Chapter 15
Capitalization rates

Theoretical basis for income capitalization

*   Theory of Interest: Interest is the payment for forgoing the use of capital resources.

*   The Theory of interest explains the difference between the value of a good at the present time and the value to be received in the future.

Components of Capitalization Rates

*   Discount rates--Return on Investment

*   Plus Recapture rate--Return of Investment

*   Roverall = yo - Doverall * an
where:

*   Roverall = Capitalization Rate

*   yo = Discount Rate for property

*   Doverall * an = Recapture Rate

*   Doverall = Expected change in value during              holding period.

*   an = Annualizer (converts value over holding        period into an value per year.)

Types of Discount Rates

*   y = General symbol for Return on     Investment

*   yo = Discount rate for overall property

*   ym = Discount rate on loan (mortgage loan interest)

*   ye = Discount rate on equity

*   yL = Discount rate on land

*   yB = Discount rate on building

Components of Discount Rates

*   Pure cost of money

*   Base Rate

*   Inflation Premium

*   Liquidity Premium

*   Risk Premium

*   Reflects the uncertainty that the expected cash flow differs from the actual amount received.

Estimating Discount Rates

*   Direct market extraction

*   Abstraction from Gross Income Multiplier

*   Mortgage Equity Analysis

Direct Market Extraction

*   Market research has discovered the following three comparable sales:

*                  CompA   CompB   Comp C

*   Sale Price       200,000 210,000 150,000

*   Building Val. 160,000 168,000 120,000

*   Net Income   24,400  22,470   16, 350

*   Useful life      25 years 50 years 40 years

*   Recapture % 4%         2%          2.5%

*   Bd. Recapture       6,400    3,360     3,000

*   Inc After Rcpt       18,000   19,110    13,350

*   Indicated Ro  9.0%      9.1%       8.9%

Recapture Rates

*   Strait-line Rates

*   Assumes recapture occurs at the same rate each year.

*   Computed by 1 ¸ useful life of improvements

*   Sinking Fund Rates

*   Assumes recapture occurs more rapidly toward the end of the assets useful life.

*   Computed by computing the appropriate sinking fund factor.

Types of capitalization rates

*   Overall capitalization rate

*   Equity capitalization rate

*   Mortgage (debt) capitalization rate

*   Land capitalization rate

Methods of estimating capitalization rates

*   Direct Market Extraction

*   Composite Rate -- i = f(base rate, inflation, risk, liquidity)

*   Return on vs Return of Building Capitalization Rates

*   Band of investment analysis (Simple mortgage-equity analysis)

*   The Ellwood formulation

*   Underwriters method

Direct Market Extraction

*   Easiest and most reliable if data is available

*   Based upon simple valuation formula:

*   Voverall = Ioverall ¸ Roverall

*   Steps:

*   Examine sales of comparable properties

*   Solve for the indicated overall rate by using the Income at time of sale as Ioverall and sales price as the Voverall

*   For example, if a comparable property sold for $352,000 and its income at time of sale was $33,440, then its indicated Return overall is .095

Composite Rate -- i = f(base rate, inflation, risk, liquidity)

*   Base rate + Inflation = Treasury yield

*   Base rate + Inflation + Liquidity = CD rate

*   Use of bracketing certainty equivalents

*   Which is more risky, a new Taco Bell or a USAir bond?

*   Which is more risky, a new Taco Bell or an IBM bond?

*   Consequently, the appropriate yield for Taco Bell should fall between the yield on a USAir bond and an IBM bond (both found in the WSJ).

Return on vs Return of Building Capitalization Rates

*   Return on Investment is the base rate desired by an investor in order to make an investment.

*   Return of Investment is an additional rate desired to compensate the investor for the depreciation of the building. It is equal to
1
¸ (Useful life of building)

*   Return overall for an investment is then equal to the return on investment plus the return of investment.

Band of Investment

*   Weights the investors position with the lenders

*   %Equity investment * Return on Investment + %Mortgage * Rate on Mortgage

*   What is the indicated overall rate if an investor puts down 20%, requires a 15% rate of return, and the bank charges 9% on the 30 year, monthly payment mortgage?

Step 1: Compute the rate for the mortgage

*   Rm= Rmortgage= Total amount of payments in a year ¸ Loan Amount

*   To calculate, simply set the loan amount (PV) as 100% or 1, then solve for the payment like any other mortgage payment problem. Then multiply the result by the number of payments per year.

