Interest rates are the input to housing cost that nobody in a city council chamber controls and everybody in a development company watches. A change of one percentage point, 100 basis points, sounds like the kind of thing that matters to bond traders. On an apartment building, where two thirds of the cost is typically borrowed and the loan is repaid from rent over decades, it is one of the largest single determinants of whether the building can exist.
This article takes Reference Project A, the garden project derived line by line in Why a New Apartment Costs $2,000 a Month, and asks a narrow question: holding everything else constant, what does a one-point rise in the permanent loan rate do to the rent the project requires? Then it asks the broader question, which is what happens when everything else does not stay constant.
Interest rate rises 1 point
+$127,090 / year
+$93/month
The number that converts a rate into a payment
A rate by itself does not tell you what a loan costs each year, because most real estate loans amortize: the payment covers interest plus a slice of principal, and the slice is set so that the loan is fully repaid over a fixed term. The figure that captures both is the mortgage constant, the total annual payment as a share of the amount borrowed. It is the single most useful number in real estate finance and it is worth seeing written out.
i = annual rate ÷ 12 n = years × 12
Monthly constant = i ÷ (1 − (1 + i)^−n)
Annual constant = Monthly constant × 12At 6.5%, 30 years: 0.0054167 ÷ (1 − 1.0054167^−360) × 12 = 0.075848
At 7.5%, 30 years: 0.00625 ÷ (1 − 1.00625^−360) × 12 = 0.083906A loan at 6.5 percent costs 7.585 percent of its balance a year, or $632.07 a month per $100,000. At 7.5 percent it costs 8.391 percent, or $699.21 a month per $100,000.
Notice that the constant rises by 0.806 percentage points when the rate rises by 1.0, not by the full point. That is because the principal portion of the payment shrinks as the interest portion grows; the lender is being repaid a little more slowly. The effect is real but it does not change the conclusion, because on a $15.8 million loan 0.806 percent is still $127,090 a year.
Debt service at five rates
Our illustrative project costs $24,265,760 to build and finances 65 percent of that, $15,772,744, with a permanent loan. The table shows what that loan costs to carry at rates from 4.5 to 8.5 percent, and, applying the rest of the pro forma unchanged, what rent the project requires at each.
| Loan rate | Mortgage constant | Annual debt service | Monthly debt service | Required rent per unit | Change vs. 6.5% |
|---|---|---|---|---|---|
| 4.5% | 6.080% | $959,018 | $79,918 | $1,822 | −$173 |
| 5.5% | 6.813% | $1,074,671 | $89,556 | $1,907 | −$89 |
| 6.5% | 7.585% | $1,196,334 | $99,694 | $1,996 | — |
| 7.5% | 8.391% | $1,323,424 | $110,285 | $2,089 | +$93 |
| 8.5% | 9.227% | $1,455,345 | $121,279 | $2,185 | +$189 |
Required monthly rent per unit by permanent loan rate (illustrative project)
See the numbers
| Category ($ per unit per month) | Required rent |
|---|---|
| 4.5% | $1,822 |
| 5.5% | $1,907 |
| 6.5% | $1,996 |
| 7.5% | $2,089 |
| 8.5% | $2,185 |
The required rent moves about $90 a month for each point, a little more at higher rates. The derivation for the one-point rise is short enough to show in full.
Added debt service = $15,772,744 × (0.083906 − 0.075848) = $127,090 per year
Gross up for vacancy = $127,090 ÷ 0.95 = $133,779
Per unit per month = $133,779 ÷ 120 ÷ 12 = $92.90Ninety-three dollars is 4.7 percent of the $1,996 the building needed before. It is roughly the entire Insurance line in the Housing Breakdown, or a little more than half the Property Taxes line, added by a decision made in Washington rather than in the city where the building stands.
What “all else constant” leaves out
The direct effect is the easy part. Interest rates do not rise in isolation, and three of the things that move with them each add to the rent a project requires.
Investors reprice too
The 8 percent cash yield we assume equity investors require is not a fixed law. It is a spread over what they could earn elsewhere with less risk. When a ten-year Treasury pays one point more, an investor who accepted 8 percent last year is likely to want something closer to 9 percent this year, or to put the money in the Treasury. If required equity yield rises by the same one point, the project must produce an additional $84,930 a year on its $8,493,016 of equity.
