Making Sense of the Capitalization Rate
The conversion of a series of periodic payments made or received over time to a capital sum (Present Value) is one of the more important financial functions. Yet many who use the capitalization method to establish value are not quite clear about what it is.
The derivation of a capitalization rate follows a basic formula for the valuation of perpetual annuities:
The basic formula for the Present Value of a future sum is:
PV = PMT,
(1+ i)n
where PMT is the payment per period n, n is the number of the future period, and i is the discount rate per period n .
It can be demonstrated mathematically that when the PMT remains equal and is to be received over an infinite number of periods,
PV = PMT + PMT + PMT + PMTn …….∞
(1+ i)1 (1+ i)2
(1+ i)3 (1+ i)n
the series reduces to the expression
PV = PMT
(Click here for proof)
i
Therefore a
capitalization rate is a single discount rate which converts an
infinite series of PMTs to a Present Value (PV).
This series assumes that the PMT occurs at the end of each period, (an Ordinary, Perpetual annuity).
If the PMT occurs at the beginning of each period ( a Perpetual Annuity-Due), the formula becomes:
PV = PMT *(1+i)
i
Common Uses of the Capitalization Rate
The most common uses of the capitalization rate are:
Each of these applications is covered in some detail in the text, but it is worth noting that the capitalization approach (using the formulas presented above) assumes: 1) that the PMT will never change, and 2) that the PMT will continue forever. Therefore, while the "cap rate" is an easy method of establishing current value (PV), it harbors these two very unlikely assumptions.
In addition, capitalizing a stock's dividend to
arrive at value presently has very limited use since the average dividend payout on the
Standard & Poor's 500 Index has now declined to a 70-year historic low (~
1.3%). Because federal tax laws tax dividends as ordinary income at a maximum of
38.5% but tax long-term capital gains at a maximum of only 20%, most public companies
distribute - evidently with stockholders' approval - only a very small portion of total
earnings in the form of dividends.
Capitalizing Stock Earnings
In the case of stocks which pay little or no dividends, some analysts resort to
capitalizing reported earnings (not paid dividends). This is an inappropriate use of the
capitalization method of establishing value since, as we have seen, the capitalization
method assumes a regular PMT which is projected to continue forever. When the
earnings per share number (EPS) is inserted into this formula, it is treated as a
regularly paid dividend, which it is not.
A stock's capitalization rate is the reciprocal
of the P/E ratio only when earnings are fully distributed as paid dividends.
For example, REITs are now required to distribute at least 90% of total earnings in
the form of paid dividends. In this instance, the capitalization of a REITs earnings may
yield an approximate
estimate of
value based on cashflow.
But in those cases in which a company retains most of its earnings, capitalization of a
meager dividend payout will not reflect the value of the stock. In these cases the value
of its stock should be determined by discounting the future payments and the net gain to
be realized upon sale at the end of the holding period.
Present Value should be estimated by Discounted Cashflow Analysis, and not by a
capitalization of annual earnings.
Capitalizing Real Estate Income
Real Estate appraisers continue to rely
heavily on the Income Approach To Value
method in establishing the market value of income-producing real estate. The most common
avenue to this value is the capitalization of a property's Net Operating Income:
Fair Market Value = Net Operating Income
Capitalization Rate
The Net Operating Income used is an estimate of the next period's (year's) income after operating expenses, but the discount rate used is most often determined by collecting data from recently sold properties similar to the one in question. Therefore prospective Net Operating Income is most often divided by retrospective capitalization rates. When interest rates are changing rapidly during periods of inflation and deflation, the results may contain significant errors in market value.
It is important to note that the Net Operating Income of a real property is not equivalent to the Net Operating Income statement prepared for a publicly held company. The latter is primarily prepared for the purpose of configuring reportable earnings after corporate income taxes, interest, depreciation and amortization deductions. The NOI of an income property is an EBITDA number: earnings before interest, (income) taxes, depreciation and amortization.
Adjusting the Capitalization Rate for Growth
If a growth factor is to be applied to the PMT, perhaps in the case of an annuity to offset inflation or, in the case of an income property to reflect rising net operating income, a simple adjustment can be made to the capitalization formula. Using g for the rate of growth in the PMT, the formula becomes:
Ordinary Annuity: PV = PMT
i-g
Annuity-Due: PV = PMT * (1+i)
i-g
These formulas are valid so long as g does not equal or exceed i.
It is also important that the period for n, i and PMT
be the same. If g is used, it must be expressed in the same
time-frame as well.
Always use the time-frame of the PMT as the determining time
frame: e.g. if the PMT is monthly be sure that n and i are expressed on a monthly basis; if the time frame of the PMT is
quarterly, all other variables must be expressed quarterly, etc....
Note: Don't use the Inflation Adjusted Rate to capitalize an infinite series of payments which are to increase at rate g per period. The IAR should be restricted to finite annuities, and should not be used with infinite (perpetual) annuities.
The more one understands the capitalization approach to establishing value, the more attractive Discounted Cashflow Analysis becomes.
Let a = PMT and let x = 1
(1+ i)
(1+ i)
Then the formula becomes:
PV = a + ax + ax2 + ax3 + ax4 + ax5 …………
Multiplying both sides by x we have,
xPV = ax + ax2 + ax3 + ax4 + ax5 ………….
Subtracting the last equation from the first, we have,
PV- xPV = a
PV(1-x) = a
PV = __a___ = PMT* (1 - 1 ) = PMT * (1+i)
(1-x)
(1+ i) (1+ i)
(1+i) (1+ i -1)
Therefore,
PV = PMT
i