Despite advanced calculation tools like Investment Analyst and Commercial
Complete, it is still a common practice today to develop a capitalization
rate using the Band of Investment.
Unfortunately, the Band of Investment is one of the principle methods still
taught and relied upon in the real estate community. It is also widely
used by real estate professionals to support a capitalization rate. While
this method gives the appearance of accuracy because it is mathematically
correct, it falls short in many important respects. Factors that are not
considered in this method are:
 Equity Buildup
 Costs in addition to the nominal equity (nominal equity is the Value less
loan amount)
 Changes in the value over the life of the investment
 Changes in annual income over the life of the investment
 Selling Expenses incurred upon sale of the property
 Holding Period  BOI assumes that investment is held in perpetuity
The BOI method is available an available option, but we recommend use of
the Mortgage Equity Technique, which is incorporated into both Commercial
Complete and Investment Analyst. This technique considers all of the above
components.
While it is possible today to quantify each of the above components, the
Band of Investment lumps them into one number  the Equity Yield Rate of
the investment. Consequently, the true rate of return is hidden.
Because the Band of Investment is so commonly referenced in the industry, we display a Band of Investment Equivalent Calculation under the Cap Rate tab of the Analyst Worksheet and reference the BOI Equivalent Yield Rate on the Summary tab. In this calculation we calculate the required equity yield that must be used in the BOI calculation in order to produce the same capitalization rate that Analyst produces.
Our software considers all of the factors that comprise the capitalization
rate: mortgage payments,equity buildup, Soft costs/Closing costs, changes
in value, changes in annual income, and selling expenses when the investment
is sold.
Required IRR
Most importantly, in Analyst and Commercial Complete, a true Required IRR
can be specified that can be compared to other investment vehicles  bonds,
stocks, savings accounts, annuities, etc. The Equity Yield Rate in the
Band of Investment bears no relationship to the actual rate of return that
an investor can expect, and it SHOULD NOT be compared with the yields of
other investment vehicles.
Band of Investment Calculation
The Band of Investment is a yield capitalization method that is used to
build a capitalization rate using just two components; financing and equity.
The formula is:
Cap Rate = F + E 
where:
F = Financing Component
E = Equity Component
The formula is usually shown in this format: 
Financing Component 
Equity Component 
Capitalization Rate 


The Band of Investment method was an early attempt to mathematically quantify the factors that comprised a capitalization rate. Before computers became widely available and Capitalization Theory was fully developed, the tools to perform this calculation were limited. The best one could do was account for Mortgage Financing (by reference to payment tables and later using the HP 12C) and the investor's required yield (simple math).
The Financing component is the Annual Mortgage Constant multiplied by the Loan to Value ratio. The Equity component is the investor's Required Equity Yield Rate (This is NOT the same as the investor's rate of return or IRR. Please read
the Required IRR paragraph earlier in this discussion) multiplied by the percentage of cash equity. For example, lets say that the typical terms for the property that we are analyzing are as follows:
Loan to Value Ratio: 75%
Mortgage Rate: 7.5%
Term of Loan: 20 yearspaid monthly
Required Equity Yield Rate: 10%
Cash Equity Percentage: 25% (100%  75% LTV)
Given the above, we can build a capitalization rate using the Band of Investment.
First, we must calculate the Annual Mortgage Constant or look it up in
a mortgage payment table. The Mortgage Constant is also known as the Partial
Payment function:

"the level periodic installment that will pay interest and provide full amortization or recapture of an investment of one in a given number of periods with interest at the given rate per period"

HP 12C steps to calculate Annual Mortgage Constant
f REG 
Clear payment registers 
g8 
Set payment to end of period 
1PV 
Present Value of 1 
7.5gi 
7.5% Annual Rate divided by 12 
20gn 
20 year term converted into 240 months 
PMT 
Monthly payment or monthly mortgage constant 
12x 
Convert result to Annual Mortgage Constant 
Algebraic formula for Annual Mortgage Constant

Annual Mtg.Constant = 12 * i / (1  (1 / (1 + i) ^ n)) 
where: i = annual mortgage interest rate divided by 12
n = term of loan in months
Note that in both the HP 12C steps and the Algebraic formula, the monthly payment must be multiplied by 12 in order to arrive at the Annual Mortgage Constant.
The Annual Mortgage Constant for a loan with a 7.5% interest rate and a 20 year term is .
0967. Once we have this factor, we have enough information to build a cap rate using the Band of Investment.

