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					Investment


Chapter 14
Hong Kong Real Estate
   According to the planning department
    rental yields on residential apartments
    are more than 5%.
   Rental yields are the annual rent divided
    by the price level.
   But interest rates on mortgage loans are
    2.5%.
   Why don’t people want to borrow at 2.5%
    to make 5.1% returns?
Objectives
   Consider the theory of investment in real
    capital.
       Evaluate the components of the cost of capital.
       Calculate the optimal capital stock as a
        function of the cost of capital.
       Apply Capital Theory to the real estate market
   Calculate Tobin’s q to estimate the
    desirability of corporate investment.
    Evaluate relationship between leverage
    and investment.
Terminology: Investment
   We use the term investment to refer to
    real expenditure (public and/or private)
    on tangible assets.
   We call the stock of tangible assets
    capital or physical capital.
   The unit of measure of aggregate capital
    is dollars.
   Gross Investment refers to purchases of
    new investment.
   Net Investment is Gross Investment
    minus depreciation.
Components of Investment

   Investment
       Fixed Investment
          Residential Investment
          Business Investment
                Structures
                Machinery & Equipment
       Changes in Stocks – Inventory
        Investment
Gross Fixed Capital Formation:
HK 2002


                  5%   3%
                            10%
            14%
                                   Transfer Costs of Land &
                                   Building
                                   Real Estate Developers'
                                   Margin
                                   Machinery & Equipment

      14%
                                   Public Construction

                                   Private Residential

                                   Private: Non-residential

                             54%
Investment Facts

   Investment expenditure is a
    substantial share of GDP, but not as
    large as consumption.
   Fixed and inventory investment are
    closely correlated with the business
    cycle.
   Investment is an especially volatile
    part of GDP.
Business Cycle Volatility
                  Business Cycle Volatility of Real Investment
                  in Hong Kong
        .20

        .15

        .10

        .05

        .00

        -.05

        -.10

        -.15
               1975   1980     1985      1990     1995      2000

                             GDP        INVESTMENT
Marginal Analysis
   Economists use marginal analysis to
    determine an optimal level of an activity.
   Most activities have diminishing marginal
    returns.
       Marginal returns are the extra benefit received
        from doing a bit more of the activity.
   Do more of the activity until that point
    when marginal returns from doing a bit
    more of the activity start to become more
    than the cost of the activity.
Optimal Capital
   Benefit of owning capital is that it allows
    us to produce more goods.
   Marginal product of capital is the extra
    revenue from the extra goods we could
    produce if we had just a bit more capital.
   MPK can be measured in either nominal,
    current price (PMPK) or real, constant
    price (MPK) terms.
   Capital has diminishing returns. MPK is a
    decreasing function of the capital stock.
Productivity of Capital
   The productivity or average productivity
    of capital is the revenue generated per
    dollar of capital.
   APK is value of output divided by the
    capital stock.       Value of Output
                   APK 
                           Value of Capital
   Value can be measured in constant or
    current price terms.
   Marginal productivity of capital is often
    thought to be roughly proportional to
    average productivity capital.
MPK




      K
Cost of Capital
   Economists define the (time) cost of capital as the
    cost of holding a unit of capital for a period of
    time.
   A firm invests in capital equipment for a period.
       The firm borrows money upfront to finance the
        purchase.
       The firm produces goods and generates revenues.
       The firm sells the capital at the end of the period,
        typically at less than the purchase price due to wear
        and tear.
       The firm repays loan.
   Cost of using capital includes interest payment
    plus loss on the resale of capital.
Optimal Capital Example.
    A firm borrows Pt                 Optimal Condition
                       K , NEW
                                
    to buy 1 capital good              Pt 1,OLD  PMPKt  1  it  Pt K , NEW
                                          K

    at interest rate 1+i.
   The firm produces                Definition of Capital
    PMPKt+1 worth of                  Cost
    goods and sells the
    capital good for P K ,OLD.       PMPK t 
                      t
   Optimal to buy capital           iPt K , NEW  [ Pt 1,OLD  Pt K , NEW ]
                                                        K

    good as long as pay-
    off is greater than the           Cost of Capital
    cost.
Capital Cost
    We can divide the       ck  iPt K , NEW  [ Pt 1,OLD  Pt K , NEW ] 
                                                         K


     capital cost into three
                              i   g    PK
                                                 Pt K , NEW
     parts.
1.   Interest cost: Net
     interest rate.                 Pt 1, NEW  Pt 1,OLD
                                        K                  K
                                
