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Bridging the gap between discount rate theory and investor surveys.

Article Excerpt
Abstract

This article is intended to assist appraisers in reconciling the differences between the theoretical relationship of discount rates and overall capitalization rates and the published market information in investor surveys. The study explains several disparities in the methodology used to estimate terminal value and define income stream that account for much of the gap between theory and secondary market data in the form of investor surveys.

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Investor surveys reflect a differential between discount rates and overall capitalization rates that is substantially smaller than basic capitalization theory would indicate. Much of this difference between theory and the survey data can be understood by examining the estimates of terminal value and how the income stream is capitalized.

Theoretical Relationship between Discount Rates and Cap Rates

In appraisal textbooks, the relationship between discount rates and overall capitalization rates, or cap rates, is a simple one: Discount rate = cap rate + income growth rate or

[Y.sub.o] =[R.sub.o] + CR

where:

[Y.sub.o] = overall yield rate, or discount rate

[R.sub.o] = overall capitalization rate, or cap rate

CR = rate of change for income

Discount Rate

A discount rate, also known as an overall yield rate, is an interest rate or yield rate used to convert anticipated future payments or receipts into present value. The resulting present value represents the amount of capital to be invested so that the investor's expected yield equals the specified discount rate. The overall yield rate ([Y.sub.o]) is the rate of return on the total capital invested. It considers all changes in income over the investment projection period as well as the reversion at the end of the projection period. It does not, however, consider the effect of debt financing. Rather, it is calculated as if the property were purchased with no debt capital. It is calculated in the same way the internal rate of return is calculated. (1)

Overall Capitalization Rate

An overall capitalization rate ([R.sub.o]), also known as an overall rate, a cap rate, or a going-in cap rate, is an income rate for a total real property interest that reflects the relationship between a single year's net operating income expectancy and the total property price or value. It is used to convert net operating income into an indication of overall property value. (2) The equation used to reflect the overall capitalization rate relationship to income and value is [R.sub.o] = [I.sub.o]/[V.sub.o]. It is considered the combination of a return of investment and a return on investment.

Income Growth Rate

The income growth rate (CR) is the constant rate of growth of net operating income on an annual basis. This requires consideration of both revenue and expense growth rates over the holding period. However, the assumptions necessary to support this relationship are often not well understood.

The necessary assumptions built into the theory of "discount rate equals overall capitalization rate plus income growth" are as follows:

* The income growth rate must be constant throughout the holding period.

* The income stream is net operating income only, i.e., without other cash flows typically reflected in discounted cash flow analysis, such as vacancy/lease turnover costs, leasing commissions, tenant improvement allowances, and replacement reserves.

* Terminal value is estimated using a terminal cap rate equal to the overall capitalization rate. This terminal value assumption applies only to the simplified model discussed earlier. In the real-world marketplace (as reflected in published investor surveys), a terminal cap rate is equal to the overall capitalization rate plus a risk increment for the greater risk of estimating cash flows several...

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