Sensitivity analysis
Also called Sensitivity table, Scenario analysis, Stress test.
Sensitivity analysis re-runs a model across a range of values for the assumptions that carry the outcome and reports how far the answer moves. Its purpose is to identify which two or three inputs the deal actually depends on, so that those get the evidence and the rest do not.
How it works
A range of returns is the output, not the point. The point is the ranking: on a typical five-year hold the exit cap rate, the rent growth rate and the hold period do most of the work, and an hour spent flexing a marketing budget is an hour not spent on the exit. A model whose most sensitive input has never been identified is a model nobody has finished reading.
The standard presentation is a two-way grid with one driver across the top and another down the side, most often exit cap rate against rent growth or against exit year. A one-way sensitivity is a single row of the same thing and is enough when the drivers are genuinely independent. Named cases, base and upside and downside, do a different job: they move several assumptions together into a coherent story, which a grid cannot do because a grid holds everything else fixed.
The failure mode is a grid that looks rigorous because it is symmetric. Ranges chosen as plus or minus a comfortable amount around the base case will produce a table in which every cell is acceptable, and a sensitivity in which nothing bad happens has tested nothing. Set the range from what the submarket has actually done, and make the downside case one that hurts.
Worked example
The sample property. Five-year hold, forward NOI of $3,602,721 in year six, all-in equity of $20,565,000.
| Sale price at a 5.40% exit cap | $66,717,056 |
|---|---|
| Sale price at a 5.75% exit cap | $62,656,017 |
| Sale price at a 6.00% exit cap | $60,045,350 |
| Swing across sixty basis points | $6,671,706 |
| As a share of the equity invested | 32.4% |
Sixty basis points of exit cap rate, which is an assumption about a market five years away, moves the equity outcome by a third. Almost nothing else in this model has that much leverage, which is why the grid gets run on it.
Conventions worth knowing
- Set the ranges from what the submarket has done, not from a symmetric band around the base case.
- Report the swing in dollars of equity as well as in return percentage. A committee reads the dollars faster and argues about them better.
The common mistake
Flexing one assumption when the drivers move together
Interest rates, cap rates and rent growth are correlated, so a grid that expands the exit cap while holding rent growth at the base case is describing a world that has not happened. The version worth building moves them coherently: a case where rates rise, cap rates expand, rent growth slows and concessions come back, all at once, because that is what the market actually delivers. Flexing one variable at a time understates the tail, and it understates it by more the more leveraged the deal is.
Related terms
- Going-in versus exit cap rateThe going-in cap rate is year-one NOI divided by the purchase price. The exit or terminal cap rate is the rate applied to the forward NOI at the end of the hold to estimate the sale price. The spread between them is one of the largest and least evidenced assumptions in any underwriting.
- Internal rate of returnThe internal rate of return is the discount rate at which the net present value of a deal's cash flows equals zero. It expresses a full investment, including the timing of every contribution and distribution, as a single annualized percentage.
- Discount rate and net present valueA discount rate is the annual rate at which a future dollar is converted into a present one. Net present value is the sum of a deal's cash flows after that conversion, less the equity invested: positive means the deal beats the rate, and the rate at which it is exactly zero is the internal rate of return.
- Break-even occupancyBreak-even occupancy is the occupancy level at which a property's collections exactly cover its operating expenses and debt service, with nothing left over. Below it, the property consumes cash instead of producing it.
- Equity multipleThe equity multiple is total distributions divided by total equity contributed, expressed as a multiple. A 2.0x means an investor received two dollars back for every dollar put in, counting the original dollar.
Keep reading
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