ARE 5.0 Practice Management : Target Percent Profit
Hello,
I'm wondering if anyone could help clarify the last step in the given practice test problem. I believed that after finding the hourly billing rate, which I found correctly, that I would then divide that number by the inverse of the target percent profit. Leading to my answer $86. Black Spectacles is saying that I should have just multiplied by the target profit percent and added that to the found hourly bill rate.
Is the concept of using the inverse percent only applicable to finding the net multiplier from the break even rate? Or is Black Spectacles incorrect in this instance.
Any input greatly appreciated.
Thank you

Maybe you can post your detailed steps here and we can see if we can help you.
Gang Chen, Author, Architect, LEED AP BD+C (GreenExamEducation.com)

Black Spectacles made a very common mistake here when calculating the hourly profit billing rate (steps 4 and 5 should be replaced with only one step):
hourly billing rate is $68.44
to calculate 20% target profit: $68.44 / .8 = $85.55 (round up to $86).
to calculate 20% mark up: $68.44 x 1.2 = $82.128 (round up to $83).

How to calculate the %%% of profit margin.
 Express percentage (in our case, 20%), in its decimal form, 0.2.
 Subtract 0.2 from 1 to get 0.8.
 Divide the original number (in our case, hourly billing rate of $68.44 by 0.8: $68.44 / .8 = $85.55
 There you go, this new number is how much you should charge for a 20% profit margin.

Relationship between break even rate and net multiplier:
Breakeven rate / Net multiplier = Inverse percent
For example, break even rate is 2.3 and net multiplier is 3 and they ask what's the profit margin:
2.5 / 3 = 0.8333
to find out profit margin, substract 0.8333 from 1: 1  0.83 = 0.17
0.17 x 100%  17% profit margin

Here's another example from ARCHIPREP software w/incorrect answer based on AHPP book.
Q. An architecture firm hires subs for drafting purposes. They pay the drafting company $50/hour for the drafting work. Fifteen minutes every hour, an architect billed at $100/hour has to instruct the drafter on how to proceed. How much should the firm charge the client for the drafting work in order to make a 10% profit?
$55
$90
$75
$82.50
Solution:
Every hour the firm spends $50 on the drafting work and $25 on the architect. The direct total is $75, and 10% of that is $7.50. The firm should charge the client $82.50/hour to make a 10% profit. The correct answer is D.
Reference: Wiley and Sons. (2013). The architect's handbook of professional practice.
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They do not seem to understand the difference between the profit and mark up.

Hi All,
Here is why:
You need the resultant total profit to equal whatever profit percentage you are targeting, not a profit percentage of what you are charging. Taken from my Pluralsight course.
If you multiply by the percentage and add the presumed profit total, your "profit" by definition is a lesser value. The mathematical check is to take the subtotal rate and divide it by the billable rate. In this case it is $87.50 / $109.38 = 79.9% or a 20.1% profit margin. If the firm wants 25% profit, that value should be taken ABOVE the subtotal value (pay rate + payroll burden).
Hope this helps!
Kevin Griendling, AIA

Julia,
Yes. Absolutely.
Kevin Griendling, AIA

Black Spectacles and ARCHIPrep are both correct.
For Black Spectacles
If you add all the totals and divide by total hours.
715000+380000=1095000 + (1095000*.20)=1314000/16000 = 82.125
You can also do this by removing all the thousands. 715+380+=1095+(1095+.2)=1314/16=82.125
Also, markups are profits. If the firm wanted to break even then in both cases the ARCHIPrep and the Black Spectacles questions wouldn't have the percentage increase (10% or 20%) just enoughin and enoughout. In order for the firm to make a "profit", they factor their breakeven rate and then multiply it by that decided profit percentage. In these cases 20% and 10%.
These questions really have nothing to do with the net multiplier because the net multiplier has to do with breaking even to cover expenses involved with running a firm and creating billable rates, not profit margins.

AHPP, pg. 415:"Overhead Rate and BreakEven Rate (as a Percentage of Direct Labor)The overhead rate and the breakeven rate are inextricably related:• The overhead rate comprises two components: indirect labor and general and administrative(G&A) expenses. Even though many G&A expenses are common to most firms, what these expenses specifically include will be a reflection of a firm’s uniqueness in its operations and the types of discretionary benefi ts it offers its employees. Refer to the sample accrual profitloss statement and the most common G&A expenses.• The breakeven rate is equal to the overhead rate plus an assigned unit cost of 1.0 for hourly salaries. A firm with an overhead rate of 1.30 would have a corresponding breakeven rate of 2.30 (1.30 + 1.0).Once a firm’s overhead rate has been established, the breakeven rate for every employee can also be calculated, based on their respective hourly salary rate.Example: For an employee who is paid a salary equal to $20 per hour ($41,600/2,080 hours) in a firm with an overhead rate of 1.30, the breakeven rate for such an employee would be: $20.00 × 2.30 = $46.00 per hour. That means for the firm to break even on this particular employee’s hourly salary and their respective portion of the firm’s overhead cost, the hourly billing rate for their direct labor can be no less than $46.00 per hour. To include profit at a targeted percentage of 20 percent, divide the breakeven rate by 80 percent (the complement of 20%).This will establish an hourly billing rate of $57.50 ($46.00 ÷ 80% = $57.50;to check: $57.50 × 20% = $11.50 + $46.00 = $57.50)."

This is actually the first time I have seen a profit percentage done this way and I really don't think this is the correct way to calculate profit margins. Dividing by the complement is not the same as multiplying by the percentage and adding it back. I have tried to calculate this a few times and it never gives the same number.
Here is an example of the maths:
20% profit of $10
(10(.2))+10= (10/1)(20/100)+10= 2+10=12
80% Complement of $10
10/.8=10/80/100=(10/1)(100/80)=1000/80=12.5

Very interesting and informative discussion.
Gang Chen, Author, Architect, LEED AP BD+C (GreenExamEducation.com)
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