Financing Component .0967 x .75 = 0.072503 
Equity Component .10 x .25 = 0.025000 
Capitalization Rate 0.097503 


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Band of Investment Summary
The Band of Investment attempts to reflect the financial circumstances
of a real property transaction. It purports to account for the two elements
of the transaction: Financing and Equity. However, it fails to achieve
its objective because it ignores critical factors that must be considered,
if one is to truely reflect the financial circumstances of a real property
transaction.
Financing Component  Erroneous Assumptions
First of all, only part of the mortgage financing transaction is considered. In the example above, payments over the 20 year term are accounted for, but these payments are comprised of both principal and interest. The principal portion of the payments (called the Equity Buildup) will be returned to the investor when the loan is paid off, either at the end of the mortgage term or when the property is sold. Equity Buildup is not considered in the Band of Investment, although it has a significant impact upon the investor's return. The Financing Component accounts for the investor's annual cost, but does not consider the return of principal sometime in the future.
Second, the structure of the Band of Investment assumes that both the Financing
Component and the Equity Component exist in perpetuity. That is, the mortgage
payments never end and the investor never sells the property. The former
assumption is erroneous. The mortgage payments end in 20 years in the above
example. The second assumption is unrealistic. The investor will sell the
property at sometime in the future. Or his heirs will inherit it.
A layman's example
Suppose that you purchase a car for $10,000 and finance the entire amount
for a term of four years. You make payments for four years and assume that
no more payments are due. The loan has been paid off and you can start
to put the extra cash in your pocket. Right? But on the first of 49th.
month, you receive a letter from the bank stating that loan payments are
expected to be made for as long as you own the car.
Or assume that you decide to sell the car at the end of four years, but
when you request that the bank release the title, the bank demands a payment
of $10,000. Their explanation is: "Sorry, but we don't take into consideration the principal portion of your
loan payments. You still owe $10,000."
This is how the Band of Investment handles the Financing Component. Although
giving the appearance of accuracy, it does not correctly reflect financing
and it produces erroneous results.


Equity Component  Misleading and Incorrect
The Equity Yield Rate is, by implication, analogous to the investor's rate
of return, or Internal Rate of Return. It is commonly used to represent
the investor's rate of return by both bankers and real estate professionals
who are not thoroughly informed on the subject. The Equity Yield Rate is not the same as the Internal Rate of Return or the Investor's Return on Equity. It must not be compared to the published rates of other investment vehicles; e.g. the Annual Percentage Rate of savings accounts or mortgage loans, bond yields, annuity yields, etc.
The Equity Yield Rate is the investor's annual Cash on Cash Yield  the funds available to the investor after mortgage payments divided by his original Equity Portion of the investment. And this is only true if Net Income from the property is assumed to be constant; i.e. does not increase or decrease each year. And this is only true until the mortgage loan is paid off, at which time the annual Cash on Cash Yield goes up substantially.
The cash on cash yield is an important consideration to the investor. He needs to know that there will be a positive cash flow after mortgage payments are made. But his required cash on cash yield will vary, depending upon the property. It should not be compared to other market interest rates or to the cash on cash yield
requirements that were observed for other real property.
For example, let's take two office buildings that are identical in all respects, except for the local market area. Market Area 1 is a suburban growth area where rents have been observed to be increasing each year. Market Area 2 is an urban market where rents are not expected to change. Common sense (and mathematical algorithms) tell us that the investor will accept a lower cash on cash yield (Equity Yield Rate) in Market Area 1 because he knows that his income will be increasing each year, resulting in an overall
rate of return (IRR) that is higher than his initial cash on cash yield.
The Band of Investment cannot account for this change in income.
A layman's example
Suppose that you are offered two investment alternatives. The first will
pay you $1,000 per year for 10 years. The second will pay you $1,000 in
the first year and the payment will go up by 1% per year in each of the
next nine years. Which investment produces the highest rate of return for
you? Which one will you choose? Obviously the second alternative is the
best. But the Band of Investment calculation cannot tell you that and cannot
quantify the difference.



