advanced capitalization methods

David Hornby

The common capitalization method of valuation for investment properties, the initial yield method, assumes two things; that the rent is paid at the end of the period and yearly. However, in practice, these assumptions do not apply. For example, rents are paid in advance and the payment period is usually monthly. However, adjustments can be made to the common capitalization method to take these factors into account.
 
See payments in advance
See nominal and effective interest rates

CONSTRUCTING CAPITALIZATION RATES

Wherever possible capitalization rates should be analyzed from sales of investment properties comparable to the subject property. However, there are circumstances where the investment property is so unique that there are no comparable sales. In such a case various methods have been devised to enable the construction of capitalization rates from other investment data. The models used for construction can also be used to explain existing capitalization rates and predict future rates. Sales of investment properties can be analyzed to determine the value of the component parts that make up the capitalization rate and therefore, the overall rate can be found with sales evidence.

BAND OF INVESTMENT

The band of investment method uses typical mortgage data and returns on equity to construct the overall capitalization rate (OCR).

EXAMPLE

An investment property has a net annual income of 15 000.
Assuming that the mortgage for this type of property is as follows:
Principal: 75% of purchase price
Interest rate: 15% per annum
Required return on equity: 19% per annum

The overall capitalization rate can be found with the following 3 steps:

1. DETERMINE THE ANNUAL MORTGAGE REPAYMENT FACTOR
This factor is found by multiplying the mortgage interest rate by the ratio of the amount borrowed to the total purchase price: 0.75 * 0.15 = 0.1125
2. DETERMINE THE RETURN ON EQUITY FACTOR
This factor is found by multiplying the required return on equity by the owner's equity ratio: 0.25 * 0.19 = 0.0475
3. CALCULATE THE OVERALL CAPITALIZATION RATE
The overall capitalization rate is found by summing the two factors: 0.1125 + 0.0475 = 0.16 or 16% 4.
CALCULATE THE MARKET VALUE OF THE PROPERTY:
The market value of the property can now be found: 15000 * 100/ 16 = 93750

THE ELLWOOD METHOD

Ellwood developed a set of valuation tables which showed the overall capitalization rate derived from mortgage data, expected returns on equity and expected capital gains (Ellwood, 1974). The Ellwood formula is as follows:

R = Y - MC - AS

Where:
R = overall capitalization rate
Y = required return on equity
M = ratio of mortgage to purchase price or market value
C = mortgage coefficient
A = expected capital gains
S = sinking fund factor for period of loan at Y%

EXAMPLE

Value the following property using the Ellwood method:
Net annual return: 65 000
Mortgage ratio: 75%
Mortgage term: 20 years
Mortgage interest rate: 15% per annum
Required return on equity: 19% per annum
Expected average capital gains: 12% per annum

The market value is found with the following 4 steps:

1. DETERMINE THE "C" COEFFICIENT
The "C" coefficient is the annual mortgage repayment factor that is, the repayment for each $1 borrowed: C = 1/ ((1-(1/(1+i)n))/i) = 1/((1-(1/1.1520))/0.15) = 0.1598

2,DETERMINE THE SINKING FUND OR REPLACEMENT OF CAPITAL FACTOR (SFF)
The sinking fund factor is the annual amount required to replace $1 in the future at the rate of return on equity. The period is the mortgage period: SFF = 1/(((1+i)n-1)/i) = 1/((1.1920-1)/0.19) = 0.0060

 3. CALCULATE THE OVERALL CAPITALISATION RATE
OCR = 0.19 - (0.75 * 0.1598) - (0.12 * 0.0060) = 0.0695
Therefore, the overall capitalization rate = 6.95% pa

4. DETERMINE MARKET VALUE

Market value = 65000 * 100/ 6.95 = 935 871 say 936 000

CAPITALIZATION RESIDUAL METHODS

The residual method of valuation recognises the dichotomy in the nature of the value of land and buildings. The land residual method is used to value the land component of investment properties and the building residual method to value the building component of investment properties.

See capital asset pricing model (CAPM)

THE "LAYER" CAPITALIZATION METHOD

The layer method of capitalization splits the expected cash flow into two components:

DIAGRAM

THE "LAYER" CAPITALIZATION METHOD
 

The initial cash flow accounts for the majority of the property's value and is valued with the "initial yield" formula and the "stepped" part of the diagram is capitalized separately. Suppose the net lettable area of the investment property represented is 2500 m2 and the initial rents and market rents are 200 and 220/m2 respectively: The remaining period of the current lease is for another 6 years but the next rent review is not due until 2 years time. Therefore, until that time the passing rent of 200 will below the market rent of 220 for a large part of the 2 year period. After analyzing comparable sales it is found that the initial yield capitalization rate is 8% pa.

