# Derivation of Point of Total Assumption (PTA) Formula

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.

Term | Description |
---|---|

Target Cost | The estimated cost of the project. It does not include seller's profit |

Target Fee | Seller's Fee or Profit |

Target Price | Total 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 Price | Maximum 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.

- Point of Total Assumption (PTA) - Introduction
- The Point behind Point of Total Assumption in FPIF Contracts
- Derivation of Point of Total Assumption (PTA) Formula (you are here)
- Point of Total Assumption (PTA) - Interesting Facts (PMP)
- Seller Fee Calculations in FPIF Contract

Image credit: Flickr / lattefarsan

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