Ellwood – A Beautiful Mathematical Formula But – Often Misused

Ellwood – A Beautiful Mathematical Formula But – Often Misused

By James R. MacCrate, MAI, CRE, ASA

I have had the opportunity to review many real estate appraisal reports over the last two years and I am amazed by the number of real estate appraisers who only use


to develop overall capitalization rates.  Commonly known as the Ellwood formula.  No wonder why folks question real estate appraisals on commercial properties.  This formula does not reflect the actions of informed real estate investors.  In fact, in 1971, Max Ramsland, MAI pointed this out succinctly in his article “Ellwood: A Practitioner’s Observations” in The Appraisal Journal.  In English, this formula basically states that an indication of the overall capitalization rate can be developed by taking the following steps:

1.      Loan to value ratio       x          Mortgage constant        =          Weighted rate

2.      Equity to value ratio    x          Equity yield rate          =          Weighted rate

Weighted average

3.      Less credit for equity build up

Loan to value ratio  x  Percent loan paid off over the holding

period x sinking fund factor at the equity yield rate          = Equity build up

Basic rate

4.      Less credit for appreciation/depreciation in value appreciation/depreciation

x  sinking fund factor at the equity yield rate                =          Adjustment

Overall rate

The Ellwood formula was designed as an analytical tool for real estate appraisers, investors and other real estate professionals.  Its misuse was clearly evident during the real estate collapse of the 1970’s and 1980’s.  The model above is for a level income stream over a specific number of years.  Who buys real estate expecting the income to be level over the projection period?  If income and value are expected to change over time, the Ellwood J or K factor must be applied and incorporated into the formula.  It appears that it is being misused again by real estate appraisers.  Mr. Ramsland points out several weaknesses that are worth revisiting at this juncture.

First, it is extremely difficult to verify the equity yield rate required to attract investors to real estate investments.  Many real estate investors will not disclose their “hurdle rates” to invest in real estate.  Abstraction of the required information to properly apply this methodology is difficult.  During the last several years many transactions that occurred were the result of a 1031 or tax-deferred exchange which created aberrations in the observed overall rates, sometimes below 4.00%.  These transactions were driven by after tax returns and appraisers generally do not have access to the information required to develop a proper analysis.  Many of the transactions were not economically justifiable and this is becoming evident now.  If this information is abstracted from historical transactions it can be very misleading without proper consideration of the market conditions as of the date of sale.  Mr. Ramsland points out that investors have various reasons for making an investment decision: some of which are well thought out and others who dream about the future and hope, but are incorrect.

Appraisers often assume that investors will hold the property for ten years and that the property will appreciate in value.  The market indicates that values do not always go up and, in fact, can decline for long periods of time and/or stay stabilized.  Finally, what investors use this analysis to make an investment decision?  I have been in this business for more than 25 years and the last time investors used this model the real estate market collapsed.

Mr. Ramsland further points out that “the allowance for depreciation can have a measured affect on the final value estimate if not realistically applied.  A more serious problem could exist, however, if the appraiser projects an equity-yield and depreciation factor inconsistent with safe investment practices.”

Terry Grissom, PhD, at the University of Ulster, Ireland points out that the issue of stable income and the assumptions behind an accumulated sinking fund growth factor is an accrual valuation measure that is inconsistent with discounted cash flow analysis and the cyclical nature of real estate investments.  Valuation needs to explicitly cope with changes over time to return to equilibrium or growth assumptions during down phase.

Don’t misunderstand me, the Ellwood formula is an excellent tool in the arsenal that appraisers have to utilize to develop overall rates if applied correctly; but with computers available today, appraisers should apply the methods employed by investors who acquire real estate.  In addition, more than one method should be used to support a capitalization rate.  The appraiser should consider the following methods to develop an appropriate overall rate:

  • Interview market participants
  • Review published surveys
  • Abstraction from comparable sales
  • Abstraction from multipliers developed from comparable sales
  • Developed by the band of investment method
  • Estimated by the debt service coverage ratio method
  • Abstraction from expected property yield rates.

All techniques to develop a capitalization rate should produce similar results if properly constructed with the correct assumptions.

Note – Thanks to Max Ramsland, MAI, Duluth Minnesota (email – maxrams@aol.com ) and Terry Grissom, PhD, University of Ulster, (email – terry.grissom@sky.com or e251744@uucde.ulster.ac.uk. Originally posted on Soapbox.


About Jim MacCrate

Real estate appraiser and valuation consultant for more than 30 years specializing in reviewing real estate appraisals, risk management and quality control.
This entry was posted in Capitalization Rates and tagged , , , , , , , , , , , , . Bookmark the permalink.

One Response to Ellwood – A Beautiful Mathematical Formula But – Often Misused

  1. Ellwood and other mathematical attempts to simulate cap rates are lame attempts that real estate practitioners use so they don’t have to get cap rates from the market. You learn more about what market participants think, what they will and won’t buy and why they bought by verifying comparable sales than by manipulating numbers in a spreadsheet.

Comments are closed.