## Fixed Price Contract Math

Firm Fixed Price Example

Scenario: A supplier is awarded an FFP contract for a special facility with certain specified features and functions. The contracted price is \$100,000 and the schedule is 120 days. The facility is ready in time with all required features and functions. The supplier announces that the actual cost was only \$80,000.

Q: How much does the project owe the supplier on obtaining a certificate of occupancy?

A: \$100,000. The price is firm and fixed regardless of whether the supplier overran or underran the estimates.

Let us move to another form of FP contract, one with an incentive fee, called FPI (fixed price incentive). In an incentive fee arrangement, some of the cost risk is retained by the project, but the supplier is given the opportunity to earn more or less fee commensurate with performance. There are several financial parameters in the FPI calculation.

### Fixed Price Incentive Example

Scenario: A supplier is awarded an FPI contract to build a special facility with certain specified features and functions. The contract cost (risk) sharing parameters are negotiated between the project and the contractor. In this example the parameters are as follows: the contracted target price (TP) is \$100,000, the target cost (TC) is \$85,000, the target fee (TF) is \$15,000, the target return on cost (ROC) is equal to 15/85 = 17.6%, the ceiling price (CPr) is \$110,000, and the sharing ratio (SR) is 80%/20% applied to cost. The schedule is 120 days.

In this example, the facility is ready in time with all required features and functions. Actual cost is denoted AC, the contractor's share is denoted SRc, and in this example SRc is equal to 20%.

The FPI formula is:

Contractor payable = (TC - AC) * SRc + AC + TF = CPr

Case 1. The supplier announces that the actual cost was only \$80,000, \$5,000 below target cost; the supplier is paid according to the formula

Contractor payable (\$000) = (\$85 - \$80) * 0.2 + \$80 + \$15 = \$96 = \$110

Case 2. The supplier announces that the AC = \$95,000, \$10,000 above TC:

Contractor payable (\$000) = (\$85 - \$95) * 0.2 + \$95 + \$15 = \$108 = \$110

Case 3. The supplier announces that the AC = \$105,000, \$20,000 above TC:

Contractor payable (\$000) = (\$85 - \$105) * 0.2 + \$105 + \$15 = \$116 = \$110

In this case, the ceiling price is exceeded. The project's cost risk is capped at \$110,000, so the contractor is paid only \$110,000.

It is instructive to understand what supplier cost, adjusted for incentive sharing, exactly equals the risk cap of the project. For this case, the contract situation has reached the point of total assumption (PTA). Costs above the cost at PTA are borne exclusively by the supplier, as shown in Figure 9-1. Below the PTA, costs are shared by the project according to the sharing ratio. The cost at PTA is defined by the formula

Figure 9-1: FPIF Risk.

Cost at PTA: (TC - AC) * SRc + AC + TF = CPr Solving for AC: AC at PTA = (CPr - TF - TC * SRc)/(1 - SRc) In the example that we have been discussing, the AC at PTA is (\$000):

AC at PTA = (\$110 - \$15 - \$85 * 0.2)/(1 - 0.2) = \$97.5