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

- PTA can be more than the Ceiling Price.
- At or above PTA, buyer pays the Ceiling Price.
- At or above PTA, the contract price is fixed, and is equal to the Ceiling Price.
- At PTA, Buyer-Seller share ratio becomes 0:100.
- At PTA, a Fixed Price Incentive Fee (FPIF) contract becomes a Firm Fixed Price (FFP) contract.
- 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.
- Beyond PTA, all costs on the project are completely borne by the seller.
- Seller is usually more concerned about the PTA.

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

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

Image credit: Flickr / islandfreedom

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