2.   Depreciation: Defined                   Pt K , NEW
     as change in value
     due to aging.
3.   Capital gain: Defined               Pt 1, NEW  Pt K , NEW
                                            K
                                gP 
                                  K

     as change in value                          Pt K , NEW
     due to change in price
     of new goods.
Real Capital Cost
   We can convert the
                           PMPK  i    gtP 1 Pt K , NEW
                                                     K


    optimal capital                             

    equation into real     MPK  i    g tP 1 ptK , NEW
                                                K

                                             
    terms by dividing both
    sides by the price     MPK  r    gtp 1 ptK , NEW  rckt
                                                 K

                                              
    level.
   Define the real price
    of capital good as                 Pt K , NEW
    price of capital good       pt 
                                 k

                                           Pt
    relative to the firm’s
    output price.
PMPK
P K , NEW




            K
Example
   A taxi agency can produce a certain
    amount of revenue with larger numbers
    of taxis.
   Assume earnings (revenues minus wages
    minus costs) per year is given by the
    schedule $200, 000 4 N
                        3


   Assume that the purchase price of a new
    taxi (with license) is $1,000,000. The
    borrowing interest cost is 4% and a taxi’s
    value depreciates by 8% per year. We
    assume that taxi’s prices increase by 2%
    per year.
Optimum Number of Taxis
   The extra earnings
    generated by                                                       Marginal Marginal

    moving from 5
                          Taxis        Revenues Costs      Profits     Earnings Cost
                                   1      200000 100000       100000      200000 100000

    taxis to 6 taxis is            2
                                   3
                                        336358.6 200000
                                        455901.4 300000
                                                            136358.6
                                                            155901.4
                                                                        136358.6 100000
                                                                        119542.8 100000

    less than cost of              4
                                   5
                                        565685.4 400000
                                        668740.3 500000
                                                            165685.4
                                                            168740.3
                                                                          109784 100000
                                                                        103054.9 100000

    capital.                       6
                                   7
                                        766731.7 600000
                                        860703.4 700000
                                                            166731.7
                                                            160703.4
                                                                        97991.42 100000
                                                                        93971.69 100000
                                   8    951365.7 800000     151365.7    90662.28 100000
   Maximum profits                9     1039230 900000     139230.5    87864.79 100000

    occurs where
                                  10     1124683 1000000    124682.7    85452.17 100000



    marginal cost
    equals marginal
    earnings.
Optimal Capital: Example

   Solve for Optimal Level of Capital
             $150, 000
    PMPK      1            (.04  .08  .02) $1, 000, 000  ck P K
                   4
                       N

              $150, 000 14 *
                         N  N *  1.54  5.0625
              $100, 000
PMPK
P K , NEW




                 ck




                      K
            K*
MPK & Optimal Capital
Q: Why does MPK         Q: What shifts the
  slope down.             MPK curve.
A: Diminishing          A: Changes in
  returns to capital.     productivity of
  Each additional         capital. An
  unit of capital         increase in
  generates less          workforce or
  additional revenue      technology will
  at a given              make capital more
  workforce and           productive and
  technology level.       shift MPK curve
                          out.
            PMPK '
PMPK
            P K , NEW
P K , NEW




                              ck




                                   K
             K*         K**
PMPK
P K , NEW




                 ck’



                 ck




                       K
K**         K*
Investment Volatility
   The stock of capital may not be
    particularly volatile over the business
    cycle.
   Capital stock is much larger than the flow
    of new investment in a given year,
    perhaps 10-15 times as large.
   A 1% reduction in optimal capital stock
    will require a 10% reduction in
    investment.
Tax Rates
   Corporations frequently must pay taxes
    on earnings. Define taxrate, .
   Corporations also receive deductions for
    costs of capital Define deduction rates =
    (s1, s2, s3, ….)
   Maximize after-tax profits implies that
    after-tax marginal product of capital =
    after-tax cost of capital.

     (1   ) PMPKt  (1  s1 )i  (1  s2 )  (1  s3 ) g P
                                                                K
                                                                    Pt K , NEW
Which cost of capital?

   Which interest rates should we use
    to calculate the cost of capital.
   This depends on several things
    including the risk of the investment
    project & flexibility and duration.
   If capital project is risky, we might
    apply a risk premium (i.e. use the
    interest rate on a risky bond).
Duration & Flexibility

