A floating-rate bridge loan whose cap expires before the extension: the Black-model cost of the replacement, why a 100 basis point move multiplies it by 5.7, and the monthly deposit that covers it.
Size the reserve on what the replacement cap will cost when it has to be bought, at a stressed rate, and spread that over the months left. On an illustrative 40,000,000 bridge loan, a 12-month cap struck at 4.50 per cent costs 33,243 if forward SOFR is 3.75 per cent on the day, but 191,001 if forwards are 100 basis points higher, so a reserve that holds through the move takes 15,917 a month, not 2,770.
Worked in full in The Real Estate Debt Investor by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
A floating-rate bridge loan usually requires the borrower to buy an interest rate cap for the initial term, struck where the property's income still covers interest. The cap is commonly bought for the initial term only, because longer caps cost more, and the extension options require a new cap. If rates have risen by then, the borrower may not have the cash to buy it, and an extension that depends on a cap the borrower cannot afford is not an extension. Lenders therefore require monthly deposits into a cap reserve during the year before expiry. The arithmetic is short, and the inputs that matter are not the ones usually discussed.
| Input | Value |
|---|---|
| Loan balance, interest only | 40,000,000 |
| Spread over SOFR | 3.50% |
| Replacement cap: strike / term | 4.50% / 12 monthly caplets |
| Forward SOFR today, flat | 3.75% |
| Cap volatility, Black lognormal | 30% |
| Reserve deposits | 12, months 13 to 24 |
| Stress for sizing: forwards | +100bp |
At the strike the all-in rate is 8.00 per cent, 3,200,000 of interest a year: that is the worst case the cap is there to guarantee. Market inputs are illustrative.
Step 1: one caplet. Each month is an option on that month's SOFR: caplet = notional × 1/12 × DF × [F × N(d1) − K × N(d2)], with d1 = [ln(F/K) + σ²T/2] / (σ√T) and d2 = d1 − σ√T.
Step 2: the last caplet, fixing 11 months after purchase (T = 0.917): d1 = −0.491, d2 = −0.778, N(d1) = 0.3117, N(d2) = 0.2182. Value = 6,002. The first caplets are worth almost nothing: a month out, a 75 basis point move is a long way.
Step 3: the cap. Sum the 12 caplets: 33,243, 0.083% of the loan, if forwards are still 3.75% at month 24.
Step 4: the stressed cap. Same strike and volatility, forwards at 4.75%: 191,001, 0.478% of the loan.
Step 5: the deposit. 191,001 / 12 = 15,917 a month.
Excel, one caplet: =Notional/12*DF*(F*NORM.S.DIST(d1,TRUE)-K*NORM.S.DIST(d2,TRUE))
The pricing mechanics are covered in more depth in how to price an interest rate cap with the Black model; the point here is what they imply for the reserve.
| Forward SOFR at purchase | Cap cost | Per cent of loan | Monthly deposit |
|---|---|---|---|
| 3.25% | 9,660 | 0.024% | 805 |
| 3.75% | 33,243 | 0.083% | 2,770 |
| 4.25% | 86,948 | 0.217% | 7,246 |
| 4.75% | 191,001 | 0.478% | 15,917 |
| 5.25% | 339,740 | 0.849% | 28,312 |
An out-of-the-money cap is convex: as forwards approach the strike, the cost does not rise in line with rates but by multiples. A reserve sized on today's forwards, 2,770 a month, covers the cap only if nothing moves, which is the one scenario in which the borrower did not need a reserve. Sized for a 100 basis point rise, the deposit is 15,917. Volatility matters less than the level: at 20 per cent the stressed cap costs 149,395, at 40 per cent 233,654.
| Strike | Cost |
|---|---|
| 4.00% | 330,323 |
| 4.50% | 191,001 |
| 5.00% | 100,445 |
| 5.50% | 53,717 |
The strike is the borrower's lever. A higher strike roughly halves the cost per 50 basis points, but it raises the worst-case interest the property must cover, so the lender will accept it only if the income supports it; that link is the subject of what NOI a bridge loan needs to refinance. The other option is to buy the extension cap now, starting in 12 months. It costs 108,703 today, more than three times the base case, because it carries a year more optionality, but 82,298 less than the stressed figure. A borrower that expects to extend fixes its cost for less than the stressed reserve; a borrower that may repay before the extension pays for a cap it may not need.
Many loan agreements size the reserve on a broker's indicative quote taken at closing or at the start of the reserve period, then never revisit it. The quote may even be for the forward-starting cap, 108,703, which looks prudent beside the 33,243 base case and still leaves 82,298 uncovered if forwards rise 100 basis points. Two fixes work: size on a stressed forward, as here, or recalculate monthly and true up the deposit, which keeps the reserve right but makes the borrower's cash needs unpredictable exactly when rates rise. Either way, model the deposit in the business plan as debt service. The reserve that covers interest during lease-up is a separate calculation, set out in how to calculate an interest reserve on a bridge loan.
All figures are illustrative, with flat forwards and one volatility for every caplet. Real caps are priced on the forward curve and a volatility surface, and usually on normal volatility; the shape of the result, a convex cost and a stressed reserve several times the base, does not change.
The book treats hedging alongside the maturity it has to reach, and the free workbooks for this book include a case in which cover falls to 1.2x only if rates climb 2.62 points past the strike.
A lender-controlled account the borrower funds monthly so that the cash to buy a replacement or extension cap is there when the existing cap expires. On the illustrative 40,000,000 bridge loan, a reserve sized for forwards 100 basis points higher than today takes 15,917 a month for 12 months to cover a 191,001 cap.
Because an out-of-the-money option gains value faster than the rate moves as it approaches the strike. With a 4.50% strike, a 12-month cap on 40,000,000 costs 9,660 at 3.25% forward SOFR, 33,243 at 3.75%, 86,948 at 4.25% and 191,001 at 4.75%: 100 basis points multiplies the cost by 5.7.
It can, and it fixes the cost. On the illustrative loan a cap starting in 12 months costs 108,703 today, more than the 33,243 expected if rates do not move but well below the 191,001 the cap would cost after a 100 basis point rise. It is a hedge against the hedge, and the lender usually accepts it in place of the reserve.
This article is one calculation from The Real Estate Debt Investor. 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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