The Inwood Premise

[Stephen J. Vertin MAI]

Here is what I have found on our income approach heroes. Much is the same as above, maybe some dates changes slightly but most comes from two sources. Red you are correct I also found a source that said Inwood was a church builder. In fact it went on more about him building churches that finance tables (which he looks like he took from John Smart) Interesting group of people.


In the history of finances there is a fairly wide array of colorful characters. However, when considering BPGS there are actually five main personality to whom the world (or at least the real estate world would give most credit to developing income capitalization of most BPGS)[1]. In my opinion, the most important (yet least recognized) is Irving Fisher (February 27, 1867 – April 29, 1947). We will talk about him shortly (since there is a lot to say). The second is LW Ellwood (June 1896 – May 1974). He was one of the first to recognize there was a relationship between equity and mortgage components. Further he discovered the mathematical relationship. However, there were others who recognized this also. One was Charles B. Akerson (Feb 2, 1923 – April 23, 2009) who realized the algebra that Ellwood was promoting was too complicated for the average appraiser (of that day). So Charles B Akerson writes a book removing most of the complicated algebraic formulas. He even called it Ellwood with out Algrabra our third character (and third most important is William Inwood (who was actually a mathematician and architect). Reportedly, Inwood (Aug 1771- Dec 1843) knew of a book by John Smart, which was kind of like an actuary guide today. Inwood believed he could make the tables easier for the common banker, actuary insurance adjuster and so on to read. It worked and William Inwood ended selling 26 editions (no copies that is editions). So why is this important? Because it also shows the relationship between equity and mortgage components which help appraisers develop capitalization rates. The method soon becomes known as Inwood’s premise. The only issue was it only worked when applied income as an ordinary level annuity was used in the analysis. However, this worked great since Ellwood without Algebra worked on the similar terms. This brings use to our final charter Henry Davis Hoskold (April 1832 - March 7, 1877), Hoskold was known for the Hoskold premise. He was actually a mining engineer who came up with the calculation before the invention of discounted cash flow.


[1] I have no delusions about appraisers’ agreements or disagreements so I can say with some certainty not everyone will agree with my list but I feel fairly confident most would recognize the involvement of those who are named.

 

[Stephen J. Vertin MAI]

Here is some other stuff that is really strange. Read this and try to figure out why they kept Irving Fisher out of most valuation text. It seems long but read it. It is really interesting.

General Purpose Formulas for Capitalization Rates: Before we discuss mortgage component and other applicable methods of capitalization rate extractions there are minor things in a referenced text called Capitalization Theory and Techniques Second Edition (first published in 1972), by Charles B Akerson that need clarification. On page 101 Lesson 12 the text states “This lesson is an explanation of the Ellwood system of mortgage-equity analysis based on prior articles by the author of this study guide[1] The Ellwood system including the Ellwood table became a popular tool for yield capitalization in the 1960 and 1970s. The text goes on to say “and was the forerunner of computerized discounted cash flow analysis”. LW Ellwood was 78 years old when he died on May 22 1974. Irving Fisher wrote The Nature of Capital and Income which fully developed the process of discounted cash flow (DCF) analysis (in 1906 but the work was not published until 1909). Ellwood’s forerunning theories would have had to be written when he was 10 to 13-years old. While both Akerson and Ellwood were brilliant developers of arranging the algebra within the 6 functions of the dollar this is probably the couple’s most important contribution. If you read their materials it becomes clear they sought to develop a yield rate formula fitting into the Irving Fisher model. Such a formula would recognize cash flow and their attribution over the holding period. It would be the algebraic glue that could piece the concept into a near prefect model.

