You should never pay more than invoice for a new car. For that matter you should never buy a new car, it doesn't make economic sense.
You can get a much better deal by just buying a used car. Try saving 90%, not 20%.
When comparing to the cost of a new vehicle, it's very hard to spend more on an older used car no matter how badly you screw up. Even if you have to (or choose to some degree to proactively) immediately replace just about everything but the engine you're coming out way ahead compared to new cars. In fact, you can probably replace the engine too and still spend less.
I know some people like the idea or feeling of new, but that's all it is: an irrational feeling, not one backed up by data in terms of a new car being more reliable than a well maintained older one (obviously a poorly maintained car will be less reliable regardless). In fact I feel safer in a well maintained car that's been around long enough that any major recalls, etc have already mostly been found and suffered through by the guinea pigs who insist on buying new.
People repeat this a lot, but it isn't that cut and dry.
People often ONLY include the direct cost of the two vehicles. They don't include the massively discounted loans on new vehicles (e.g. 0% APR), the warranties (e.g. 3-5 years bumper to bumper), sometimes better MPG (newer model, etc), cheaper insurance, skipping state inspection for the first three-five years, new tires & other consumables, et al.
Obviously you have to look at specific vehicles to know for sure; but when I last looked at exactly this (recently used Vs. new) without the externalities it was approx $2-3K cheaper (talking CarMax, non-negotiable pricing) but after factoring in all the things listed above it was damn close (within $500-800).
And as you go more used are you really getting a deal or just exchanging miles/wear&tear for cash? The asset also has depreciated in value by then.
Just to be clear, I am simply saying you have to look at each vehicle one by one, a lot of models/manufacturers depreciate at varying speeds (e.g. a Kia depreciates a lot faster than a used Toyota or Honda).
Just to be clear, that's a GOOD thing. You want depreciation to happen NOT on your watch, BEFORE (or after) you own it.
Something that starts at $20,000 will lose a lot of value on your watch pretty quickly. Something that starts at $2,000 has already lost most of its value on someone else's watch and by the time you sell it you may only have lost say, $500 on depreciation. There's just not as much room to go down, and frankly if you keep replacing parts you can usually keep it going very economically for hundreds of thousands of miles, till the engine fails and needs rebuild/replace.
It takes a hell of a lot of savings on all those things you listed to make up the $18,000. It is especially common for people to way overpay for better MPG, when it would take decades to make it back (by which time they have another new car again)
It probably also makes no economic sense to shop at Macys rather than Goodwill or to buy a house rather than a shack. People pay more for things they want.