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I'm not sure how to best describe this in the title, so I will do my best here:

Let's say we have an order that prices out to $48,967.00 - but we have a few categories that make this up: taxes, delivery, products, labor, and installation. To make it simpler, those are bundled together into two variables: a total taxable and a total non taxable.

So in this example, the total with tax is 48,967.00 The taxable total is 40,130.00 The tax itself is 2,809.10 (7% tax rate as example) The non-taxable total is 6,027.90

The contract however is for 50,000.00 even.

What I want to be able to do, is adjust the taxable total to a new value that allows for the price to be $50,000.

In this case, I obviously need to increase the taxable total until it and it's taxes add up with the non-taxables to $50,000.00

The problem is that I don't seem to be capable of figuring out a way to do this that doesn't involve recursively trying values one at a time until I find the right taxable total that will add up with it's non-taxable lines, plus the new increased tax, to $50,000.

Obviously if I'm increasing the taxable total to reach 50,000 then taxes go up as well. My problem seems to be that I can't predict or figure out a formula that accounts for the fact that the taxes go up as I increase the taxable total too. This is important because the total of 50,000 includes taxes. So a simple variance between the contract price and the original is not working.

If this is a question that has been asked before, please direct me to the applicable answer. I searched for a while and was not able to find something similar to this particular problem.

Brandon Ragland
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1 Answers1

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Keeping the non-taxable total the same, the taxable total including tax is

$$\$50\,000 - \$6\,027.9 = \$43\,972.1.$$

Then with the same $7\%$ tax rate, the pre-tax amount for the taxable part is

$$\frac{\$43\,972.1}{1+7\%} \approx \$41\,095.42.$$

peterwhy
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  • Perfect! Thanks so much. My math skills are not the best. This is so eloquent and simple, and works perfectly for my scenario. – Brandon Ragland Feb 03 '24 at 15:33
  • what would the formula be if I was using Use Taxes instead of simple Sales Taxes? Your equation works perfectly for the typical sales tax, but I also have orders that use "Use Tax" and I'm struggling there now too. – Brandon Ragland Feb 03 '24 at 17:34
  • What is "Use Tax"? – peterwhy Feb 03 '24 at 17:35
  • Use tax is taxes done on the cost of an item instead of the selling price. Here's a good link on the difference: https://tax.thomsonreuters.com/blog/sales-tax-vs-use-tax-the-differences/ – Brandon Ragland Feb 03 '24 at 17:38
  • @BrandonRagland I think the sales tax and use tax cases are different enough, that asking another question would be better and keep this question focused. – peterwhy Feb 03 '24 at 17:46
  • I believe you're correct, it is different enough to be a separate question. Thanks for pointing that out. – Brandon Ragland Feb 03 '24 at 18:03