I currently use a United Airlines visa card for nearly all of my
purchases, but am fed up with United telling me "no" when I want to
upgrade a class or purchase flights with my accumulated miles. Costco
and American Express are now offering a joint card with no fees, that
will give me cash back for all purchases at any store(not restricted
to Costco). They give 1% back for store purchases, 2% back for
resturants, and 3% for any travel expenses(plane flights,, car rental,
hotels etc).  Since it's very difficult to redeem visa miles with
United for travel, would I be better off to switch all purchases to
the Costco/American Express card and drop the United mileage program,
and then just use the cash back from Costco/American Express to
purchase airline tickets outright?  Please calculate the differences
between the two cards based on $10,000 charged monthly, paid off
monthly(no interest charges).  Retail purchases represent 85% of my
monthly bill(1% cash back), resturants 10%, and travel 5%.  Since I
Don't know what formula United uses to convert miles into purchase
prices, I've decided to give the experts a shoy at it.

Thank you for your interesting question.

I obtained the United point award formula from the following website: 
"Mileage Plus Platinum Visa" United Airlines (2005)
http://www.united.com/page/article/0,1360,3865,00.html.  I assume that
is the card you have since it is the only one that would allow you to
earn miles on $120,000 in annual spending.  It has an annual fee of
$140, and it includes one free roundtrip companion ticket each year.

Its point calculation formula is:

"Earn 2 miles per $1 spent on groceries, dining, gas at the pump and
home improvement purchases
- Earn 2 miles per $1 spent on United and Star Alliance purchases
- Earn 1 mile per $1 spent on all other purchases"

Based on your spending habits, that amounts to (2 miles x 0.10 x
$120,000 + 2 miles x 0.05 x $120,000 + 1 mile x 0.85 x $120,000) =
138,000 miles/yr.  The question is then how to derive a dollar amount
for these.  As this article explains ("Assessing the value of
frequent-flier miles" Joe Brancatelli, USAToday (March 8,
2005)http://www.usatoday.com/travel/columnist/brancatelli/2005-02-28-brancatelli_x.htm),
this is not a straightforward conversion.  I have used the old standby
of $0.02/mile, but you could wind up with less than $0.01/mile or as
much as $0.04/mile, depending on where, when, and in what class you
travel.  So, you should wind up with something like 138,000 miles/yr.
x $0.02/mile - $140 annual fee = $2,620.  However, this could range
from being less than half that to being double that, depending on how
you redeem your miles.  I am excluding bonus opportunities to earn
additional miles, like they are running now, as well as the value of
the free companion ticket.

The terms of the Costco card are "Eligible Purchases earn a rebate of
1, 2 or 3 percent, as follows: 3% at restaurants, 2% for travel
purchases from airline, lodging, car rental, cruise line, travel
agency and tour operator merchants (excluding bus and train travel
purchases); or 1% on all other Eligible Purchases." The terms are
available at  "TrueEarningsSM Card from Costco and American Express"
Costco https://www.costco.com/Membership/amexplat.aspx?whse=BC&topnav=&hierPath=
by clicking on the Terms and Conditions link at the bottom of the
page.  There is no annual fee.  You receive your rebate annually in
the form of a certificate you can redeem for merchandise or cash at
any Costco location.  Your rebate looks like this:  0.03 x 0.10 x
$120,000 + 0.02 x 0.05 x $120,000 + 0.01 x 0.85 x $120,000 = $1500.

So, assuming you are getting $0.0108/mile or better when you use your
miles to buy airline tickets, the United Airlines card is more
advantageous.  Of course, this assumes you can get the flights you
want and use the miles.  Cash certainly gives you a great deal more
flexibility.

I hope my answer helps you to figure out what the best card is for you.

Sincerely,

Wonko

Search terms:  value of frequent flier miles; Costco/American Express
card; United Airlines visa card

Thanks for the prompt amswer, which was clear, logical, and
comprehensive without being too long.