Let’s assume XYZ has a project with a capex of $500M and they have spent about $50M of that budget, so $450M remains in capex. Do you make these changes when calculating NPV? So let’s say discounted cash flows come to $1 billion, then you subtract $450M from that to get overall NPV of $550M? Does that make sense?
Or it remains $1B subtract the $500m so NPV of $500M?
Have they made the decision to do the project, or not? Was the $50M spent before or after the decision was made?
Decision is made to progress with the project. $50m spent after the decision to construct the project.
Then it’s part of the project cost.
So you do subtract $50M from the $500M? 
No. It’s part of the project cost.
I think you must have a disbursement schedule of your capex so they are inside the cash flows when you calculate NPV.
Let’s say your CAPEX schedule is 50, 250, 200 for t = 0 to 2, so your cash flows start at period t=1 and the t=0 is the initial investment amount with -50.
So when you calculate NPV you is cash flows present value + (-50M) in this case. But if the 50 is on t=1 or further the amount must not be deducted.
What if the company (gold miner) is nearing production (next month or so) and says CAPEX spent to date is $400 million and they need to spend another $50 million before they can start production. However, initial capex was $300 million. How do you account for that in NPV? Do you use $450 million oppose to the $300 million since $450 is way over the initial estimate?
If the costs are relevant(Relevant Costing) to investment projects, then they will be included in NPV calcuation I guess. For instance, any costs related to research done to analyze whether the project is feasible or not will not be included in NPV calculation as these costs are sunk and have no oppurtunity costs.