Beer Pricing and Sizing: Discounts
COVID-19 may have absolutely DUNKED on the nation’s bars, but taprooms have so far found two potent revenue streams: food to-go, and cans/crowlers/growlers. While this is a phenomenal and crucial lifeline, and while people (at least here) certainly seem willing to pay full price for stuff, you may be tempted, as we are, to offer discounts and sales in order to drive short-term sales and draw in cash, in order to insure against, say, a stay-in order.
SO, the big question: obviously, you have to sell more of a thing if you discount it to make the same profit, but how much of said thing? Well, the answer is (mercifully) very straightforward
As per usual, let’s outline assumption (a great habit from my physics days):
Your margin is 60%
You’re selling a thing that’s normally $15 (our 4-packs, say)
that’s it!
So, question 1: how much of your revenue is profit? Simple: $15*60% = $9
Next, there are two ways to offer a discount: $x or x%
Dollar-based discounts
First, the $x model (simpler mathematically):
If you offer a $1 discount, your profit drops from $9 to $8 (since you only keep the money above break-even, here $6), and thus ~11%. BUT, this doesn’t mean you have to sell 11% more beer; in order to make the same profit, you need to sell:
100% = 89% * x%
here, 100% means you make 100% of your profit, and 89% is your reduced “margin” (not exact in this sense)
or, x% = 100%/89% = 112.5%
Interestingly, this is simply (profit before)/(profit after), here $9/$8
So you need to sell 12.5% more 4-packs in order to make the same profit with this discount. Totally possible, but not insignificant!
What about a heftier $3 discount? Using the rule above, your increase needs to be $9/$6 or a whopping 50%! Again, possible, but a massive increase in order to justify a mere 20% discount off of sticker price
Percentage-based discounts
This would have been hairier to start with, but now that we know about the profit before/profit after trick, it’s a bit simpler.
So, let’s start with a 10%: if your original price was $15, your new price is $13.50, so your new profit is $7.50. Thus, you need to sell 20% more beer to make this worth it - by now I’m sure you’re getting the rhythm
For 25%, your new price is $11.25, your profit is $5.25, and you need to sell a shocking 71% more 4-packs!
Finally, there’s a more general formula we can use when dealing with percentage-based discounts, that applies very generally to any product, really:
(profit before)/(profit after) = (rev*margin)/(rev*(1-discount) - rev*(1-margin))
the denominator on the RHS is derived directly from profit = revenue - costs, where costs = revenue*(1-margin)
so, simplifying this, we get = margin/((1-discount) - (1-margin))
and plugging in our 10% discount and 60% margin, we get upsell percent = .6/(.9 - .4) = .6/.5 = 120%
which is exactly what we found above! So great, we can now calculate the volume increase needed for literally any product in the world, assuming the volume increase doesn’t change our margin appreciably
Profit above break-even
Let’s say, with that 10% example, you end up selling 50% more cans than your average beforehand (A/B test post coming soon). Congrats! How much money did you make?
As hinted at before, your new profit (and let’s say you sold normally sell “n” 4-packs) is $15*60% - $15*10% per 4-pack, or $15*(60% - 10%) = $7.5 per 4-pack
If you sold 30% more than the break-even of 20% (so, that 50%), you made an extra n*150%*$7.50 - n*$9, or $2.25*n, which can be considerable if n is large, obviously. More generally, your extra profit is:
Price*(margin - discount)*(percent sold above 100%)*(items sold) - price*margin*(items sold)
or more simply, price*(items sold)*( (margin-discount)*(pct sold) - margin)
So just plugging in the numbers from above, we get: $15*n*((.6-.1)*1.5 - .6) = $2.25*n
Or, with a $20 item, a 25% discount, and a 10% increase, we’d have (and henceforth we’ll drop the n):
$20*((.6 - .25)*1.1 - .6) = -$4.30 per unit
Again, here n is the average number of, say, 4-packs sold (if that seems contrived, you need to compare your sales to something in order to know relative profit)
So with numbers that, on paper, aren’t all too jarring (more items sold, a 25% discount), we’d lose a ton of money! Ouch!
And a very potent takeaway - if your discount is bigger than your margin, you lose money no matter what!
So we’re in a position now to understand the opening plot: it shows the extra profit, per $15 “thing” that you sell on average given both the percentage discount and the percentage sold above average. Obviously, a 0% discount maximizes your profit, a 60% discount means you lost all of your profit no matter what, and there’s everything in between. The max is obviously doubling your sales with no discount, meaning if you normally sell 100 things, and after a 0% discount you sell 200 (don’t worry about the logic), you make an extra $9*100 or $900, the profit on the extra things. The below plots are the same graph from different angles - see if you can’t find the break-even point for a 20% discount! (two “lines” in from the edge)
Closing thoughts
Two thoughts for you:
While the short-term boost in sales due to discounts is sure to taper, I have no doubt there’s a “sweet spot” discount, where you get a maximal profit. Clearly, from the last example, a big discount and small gains may leave you with a tiny relative profit and potentially a stock issue, so be careful with discounts!
One extreme in the world of discounts is what it seems Pico Brew does, which is to have eternal discounts, which amounts to pricing low, claiming to price high, and using “discounts” to drive sales artificially. Does this work? I have no idea!
And one thought that may have occurred to you - if you see a permanent increase in sales, why not just keep your pricing that way permanent? This touches on ominous economic theory, and will be covered post haste, as it is clearly of massive importance - it’s arguably the centerpiece of this whole line of thinking!
See ya shortly!
