Signing up for a mobile carrier smartphone plan has reached the most advanced stage of capitalism – like hot dog buns and hot dogs. In the US, when you buy hot dogs they come in packs of ten, but the hot dog buns you would presumably put them in come in packs of eight or twelve. Consumers always have to buy an excess of something.

This week I tried to buy a new iPhone. I am eligible for an upgrade from AT&T, but that phrase has lost all meaning. The only obvious* way to do that online is to either buy the phone unlocked at full price, or to sign up for an installment plan. There are two installment plans available: one from Apple and one from AT&T. The AT&T plan is fiendishly convoluted. Under both plans, consumers are eligible for a new phone after twelve months, but using the AT&T plan you get the new phone after 12 months, but you owe them 20 months of payments for that privilege. Stay on that plan for three years and you will be in the hole to AT&T for two years of service.

I admit that I do not entirely understand the plan. I read the fine print on the website, and that just raised more questions than answers. I tried going into the store, but it takes an hour wait just to talk to someone. And as much as I love writing for this site, calling an AT&T customer service line is just asking too much of me.

So I do not know how AT&T expects consumers to reconcile that over-payment option. It could just mean that eventually you do not get an annual upgrade. But it could just as easily mean that at the end of five years on the program you get sent to the Fleet Street Debtors’ Prison.

So I ran the math on the various options. Looking at a 128 GB iPhone 6S (Gold), I compared the prices of all the various options. I factored in things like the $15 “Activation Fee” (again, thank you AT&T), Apple Care (for $129), and then I calculated the discounted, net present value (NPV) of all the options to adjust for timing differences in payments. (If you care, I used a 6% discount rate, just because.)

Below are the results of that NPV calculation:

At first blush, the AT&T Next plan looks like a huge win because it includes a $25 per month saving on the wireless bill. However, I then adjusted that calculation to include the billing for the extra months. So that is 20 months of commitments amortized over 12 months. Strictly speaking this is not 100% accurate because of the timing of payments, but the time value ends up being pretty small relative to the fact that consumers are effectively overpaying by eight months.

For loyal AT&T customers, the kind who have multiple AT&T (i.e. business) accounts, the AT&T Next program may work out. For everyone else, the Apple Upgrade plan wins. However, the upgrade plan is essentially the same price as the no-contract plan (24 payments X $40.75 + Apple Care + Activation Fee = $993, the same as the no contract price). The real difference between the two Apple options is the time value of money and the ability to get a new phone in a year.

Oh, there is one more difference, to get the upgrade plan from Apple you need to purchase the device in the store, and of course, there are no 128GB available any time soon at stores near me.

————————————————————————————————————————————————*  * By Obvious, I mean this is my best guess, because nothing about this process is obvious or easy to read.