*   P/YR =12; I/YR = 9; PV = 1; N = 360 (30 cream N); solve for PMT; * 12

*   Rm= .0966

Step 2: Compute the percentage of the investment that is mortgage

*   Mortgage percentage = 100% - equity percentage

*   100% - 20% = 80%

*   Now you have all of the information necessary for the solution!

Solution for Band of Investment

*   %Equity investment * Requity = .2 * .15 = .03

*   %Mortgage * Rate on Mortgage (Rm) = .8 * .0966 = .0773

*   .03 + .0773 = .1073 = 10.73% = Roverall = Ro

Ellwood Mortgage Equity

*   Based upon a logical extention of the band of investment technique

*   Reasons that the return overall yielded by the expected annual income does not need to be as high if the annual cash flows are used to pay down the debt since the investor will receive the debt reduction cash flow when the property is sold.

*   Further reasons that the annual return overall might be lower or higher if the property appreciates or depreciates during the holding period since that appreciation or depreciation cash flow is realized when the property is sold.

Steps in computing the Return Overall with Ellwood

*   Ellwood begins with the rate of return demanded by the typical investor. This is usually determined through interviews of typical investors.

*   Next the annual impact of debt financing is computed.

*   Includes impact of leverage

*   Includes impact of debt amortization during holding period

*   Finally the annual impact of expected appreciation or depreciation is computed.

Computing the annual impact of debt financing

*   Basic formula: m(ye - Rm + p * an) where:

*   m = the percentage loan

*   ye - Rm = the difference between what the investor expects to earn (ye) and what the lender is charging (Rm).

*   p = the percentage of the loan paid off during the holding period

*   an = annualizer (a factor which converts a future value into an annual percentage This is known as a sinking fund factor.)

Calculation of p

*   Simply begin with 100% or 1 as the PV and calculate the percentage mortgage payment just as any mortgage payment is calculated.

*   From the original term of the loan, subtract the holding period and enter as N. (If there is more than one payment per year, remember that the number of years must be multiplied by the payments per year before entering as N.

*   Solve for the percentage of the original balance remaining by recomputing PV.

*   Finally, subtract the percentage remaining from 100% to determine the percentage paid off.

Calculation of an

*   The annualizer is the annual percentage of the whole necessary to invest to accumulate that amount in the future. It is the payment necessary to accumulate a future value.

*   Simply enter 100% or 1 into FV.

*   Enter the number of years into N. (Annualizers assume only one payment per year.)

*   Enter the investor’s desired rate of return (ye)

*   Solve for payment. This is the annualizer.

Computing the annual impact of appreciation or depreciation

*   First the expected appreciation or depreciation in the sales price (Doverall) must be determined as a percentage change in the value of the property at the time of the valuation until the end of the expected holding period.

*   This is usually estimated based upon percentage appreciation or depreciation of comparable properties unless the market is not expected to react as it had in the past.

*   This percentage is then multiplied by the annualizer (an) to convert it to an annual impact.

The Complete Ellwood Formulation

*   The investor’s desired rate of return = ye

*   The debt financing component = m(ye - Rm + p * an)

*   The appreciation/depreciation component = Doverall * an

*   The entire formula is: Ro = ye - m(ye - Rm + p * an) - Doverall * an

Example Ellwood problem

*   What is the indicated overall rate if an investor puts down 20%, requires a 15% rate of return, and the bank charges 9% on the 30 year, monthly payment mortgage? The property is expected to depreciate 20% over the 10 year holding period.

*   Calculate each of the following first:

*   m

*   an

*   Rm

*   p

Calculation of Debt financing component

*   m = 100% - 20% investor’s equity = 80%

*   Rm = .0966 (P/YR =12; I/YR=9; PV=1; N=360 (30 cream N); solve for PMT; * 12)

*   p = .1057 (Original term = 30 years - 10 year holding period = 20 years remaining; 20 cream key N; solve for PV = .8943; 1 - .8942 = .1057)

*   an = .0493 (P/YR = 1; I/YR = 15; n = 10; FV = 1; solve for PMT)

*   m(ye - Rm + p * an) = .8 (.15 - .0966 + .1057 * .0493) = .0469

Final Calculation of Ellwood

*   Appreciation/depreciation component = Doverall * an = -.2 * .0493 = .0099

*   Thus: Ro = ye - m(ye - Rm + p * an) - Doverall * an = .15 - .8 (.15 - .0966 + .1057 * .0493) - (-.2 * .0493)

*   .15 - .0469 + .0099 = .1130