Understanding Direct Capitalization

Capitalization Rate

This article is intended as a review for practising appraisers as well as an introduction to the new terminology and subscript notations being used in current appraisal texts. Much of it has been excerpted from the new textbook of the APPRAISAL INSTITUTE OF CANADA Basics of Real Estate Appraising, First Edition, which is now used in the academic program which commenced in September, 1991. Similar methodology and terminology is presented in the Appraising of Real Estate, 9th Edition, American Institute Of Appraisers.

Capitalization is the process of converting income (as defined) from a property into an expression of capital value. Therefore, a capitalization rate is nothing more than the mathematical relationship between the income and the capital value. There are two basic methods of capitalization: the direct method and the yield method.

Many rates can be used in capitalization, including the following list, which also indicates the method associated with the rates:

Direct Method

1. Gross Income Multiplier (GIM)
2. Equity Capitalization Rate (Re)
3. Mortgage Capitalization Rate (Rm)
4. Overall Capitalization Rate (Ro)

Yield

5. Interest Rate (i) (may also be called ‘discount rate’)
6. Internal Rate of Return (IRR)
7. Equity Yield Rate (Ye)

The GIM, R_o, R_E, and R_M are all current income rates and are used in the direct method of capitalization. The i, IRR, and Y_E are yield rates and are used in the yield method of capitalization. Under certain conditions, the yield rate for a particular property can be numerically equivalent to the corresponding income rate, but the rates are not the same conceptually, and are not interchangeable.

This article examines the direct method only, which is based on one year's income. The yield method is based on a discounting process of future benefits over a finite investment period and is examined in detail in advanced appraisal texts.

A current income rate is the ratio of one year's income to value (in the case of net income) and cash flow income, but, when the gross effective income is used, it is a value to income ratio. Yield rates apply to a series of individual incomes over an investment holding period to obtain the present value of each.

Example I features a comparable sale and a subject property to be appraised that will be used to demonstrate the relationship of these various rates and the analysis of both the sale and the application to the subject. The sale and the subject have been analyzed using the first year's income and expenses. For the purpose of demonstration in this example, the subject is illustrated to have either new financing to be arranged or an existing
assumable mortgage.

It should be noted that one sale is being used for demonstration purposes, but the appraiser should select at least four or five comparable sales to analyze the typical market, and should reconcile these rates to select the appropriate rate to be applied to the subject.

EXAMPLE I
	Sale #1	Subject (new financing)	Subject (existing financing)
Sale price	$300,000
EGI	$50,000	$47,500	$47,500
Expenses	$20,000	$18,250	$18,250
Mortgage	$225,000	Ratio .70	$210,000
SAR	12%	11.5%	12%
FAP	25 years	25 year	23 years
Monthly payment	$2,321.55		$2,199.96
Annual debt service	$27,859		$26,400
Net operating income	$30,000	$29,250	$29,250
Cash flow	$2,141		$2,850

Income rates can be applied to component parts or interests in a real property. Property can be split into physical components such as land, buildings and chattels, or into financial components such as equity and mortgage interests. Appraisers might also want to estimate the value of the unencumbered fee simple, the leased fee, and the leasehold estate.

Current income Rates

A rate can be defined as a "Fixed relationship between two magnitudes and used as a means of measurement." Appraisers use actual sales and income data to derive the income rates. In advanced appraisal theory, other comparative methods can be used in the
absence of comparable sales data.

Gross Income Multiplier (GIM)

A GIM expresses the relationship between the gross income and the selling price of a comparable sale. Therefore, even though it is not expressed as a per cent, it falls within the definition of a "rate" and appraisers have used the word multipliers to differentiate it
from the net income and equity dividend rates.

By convention, appraisers in Canada use the effective gross income as the unit of comparison. Some appraisal texts use gross potential income multipliers, as well as effective gross, providing an additional capitalization rate. it should be noted that earlier appraisal teachings in Canada treated the GIM as a method to be used in the direct comparison approach. The current thinking allows that since income is being used as the unit of comparison, and is being capitalized by the use of a multiplier, this approach belongs more properly in the family of income-capitalization approaches to value.

A distinction is made in some texts between GIM and Gross Rent Multipliers (GRM), the difference being that GIM might include ancillary income such as parking and income from laundry facilities, signs, etc. To avoid the proliferation of different approaches, this article uses the GIM definition, and, obviously, where there is no ancillary income, the
gross rent would be the same as the gross income.

