Point of Total Assumption (PTA) Calculator
The Point of Total Assumption (PTA) is a critical concept in Fixed-Price Incentive Fee (FPIF) contracts. It represents the cost point at which the seller assumes all additional costs beyond that point, up to the contract's ceiling price. Understanding PTA helps both buyers and sellers manage risk and understand the financial implications of cost overruns.
In an FPIF contract, the buyer and seller agree on a target cost, a target profit, and a sharing ratio for cost overruns or underruns. There's also a ceiling price, which is the maximum the buyer will pay. The PTA is the cost at which the seller's share of cost overruns would cause their profit to be completely eroded, meaning any further cost increases come directly out of their pocket, up to the ceiling price.
How to Calculate Point of Total Assumption
The formula for the Point of Total Assumption (PTA) is:
PTA = ((Ceiling Price - Target Price) / Seller's Share Ratio) + Target Cost
Where:
- Target Cost: The estimated cost of the project agreed upon by both parties.
- Target Price: The price the buyer will pay if the project is completed at the Target Cost. This includes the Target Profit.
- Ceiling Price: The maximum price the buyer will pay, regardless of how high the actual cost goes.
- Seller's Share Ratio: The percentage of cost overruns that the seller is responsible for. This is usually derived from the sharing ratio (e.g., if the sharing ratio is 80/20 (Buyer/Seller), the Seller's Share Ratio is 20% or 0.20).
Understanding the Result
The PTA value represents a critical threshold. If the actual project cost exceeds the PTA, the seller will absorb 100% of any additional costs, up to the Ceiling Price. At the Ceiling Price, the buyer's payment obligation stops, and any further costs are entirely borne by the seller, potentially leading to significant losses.
Example Scenario
Let's consider a project with the following parameters:
- Target Cost (TC): $1,000,000
- Target Price (TP): $1,100,000
- Ceiling Price (CP): $1,200,000
- Sharing Ratio: 80/20 (Buyer/Seller), meaning the Seller's Share Ratio is 20% (or 0.20)
Using the formula:
PTA = (($1,200,000 - $1,100,000) / 0.20) + $1,000,000
PTA = ($100,000 / 0.20) + $1,000,000
PTA = $500,000 + $1,000,000
PTA = $1,500,000
In this example, the Point of Total Assumption is $1,500,000. This means if the actual project cost exceeds $1,500,000, the seller will bear 100% of the additional costs. The buyer's maximum payment will be the Ceiling Price of $1,200,000, which would be reached when the actual cost hits $1,500,000 (because at $1,500,000 actual cost, the buyer pays $1,100,000 (target price) + ($1,500,000 – $1,000,000) * 0.80 (buyer's share) = $1,100,000 + $400,000 = $1,500,000. Wait, this is incorrect. Let's re-evaluate the example explanation for clarity.
Let's re-examine the example's implications:
- If the actual cost is $1,000,000 (Target Cost), the buyer pays $1,100,000 (Target Price). Seller's profit: $100,000.
- If the actual cost is $1,500,000 (PTA), the cost overrun is $500,000 ($1,500,000 – $1,000,000).
- Buyer's share of overrun: $500,000 * 0.80 = $400,000.
- Seller's share of overrun: $500,000 * 0.20 = $100,000.
- Buyer pays: Target Price + Buyer's Share of Overrun = $1,100,000 + $400,000 = $1,500,000.
- Seller's profit: Target Profit – Seller's Share of Overrun = $100,000 – $100,000 = $0.
At the PTA of $1,500,000, the seller's profit has been completely eroded to $0, and the buyer's payment has reached $1,500,000. However, the Ceiling Price is $1,200,000. This means the buyer will never pay more than $1,200,000. The PTA calculation tells us the cost point where the seller's profit hits zero *if the ceiling price wasn't there*. Since the ceiling price is lower than the buyer's payment at PTA, the ceiling price becomes the effective cap much earlier.
Let's adjust the example to make the PTA more illustrative in relation to the Ceiling Price:
- Target Cost (TC): $1,000,000
- Target Price (TP): $1,100,000
- Ceiling Price (CP): $1,300,000 (Changed from $1,200,000)
- Seller's Share Ratio: 20% (0.20)
PTA = (($1,300,000 - $1,100,000) / 0.20) + $1,000,000
PTA = ($200,000 / 0.20) + $1,000,000
PTA = $1,000,000 + $1,000,000
PTA = $2,000,000
In this revised example, the PTA is $2,000,000. This means if the actual cost reaches $2,000,000, the seller's profit will be $0. The buyer's payment at this point would be $1,100,000 (TP) + ($2,000,000 – $1,000,000) * 0.80 = $1,100,000 + $800,000 = $1,900,000. Since $1,900,000 is less than the Ceiling Price of $1,300,000, this example still doesn't quite show the PTA being the point where the buyer hits the ceiling. The PTA is the cost at which the seller's profit becomes zero. The buyer's payment at PTA is not necessarily the ceiling price.
Let's use the initial example values in the calculator and explain the implications clearly:
- Target Cost (TC): $1,000,000
- Target Price (TP): $1,100,000
- Ceiling Price (CP): $1,200,000
- Seller's Share Ratio: 20% (0.20)
The calculated PTA is $1,500,000. This means that if the project's actual cost reaches $1,500,000, the seller's profit will be completely eroded to $0. However, the buyer's maximum payment is capped at the Ceiling Price of $1,200,000. The buyer will reach this maximum payment when the actual cost is lower than the PTA. Specifically, the buyer reaches the ceiling price when:
Ceiling Price = Target Price + (Actual Cost - Target Cost) * Buyer's Share Ratio
$1,200,000 = $1,100,000 + (Actual Cost - $1,000,000) * 0.80
$100,000 = (Actual Cost - $1,000,000) * 0.80
$100,000 / 0.80 = Actual Cost - $1,000,000
$125,000 = Actual Cost - $1,000,000
Actual Cost = $1,125,000
So, in this scenario, the buyer hits their Ceiling Price of $1,200,000 when the actual project cost reaches $1,125,000. Beyond this cost, the buyer will continue to pay $1,200,000, and the seller will absorb 100% of all additional costs. The PTA of $1,500,000 is the point where the seller's profit would theoretically become zero if the ceiling price didn't intervene earlier. Since the ceiling price is hit at $1,125,000, the seller starts absorbing 100% of costs from $1,125,000 onwards, and their profit will be zero well before the calculated PTA of $1,500,000. The PTA is still a useful metric for understanding the theoretical point of profit erosion.
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