The Advanced Mortgage Equity Technique employed by Commercial Complete
and Investment Analyst

Mortgage equity analysis has evolved over many years. It is a mathematical technique used to calculate
the value of an investment, based upon a specified yield requirement. As
the name suggests, financing is one of the factors which is considered
in the calculation. The method is applied extensively when analyzing real
estate investments, which very often are highly leveraged, because it recognizes
the impact that financing has on the investor's expected yield. However,
even when there are no borrowed funds, the technique is effective in estimating
the value of an investment.
It is beyond the scope of this discussion to describe the Advanced Mortgage Equity Techique in depth, but this technique properly considers both the Financing Component and the Equity Component of an investment because it considers all of the factors that are ignored in the Band of Investment. Factors considered are:
 Equity Buildup
 Costs in addition to the nominal equity (nominal equity is the Value less
loan amount)
 Changes in the value over the life of the investment
 Changes in annual income over the life of the investment
 Selling Expenses incurred upon sale of the property
 Holding Period  BOI assumes that investment is held in perpetuity
Analyst enables you to calculate the true IRR to the investor. To illustrate
the difference between the Band of Investment and the Mortgage Equity Technique,
we offer a simple comparsion using the same information that is used in
the Band of Investment calculations above.
Loan to Value Ratio: 75%
Mortgage Rate: 7.5%
Term of Loan: 20 yearspaid monthly
Required IRR: 10%
Cash Equity Percentage: 25% (100%  75% LTV)
Holding Period: 10 years
We specify a holding period, which cannot be done in the Band of Investment.
We also have changed the reference to the Required Equity Yield Rate. It
is now the Required IRR and reflects the true rate of return to the investor.
The calculation is as follows:
Financing Component  Rate Attributable to Loan (.0967 x .75) = 0.072503 
Equity Component .10 x .25 = 0.025000 
Equivalent Band of Investment Rate 0.097503 
Less Equity Buildup 0.015122 
Indicated Capitalization Rate 0.082382 
Note the difference in the final capitalization rates. The Band of Investment
indicates 9.7503% and the Mortgage Equity Technique indicates 8.2382%.
If we assume an annual net income of $10,000, the value by the Band of
Investment would be $102,560 and the value using the Mortgage Equity Technique
would be $121,386  an $18,826 difference or 18.36%.
So How Do We Reconcile This Difference?
Let us assume that we already independently know the value of the property.
It is $102,560. Can we conclude that the Band of Investment calculation
is correct? The math is correct and it produces the correct value. But
it tells us nothing about the investor's Rate of Return  only the Equity
Yield Rate or the Cash on Cash Yield.
The actual IRR is 14.7957% ! We can verify this by recalculating the Mortgage
Equity Technique.
Financing Component  Rate Attributable to Loan (.0967 x .75) = 0.072503 
Equity Component (14.7957 x .25) = 0.036989 
Equivalent Band of Investment Rate 0.109492 
Less Equity Buildup 0.011989 
Indicated Capitalization Rate 0.097504 
Alternatively, let us assume that in fact an investor will accept an IRR
of 10% for the particular property that is being analyzed. Then the Band
of Investment is significantly underestimating the value of the property.
If the Required IRR is 10%, the Capitalization Rate is 8.2382% and the
Indicated Value is $121,386, not $102,560.
Theory Versus Practice
In theory, the development of the capitalization rate is supposed to lead
to a conclusion of value. In practice, the analyst using the Band of Investment
independently determines the value by observing sales of similar properties
and/or their cap rates. Then he "backs into" the Equity Yield
Rate in order to calculate the cap rate of his property and make the math
work. It is the only way that he can do it because he only rarely can go into the market and
observe other published "equity yield rates." As discussed extensively
above, equity yield rates vary from property to property and one cannot
use the rates of other investment vehicles for comparison because they
represent actual rates of return and not cash on cash yields.
Using the Mortgage Equity Technique, the analyst can actually "build"
a capitalization rate because he can select a Required IRR based upon the
published rates of other market instruments like savings rates, bond rates,
stock yields, mortgage rates, etc. Consequently, he can build the cap rate
from the ground up, apply it to net income, and produce an indication of
value. He does not have to choose the value and then back into a Band of
Investment calculation in order for the math to work.

Summary

This discussion is intended to point out the weaknesses inherent in the Band of Investment. An in depth discussion of the Advanced Mortgage Equity Technique that is employed by Investment Analyst is beyond the scope of this discussion. We offer a simplied example of the Mortgage Equity Technique in order to contrast it to the Band of Investment. The Advanced Mortgage Equity Technique used in Investment Analyst goes into much greater detail and considers all factors that affect the capitalization rate and not just Equity Buildup.

Financial Masterplan, Inc.