To estimate the correct multiple to be used, a market study of all sales and rentals of truly comparable properties must be carried out for the neighbourhood. This information is then set up in grid form from which an analysis and conclusion can be reached as to the
proper GIM to be used for the subject property being appraised.

Care must be taken that the properties have similar characteristics before multipliers can be used. If it is an appraisal of an apartment building, comparables must be in the same price range and size, and have similar locations, financing, expense ratios and rents.

Some apartment gross rents include parking, appliances, heat and utilities, and sometimes furniture. It is obvious that the appraiser must compare like with like when arriving at an appropriate multiplier to be applied against the subject property. As in all other approaches, the analysis of the comparables must be the same as the application against
the subject.

The GIM is calculated from comparable sales as follows:

Analysis

GIM = sale price : effective gross income

GIM = $300,000 : $50,000

GIM = 6.0

This calculation demonstrates that the comparable property sold for six times its gross effective income. This multiplier is then applied against the effective gross income of the.
subject property being appraised.

Application

V = GIM x EGI

V = 6.0 x $47,500

V = $285,000

Based on the GIM, the appraiser would then conclude that the market value of the subject
property is $285,000

The sale price used in the formula to estimate the multiplier is the unadjusted price with no adjustments being. Made for time, location, physical, financial, etc.

The gross effective income should be the forecasted gross effective income at the date of the sale. Usually, appraisers forecast the next 12 months' rent and vacancies to estimate the effective income for the subject property. Therefore, the same analysis should be
done for the comparable.

Since most owners account for income and expenses on an annual basis, some appraisal firms use a six- month rule when estimating incomes. That is, if the date of the sale, or the effective date of the appraisal of the subject, is within the first six months of the calendar year, then the current year's income is used. If the date of sale or appraisal occurs in the latter six months of the year, then the next calendar year's income is used.
Again, this is consistent with die analysis/application rule.

Normally, no adjustments are made to the rents when deriving the multiplier. In many areas, however, and when there are insufficient comparables, it might be necessary to make adjustments. For example, if some apartment rents include utilities and others do not, it could be possible to calculate multipliers based on rents without utilities, by deducting the utility costs from the gross rents when calculating the modifiers. Similarly, adjustments could be made for other variables such as appliances and furniture.

The strength of the GIM as an appraisal tool is that it is relatively easy to calculate and apply to a subject property. This method is easily understood by non-appraisers, and, in fact, non-technical investors can use it in formulating offer prices for smaller income properties. Usually, the relevant data is easily acquired.

One weakness of the GIM is that it does not take into account the expenses that can vary from property to property. Another is that it does not account for any variations in financing that can affect the value of the equity interest being appraised.

Equity Capitalization Rate (R_E)

The R_E is the relationship between the forecasted before-tax cash flow and the equity capital of the purchase price. It is derived from sales of comparable properties as follows:

Analysis

R_E = I ñ ADS Sale price - $Mortgage

R_E = $30,000 - $27,859 (Cash flow) $300,000 ñ $225,000 Equity

R_E = $2,141 $75,000

_E = 0.02854666 rounded to 0.0285, or 2.85%

The rate of 2.85 per cent merely reflects that purchasers are willing to buy with the use of mortgage funds and are willing to accept a positive cash flow out of the current year's income only, equal to 2.85 per cent of the equity invested. The rate does not explain the investment return or yield to the investor. As was the case with the GIM, the analysis of the income and expenses of the sale should be similar to the analysis of the income and expenses of the subject, i.e., the next year's or the past year's operation.

Application

The equity capitalization rate can be used to capitalize the cash flow of the subject property directly, on the assumption that the existing mortgage is assumable by a potential purchaser.

V_O = M_S + Cash flow R_E

V_O = $210,000 + $2,850 .0285

V_O = $210,000 + $100,000

V_O = $310,000

Since the value of the mortgage was known, the appraiser estimated the value of the equity by capitalizing the cash flow, and then added the result to the value of the mortgage to estimate the leased fee interest subject to existing financing.

The R_E can be used also in the band of investment method of calculating an overall rate (see section entitled Overall Capitalization Rate).

If financing is a factor, the strength of the R_E is that only the equity portion of the investment has to be estimated by the appraiser, since the mortgage is either existing and establishes the mortgage portion of the purchase, or the current mortgage market conditions will clearly set the rate, the lending ratio, and the amortization period and lending term. If typical financing provides 70 per cent mortgage ratios at current mortgage rates, then the appraiser's judgement must be used to estimate the remaining 30 per cent of the capitalization rate. Since most income properties are purchased with the use of borrowed funds, there might be adequate comparable sales data from which the appraiser can derive equity dividend rates.

