Posted by sirtheta on January 10, 2017
Credit Card Review Arrival+ Card

Published on January 10th, 2017 | by sirtheta

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The Arrival+’s 2.1%, or: Why a 2% card is better

Hot on the heels of my post analyzing the 50% Airline Bonus for the American Express Business Platinum, I’d like to delve into the Arrival+ and a common misconception: that the card earns 2.1x miles on all purchases due to the 5% rebate on miles when you redeem points.

The Arrival+’s signup bonus is still quite good, but the Arrival+ is in no way worth keeping as a daily driver, as it presents a truly abysmal value compared to a 2% card.

This post tends towards very math-y. However, you can skip all the math and get some good mileage out of the optimal breakpoints tables if you’re an Arrival+ cardholder.

How does redemption work?

In order to redeem your points at 1 cpp, you must redeem a minimum of 10,000 miles against a charge that codes as travel and is at least $100. Any redemption over 10,000 miles must be in increments of 5,000 miles, or a full charge’s value in miles ($211.46 charge = 21,146 miles). Note that I am disregarding, for convenience’s sake, the effect of additional minimum redemption thresholds greater than 10,000 miles, which would really hurt you. Because you get a 5% rebate on miles redeemed, the card is often quoted as earning 2.1x miles on every purchase.

Where’s the 2.1x?

Since we want to determine the earn rate of the Arrival+ for every day use, we will disregard the signup bonus.

Starting at a balance of 0 points, you put exactly $28,000 dollars on your Arrival+ in 6 months, and earn 56,000 points.

As discussed at Loophole Travel, there’s a bit of a calculation involved to obtain the optimal redemption because you are getting 5% of your redemption back and you need at least 10,000 miles to redeem again. It depends on whether you are (a) cashing out your balance on existing charges or (b) adding new travel charges to cash out your balance.

(a) To achieve optimal redemption, {Total Balance} – {Redeemed Balance} + 0.05 * {Redeemed Balance} = 10,000, which re-arranges to: rounded down, redeem ({Total Balance} – 10,000) / 0.95 miles.

(b) To achieve optimal redemption, {Total Balance} – {Redeemed Balance} + 0.05 * {Redeemed Balance} + 2 * {Future Purchase} = 10,000, which re-arranges to: rounded down, redeem ({Total Balance} – 10,000 + 2 * {Future Purchase}) / 0.95 miles.

Let’s assume option (a) is possible with your 56,000 miles, as you recently made a $500.30 travel purchase. 46,000 miles / 0.95 means you would want to redeem 48,421 miles to be left with exactly 10,000 miles. Alas, the strictures of the Arrival+ redemption program prevent you from doing so because you must redeem in increments of 5,000 miles if not covering the full value of a charge. You instead redeem 45,000 miles, leaving 11,000 miles in your account and getting a redemption bonus of 2,250 miles—a total of 13,250 miles left. You can now either spend $875 and redeem 15,000 miles or redeem 10,000 miles.

As spending $875 presents the best earning option, you does so: you’ve spent $28,875 on the card, redeemed 60,000 miles against $600 in travel charges, and have 750 miles in your account. You’ve done about as well as possible and earned $600 / $28,875 = 2.0779% cash back. Because the balance is so low, I have valued the 750 miles at $0 (you need 5,000 miles to redeem miles at 0.5 for a cash back statement credit).

If you don’t choose to spend another $875, however, and redeem 10,000 of your 13,250 miles, you’ve has spent $28,000, redeemed 55,000 miles against $550 in travel charges, and have 3,750 miles in your account. Even counting the 3,750 at 0.5 cpp (as it is close to the 5,000 mile redemption mark for a 0.5 cpp cash back credit), you’ve done remarkably poorly and only earned $568.75 / $28,000 = 2.03125% cash back. (if you take out the 0.5 cpp valuation of the miles currently in your account, you’ve only earned 1.9643% cash back. yikes!).