Assuming a vacancy rate of 4% per annum the value of the initial rent part:

(500 000*.96) * 100/8 = 6 000 000

The expected marginal rate to bring the rent to market rent ($20/m2) is capitalized at a higher rate than that for the initial rent. This is because it is riskier being in the future (at the time of the next rental review) and there is not guarantee that $220/m2 will be achieved. On the other hand, the initial yield rent is guaranteed at least until the end of the lease period as it cannot drop below the initial rent because of the "ratchet" clause in the standard form lease document.

The value of the marginal market rent part is as found as follows assuming a margin of risk of 1.5% per annum net:

(50 000*.96) * 100/(8+1.5) = 505 263

The present value over 2 years is found.

Assuming the applicable discount rate is 10% per annum:

PV(1) = 1/(1+i)n

Where:

PV(1) = the present value factor ie the PV of 1
i = interest rate as a decimal ie 10%= .1
n = period = 2 PV(1) = 1/1.12 = 0.8265

Therefore, the value of the property = 6 000 000 + (0.8265*505 263) = 6 417 560 say 6 420 000

The advantage of the layer method is that it splits the expected income streams into two parts; a low risk part and a high risk part. Therefore, the resultant capitalized value better reflects the relevant weighting of the two parts compared to the simple initial yield method. See shortfall method

REFERENCES

Ellwood L W, "Ellwood Tables - Part 1 - Explanatory Text", American Institute of Real Estate Appraisers, Chicago, 1974. Sharpe W F, "Capital Asset Prices: A Theory of Market Equilibrium Under Conditions of Risk", Journal of Finance, September, 1964.

PROBLEMS

1. Determine the effective annual rate for the following nominal rates: 21% per annum payable daily 21% per annum payable monthly 21% per annum payable quarterly 21% per annum payable half yearly

2. What is the effective monthly equivalent of 21% per annum effective?

3. A property has sold for 800 000 with a net annual rent of 70 000 payable quarterly. Determine the annuity due capitalisation rate if the lessor's rate of investment is 12% per annum nominal.

4. A property comparable with that in question 3 has a net annual income of 90 000 payable quarterly. Using the other information and data in question 3, what is the market value?

5. Determine the market value of the following property adjusting for payments in advance and using an effective capitalization rate: Quarterly rent: 25 000 Capitalization rate: 9% per annum

6. Compare the answer to 5 against the market value using a monthly rent of 8 333. At what payment period would it be unnecessary to adjust for payments in advance?

7. An investment property has a net annual income of 550 000. Determine market value from the following information using the Band of Investment method: Mortgage interest rate: 19% per annum Ratio of mortgage to value: 90% Required return on equity: 25% per annum

8. For the property in question 7 determine the market value using the following additional information with the Ellwood method: Expected capital gains: 12% per annum Mortgage term: 25 years

9. An investment property has a net annual income of 600 000. Determine the market value from the following information using the "land residual" method: Building value: 3 000 000 Required return from building: 12% per annum Replacement of capital: 10% per annum Expected life of building: 15 years Required return on land value: 9% per annum

10. Determine the market value of the following investment property using the Building Residual method: Net annual income: 380 000 Land value: 2 000 000 Required return on building value: 8% per annum Replacement of capital: 10% per annum Expected life of building: 8 years Required return on land: 8% pa

11. List 3 advantages and 3 disadvantages from a valuation point of view of using the CAPM method.

12. Determine the market value of the following property using the CAPM method: Risk free rate: 8%pa Market return: 10.5%pa Beta value: 1.5 Net annual income: 250 000

13. Determine the market value of the following property using the "layer" capitalization method: Initial net rents: 25 000 pa Initial rent capitalization rate: 8%pa Expected market net rents due in 5 years time: 50 000 pa Expected market rent capitalization rate: 10%pa Discount rate: 9%pa

14. Value the above property using the "shortfall method". Assume a capitalization rate of 6%pa.

15. Determine the market value of the above property using the "increasing annuity" method and the following extra information: Length of lease: 20 years Rent reviews: Every 5 years Discount rate: 8%pa Expected annual rental increase: 5 000 pa
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