24.5k. Average those two is $17k. I know that not all of the diesels that were sold were Tdi sportwagens, so say the average TDI worth is ~$15k.
b) $15000 * 500000 cars = $7.5B charge-off. That's still do-able and could be ammortized on the balance sheet over a few years.
c) If offered 150% or 200% of KBB for a trade-in, many people would take the trade in. VW could modify the cars traded-in and sell them abroad (at a loss, but still not a total write-off), possibly with the mods (urea injection into the exhaust + urea jug in the storage area in the rear + extra catalytic converter to process the ammonia in the exhaust that the urea converts the NOx into).
d) Offering a generous trade-in also helps increase sales, which partially offsets the loss.
If a software fix is possible, then you're compensating people $3k-$10k per car in the US (i.e. $1.5B - $5B - this range is just my wild guess) for the decreased value in their car both in terms of resale value and in fuel economy. You have to be a bit generous here because this is a big scandal and your reputation is at stake.
The trouble is that: a) VW could face fines from the US AND Europe AND other countries. That cuts into the amount that they can offer in terms of a settlement. b) The above was just a rough calculation for a car buy-back for US cars. Settling for any portion of the other 11M cars out there worldwide obviously causes much larger scale headaches financially, and limits what can be offered in the US and those other countries.
I think that VW will have to offer a combination of the two and offer us either a cash settlement, or a very generous trade-in value.
