PcM Quiz Break 6, Q3

Practice Management
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Really scratching my head on this one!

The question is as follows:
The principal at a firm is determining billing rates for the upcoming year using the profit plan. The firm’s business plan outlines a projected profit of 22% of net operating revenue (NOR) yearly. They’ve already determined the following information:

  • Projected net operating revenue (NOR): $800,000
  • Projected overhead rate: 1.35
  • Projected consultant costs: $150,000
  • Projected direct labor: $352,000

What should the billing rate be for an employee with a utilization rate of 85% and a direct labor expense of $75,000? Round to the nearest $5.

And the answer:
There are two major steps to solve this problem. First, determine the firm’s net multiplier. Then, determine the hourly rate of the employee. Once you have those two numbers, multiply them together to determine the billing rate. We discuss the relationship of net multiplier to hourly rate in our video Firm Financials: **Profit Plan + Annual Budget **(4:33)

To find the net multiplier, start by figuring out the break-even rate:

  • Break-even rate = overhead rate + 1.0
  • Break-even rate = 1.35 + 1.0 = 2.35

Then, find the profit multiplier:

  • Profit multiplier = profit / direct labor costs
    • Projected profit = 22% x $800,000 = $176,000
  • Profit multiplier = $176,000 / $352,000 = 0.5

Calculate the net multiplier by adding together the break-even rate and the profit multiplier:

  • Net multiplier = 2.35 + 0.5 = 2.85

Remember, all of these multipliers are multiples of direct labor.

Now that you know the firm’s net multiplier, find the employee’s hourly rate. Since hourly rate = total labor / 2,080 hours per year, you need to find the employee’s total labor. You have their utilization rate and direct labor costs, so you can use the utilization rate formula to find the total labor costs:

  • Utilization rate = direct labor / total labor
    • 0.85 = $75,000 / total labor
    • Total labor = $88,235.29
  • Hourly rate = $88,235.29 / 2,080 = $42.42

Finally, multiply the hourly rate by the net multiplier to find the employee’s billing rate:

  • $42.42 x 2.85 = $120.89

The question asks for the billing rate to be rounded to the nearest $5, so $120.89 rounds down to $120.

HOWEVER: why not just calculate the Net Multiplier by dividing the NOR by the DLE? Profit is already included in the NOR. This gives a Net Multiplier of 2.27. If we take the same Hourly Rate of $42.42 and multiply by the Net Multiplier, I get an answer of $96.29, which rounds to $95.

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Welcome to the ARE Community, @adie.mitchell! Thank you for your question.

An important note about this question is that we’re talking about someone who is profit-planning for the following year, using projections. NOR/DL works when looking backwards at a previous year to determine that year’s net multiplier, perhaps to apply that information to future years. However, when planning for an upcoming year, particularly with a specific profit goal in mind (like in this question), you need to start with the overhead rate to figure out the net multiplier as we describe in the explanation.

Put another way, if you use the net multiplier of 2.27, you would actually lose money, because the break even rate is 2.35. This is a great way you could check your work to determine if the answer you are obtaining makes sense from a practical standpoint.

In reality if you were doing these calculations, you’d realize that you need to either increase revenue, decrease expenses, or both, in order to achieve your profit goal.

Hope this helps. Happy studying!

Kiara Galicinao, AIA, NCARB
Black Spectacles

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OK,
I think this makes sense, and good point about the fact that a net multiplier of 2.27 would make the firm lose money.

It seems that the NOR must be incorrect then. DLE x Net Multiplier should be NOR. But that clearly doesn’t hold true here. $353,000 * 2.85 does not equal $800,000.

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@adie.mitchell, going back to what was previously noted - the NOR/DL relationship applies when looking backwards at a previous year. Because these numbers are projections, we are using the relationships between overhead rate, breakeven rate, and profit multiplier to determine the net multiplier.

This discrepancy you pointed out indicates that figures might need to be adjusted at a later time, in order to achieve the desired profit.

Kiara

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I just bumped with this question as well. I just came up with the same conclusion.

If the Net Multiplier = NOR / Direct Labor, why could I not jump ahead and say that the net multiplier for this case is $800,000 / $352,000?

I agreed with the explanation provided to resolve this question and actually followed the same sequence explained, except that the result of NOR/Direct Labor was supposed to give me directly a net multiplier greater than 2.35

The tricky part of this case is that unlike other example questions I have done previously, the result is 2.27, which is less than the break-even multiplier of 2.35. The net multiplier must be greater than the break-even to accommodate a profit for the firm.

Thank you Kiara for the clarifications on this practice question.

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Hi! My exam is in 3 days so I’d greatly appreciate clarification on this question:

The explanation makes sense, but why not divide the break even rate by the complement of the projected profit (Net multiplier: 2.35/ 1-0.22 = 2.35/0.78 = 3.01)?

