# Derivation of Point of Total Assumption (PTA) Formula

4 minute read    Updated:    Harwinder Singh Point of Total Assumption (Part 3): In this post, we’ll look at the formula for Point of Total Assumption (PTA) and learn how the formula is derived. This will help you understand the PTA concept in a way that you would never feel the need to memorize its formula again! Before you read further, I suggest you read The Point Behind Point of Total Assumption in FPIF Contracts, if you haven’t already done so.

There is an ancient Chinese proverb, which says -

Give a man a fish and you feed him for a day. Teach a man to fish and you feed him for a lifetime.

I apply the same principle to the formulas for the PMP Exam. I say -

Memorize the formula and pass the exam. Understand the formula and pass the challenges of a real project.

PTA comes into picture only in case of cost overrun. PTA tells the seller the cost up to which the losses will be shared with the buyer. It doesn’t tell whether the seller will make a profit or loss at that point. Let’s calculate PTA without using the formula. First, I’m listing the basic terms which will be used to derive the formula.

TermDescription
Target CostThe estimated cost of the project. It does not include seller's profit
Target FeeSeller's Fee or Profit
Target PriceTotal estimated price of the project (including seller's fee).
Target Price = Target Cost + Target Fee
Buyer's Share Ratio (BSR)In case of cost overrun, the ratio of the cost that buyer will bear.
Ceiling PriceMaximum Price that the buyer is willing to pay - really the maximum, not even a penny more! It includes Target Price plus buyer's share of the cost overrun.

Assume that PTA value is say \$PTA (how innovative !).

As I mentioned above, PTA comes into play only in case of cost overrun. So, we can safely assume that PTA will be more than the Target Cost.

Cost overrun at PTA = PTA - Target Cost

At PTA, buyer share’s of the cost overrun = (PTA - Target Cost) x BSR

Total Price that the buyer pays at PTA = (Target Cost + Target Fee) + Buyer’s share of the cost overrun

since (Target Cost + Target Fee) = Target Price

=> Buyer’s price at PTA = (Target Price) + (PTA - Target Cost) x BSR … (1)

We also know that the Total Price that the buyer pays at the PTA is also known as the Ceiling Price. In other words, when Actual Cost reaches PTA, buyer pays the Ceiling Price.

Therefore, Buyer’s Price at PTA = Ceiling Price … (2)

Equating (1) and (2), we get

=> Target Price + (PTA - Target Cost) x BSR = Ceiling Price

=> (PTA - Target Cost) x BSR = Ceiling Price - Target Price

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

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

There’s your formula for PTA.

If you understand the concept well, even if you forget the formula in the exam, you can still derive it. And 2 or 5 years after your exam, you’ll surely forget the formula, but you might still remember the concept.

I hope you found the post useful. In the next post, we’ll solve some numericals and learn a few interesting points about PTA.

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

Image credit: Flickr / lattefarsan This comment has been removed by a blog administrator. Dear Mr.Harwinder:

First Thank you for this intersting post on PTA formula.
Second let me tell you why i am here reading this:
1- i was not able to memorize PTA formula for long time so,
2- today i decided to try to derive the formula utilizing my understanding of logic so,I started with the fact that CP= AC(PTA)* AF,and
3- I got the same result as the formula then.
4- then i search for easy way and i fond it ( Yours).

what i am trying to say is that i beleive the same as you "understanding is better"
SO,now i have two ways now if i forget the formula to drive it again.

Thanks and apologies for long story Hello Hany,

No need to be sorry. I'm glad to hear your comments. Even if you ask me today what the formula for PTA is, I honestly do not remember. But I can solve these problems without pen and paper because I understand the concept now.

I encourage everyone to feel free to share their experience and thoughts.

BTW, you can also take the free PTA Quiz online at:

BrainBOK

Thanks. Wonderful job this is super clear derivation... awesome! Thanks very much for the detailed information, the formula was driving me crazy :-)) Real good!! Thx great! thanks for your effort