“We expect customers who do the math to opt for the iPhone,” writes Deutsche Bank’s Chris Whitmore in a note to clients Monday.

Moreover, he adds, so will customers who don’t do the math.

Whitmore’s analysis involves comparing the price, features and total cost of ownership of the refreshed iPhone 4S with its leading competitors.

At $199 with a two-year contract (and $649 unlocked), the iPhone 4S is roughly the same price as the 3G handsets that run Google’s (GOOG) Android OS, and an average of about $60 less than 4G-based phones such as the Samsung Galaxy S 11 ($229 with contract), Droid Bionic ($299) and HTC Thunderbolt ($249).

And total cost of ownership for a 16 GB iPhone 4S, amortized across 24 months, is about $93 per month (450 min, unlimited text and 2GB data plan), roughly comparable to the other smartphones.

Moreover, because Apple (AAPL) is able to command higher subsidies from its carrier partners (about $450 for the iPhone 4 and 4S) Whitmore estimates that the company is making more money per sale than any of its competitors, as indicated by the chart above.

With an estimated bill of materials between $170 to $220, depending on capacity, the manufacturing margins on the iPhone 4S are roughly 71-73%.

That, Whitmore concludes, “should support attractive corporate margins for AAPL for multiple quarters.”

Below: Deutsche Bank’s chart comparing purchase costs and monthly total cost over the course of a two year contract.