Thanks in advance!

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Hi @amirhossein.jafarii & @kiaragalicinao I have the same question. AHPP p.422 lays out the formula exactly as @amirhossein.jafarii has calculated. Why is that not correct for this question?
from AHPP p.442:
Targeted Net Profit (22%) Multiplier:
B-E Multiplier / .78* - B-E Multiplier
*To calculate the Targeted Net Profit Multiplier, divide using the complement (.78) of the Targeted Net Profit percentage (22%).
2.35 / .78 - 2.35 = .66
Targeted Net Multiplier:
2.35 + .66 = 3.01

P.S. I also don’t understand why you have to substract the B-E Multiplier to get the Targeted Net Profit and then add it to the B-E Multiplier to get the Targeted Net Multiplier when you can just divide the B-E Multiplier by the profit percentage and get the same number. (ie: 2.35 /.78 = 3.01). (from AHPP p.442)

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Hi @amirhossein.jafarii - the reason that doesn’t work is that the ‘projected profit’ noted in this question is mostly a distractor because, as @kiaragalicinao explained, it’s just essentially a guess at how much the principal thinks the firm will make next year (I say mostly a distractor because it is used in determining your profit rate). If you base your hourly rates on this guess alone, you’re essentially working towards this number, rather than charging enough for your services to ensure that you cover your expenses and make a profit.

A simpler way of thinking about it -

Let’s say you’re opening a lemonade stand, and think that you can sell 100 lemonades for $1 each on a given weekend (you think that your NOR will be $100).

Should you just charge $1 per lemonade based on that hunch, or should you think about the cost of ingredients, cost of your time spent selling them, and the cost to build the stand, in order to determine if your $1 price is accurate? In going through this process, you might find that you need to charge $1.50, for example, or that you can actually charge less and maybe sell more lemonades.

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@coachchrishopstock Please take a closer look at the ‘profit multiplier’ formula. The answer to this question claims that the profit multiplier equals the profit divided by the direct labor costs.

Profit multiplier = profit / direct labor costs

projected profit = 22% x $800,000 = $176,000

Profit multiplier = $176,000 / $352,000 = .5

Where does this formula come from? It does not come from the AHPP. The AHPP p.441 & 442 calculates the net profit multiplier as both @amirhossein.jafarii and I have done above. This is very confusing. What is the correct way to calculate the profit multiplier?

P.S. I found the reference for the profit multiplier formula. It is in the Firm Financials: Profit Plan + Annual Budget video as described in the answer. Now my question is: this formula is in conflict with the formula in the AHPP. How do we know which one to use?

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@coachchrishopstock There are different formulas for calculating the net multiplier and the profit multiplier. Can you help me understand the differences?

Net Multiplier = Net Operating Revenue / Direct Labor (AHPP p. 410)

Net Multiplier = Break-even Rate + Profit Multiplier (AHPP p.441-2)

Profit Multiplier = Profit / Direct Labor (BS Firm Financials video)

Profit Multiplier = Break-even Rate / Inverse Target Profit % (AHPP p.441-2)

Is this the difference between looking back at the previous year vs. looking at the year ahead? If so, which one is which?

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I agree that AHPP p. 441 & 442 show how you’d arrive at a profit multiplier, generally. Page 441 begins by saying that ‘the bottom section [of a profit plan] provides an alternate method of calculating a targeted set of goals for NOR…’. Basically this means, if NOR is not known, use this method to determine the profit multiplier.

This specific question gives a different set of circumstances - it says that the principal has a target NOR in mind (800k) and directs you to use that number and a 22% profit margin to answer the question.

This question is a good example of an ARE question that’s giving you a specific scenario/set of instructions to follow in order to arrive at an answer. We understand that there will be questions on the ARE like this, so we include them in our practice materials as well.

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@coachchrishopstock Since the NOR is given, why wouldn’t you use a formula that already has the net operating revenue in it? For example, why wouldn’t you calculate the net multiplier like this:

Net Multiplier = Net Operating Revenue / Direct Labor.

Since that doesn’t include the profit, I would add the profit to the NOR and get:

Projected profit = 22% x $800,000 = $176,000

NOR + Profit = $800,000 + $176,000 = $976,000

Net Multiplier = $976,000 / $352,000 = 2.77

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Although that formula seems to get closer to the net multiplier, it doesn’t work because profit is a part of the NOR, it’s not in addition to the NOR.

Going back to the lemonade stand example where you thought you could make an NOR of $100 in a weekend - if you wanted a 20% profit, you wouldn’t adjust your NOR upward to $120. You would take the $20 out of the NOR and figure out of the remaining $80 is enough to cover your expenses.

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