Another problem that haunts me is Inwood, Ellwood and Hoskold make their first cameo appearance in The Appraisal of Real Estate, Fourth Edition, 1964 by the American Institute of Real estate Appraisers. I guess you could call this the year of the level cash flow (or at least more level than others). It appeared these mathematicians were trying to come up with a yield extraction rate that could be place at various levels over certain time periods (and the only one working well at that time was the Irving Fishers model) so more accuracy could be incorporated into market levels. In other words they had the DCF cash flow model but a very limited formal way of rate extractions. This was echoed by Charles B Akerson himself who said:

“All capitalization techniques employ the same rationale. Some of the techniques refine the process with more elaborate mathematics, but the fundamentals are the same. In one form or another, the procedure is to ascertain the expectable benefits, establish the proper relationship between these benefits and value, and perform the necessary mathematics to obtain an indication of value.” [2]

While some see them as great thinkers in the industry, there are more than a few who believe they set real estate valuation back for decades devising complicated formulas that only operated properly under restrictive cash flow assumption. It seemed odder yet (that they would even work on such models) since Fisher’s DCF cashflow analysis worked under all variations in market conditions. The building of new models may have made more sense if Fisher had little to no credibility and his DCF model was a bust. But nothing was further from the truth. This story is perplexing.

No matter how it is told it seems something does not seem right. Dr Irving Fisher’s Ph.D. in Economics from Yale University and writer of nearly 22 books and academic articles comes up with an earth-shattering theory concerning the time value of money. He worked with Milton Friedan and John Maynard Keynes and was the first to print mathematical concepts developing discount cash flows written over 100-years ago and which are still used today. But anyone who lived in the 1960-70s realized for years they tried to change the model into an algebraic formula.

One day while contemplating some of these issues I picked up a short paper (about 45 pages) called The Mathematics of Real Estate Appraisal by Dr. David Ellerman, written in May 2004. The introduction stated:

Real estate appraisal is more of a practical art than a theoretical science. Appraisers use a number of time-honored formulas without great attention to the theoretical derivation of the formulas. While this "cookbook" approach may work as a matter of everyday practice, it leaves much to be desired from a pedagogical viewpoint. When valuation formulas do have a derivation from a certain set of assumptions then it is quite inappropriate—particularly for the technically-oriented student—for the formulas to be taught as "recipes" established by some authority and simply to be memorized and used.


[1] Charles B. Akerson, “Ellwood Without Algebra: the Appraisal Journal (July 1970) and Charles B Akerson, An Introduction to Mortgage Equity Capitalization *Chicago: American institute of Real Estate Appraisers, 1975

[2] Capitalization Theory and Techniques p7Charles B Akerson, 2000

 

[Zephyr999]

You had me at Inwood...
Many great minds of those times did things not of their education and way left...i.e. master artists Michelangelo and DaVinci engineering war devices.

 

[Terrel L. Shields]

from my book

Hoskold’s Premise is similar to the Inwood Premise and is rarely used for oil and gas properties. Hoskold’s Premise is a sinking fund formula that is most often used in mines and quarry valuation. The unrisked rate (usually a treasury bond interest rate for a similar length as the term of the analysis) is added to a risk rate and allows for both yield and a return of the investment.
The formula accounts for the length of the investment and the T-bill interest rate is added to a risked rate. That risk rate varies but is often calculated at three times the T bill rate or perhaps as high as five times the safe rate.

This example also calculates the years to payout as present worth divided by the annual income. The formula provides for a return on the property in addition to a return of the investment.
Hoskold, a Swedish mining engineer, suggested that this technique might be appropriate for valuing mines where the value is reduced to zero as minerals are extracted but annual production can be maintained; thus funds have to be set aside to invest in a new mine once the minerals are totally depleted (the reversion equals zero).​

 

[Zephyr999]

@Stephen J. Vertin MAI
Funny thing...reviewing some of Grasskamp's work via the Lum Library and what do I come across? More background about Inwood...
A search for the title "Dollars and Cents of Shopping Centers 1969" should populate a 4-page 'Notes and Comments' section from The Appraisal Journal 1970 edition.

 

[Stephen J. Vertin MAI]

Man what I am learning faster than the speed of light is the more I think I know the dumber I seem. I think I am coming to the end of this road. An amazing journey. I have to put in a burner and stop pondering "X= Y - Δa" Need to get some work done.