Comparing two of the very similar questions below. One that said profit margin is a distractor, whereas the other actually uses it. I am still confused about when the profit margin should be used after reviewing both answers and explanations many times. Can someone read the below and explain so we are clear when exactly we need to consider the profit margin in this kind of question?

Q1 -

An architect has been awarded a new construction library project and is waiting to develop the work plan until after they have determined the total hours that the project team can devote to the project. They have agreed to the following with the client and their consultants:

- Budget: $6,000,000
- Architect’s fee: 8% of construction cost, additional $100,000 for supplemental services
- Consultant’s fees: 15% of architect’s basic service fee
- Architect’s profit margin: 15%

If the project team’s average billable rate is $215 and the project team members will all work the same number of hours, how many total hours can be devoted to the project? Round down to the nearest hour.

hours

Incorrect - the answer is 2362

First, find the architect’s gross fee, which is 8% of the construction cost plus a fixed fee for supplemental services:

- ($6,000,000 x .08) + $100,000 = $580,000

Next, find the consultant’s fees, which will be subtracted from the architect’s gross fee in the next step to find the architect’s net fee. The consultant’s fees are based on a percentage of the architect’s basic fee (i.e. they do not include the supplemental services):

- ($6,000,000 x .08) x 0.15 = $72,000

Next, find the architect’s net fee received by subtracting the consultant’s fees from the architect’s gross fee:

- $580,000 – $72,000 = $508,000

With $508,000 available and an average billable rate of $215 per hour, we can divide the fee by the average hourly rate to determine how many hours are available to work on the project:

- $508,000 / $215 per hour = 2,362.79

Since the question specifies to round down, which is also typical when performing hourly calculations, the answer is 2,362 hours.

Note that profit is a distractor in this question; since profit is included in billable rates, accounting for it again would be double-dipping.

Reference: The Architect’s Handbook of Professional Practice, 15th Edition, Chapter 7.4

Q2 ----

A project manager is beginning to develop the work plan for a new construction library project. They’ve reviewed the contract between their office and the client and have determined the following information:

- Client’s budget: $3,500,000
- Architect’s fee: 8% of construction cost
- Reimbursable expenses: cost plus 10% fee
- Retainer amount: 6% of total fee

After discussing the project with the principal who negotiated the contract with the client, the project architect learns that the principal has entered into contracts with consultants for the project that total 25% of the architect’s gross fee and that the principal has included a target profit of 15% of the architect’s gross fee in the project budget.

What percentage of the total architect’s fee can the project manager devote towards labor for the project? Round to the nearest whole percentage.

%

Incorrect - the answer is 60

First, determine the architect’s total fee for this project, which is based on a percentage of the construction cost. At the onset of a project, that number is the client’s budget, so use that figure for this question:

$3,500,000 x 8% = $280,000

Next, subtract the portion of that fee that is going to be devoted to the consultants on the project. The question notes that figure to be 25% of the architect’s gross fee. Subtract that portion in one step, as opposed to two, by multiplying the architect’s fee by the complement of the consultant’s fee percentage: 100% – 25% = 75%, meaning that the architect will have 75% of the total fee remaining after paying their consultants:

$280,000 x 75% = $210,000

Next, determine the amount of the fee that the architect’s office will account for as profit. The question states that this is 15% of the **architect’s gross fee**, which is $280,000. Note that this step must be performed using the architect’s gross fee ($280,000), not the figure found in the previous step of the solution ($210,000):

$280,000 x 15% = $42,000 profit

Next, subtract the profit from the amount of fee left over after paying consultants:

$210,000 – $42,000 = $168,000

Finally, the question is asking about the the percentage of fee left over for labor hours, compared to the total architect’s fee. To find this percentage, divide the amount left over for labor by the total fee found in step 1:

$168,000 / $280,000 = 0.6, or 60%

*Note that the reimbursable expenses and retainer amount are not required to answer the question - they’re distractors.*

Reference: The Architect’s Handbook of Professional Practice, 15th Edition, Chapter 15.2