Follow-up from 3/21 Workshop - Practice Exam Form 2, Question 14

The following question was submitted for this past Sunday’s workshop and required additional followup in order to answer. I’m posting it here in hopes that folks will see it.

Q: I am having an issue with the answer provided in one of the practice exams. I am getting a different answer using a different approach. Please let me know what I am missing. Here is the question:(#14 Exam form2)

The billable rate for employees at an architecture firm is comprised of base salary plus the rate of benefits, overhead, and profit margin. The firm has a benefits rate of 30% and an overhead rate of 110%.

If the base salary for an employee at the firm is $30/hour and the billable rate for the employee is $80/hour, what is the net profit margin? Round to the nearest whole number.

My answer: 20%

I am using a formula which I believe was used in another practice exam to find the target profit percentage. Please confirm this is a correct formula:

Net multiplier= Breakeven rate / Inverse of target profit percentage

  • Overhead rate=110%=1.1
  • Breakeven rate=1.1+1=2.1
  • Net multiplier=80/30=2.66

2.66= 2.1 / Inverse of target profit percentage
Inverse of target profit percentage=0.79
Profit percentage=20%

Answer provided in the practice exam:10%

Use the formula stated in the question: the billable rate = base salary + benefits rate + overhead rate + profit margin.
The base salary for the employee is $30/hour. First, find the amount to be added to the base salary for the benefits rate:

  • $30 x 30% benefits rate = $9/hour

Next, find the amount to be added to the base salary for the overhead rate:

  • $30 x 110% = $33/hour
  • Base salary + benefits rate + overhead rate = $30 + $9 + $33 = $72

Then, subtract from the billable rate:

  • $80 - $72 = $8

Lastly, find the percentage of net profit. Net profit should be calculated from the total revenue, not the base salary or net revenue.

  • $8 / $80 = 10%

  • Alternatively, use the formula for net profit margin: (revenue-cost)/revenue ($80-$72) / $80 = .10 = 10%

(Response in comments)

In answer to this question:

This formula does seem to work; the error in the candidate’s answer is that they are not adding the 30% benefits (as described in the question) to arrive at the correct breakeven rate.
The breakeven (BE) rate should be 2.4 (i.e. 1+1.1+0.3). Solving for x using this BE rate yields the correct answer of 10%.

However, our staff who review and update the practice exams were not able to find the formula referenced in other practice questions, nor via an internet search or in the AHPP. We would advise against using the alternate formula and would use the one found in our answer explanation (billable rate = base salary + benefits rate + overhead rate + profit margin).