Point of Total Assumption (PTA) - Interesting Facts (PMP)

4 minute read    Updated:    Harwinder Singh

Key Points about Point of Total Assumption (PTA) in Fixed Point Incentive Fee Contracts for PMP Point of Total Assumption (Part 4): In this article, we’ll learn some interesting facts about Point of Total Assumption (PTA) by working through some numerical problems. Before you read further, I suggest you review the PTA Formula.

Formula for Point of Total Assumption (PTA)

Following is the formula for calculating PTA:

PTA = (Ceiling Price - Target Price) / BSR + Target Cost

PTA Sample Questions Set 1

Given the information below:

Target Cost: $60,000
Target Fee: $15,000
Target Price: $75,000
Ceiling Price: $100,000
Buyer-Seller Share Ratio: 60:40
  • Q1.1 What is the PTA?
  • Q1.2 How much does the buyer pay when the actual cost reaches PTA?
  • Q1.3 How much profit/loss does the seller make when actual cost reaches PTA?

Solution:

  • A1.1 By substituting the values in the PTA formula above, we get:

    PTA = (100,000 - 75,000) / 0.6 + 60,000 = 25,000 / 0.6 + 60,000 = 41,666 + 60,000 = $101,666

  • A1.2 Cost overrun = 101,666 - 60,000 = 41,666

    Buyer share ratio (BSR) = 60% or 0.6 Buyer’s share of cost overrun = Cost overrun x BSR = 41,666 * 0.6 = 25,000 Amount buyer pays at PTA = Target Price + Buyer’s share of cost overrun = 75,000 + 25,000 = $100,000 (= Ceiling Price)

    From here on, even if the actual cost rises to $150,000 (or more), buyer still pays $100,000 only. Do you know what this implies? Refer the conclusion section at the end of this post.

  • A1.3 The amount seller spent (actual cost) = $101,666

    The amount seller received = the amount buyer pays = $100,000 So, the amount seller makes = 100,000 - 101,666 = - $1,666 (net loss).

    So, in this case, seller is already in losses when the cost reaches PTA.

    Now, let’s modify the terms of the contract slightly.

PTA Sample Questions Set 2

Target Cost: $60,000
Target Fee: $15,000
Target Price: $75,000
Ceiling Price: $80,000
Buyer-Seller Share Ratio: 60:40
  • Q2.1 What is the PTA?
  • Q2.2 How much does the buyer pay when the actual cost reaches PTA?
  • Q2.3 How much profit/loss does the seller make when actual cost reaches PTA?

Solution:

  • A2.1 By substituting the values in the PTA formula above, we get:

    PTA = (80,000 - 75,000) / 0.6 + 60,000 = 5,000 / 0.6 + 60,000 = 8,333 + 60,000 = $68,333

  • A2.2 Cost overrun = 68,333 - 60,000 = 8,333

    Buyer share ratio (BSR) = 60% or 0.6 Buyer’s share of cost overrun = Cost overrun x BSR = 8,333 * 0.6 = 5,000 Amount buyer pays at PTA = Target Price + Buyer’s share of cost overrun = 75,000 + 5,000 = $80,000 (= Ceiling Price)

  • A2.3 The amount seller spent (actual cost) = $68,333

    The amount seller received = the amount buyer pays = $80,000 So, the amount seller makes = 80,000 - 68,333 = + $11,666 (net profit).

    So, in this case, seller is making some profit even when the actual cost reaches PTA.

Key Takeaways about PTA

  1. PTA can be more than the Ceiling Price.
  2. At or above PTA, buyer pays the Ceiling Price.
  3. At or above PTA, the contract price is fixed, and is equal to the Ceiling Price.
  4. At PTA, Buyer-Seller share ratio becomes 0:100.
  5. At PTA, a Fixed Price Incentive Fee (FPIF) contract becomes a Firm Fixed Price (FFP) contract.
  6. PTA doesn't mean point of zero profit for the seller. At PTA, seller may be making profit or loss, or no profit and no loss.
  7. Beyond PTA, all costs on the project are completely borne by the seller.
  8. Seller is usually more concerned about the PTA.

If you found these posts useful, do post your comments and let me know.

5-part series on Point of Total Assumption in FPIF Contracts
  1. Point of Total Assumption (PTA) - Introduction
  2. The Point behind Point of Total Assumption in FPIF Contracts
  3. Derivation of Point of Total Assumption (PTA) Formula
  4. Point of Total Assumption (PTA) - Interesting Facts (PMP) (you are here)
  5. Seller Fee Calculations in FPIF Contract

Image credit: Flickr / islandfreedom

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46 Comments

Missing Avatar

This is by far the best and simple clarification I have found on the FPIF PTA and Seller's Profit Calculations, So now I am using following formulas for Seller profits calculations derived from this post...
Seller Profit @ PTA = Ceiling Price - PTA
Actual Seller Profit for Cost Overrun = Seller Profit @ PTA - Cost Overrun

Reply to Mangesh Lolge
Harwinder Singh Avatar

Hi Mangesh,

Thanks for your comments.

