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# The Math Behind a Sale

I had a vendor recently ask me to offer their items at 25% off for a month. They would split the difference of the sale off the wholesale price (12.5% discount on the cost). They figured this would be a big enough deal to drive a lot of traffic.

On the surface it looks good. 25% off a popular brand would probably drive some business. So I decided to do the math.

We’ll use a hypothetical item, but the math comes out about the same no matter how you slice it. Let’s assume two things… First, I have an item that I buy for \$10 and sell for \$19.99. Second, I expect to sell 10 units of this item every month.

In a typical month, my numbers would look like this:

Total Cost = \$100 (10 units x \$10 each)
Total Revenue = \$199.90 (10 units sold x \$19.99 each)
Gross Profit Dollars = \$99.90 (Revenue minus Cost)

Now let’s do the math with the sale discount. My new cost is now \$8.75 (\$10 minus 12.5%). My new retail is \$14.99 (\$19.99 minus 25%)

If I sell the same 10 units the math looks like this:

Total Cost = \$87.50 (10 units x \$8.50 each)
Total Revenue = \$149.90 (10 units sold x \$19.99 each)
Gross Profit Dollars = \$62.40 (Revenue minus Cost)

Even though my discount was only 25% and the company was willing to lower the cost, the same ten units I was expecting to sell yielded a 37.5% decrease in Gross Profit. Wow!

Just to make the same Gross Profit Dollars as I already expected to make, I would need to sell 16 units at these new prices.

Total Cost = \$140 (16 units x \$8.75 each)
Total Revenue = \$239.84 (16 units sold x \$14.99 each)
Gross Profit Dollars = \$99.84 (Revenue minus Cost)

To make this promotion worthwhile, I would need to sell 60% more units. More importantly, those 6 extra units had to be extra sales, not just sales from next month’s expected ten units sold.

How do I sell 60% more units to new customers? I have to advertise. I have to announce the sale, create signs, post notices, change numbers in the cash register, alert the staff, order more products, schedule more staff.

Gee, by the time I do all that, I’m going to need an 80% increase in units sold to cover all the increased expenses.

It takes a lot more volume than you might think to make it up with volume as the old adage says.

-Phil Wrzesinski
www.PhilsForum.com

PS The math isn’t that hard. Do the math and see what the numbers tell you. If you believe you will definitely sell 60-80% more units at the lower price, go for it. If you believe your Transactional Customers will jump on this item, go for it. If you believe the sale will draw enough traffic that will buy other regularly priced items, then consider the lost dollars on the sale items an advertising expense. If you need to move out a dog that isn’t selling, go for it. Just do a little math first, so that you know what results you’re shooting for.

PPS If your initial profit margin is lower than 50%, your increase in units sold to make the same gross profit dollars in a sale like this goes up. Just saying…

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