Sales Tax Calculations (Penny Rounding)

Table of Contents:

• Penny-Rounding Calculations
• General Retail sales
• Tax-Included

• New Layaways vs. Layaway Final Sales

• Bankers Rounding

Penny-Rounding Calculations in Bravo

Sometimes, the amount of tender you expect to collect from a customer may be off by one or two pennies. This article is intended to provide some insight into Bravo’s payment calculations, and help you understand what is happening to your missing (or, in some cases, extra) penny.

General Retail Sales

Suppose your General Retail Sales Tax is 7.725%. As a decimal, this is a factor of 0.07725 times the total sale price of an item. Often, when calculating sales tax on a retail sale, Bravo will first sum up the sale prices of all items being sold, then calculate sales tax by multiplying this sum by the tax factor. Let’s look at an example:

$232.07 * 0.07725 = $17.9274075

To simplify the sale, Bravo will round this value up, and it will show $17.93. The total amount to collect from the customer will be $232.07 + 17.93 = $250.00

Now, suppose you are going to sell two of these items for the same $232.07 per item. Without knowing the base value of the rounded tax (i.e., the fact that Bravo rounded from 17.9274075), you might assume that doubling the item count would double every value. Doing this, you’d expect the following:

Sale Price: $232.07 * 02 = $464.14

Tax: $17.93 * 2 = $35.86

Total: $464.14 + $35.86 = $500.00

However, Bravo doesn’t simply double all values. First, it doubles the sale price, then it calculates the tax on the total sale price. You’d end up with the following:

Sale Price: $232.07 * 2 = $464.14

Tax: $464.14 * 0.07725 = $35.854815

Total: $499.994815

Tax can also be seen as a doubling of the initial, non-rounded tax value:

Tax: $17.9274075 * 2 = $35.854815

Where a doubling of every initial calculation would result in a flat $500.00 total sale, we can see that Bravo will actually round down the total sale of the two items to $499.99. In terms of an order of operations, the $500.00 calculation is a result of rounding, then doubling (or summing), but the $499.99 calculation is a result of doubling (or summing), then rounding. On all final sales, Bravo calculates tax by summing first, then rounding.

Tax Included Sales

When you use the [Tax Included] checkbox in Bravo, you first enter in the total sale amount of an item, including what you would collect in tax. Using our examples from earlier, we might enter $250.00 as the tax-included amount for each item. Once we tell Bravo that this $250.00 is the tax-included amount, Bravo will back-calculate the Sale Price by first considering the following calculation:

Tax Included Amount = Sale Price + (Sale Price * Tax)

Filling in the values for our example:

$250.00 = Sale Price + (Sale Price * 0.07725)

Now, we divide out to get the Sale Price:

$250.00 / 1.07725 = Sale Price = $232.0724066

This raw value needs to be rounded to show a clean Sale Price to the customer, so in our specific example, Bravo will round down to $232.07. However, as we explained above the Tax on this tax-included sale is calculated at the end of the transaction, after summing everything. In effect, if you sold two of these items at $250.00 tax-included, Bravo would round (to get the Sale Price), sum (to get the total Sale Price), then round (to get the tax amount). You would end up with $499.99 due from the customer, even though two items were rung up for $250.00 each, tax-included.

New Layaways vs. Layaway Final Sales

The same scenario with tax-included sales occurs when multiple layaways are picked up within the same transaction. A layaway might be created for $250.00 tax-included, but if it is rung up with a second tax-included $250.00 layaway, the total of the two layaway final sales, if rung up in the same transaction, would result in a total of $499.99 to be collected from a customer.

It is worth noting, in all sales scenarios, that multiple items in a single transaction may result in a different Total Amount than you might collect when selling single items per transaction in multiple transactions. In addition to merchandise sales, these rounding practices can also apply to the sale of fees, shipping, and pawn service charges, and a number of other transaction types.

Banker's Rounding

Bravo uses "banker's rounding" when rounding to the hundredth place.

Here’s how it works:

• If the hundredths digit is even, the number stays the same (rounds down).

• If the hundredths digit is odd, the number rounds up to the next even number

Examples:

This method helps avoid rounding bias. Instead of always rounding .005 up, Bravo balances it by rounding to the nearest even cent.