Lets say you got cancer and died. You just saved the health care system millions in end of life costs. Nursing, medicine, stents, surgery, all of that is not needed anymore. So in that case, preventative medicine cost more money.
I went over that. But let's say I get cancer and am cured. Then I incur the costs of curing my cancer AND my end of life costs. What about then? That's why you formula is too simplified. You are confusing a lot of things, such as
a) Treating cancer caught early is preventative care. Testing for cancer is preventative care, not treating cancers caught early.
b) Anyone who gets a disease who hasn't done any preventative care will die. My dad did basically everything wrong in terms of prevention. He had a heart attach, but guess what, he didn't die. Now he has the cost of a heart attack AND end of life costs on his tab. How would have quitting smoking and jogging increased his lifetime health costs?
Also, you're still purely looking at things from an outlay perspective. What about the lost value to the economy of someone dieing early? How will that be replaced, even if costs aren't 'reduced'?