Optimal breakpoints

Naturally, the next question is what point values in your account are “optimal”, in the sense that you should be able to redeem them for maximum cash back (nearest 2.1%) without spending additional money. Thus, we define maximum cash back as an initial balance from which you can redeem integer multiples of 5,000 miles and wind up with 10,000 miles left. As it turns out, this is fairly easy: it is numbers of the form 4,750 * n + 10,000, with n > 2. The derivation of this formula is left as an exercise to the reader; n > 2 because lower values cannot leave you with 10,000 miles remaining.

Note that we are ignoring redemption options that do not involve multiples of 5,000 miles, even though it is possible to redeem your miles in non-5,000-mile increments if you are covering a full charge and it is possible to calculate an optimal breakpoint with that redemption. (see Update)

nInitial MilesMiles to RedeemnInitial MilesMiles to Redeem
324,25015,0001267,00060,000
429,00020,0001371,75065,000
533,75025,0001476,50070,000
638,50030,0001581,25075,000
743,25035,0001686,00080,000
848,00040,0001790,75085,000
952,75045,0001895,50090,000
1057,50050,00019100,25095,000
1162,25055,00020105,000100,000

You will notice the gap between the initial miles and the miles to redeem narrows as the initial miles increases; the two values converge at 200,000 miles (as 5% of 200,000 is 10,000).

There are several important takeaways from this table. First is that the worst possible redemptions are when your balance is just lower than the initial miles column (but the good news is that it’s easily fixable by redeeming the “miles to redeem” column and spending enough to get to an optimal breakpoint). We’re talking 1.9277% cash back bad, in the case of 62,249 points and no more incoming. Second is that being halfway between an optimal breakpoint sucks, as you are +/- spending $1,187.50 from an optimal breakpoint. Third is that you do not need to start with 105,000 miles to ultimately redeem 100,000 miles and have 10,000 miles left over—all that is necessary is that you spend $52,500 on the Arrival+ (earned 105,000 miles) and have redeemed in increments that add up to 100,000 (say, 15,000 + 20,000 + 30,000 + 35,000 miles).

The most important thing to note is that you have not achieved the maximal cash back of 2.1% until you have spent $100,000 on the card (as you would have 200,000 miles, and redeeming all of them would leave you with 10,000 miles). Converting the above table to money spent ({initial miles} / 2) and travel credit redeemed ({miles to redeem} / 100 + 100), we can find the percent cash back rate of the card at the optimal breakpoints. For this exercise, the 500 miles remaining in your account after redeeming 10,000 miles are valued at $0. Were they to be factored in at 0.5 cpp, the values would be bumped up slightly and the card would earn 2.1025% back when spending $100,000.

If you have redeemed for a full charge (i.e. not redeemed in 5,000 mile increments), your cash back rate will fall somewhere between two consecutive cash back rates in this table; in other words, it is bounded by cash back values for two consecutive “optimal breakpoints”. (see Update).

n$ Spent$ Redeemed% Backn$ Spent$ Redeemed% Back
3$12,125$2502.0619%12$33,500$7002.0896%
4$14,500$3002.0690%13$35,875$7502.0906%
5$16,875$3502.0740%14$38,250$8002.0915%
6$19,250$4002.0779%15$40,625$8502.0923%
7$21,625$4502.0809%16$43,000$9002.0930%
8$24,000$5002.083(3)%17$45,375$9502.0937%
9$26,375$5502.0853%18$47,750$1,0002.0942%
10$28,750$6002.0870%19$50,125$1,0502.0948%
11$31,125$6502.0884%20$52,500$1,1002.0952%

Comparison – flat 2% card

With an annual fee of $89, the extra 0.1% (theoretical) cash back would require you to spend $89,000 to equalize with a flat 2% cash back card. With the nearest optimal breakpoints of $88,125 and $90,500 in spending giving 2.0993% and 2.0994% cash back, respectively, the value is actually closer $89,500 (admittedly—a small difference when we’re talking about $89,000 in spending!). In other words, for every $100,000 * n you put on the Arrival+, you get $11 + $100 * n more $ than if you had used a flat 2% card.

