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In Europe, retailers commonly offer cash discounts for up-front payment, as well as interest-free installment plans.

For example, if I'm making a €10,000 purchase, I could pay today and receive a 10% cash discount, or I could pay over 36 months in equal interest-free installments.

What's a reasonable way to figure out if one of these options is likely to offer substantially better value than the other?

Given each potential purchase offers a different cash discount and installment period, I'd like to figure out a good rule of thumb for making these choices. Am I on the right track in thinking I need to estimate the future value of the installment plan and compare to the present value of the cash payment? Is there anything else I need to consider, like fluctuating inflation rates, or the opportunity cost of not investing in the meantime?

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  • There’s an Excel function to determine the net present value of a recurring investment. Sadly, I don’t remember the name.
    – RonJohn
    Commented Dec 24, 2023 at 23:44

1 Answer 1

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Working out the actual cash benefit is easy. Work out how much interest you would receive if you did something else with the $10,000 instead of using it to buy the item. For example, invest it or pay down other debt.

Assume you can get 1.2% on a savings account, or 0.1% per month. In detail you can work out how much each individual payment would earn - so the first payment would be invested for a month and get

 $10,000/36*0.1%=$0.27;

the second would be invested for 2 months

$10,000/36 * (2*0.1%)=$0.54

etc. For a simpler approach just average the amount of time the payments are invested -

$10,000*0.1%*18=$180

So if you were getting more than $180 discount it would be worth paying up front. If you want to be very thorough factor in the tax you would pay on that interest - so if you paid 30% tax the actual benefit of keeping the money would be 0.3 times the above calculation.

If you already have debt that you aren't going to be able to pay down if you pay cash for this item, and the $10,000 could be used to pay down that debt, replace the interest rate in the calculation with the interest rate on the loan you would be paying down. So if you had $10,000 of existing credit card debt at 12% (1% per month) then the calculation becomes:

$10,000*1%*18=$1800

and you should take the installment plan and pay down the debt. Though if you are already in debt you should think carefully about taking on more debt, and only buy this thing if you absolutely need it. You would not need to factor in tax here.

If you don't have the $10,000 and would have to borrow it, work out how much interest you would have to pay to borrow that money using a similar formula.

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