You ask:
In theory what is 'cheaper': buying a home or building one?
In theory, the cost is the same whether you buy or build.
The broad components are:
- the direct costs (builders, material, fees, etc)
- the opportunity cost of commissioning the building (owner's time used in the process, and other intangibles)
In theory, with perfect information and a free-market economy etc, the direct costs will be equal. Opportunity cost can be very different, but if it's a simple 'yes' or 'no' to a standard model in either case, one can argue that the difference is insignificant regardless of whether the one who commissioned the job was you (in the build scenario) or someone else (in the buy scenario).
In practice, we don't have perfect information, there is non-uniformity in the cost of builders and suppliers, especially when the client is different, and people value opportunity cost differently.
You close your question with this comment:
What I'm looking for is for a simple formula to evaluate if it's more convenient buy or build.
The simple formula is
- convenience('buy') >> convenience('build')
When building, you need local government approvals, you need to deal with builders, and you need to wear the risk of things not going to plan, as well as get involved with contingency plans and delays, etc.
When buying, you see the finished product and just need to hand over the money and go through the settlement process.