The weakness of this rate is that it can be misapplied. In the previous example, if the equity dividend rate were applied to a similar property where only 50 per cent financing was available, the resulting estimate of value would be much higher, because a larger equity cash flow would be capitalized at a lower rate (the lower the rate, the higher the value). In an example of absurd lengths, a similar property with no financing would have an even higher capitalized value, this, of course, being completely unrealistic.

Another weakness can be the application where financing is only short-term. In the case of short-term financing, the current cash flow might not be a significant factor, because the purchaser might be anticipating lower mortgage rates in the near future. Therefore, the appraiser should be cautioned to analyze the market data carefully to identify the trends, and use the market-derived equity dividend rate only when there is clear evidence that there is some consistency in the behavior of the investors in similar types of properties.

Mortgage Capitalization Rate (R_E)

The R_E expresses the relationship between the annual debt service and the principal amount of the mortgage at the date of the sale. This rate can be found by multiplying the column six factor from column six of the Six Functions of One Dollar by 12, using the appropriate rate and amortization period as follows:

R_M = Column Six factor x 12 OR R_M = Annual debt service


Mortgage principal Analysis

From the given comparable sale:

R_M = .010318 X 12 = .123816, or 12.3816% OR

R_M = =$27,859 $225,000 = .123818, or 12.3818%

The slight difference in the two methods is a result of rounding.

Application

The R_M is used in the band of investment method for calculating the R_O. The R_M is fairly straightforward and based on the mathematics of mortgages. The Six Functions of One Dollar are used for Canadian mortgages with blended monthly payments. Other mortgage variations can exist, and therefore the column six factor might not always be applicable.

The strength of this rate is that it is relatively easy to calculate and market information is usually readily available. The weakness might be that, in volatile economic conditions, mortgage rates can be changing quickly, and an appraiser might use a new mortgage rate without having any sales evidence to see what impact, if any, the mortgage rates can have on the equity rates. It could be that, in situations where mortgage rates have increased, the purchaser might be willing to accept lower dividend rates because they expect long-run mortgage rates to decline.

OverallCapitalization Rate (R_O)

The Ro expresses the relationship between the current year's income and the value of the property. The applicable formula is:

Value = Net operating income

Overall capitalization rate, or

V_O = I R_O

This is the basic capitalization formula, and it applies to the rates and incomes (as defined) for all of the current ratio capitalization methods. From this formula, it is easy to derive the following relationships:

I = V_O X R_O R_O = I V_O

The overall rate can be derived from three sources described as follows:

1. Sales of comparable properties, by comparing the net incomes to the selling prices:

R_O = I Sale price

This is the most direct of the three methods of estimating overall rates. The appraiser analyses sales of comparable properties having similar investment features, expense ratios, financing, ages, and types of properties. For each of the sales, an analysis must be made of the income and expenses to obtain the net operating income, in the same manner as for the subject property being appraised. If the first year's income is being used for the subject, the first year's income must also be used for the sale. The sale price used is the unadjusted price. The appraiser should use several sales (preferably four or five) to establish the trend. The individual rates derived should be reconciled by the appraiser, and the appropriate rate should be applied to the subject property.

Analysis

The example can be used to demonstrate the calculation of the rate from a sale.

R_O = Net operating income Sale price R_O = $30,000

$300,000 R_O = .10, or 10%

The overall rate of 10 per cent does not explain the yield or rate of return on the investment. It merely expresses the relationship between the sale price and the next year's net operating income at the date of the sale. If it was expressed as a multiplier, it would be 10 times the net operating income. As indicated earlier, by convention, appraisers in Canada have used capitalization rates rather than multipliers when dealing with net operating income.

Application

V_O = I R_O

V_O = $29,250 .10

V_O = $292,500

Therefore, based on the overall rate calculated from sales, the appraiser would estimate the market value of the property to be $292,500.

The strength of the overall rate based on direct sales analysis is that it is easy to calculate, and it does not require any adjustments or hypotheses about future incomes or existing or future financing. It is also easy to explain to the non-professional appraiser. Since the calculation is relatively easy, it is conceivable that investors could also use this method as a tool to formulate an offering price for a property. Therefore, the rate is directly supported by the activities and actions of the marketplace.

