# Estimating value diminution by the income approach.

When an income-producing property is affected by a condition that causes value to decrease, the sales comparison approach is often the primary means of estimating value diminution. The incorporation of the income approach depends on whether sufficient data are available to support the analyses. A new formula that relies on data that are frequently available from the market may make inclusion of the income approach simpler, however.

The fundamental relationship for measuring diminution of value is:

[Mathematical Expression Omitted]

where D = Diminution of value, expressed as a decimal fraction of the value in the unaffected condition Vu = Value in the unaffected condition Va = Value in the affected condition

From the direct capitalization method of the income approach, Vu and Va may be expressed as:

[Mathematical Expression Omitted]

where Iu = Net operating income (NOI) in the unaffected condition Ru = Overall capitalization rate in the unaffected condition IA = NOI in the affected condition RA = Overall capitalization rate in the affected condition

When the NOI in the affected condition is divided by the NOI in the unaffected condition, the result is a lowered income ratio, L. Thus:

[Mathematical Expression Omitted]

If the NOI of a property is normally \$10,000 and the condition affecting the property has reduced the net income to \$9,000, then L = 0.9 (\$9,000/10.000).

A rearrangement of the equation for L express Ia in terms of Iu:

[Mathematical Expression Omitted]

When the sujbect property is an industrial property for which the rents are net, and if rental rates have not been affected, the ratio between occupancy rates of affected and unaffected properties may be substituted for NOIs.

The other factor necessary to estimate the amount of value diminution is the risk premium required by buyers to induce them to buy property in the affected condition. This is a mark-up premium (RISK) that is applied to the overall capitalization rate. Thus:

[Mathematical Expression Omitted]

If the normal cap rate were 10% and the risk premium were 20%, the risk-modified cap rate would be 10% x 1.2 or 12%.

When the formula for Va is restated to incorporate L and RISK, the result is:

[Mathematical Expression Omitted]

Substituting the restated Va in the fundamental equation for value diminution yields:

[Mathematical Expression Omitted]

Table 1 and Figure 1 exhibit value diminution for a wide range of reduced income and risk premiums. These were developed for the entire range of NOI reduction, including the complete elimination of all net income. Before a condition reduces a property's income to this point, however, the need for a change in property use is likely to become apparent.

TESTING THE FORMULA

This formula was derived in connection with a case that involved hazardous material contamination of an industrial property in the Los Angeles area. In addition to data researched by the author, the market data developed by Peter J. Patchin, who pioneered the estimation of value diminution caused by hazardous contamination, 1 were employed in this case. Sales comparison analysis of these market data indicates that the diminution of the subject property's value ranged between 20% and 25% of its value in the uncontaminated condition.

[TABULAR DATA OMITTED]

Becuase the subject property was an industrial property leased on a net basis, the gross and net operating incomes were the same. In such a situation, the reduction in occupancy rate may be substituted for the reduction in net income.

Two properties were found in the Los Angeles area for whcih occupany rates in the contaminated condition were measurably reduced. The marketing time for these properties had lengthened; however, the rental rates achieved were essentially at market levels. The occupancy level of one property was reduced to between 91.2% and 95.5% of normal occupancy in the uncontaminated condition.

The other property exhibited an occupancy rate that was 92.73% of the average occupancy of surrounding properties, as measured by CB Commercial.2 The correlation between these two reduced occupancy rates in strong. The reduced occupancy that was selected for use in the analysis was 93%. Thus, L = 0.93.

Only one contaminated property with a risk premium was found. The overall rate for this property was specifically raised from 8.9% to 10.44%, an increase of 17.3%. Thus, RISK = 0.173.

When these values of L and RISK are used in the formula, the resulting estimate of value diminution is: [Mathemaical Expression Omitted]

The 20.7% value diminution indicated by the formula correlates well with the 20% to 25% range indicates by sales comparison and serves as a validation of the formula:

[Mathematical Expression Omitted]

(1) Peter J. Patchin, "Valuation of Contaminated, "The Appraisal Journal (January 1988): 7--16; and Peter J. Patchin, "Contaminated Properties--Stigma Revisited," The Appraisal Journal (April 1991): 167--172.

(2) CB Commercial Industrial Space Real Estate Market Bulletin, South Bay of Los Angeles County, (First and second quarter, 1991), published by CB Commercial Real Estate Group.

Richard A. Neustein, MAI, SRA, is the principal of R.A. Neustein & Associates in Los Angeles, where he specializes in the appraisal of unusual and problem properties with a focus on litigation. He received a BS in mechanical engineering from Northrop University in Los Angeles and an MBA from the University of California in Los Angeles.