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.
This 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.
Development of the capitalization rate using the Mortgage Equity Technique
is built into both Commercial Complete and Investment Analyst.
Despite advanced calculation tools like Commercial Complete and 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 the Band of Investment 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 Mortgage Equity Technique, sometimes referred to as the Ellwood Method (also "Ellwood without algebra as developed by Charles Akerson), addresses the Equity Buildup and Holding Period, but not the other factors that are mentioned in the list above. The technique implicitly relies upon the Time Value of Money concept. It builds (develops) a multiplier, referred to as the Capitalization
Rate that mathematically represents the series of cash flows produced by
an investment over the holding period of the investment. The first year
(stabilized) income of the investment is then capitalized to determine
the value of the investment's cash flows. The Mortgage Equity Technique
is superior to the Band of Investment because it better reflects the circumstances
of a real property transaction by recognizing three important factors that
are excluded from the Band of Investment.
- The investment is typically not held forever - there is a "holding
period".
- There is an "equity buildup" as the mortgage loan is paid down.
- The investor receives the proceeds of the sale at the end of the holding
period.
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Recent Testimonial - 7/18/2014 |
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Cash Investment
To explain the mortgage equity concept further, let us first assume that
an investor acquires an investment for cash (no borrowed funds), and that
he requires a 10% yield on his investment each year, as long as he holds
it. What should he pay to acquire the investment? The following statements
are analogous:
- The investor wants to receive a 10% yield on his investment each year.
- The investor wants the annual rate of return on his investment to equal 10%.
- The investor wants the Annual Percentage Rate on his investment to equal 10%.
- The investor wants the Internal Rate of Return on his investment to equal 10%.
To find the amount that he should pay, he would simply divide the net income
produced by the investment (net income is assumed to be constant each year)
by the yield which he requires. Assume a net income of $10,000.00.
Net Income
|
Capitalization Rate
Required Yield
APR
IRR |
Value
|
| $10,000 |
divided by .10 = |
$100,000 |
To prove that his annual yield is 10%, divide the net income produced by the investment ($10,000.00) by the value of the investment ($100,000.00).
| $10,000 |
divided by $100,000 |
= .10 per annum |
In the example above, the required yield and the Capitalization Rate are the same. This method is sometimes referred to as Capitalization in Perpetuity.
When There is a Loan
If a loan is used to partially fund the investment, then the analysis must
be modified in order to calculate the value of the total investment that
will still produce a 10% annual return on the investor's cash investment.
To simplify the discussion, assume that the loan is interest only, i.e.,
the investor is not required to pay back any principal as long as he holds
the investment. Further, assume that he will be able to borrow 50% of the
value of the investment and that he will pay an interest rate of 12% on
all funds borrowed. The other 50% will be the investor's cash.
In order to calculate the value necessary to give the investor a 10% return on his cash, we must calculate the amount that the investor will receive each year, after he pays the interest on his loan. The calculation is as follows:
- Calculate the annual amount necessary to repay loan interest (Step 1)
- Calculate the annual amount necessary to pay 10% to investor each year
(Step 2)
| Step 1: 50% of value multiplied by 12% interest rate |
= |
.06 |
| Step 2: 50% of value multiplied by 10% required yield |
= |
.05 |
| Capitalization Rate |
|
.11 |
The above example is a special case of the Band of Investment that is applied correctly because the loan is Interest Only. This will be proven below. The sum of Step 1 and Step 2, the Capitalization
Rate, is equal to 11%. We divide the income produced by the investment
($10,000.00) by the Capitalization Rate (11%), in order to find the value
of the investment.
Net Income
|
Capitalization Rate
|
Value
|
| $10,000 |
divided by .11 = |
$90,909.09 |
To prove that the investor's annual yield is 10%, we first calculate the
amount that the investor will receive after he has paid the interest on
the loan.
| Net Income |
|
$10,000.00 |
| Interest paid (90,909.09 / 2 * .12) |
|
-5,454.55 |
| Received by the Investor |
|
4,545.45 |
Then we divide this remainder (the amount received annually by the investor)
by the investor's cash investment ($4,545.45 divided by $45,454.55). The
result equals 10% - the investor's annual yield.
The Mortgage Equity Technique
Discussed above is a simple example of what is often called the Band of Investment. It is a special case, where the Band of Investment is used correctly.
