Lesson 20 of 25 · 6 min
Tiered pricing, and why the band matters more than the rate
Crossing a threshold by a single dollar can reprice every dollar behind it, which makes a boundary a strange place to sit.
The pricing grid from lesson 17 uses size bands rather than a smooth curve. That choice has an arithmetic consequence that has nothing to do with risk.
In a banded structure the whole balance is priced at the band's spread. A facility at $998,000 is priced in one band and a facility at $1,002,000 in the next, and the second spread applies to all of it. The alternative structure, which some facilities use, is marginal: each tranche is priced at its own spread and only the incremental dollars get the lower one. The two produce very different behaviour near a boundary.
Under a banded structure, the marginal cost of borrowing near a threshold is not merely low; it is negative. Four thousand dollars of additional balance that crosses a band can reduce the annual interest charge by more than five thousand, because it repriced the nine hundred and ninety-eight thousand behind it. Expressed as a rate on the increment, that is a figure with no sensible interpretation.
Lenders use bands because they are simple to administer, simple to quote, and because they reward the size of a relationship rather than the size of an increment. The discontinuity is a side effect, not a feature. But it means the quoted rate on a facility describes the band it sits in, and near an edge the band and the increment are not even the same sign.
Key terms
- Banded pricing
- A structure in which the whole balance takes the spread of whichever size band it falls in. Produces a step change at each boundary.
- Marginal pricing
- A structure in which each tranche of the balance carries its own spread. Continuous at the boundaries, and less common in these facilities.
- Boundary effect
- The discontinuity in total cost at a band edge, where a small change in balance reprices the entire amount behind it.
Worked example
Four thousand dollars at a band edge
Illustrative bands: below $1,000,000 at 265 basis points, from $1,000,000 to $2,500,000 at 210, above that at 160. Index 4.40 percent.
- Balance $998,000, rate 7.05%
- $70,359 a year
- Balance $1,002,000, rate 6.50%
- $65,130 a year
- Additional balance
- $4,000
- Change in annual interest
- minus $5,229
- Implied annual cost of the marginal $4,000
- minus 130.7%
$998,000 × 0.0705.
$1,002,000 × 0.0650.
$5,229 divided by $4,000.
The quoted rate describes the band, not the increment. At a boundary the two carry opposite signs, which is an artefact of the structure rather than a view about risk.
Check yourself
A banded grid charges 240 basis points below $2,000,000 and 175 at or above it. The index is 5.05 percent. Compare the annual interest on balances of $1,985,000 and $2,010,000.
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Educational only. Nothing in this lesson is investment, legal or tax advice, or a recommendation to enter into any transaction. Figures are illustrative and computed from the inputs stated in the lesson.