Your second equation sound a bit convoluted to me. Another point which I hope you understand is that seller profit at PTA may in fact be negative i.e. a loss.

To calculate the seller profit at any point, simply use the equation:

Seller Profit or Loss = Buyer's Price - Actual Cost

Buyer's Price = Target Price + Buyer's share of cost overrun

Therefore,

Seller Profit or Loss = Target Price + Buyer's share of cost overrun - Actual Cost

I have a few examples on this post:

http://www.deepfriedbrainproject.com/2009/12/seller-fee-calculations-fpif-contract.html

Let me know whether they make sense. If you have further comments, feel free to post them.

Thanks.

Reply to Harwinder Singh
Harwinder Singh Avatar

@ Anonymous,

That's a good question:

"Benefit/Cost sharing" and "Buyer-Seller Share Ratio" mean the same thing and usually expressed as X%/(100 - X)% or X:(100-X). For example, 80%/20% or 80:20.

BSR means Buyer's Share Ratio (X). Usually it's expressed in decimals. For example, if the Buyer-Seller Share Ratio is 80%/20%, then BSR will be 0.8 (or 80%). Similarly, if Buyer-Seller Share Ratio is 60%/40%, then BSR will be 0.6.

I hope this answers your question. Feel free to ask more questions.

All the best.

Reply to Harwinder Singh
Missing Avatar

What are the definitions of the PTA Terms:

target cost - is this supposed to be out of pocket cost to seller without profit built in?

target price - is this what the seller and buyer believe is a fair price to pay for the project?

Reply to Dave
Harwinder Singh Avatar

Hello Dave,

These are good questions. I think I should have done a post to explain the basic terms first.

===============
Target Cost
===============
a. Target Cost is what the project is estimated to cost. It may include cost of raw materials, labor, equipment, facilities etc.
b. It does NOT include seller's profit.
c. It's an estimate, not the actual cost.

===============
Target Price
===============
a. Target Price is Target Cost plus Target Fee.
b. Target Fee is also known as seller's profit.
c. Target Fee is decided in the beginning of the project, as part of the contract between the buyer and seller.

I hope it's clear now.

Thanks again.

Reply to Harwinder Singh
Harwinder Singh Avatar

Hello Vikram,

If you refer to point 2 in the conclusion, buyer will pay the ceiling price only when the actual cost is at or above the PTA.

Buyer does NOT pay the Ceiling Price if the cost is below PTA.

So, I'm NOT assuming buyer will pay the Ceiling Price for "all transactions".

If you have further questions, let me know.

Thanks.

Reply to Harwinder Singh
Missing Avatar

Hi,
could you please provide an example of when the PTA can be above the Ceiling Price? I think that by definition this is not possible ... but I am still struggling to understand the concept (thought your posts have been very helpful)
thanks!

Reply to Anonymous
Missing Avatar

Hello Harwinder,

Examples really giving insights into PTA calcs.
Two points I would like to clarify:
-I see it is assumed that if sellers' costs does not go higher or equals PTA, the target fee is paid. I mean it is implicit in the PTA formula, but is this the general legally contracted condition?
-What do you mean by Conclusion #5?

Thanks,
Gabor

Reply to Anonymous
Harwinder Singh Avatar

Hello Anon.,

Sorry for not responding sooner.

I didn't really get your first question. Can you rephrase it?

Regarding the second question (conclusion #5 - at PTA, FPIF contract becomes FFP contract), I mean that "at or above" PTA, the buyer pays the "Ceiling Price". Here, that "Fixed Price" is referring to the "Ceiling Price". Once the project cost reaches PTA, no matter what the final cost of the project is, the buyer pays the "Ceiling Price". The seller has to absorb all the cost beyond the PTA. So, from the buyer's perspective, once the project cost reaches PTA, the project is a FFP contract with the contract price fixed at the "Ceiling Price".

Let me know whether it's clear now.

Thanks.

Reply to Harwinder Singh
Missing Avatar

Hi Harwinder,

Thanks for FFP, it is ok this way.
Regarding 1):
In the PTA formula it is inherent that the target fee is paid, even if the costs exceed the target costs. So for me it is just a bit strange that this being an incentive is talked about even if the target costs are exeeded.
Maybe if target costs is used instead of target price in the formula, then seller should take cost sharing responsibility over a bigger part.

Regards,
Gabor

Reply to Anonymous
Missing Avatar

Looks my answer did not pass validation :).

Let me repost.
Thnx for 2), FPP it is clear now.

For 1), my concern is:
Why PTA formula talks about target fee (incentive) when costs exceed target costs at all?
That is, in my opinion it would be better to use target cost instead of target price in formula to put a bigger part for shared responsibility.

Regards,
Gabor

Reply to Anonymous
Missing Avatar

Hi,

I'm not clear on answer A2.3.

