Shoppers Math

Shoppers math can be misleading.  Sometimes, because of clever marketing, it's meant to be misleading.

For example, what does BOGO really mean?  Well, if it's Buy-One-Get-One-Free, that really means that you are getting a 50% discount on a single item.  Do you want the item enough to pay half the amount of the original price for it?  Sometimes BOGO means Buy-One-Get-One-Half-Off (like at Payless Shoes), which is the equivalent of getting a 25% discount (or less if the second item costs less than the first).  Would you buy one of the item if you were getting a straight 25% off?  Something to think about before you buy something thinking that it is "free," so it doesn't matter if it's a little overpriced.

Coupons sometimes come in weird phrasings.  For example Lowe's has a "$25 off of $250" coupon.  So that's basically 10% off, yes?  Yes and no.  Unless you find an item(s) that costs exactly $250, you'll probably be buying more than that in order to meet the coupon requirement, bringing the percentage value of the coupon down.

What about those coupons for "$3 off Cheer liquid, any size?"  So normally, when you are buying something like, say, detergent, you look for the cheapest price per ounce, right?  And the cheapest price per ounce usually comes in the larger sizes.  Let's take a look at the Walmart.com prices on liquid Cheer:
 

# ounces	price	price/oz.
50	$6.97	$0.14
100	$12.52	$0.13
150	$16.74	$0.11

So this makes sense and is intuitive.  The more you buy, the more you spend, the less it cost per ounce.  The smallest size cost 14 cents per ounce.  The largest size cost 11 cents per ounce and is the best value size.  Now let's throw in a high-value $3 off coupon, and everything gets skewed:

# ounces	price	price/oz. after $3 off coupon
50	$3.97	$0.08
100	$9.52	$0.10
150	$13.74	$0.09

Whoa.  Now it seems that the smallest size is the greatest value.  And it is.  Because the coupon is a fixed amount and value increase is based on a ratio.  So your denominator (price) is shrinking, but your numerator (# ounces) is fixed. What does this translate to? Well, as a general rule (there are exceptions), if you have a coupon for a fixed amount (i.e. $3 off), it makes more sense to use it on the smaller-sized, cheaper item.  The higher the coupon value, the more true this is.  If you have a coupon based on a percentage (15% off), it makes more sense to use it on the largest sized item.

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