Two tests, not one: leverage is negative on cash yield when the interest rate beats the cap rate, and negative on IRR only when it beats the unlevered IRR.
Negative leverage is debt that costs more than the property yields. Buy at a 5.0 per cent cap rate with a 60 per cent loan at 6.5 per cent and the year-one cash-on-cash return falls from 5.00 to 2.75 per cent. It does not automatically lower the IRR: with 3 per cent income growth and a flat exit cap rate, the levered IRR is 9.97 per cent against 8.00 unlevered. On IRR, the debt only destroys return if growth falls below 1.5 per cent or the exit cap rate widens.
Worked in full in Private Equity Real Estate by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
An illustrative stabilised acquisition, bought at a cap rate below the cost of interest-only debt, which is the position many core and core-plus buyers found themselves in once rates rose. No transaction costs, no amortisation, and an exit at the same cap rate as entry, so that the leverage effect is isolated.
| Input | Value |
|---|---|
| Purchase price | 50,000,000 |
| Going-in cap rate | 5.0% |
| Year-one NOI | 2,500,000 |
| Loan at 60% LTV, interest-only | 30,000,000 |
| Interest rate | 6.5% |
| Annual interest | 1,950,000 |
| Equity | 20,000,000 |
| NOI growth a year | 3% |
| Hold, exit cap rate | 5 years, 5.0% |
Cash after interest is 2,500,000 − 1,950,000 = 550,000. On 20,000,000 of equity that is a year-one cash-on-cash return of 2.75 per cent, against 5.00 per cent with no debt. The formula shows why:
Cash-on-cash = cap rate + (cap rate − interest rate) × D/E
5.0% + (5.0% − 6.5%) × 1.5 = 2.75%
Excel, with cap in B1, rate in B2 and LTV in B3: =B1+(B1-B2)*B3/(1-B3)
Every dollar borrowed at 6.5 per cent buys income at 5.0 per cent, a negative spread of 1.5 points, and the debt-to-equity ratio of 1.5 multiplies it. The more you borrow, the worse it gets: at 70 per cent LTV the cash yield is 1.50 per cent. With an amortising loan, compare the cap rate with the loan constant instead of the interest rate, and the picture is worse still.
The IRR includes the sale, and that is where growth enters. At 3 per cent a year, year-six NOI capitalised at 5.0 per cent gives a sale price of 57,963,704, a gain of 7,963,704. Because the exit cap rate equals the entry cap rate, the unlevered IRR is exactly the cap rate plus growth, 8.00 per cent.
| Year | Unlevered | Levered |
|---|---|---|
| 0 | −50,000,000 | −20,000,000 |
| 1 | 2,500,000 | 550,000 |
| 2 | 2,575,000 | 625,000 |
| 3 | 2,652,250 | 702,250 |
| 4 | 2,731,818 | 781,818 |
| 5, with sale | 60,777,476 | 28,827,476 |
| IRR | 8.00% | 9.97% |
The levered IRR is 9.97 per cent, 1.97 points higher, and the equity multiple rises from 1.42x to 1.57x. The test for IRR is different from the test for cash yield:
Leverage raises the IRR when the unlevered IRR exceeds the cost of debt, not when the cap rate does.
Here: 8.00% unlevered against 6.5% debt, so leverage is positive on IRR while negative on cash.
Negative leverage is a bet that growth will arrive. The investor gives up income today, 2.75 per cent instead of 5.00, in exchange for a geared share of appreciation later. The whole return now sits in the exit, which is the least certain number in the model.
| NOI growth | Unlevered IRR | Levered IRR | Leverage effect, points |
|---|---|---|---|
| 0.0% | 5.00% | 2.75% | −2.25 |
| 1.0% | 6.00% | 5.28% | −0.72 |
| 1.5% | 6.50% | 6.50% | 0.00 |
| 2.0% | 7.00% | 7.69% | +0.69 |
| 3.0% | 8.00% | 9.97% | +1.97 |
| 4.0% | 9.00% | 12.17% | +3.17 |
The break-even is clean: at 1.5 per cent growth the unlevered IRR equals the 6.5 per cent cost of debt and leverage does nothing. Below it, every turn of debt subtracts return. The required growth is simply the interest rate minus the cap rate, provided the exit cap rate holds.
| LTV | Year-one cash-on-cash | Levered IRR |
|---|---|---|
| 0% | 5.00% | 8.00% |
| 40% | 4.00% | 8.91% |
| 50% | 3.50% | 9.35% |
| 60% | 2.75% | 9.97% |
| 70% | 1.50% | 10.95% |
The exit is the other risk. Widen the exit cap rate by 50 basis points to 5.5 per cent and, even with 3 per cent growth, the unlevered IRR falls to 6.24 per cent, below the cost of debt, and the levered IRR to 5.87 per cent. A deal that relies on negative leverage has two ways to fail and only one way to work.
Treating a higher levered IRR as proof that the debt is accretive. In a negative-leverage deal the levered IRR rises with LTV only because the model assumes growth above the 1.5 per cent break-even and a flat exit cap rate. The cash yield, which is real and contractual, moves the other way: 5.00 per cent falls to 1.50 at 70 per cent LTV. Show the investment committee both rows, and the break-even growth rate, before it approves the loan. If the business plan cannot clear interest rate minus cap rate with room to spare, buy with less debt or not at all.
The capital stack workbook that accompanies Private Equity Real Estate works the leverage arithmetic from no debt to 85 per cent loan-to-value; it is in the free workbooks for this book. For the positive case, where the cap rate exceeds the cost of debt, see how much 70% LTV amplifies equity returns, and for the cash yield on its own, how to calculate cash-on-cash return.
Cash-on-cash equals the cap rate plus the spread between the cap rate and the interest rate, times debt to equity. At a 5.0 per cent cap rate, a 6.5 per cent interest-only loan and 60 per cent LTV, the debt-to-equity ratio is 1.5, so cash-on-cash is 5.0 + (5.0 - 6.5) x 1.5 = 2.75 per cent, down from 5.00 per cent unlevered.
Yes, if the unlevered IRR, cap rate plus growth with a flat exit cap rate, exceeds the cost of debt. In the worked case 3 per cent NOI growth gives an 8.00 per cent unlevered IRR against 6.5 per cent debt, so 60 per cent leverage lifts the IRR to 9.97 per cent even though year-one cash yield falls to 2.75 per cent.
With an interest-only loan and an exit at the entry cap rate, growth must exceed the interest rate minus the cap rate. At a 6.5 per cent rate and a 5.0 per cent cap that is 1.5 per cent a year. At 1.0 per cent growth the 60 per cent loan costs 0.72 points of IRR; a 50 basis point wider exit cap also turns it negative.
This article is one calculation from Private Equity Real Estate. 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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