It is also the beginning of what is known as the Mortgage Equity Technique.
The simple examples described above, Capitalization in Perpetuity and Band
of Investment, inadequately reflect most typical investments in the marketplace.
In the marketplace, loans are usually amortized, requiring that principal
as well as interest be paid each year. This additional payment reduces
the cash that the investor receives each year. Also, as principal is repaid,
the loan balance is reduced. This too, must be considered.
The Mortgage Equity Technique was developed to build loan amortization
and the value of the Reversion into the Capitalization Rate. An additional
variable, the "holding period", was introduced into the Mortgage
Equity Technique, recognizing the fact that an investment typically is
not held forever. Now, instead of assuming that an investor's yield is
received in perpetuity, the yield is received over a specific period of
time.
As a result of introducing a Holding Period, an additional factor, Equity Buildup, must be added to the calculation. To illustrate, we use the same assumptions that were used in the example immediately above. But instead of an Interest Only loan, we assume that the loan will be amortized over a period of 25 years. We also add the assumption that the investment will be held for 10 years - the Holding Period.
In order to calculate the value necessary to give the investor a 10% return on his cash over the Holding Period, we must calculate the amount that the investor will receive each year, after he pays both principal and interest on his loan. The calculation is as follows:
- Calculate the annual amount necessary to repay loan - Annual Mortgage Constant
(Step 1).
- Calculate the annual amount necessary to pay 10% to investor each year (Step 2)
- Calculate the Equity Buildup at the end of the 10 year Holding Period
| Step 1: 50% of value multiplied by 12% interest rate |
= |
.063193 |
| Step 2: 50% of value multiplied by 10% required yield |
= |
.050000 |
| Step 3: Calculation of Equity Buildup |
|
-.003841 |
| Capitalization Rate |
|
.109352 |
The sum of Step 1 Step 2 and Step 3, the Capitalization Rate, is equal
to 10.9352%. We divide the income produced by the investment ($10,000.00)
by the Capitalization Rate (10.9352%), in order to find the value of the
investment.
Net Income
|
Capitalization Rate
|
Value
|
| $10,000 |
divided by .109352 = |
$91,447.80 |
HP 12C steps to calculate Annual Mortgage Constant - Step 1
| f REG |
Clear payment registers |
| g8 |
Set payment to end of period |
| 1PV |
Present Value of 1 |
| 12gi |
12% Annual Rate divided by 12 |
| 25gn |
25 year term converted into 300 months |
| PMT |
Monthly payment or monthly mortgage constant |
| 12x |
Convert result to Annual Mortgage Constant |
| .5x |
50% of value - Annual Mortgage Constant |
HP 12C steps to calculate Equity Buildup - Step 3
| Assumes HP registers above have not been cleared |
| 10gn |
Year that balance will be paid off - Holding Period |
| FV |
Balance at end of 10 years |
| 1+ |
Displays amount of loan paid off after 10 years |
| .5x |
50% of value - Loan Ratio |
| Interim Answer = .061218 |
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|
| Sinking Fund Factor |
| 1.10 Enter |
1 + Required Yield |
| 10 (yx Key) |
Raise 1.10 to power of 10 (holding period) |
| 1 - |
Interim Answer |
| (0.10 / 1/x Key) |
Get reciprocal |
| Sinking Fund Factor = .0627454 |
|
|
| .061218 x |
Calculate Equity Buildup factor |
| Equity Buildup Factor = .03841 |
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Investment Analyst - The Advanced Mortgage Equity Technique
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As stated at the beginning of this discussion, Mortgage equity analysis
has evolved over many years. The ready availability of desktop computers
has allowed us to introduce complex algorithms into the Mortgage Equity
Technique that permit us to recognize the other factors that influence
an investor's actual IRR. In addition to Equity Buildup, the Advanced Mortgage
Equity Technique that is used in Investment Analyst considers these additional
factors.
- 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
It is beyond the scope of this discussion to describe the algorithms used
in 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 and the simple Mortgage Equity Technique.
Investment Analyst enables one to calculate the true IRR to the investor,
which can be compared to 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. And he not limit his analysis to the simple Mortgage Equity Technique,
ignoring the other factors that influence IRR and value.
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Financial Masterplan, Inc.
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