A fixed price looks dear against the supplier's estimate plus margin. Against the expected cost of cost-plus, the gap is the price of insurance.
Compare the fixed price with the expected cost of the cost-plus contract across realistic outcomes, including the cost drift cost-plus invites and the buyer's own audit costs, not with the supplier's base estimate plus fee. On an illustrative 1,000,000 job with a one-in-four chance of a 30 per cent overrun, a fixed price of 1,209,600 against an expected 1,171,000 on cost-plus with a fixed fee means the buyer pays 38,600 for certainty, and cost-plus with a percentage fee saves only 10,240. In the bad case, cost-plus costs 216,400 more.
Worked in full in Contract Management by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
The usual comparison is the wrong one. The buyer sees a fixed price with a 12 per cent contingency in it, works out that cost-plus at the same margin would be 1,080,000, and concludes that the fixed price wastes 129,600. That treats the base estimate as the outcome. The real question is narrower: what does the buyer pay, on average and at worst, under each form of contract, and is the difference a fair price for moving the overrun risk to the supplier?
| Input | Value |
|---|---|
| Supplier's base cost estimate | 1,000,000 |
| Cost outcomes: low / base / high | 900,000 / 1,000,000 / 1,300,000 |
| Probabilities | 25% / 50% / 25% |
| Supplier margin | 8.0% |
| Risk contingency priced into a fixed price | 12.0% |
| Cost drift under cost-plus with a percentage fee | 4.0% |
| Cost drift under cost-plus with a fixed fee | 2.0% |
| Buyer's audit and open-book administration under cost-plus | 20,000 |
The drift figures are the judgement call. Under a percentage fee the supplier earns more when cost rises, so some inefficiency is likely; under a fixed fee it earns the same either way, so drift is smaller but not zero, because nobody is rewarded for saving. Both are illustrative.
Expected cost of the work. 0.25 × 900,000 + 0.50 × 1,000,000 + 0.25 × 1,300,000 = 1,050,000, 5.0 per cent above the base estimate.
Fixed price. 1,000,000 × 1.12 = 1,120,000, plus 8.0 per cent margin of 89,600 = 1,209,600 in every outcome.
Cost-plus, percentage fee. Cost × 1.04 × 1.08 + 20,000. Expected: 1,050,000 × 1.04 = 1,092,000, plus 87,360 of fee, plus 20,000 = 1,199,360.
Cost-plus, fixed fee. Cost × 1.02 + 80,000 + 20,000. Expected: 1,071,000 + 80,000 + 20,000 = 1,171,000.
In Excel, with outcomes in B2:B4 and probabilities in C2:C4: =SUMPRODUCT(B2:B4*1.02+80000+20000,C2:C4) for the fixed-fee contract.
| Outcome | Probability | Fixed price | Cost-plus, % fee | Cost-plus, fixed fee |
|---|---|---|---|---|
| Low (900,000) | 25% | 1,209,600 | 1,030,880 | 1,018,000 |
| Base (1,000,000) | 50% | 1,209,600 | 1,143,200 | 1,120,000 |
| High (1,300,000) | 25% | 1,209,600 | 1,480,160 | 1,426,000 |
| Expected | 1,209,600 | 1,199,360 | 1,171,000 |
On expected cost, cost-plus with a fixed fee is cheapest, by 38,600 against the fixed price. That is the premium the buyer pays to cap its cost at 1,209,600 instead of facing 1,426,000 one time in four. The supplier, for its part, expects to earn 159,600 on the fixed price, 15.2 per cent on expected cost, against 80,000 under the fixed fee: it is paid nearly double for carrying the overrun.
Cost-plus with a percentage fee is the worst of both. It saves only 10,240 on average, because the fee grows with the overrun and the drift, and it is the dearest contract in the high case at 1,480,160. Of the 28,360 by which it trails the fixed-fee version, 21,000 is the extra cost drift the percentage fee invites and 7,360 is the fee earned on the expected overrun and on that drift.
| Probability of high case | Expected cost of work | Fixed price | Cost-plus, % fee | Cost-plus, fixed fee |
|---|---|---|---|---|
| 10% | 1,005,000 | 1,209,600 | 1,148,816 | 1,125,100 |
| 25% | 1,050,000 | 1,209,600 | 1,199,360 | 1,171,000 |
| 40% | 1,095,000 | 1,209,600 | 1,249,904 | 1,216,900 |
The fixed price wins on average once the chance of the high case passes about 38 per cent, and the percentage-fee contract loses to it much sooner, not far above the 25 per cent base case. Put the other way, at a 25 per cent chance of overrun a fixed price is worth taking only if its contingency is below 8.4 per cent. A supplier pricing 12.0 per cent is charging for more risk than the buyer believes exists, which is the moment to test the contingency line in a should-cost model.
The usual error is to compare the fixed price with base cost plus margin, 1,080,000, and call the 129,600 difference waste. The real expected saving from cost-plus is 38,600 at best, and it comes with a 25 per cent chance of paying 216,400 more. The second error is to ignore the buyer's own costs: open-book auditing, invoice checking and the time spent arguing about allowable costs. At 20,000 here, they equal more than half of the 38,600 saving that remains.
For the approval paper: show the expected cost and the high-case cost of each form side by side, and the contingency at which they break even. If the business cannot absorb the high case, the 38,600 is cheap insurance. If it can, a cost-plus fixed-fee contract, or a target cost with a shared overrun, keeps most of the saving.
Price each contract form over the outcomes, not at the estimate. Here: fixed price 1,209,600, cost-plus fixed fee 1,171,000 expected and 1,426,000 at worst, percentage fee 1,199,360 and 1,480,160. Never a percentage fee if a fixed fee is available. How a signed price and the clauses around it diverge from the approval case is worked clause by clause in the free workbooks for this book.
On average it can be, because the buyer does not pay the supplier's risk contingency, but it carries the overrun. In the illustration cost-plus with a fixed fee costs 1,171,000 on average against a 1,209,600 fixed price, a saving of 38,600, while in the high case it costs 1,426,000, which is 216,400 more.
Because the supplier's fee rises with the cost, so it is rewarded for overruns and inefficiency. In the illustration it saves only 10,240 against the fixed price on average and is the dearest option in the high case, at 1,480,160, against 1,426,000 with a fixed fee.
One that matches the expected overrun plus a fair premium for carrying it. With a 25 per cent chance of a 30 per cent overrun, the illustrative fixed price breaks even with cost-plus fixed fee at a contingency of 8.4 per cent. A 12.0 per cent contingency charges the buyer for more risk than the outcomes imply.
This article is one calculation from Contract Management. The book takes the same case from first principles to the decision, chapter by chapter, and every figure it prints is a live formula in the free companion workbooks.
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