   If we must own capital for many
    periods before resale, we might
    want to equalize average marginal
    product of capital during the period
    to a long term interest rate plus
    average depreciation less change in
    the price of capital.
Real Estate
   Real Estate is an important type of
    physical capital investment and a
    special type of financial investment.
       Uniqueness- Each location of property
        is unique, making it harder to value.
       Illiquid – Harder to sell than paper
        financial assets, longer lead times for
        building real property.
       Large share of the wealth of middle
        income households.
Rental Yields & Cost of Capital
 Payoff to owning       Capital cost of real
  property is rent, R.    estate includes
 Define rental yield,      Interest rate, i

  y, as the ratio of        Depreciation/Maint

  rent to property           enance Costs δ
                            Property Taxes: τ
  prices, PPE.
                            Other Costs: c
 PMPK RE  R                                   RE
                                                 P
                            Capital Gains, g
      R
  y  RE
     P
                     ck  (i    c    g ) P RE
                       RE                   P RE
Cost of Capital Theory & Real Estate

   Constructing New Buildings has long
    lead times. For a fixed stock of
    buildings we can use cost of capital
    theory (y = ckRE) to derive prices as
    a function of rents.
         R         1               1
y  ck  RE  P 
               RE
                     R                        R
        P         ck    (i    c    g )
                                          P RE
Ceteris Paribas
                     Curve PRE
         R↑          →     ↑
         i↑          ←     ↓
         δ↑          ←     ↓
         τ↑          ←     ↓
         c↑          ←     ↓
         g   P RE
                    ↑ →    ↑
Real Estate Pricing




                       1
                         R
                      ck
       45%


                      PRE
             P*
Expectations

   A key determinant of the price of
    real estate is the expected capital
    gain.
   Expected deflation explains why
    rental yields are so much higher in
    HK than mortgage rates.
   Waves of optimism and pessimism
    may lead to persistent fluctuations
    in property prices.
       HK Property Prices
                           HK: Property Capital Value: Residential: Medium
                                              HKD/Sq ft

7000


6500


6000


5500


5000


4500


4000


3500


3000


2500


2000


1500
  Dec-1988   Dec-1990   Dec-1992      Dec-1994       Dec-1996        Dec-1998   Dec-2000   Dec-2002
q theory & Corporate Investment
   A benchmark theory of corporate investment is
    that investment is a function of a quantity q.
   The measure of q for a firm is
                 Market Value of Firm
          q
              Replacement Cost of Capital
   The market value of a publicly listed firm without
    debt is market capitalization (stock price * shares
    outstanding).
   The market value of a publicly listed firm with
    debt is the market capitalization plus value of
    debt (i.e. the cost of owning the firm lock, stock
    and barrel).
q theory
   If value of firm is greater than the cost of
    capital (q > 1) than the value of capital
    inside the firm is greater than the value of
    capital outside the firm.
       If q > 1, firm should have positive net
        investment.
       If q = 1, firm should have zero net investment.
       If q < 1, firm should have negative net
        investment.
q as Cost of Capital Theory
   We might think of q theory as similar to
    cost of capital theory for firms that get
    financing through the stock market.
   Owners of equity have a claim to the
    profits of the firm. They might require a
    certain amount of profits relative to what
                                          Profits
    they pay for the stock.   ck 
                                   Market Capitalization


   A firm generates a certain amount of
                                                  Profits
    profits per unit of capital     MPK 
                                            Price of Capital

                                             Profits
                                       Price of Capital
            Market Capitalization                                 MPK
       q                                   Profits
                                                              
             Price of Capital                                      ck
                                      Market Capitalization
Investment & the Stock Market
   Q theory suggests that a      Why?
    rise in stock market              Many firms change their
    theories could be                  capital stock
    thought of as a decline            infrequently. Short-
    in the cost of raising             term fluctuations in
    funds through equity.              stock market may have
                                       little effect.
   Empirically, q theory
                                      Stock market bubbles
    seems to do a poor job             may keep stock prices
    of explaining                      from reflecting a
    connections between the            realistic assessment of
    stock market and                   value of corporate
    investment.                        capital.
                                      Firms may be limited in
                                       ability to raise funds in
                                       stock market.
Corporate Finance
   Two kinds of Finance
       External Finance – Funds for investment raised
        through loans or issuing securities.
       Internal Finance – Funds for investment raised
        through retaining profits instead of paying
        dividends.
   Benchmark M-M Theory says investment
    decisions and firm value should not
    depend on sources of financing.
    Requirements:
       No distortionary taxation
       Perfect financial markets with perfect
        information.
Reality

   Internal Funds are cheaper form of
    financing than external funds.
       Much of corporate financing is through
        internal finance.
       Investment is more strongly affected
        by cash flow than q.
   Cost of capital depends on collateral
    value that firms can pay if they
    default on loans or bonds.
Credit Cycles: Real Estate
   Much of corporate collateral is real
    estate.
   Real estate is good collateral
    because it cannot be easily moved
    and its value is relatively easy for
    outsiders to derive.
   Fluctuations in property price have
    effects on cost of capital and
    investment.

				
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