Buying a house vs Building one

There's not a "formula". You need to figure out what house you want to build, get a design, get a quote from a builder (including all of the options you want), add the cost of the land to that quote, and compare with buying an existing house. There are a lot of variables there - how "complex" is the house to build? How expensive do you want the appliances, fixtures, etc. to be?

I will say that it's not always cheaper to build your own house. The main benefit of building your own house is that you can get almost exactly the house you want, but that comes with a LOT of planning upfront, decisions to make along the way, and responsibility if anything doesn't come out how you envisioned it.

It's a long, time-consuming process, it's not an easy way to get a "cheap" house. You might save some money if you pick a pre-designed plan from the builder and let them choose all of the options, but that takes a lot of the fun out of having a new house. And the builder may just mark up the house to market value rather then building it for you for "cost".

The question is "in theory," so the answer may be that custom house building is more expensive in theory than the semi-automated house building by a professional homebuilder, even including the professional homebuilder's profit.

However, if you enjoy the process of haggling with landowners, lenders and contractors, getting government approvals and wrangling the contractors, then you could value your time at zero and come out ahead. Some people do genuinely love this stuff and it could count as a beloved hobby for them.

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.

In theory what is 'cheaper': buying a home or building one?.

Usually building a house is slightly (but not much) cheaper due to several reasons:

• You need to purchase the land to build the house on at some cost. As you are going to build a house on the land anyway, you know you have a use for it. A company that builds houses for sale later doesn't know whether they can sell the house later at a price which funds the purchase cost of the land. The cost of houses is at all times defined as the cost to build plus the cost to purchase land. In housing shortages, the costs usually capitalize to the price of land, so that in populated areas the price of land is defined as whatever house buyers are willing to pay minus the cost to construct. If there's housing shortage, price of land is sky-high and the company constructing houses does not know whether price of land is going to increase or to crash. They have to account for all possible risk.
• You pay incrementally if building. Thus the sum of all payments does not include the time value of money. Now of course if you include the time value of your money in your calculations, then this does not apply. However, usually a typical bank loan is cheaper than the cost of equity for large companies so even if you include all interest costs, your effective interest rate may be lower than for big companies.
• If something unexpected happens during building, you are the one who pays. Most likely nothing unexpected happens, so it's cheaper to build than to buy. However, there's always a risk that something unexpected happens. When you buy a house, you are essentially paying for an "insurance" about the unexpected things, and insurance always has a cost higher than the expected payout from the insurance.

However, do note I'm not arguing which is 'better': buying a home or building one. I'm only arguing which is 'cheaper' on the average. For someone who doesn't have a lot of money and needs to take a loan from a bank for the house, it very well may be 'better' to just pay extra and buy a home, than to take all the risk involved in building a home. Much like it's better for a property owner to have insurance than to put some saved money aside from which unexpected damages will be paid. However a large real estate investment company owning hundreds of thousands of houses will probably not find it useful to purchase any kind of insurance. They are effectively their own insurance company.

And also, when building instead of buying it's all too alluring to do a lot of customization. All of that has a cost, so my comparison is for constructing according standard already designed plans instead of according to custom plans.

It's much cheaper to buy a house than build one. Modern house builders take lots of shortcuts to try to make their products competitive with older houses in price and the result of this is that modern houses are much lower quality than houses made in the 1950s or before. The only houses that are worse than the houses now are houses built in the 1970s. Never buy a house built between 1968 and 1978. Houses built in the 1990s will be higher quality and cheaper than anything you could build now.

Also, building a house takes at least a year, if you can even find the workers. Due to government free money it is hard to find people willing to work, especially on manual labor jobs, so cost of construction is astronomical right now as well as being slow.