The actual cash flows are reduced by the $10,000 but the taxable income is not reduced by the $10,000. As a result the tax benefit of depreciation is only $1,376 as opposed to the $4,176 benefit above. Still a great benefit, but not as great.
The takeaway is that depreciation is not a free lunch. Real Estate investors need to set aside funds to cover both expected and unexpected capital improvements.
Notice that land is not depreciated
The value of land is not depreciated. Theoretically the usefulness of the land cannot be used up. Even if a building was lost to fire the land would still be there and have the same value as before.
The fact that land retains its value while buildings depreciate is why single-family homes usually appreciate faster than condominiums. A higher percentage of the purchase price of a condominium belongs to building vs. land. A condominium owner shares the same plot of land with all the other condo owners in the building. On the flip side the value of a single-family home is mostly in the land that it sits on. The single-family homeowner owns the entire plot of land and thus benefits more when the value of land increases over time.
This is the reason why the cost to own a single-family home in Seattle and other coastal cities with acute land constraints is so expensive compared to rent. A substantial portion of the purchase price of a single-family home is for the land it sits on. Often times the value of the building you are buying is close to the actual cost to build a building.
For example a 1,800 square foot single family home in my neighborhood recently sold for $925,000. The county record has the land value at $580,000 putting the implied building value at $345,000, or $191 per square foot. It costs well over $191 per square foot to build a house. By this metric single-family homes in Seattle are actually quite inexpensive!