Title: Land and Construction Economics - Advanced Investment Appraisal The lecture notes on this component can be downloaded from the web page : http://hkusury2.hku.hk/li in the file : LCE-Notes 01 , under the heading : Notes to BSc. In Surveying Students
1Land and Construction Economics - Advanced
Investment Appraisal The lecture notes on this
component can be downloaded from the web page
http//hkusury2.hku.hk/liin the file
LCE-Notes 01 , under the heading Notes to BSc.
In Surveying Students Year Two
2Please Switch Off Your Mobile Phone and Pager as
I DO NOT Want to Talk To Your Friends !
3Investment Valuation
- The basic logic of the investment method is the
understanding that money has a time value. Money
receivable in the future is worth less then money
of the same amount receivable today.
4- Hence, the present value (PV) of one dollar
receivable after n years at an interest rate (or
discount rate) of i is worth -
- The product of formula can be called a PV factor.
This is a factor for this can be multiplied to
any future value of a fixed sum (as opposed to a
stream of future values in the case of years
purchase factor, discussed later) of money to
find the present value. - The PV factor is always less than 1 because
future value is always less than present value in
real terms. The reasons for this are mainly
twofold. One is the opportunity cost in
expecting future value. Opportunity cost is the
return forgone in other investment opportunities
when investing in a particular project.
5- For instance, if an investor has HK100 and he
invests all of this sum into project A, the
opportunity cost for this decision is the likely
return he could have achieved from projects B,C
or D had he chosen to do so. So long as project
A compensates him enough or opportunity cost is
less than return from project A, the investment
is a sound one. In the present value situation,
the utility of immediate consumption is always
greater than deferred consumption. Hence future
value is less than present value. - The second reason is the age of inflation.
Future value is always readily eroded by
inflation in terms of purchasing power. - In fact, the PV factor formula can be analyzed
from reverse in an investment angle. For
instance, if we have HK100 today and invest this
sum into a regular investment giving a 10 return
per annum. - In one years time, we will have HK110 (since
HK100 x (110) HK110). In this case, 10 is
our required rate of return.
6- Now, lets look at this from the future. If we
are given an opportunity to receive HK110 in one
years time, how much are we prepare to pay for
such opportunity ? Since we can earn 10 from a
regular investment, we will use 10 as the
discount rate to find the present value. As a
result, the present value of HK110 in a years
time is HK110 x 1/(110) HK100. This
illustrates the fact that the discount rate and
rate of return for investment are closely
related. To a certain extent, we can even assert
that they are the same.
7- When the value of the stream of incomes (I) is
fixed within the holding period, the capital
value (V) of the interest in property (hence the
summation of the future incomes) during the
holding period then becomes -
- It is also obvious that when the holding period
approaches infinity, the re-sale value of the
asset approaches zero, hence it becomes
relatively insignificant. In infinity, PV of the
reversionary capital value approaches 0 such that
formula becomes
8- Suppose a property whose rental income per annum
is HK 20. This amount is fixed and unchanged
forever. Assuming rental income is receivable at
the end of each year, and our required rate of
return for property is 20, well be able to find
out the value of this property by formula. Since
the property is for rental forever, there is no
reversionary sale price, formula becomes - Assume year 1000 is a proxy for eternity, the
summation incomes is HK100. This is obtained
either through the serial calculation or just
HK20/20 HK100.
