PjM day 10- practice exam Q-15

Project Management
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1

The question is :A local architect has just won the contract for a 30 table restaurant with a fee of $30K. The architect’s break-even rate is $120/hr.

In order to achieve a 20% profit, how many hours does this give the architect to complete the job?

THE CORRECT ANSWER IS:

200 and i do not get the explanation:

Correct. Determine the percentage of the fee that is based on the break-even rate by subtracting the 20% profit. 100%-20% = 80%.

To determine the hourly billing rate, divide the break-even rate by its percentage.
$120/0.8 = $150. The hourly rate will be $150/ hour.

Next, divide the total fee by the hourly rate to get the number of hours.
$30,000 / $150 = 200 hours.

WHY DO WE Do this 100%-20%. My go to is to add 1.2X$120 to get to the new cost per hour. Than devide 30K/144= 208…

And this is not the right answer. I am confused. Can you explain?

2

Happy New Year @sevanb!

You subtract 20% from 100% because a 20% profit means the break-even costs can only be 80% of the fee. So the $120/hr break-even rate represents 80% of your billing rate.

  • Billing rate = $120 ÷ 0.8 = $150/hr

  • Hours = $30,000 ÷ $150 = 200 hours

If you do $120 × 1.2 = $144, that’s a 20% markup on cost, which equals only 16.67% profit on the fee (not the 20% profit margin the question is asking for).

Hope this helps :slight_smile:

Kiara Galicinao, AIA, NCARB
Product Coordinator
Black Spectacles

3

It is a little tricky and I still don’t get why this is done with 80% and 20% to 100%. Why is it not 100% and 120%?

So if $120 - 100%,

This seems intuitive to me but gets the wrong answer. How did you get 16.7%? when I take 20% of $120 it equals $24. so adding that would be 120+24 = $144.

  $120 - 100%
    X  - 120% 

X= $144 

For the same amount of hours ( 250) for $144 you would get a profit of 20% (120%). 144x250= 36000

witch is a profit of 6000 = 20%.

and if you got the other way around ( the question was how many hours do you need to get a profit of 20%) than I took the total 30K divided by $144 = 208.
4

@sevanb I see your confusion - the issue here is what the 20% is of. Your method ($120 x 1.2. = $144/hr) is a 20% markup of the cost. However, the question is using a 20% profit margin on the fee (profit = 20% of the revenue); which is why the fee is split into 80% cost + 20% profit = 100% total fee.

Think of it this way: the total fee is $30K (100% of the fee). The profit is included in that amount, not in addition to the amount.

Here’s why $144/hr gives 16.67%, not 20%, on a $30K fee:

  • Hours = $30,000 ÷ $144 = 208.33 hrs

  • Cost = 208.33 × $120 = $25,000

  • Profit = $30,000 − $25,000 = $5,000

  • Profit margin = $5,000 ÷ $30,000 = 16.67%

For the specified 20% profit margin, profit must be $6,000 (0.20 × 30,000), so only $24,000 can go to cost:

  • Billing rate = $120 ÷ 0.8 = $150/hr

  • Hours = $30,000 ÷ $150 = 200 hrs

I know it’s confusing, and it might be a bit different than you’re familiar with in practice. But remember, for the ARE you need to answer questions in the way that NCARB wants you to.

Kiara