The weakness of the overall rate based on direct sales is that the appraiser must carefully analyze the income and expenses from both the sales and the subject property to make a comparison. Information might not always be available from the comparable sales. The sales method does not directly take financing into account, and, if variations in financing affect the value, this is not compensated for. This method does not explain the "return on" or "return ofî the investment, and it does not provide any "investment analysis" information. The method is applicable only where there are a sufficient number of comparable sales to provide the appraiser with enough information to make a realistic analysis of the rates.

2. Band of investment (financial), blending the weighted rates of mortgage and equity into an overall rate.

R_O = (M x R_M) + (I -M(R_E)

The band of investment equation is also known in the following format when the subscript notations are not used:

R = (M x f) +(E x y)

It is acceptable to write the equation in either algebraic formula, and the reader should recognize that both methods are the band of investment.

This method blends the R_M with the R_E. It is used when the amount of the mortgage is unknown, because lenders will usually lend on a ratio of the market value of the property that the appraiser estimates. The mortgage and equity ratios are based on what the market activity appears to indicate, and upon discussions with mortgage lending officers with respect to rates, ratios and types of properties to which they are extending mortgages.

Analysis

R_O = (M x R_M) + (1 - M)(R_E)= .70 R_M = 12 x .009970

(i.e., 12 x Column 6) = 0.11964

Therefore, R_E = 0.0285

In this analysis, the mortgage rate and financing ratio would have come from an analysis of the mortgage market based on the financing available as of the effective date of appraisal. The equity dividend rate was based on the analysis of the sale.

Application

R_O = (.7 X 0.11964)+ (1 - .7)(0.0285)

R_O = 0.083748 + 0.00855

R_O = .092298

V_O = u>$29,250 .092298

V_O = $316,908 rounded to = $317,000

Therefore, based on the overall rate, and using the band of investment analysis, the estimated market value of the "leased fee interest subject to typical financing" is $317,000.

The strengths of this approach, in addition to those for the rate based on direct sales analysis, are that the financing aspects are taken into account, and that the appraiser has to estimate only 30 per cent (in this case) of the R_O, because the mortgage portion can be obtained from known sources. It should be recognized also that the dividend rate is based on sales analysis, which reflects the actions of buyers and sellers.

As indicated earlier, the weakness can be in the misapplication of dividend rates to properties that are not comparable, or to financing terms, or financing ratios, that are not typical.

3. Gross income multipliers, combined with comparable Operating Expense Ratios (OER).

R_O = 1 - OER GIM

This approach may be used when GIMs are available - but operating expenses are not - for comparable sales. The appraiser can use typical expense ratios for similar-type properties to derive the overall rate.

Analysis

R_O = I ñ OER GIM

OER = $20,000

$50,000 = .40

R_O = 1 - .40 6.0

R_O = 0.60 6.0

R_O = 0.10, or 10%

This calculation confirms the R_O calculated from the direct sales analysis when the net operating income was known. In the example, we did know the expenses and we could calculate the R_O directly, however, the application of this formula would apply where actual expenses for comparables were unknown, but GIMs could be calculated from known sales, and expense ratios could be estimated based on similar-type properties.

Application

The application of the overall rate is the same in this instance as that indicated in the section entitled Sales of Comparable Properties.

Rate comparison

Each method can produce a different result, as indicated by Example 11.

The GIM produced the lowest estimate and the overall rate based on the band of investment produced the highest estimate. The inconsistencies are apparent when only one sale is used' s a comparable. The appraiser should use four or five comparables to make an analysis of the rates, however, and should reconcile the rates to estimate which are more consistent. If little variation is found in overall rates based on sales, that rate should then be used on the basis that investors appear to be ignoring financing. If little variation is found in dividend rates, it would then appear that financing is important to the investor, and the appraiser should reflect these actions by using the band of investment (financial) method of estimating the overall rate.

EXAMPLE 3

Rate used: Market value estimate

Gross income multiplier...................... ……………$285,000

Equity dividend rate*.............................................. 310,000

Overall rate from sales............................................ 292,500

Overall rate from band of investment..................... 317,000

Overall rate from GIM and OER............................ 292,500

*This estimate was based on existing assumable financing.

Summary

If the appraiser understands the various methods of capitalization, it is possible to analyze the market transactions to determine which method investors appear to be relying upon in current market locations and conditions. It is possible for markets to act differently across the country, and one method may be applicable in one location, but not necessarily in another. Also, there may be various sub-markets within a local market, and the investors' analysis may differ in each.

Therefore, if the analysis of the market and application to the subject are consistently applied, the appraiser can estimate the market value of smaller income properties, based on the local market conditions, through the use of the direct capitalization methods.