When calculating NPV, many text books indicate that the after-tax cash flows should be used. Does this apply to the Initial Investment.

For example - if required $50,000 for a project that produced annual cashflows of $65,000 for three years (9% WACC) (40% tax rate) then does the $50,000 get reduced by the taxes or just the annual cash flows. Why or why not?

No and yes. No, not directly... the key to any PV work is getting all the expected cash flows scheduled out accurately, and that 50k should stand as-is, as an immediate outlay, in that schedule.

But the cost of the asset might give rise to tax-deductible depreciation deductions, in which some or all of the cost is deducted against taxable income over a prescribe time frame. It depends on a lot of factors, including the nature of the asset.

If so, then you'd want to include the resulting tax savings (as positive elements) in that same cash flow schedule.