# The weird math of buying points

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What’s better, buying points for .5 cents each or for .7 cents each?  Obviously .5 is better because it’s cheaper.  What if the points in question were Ultimate Rewards points?  Same answer, of course.  What if you could buy more points at .7 cents each than you could at .5 cents each?  Well, then things get interesting…

This line of questioning is driven by the fact that its possible to earn 5 points per dollar when purchasing \$200 MasterCard and Visa gift cards at office supply stores by paying with a Chase Ink card.  Let’s call this the 5X approach.  Similarly, one can earn 2 points per dollar buying \$500 MasterCard and Visa gift cards at gas stations by paying with a Chase Ink card.  This is the 2X approach.

Assuming the cost to liquidate gift cards is zero, the 5X approach is like buying points for about .7 cents each (due to the card fees), whereas the 2X approach is like buying points for about .5 cents each.  At Staples, the 5X approach is improved considerably by enrolling in Visa Savings Edge which can give you an extra 1% cash back, but let’s leave that off the table for the sake of this discussion.  Also, for the sake of argument, let’s assume that its equally easy to deal with \$200 cards and \$500 cards.  That’s obviously not true, but it is a useful assumption for simplifying the argument to be made here.

Given the price points I quoted about, it appears that buying \$500 gift cards at gas stations (the 2X approach) is a much better solution.  And, for those with an unlimited ability to cash out gift cards with no fee, that’s true.  What if you have a limit, though?

### Assuming \$10K limit

Let’s assume that you are limited to making use of \$10,000 in gift cards in whatever unit of time you’re comfortable with: 1 week, 1 month, 1 quarter, whatever.  Then, we can do the math to see which approach is really better:

#### 5X approach: office supply \$200 cards

• 50 cards
• Total fees: 50 x \$6.95 = \$348
• Total points earned: \$10,348 x 5 = 51,740
• Cost per point: .67 cents

#### 2X approach: gas station \$500 cards

• 20 cards
• Total fees: 20 x \$4.95 = \$99
• Total points earned: \$10,099 x 2 = 20,198
• Cost per point: .49 cents

### When paying more per point is better

To some, it may still look like the 2X approach is better.  After all, you would have paid only \$99 in fees vs. \$348.  And, as a result, your cost per point would be only .49 cents vs. .67 cents.  On the other hand, the 5X approach results in over 2.5 times more points.

Keep in mind that Ultimate Rewards points are worth a minimum of 1 cent each since they can be traded in for cash.  So, the 5X approach is not really more expensive since we can pay ourselves back in points.  In fact, with the \$200 gift card scenario, we could cash in \$249 worth of points to leave us with a total expense of \$99 and still have 26,840 points remaining.  Now, we have the same overall cost as the gas station approach, but by cashing in some of our points we’ve lowered our cost per point to only .37 cents each.

We could take it even further and cash in enough points to fully pay ourselves back for all fees such that we now have purchased points for free.  You can do the same with the 2X approach, but you’ll still have more points remaining with the 5X approach.

By selectively cashing in points, the 5X approach results in more points earned than the 2X approach.  The 5X approach, therefore, is better (aside from the pain in the butt of dealing with many more gift cards).

### Why I care

Often, when evaluating a deal involving earning points by buying gift cards or reload cards, it is convenient to calculate the cost per point to determine how good of a deal it really is.  As I’ve shown here, though, that cost per point calculation can be deceiving.  An approach with a higher per point cost can be better under certain circumstances.

The key is that Ultimate Rewards points can be cashed in for a penny each.  So, anytime you have the opportunity to buy Ultimate Rewards points for less than a penny, you should take it.  When faced with choosing between different price points (all below 1 cent per point), its important to look not just at the cost per point as the deciding factor, but also the number of points that can be purchased with either approach.  Let’s take an extreme example: suppose you can choose to buy 1000 points for only one tenth of a cent each or to buy a million points for half a cent each.  In the latter case, you would come out way ahead despite the much higher cost per point.