What is the actual discount? Doing the math for coupons and sales that sound better than they actually are

image credit: CosmicKitty

I remember when discounts were easy to understand. Most stores would have sales like “25 percent off” and that would be that. Even the foolish K-mart ad shown above of “0 percent off” can at least be praised for its transparency.

Nowadays discounts come in a variety of coupons and sales, and they are much harder to understand. So many offers only seem good, and so many others offer illusory savings.

I’ll briefly refresh how to evaluate a discount percentage and then go into a few examples of offers that sound a lot better than they actually are.

How to calculate a discount percentage

The discount percentage is a simple formula. It’s calculated by dividing the discount from the full price (and interpreting the decimal as a percent)

discount percentage = discount / full price

An entirely equivalent method is to divide the amount paid (which is the discounted price) by the full price and subtract that from 1.

discount percentage = 1 - (amount paid / full price)

And of course, it is important to remember to include all parts of the costs, like shipping and taxes. These two things can often kill an otherwise good deal.

So with that in mind, on to a few examples.

Example 1: Target coupon for $5 off of a $10 purchase

I’ve occasionally seen Target offer a coupon for $5 off of a $10 purchase. I like these offers though I am careful to think twice.

A coupon that states a dollar amount off can be one of the sneakiest offers. These offers almost always seem better than they are because of taxes and lack of items at exactly the cutoff value (the many items at $9.99 don’t qualify).

There are three items that I like to compare. The first is the perceived discount which is the amount you think you’ll be saving. The second is the actual discount which is the amount you can theoretically save if you find an item that maximizes the offer. And the third amount is the practical discount which is an estimate of how much you’ll actually save if you go shopping.

Here is my calculation for the Target $5 off of $10 coupon:

Perceived discount: 50 percent
Actual discount: 45 percent
Practical discount: around 40 percent or less

Here is how I came up with those numbers.

The perceived discount is 50 percent. It seems like you’re getting half off when you get $5 back on a $10 purchase. That is part of the game that they want you to feel it’s an amazing deal. The true discount is 5 to 10 percent less, as I’ll explain.

The actual discount is 45 percent. The reason for this is sales tax which is not discounted. In my neck of the woods, sales tax is around 10 percent and that can make a big difference. The resulting actual discount is 45 percent [= 5 / (10 x 1.1)].

The practical discount is 41 percent or even lower. It’s not practical to be able to get an item that you want at exactly $10. Part of this is that so many items are priced at $9.99 that are not eligible for the offer. One has to choose between buying two smaller items, or instead to get an item that’s a little bit more. In my experience, I often end up getting something around $10.99 for an offer like this. The resulting practical discount is then 41 percent [= 5 / (10.99 x 1.1)].

In sum, the Target offer is pretty decent though it is not what it seems at first.

Example 2: Sweet Tomatoes buy one, get one free (must purchase two drinks)

This one gets me, even though I otherwise love Sweet Tomatoes, the restaurant with an amazing salad and soup buffet.

I’m on their loyalty list so I get coupons emailed to me. The bold print on the coupon is “buy one, get one free” and it is only in small text that you have to get drinks.

So how does this coupon stack up? It really depends if you were going to get drinks anyway. I know a lot of people would and this coupon would work out perfectly. For me, I prefer water to quench my thirst.

The coupon still offers savings over not using it–I often buy a drink and just have water–so here is how the savings turn out:

Perceived discount: 50 percent
Actual 1 discount, if getting drinks anyway: 40 percent
Actual 2 discount, if not wanting drinks: 26 percent

Here are some of my supporting calculations, using a $10.49 cost of meal, a $2.49 cost of drink, and a 10 percent sales tax.

Getting drinks anyway: 40 percent = (1 – (10.49 + 2.49 x 2)(1.1) / ((10.49 + 2.49) (2)(1.1)))

If you were not going to get drinks, the discount turns out to be much less, at 26 percent = (1 – (10.49 + 2.49 x 2)(1.1) / (10.49 x 2 x 1.1))

All in all, still a coupon I use but clearly not as amazing as it first seemed.

Example 3: Kohl’s every $50 spent = $10 store cash for next purchase

Another tricky discount is getting store cash on a future purchase. These again seem like amazing deals but they really do not always turn out to be so.

This Kohl’s promotion is interesting. It gives an incentive to purchase up to a $50 increment for the current visit, and it makes a customer come back another time just to redeem.

What is the math on this promotion? Here is my thinking:

Perceived discount: 20 percent
Actual discount (max): 18 percent
Practical discount: 15 percent, or less

The perceived discount is 20 percent. The offer can give the impression that you are essentially getting $10 off of a $50 purchase. Not so. You have you spend $50, and then you get $10 off of a future purchase.

The actual discount is thus more like 18 percent because of sales tax. As seen in the first example, a cash discount does not affect the tax. A 10 percent sales tax means an extra $6 in spending from the two combined purchases ($50 x 1.1 + $10 x 1.1). With perfect denominated purchases, this sale is just a bit worse at 18 percent [ = 10 / ($50 + $6 in taxes)].

The practical discount is of course lower. I find it hard to plan purchases that add up to exactly $50 and exactly $10. More likely I can do something like $55 and $15 if I’m going for items that I actually want to buy. The result is the actual discount becomes 14 percent [= 10 / ($55 + $5)(1.1)].

All in all, this is not really a good deal at Kohl’s where 15 percent off is a standard promo for store card holders, and you have to visit the store two times.

What discounts mislead or irk you?

I’ve shared a few of the promos that I find a bit overblown. I notably omitted rebates which are so annoying sometimes that I want to write a separate post about them. Now I’m curious if you’ve noticed any offers lately.

What offers are not as good as they seem? What is the perceived discount and what is the actual discount? Share in the comments to save fellow shoppers from saving disappointment.