Discount rate and net present value
Also called NPV, Net present value, Discount rate.
A 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.
How it works
Net present value and IRR are the same calculation read in opposite directions. IRR solves for the rate that makes the present value of the cash flows equal the investment. Net present value fixes the rate and reports the surplus in dollars. Which one is more useful depends on whether the question is how fast the money compounded or how much better than a hurdle the deal is, in money.
The dollar answer has one property IRR does not: scale. A 20 percent return on $500,000 and a 20 percent return on $50 million are the same number and are not the same opportunity, and IRRs cannot be added across deals while present values can. That is why net present value is the standard tool in corporate finance and the honest way to rank differently sized deals against one required return.
Its weakness is that the rate has to come from somewhere, and in private real estate nobody can read one off a market. In practice it is a policy choice: an investor's required return, a fund's hurdle, or a weighted cost of capital assembled from the debt rate and a target equity return. Because a chosen number moves the answer substantially, a present value should always be reported at more than one rate.
Formula
NPV = the sum of each cash flow divided by (1 + discount rate) raised to its period, less the equity invested- Positive when the deal returns more than the discount rate, zero when it returns exactly that rate
- The rate at which the present value is zero is the internal rate of return
- Levered cash flows are discounted at an equity rate; unlevered cash flows at a rate that reflects the property rather than the financing
Worked example
Illustrative. $10,000,000 of equity, four years of modest distributions, then $14,500,000 in year five. This is the stream that produces an 11.14 percent internal rate of return.
| Equity invested at period zero | ($10,000,000) |
|---|---|
| Distributions, years one to four | $400,000, $450,000, $500,000, $550,000 |
| Year five, including sale proceeds | $14,500,000 |
| Net present value at a 10% rate | $490,211 |
| Net present value at a 12% rate | ($351,005) |
| The rate at which the present value is zero | 11.14% |
Two hundred basis points of discount rate is $841,216 of present value on a $10 million commitment. The deal clears a 10 percent hurdle by nearly half a million dollars and misses a 12 percent hurdle by a third of one, and nothing about the property changed between those two sentences.
Conventions worth knowing
- Report the present value across a range of rates rather than at one. The rate is chosen, and showing only the flattering choice is a presentation rather than an analysis.
- Discount unlevered cash flows at an unlevered rate and levered cash flows at a levered one. Mixing the two values the financing twice.
The common mistake
Discounting levered cash flow at a property-level rate
Levered cash flow is what is left after the lender has been paid, which makes it riskier than the property's income, not less risky. Applying a property-level rate to it treats leveraged equity as though it carried unleveraged risk, and it overstates the present value every time, by more the higher the leverage. Match the rate to the stream: property cash flow at a rate that reflects the asset, equity cash flow at the return an equity investor requires for that capital structure.
Related terms
- 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.
- 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.
- Cash-on-cash returnCash-on-cash return is a year's cash flow after debt service divided by the total equity invested. It measures the current income yield on the money actually at risk, ignoring appreciation and any eventual sale.
- Cap rateA cap rate is a property's net operating income divided by its value or price, expressed as a percentage. It is the unlevered first-year yield on the purchase price and the standard shorthand for what a market is paying for a stream of property income.
- Sensitivity analysisSensitivity 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.
Keep reading
Every figure, traced to its source
Altyst computes these in exact decimal arithmetic, not with a language model, and clicking any number shows the formula behind it.