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

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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

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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


1
Land 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
2
Please Switch Off Your Mobile Phone and Pager as
I DO NOT Want to Talk To Your Friends !
3
Investment 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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