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Using the example of the proposed Donald Trump Mexico-USA Border Wall; various figures for the estimated cost have ranged considerably.

Mr Trump claims the total cost of the wall will be $10bn (£7.5bn) to $12bn. But estimates from fact checkers and engineers seem to be universally higher. Senate Majority Leader Mitch McConnell estimated it will cost between $12-15bn, as he addressed reporters at a Republican conference in Philadelphia.

Contrasted with

A study by the Washington Post estimated the cost of the president's wall would be closer to $25bn

Another example might be the proposed High Speed Rail 2 in the UK. The Department for Transport initially estimated the cost to be £30 billion; in June 2013 the projected cost rose by £10 billion to £42.6 billion. The Institute of Economic Affairs estimates that the final cost will be over £80 billion.

How do PPO organisations estimate supra-national or excessively large infrastructure projects?

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    Mostly based on politics, with a smattering of greed and a trace of fantasy. There are cost estimation standards (OMB), but political projects cost what politicians say they do. Until the politician is replaced, at which point it is discovered that the prior administration was corrupt and deceptive. – Mark C. Wallace Mar 2 '17 at 14:20
  • As Cornelius Fichtner says in his PMP prepcast... How do you eat en Elephant? One bite at a time!. – Tiago Cardoso Mar 2 '17 at 14:21
  • Guys...if you want to post an answer, post an answer not a com-nswer. – Venture2099 Mar 2 '17 at 16:28
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The U.S. GAO has developed a 440 page guide for cost estimation of Capital Programs

Here is the GAO (Government Accountability Office) Cost Estimating and Assessment Guide - Best Practices for Developing and Managing Capital Program Costs. What they call 'Capital Programs' include infrastructure projects. According to the GAO:

We developed the Cost Guide in order to establish a consistent methodology that is based on best practices and that can be used across the federal government for developing, managing, and evaluating capital program cost estimates.

The ability to generate reliable cost estimates is a critical function, necessary to support the Office of Management and Budget’s (OMB) capital programming process. Without this ability, agencies are at risk of experiencing cost overruns, missed deadlines, and performance shortfalls—all recurring problems that our program assessments too often reveal. Furthermore, cost increases often mean that the government cannot fund as many programs as intended or deliver them when promised. The methodology outlined in this guide is a compilation of best practices that federal cost estimating organizations and industry use to develop and maintain reliable cost estimates throughout the life of a government acquisition program.

However, it is unlikely the numbers that you cited above were arrived at following this rigorous methodology. Most likely, those are 'back-of-the-envelope' calculations.

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