What impact does the choice (or lack) of a residual value have on the income statement and balance statement of an entity in the year the asset is purchased?

You need to think about the relationship between the purchase price, residual value, and the depreciation for the asset purchased and how the residual value or lack thereof will affect the depreciation amount. Then you need to figure out how the Depreciation expense will affect the Income Statement and how will the net income flow through to the Balance sheet. Also you will have to figure out how accumulated Depreciation will affect the balance sheet.

One way to solve this is to set hypothetical amounts for different scenarios for the purchase price and residual value and solve for the depreciation amount for year one. Since you did not list the depreciation method to use I would use the straight line and double declining balance method for your scenarios for a few years and solve for year one with a residual value and no residual value. This will show you different depreciation amounts that will help you figure out how this affects the income statement. Then you can figure out how this affects the balance sheet (hint: net income and retained earnings).