$8,493,016 × 0.01 ÷ 0.95 ÷ 1,440 = $62.08
Construction loans reprice first
Before the permanent loan there is a construction loan, usually at a floating rate, whose interest accrues while the building earns nothing and is capitalized into total cost. If the construction rate also rises one point, we estimate the added interest at about $157,727, using the same rough sizing as the breakdown’s financing assumption (a loan of about $15.8 million, outstanding for 24 months at an average balance of 50 percent). That $157,727 becomes part of development cost and is carried like any other capital cost: about $8.91 a month more.
The combined effect
Put the three together and a one-point move in rates raises the rent the project requires by about $164 a month: $93 from the permanent loan, $62 from the equity, $9 from construction interest. That is 8.2 percent of the original required rent, from a change that reads as a footnote in a monetary policy statement.
| Effect | Annual amount | Rent impact |
|---|---|---|
| Permanent loan, 6.5% → 7.5% | +$127,090 debt service | +$92.90 |
| Equity yield, 8% → 9% | +$84,930 required return | +$62.08 |
| Construction interest, +1 point | +$157,727 capitalized cost | +$8.91 |
| Combined | +$163.90 |
The effect that does not show up in rent
Everything above assumes the project gets built and rent adjusts. That is not what usually happens. Rent for a new building is set by the market, not the pro forma; the building that needed $1,996 and now needs $2,089 does not get to charge $2,089 if comparable apartments rent for $2,000. It gets shelved.
The arithmetic of shelving is worth seeing. At $2,000 rent, the project’s net operating income is fixed by the market at about $1,875,000. At 6.5 percent, that NOI supports $24.27 million of cost. At 7.5 percent, with the equity yield unchanged, the same NOI supports only $22.73 million, 6.3 percent less. Something in the budget has to give by $1.54 million: the land price, the construction scope, the developer fee, or the decision to proceed. In the short run, land is the usual candidate, which is why rising rates tend to show up first as falling land values and stalled land sales rather than as higher rents. In the longer run, if land does not fall enough, the project is not built, and the effect on rent arrives through the supply channel described in Why Housing Costs What It Costs.
There is one more constraint. Lenders require a cushion between NOI and debt service, the debt service coverage ratio, commonly around 1.20 to 1.25. At $2,000 rent, our project covers its debt 1.57 times at 6.5 percent, 1.42 times at 7.5 percent, and 1.29 times at 8.5 percent. It still qualifies at every rate in the table, but a project that started closer to the line, as many do, would find that the loan it was promised shrinks as rates rise, forcing it to raise more equity at exactly the moment equity has become more expensive.
Why the pain is not evenly distributed
Two projects facing the same rate increase can have very different experiences, and the difference is usually timing rather than skill. A project that closed its permanent loan before rates moved is insulated for the length of its fixed term; its rent requirement was locked in years ago. A project that is mid-construction on a floating-rate loan absorbs the increase immediately as capitalized interest and then has to refinance into whatever the permanent market offers at completion, which is the single most dangerous moment in a development timeline. A project still on paper has the most flexibility and the least to lose, because it can simply not proceed.
This is why rate increases show up in housing production statistics with a lag of a year or more. The buildings under construction when rates rise are finished, because stopping is more expensive than continuing. The buildings that were about to start are the ones that disappear, and they would have opened two to three years later. The shortage that results is dated to the year the buildings did not open, not the year the rate changed, which is one reason the connection between monetary policy and housing supply is so often missed.
Try it with your own assumptions
The calculator below is preloaded with the illustrative project. Change the interest rate and watch required rent move; change the loan-to-cost and watch the sensitivity to rates shrink as the project relies more on equity and less on debt, and then watch it grow again as the equity yield is raised.
- $24.3M
- 120
- $202,215
- $2M
Estimated rent impact
+$1,371/month per unit
Change the variables
See the assumptions
- 65% of the cost is financed with debt (loan-to-cost)
- 6.5% interest rate, amortized over 30 years
- 8% annual cash-on-cash return required on the 35% equity share
- 5% vacancy and collection loss
- Costs are spread across every unit and expressed per month
| Debt | $15,772,744 |
|---|---|
| Equity | $8,493,016 |
| Annual debt service | $1,196,334 |
| Annual return on equity | $679,441 |
| Required net operating income | $1,875,775 |
| Required revenue (after vacancy) | $1,974,500 |
| Per unit, per year | $16,454 |
| Per unit, per month | $1,371 |
Reference Project A (the garden project): an illustrative 120-unit three-storey wood-frame project with 180 surface parking spaces; total development cost $24,265,760 ($202,215 per unit); operating costs $854,658 per year ($7,122 per unit); required rent $1,995.93 per unit per month; 5 percent vacancy allowance. Why this project: it is the project the Housing Breakdown derives line by line, so a rate change can be run against a pro forma the reader has already seen in full. Both reference projects are defined side by side on our Methodology page.