It seems that the Amount Seller Spent would be (cost overrun ($8333) x seller share ratio (0.4)) + Total Cost ($60,000)=$63,333. The answer given is $68,888. I'm confused.

Thanks for any help.

Reply to Anonymous
Harwinder Singh Avatar

@Anonymous (May 23, 2011),

I must have overlooked your question. I hope you've already passed the PMP exam by now. For the benefit of others who might be following these comments, I'll answer your question.

Q2.3 is asking for seller/profit lost when actual cost reaches PTA. The actual cost is what the seller actually spent. The buyer share of the cost run, which is $5000 and is calculated in A2.2, has already been added to $75K to arrive at $80K price that the buyer pays.

So, I'm just looking at the net output and net input of the seller. The seller spent $68,333 on the project (net output), and received $80,000 from the buyer (net input). So, the total profit that the buyer made is $11,666.

Let me know if it still doesn't convince you.

Thanks.

Reply to Harwinder Singh
Missing Avatar

Great explanation. In summary PTA can be viewed as what the buyer is willing to help the seller with costs but not beyond. It can be confusing if one thinks of the PTA as the full amount the buyer reimburses the seller. It is the sum of two values. The first value is the target cost ($60,000). The second value can be confusing. It is the total overrun cost that the buyer is still willing to "pitch in" and pay for a percentage of the cost. The buyer will pay for some not all. But the PTA is helpful for the seller as it will tell the seller that any costs beyond PTA, the buyer will not help out and they are on their own. The PTA should not be confused with profit. As in the example above, if the target fee was a measly $10 rather than $15,000 with ratio of 60/40, then the seller will lose all the $10 profit after spending $40 beyond the $60,000 target cost. Even though the buyer is willing to pitch in to assist well beyond the $40 (up to $41,666 in the first example) the seller should make sure the target fee is sufficient to cover overruns and still have profit left over.

Reply to Anonymous
Missing Avatar

Hi Harwinder,

I have a question. In FPIF consider a scenario where Actual Cost is less that Target Cost:

Target cost 100,000
Target Fee/Profit 20,000
Target Price 120,000
Actual Cost 90,000
Ceiling Price 130,000
Share ratio 80/20

This this case will the 10,000 (Difference between Target Cost and Actual Cost) be distributed between the buyer and seller?

I feel that it should not because the Seller should get it as profit as he managed the cost well, but i think I saw in some website that it is divided. Can you please confirm?

Thanks,
Priya

Reply to Anonymous
Missing Avatar

Thanks for your quick response. Assume that there is a BSR ratio of 80/20. My question is that even if the Actual Cost is less than Target Cost will there be any division based on the ratio?

I feel that in the above question which I have posted the sellers profit should be 20,000(Fee/Profit)+10,000 (which is Target Cost - Actual Cost) = 30,000.

Is this correct?

Thanks,
Priya

Reply to Anonymous
Missing Avatar

@Harwinder.

Thanks a lot for excellent article.

Just a small correction to your post to Anonymous on Aug 12, 2011)(10:16AM).

You mentioned: " So, the total profit that the buyer made is" - it's actually "Seller". Kindly check the same.

Have a great day.

- Amar

Reply to Anonymous
Missing Avatar

In terms of the sellers total profit/loss, I came up with the formula:
-- SSR(TC-AC) + Target fee --
Also, to get the Total Cost, I have:
-- AC + Target Fee; or if AC = CP, then just simply the CP --
For me, they are very straight forward formulas - almost too easy. Is there any flaw in them that I am missing?

Reply to Steven
Missing Avatar

On your conclusion point 7, you mention that at PTA all costs are borne by the seller. This is not necessarily true. The seller assumes all costs when actual costs reach the ceiling price. If PTA is below the ceiling price, the seller's profit deceases, but up until the ceiling price is hit, the buyer is sharing in a portion of the costs.

Reply to Anonymous
Harwinder Singh Avatar

Hello Steven,

Your formulas may actually be correct. But personally I find it hard to remember formulas. The PTA concept is not that hard to grasp. If I can understand the concept, I don't need to remember the formulas at all. Having said that, if you can make nifty formulas and actually memorize them for the exam, there's nothing wrong in it.

Thanks for sharing your work!

Reply to Harwinder Singh
George Palmer Avatar

This thing was the first formula that was not intuitive to me. Finally figured it out in a fashion that is intuitive to me.

It is just the ACTUAL COST, when the contract hits ceiling price. Boom, end of story. After that deriving it is no problem.

The issue with a lot of the explanations on the net is they are not clear of what PTA is a point of. It’s a cost number, not a price number. Was really scratching my head as obviously the seller is still paying part of the marginal increase every dollar up to ceiling price. But at that point, he stops.

For me, the key insight was as simple as PTA is a cost number, not a price number. Despite the P hiding in PTA. In fact if they just changed the name to CTA (or PTCA), that might help other people that get confused like I did.

Reply to George Palmer