Since you did not elect to report this as a like kind exchange - you are going to have 2 assets on the depreciation schedule.
1. Old vehicle with the remaining cost basis $18,615(as it appears) and depreciate it over the remaining life. You may want to rename it to Old vehicle traded in for XYZ vehicle.
2. New vehicle - with cost basis equal to the basis over the old vehicle's carryover basis. Normally the basis in the property is the cost basis of the old property plus any additional amount you pay. Since the cost basis of the old asset is considered separately. The cost basis for new vehicle would be the additional amount you pay which is New Loan amount - the old loan amount taken over for the old vehicle. So the basis would be $36394 - $16,306 (which is the loan from the old vehicle) = $20,088 as this would be the loan pertaining to your new vehicle.
Note that no loss is recognized on this disposition. It is deferred until the new vehicle is disposed off.
Here is an extract from the publication 946 explaining this in detail-
If you acquire a passenger automobile in a trade-in, depreciate the carryover basis separately as if the trade-in did not occur. If the automobile acquired in the trade-in is qualified GO Zone property, the carryover basis is eligible for a special depreciation allowance. See Qualified Gulf Opportunity Zone Property in chapter 3. Depreciate the part of the new automobile's basis that exceeds its carryover basis (excess basis) as if it were newly placed in service property. This excess basis is the additional cash paid for the new automobile in the trade-in.
The depreciation figured for the two components of the basis (carryover basis and excess basis) is subject to a single passenger automobile limit. Special rules apply in determining the passenger automobile limits. These rules and examples are discussed in section 1.168(i)-6(d)(3) of the regulations.
Instead of figuring depreciation for the carryover basis and the excess basis separately, you can elect to treat the old automobile as disposed of and both of the basis components for the new automobile as if placed in service at the time of the trade-in.
Let me know if you have any question.
Please note: This advice is provided with the understanding that all the relevant facts have been provided by you. Any change in facts might affect the advice given and hence may not be relied on in such cases. Nothing contained in this reply was intended or written to be used, can be used by any taxpayer, or may be relied upon or used by any taxpayer for the purposes of avoiding penalties that may be imposed on the taxpayer under the Internal Revenue Code of 1986, as amended.