I rent out two rooms in my home through Airbnb and use my car to pick up room supplies and repair materials. Is it appropriate for me to deduct the cost of repairs to the vehicle?
Is it appropriate? Sure. Is it worth it? Not at all. In fact, you're probably wasting your time for not one penny of gain, and more in taxes when you sell or otherwise dispose of the car or "close" the rental business. You're talking such a minuscule amount of miles driven "for the business" when compared to the miles driven for personal use, that it probably won't even amount to one percent. So in my opinion (and we all know what opinions are like) you're wasting time, paperwork and effort for absolutely nothing.
You can claim the the stuff you purchase for repairs and maintenance already. So that "should" more than suffice. Of course if audited, you may need to prove to the IRS the "repair/maintenance" expenses you paid were for the business, and not for personal use areas of the house. Generally the chances of an audit are low. But still.............
