An addition to an elementary school has negotiated fee of 5% of a $5,000,000 construction budget, consultant expenses of 35%, gross profit target of 10%, and no other adjustments. What is the available architectural fee?

• A. $250,000
• B. $137,500
• C. $162,500
• D. $25,000

Answer: (B)

The amount available for the architectural fee is found by looking at how the budget is allocated within that 5% negotiated fee. Start with the 5% of the construction budget, which equals 250,000. However, within that negotiated amount, portions are already earmarked for consultant expenses (35% of the construction budget) and for gross profit (10% of the construction budget). Since those two allocations consume part of the overall pool, the remaining portion of the negotiated fee available to pay the architectural services is 5% times (1 minus 0.35 plus 0.10), i.e., 5% × (1 − 0.35 − 0.10) = 0.05 × 0.55 = 0.0275 of the construction budget.

Applied to a 5,000,000 budget, that remainder is 0.0275 × 5,000,000 = 137,500.

So the available architectural fee is 137,500. The other answer choices would come from not accounting for both allocations (consultant expenses and gross profit) or applying the percentages in the wrong way.