Band of Investment




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BAND OF INVESTMENT

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Despite advanced calculation tools like Investment Analyst, it is still a common practice today to develop a capitalization rate using the Band of Investment. Unfortunately, it 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

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.

The advantage of Analyst is that it 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 you can specify a true Required IRR 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 years-paid 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

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.

Investment Analyst - The Advanced Mortgage Equity Technique

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 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 years-paid 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 Build-up 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 re-calculating 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 Build-up 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.

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