It depends on exactly what the funds were used to pay. If it was actually a 'buy up' in your exchange (your New Property cost more than you sold your Old for), the answer is easy – you treat the additional cash part as you would a new addition to an existing property. In other words, you treat the amount of the buy-up the same as you would the cost of a capital improvement. The date placed in service becomes the starting point for depreciation to begin on the buy up portion.
If none of the loan was considered a buy up then only the interest would be deductible as a rental expense in the 1031 exchange.
The basic concept of a 1031 exchange is that the basis of your Old Property rolls over to your New Property. In other words, if you sold your Old Property for $100,000, and bought your New Property for the same, your basis on the New Property would be the same. Your depreciation schedule would be exactly the same! In other words, you continue your depreciation calculations as if you still own the Old Property (your acquisition date, cost, previous depreciation taken, and remaining un-depreciated basis remain the same). You can re-name your property and keep good records for the tax free exchange because you will need them when you sell.
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