9- In any case, we can prove that if we pay HK100
today, and getting HK20 per year, it is an
investment with return of 20 p.a.( i.e. return
or yield is equal to annual income divided by
capital value). This exactly reflects what we
require before the valuation process. - Now, lets assume a more realistic situation that
rental does grow as time goes by. Assuming a 12
rental growth per year due to an upsurge of
demand for this kind of property,
10- If we are patient enough, we can try to add up
all these together and V will turn out to be HK
250. In this case, the yield has dropped to
HK20/HK250 8 ! Superficially, it does not
make sense. Logically, when there is an increase
in demand leading to a rise in rental income, the
rate of return should increase as well ! In
fact, the opposite happens. This is the case
even when we assume that the increase in rental
value starts immediately so that it becomes
11- In this case, V becomes HK280 but yield remains
8 (i.e. HK22.4/HK280 0.08). - When there is future growth in the rental income,
a new definition of yield is spinned off from the
general concept of the rate of return. - In fact, in both cases, we are not getting less
than 20 p.a. - This is because in both cases, we are using 20,
the required rate of return to discount future
values. - What is different is the initial yield we are
getting. - As the initial income of HK20 or HK22.4
represents the initial rental level only with an
implication that in the future, this level will
go up at a rate of about 12 p.a. - As a result, we are willing to accept a yield
initially lower than what we require in the
understanding that the rental income we are
getting from this property will go up in the
future.
12- Since the definition of yield is always income
divided by capital value. - When there is future growth in the rental level,
the initial rental income is always lower than
the future rental level. - Hence, the initial yield will be lower than the
expected rate of return. - In addition, there is a hidden relationship in
both cases. In these two cases, we have a
required rate of return of 20 p.a. and a rental
growth rate of 12 p.a. - When we deduct the rental growth rate from the
rate of return, it becomes 8, which is equal to
the initial yield ! As a result, initial yield
may be applied to future inflated income etc.
13- Discount Rate
- 1) Weighted Average Cost of Capital (WACC).
Damodaran (1996) defines WACC as the weighted
average of the costs of the different components
of financing used by a firm. He gives the
following formula for the WACC as - WACC ke(E/EDPS)kd(D/EDPS)kps(PS/EDP
S)
14- Where ke cost of equity
- kd after-tax cost of debt
- kps cost of preferred stock
- E/EDPS market value proportion of equity in
funding mix - D/EDPS market value proportion of debt in
funding mix - PS/EDPS market value proportion of
preferred stock in funding mix, if any - In some cases, this component does not exist
15- 2)Dividend Discount Model DDM
- In the simplest case, discount rate is equal to
cap. Rate plus growth rate - Case 1
- Value 10,000,000
- Initial rental 700,000
- Growth rate 4
- Holding period 5 years
- Disposal cap. Rate 7
16- Year 1 Year 2 Year 3 Year 4 Year 5
- 700,000 728,000 757,120 787,405 818,901
- PV_at_11 0.9009 0.8116 0.7312 0.6587 0.5935
- P.V. 630,631 590,861 553,600 518,688 485,978
17- Disposal Value
- Expected Year 6 Rental 851,657
- Cap. Rate 7
- PV. _at_ 11 0.5935
- Equals 7,220,243
18- Hence, the value of this real estate is
- PV of
- Year One Rental 630,631
- Year Two Rental 590,861
- Year Three Rental 553,600
- Year Four Rental 518,688
- Year Five Rental 485,978
- Year Six Disposal Value 7,220,243
- Total 10,000,000
19- Case 2
- Value 10,000,000
- Initial rental 900,000
- Growth rate 3
- Holding period 5 years
- Disposal cap. Rate 9
20- Year 1 Year 2 Year 3 Year 4 Year 5
- 900,000 727,000 954,810 983,454 1,012,958
- PV_at_12 0.8929 0.7972 0.7118 0.6355 0.5674
- P.V. 803,571 738,999 679,615 625,003 574,780
21- Disposal Value
- Expected Year 6 Rental 1,043,347
- Cap. Rate 9
- PV. _at_ 12 0.55674
- Equals 6,578,032
22- Hence, the value of this real estate is
- PV of
- Year One Rental 803,571
- Year Two Rental 738,999
- Year Three Rental 679,615
- Year Four Rental 625,003
- Year Five Rental 574,780
- Year Six Disposal Value 6,578,032
- Total 10,000,000
23- The Capital Asset Pricing Model (CAPM) evolved
from stock market valuation in mid-60s. - In the simplest and non-mathematical terminology,
CAPM states that an assets expected return,
which has included the basis of a risk free
return, is a positive and linear function of its
correlation (in the form of covariance) of
returns with a portfolio of all other risk assets
available in the market.
