The cheap loan is smaller and shorter than the buyer wants. Value it against the financing the buyer would otherwise use, not against the same balance at today's rate.
An assumable mortgage is worth the present value of the interest it saves against new debt, less the assumption fee and the cost of filling any gap to the buyer's target leverage. On an illustrative $60.0M purchase, assuming a $30.0M loan at 4.00 per cent with four years left saves $750,000 a year against a 6.50 per cent new loan, $2,569,349 in present value. Topping it up to 65 per cent loan-to-value with mezzanine at 10.00 per cent cuts the value to $1,445,222, 2.41 per cent of the price: the figure a buyer can afford to pay for the loan.
Worked in full in Real Estate Finance by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
When rates rise, fixed-rate loans written earlier become assets. A seller with a 4 per cent loan that the lender will let a buyer assume can argue for a higher price; a buyer has to decide how much of that cheap debt is really worth paying for. The answer is rarely the headline rate gap times the balance, because the old loan is usually smaller than the buyer wants, shorter than a new loan, and comes with its own fees.
| Input | Value |
|---|---|
| Purchase price | $60,000,000 |
| Existing loan | $30,000,000 (50% LTV) at 4.00%, 4 years left |
| Buyer's target leverage | 65% ($39,000,000) |
| New senior loan rate | 6.50% |
| Mezzanine rate for the $9,000,000 gap | 10.00% |
| Assumption fee | 1.0% of the assumed balance |
| Mezzanine fee / new loan fee | 1.5% / 1.0% |
Value of the rate = balance × (new rate − old rate) × annuity factor at the new rate
$30,000,000 × 2.50% = $750,000 a year. Over 4 years at 6.50% the annuity factor is 3.4258, so the saving is worth $2,569,349 today, or $2,269,349 after the $300,000 assumption fee. In Excel: =PV(6.5%,4,-750000)-300000
The discount rate is the new loan rate because the saving is a debt cash flow: it is what the buyer would pay a lender to borrow the same amount for the same period. Discounting at an equity return would undervalue it; not discounting at all, $3,000,000, overstates it by 17 per cent.
The buyer does not choose between $30.0M at 4.00 per cent and $30.0M at 6.50 per cent. It wants $39.0M of debt. Assuming the loan means taking the $30.0M and filling the $9.0M gap with expensive subordinate debt; not assuming it means a single new $39.0M loan.
| Line | A: assume + mezzanine, $ | B: new senior loan, $ |
|---|---|---|
| Senior interest | 1,200,000 | 2,535,000 |
| Mezzanine interest | 900,000 | 0 |
| Total interest a year | 2,100,000 | 2,535,000 |
| Blended rate | 5.38% | 6.50% |
| Upfront fees | 435,000 | 390,000 |
The annual saving falls from $750,000 to $435,000, because the $9.0M of mezzanine costs 3.50 points more than senior debt, $315,000 a year. Package A also pays $45,000 more in fees: a $300,000 assumption fee and $135,000 on the mezzanine, against $390,000 on a new loan.
Net value = PV(annual interest saving) − (fees A − fees B)
$435,000 × 3.4258 = $1,490,222; less $45,000 = $1,445,222, which is 2.41% of the $60.0M price.
| Years left | Rate saving alone, PV $ | Net value of package A, $ | Share of price |
|---|---|---|---|
| 2 | 1,365,470 | 746,972 | 1.24% |
| 3 | 1,986,357 | 1,107,087 | 1.85% |
| 4 | 2,569,349 | 1,445,222 | 2.41% |
| 6 | 3,630,760 | 2,060,841 | 3.43% |
| New loan rate | Annual saving, $ | Net value, $ | Share of price |
|---|---|---|---|
| 5.50% | 45,000 | 112,732 | 0.19% |
| 6.00% | 240,000 | 786,625 | 1.31% |
| 6.50% | 435,000 | 1,445,222 | 2.41% |
| 7.50% | 825,000 | 2,718,194 | 4.53% |
Below a new loan rate of about 5.42 per cent, assuming the loan and buying mezzanine is worth nothing: the expensive gap financing eats the whole rate advantage. The value is also very sensitive to the term left. With two years to run the buyer pays fees and takes a short refinancing horizon for $746,972.
Pricing the assumption as the rate gap on the balance, $750,000 a year for four years, and adding $3,000,000 to the offer. That ignores discounting, the gap financing and the fees, and it ignores the maturity mismatch: in four years package A must be refinanced at whatever rates are then, while a new loan may run for five or ten. A buyer who pays the full rate saving for an assumable loan has bought cheap debt at the price of expensive debt, plus a refinancing risk four years out. The fair premium is the net value, here $1,445,222, and less if the buyer puts a cost on refinancing early.
Assumption terms, fees, lender consent and whether a loan is assumable at all depend on the loan documents. Rates are illustrative; this is not advice on any transaction.
How a lender sizes and prices the debt on the same property is the subject of the free workbooks for this book. The fees-in cost of a new loan is worked in the all-in cost of a commercial mortgage, and the gap financing in mezzanine vs preferred equity.
Take the annual interest saving against the buyer's alternative financing, discount it at the new loan rate over the years left, and deduct the extra fees. A $30.0M loan at 4.00 per cent against 6.50 per cent saves $750,000 a year; over four years that is $2,569,349, or $2,269,349 after a 1 per cent assumption fee.
Up to the net value of the financing, not the headline rate gap. Where the assumed loan is only 50 per cent LTV and the buyer wants 65 per cent, the $9.0M gap at 10.00 per cent cuts the annual saving from $750,000 to $435,000 and the value to $1,445,222, 2.41 per cent of a $60.0M price.
The rate at which the buyer could borrow the same amount today, here 6.50 per cent, because the saving is a debt cash flow. Leaving it undiscounted gives $3,000,000 over four years, 17 per cent more than the $2,569,349 present value.
This article is one calculation from Real Estate Finance. 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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