If you’re going to drop $100,000+ on a single credit card per year, there are better options with a lot less hassle (you certainly don’t need a table of optimal breakpoints to redeem cash back on the Fidelity Visa). The Arrival+ is like the plague: you should avoid it.

Except for that sweet, sweet signup bonus, of course.

Concluding Unscientific Postscript

If you spend $2,000,000 on the card, you can redeem all your miles twice, for a 2.105% cash back rate (+5% of 0.1%); if you spend $40,000,000, you can redeem all your miles three times, for a 2.10525% cash back rate (+5% of 0.1% and +5% of 5% of 0.1%), etc. For every twenty-fold increase in spending, you get another +5% on the last marginal increase in cash back.

Update

I have updated this post to reflect the fact that you can redeem in non-5,000-mile increments if covering a full charge. Ultimately, it doesn’t change any of the cash back rates or conclusion, so I have kept the 5,000 mile convention out of convenience (because it’s very easy to determine the closed form solution in this case). The thing that happens is that the points in the table serves as endpoints on a continuum instead of discrete points. Using a value from the comments, here is a quick example for proof: redeeming 21,146 miles for a $211.46 travel charge.

In order to wind up with at least 10,000 miles left, you would need to start with 30,089 miles (spent $15,044.50). You will have then redeemed $311.46 against $15,044.50 in spending: 2.0703% cash back. Note that 30,089 initial miles corresponds to 4 < n < 5, just as 2.0703% corresponds to 4 < n < 5.



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Joe
Joe

If I have a $308 travel charge … I can apply 30,000 pets against the $300 but not 30,800?

mastervk
mastervk

I was able to apply my miles for $273 charge.

Ken
Ken

Provided you have enough points you can redeem down to the penny. So a $100.08 charge would take 10,008 points successfully.

Jack
Jack

A tip for getting close to clearing out all your remaining points when you plan to close the card soon: points from refundable travel charges hit your point balance quickly after they’re made.

Apple
Apple

There is one overlooked aspect in all of this…a product change. Those last 500 miles can be redeemed at 1 cpp on conversion to the Barclay Rewards MasterCard (2% at grocery stores among other categories). Currently you’ll get 1000 miles just for doing so and making a single purchase! Redemptions start at 2500 miles on this card at 1 cpp. So one 500 VGC at a grocery store and you’ll hit the 2500 threshold, cash out the miles, and close the card.

Kevin
Kevin

This option may or may not be available much longer, since the Rewards card is now closed to new apps. It’s unclear how long they’ll continue to allow PCs, but probably not for too long.

Apple
Apple

You can always downgrade to the normal Arrival Card, and get similar math in the process. If you aren’t keeping the card anyway, and waiting a month or so to re-sign up…why not?

Alex
Alex

I have an Arrival+ and you are able to apply a custom amount of points for charges. I wiped out a charge of $211.46 with 21,146 points last week.

I was not able to choose the exact amount of points but it offered me the option of using 15000, 17500, 20000 or 21146 when I was redeeming.

pizzywoah
pizzywoah

When did you get your card?

Sikachu
Sikachu

Seconded Alex. I had a charge at $542 that I could redeem 54,200 points against it. But yeah, it will dependa if you could find a charge that is very specific like that.

For me, for the sign up bonus, I was able to find a charge for $570 which I redeemed about 57,000 points (56,000 + 11,400 points from that $570 charge) and I am done with it. Good enough for me. me.

Yehuda J Katz
Yehuda J Katz

Thirded. I just erased a charge of $187.44 for 18,744 points.

Ben
Ben

I’m gonna ask a stupid question….
Say I have 57k pts. I book a refundable Expedia hotel for $565. I then use my 57k points to redeem against the charge, which is effectively a statement credit bringing my Current Balance to $0. Then I cancel the hotel booking and Expedia refunds me $565. My Current Balance will then be -$565.

Will Barclays send me a check in the mail? Is it automatic? Or do I need to call?

