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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

f REG	Clear payment registers
g8	Set payment to end of period
1PV	Present Value of 1
12gi	12% Annual Rate divided by 12