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Investment
Chapter 14
Hong Kong Real Estate


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
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

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
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
GDP
1990
1995
INVESTMENT
2000
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.


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A firm borrows Pt
to buy 1 capital good
at interest rate 1+i.
The firm produces
PMPKt+1 worth of
goods and sells the
capital good for Pt K ,OLD.
Optimal to buy capital
good as long as payoff is greater than the
cost.
K , NEW


Optimal Condition
Pt K1,OLD  PMPKt  1  it  Pt K , NEW
Definition of Capital
Cost
PMPK t 
iPt K , NEW  [ Pt K1,OLD  Pt K , NEW ]
 Cost of Capital
Capital Cost

1.
2.
3.
ck  iPt K , NEW  [ Pt K1,OLD  Pt K , NEW ] 
We can divide the
capital cost into three
PK
i   g
Pt K , NEW
parts.
Interest cost: Net
Pt K1, NEW  Pt K1,OLD
interest rate.

Depreciation: Defined
Pt K , NEW
as change in value
due to aging.
K , NEW
K , NEW
Capital gain: Defined
K
P

P
P
t 1
t
g

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
optimal capital
equation into real
MPK  i    gtP1 ptK , NEW
terms by dividing both
MPK  r    gtp1 ptK , NEW  rckt
sides by the price
level.
Define the real price
of capital good as
Pt K , NEW
k
pt 
price of capital good
Pt
relative to the firm’s
output price.
K
K
K

PMPK
P K , NEW
K
Example


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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
3
schedule $200,000 4 N
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
moving from 5
taxis to 6 taxis is
less than cost of
capital.
Maximum profits
occurs where
marginal cost
equals marginal
earnings.
Taxis
1
2
3
4
5
6
7
8
9
10
Revenues Costs
200000 100000
336358.6 200000
455901.4 300000
565685.4 400000
668740.3 500000
766731.7 600000
860703.4 700000
951365.7 800000
1039230 900000
1124683 1000000
Profits
100000
136358.6
155901.4
165685.4
168740.3
166731.7
160703.4
151365.7
139230.5
124682.7
Marginal Marginal
Earnings Cost
200000 100000
136358.6 100000
119542.8 100000
109784 100000
103054.9 100000
97991.42 100000
93971.69 100000
90662.28 100000
87864.79 100000
85452.17 100000
Optimal Capital: Example

Solve for Optimal Level of Capital
PMPK 
$150, 000
1
4
N
 (.04  .08  .02) $1, 000, 000  ck P K
$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
slope down.
A: Diminishing
returns to capital.
Each additional
unit of capital
generates less
additional revenue
at a given
workforce and
technology level.
Q: What shifts the
MPK curve.
A: Changes in
productivity of
capital. An
increase in
workforce or
technology will
make capital more
productive and
shift MPK curve
out.
PMPK
P K , NEW
PMPK '
P K , NEW
ck
K
K*
K**
PMPK
P K , NEW
ck’
ck
K
K**
K*
Investment Volatility
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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
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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
PK
Pt K , NEW
Which cost of capital?


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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.
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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
property is rent, R.
 Define rental yield,
y, as the ratio of
rent to property
prices, PPE.
PMPK RE  R
R
y  RE
P

ck

Capital cost of real
estate includes





RE
Interest rate, i
Depreciation/Maint
enance Costs δ
Property Taxes: τ
Other Costs: c RE
P
Capital Gains, g
 (i    c    g
P 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
RE
y  ck  RE  P 
R
R
P RE
P
ck
(i    c    g )
Ceteris Paribas
Curve PRE
R↑
→
↑
i↑
←
↓
δ↑
←
↓
τ↑
←
↓
c↑
←
↓
P RE
↑ →
↑
g
Real Estate Pricing
1
R
ck
45%
PRE
P*
Expectations
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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
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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.
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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
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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
ck 
they pay for the stock.
Market Capitalization
A firm generates a certain amount of
Profits
MPK 
profits per unit of capital
Price of Capital
q
Market Capitalization

Price of Capital
Profits
Price of Capital
Profits
Market Capitalization

MPK
ck
Investment & the Stock Market
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
Q theory suggests that a
rise in stock market
theories could be
thought of as a decline
in the cost of raising
funds through equity.
Empirically, q theory
seems to do a poor job
of explaining
connections between the
stock market and
investment.

Why?
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Many firms change their
capital stock
infrequently. Short-term
fluctuations in stock
market may have little
effect.
Stock market bubbles
may keep stock prices
from reflecting a
realistic assessment of
value of corporate
capital.
Firms may be limited in
ability to raise funds in
stock market.
Corporate Finance

Two kinds of Finance

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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.

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
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
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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.