If you have liability
coverage on your vehicle, which your state
requires, the damage will be covered. However, if you file a claim you will most likely suffer a rate increase for what your car insurance company would consider an at-fault accident. In California in 2017, the average rate increase after an at-fault accident was around 39%
. Now, you need to consider this over 3 years, as that's how long it will stay on your insurance record. I would recommend getting an estimate for the damage to the fence prior to taking out a claim. Then you can compare the value of the claim compared to the value of the premium increase. Whichever is less financially difficult, do that.