Capital Market Theory and Real Estate Valuation: A Case Study in Choosing an `Appropriate' Discount Rate
Adams, A. Frank,, III, Jackson, John D., Cook, J. Philip, Journal of Forensic Economics
In a typical police action by a state property commission in a condemnation, property owners and their attorneys enlist the services of state licensed real estate appraisers for valuation analysis. In cases where an entire tract or parcel of land is condemned, the appraiser's primary purpose is to estimate the market value of the complete taking at the time of the condemnation. When only a fraction of a tract or parcel of land is condemned, the appraiser must not only estimate the market value of the taking at the time of the condemnation, but must also estimate the consequential damages to the remaining part of the tract or parcel, less any benefits to the remaining part of the tract or parcel. As such, positive and negative externalities are given due consideration in determining a final estimate of the value of the taking.
Although property appraisers undergo extensive training for certification purposes and routinely complete continuing education courses to meet state licensing requirements, variation can and does exist for estimates of market value on condemned property for which certain facts are not in dispute. In addition, when condemned property has previously supported an on-going business, there may be even greater variation in estimates of market value resulting from differences of opinion concerning relevant cash flows, timing and longevity of cash flows and appropriate discount rates used to value those cash flows. But, when condemned property has existing lease arrangements in place, one would expect that differences of opinion concerning value would be much less variable than in those circumstances where cash flows have to be estimated. In such circumstances, when there are differences of opinion concerning market value, the differences in the estimates lie primarily in the choice of an `appropriate' discount rate.
This paper focuses on the construction of, and relationship between, discount rates and capitalization rates and then illustrates their proper application and construction in the context of a recent valuation assignment in a property condemnation.
II. The Relationship Between Discount Rates and Capitalization Rates
Discount rates and capitalization rates are often used interchangeably, which is incorrect. While the two concepts are similar, they are not identical. The use of a discount rate to determine the present value of an income stream captures all of the expected future cash flows generated from an investment while the use of a capitalization rate, or cap rate, assumes that an income stream is nominally constant in perpetuity, and only takes into account the initial periodic cash flow in determining a present value for the investment. To illustrate these concepts we define the following variables
V present value of the investment CF periodic cash flow from the investment (annually-end of period) k total or required rate of return from the investment g annual growth rate of the investment's cash flows
When the cash flows from an investment are expected to occur in perpetuity, and to grow at a constant rate, the relationship between these variables can be expressed as (1):
(1) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
Equation (1) can be further reduced to the following form (2):
(2) V = C[F.sub.1] / k - g
Assuming that the cash flows are received in perpetuity, and that the growth rate is constant, the present value of an investment is found by dividing the cash flow received in period I by the required rate of return minus the growth rate. Obviously, if the cash flows are not received in perpetuity, equation (2) cannot be utilized to find the present value of the investment. (3) Used in the context of equations (1) and (2), k can also be referred to as a discount rate. (4)
In circumstances where the cash flows received from an investment are expected to remain nominally constant in perpetuity, i. …