# Practice exam answer - possible error

PcM practice Exam 3 question:

The architectural firm has calculated the following financial projections:
Annual hours for 8 billable employees = 16,000 hours
Annual payroll = \$715,000
Firm is targeting 20% profit.
What is the hourly billing rate? Round answer up to the nearest whole dollar amount.

Step 5: Calculate total billing rate with profit: \$ 68.44 + \$13.69 = \$82.13/hour

Round up to \$ 83/hour.

I would say that the round-up is \$82, but if I’m not familiar with how it usually works, an additional thought would help.

Looking into it, thanks for mentioning this!

The question stated to round-up to nearest whole dollar which is \$83 since the actual answer has change in the amount. \$82 would be rounding down to the nearest whole dollar.

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Correct. This has come up in past coaching groups. Considering this is a billing rate, wouldn’t you want to round up to get (slightly) more fee? Think about it like you do for occupancy calcs - you wouldn’t have 0.1 person so you always round that up to the nearest whole, even though that goes against typical math norm for rounding.

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Another question on this same question … why does this question not account for the Break-Even rate in addition to the Overhead? In AHPP p.415, 442, hourly billing rates are created from = (hourly payroll)(Break-even Rate)(1/(1 - target profit %)). Also from AHPP 7.2 p.410, “Overhead” is described as (total indirect expenses/total direct labor) and “Break Even Rate” is described as “the Overhead rate plus the unit cost of 1.0 for every hour of salary.”

It seems like you could reasonably approach this problem as follows, but then end up with the wrong answer?
Step 1. Calculate hourly payroll: \$715,000/16,000 = \$44.69
Step 2. Calculate Overhead rate as ratio of indirect expenses to direct labor expenses: \$380,000/\$715,000 = 0.53
Step 3. Calculate Break-even rate from Overhead rate: (0.53 + 1.0)
Step 3. Multiply by complement of target profit percentage, 20% profit

= (\$44.69)(1.53)(1/0.8)
= \$85.4

Why wouldn’t this question encourage typical profit planning? Confused about this question … what am I missing? Thanks!

Hi @kstolzenberg and welcome to our ARE Community!
@cat.heard9 or @heatherrivera could you clarify this question for us?

Thanks!

Hi @kstolzenberg! Welcome to the Community!

Great question, but I’ll admit I had to read it a couple of times and take a few sips of coffee.

The information we are given in the question already accounts for the break-even rate. Page 410 of AHPP says that the break-even rate is “the overhead rate plus the unit cost of 1.00 for an hour of salary.” We know that our overhead is \$380,000. We know that the yearly payroll is \$715,000 (the math here has already been done for us so we don’t need to calculate salaries). Given the definition above, the break-even rate is \$715,000+\$380,000. Given that this is out break-even and we desire 20% profit, multiply the sum by 1.2 and divide by the man hours to get your answer.

I’ve done the math in your method and have actually still come up with \$83; and herein lies the discrepancy: you are dividing the entire equation by 0.8. You can’t do this to calculate the profit with your method. You need to multiply by the profit. Do exactly as you have done until the very last step, but rather than multiply by (1/.8), you want to multiply the entire equation by 1.2 (120%=100% break even+20% profit).

(\$44.69)(1.53)(1.2)=\$82.05

That would still round up to \$83.

I hope that provides some clarification!

Some serious smarts working over there. Keep up the good work!
Heather

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Ok makes sense… thanks for the response!