24- The risk free return is normally referred to as
the government bond or debenture rate. In the
stock market, it has been widely used to apply in
the estimation of the performance of stock, in
terms of rate of return. Basically, the model
states that the expected return of any asset is - Expected return risk free return plus risk
premium
25- For the estimation of risk premium, a Beta value
is required to be estimated which shows the
covariance of the asset with the general market
return. - Again, in the simplest wording, the risk premium
is the market risk factor of the asset multiplied
by the difference between the general market
expected return and the risk free return. - Due to the theoretical attractiveness of the
model and the general lack of other models in
estimating rate of return for real estate, there
has been a growth interest in the application of
this model in the property market.
26- In 1984, Gerald Brown carried out an empirical
test for this model using market returns in the
U.K. , Brown tried to estimate the expected
returns for various property sectors. - According to his findings, the return on
long-date gilts at that time was 11 while the
general broaaly-based market return was estimated
to be 20. - In addition, he calculated that the Beta value
for property, hence the estimation of market risk
for property was 0.2. Using a CAPM model, the
expected return for property in general was - 11 0.2(20 - 11) 12.8
27- In his next step, he estimated the market risk of
each sub-sector in the property market relative
to the property market as a whole. - He did this by carrying out a regression analysis
on the returns of each sectors against the
general property market returns. - When this was done, he found the Beta values for
each sub-sector and when these Beta values were
multiplied by the Beta value of the property
market as a whole, he further deduced the risk of
each sub-sector relative to the whole investment
market as follows
28- Retail 1.16 1.16 x 0.2 0.23
- Office 0.87 0.87 x 0.2 0.17
- Industrial 0.69 0.69 x 0.2 0.14
- Accordingly, the expected returns for each of
these sub-sectors can now be deduced as follows - Retail 11 0.23 ( 20 - 11) 13.07
- Office 11 0.17 ( 20 - 11) 12.53
- Industrial 11 0.14 ( 20 - 11) 12.26
29- Nevertheless, due to the fundamental differences
between the property market and other capital
markets, the application of CAPM in the property
market emerged only recently and is still in the
trial stage. - Such differences include the availability of
market data due to the lack of a central clearing
house similar to a central stock exchange for
real estate the heterogeneous nature each
property and the indivisibility of real estate.
30- The traditional approach of investment method of
valuation tends to rely on initial income and the
market yield to carry out capitalisation process.
- The market property yield, which is commonly
derived from the relationship between the current
open market rent and the current market value of
similar properties, has itself carried an
implication of future rental growth potential (or
diminution). - This is because the open market rent at any time
represents the maximum initial rental receivable.
- Under most of the circumstances, rental value
will vary with the economic environment and the
property market sentiment. - If we take a very long span of time, say 50
years, rental value should have a positive growth
rate per year, on average.
31- This is the point which most valuers will find
puzzled when trying to adopt a suitable discount
rate for future incomes. Traditional text books
teach us that it is the market property yield
that should be used in the capitalisation
process, regardless of the implications of the
future incomes. - A more reasonable in adopting the rate is to
look at the potential movement of these future
incomes. - If the capitalisation process takes into account
of the current market rent only, then the current
market yield should be used. Where we are
capitalising a stream of fixed future values, the
discount rate, taking into account of the
expected rate of return, opportunity cost and the
risk premium should be used.
