How is this correct?
Why did they flip the profit here and divide by 80% , can someone please explain?

Yes, this is something that seems counterintuitive, and in fact, NCARB itself got this wrong on early versions of their practice exam in 2018 until users yelled at them enough to fix it on this very forum…if you multiply your breakeven rate by 1.2, you’ll underbill your clients! This is kind of a math trick. Your goal is to have 20% of your total billing be profit (remember that)…. Let’s say your break even rate is one dollar. And you multiply that by 1.2 and charge your client $1.20.
Do the math, 1.20 x 20% profit is 24 cents profit …subtract 24 cents from 1.20 and you only have 96 cents (not one dollar) to pay for breakeven costs if 20% of your billing rate is set aside as profit. To correct for this, instead of multiplying by (1+0.20), DIVIDE by (10.20) so divide a dollar by 0.8 and get a billing rate of 1.25 dollars…to check on that, multiply 1.25 by 20% profit returns 25 cents profit. Subtract the 25 cents profit from the 1.25 you billed and you have a dollar left to pay for expenses.Multiplying by 1.2 would have given you a “markup” but not a “profit”
It is easier sometimes to grasp the other side of this same concept when thinking about investing. Imagine that a stock loses 25% of its value…how much, as a percentage, does the stock have to go up to get back to its original value? You’d think the obvious answer is that it has to increase by 25% to regain its value but in fact that’s not correct! Try it with real numbers. Imagine that the stock is at 100 dollars before losing 25% of its value so it now sits at 75 dollars per share. For it to return to 100 dollars it will need to increase by 75 x .33 = 25 (because one third of 75 is 25)…. So to return to 100 dollars we’ll need the stock to increase by 33% not 25%
Michael Ermann, Amber Book creator
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