Mike L
Mike L

I’m also curious as to whether they would catch on to the refund or not. As a DP, with the CSR, they do not pull back the $300 travel credit when the refund is issued. Regarding refunds, this is some useful information about refunding credits on https://www.helpwithmybank.gov/get-answers/consumer-loans/refunds/faq-consumer-loans-credit-balance-refund-02.html

Alex
Alex

I kind of got lost in the math mentioned above. I use this card for our daily charges and I do think it is the highest reward points card available in the market (that does not have a gazzilion restrictions). We do charge roughly $100,000 (tuition, company expenses and household expenses) on the card and I do earn the 2.1%. I’ve vetted the calculation a million times and in my opinion, this is the best card out there offering convenience and highest rewards

Kent C
Kent C

Not bad if you are redeeming for travel and if you don’t want to use multiple cards. I used the arrival+ for about 3 years as my go to in between promo bonuses. If you don’t do new cards with promos, this is a decent card. However, there are others that give 2% on your stmt automatically such as Fidelity, Capital One business, etc. If you spend a lot at Amazon, like I do for my business, you can get 5% cash back automatically.

Ian
Ian

excellent post. great presentation of the math

Patrick
Patrick

Keep in mind this was until very recently the only 2.x% CB card with no FTF and ran on the MC network (which generally gets the best exchange rate).

A great card for international non bonus spend.

Now that the Cap One Venture is a MC, it might have some competition. However the Cap One doesn’t support Chip + PIn as.secondary CVM. So the Arrival+ definitely fits a niche.

Ian
Ian

For points, I would choose Bank of America Travel Rewards (if you have at least $50k in Merrrill Edge investment for Platinum Preferred Rewards) over Arrival. It’s a toss up between Arrival and Capital One Venture card.

since when did Cap One Venture change from Signature Visa to World Elite MC?

Andrey
Andrey

It was very short-lived. I got one in December 2016, but they switched back to Visa after that.

Chris M
Chris M

This is a great post!

I got this card for the signup bonus years ago and back then, if I recall correctly, there was a 25% bonus on points redeemed for travel, not 5%. This was also before the Citi Double Cash card existed. When it came time for the second annual fee, I redeemed as much of my points for travel as I could (probably around $400-450 worth) and downgraded to the basic no-fee arrival card. The no-fee arrival card allows point redemption into a statement credit, but I think the minimum amount of statement credit you could get was $25, so 2,500 points. Thanks to the 5% bonus, I had 2,000-2,250 points left. I was done with the card, but those points were useless until I got up to 2,500 to redeem them. I spent the required $250-$500 on the card and redeemed the 2,500 points for a $25 statement credit. I carried around the card for several months in my wallet to be used as a de facto $25 gift card, but kept forgetting about it. Then one day, a $25 check from Barclays showed up in the mail. I’m glad I caught it because that solved my problem of never getting around to using the $25 credit on my account.

Margaux
Margaux

This was a wonderfully timed post–I just finished the min spend on my card last week, and I have just over 57,500 points in the account. Thanks for doing the math for calculating the optimal redemption strategy so I didn’t have to :).

Waingro
Waingro

Additional increment of 5,000 point requirement is wrong as others have pointed out. You should really get the card for that sweet 50,000 bonus and then try it out yourself!

ABC
ABC

“If you’re going to drop $100,000+ on a single credit card per year, there are better options with a lot less hassle ”
Only referring to other 2x cards? Or do you have something else in mind?

Sam C
Sam C

Great post and perfectly timed for me as I’m trying to simply my wallet and minimize AFs right now.

I geeked out on this and found another couple of important formulas. If you’ve got an A+ with no existing charges and want to cancel, you’ve got two choices. You can make a single charge/redemption or, if your balance is high enough, optimize things by making 2 charges and redemptions.

If you want to make a single charge, the best charge to make is B/98 where B is your balance.

If you have over around 19,300 points, two stage is a better option. In that case you want your first charge to be (B-10,000)/93 and your second charge will be around $102.

I made a spreadsheet to make this all easy to figure out. It even shows the savings of the two stage model over the simple model. Check it out here:

https://goo.gl/gHpsZa

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