What is a BRC card?

What is the rational, mathematical way to calculate the effective cashback rate of a points credit card?

• Consider the Barclay's World Arrival card.  The card awards 2 points per dollar spent. If you redeem these points against travel charges on your statement, you get a value of one cent per point. Additionally, Barclay's gives you a 10% "rebate" on the points. For example, if you redeem 2000 points for a $20 travel charge, the travel charge will be erased from your statement, and Barclay's will give you 200 points back. Take John, a frequent traveler with more than enough expenses to redeem against. Many people would call the World Arrival a 2.222~% cashback card for John: 2% from the base points, and the additional 0.222~% from the "recursive" rebates. Recently, however, The Points Guy blog made the argument that it's actually a 2.27% card: Doing the simple math, it would seem as if your per-dollar return on spending is just over 2.2% thanks to the earning rate and mileage refund (100 cents divided by 90 miles). However, the way you redeem Arrival miles (which I’ll show below) is to actually make that purchase and then redeem your miles for a statement credit (within 90 days) on that purchase. The thing is, you’re actually also earning Arrival miles on your travel purchase at the usual rate of 2X miles per $1 before redeeming points for it. So in effect, by subtracting the 2X miles per $1 from you redemption total, you’re only using 88 miles per dollar – a redemption rate of 1.136 cents per mile. And since you’re earning 2X miles per $1, you are in actually getting a return-on-spending rate of…2.27%. (from http://thepointsguy.com/2014/02/analyzing-the-barclaycard-arrival-earn-ratio-of-2-2-7-when-redeeming-for-travel/) At first glance, this argument made sense to me. I broke it down into a series of simple steps: 1) Spend $10,000 on the card. Get 20,000 points back. 2) Redeem those points against a $200 travel charge. Now I'm left with 2000 points (10% rebate) + 400 points (points earned on the $200 charge itself). 3) Redeem those points against a $24 travel charge. Now I'm left with 200 points + 48 points. 4) Redeem those points against a $2.48 travel charge. Now I'm left with 20 points + 4.96 points. 5) Redeem those points against a $0.2496 travel charge. Now I'm left with 2 points + .4992 points. And so on and so forth with increasingly smaller numbers. At the end, you will have spent $10,000 out of pocket to receive $200 + $24 + $2.48 + $.2496 + ... of value, or approximately $227, which indeed amounts to 2.27%. However, something didn't sit well with me here. Should you really count the points earned on the subsequent charge (against which you are redeeming) as a return on the original spend? It's hard to argue that between step 1 and step 5 above, you have spent $10,000 to receive approximately $227 in value. But what if we made a tiny tweak to the card mechanics: Rather than receiving points that can only be used for statement redemptions, what if we received cash that we could decide to use to pay off credit card statements, the way the Fidelity Amex works? Now our scenario looks like this: 1) Spend $10,000 on the card. Get $200 back. 2) Use that cash to pay my CC bill of $200. Now I'm left with $20 (10% rebate) + $4 (cashback earned on the $200 charge itself). 3) Use that cash to pay my CC bill of $24. Now I'm left with $2 + $0.48. 4) Use that cash to pay my CC bill of $2.48. Now I'm left with $0.20 + $.0496. 5) Use that cash to pay my CC bill of $0.2496. Now I'm left with $.02 + $.004992. And so on. In this case, however, it seems ludicrous to say that I received ~$227 on a $10,000 spend, because from step to step I chose to spend additional money that I had in my pocket. After spending the $10,000, I then chose to spend $200, and then $24, and then... If you factor that in as spend, then you spent $10,227 to receive $227 in value, bringing you back to 2.222~%. So it would seem crazy to factor in the value received on subsequent transactions as a return on the original spend if the card gave cash back rather than points back. And surely a points-only card shouldn't be "rewarded" for being less flexible than cashback cards by boosting its perceived cashback rate. But just when I'm about the conclude that the Barclays World Arrival is a 2.222~% card after all, the seemingly unshakeable logic of the first stepwise list above smacks me in the face. Would you call this a 2.222~% card or a 2.27% card, and can you explain it in a way that might make sense to my brain? (Note: I am purposely ignoring all other considerations here, such as the issuer's limitations on redeeming against partial dollar transactions, minimum redemption amounts, etc. I am only trying to understand the narrow issue of whether the points received on the subsequent transactions against which you redeem should count as return on original spend, and thus increase the effective cashback value of the card.)

• Answer:

  Interesting observation.  The Points Guy made a mistake.  TL;DR, he double-counted points. In your first five-step scenario, supposedly John receives a 2.27% reward by spending $10,000 and getting $227 back.  But Step 2 contradicts that. 1) Spend $10,000 on the card. Get 20,000 points back. 2) Redeem those points against a $200 travel charge. Now I'm left with 2000 points (10% rebate) + 400 points (points earned on the $200 charge itself). For the remitted $200 travel charge mentioned in Step 2, there are two possibilities: A.  The $200 was part of the original $10,000 purchase.  Contradiction: John already received 400 points on that purchase in Step 1.  He doesn't get another 400 points in Step 2, so the reward per dollar spent is overestimated. B.  The $200 was from another purchase, NOT part of the $10,000 from Step 1.  Contradiction: John spent more than $10,000 to get his $227 reward, so the reward per dollar spent is overestimated. Either way, the same issue shows up again for the $20 in Step 3, the $2 in Step 4, and so on.  And either way, if you fix the issue, you get the correct, lower reward: A.  John spends $10,000 and earns $222 ($200 in Step 1, $20 in Step 2, $2 in Step 3, etc.) for a reward of 2.22%. B.  John spends $10,222 ($10,000 plus $200 in Step 2, $20 in Step 3, $2 in Step 4, etc.) and earns $227 for a reward of 2.22%. Credit card companies make this stuff confusing on purpose.  The less transparently points and money are related, the harder it is for the consumer to realize how small the rewards are.  Still, I'm impressed that someone who makes a living by comparing credit cards messed it up.