For example, if you’re debating whether to use a 2% rewards credit card or to use BNPL and keep the difference in a savings or money market account for 90 days, the latter strategy only wins if that account is yielding more than ~8%. Or if you’re deciding whether to use BNPL to let you pay down other debt a little faster, it’s only worth it if the interest rate on that debt is above ~8%.
Does every cash purchase also have an infinite APR? Because there I’m paying $200 for nothing. If that’s not logical then where does it start being logical?
a) pay with a 2% reward credit card
b) pay with BNPL scheme with a 3 month term.
In the scenario a) you effectively paid $98 right away and in the scenario b) you pay $100 but after 90 days (let's say you don't have monthly payments for simplicity). For b) to be no more expensive than a) you need a way to make at least $2 from a $100 investment in 90 days. This means that whatever investment you make with the $100 has to yield 8% annually. Even though you withdraw money after 90 days.
If you have monthly payments you need even higher yield to compete with the 2% reward. E.g. if you pay $33.33 every month then you need to make 1% yield per month to collect $2 off your initial $100 in 3 months: you get 3 months of yield from the final $33.33 payment, 2 months of the previous payment and 1 month of the first payment for total 6 months yield from $33.33. That's 12% annualized yield.
Scenario 1: You use a credit card with a 2% cash back reward to make the purchase. You immediately pay off the credit card balance and claim the $20 of rewards. Your net cash flow is -$980 at time 0.
Scenario 2: You buy a 3-month zero-coupon CD for $980 today, and then use 3-month BNPL to make the purchase. In three months, the CD earns $20 of interest. You cash in the CD for $1000 and then use that $1000 to pay off the BNPL. Your net cash flow is again just -$980 at time 0.
The annual effective interest rate yielded by the CD for scenario 2 to work out exactly as described is roughly 8% (actually around 8.42%).
You’re incorporating a theoretical (and unrelated to 2% credit card rewards) interest rate into your calculations. I could easily say a CD yields 10% and this is a 50% APR then.
EDIT: Maybe to help you think about this: this is a purchase loan. It is not a cash loan. You got $1k worth of goods for $1k dollars. You can make arguments about opportunity costs, but that’s different than the traditional concept of APR.
EDIT 2: I’m posting banned but indulge me, what’s the APR of cash purchases?
Don't think of equalizing the terms by extending the BNPL. Think of equalizing the terms by shortening the CD.
> You’re incorporating a theoretical (and unrelated to 2% credit card rewards) interest rate into your calculations. I could easily say a CD yields 10% and this is a 50% APR then.
I'm not claiming that the ~8% interest rate is real. My calculations mean that if you can get that rate or better, then you should use 3-month BNPL, and if you can't, then you should use your credit card with 2% cash back instead.
> EDIT: Maybe to help you think about this: this is a purchase loan. It is not a cash loan. You got $1k worth of goods for $1k dollars. You can make arguments about opportunity costs, but that’s different than the traditional concept of APR.
I fail to see how that makes any difference.
> what’s the APR of cash purchases?
It's either the highest APR of any of your debt, if you have any, or the risk-free APR you could get from a savings account otherwise.
Yes, by your logic it is literally an infinite APR. $200 numerator / 0 years denominator. Doesn’t that imply that maybe your formula has some holes in it and this is a fundamentally different transaction (a take rate rather than an interest rate) than what you’re characterizing it as?
You get $200 rewards on a $10k purchase.
In no world do you get $800 on $10k. You only get $800 on $40k because the 2% isn’t a rate in principle so 8% literally never happens.
I love your chutzpah, but you don’t get to do that math that way. The 2% doesn’t compound, it’s a one-time thing (unless you’re continually rolling over your BNPL purchases)