Permanent loan: we assume 65 percent loan-to-cost, $15,772,744, fully amortizing over 30 years with level monthly payments. Base rate 6.5 percent; sensitivity rates 4.5, 5.5, 7.5 and 8.5 percent.
Equity: we assume $8,493,016 (35 percent of cost) requiring an 8 percent cash-on-cash yield in the base case and 9 percent in the second-order case.
Construction interest sensitivity: we assume a construction loan of about $15.8 million outstanding for 24 months at an average balance of 50 percent, so that one point of additional rate adds about $157,727 of capitalized cost.
In the direct case, every input other than the permanent loan rate is held constant, including development cost, operating costs, equity yield and vacancy.
Rates are illustrative and are not forecasts. The base rate of 6.5 percent is the default of our Rent Impact tool.
Debt service is computed with the standard level-payment amortization formula shown in the formula block; constants are carried unrounded (0.060798, 0.068133, 0.075848, 0.083906, 0.092270) and multiplied by the loan balance. Required rent at each rate is (debt service + equity return + operating costs) ÷ 0.95 ÷ 120 ÷ 12, the same method used throughout Housing Unpacked and on our Methodology page.
The second-order effects are additive approximations. The construction-interest effect is carried into required rent using the blended capital charge (0.65 × 0.083906 + 0.35 × 0.09 at the higher rates would be marginally different from the 0.077301 used; the difference is under a dollar a month and is ignored). The supportable-cost calculation holds NOI fixed at $1,875,775 and divides by the blended capital charge at each rate: 0.077301 at 6.5 percent and 0.082539 at 7.5 percent.
The model does not include interest-rate caps, floating-rate permanent debt, interest-only periods, prepayment terms, or the effect of rates on cap rates and exit values, all of which matter to investors and none of which change the rent the building must collect in a stabilized year.
The rates in the table are a range we chose in order to show the slope of the relationship. They are not a rate survey, a lender quote or a forecast, and no external data set was used to produce any figure in this article; everything follows from the assumptions stated above. Readers who want to see where benchmark rates actually stand can consult the daily Treasury yield curve published by the U.S. Department of the Treasury, and readers pricing a specific loan should take the spread, the coverage requirement and the term from the lender quoting it.
If the project relied less on debt, the direct effect would be smaller in proportion. At 50 percent loan-to-cost the one-point rise adds about $71 a month rather than $93; at 75 percent, about $107.
If loans amortized over a longer period, the constant would be lower and the sensitivity slightly smaller: a 40-year amortization at 6.5 percent has a constant of 7.025 percent versus 7.585 percent at 30 years. Longer amortization is a feature of some public and agency loan programs, examined in Could Government Finance Housing More Cheaply?, which works on Reference Project B, the costlier podium building, and so starts from a base rent of $2,415 rather than $1,996.
If equity yields did not move with rates, the combined effect would be about $102 rather than $164. Historically they move together, but with a lag and not one-for-one.
If rents in the market were rising quickly, a project could absorb higher rates through rent growth over the lease-up period rather than through a higher opening rent; this is how projects underwritten at low rates in a rising-rent market survived rate increases, and how others did not.
If land sellers cut prices in response to higher rates, the cost side of the pro forma would fall and the required rent with it; the 6.3 percent drop in supportable cost is the size of the land discount that would fully offset a one-point rise on this project.
What this means
On a building financed the way most apartment buildings are financed, one percentage point of interest is about $93 a month per apartment in required rent, and closer to $164 once the people supplying the equity and the construction loan reprice alongside the permanent lender. Those figures are specific to our illustrative project, but the proportions travel: a point of rate is roughly 5 to 8 percent of required rent on a two-thirds-leveraged project.
The larger consequence is not the rent that rises but the building that does not get built. Because the market, not the pro forma, sets rent, a rate increase usually cannot be passed through. It has to be absorbed by land, by scope, by returns, or by abandoning the project. When it is absorbed by abandonment, the effect on rent arrives years later, as a shortage, and by then the interest rate that caused it is rarely mentioned.