Two base prices, two firm periods, one cap, and the quarter in which the cheaper bid becomes the dearer contract.
An indexed price overtakes a dearer firm bid in the first quarter its indexed price rises above the rival's price, which, while the rival is still firm, is the quarter its cumulative indexation exceeds the gap between the two base prices. A bid at 104.00, firm for twelve months and then indexed quarterly at 8.4 and 5.1 per cent a year, crosses a rival at 109.50 that is firm for twenty-four months in month 19. Over three years the indexation costs 892,881.88, and a headline saving of 878,350.00 shrinks to 87,304.04, 9.9 per cent of what the price gap promised.
Worked in full in Contract Management by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
Tender evaluations compare year-one prices because those are the numbers on the bid forms. The price paths are what the buyer pays, and two clauses, the firm period and the cap, decide where those paths cross.
The case is Larchmere Industrial, the fictional buyer in the companion files of Contract Management, which chose between two bids for a three-year supply agreement.
| Term | Signed bid | Rejected bid |
|---|---|---|
| Base price | 104.00 | 109.50 |
| Firm period | 12 months | 24 months |
| Indexation after the firm period | quarterly, uncapped | quarterly, capped at 3.0% a year |
| Index movement, year two | 8.4% | 8.4% |
| Index movement, year three | 5.1% | 5.1% |
| Units, years one to three | 58,400 / 51,400 / 49,900 | |
Convert each annual index movement into a quarterly step, then compound the price from the end of the firm period.
Quarterly step = (1 + annual movement)1/4 − 1
Priceq = Priceq−1 × (1 + step), from the first quarter after the firm period
=MATCH(TRUE,INDEX(B2:B13>C2:C13,0),0) returns 7.| Quarter | Months | Signed | Rejected | Signed minus rejected |
|---|---|---|---|---|
| 1 to 4 | 1 to 12 | 104.00 | 109.50 | −5.50 |
| 5 | 13 to 15 | 106.12 | 109.50 | −3.38 |
| 6 | 16 to 18 | 108.29 | 109.50 | −1.21 |
| 7 | 19 to 21 | 110.50 | 109.50 | 1.00 |
| 8 | 22 to 24 | 112.75 | 109.50 | 3.25 |
| 9 | 25 to 27 | 114.16 | 110.31 | 3.85 |
| 10 | 28 to 30 | 115.59 | 111.13 | 4.46 |
| 11 | 31 to 33 | 117.03 | 111.95 | 5.08 |
| 12 | 34 to 36 | 118.49 | 112.78 | 5.72 |
Average prices paid are 104.00, 109.41 and 116.32 on the signed contract against 109.50, 109.50 and 111.54 on the rejected one. On the volumes actually taken:
| Year | Signed | Rejected | Saving |
|---|---|---|---|
| 1 | 6,073,600.00 | 6,394,800.00 | 321,200.00 |
| 2 | 5,623,843.62 | 5,628,300.00 | 4,456.38 |
| 3 | 5,804,238.26 | 5,565,885.92 | −238,352.34 |
| Term | 17,501,681.88 | 17,588,985.92 | 87,304.04 |
The price gap of 5.50 on 159,700 units promised 878,350.00. The cheaper bid still wins over the term, but by 87,304.04, and only because year one was banked before the paths crossed. Any extension beyond month 36 runs at the dearer price.
| Annual cap on signed indexation | Cost of indexation | Saving against rejected bid | Crossover |
|---|---|---|---|
| 0.0% (held at 104.00) | 0.0 | 980.2 | never |
| 2.0% | 238.2 | 742.0 | never |
| 3.0% | 354.6 | 625.6 | never |
| 4.0% | 477.1 | 503.0 | never |
| 6.0% | 685.4 | 294.8 | month 22 |
| Uncapped (as signed) | 892.9 | 87.3 | month 19 |
With the rival's own 3.0 per cent cap, the signed contract would have saved 625.6 thousand against the rival, more than seven times the 87.3 thousand it actually saved. Priced this way, the cap is worth more than whatever was left of the base price gap.
The price paths and the cap table are built quarter by quarter in the free workbook for this case on the Contract Management companion page. The indexed prices also drive the volume band, worked in what a minimum volume surcharge costs per unit short, and the case's warranty clause is in is a longer warranty worth more than a better remedy.
Take the fourth root: quarterly step equals (1 + annual movement) to the power of one quarter, minus one. An 8.4 per cent annual movement gives 2.04 per cent a quarter, so a 104.00 price becomes 106.12 in the first indexed quarter. Dividing by four instead overstates the compounded annual rise slightly.
Price both paths with and without it. In the worked case an uncapped signed contract saves 87.3 thousand against the rival bid over three years; with a 3.0 per cent annual cap it would have saved 625.6 thousand. The cap was worth more than the base price gap left after indexation.
Not if the price comparison already uses indexed price paths. The 892,881.88 of indexation in the case is the difference between the indexed path and a flat 104.00; it is already inside the 87,304.04 saving. Adding it again to a list of clause costs double counts it.
The two price paths and the crossover are built in the contract priced workbook, which covers chapters 1 to 17 of 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.
Get the book on Amazon →Free companion files
Also on Amazon UK · Amazon Germany · Amazon France · Amazon Canada
Reading guide: business operations: cost, contracts, pricing and supply chain → · All 453 articles →
If this book helped, or didn’t, a few lines on Amazon are worth more than they look: they are what the next reader goes on. Write a review. The workbook stays free either way.