Price spread and floor differences across changing balances, showing why identical average index paths can reverse the total-cost result.
A lower floor is most valuable when the index is low and the outstanding balance is large. A lower spread becomes more valuable above the relevant crossover. If the balance changes during the hold, an average index rate cannot tell you which quote costs less.
This comparison prices the floor tradeoff over two years with a planned principal paydown. It extends beyond comparing two coupons at one index level by including a fee difference and the order in which high and low rates occur.
Transcribe both formulas exactly
Assume two invented interest-only offers on the same $8 million initial principal. Proposal A charges a 2.50% spread over an index floored at 4%. Proposal B charges a 3.25% spread over the same index floored at 1%. Both observe the identical benchmark on the same dates and use the same interest convention.
A coupon = max(index, 4%) + 2.50%
B coupon = max(index, 1%) + 3.25%
A charges $25,000 of initial fees. B charges $85,000, an additional $60,000. Both permit the same $4 million principal paydown at the end of year one without charge, leaving $4 million for year two. The paydown comes from the same separately funded property event under each route; its source and amount are not dependent on the interest savings.
Floor language must be read rather than inferred. For example, the Fannie Mae SARM summary states its own rate floor by reference to the margin. It does not supply the 4% and 1% index floors invented here. A floor on the total coupon would require a different formula.
Locate the coupon crossover
When the index is between 1% and 4%, A stays at 6.50%, while B equals the index plus 3.25%. The coupons are equal at a 3.25% index. Below that point B has the lower coupon; above it A has the lower coupon under these formulas.
| Index | A coupon | B coupon | B minus A on $8 million for one year |
|---|---|---|---|
| 0.50% | 6.50% | 4.25% | ($180,000) |
| 2.00% | 6.50% | 5.25% | ($100,000) |
| 3.25% | 6.50% | 6.50% | $0 |
| 5.00% | 7.50% | 8.25% | $60,000 |
Parentheses represent B costing less. The table isolates interest and excludes B’s additional $60,000 initial fee. Above the 4% floor, both coupons move with the index, and B’s 0.75-percentage-point larger spread makes it more expensive on equal balances.
The coupon crossover is not a total-cost break-even. At the 3.25% index the interest is identical, but B still costs $60,000 more because of its fee.
Apply the same two index levels in opposite orders
Now compare two paths. In each, the arithmetic average annual index is 3.50%. One path has a 2% index in year one and 5% in year two; the other reverses the order. Each annual rate is held constant within that year, using simple annual interest.
| Low index first | A | B |
|---|---|---|
| Year one: $8 million at the 2% index | $520,000 | $420,000 |
| Year two: $4 million at the 5% index | $300,000 | $330,000 |
| Initial fee | $25,000 | $85,000 |
| Two-year financing expense | $845,000 | $835,000 |
B saves $100,000 in year one, costs $30,000 more in year two, and requires $60,000 more upfront. It is $10,000 cheaper overall in this path.
| High index first | A | B |
|---|---|---|
| Year one: $8 million at the 5% index | $600,000 | $660,000 |
| Year two: $4 million at the 2% index | $260,000 | $210,000 |
| Initial fee | $25,000 | $85,000 |
| Two-year financing expense | $885,000 | $955,000 |
B now costs $70,000 more. The same pair of index levels produces an $80,000 swing in the relative result because the larger balance is exposed to a different rate state. Averaging the index and applying it to an average balance would lose that relationship and can also mishandle the nonlinear floors.
Price the fee against the relevant exposure
At a constant 2% index with the full $8 million outstanding, B saves $100,000 annually before its additional fee. Recovering the extra $60,000 takes 0.6 years, or 7.2 equal months, under this simplified path. That is a conditional fee-recovery calculation, not a forecast.
If the principal were only $4 million throughout, the annual saving at that index would be $50,000 and recovery would take 1.2 years. If the index stayed at 5%, B would never recover the extra fee through interest savings under these two formulas; its coupon would also be higher.
For a real schedule, calculate each period’s balance multiplied by its coupon difference and day-count fraction, then add the fee difference. Retain the sign: a positive B-minus-A result means B costs more. Use dated cash flows and discounting if the timing of costs matters to the owner, rather than labeling the nominal sum a present value.
Verify the assumptions before negotiating the floor
Ask whether a quoted floor applies to the index or the all-in rate, whether a benchmark adjustment is inside or outside it, and whether the spread changes during extensions. Confirm how scheduled or voluntary principal reductions affect the interest calculation and whether the quoted paydown is permitted.
A cap would add another payment stream and upfront cost. It cannot be inserted simply by replacing the loan’s contractual coupon with a lower number unless the settlement terms and timing support that treatment. This example has no cap, no amortization, and no additional exit fee.
The completed comparison should identify the index states and balance periods where each offer gains or loses, the cash paid for the lower floor, and the event that changes the exposure. A floor concession is valuable only in the periods when it affects the actual coupon on money still outstanding.
Sources and evidence
- Fannie Mae — SARM Loans Term SheetInterest Rate Adjustments; Interest Rate Cap; Conversion to Fixed Rate · Checked 2026-10-21 · Applies to the identified SARM product; not every adjustable-rate loan.
Source dates and applicability matter. Report an error or a changed source.