Finance: buy-now-pay-later in the time of inflation

23 April 2022

In a time of high inflation, if one can pay the same amount later it makes sense to do so, because inflation means that some quantity of money is worth less in the future.

Consider a common payment structure offered by one of the newish buy-now-pay-later companies, which offers a split payment without charging interest.

For a purchase of value 1, repayments are:

  • 13\frac 13 at the time
  • 13\frac 13 1 month later
  • 13\frac 13 2 months later

Let’s assume that payments are made with a credit card where the balance is paid at the end of a given month. On average, spending will be in the middle of the month, and so we can assume the balance is on credit for half a month. We then have:

  • 13\frac 13 1/2 a month later
  • 13\frac 13 after 1 1/2 months
  • 13\frac 13 after 2 1/2 months

Assuming inflation at 8%, how much would we save?

Our discount rate is (11+r)t/12(\frac{1}{1+r}) ^ {t/12} where rr is rate of inflation and tt is time period to in months, so the present value of our payments become:

  • 13×(11.08)0.5/12\frac13 \times (\frac{1}{1.08}) ^ {0.5/12}
  • 13×(11.08)1.5/12\frac13 \times (\frac{1}{1.08}) ^ {1.5/12}
  • 13×(11.08)2.5/12\frac13 \times (\frac{1}{1.08}) ^ {2.5/12}

Or, spreadsheet-style:

Payment Timing (months) Discount rate Present value
First payment 33.3 D+0.5 0.9968 33.2
Second payment 33.3 D+1.5 0.9904 33.0
Third payment 33.3 D+2.5 0.9841 32.8
Sum 100 99.0
Implied discount 1.0%

Clearly, if at any point one pays interest this does not work. But if one can avoid that, it becomes a 1% discount on the price of consumer goods, and so it makes sense to do that if you can.

And so if the consumer can pay these charges without recourse to credit with interest, and they are rational, they will do this.

Homo economicus could very well then lead to more articles along the lines of Klarna and fintech peers fuel fears of fresh wave of retail debt in the FT.