32- The traditional wisdom of using the years
purchase factor for both eternally receivable
incomes and fixed period incomes therefore
attracts the problem of this yield choosing
criteria. - A relatively simple solution to this yield
choosing problem is to turn to discounted cash
flow model (D.C.F.) where only the discount rate
for future values is to be used. - However, as with other financial analytical
techniques, the D.C.F. model is itself not
without drawbacks. - Criticisms have been raised by various
authorities on different aspects of the model. - These cautious notes include the need to
consider the relationship of risk as it applies
to the discount rate as opposed to the
capitalisation rate in the D.C.F. model, the lack
of substantial proof that the use of D.C.F. model
actually improves an investors performance and
the reasonableness in setting the various
assumptions in the D.C.F. model.
33- Nevertheless, compared to the conventional
capitalisation process for varying incomes, the
D.C.F. model can avoid the problem of defining
and justifying the use of market yield in various
stages of the valuation. - In a D.C.F. model, the discount rate is simply
the required rate of return. What we need to
focus on is the rate of compensation for future
cash flows at different points of time in the
future. Deriving from this, we may even have
different discount rates for different stages of
future incomes, depending on the risk premium
required for each stage of the cash flow.
34- Furthermore, D.C.F. makes realistic assumption to
the valuation, especially on the part of property
finance. - If we accept that most property investments are
carried out with property finance, or on a
mortgage-backed system, the value of this real
estate should in fact be composed of two elements
in terms of property rights, namely the part that
belongs to the equity investor and the part that
belongs to the lender, or the bank. Hence, the
value of real estate assessed on a
mortgage-equity model will be equal to
35- When we further break down these two components,
we may see that the value of the mortgage is made
up of the total discounted value of the debt
service (i.e. total periodic loan repayments
made) and the mortgage balance(residual amount of
the mortgage loan at the point of re-sale) and
the total discounted rental cash flow plus the
net equity reversion (net sale proceed to the
equity investor after deducting the mortgage
balance) receivable at the point of re-sale.
Hence
36- Where
- V1(m) mortgaged value of the real estate
- V2(drcf) total discounted rental cashflow
- V3(ds) discounted values of total debt service
or re-paid mortgage loan - V4(ner) net equity reversion, or disposal value
minus mortgage balance - Assuming a property will give the following
schedule of incomes for the five-year holding
period - Year One HK120,000
- Year Two HK120,000
- Year Three HK150,000
- Year Four HK150,000
- Year Five HK150,000
37- In addition to this expected cash flow, the
investor expects an average annual capital growth
rate of 5 per year. In using a 20 discount
rate for his expected rate of return, he is
taking out a mortgage from his banker at a
mortgage rate of 11.75 p.a. or 0.98 per month
for a maximum loan term of 25 years at 70 of the
value of the property. He can utilize the above
mortgage-equity model to estimate the value of
this property by the following steps - 1) V1(m) - mortgaged value of the real estate
0.7 x V - 2) V2(drcf) - total discounted rental cashflow
402,758.49 - 3) V3(ds) - discounted values of total debt
service - Mortgaged value times annual mortgage constant
times YP factor _at_ investors discount rate
38- Hence
- We may notice that if we calculate the annual
mortgage constant from the annual mortgage rate
instead of the monthly rate, the constant would
become 0.125.
39- V4(ner) - net equity reversion disposal value
minus mortgage balance - Where mortgage balance at the point of re-sale
- This is the ratio annual mortgage constant on the
original term of loan to the annual mortgage
constant on the remaining term of loan at the
point of re-sale, times the mortgaged value of
the real estate
40- Hence the value of this real estate is
41- This can be compared with a less complicated
example below using a finance-explicit D.C.F.
model incorporated with the above mortgage
assumption. By this D.C.F. model, the financial
market is more closely and easily linked to the
property market. - The value of the property based on this D.C.F.
model is assessed at 1,275,915.03. The apparent
difference with the above figure of 1,258,620 is
due to rounding problem in the computer
calculation. We may further analyse the
mechanism of this model by looking at the
individual components of the model. Option (a)
gives the same assumptions as above while option
(b) shows that the model is easy to cope with
variations in these assumptions. In option (b),
rental variation is assumed to be downward
adjusted after two years.
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