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That's not quite right. The disposition fee only applies if he turns in the leased vehicle. Also, the $2k remaining payments shouldn't be treated the same both now and 8 months from now. Here is the situation as I see it. I make the following assumptions to simplify things.
1) Money has no time-value to him
2) His next lease payments will equal his current lease payments
3) private party sale if off the table

Note that all options are computed for 8 months in the future

Option 1: Lease-end disposition into new lease
Remaining lease pmts: $2k
disposition fee: $900
equity: $0
Summary: Spend $2.9k to drive current car for 8 more months and start over. $900 can be saved if you lease at same dealer.

Option 2: Lease-end Buy-out into new lease
Remaining lease pmts: $2k
disposition fee: $0
buy-out: $9500
trade in value: $11k (should be a bit less 8 mo from now)
equity: $1,500 (less sales tax at buy-out)
Summary: Spend (net) $500+(buyout sales tax) to drive current car for 8 more months and start over in new lease.

Option 3: Dealer bail-out now into new lease now
Remaining lease pmts "saved": $2k
8 months of new lease pmts: $2k
disposition fee: $0
buy-out: $12k (remaining lease payments are actually built in here)
trade in value: $11k
equity: -$1,000
Summary: Rolling $1k debt into new lease and $2k of new lease pmts costs you $3,000 to drive a new car over the next 8 months. Of course since we've kept payments the same and you started $1k in the hole, this new car should be cheaper than the one you are getting rid of. This sounds unrealistic.

Conclusion: Clearly Option 2 is cheapest. Options 1 and 3 are very close, but that assumes the fiction that your next car will be cheaper than your current car was. Option 1 doesn't make much sense. The cost of Option 3 over Option 2 (which will end up being at least a few thousand) can be weighed against the desire to get a "better" car now.
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