Last updated on February 21, 2016

## Point of Total Assumption Formula in Fixed Price Incentive Fee Contract

How do you remember any formula?

Simple! Understand the concept you will not need to remember the formula.

I heard about Point of Total Assumption when I was preparing for PMP® Exam. At the beginning, it sounded very funny. One of the meanings of word “Assumption” is “the act of taking possession of something” e.g. “Assuming the power”. Although this is a more popular meaning, but there are other connotations of this word. It also means “the act of taking over another person’s debts or obligations”. In Project Management, the word refers to **“taking over Extra Costs**”. More on that later…

I have written two articles on **Fixed Price Incentive Fee Contract** **(FPIF)**. This is the third and concluding article on the subject. I gave a general description of FPIF Contract in my first article. In the second article, I talked about 5 mathematical formulas of FPIF Contract. In this article, I will talk about Point of Total Assumption Formula.

### What is Point of Total Assumption?

In the previous article, we discussed **cost driven FPIF Contract**. We determined how additional expenditure above the Target Cost (TC) is shared between the buyer and the seller. The share of the additional cost is governed by the agreed upon Share Ratio (SR). But we also saw that Buyer’s liability is limited only up to the Ceiling Price (CP). If the cost goes above a particular limit, then the seller has to bear the full cost above that limit. This limit is called **Point of Total Assumption (PTA)**.

The Point of Total Assumption is the point above which the seller starts assuming the cost of the contracted work.

Let us understand this through an example.

#### Example

Let us go consider the example from the previous post.

Target Cost (TC) = 100K

Target Fee (TF) = $20K

Ceiling Price (CP) = $130K

Share Ratio = 50:50 (both the buyer and the seller get 50% of the Cost Variance)

Target Price (TP) = $100K + $20K = $120K

Let us look at a particular scenario when Actual Cost is $120K. Let us calculate the Actual Price.

Actual Cost (AC) = $120K

Referring to the Formula II from the previous post

Cost Variance (CV) = $100K – $120K = -$20K

The seller has spent $20K more than the Target Cost. The extra cost will be divided between the buyer and the seller in the ratio of 50:50. Referring to the Formula II from the previous post.

Seller’s Share = (-20)*50% = -$10K

Referring to Formula V from the previous post

Fee = $20K – $10K = $10K

Referring to Formula I from the previous post

Price = $120K + $10K = $130K

The buyer will pay $130K to the Seller, which is also the Ceiling Price. The price is capped at $130K. So, if the seller spends anything more than $120K, the extra cost will have to be borne by the seller. For our example, PTA is $120K.

### Formula VI – Point of Total Assumption Formula

PTA = (Ceiling Price – Target Price)/Buyer’s Share Ratio + Target Cost

Let us first derive this formula. We will use the following abbreviations for the ensuing discussion

Going by the definition and above example, we already know two things. At PTA

Referring to Formula I from the previous post

CP = PTA + Fee

Referring to Formula II, IV & V from the previous post

CP = PTA + [TF + (TC – AC) *SR]

In our case, AC is PTA. Replacing AC with PTA we get

CP = PTA + [TF + (TC – PTA)*SR]

The total of Buyer’s and Seller’s Share Ratio is 1. So we can say SR = 1 – BR. Replacing this in the above equation

CP = PTA + [TF + (TC – PTA)*(1-BR)]

CP = PTA + TF + TC – TC*BR – PTA + PTA*BR

CP = (PTA*BR – TC*BR) + (TF + TC)

CP = (PTA – TC)*BR + TP

Solving the above equation for PTA, we get our final PTA formula

PTA = (CP – TP)/BR + TC

PTA formula also gives us $120K as the answer.

You should be able to remember the formula now. Please leave a comment if you have a question.